Complete Electrical Machines in Electrical Engineering

1. Electrical Machines Promo: Hi, and welcome everyone to our course for electrical machines. I'm Ahmed Mahdi electrical power engineer, and I have prepared this course to help you learn about electrical machines without any previous knowledge. So let's start by learning what are we getting from this course or what are we going to learn from this course? First, we are going to start by learning about the magnetic circuits. Magnetic circuits are really, really important in understanding how does an electrical machine work? Or how can we convert the electrical power into mechanical power or mechanical power into electrical power. The magnetic circuits or the magnetic flux is really really important in understanding this process. Then we are going to start learning about the DC machines, which is the first type of electrical machines, which is reducing or provide DC power or uses DC power in order to provide mechanical power. Will discuss its different types, such as separately excited, the jump and series DC machines. All of this, of course, with solvid examples. Then we are going to start learning about the construction of the electrical transformer. The electrical transformer is the most important or one of the most important components in the electrical power system. In order to understand how does a transformer work and what is the construction of that transformer, we will learn what does a transformer mean and how can we form a transformer. All of this with solvit examples. Then we are going to start learning about the synchronous machines. What does the synchronous machines do? They can be motors or generators. We usually use synchronous generators in our electrical power system. You will find that almost 99% or 98% of the generators in the electrical power system are synchronous generators. So we will understand synchronous generators and synchronous machines in general with its different types and with many solvid examples. Then we are going to start learning about the induction machines. What does an induction generator mean? What does an induction motor mean or how does they work or how do they work? And we are going to have many solvid examples on them. Then we are going to start learning how can we simulate different electrical machines such as the DC module, the induction machine, the synchronous machine. All of this, we are going to learn how can we simulate them in the Matlab simulate. Now as a reward or as a bonus for joining my own course for electrical machines, I'm going to give you my own course for ETAb. ETAb is a very important electrical power system, simulator that helps us to simulate the electrical power system. We can do short circuit analysis, the voltage drop analysis, and much more analysis. We'll get this course completely free. Not only this but you will get also my own course for Logic Sero. Logics Pro is a PLLC simulator. It will help you understand the do diagram or the basic concepts of the PLC programming by using this fun simulator. We will be able to simulate different tasks, such as, for example, valves inside a factory. How can we fill and empty a tank? By using sensors and bombs. Also, we are going to have the door simulator. How can we open and close door using the PLC programming and much more. So if you are looking for one course about electrical machines, then definitely this one is for you. It is used or it is prepard to help anyone who would like to learn about electrical machines. And of course, you will have two bonus courses or two additional free courses, EAP, and Logics P. I hope you join me in this course, and for any question, you can send me a message. Thank you and see you in our course for electrical machines. 2. Magnetic Flux, Flux Density, and MMF: Hi and welcome everyone to our course for magnetic circuits. This course, we are going to study them. Magnetic circuits or the importance of magnetic circuits. You will find that magnetic circuits are available in all of the electrical machines. So we would like to understand why do we need to study magnetic circuits. Will find that as our starting with magnetic circuits is important in the study of energy systems. Because they are available in very important machines such as transformers, that DC machines, induction machines, and synchronous machines. So all of these types of machines are characterized using the magnetic circuits. So magnetic circuits will help us to understand the behavior of magnetic fields inside any device. So we are going to use, all are going to learn what is the analogy between magnetic circuits and electric circuits. Okay? So we will understand some basic concepts about magnetic circuits, which will help us understand what is the relation between an electric circuit. Okay? And a magnetic circuit. This will help us to use all of our laws such as KVL, Kirchhoff's Voltage Law, KCL Kirchhoff's Current Law, and so on. Okay. So first, let's understand what does even a magnetic field? So, magnetic field is found in nature in the permanent magnets. If you look at any magnet, any magnet, this one is called a permanent magnet, consisting of two poles, north and south. Use what it is made of steel or iron alloys. You will find that any magnet, which we have seen in neutral, if we have two magnets and we start making them close to each other, there will be a force of attraction or a force of repulsion. Now, where does this force come from? It comes from the magnetic field. So the magnetic field inside any magnet is a format of lines, magnetic field lines that goes from north to south. When this magnetic fields becomes a close to another magnet. With Amazon magnetic field, they will start exerting force on each other, or they will start interacting with each house. This magnetic field is forming of lions magnetic lines that moves it from the Norse going to the South. So that lines go from north to south. Now, here's, you will find the magnetic field around any magnet. Now, if you look at this magnet, e.g. you can see Norse lines going towards the South. The magnetic field lines go from north to south. Now you have to understand that these lines, this magnetic lines, we call them the magnetic flux or phi folly, or the magnetic flux representing the magnetic field lines coming from zonules going to the south. And as you can see here is they are forming a closed loop. So you can see any line like this and goes from north to south inside the magnetic. So it's forming a loop. So first the concept that we have now is the magnetic flux lines or the magnetic flux. So the magnetic flux is simply called Phi or the measured in Weber. Weber is the unit of measurement of the flux. So you have to understand that any flux, how many lines? So you can see this magnets, we have north and south. You can see this lines 1234 and so on. So if we have ten to the power eight lines or one and then beside it, eight zeros. It means that we have this amount of lines representing one-way bar of the flux, or the flux is equal to one weapon. Okay? What does one way per mean? It means that we have ten to the power eight of this magnetic lines. Okay? So you will find that here this flux are cutting an area. So the total flux passing through an area a is denoted by phi. Okay? Okay. So that is the first concept that magnetic lines are the magnetic flux. Is the flux is uniformly distributed over an area a. We call it the magnetic flux density. Okay, so the magnetic flux density is representing the amount of flux per unit area. So you can see here we have a unit area 1 m square, this square of an area of 1 m squared. The amount of flux passing through 1 m squared is the magnetic flux density. How many flux per unit area? Similar to here, if this one is 1 m square. So the amount of flux passing through this area will give us the magnetic field or the magnetic flux density. Okay? So you will find that beta or the magnetic flux density is measured in tesla. So that strength of that, of that density of the magnetic flux is measured in tesla. And one tesla equal to one waypower pair, 1 m square. So you can see one way per square meter or one weber per meter square here, WB, WB naught w only. You will find z. If you look at a magnet, e.g. you can see lines are coming and going from north to south. You can see that the lines are very close to each other at the North, near the magnet. And as we go further away, you can see the distance in between lines starting to increase. So we say that the flux lines near the magnet are more closely spaced. Now also, of course, as a strength of the magnetic field decreases with distance, as the distance increases. So let's say e.g. this magnet and we are here and here. So the strength of the magnetic field here is much, much lower than this point. Why? Because the distance is much larger here. Okay? So the magnetic field strength similar to the electric field, as the distance increases, the magnetic field decreases or the electric field decreases. Okay? Okay. So we now know about magnetic flux, which is alliance, and the magnetic flux density, which is magnetic flux per unit area. Okay? So what do we have seen in the previous slide? We have seen that we have a permanent magnet, which is found in nature and producing a magnetic field. But can we produce a magnetic field with another way? Yes, you can produce it using another way. So in electric circuits in general, you will find that any conduct, any conductor like this, Let's say copper or aluminium or whatever. And the current passes through it when a current to pass through it, and we will have a magnetic field around it. But this magnetic field is very, very low, so we don't descend set. So any conductor when it is having a current passing through it, it will have a magnetic field around it. Okay? But this magnetic field is very, very small. Okay? Now, the same idea, the same idea is that we use a solenoid or a coin. You will usually find this in transformers, in DC machines, in electric machines and so on. Okay? So what we do is that the solenoid or the coil. You can see here we have, instead of having a long conductor like this, we will take this conductor and make a group of tones like this. Okay? This toners will form us at coin. Having a certain number of turns. You can see 1234 and so on. So these are number of turns. And as you will know, that number of turns when number of donors increase, the strength of the magnetic field or the magnetic flux produced. A store is to increase. Okay? So what we do is that we take this solenoid or this coil and we connect it to a battery or an AC supply. So when the current passes through it, like this goes here and here, like this, you will find that we will have magnetic field around it. So you can see the coils are pointing upwards. So we'll find that the magnetic flux are produced will go out from this direction, as you can see here. So this part will be north and this part will be cells. So the magnetic flux will go out from here and go to south here and goes south and so on. Okay, forming a loop. Okay? Now, how can we find the other direction? We will find the direction using the right hand rule. So you can see we have here, how can we do this? You can see we have a current connected here, current going like this. Like this and coming like this up, pointing upwards and coming out from here. Okay. So our fingers, we will put it in the same direction of the current. You can see I'm putting my finger in the same direction of the current. My own. Some people will point to the nose or the direction of the magnetic field. So this direction means likes us. So it means this part is the Norse and this part is a south magnetic flux. Flux coming like this and going to the south, coming like this, and go to the South like this to the sauce. Okay? Okay. So here, the current going through any conductor will form a magnetic field. Considering a current I flowing through a solenoid, as we have seen, we will have a flux which will form a magnetic field around the coil. And the direction of the magnetic field is defined by Maxwell's right hand grip rule, or sometimes we call it and bear right-hand rule. And sometimes we say Maxwell and bear right-hand rule. So all of them means this rule. You are putting your fingers in the direction of the current and your thumb will point to the direction of the moles, all direction of the magnetic field. Okay? So direction of the field or the current here, we will understand we have the Ampere's law or the, we call it also the Maxwell's right-hand rule. We have the magnetic field. We can use a magnetic field and our sample will lead to the current. Answer is also there, but you also have our two Lou law, which we have current. We have our fingers pointing to the current. N is our sample point due to the magnetic field. So both of them, you'll find that they are actually similar to each other. If you put your fingers in the direction of current, then you will have magnetic field. If you put your fingers in the direction of magnetic field, you will have a current. Okay? So sometimes if we have account like this, we have a conductor and current flowing like this. If we use any of these two rules, e.g. if you use this rule, we have our sample axis. So our finger will lead to a magnetic field coming like this. Okay? Legs us around the Zak conductor. If we have a solenoid and the current is in this direction, like this, going upward, it means is that the magnetic field is in this direction, okay, So they are similar to each other. So we can say I'm bird law or the Maxwell law or the law. So what is the benefit of this? This will help us in order to find the direction of the magnetic field. That's what we all need for this part of the course. Okay? So we learned about flux, okay? Which is a magnetic field lines. And we know about Beta, which is the magnetic flux density or the flux per unit area. Okay? So what do we need to find is the analogy between magnetic circuits and electric circuits. So I can work with any magnetic circuits similar to any electric circuit. Okay? So if you look at this figure, e.g. this representing a magnetic circuit, this one representing an electric circuit. So if you have a coy similar to the square root and you connect it to as a supply. So we have a current flowing like this. So the current will be like this and this direction coming like this, like this, and then go like this and so on. So we have the direction of the current. So if you use e.g. the embed right-hand rule or whatever it is, you will find that e.g. the flux in this direction going downwards as an example. Okay? So you can see that here we have the current reduce the magnetic field. So this magnetic field, which will go from, let's say, this Norse and this one is South. So it will go like this and would like to go and get back to the South. All of the lines would like to go and like this from Darwin terms honours to that sauce. Okay. Now this, if you look at any electric circuit, we have also that EMF or the supply, and we have our resistance. Now, this EMF, or the electromotive force, is the one which are drives as electrons, which pushes the electrons, leading to formation of current. So if you look at the EMF or the electromotive force, this supply produces a current and that will push it through the resistance and get back to the negative terminal. Similar here you can see we have, instead of electromotive force, we have MMF, or the magneto motive force. This is the magnetic force, or the magneto motive force which pushes zap flux. Okay, so what do we can learn from here? Let's just delete all of this. What we can learn is that here we have EMF, here we have MMF. Emf is the one which will drive the current. The MMF is the one which drives is our flux bushes or flux. Okay? So what we can see here is that electromotive force pushes electrons, which lead to current, the MMF bushes or flux or the magnetic field lines. So what we can see as an analogy is that we have MMF similar to EMF. And at the same time, the current flowing through the circuit is similar to the flux. So the flux which removes it from north to south is similar to the Current which moves it from positive to negative. Okay? Now when this flux of law is like this, it moves through a medium. Any medium has a resistance. So we have here magnetic resistance, or we call it the reluctance for the electric circuits. So we have the resistance which are preventers the current from flowing. So we have to, you can see here the analogy between them. Okay? So let's take it back to them. Magneto motive force. So as a magnetic motive force is similar to the magnetic potential, We have here EMF, or the electromotive force, or the electric potential. Here we have the driving force, pushing current. However, MMF is magnetic potential, which is a driving force that causes a magnetic field or pushes them magnetic flux line from positive or from North to South. So that magneto motive force is similar to or is analogist to electromotive force or the voltage in electricity. Now what is the value of MMF? That value of the force that pushes this flux is equal to n, which is the number of turns of the coil multiplied by the current. So the forces that pushes this flux or mixes a magnetic field much stronger, is dependent on the number of donors and the current. That's why as single conductor like this, when a current flows through it, it has a weak magnetic field. Why? Because number of tone is equal to one. However, when we have large number of donors, we will have much stronger magneto motive force, or MMF, which produces a stronger magnetic field or stronger flux. Now, let's go to, so we have now, let's get back here. We talked about, here is the elements of the analogy. We talked about the flux, which is similar to the current in electric circuits. We talked about MMF, or the magnetomotive force, which is similar to the voltage in electric circuits. Now the final part which we need to discuss is that reluctance or the resistance. So in order to understand what is the value of reluctance in the magnetic circuits, we need to understand the forest that meaning of magnetic permeability. 3. Magnetic Permeability, Magnetic Intensity, and Reluctance: That magnetic permeability or Anza magnetic intensity. What does this even mean? So that magnetic permeability is defined as the ratio between the magnetic flux density to the magnetic intensity. Okay, so we learned about magnetic flux density, which is beta. Here, beta. So what does even magnetic intensity mean? This is denoted as etch. Let's continue on for now. You will find that the magnetic permeability is equal to mu. Mu is a magnetic permeability equal to beta or the magnetic flux density divided by h or the magnetic intensity. Now what does even mean etch or the magnetic intensity is that MMF pair unit length. So we learned in the previous slides that the magneto, motive force is equal to the current multiplied by the number of donors. So if we take N divided by l, what does, I mean? It is the length of the magnetic boss. So you can see here as an example, we have here our nose, and we have here our South. So let's say we will take one line, just one line like this as a flux of flowing like this exists. And getting back to the South. You can see this boss has a certain length, let's call it L. So when we take n, or the MMF divided by the magnetic pulse from north to south, we will have the magnetic intensity. Okay? So the relation between beta or the magnetic flux density to the magnetic intensity is called mu, or the magnetic permeability. That magnetic permeability helps us measure the material's resistance to the magnetic field, or measure of the degree to which the magnetic field they can penetrate through a material. So remember that conductivity in electric circuits, conductivity, what does the conductivity mean? We have elements which are good conductor of electricity and other elements which are our bad conductor of electricity. So as an example, if you remember what e.g. is a bad conductor of electricity, it doesn't allow electrons to flow through it. However, another materials such as copper or aluminium, these two elements are good conductor of electricity or allow the electrons. So we say that wood has a bad conductivity, bad conductivity, however, copper and aluminium, we call them. All we say is that they have good conductivity. So y, z are good conductivity because they allow more current to flow or electrons to flow. And the world is a bad conductor of electricity because it does not allow much electrons to flow. Okay? So similar to the same idea of the conductivity we have here that permeability permeability assembly. The permeability of any materials, how much it will allow the magnetic flux to flow through it. So the higher the permeability it means it will allow more flux to pass through it. So if you look at here, we have different materials and their magnetic permeability. So we have air best, most copper, iron, nickel, carbon steel, hydrogen, water. And if you look at this, we have the magnetic permeability, which is the ratio between the magnetic flux density to the magnetic intensity. So the ratio here is measured in Henry per meter. Okay? So what do we need to learn is that you can see here air, it has a value multiplied by tan to the power negative six. We have here cover ten to the power negative six. However, if you look at materials such as iron, it has done to the power negative three. So you can see that it is almost 1,000 times than air, or much stronger than air. Probably 1,000 times. Ion has a good permeability or it will allow more flux to pass through it. So that's why if you look at here we have a cool this score or iron core made of cohorts of iron. So when we have magnetic flux, we have North and South. Okay, so here is the magnetic flux has two options, either to go through whole material law exists from north to south, or a trustee goals like this through air and go to sounds. So which one is better for the flux? You will find is that the iron core is much better for magnetic flux. Why is this? Because my iron core has a good permeability or would allow more flux to pass through it. Okay. So that's why most of the flux, or 929999 per cent of the flux will go through the iron core, not through air. Because iron has a good permeability and air has a low permeability, which is equivalent to iron, have a low resistance or low magnetic resistance, but air has a high magnetic resistance, which is denoted as the reluctance. So you can see we have Mu equals p over h. The h, which is a magnetic intensity equal to n I over L, beta equal phi over area. We, using this three equations, we can say that the flux, which is beta multiplied by area, is equal to mu and pi r-squared over L. Now, where did we get this? Okay? So you can see from this equation for Y equal to beta multiplied by area. Beta itself is equal to mu H, equal to mu H to blow by area. What about h? H itself is n pi over L. So we say mu and r over l multiplied by area. So you can see all N mu. And we have area. If it is a circular, circular cross-sectional area, then it will be Pi r squared, which is the one. We obtained, a relation between phi and the other elements. Now what is the value of the permeability? Permeability of free space? Free space is similar to the permeability of air, similar to the permeability of copper. You can see these two values are close to each other. There is, these values are equivalent to four pi multiplied by ten to the power negative seven wipeout pair and bear meet. Another definition which is relative permeability mu r, which is our issue between the actual mu divided by mu naught. You can see here e.g. if you look at the iron, e.g. if you take this value and divide it by this value of air, then you will have the relative permeability. You will find that for air and the cover is that relative permeability is equal to one because mu is equal to mu naught. However, for ferromagnetic materials such as iron, nickel steel, cobalt II, you will find that it is, it's a value or mu r 1,000 all grid. So if you take this value and what it buys us, it will be 1,000 or more. Okay? That's why you will find that the permeability of iron is much, much greater than n. Okay? So here we will reach to the final parameter of our circuit, which is magnetic reluctance. So the magnetic reluctance or the magnetic resistance is a concept used in the analysis of magnetic circuits. Okay? So it is similar to the electric resistance. So it is defined as the ratio of the magnetic motor force, MMF. Those are magnetic flux. So if you remember the electric circuit, which we had in our supply like this, let's say E. And we have a resistance and we have our current. According to Ohm's law. We said before that the resistance e.g. is equal to E over R. The electric resistance equal to the electromotive force divided by the current. Now, if we use this analogy on magnetic reluctance or the magnetic circuits, you will find that the resistance or the magnetic resistance or the reluctance equal to E, which is the electromotive force in magnetic circuits, it will be MMF and the current will be our magnetic flux. So you can see dividing MMF to the magnetic flux gives us the reluctance, which is the analogy of the elements inside the electric circuits. Okay, so let's apply this and see what will happen. Of course is a reluctance is the opposition to the magnetic flux is the one which is bereavement. Does the flux from flowing similar to the electric resistance which will prevent the electrons from flowing. It's a value depends on the geometry and the composition of an object. So we would like to see what is this value or what is the relation between this elements. So if you remember that phi or the flux as we just obtained, equal mu n over l. Okay? Now, here is the magnetic motive force, or MMF, or equal to n i. Now, that reluctance, reluctance R is equal to MMF, which is n i divided by flux. This is a value of flux and mu n divided by l. So we'll find that abnormal goal is n is odd. So we will have L divided by mu area, which is a reluctance. You can see reluctance equal to L, which is the length of the magnetic path, divided by mu, which is the permeability of the material itself here, e.g. here, the iron core is the permeability of the iron core multiplied by the area which is the cross-sectional area. You can see any material such as iron here has a cross-sectional area. This area is the area in which the flux will flow perpendicular to it, like this. So this area which is the area of this lamp of the core is called the Zak cross-sectional area required. Okay? So in general, you will find that here if we look at this relation, we have MMF divided my magnetic flux that gives us reluctance. Magnetic motive force, or the MMF, is equal to flux multiplied by reluctance, as you can see here. So the magnetic motive force and I equal to the flux flowing multiplied by the reluctance of the system. If you look at this, it is similar to E, or the electromotive force equal to the resistance multiplied by current that owns a low. Okay? So this will lead us to the analogy. Here. This is the final part of the lesson. You can see we have electric circuits, so we have magnetic circuits. As you can see here, the electromotive force is similar to the F or the MMF, or the magnetic motive force. That current is similar to the flux. Resistance is similar to the reluctance. So the current is equal to supply divided by resistance. The flux equal to the supply, which is a magnetic motor force divided by the reluctance. And here the values as we have zoster vaccine. Here you can see that all of the values in that electric circuit and the magnetic circuit and the opposite value of it. So you can see force, exciting force, or EMF is the MMF. That current is similar to flux. The voltage drop, which is voltage multiplied by current, or voltage multiplied by the current. Here, voltage current multiplied by resistance. Okay? I don't know why this book even wrote V. It is resistance multiplied by current, which is similar to reluctance, multiplied by the flux that field, the density, the electric field we don't see is the voltage divided by the lens. Here's the magnetic field intensity is similar to, is equal to Zan MMF divided by the lens. That current is equal to voltage over resistance, flux equal to MMF over the reluctance. That guarantee density is similar to the flux density and so on. Okay, so in this lesson, we learned about the different concept in magnetic circuits such as voltage or the MMF, reluctance, flux. And we understand now that we can represent as a magnetic circuit similar to an electric socket, because there is an analogy between them. So let's have just a quick example before we start learning how can we deal with different magnetic circuits. 4. Solved Example 1: Hey everyone, In this lesson, we are going to have the first example on the magnetic circuits. So we learned in the previous lesson about the flux, the reluctance of the magnetic field in dynasty, or the density and magnetic field intensity. So let's start by learning an example. You can see in this figure, we have a solenoid. This one is a solenoid or a coin. Let's say in this coil and have a radius or the core at which it is turning it around. The score has a radius of 0.0, 1 m, and the length of 0.2 m. So you can see that we have here, our coil is tone at, around this iron core. So first you will find that this core has a radius, looking like this circular core with a radius equal to 0.01. Okay? And we have a length of 0.2, 0.2 meter. What does this represent them presenting that lens of magnetic boxes. So as it goes from north, from nodes too, south, this big lens is equal to point to meet. Now what we need to find is that we need to find the number of donors. So we need to find n number of donors for our current of one amp pair. So the current is one ampere applied to the query to produce a magnetic flux density of 0.1 test 0.1. Okay? Now, in what cases when we have a core material, when the material of the core is made of air, e.g. we have like this okay. Exists made of air. So it will go like this and goes towards a larger pores and the return is back. Or when it is made of iron, as you can see here. Okay? So let's take all of these inputs and start learning how can we get the number of donors? So we're given the radius is 0.0, 1 m. The lens of the magnetic pulse, the pulse of the magnetic flux is 0.2 meter. The current one I'm pair and Beta equal 0.1 tesla and we need to find. And so if you remember that the flux equal to beta multiplied by area and beta is equal to mu n I over L. So simply it is a direct substitution. So you can see is that beta itself is equal to mu n over l multiplied by the current. So the number of turns from this equation will be beta l divided by i divided by mu. So we have n or the number of donors equal beta l over mu i. Okay? So beta 0.1 tesla, which is Alan's 0.2 m mu is the permeability. Permeability depending on a or B. If a is n, mu will be four pi multiplied by ten to the power negative seven and the current one and bear like this. So you can see for an air core in the first part, Mu will be equal to mu naught, which are sore point multiplied by ten to the power negative seven. And beta is equal to mu N. Beta itself is 0.1 Tesla and xylene. So suppose is 0.2 m. So now we have a number of donors. Now for the same ideas, the same idea, but we have ion. So what we will change is that Mu will be equal to mu r, which is relative permeability multiplied by mu naught. Okay, So when you multiply this value by how much by 1,200? Like this, you can see the number of turns, 13.3 tons. Okay? Now, what we can learn from this example, the first thing you will see here that here I would like amount of Tesla, 0.1 tesla of the magnetic flux density. Okay? So the magnetic flux density, you can see 0.1 tesla. In order to achieve this in, in the air core, we need lots of number of donors. You will need 51515900 tonnes in order to produce this amount of magnetic flux density. However, if we have an I or corn and iron core, we will just need certain 0.3 tons, very small amount of terminus. This is approximately 13 or 14. Whatever it is. Approximately, there is no 0.3 approximately, we make it the nearest integer value. So you can see is that using an iron core, we need very low amount of number of donors to achieve the same amount of magnetic flux density in the IR or in the Air Corps case. Okay. So this, this was the first example on the magnetic sockets. 5. Solved Example 2: Now let's have another solver, the example on the magnetic socket. So as you can see in this figure, we have a rectangular iron core. So it is made of a rectangle. As you can see, a rectangular iron core. You can see this lens is 18 centimeter, and this lens is a lens, let's say lens is 20 cm from here to here. And the width of this is from here to here is equal to 18 centimeter. You can see is that each lamp, this one, this part is called the Tsar lamba of the iron core. Okay? So this lamp has a width of four centimeter. As you can see, a four centimeter. So we have an ion courses are in accord with a relative permeability of mu r equal to 1,500. Now what we need is to find that reluctance and the magnetic flux in the score. So we need all and we need magnetic flux. Phi and z score wins. The number of donors is equal to 200 and the current is equal to two. Okay? So how can we solve an example like this? The first step is that we need to find what we need to find the flux. Okay? So in order to find the flux, we need also the reluctance. The first step is that we need that reluctance. If you remember that we said from what we learned is that the reluctance is equal to L, which is a lens of Zappos, divided by mu, which is a permeability of the material itself multiplied by the area. So first step is that we need to find Zealand's what lens, lens here is the mean length or the average distance, or the average lens. So here you can see that we have here our magnetic flux coming out from here and troubles like this. And it goes back. So what is the length of this path? You can see that it is flowing. We assume that it is in the middle, okay? Exactly in symmetric. So what I need is that I need the length from here to here, plus from here to here, plus from here to here, and from here to here. Okay? This is a lens of the magnetic flux. Magnetic flux lens is not 18 plus 20, plus 18 plus 20. Okay? Not this lens. It is in the middle of the code or the middle of the iron core. So we need this median lens or the average lens. Okay? Okay. So if you look here, you can see that we have this distance is 20 centimeter. You can see that this distance is four centimeter and this one is four centimeter. So we have here four centimeter like this. And do we have here 4 cm, okay? So if this line is in the middle exactly, then this distance is 2 cm. And this one is also 2 cm. Okay? Here's the same idea to centimeters. And 2 cm. If we look at the vertical distance than sensors, this part, all of this as similar to here, 4 cm. So this part is 2 cm and this part 2 cm, okay? So here also 2 cm here to centimeters. Okay? So you can see is the distance from here to here is 18 centimeter. So I need the distance from here to here. So this distance will be the 18 centimeter minus this 2 cm, the above 2 cm here, minus the balloon to centimeters. So the length of this path, the sport, is equal to 14 cm. The same idea for the 20. You can see from here to here is 20. And we have here 2 cm here and two centimeter z. So it will be say, minus two, minus two will give us 16 something. So what we can see is that this distance is 16 cm. This distance is 14 cm. 16 cm and 14 cm. You can see that the average length will be equal to 14. We have how many 14 we have this part 14 and this port 14. Okay, so we have 14 plus 14. And we have this distance which is 16, and this distance which is 16. So we have 16 and so there's some mason will give us the mean lens or the average length of the flux boss, which is 16 60 centimeter, which is 0.6 meter. Remember, when we are substituting these values, they must be in meter, not centimeter. We have to substitute with meat. Okay? So we have the lens equal to 0.6 meter. So that is the first part. So we have the lens equal to 0.6 meter. Now, the permeability is equal to mu r, which is 1,500, multiplied by mu naught. Okay? What about the area? Is the area, if you remember from the previous figure, the areas like this square, this square, which is the area at which the flux will go perpendicular to it. You can see we have this distance is four centimeter and this depth and distance is 3 cm. So the area will be four multiplied by three, which is the world centimeter square. And we said we use meter, not centimeter. Okay? So we will convert from centimeters squared to meter squared by multiplying by ten to the power negative 4 m square, negative four because we have centimeter square, not centimeter or centimeter square. So fun that area as we have just the set 0.03 meter multiplied by meter equals 0.0, 12 meter squared, which is similar to 12, multiplied by ten to the power negative four. You can see 123.4. So it will be 124 multiplied by ten to the power negative four. Okay? So we have now the Asia. So by substituting this values, we will get our reluctance. The reluctance here representing the resistance of the iron core, you can see it is 2.625 multiplied by ten to the power five. And bear, turn a pair, Weber. Okay? So that is a first requirement. Can see we need the reluctance. Now we need the magnetic flux, okay? Now, if you remember, we said before that n i, the MMF of the magnetic field, or the current multiplied by the number of Turner's gives us as a flux. Multiply it by the reluctance. Okay? So we have the reluctance, which is this value and we have the current, whereas the current two and there's k. And we have a number of donors to 100, so we can get the flux. Okay? You can see MMF divided by the reluctance, or n multiplied by the reluctance, 200 multiplied by two amperes divided by the reluctance. So it will give us this value, 1.51 multiplied by ten to the power negative three Whipple or 1.51 milli weapon. Okay. So this was a muzzle example on the magnetic circuit. 6. Fringing Effect in Magnetic Circuits: Hey everyone. In this lesson, we are going to discuss the fringing effect in the magnetic circuits. So what does this mean? You can see that we have our Here we have the number of donors or Tsar solenoid or that coil around an iron core. However, in this case we have an iron core with a small air gap. You can see this is an air gap. So we said that most of the flux will go like this through the iron core and you get back from Norse going into cells. Okay. Now you will see that we said also before that the most of the flux goes through like this. Like this. However, we said before that there will be some leakage flux, a very small amount flux that will go like this through the air and the comeback. Now, most of the flux will go through the iron core and very small one goes where? Now why is this? It is similar like this. If you have a battery like this, you have this reluctance, which is an iron core reluctance, or the resistance of the ANA Code is very small. Like this, very, very small resistance, resistance of the iron core. And we have a very large resistance of the air or air. Then what will happen? Let's say e.g. we have a resistance which is very similar to the small reluctance of the core and we have very large resistance, similar to the resistance of air here. You will find that most of the current will go here. One, which is most of the current. And very small part two, we go through the air or goes through that very large resistance. So the same idea in magnetic circuits. Most of the flux will go through the iron core and the very small leakage flux will go through. Okay? Now, this is not the fringing effect, is a fringing effect. You can see that here. At the air gap, you can see the flux should go like this. Perpendicular. However, you will find that if you look at this figure, you can sign that there is a small inclination like this. Small inclination in the wire itself. This is more inclination of the wire. You can see it made the air gap, the area of the air gets much bigger. So you can see that instead of having the area which is this lens, multiplied by his depths, Okay? Now you can see we have a much bigger area. So the area will be something like this. Let's say the leads us. Okay? So let's say the area will become much bigger like this due to the fringing effect. So you can see that when the magnetic field lines passing through an air gap, they tend to bulge out. It is because the magnetic field lines rebel each other when passing through air or so non magnetic materials. So in this case we have an effect to call that fringing effect, which makes this inclination in the lines itself or not inclination that bending in the lines itself and zap bending in the flux. So this bending will increase the area. Okay? So you can see that here is the effective area of the magnetic field of the air will start increasing. The area well installed increase, ends or reluctance will decrease. Due to the magnetic fringing, the effective area of the air gap is increased and thus the magnetic flux density, density is decreased in the air gap. Why is this u, if you remember that beta, beta is equal to phi over area. So when the effective area increase, the magnetic flux density starts to decrease due to the presence of this effective area. In the, due to the fringing effect, the effective area increased. Okay? That's why this will lead to reduction of the magnetic flux density in this air gap. Okay? Now we will find that the longer the air gap, the higher is the fringing and vice verse. That longer the more length of this and again, the higher the effect. So how can we solve this problem by selecting high-quality magnetic material and the making the air gap as normal as possible. So how can we represent something like this in the magnetic circuits? So how can I find the effective area? So here, let's say we have this ionic core. It has a width and depth and the length of the air gap is algae. Now, for Zao, cool itself, area is equal to widths multiplied bys adepts metalloid boy, depths, which is this part. However, when we have a fringing effect, what we do is that this area becomes, the area of the air gap becomes bigger due to the bending in the flux line. Okay? So the new area, what it will be, it will be the widths loss, the lens of the air gap multiplied bys plus zillions of the air gap. So we increase the Spice Islands of their gap. And we increase this point the lens of their game. So what you can see is that as the length of the air gap increase, the more effective area or Tsar, more fringing effect. Now if we neglect fringing effect, senza of the air gap will be with Zomato blood binds at depths as we learned before. Okay? Okay. So usually ends up problems. We neglect the air gap unless something else is stated in the problem. 7. Representation of a Magnetic Circuit: Now, how can we represent our magnetic circuit? So in order to analyze our electric or magnetic circuit more, we need to represent it in the electric circuit form. So you can see that here we have series magnetic circuit and the parallel magnetic circuit. So what does this even mean? You can see that here we have a flux of flowing like this. The same flux flowing through that material or self or a laminated this teal or Zach cast iron is the same flowing through the air gap. So when we represent something like this, I have those haploid. I exist. And I, which is the MMF series was it, Here's a flux coming out. Okay? So this flux will pass through three reluctance in series the forest. Let's make it like this. The first two reluctance is a or C, which is a reluctance of a cast iron series was eight. The reluctance of the laminated steel series was it? The reluctance of the air gap? All of them are series with each. As you can see, it's a flux flow is through all of them, so they are all in series. That's why this is called SCR is magnetic circuit. So we can represent this how, why supply and each of the reluctance flowing at which the flux is flowing. If you go to the parallel magnetic circuit, we have the supply, okay? We have the supply like this and the flux coming out of it for you one. Now, remember this flux is flowing through iron. Here. We have the first reluctance, or iron or any method, let's say iron ore, which is what is this resistor? Resistor is a reluctance of this part. This big box in which is the total flux is flowing, see here is with the supply. Now if you look at here, we have the flux at this point will be divided into two parts. One going to the right and one going to the left, like this and get back, and this will get back. So as if we have two parallel branches, one branch like this taking 43. And also our branch taking phi to. This branch has a reluctance. This core or this, or in Nepal has a reluctance, let's say it or two. And this one has a reluctance, let's say or three. Then both of them will be combined to form phi one again. So it will be like this, connected like this, and connect eight lines. As you can see, we have a parallel magnetic circuit. Flux is divided into right branch and the left branch. So you can see in these two cases, we represented our magnetic circuit as if it is an electric socket button. Instead of having voltage, we have MMF or the magneto, motive force. And instead of the current, we have flux. And then instead of resistance we have reluctance. Another example here you can see we have this core series was the reluctance of the air gap. So if I would like to find the value of each of these reluctance, how can I do this? You will know that the reluctance equal to lens over mu multiplied by area. Now we have a part which is iron or steel or whatever the material, let's say cast iron. So first we need this reluctance, okay, so this circuit is plus minus, we have n i. Then the flux will flow like this through that cast iron. So we have our C. C here is, was it the air gap? So we have our g, then it will get back like this. Okay? So our c itself is a reluctance, lc over mu c Area C, or G is G over Muji area G. So the area of the air gap is simply equal to this lens. The lens of the air gap, multiple depths. Okay? Sorry, not know the length of the air gap. The area will be this width multiplied by the, this is the early width multiplied by the force or ion is the same idea. Lens that width multiplied boys at depths. So we have the true area. Now, permeability is the permeability of air. For Zack cast iron, it will be mu naught multiplied boys, or relative permeability. The length is the length of the magnetic poles. Officer IN could only. This bottle here lie exists still here. And for LG is that lens of the air gap on. Okay? So from here we can get these two values and from which we can get the flux as required. So from here, from this circuit, as if we have a caveat, we have the flux. So if you apply KVL here, supply in I equal to flux multiplied by the total resistance. So n i equal to flux multiplied by RC plus origin as if we have a KVL. So flux itself will be n divided by the total reluctance. So we have like this, okay? Now another equation is that we can say, we said n equal to phi c plus phi or gene. The same idea. And instead of using flux and reluctance, we can use that in tennis team multiplied by land surplus and tennis team multiplied by lens, you will find that the intensity flux is constant. The same flux is constant. However, the intensity in the iron is different from the intensity in the air gap. Remember this. So why does this one is similar to this one? Simply, if you remember that first flux equal to beta multiplied by area and are reluctant, So let's say L over mu area. Okay? And we have H is equal to n i over n. Okay? So from here, this equation and this equation, we have the first one, phi equal to NI over all siblings RG. From this equation you can see edge equal to n pi over L. So H L equal to NI. You can see HL equal to n by exist. So sometimes we use this equation and sometimes you use this equation. We will learn when do we use this? And when do we use this? Usually we use this equation. Unless the permeability of the material here is not constant. If it is variable, then we cannot use this equation of the reluctance. We have to use this. Don't worry, we will take an example on this one. Okay? So if you neglect fringing effect, we said that here, the area of that I'm Nicole would be similar to the area of air gap lens. Lens multiplied by the same dips like this. So it will be W multiplied by d. Now here is another representation. This circuit will be like this. Okay? So we have the supply. Then we have the reluctance of the first lens, L1 distance. So we have a reluctance R1, then we have a reluctance, R2, then we have a reluctance or three. Then we have the reluctance of the air gap. Then we'll have reluctance, R4 and reluctance or five, usually we don't do this. Usually we combine 12 and 3.4, 1.2 and 3.4. Yes, this for reluctance together. So R1, R2, R3, R4, and R5. All of them can be our iron, e.g. or we have one reluctance for the air. Now another one here we have an OI, which is a supply. This will produce a flux that will go to the right and go to the left. So we can represent it like this. You can see we have n, i and series with distance here. Okay? Distance here in which is the total flux will flow of the core itself. We will say that this length is L I3. So we say that the reluctance is our i3, which is a reluctance of this part. Then the flux will be divided into one part to the right and one to the left. You can see if Y1 and Y2, we have a lens here called the E1. So it has a reluctance or IL-1 and part of it go to zero here, we'd have a lens ally to which is the length of the core itself. Spot. So it will be alright to series was the reluctance of the air gap. Now from here you can find that we can apply KCL. You can see here, if you remember KCL current entering equal to summation of the two currents leaving. So phi equals Y1 plus Y2 as KCL. And we can apply KVL. You can see we can apply KVL in this loop. This one, we have n equal to phi or three plus phi two are I1, okay? Or we can say n equal to h three multiplied by a live stream. You can see a choice three multiply by LI three, then plus one, which is in Tennessee in this part, multiplied by L one. Ask you feel as if you have made a KVL in this loop. Same idea. You can do KVL in this loop two. Okay, so we have n equal to three, which is this here. Stream plus X1, X2, Y2 plus Hg Zhe. Okay? Now you can see here someone will tell me, okay, is this is flux and reluctance, okay? It's the same idea. You can do like this. If the material is linear as we will learn in the next lessons, you will find that HOI LI is similar to phi. Okay? So the flux multiplied by reluctance is similar to intensity multiplied by the lens. So you can say is that here you can see HI, three. Let's delete this. And this lobe. You can see n equal to phi or I3, I3, I1, or I2, I1, i2 Phi one origin, phi one of Zhe. Okay? So it is the same ID. Okay? You can also, in that second loop here you can see n equal to five or IC for our city. And Y2, Y1, Y2 are I1. Okay? So you can see here that this equation is similar to which one similar to this one. You can see phi or i3 is similar to HI three alizarin. And the Phi one RG is similar to HAG elegy and E1 or E2 is similar to H1 l2. And this equation is similar to this one. Phi or i3, similar to HI three LI screen and Y2 are I1 is similar to HIV-1, a lie one. Now, what does it mean? It means iron. And numbering here representing one, e.g. three-year representing this branch and the one representing this branch and to representing this branch. Okay? So you can see we can apply KVL and KCL to any magnetic circuit. And the work as if we have an electric socket. So in the next lesson, we are going to have some examples on the representation of magnetic circuits to understand how are we going to deal with this different laws. 8. Solved Example 3: Hey everyone. In this lesson, we are going to have Solver the example on the representation of a magnetic circuit. So you can see in this figure we have a synchronous machine, which will be discussed in the synchronous machine part of the electrical machines course. You can see we have that rule. This coil around an iron core. This rotor is the one which rotates in the synchronous machine. And we have a state or this one which is static board of the machine. So you have to understand that synchronous machine can act as a generator and as a moat. We will learn more about this in the asynchronous machines. But anyway, you can see that we have here a coil, turn it around an iron core. And that we have here with a number of turns, N. N is the number of donors and the current entering. So you can see is that the current is moving like this and this direction. So it will produce a flux going up all the legs is going like this through the air gap here you can see there is an air gap between Zap, Router and stater. Here is our flux will go like this and be devoted one to the left and one to the right. And then go back like this, through like this. Okay, so goes from Norse, going into the subs. Okay? So let's see what we have here. We have the lens of the air gap is this length of this air gap is 1 cm. Zach current, which we use in the coil is ten amperes. The number of turns is 1,000 tonnes. And we have Zao rotor pole face area a r equal 0.2 meter squared. What does this mean? The area of this pole, you can see this one is something circular like this. Like a cylinder. My exists. So we have our I'm rotating like this. Okay? Like this. Okay, like this, and so on. So we have the current going like this and the flux coming out from the poles or from the coils. Okay? So the magnetic flux is flowing through the cross-sectional area of this rule to the area of the spot at which it will be perpendicular to the magnetic flux lines. This area is equal to 0.2 meter squared, which is the area of this pool. Okay? Now assume that the rotor and the state or the synchronous machine have negligible reluctance or they're pretty mobility. Permeability is equal to infinity. So if you remember that, that reluctance is equal to L over mu multiplied by area. Okay? So here, when we say that we will neglect reluctance, we will say that reluctance is very, very low. It means that mu is very, very large or approximately equal to infinity, very large value. So when mu is infinite, we assume this is an assumption, okay? When we say it is an infinite value, it means it's a very, very large, okay? So in this case we neglect that reluctance. So that reluctance on the stator and rotor, they will be equal to zero. And the neglect fringing effect, which is available inside the air gap itself. Okay? Now we have some requirements here and we need to find, okay? So first requirement is that we need to draw the magnetic circuit. Okay? So let's draw it in the normal state. So we have n, which is our supply, exists with a flux coming out from it. Okay? Now, this flux will pass through an air gap here and another air gap here. Okay? However, we have the reluctance of the router itself, this pool. So let's say it is, we have here reluctance or poor, okay? Which is a reluctance of this part. Then we have the flux will go like this. Sita's reluctance of the air gap. So we have I exist or gap. Then the flux will be the one to the right and one to the left. So we will say like this, we have our state-owned and like this or state, okay? Then it will go like this and we collected back again my exists like this. Exist. Then it will come back with another gap. Okay? Like this, or gap. Okay, So here what you can see in this figure is that we said that the reluctance of the air gap has a reluctance of the stator and the reluctance of the rotary can see here, rotor and stator have a negligible reluctance. So this does not exist. This one does not exist. The article does not exist. So you can see is that in the end, we have a supply with our gap and Amazon likes us. You can see we have a supply then our gap and Amazon or gap because the other reluctance or neglectful. This is the equivalent circuit system. We only have the reluctance of this gap or gap one. And the reluctance of this gap, our gap holes and the flux coming out of it. Sometimes they use, usually we say use phi. Phi to represent the flux. Phi lie exists as our people use epsilon. Epsilon is also means the flux. Okay? So that's the first requirement. Draw the magnetic circuit. Second requirement finds a magnetic motive force. So if you remember what is the magnetic motive force, it is the number of turns multiplied by current or the supply value. So it will be like this, n multiplied by n, the number of donors 1,000. And the current is ten and pairs. So we'll have ten to the power four and bear turns N, It's Sian, it is toners, and its unit is unpaired. So the requirement finds a reluctance of each air gap. So we need the reluctance of this one and this one. You can see both of them have a length of 1 cm and the most of them have the same cross sectional area. So both of them will be equal to each other. So our gap is equal to the other organ. So let's take just 21 reluctance or one reluctance of the air gap. Reluctance of the air gap will be lens divided by mu multiplied by area. Now first, what is the permeability of air or air gap is equal to four pi multiplied by ten to the power negative seven. What is the area of that cross sectional area? It will be 0.2 meter square. And what is the length of the air gap lens? Of the air gap, it will be equal to 1 cm, which is 0.0, 1 m. So this will give us our reluctance of the air gap of 3.298 multiplied by ten to the power four, one over Henry. Okay? So here, this is a reluctance of one of the air. Okay? Now, you can see that here. Why didn't we use any other role? Because we don't have here the fringing effects. You can see we neglected the fringing effect. So we use this area normally. Okay? Okay. Now that so the requirement needs a, finds a reluctance, we obtains a reluctance. We need to find the total magnetic flux. So we have n, which is our supply. And we have the two reluctance of the air gap. So it is a, we have an electric circuit. So our current is our flux. So the flux will be equal to the supply, which is n divided by the total reluctance. So it will be n divided by two or gap. Like this as if we have done KVL in this loop. Okay? Kvl or we use the Ohm's law, whatever it is. So I tend to see power for our gap is two multiplied by this value. So it will give us 0.1 to six weapon. Now, the last requirement is that we need to find the magnetic flux density in each air gap. So we need to find the Beta. So Beta, if you remember, Beta is equal to Phi Beta unit area, so phi divided by area. So we have flux value of the flux which is 0.126 Weber area, area, which is a cross-sectional area of 0.2 meter squared, like this. So we have 0.1 to six divided by 0.2 gives us 0.6 is three Tesla. Okay? So this was a very simple example. Owns a magnetic sockets. 9. Solved Example 4: Now let's have another example on Zoom magnetic circuits. So here in this example, determine the magnetic field, determines the magnetic field in the air gap of the magnetic circuit shown below. The cross-sectional area of all branches is ten centimeter square and mu are equal. 50. Value is relative permeability. So as you can see here, we have our coil around the iron core. The current entering is 45 amperes and number of donors for hundred. This will produce a flux that will go through an air gap of 1 cm. Then this flux will goes through a pool like this. Then it will be divided into two branches, one to the right and one to the left. So we have phi one and phi two, then it will go like this and they get back to the poll, go back like this, and get back to the board. Okay? So first step is that we would like to represent as this magnetic circuit. So simply you can do like this. First we have our supplies, so I will add a supply like this plus minus the flux coming out from it. Okay, So you can see currently exist, I exist in this direction. So using the right-hand rule or the Maxwell Amber right-hand rule, it will be going upward. Okay? So first you will find that we will face. First we have the reluctance of the score. So let's say here, reluctance of Zappos, e.g. then we will meet an air gap. So I will have here like this gap. Okay? Then I will meet here. Another reluctance of the magnetic core is this part, this part here. And zeros was it like this or poorly? Okay? Now we have to understand that this, this reluctance plus this reluctance that can be combined. So our poll and RPA can be combined into just one reluctance. So just for illustration that I divide them into two parts. Then we have two flux, one to the right, Y2, Y1, and Y2. Then we have the reluctance of all of these parts and the reluctance for all of these parts. So we have a tool reluctance like this. Like this, let's say or outward. And our outer. Okay, you can see here out or any any name, okay, it doesn't matter at all like this. So we have our magnetic circuit. So because the equivalent of a circuit like this, you can see here supply. Then we have the reluctance of the air gap, reluctance of the air gap, then another reluctance of that pool. Then if psi divided one or outer and on other one out are then combined together. Okay? So you can see this is our circuit. Now, what does an excess stubs and ecosystem? We need to find the reluctance of each of these elements. We need our outer or gap or pole and so on. So first what we do is that our outer, okay? So our outer or any reluctance is equal to lens divided by mu area. Now, all of the branches, all of that system here have a one cross-sectional area of ten centimeter square. So it will be at ten multiplied by ten to the power negative four meter squared centimeters squared. To convert it to meter square, we will multiply by ten to the power negative four. So ten multiplied by ten or negative four gives us ten to the power negative 3 m squared. This representing our area in meter squared. You can see we are going to use, in all of these reluctance, we are going to use the same area, ten to the power negative three. So we have area tend to SBA, negative three, areas tend to be about negative three areas tend to be bounding. They've seen. Second part is that we need to find mu is the permeability of our outer or core, iron core itself or the pool itself. Iron core or the pool. All of them have the same reluctance, which is Mu will be equal to mu r multiplied by u mu naught. Mu r is 50, and the mu naught is four pi multiplied by ten to the power negative seven. So for our outer, which is this part. Or the sport, or these two poles here. Okay? In this case you will find that our outer or our poll, we use 50, which is Mu r multiplied by mu naught, 50 multiplied by mu naught. As you can see here. For the air gap, we use only mu equals mu naught. Okay? Okay. Now, the last part we need is that we need to find the lens, okay? So the air gap blends, then solves the air gap is 1 cm, which is 0.0, 1 m. You can see for reluctance of the air gap ZA lens is 0.01, which is 1 cm but in meter. Okay? For the other two reluctance. Okay, let's look at them carefully. You can see here I'm talking about our pool, which is a lens of this part or the length of this part. Here. They are equal to each ours. So you can see the distance from here to here is 10 cm. Okay? Now we will subtract from it the air gap -1 cm of the Earth. Again, it will be equal to 9 cm. So mine centimeters is the length of this part plus the length of this part. So this distance is equal to this one. So what we're going to do is that the length of this bar to only will be 9/2, which is 4.5 cm. So the length from here to here, 4.5 centimeter, from here to here, 4.5 cm. So the summation of all of this will give us 10 cm. Okay? 4.5 is equal to in meter. We will multiply by ten to the power negative two. Okay, So it will be 0.045 meter. That's why you can see the reluctance of the pool. Length of the pole is 0.045 m. Okay? Now, instead of saying our poll and you can combine them together and use the nine centimeter. It is the same. Okay. Now with that last one which is r out of the reluctance, we need lens of the outer. Outer here representing the lens of this part, which is similar to then solve this part and equal to the length of the other part. Okay? So here, let's find the distance. You can see from here to here. Ten centimeter plus from here to here, then some to meet. Then from here to here, 10 cm. Okay? So the reluctance of this part will have a length of certainty, some 2 m or 0.3 meter. So you can see 0.3 m. Okay? So here we obtain, by substituting, we obtained reluctance outer reactants of the pool, reluctance of the air gap. Okay? Now what does an ecosystem simply we need to simplify this circuit. You can see that Z it as with article, gives us to our poll and our outer battery to our outer gives us our outer over two legs us. So you can see we have the supply. Then show our pole to pole plus the reluctance of the air gap. Okay? And the equivalent of this two is our outer over to our outer over two. Now, all of this reluctance together gives us our total. So our total, which is equivalent to reluctance, similar to electric circuits, is that equivalent to reluctance will be our gap plus to our poll plus r outer over two, like this. So now we obtained our total reluctance of the circuit. Now what do we need? We need the flux. So how can we get the flux is simply using Ohm's law. Okay? So supply and I divide it by the total reluctance will give us the flux. So you can see flux. You have to understand that's our fluxes through the air gap is similar to the flux going through that iron core. The flux will be equal to n divided by the total equivalent reluctance for hundred multiplied by 45, which is a two given values. So it will give us 1.4 853 milli Weber. Okay, So here, let's get back to here. So you can see is a flux moving through that iron core is similar to the air gap, similar to this pole. However, flux here will be divided by two. So if this one is the total flux, then we will have a 5/2. And year five or two or as if we have a current. Okay? So the flux is constant as the air gap is similar to the two poles here. Okay? Now what we need also is beta. Beta is equal to or the magnetic flux density. It will be flux divided by area. Like this. Flux is what my area area is given as ten to the power negative three, as we said before. And the flux 1.53 and mainly Weber, which is ten to the power negative three. Okay? Now, the last thing we need is that we need to find the magnetic flux, flux intensity. Okay? So if you remember that the magnetic flux intensity is equal to etch, we need to add the air gap. Remember h at L gap, this is a requirement. So we know that beta is equal to h multiplied by mu. Okay? So we have beta which is 1.53 Tesla, and the mu is mu of the air gap, which is mu naught. From here we can get h equal to 1.22 mega and bear, bear meter. Okay? So this was the requirement gap, big gap and epsilon. Now, one important note here is that you will find that that etch, etch in this pool. The magnetic flux intensity here is different from H through the air gap, different from edge here we'll have also each fall and different from h outer edge out. Now you can see this value is different from a two-pole, different from HCG. Okay? Now why is this? Because we have a different permeability and different values of flux. So as an example, HE gap is equal to beta divided by mu naught and edge of the ball will be equal to Beta. Here, beta divided by mu, which is mu r multiplied by mu naught. So you can see each pole is different from h in the air gap. Now, h outer itself is equal to beta outer divided by Mu. Now, what does the difference of the speed as this beta will be equal to 5/2 divided by the area. Remember the flux here is equal to Phi over two. Here we have the total flux. So you can see we have three different values of honesty. That's why we use, usually we use KVL as phi multiplied bys or reluctance in instead of x and multiply it by a lens because h is different in each part of the circuit. So the intensity is not constant in this part. Intensity is not constant different in each part. However, the flux is the same. Beta is also the same. Okay? 10. Magnetization Curve and Hysteresis Loop: Hey everyone, In this lesson we are going to discuss the magnetisation curve of magnetic circuits. So what does a magnetisation curve mean? The upload of the flux density, beta versus magnetic field and tonicity edge gives us exam magnetisation curve, or we call it as B H curve. It describes the average relationship between beta and edge. So as you can see, this graph, which is edge versus beta or flux intensity or the field intensity. Combine the two is the flux density. Okay? So this curve is known as the magnetization golf. We have two types of curves, as you can see here. The first one, we have the linear relation, which means that as h increases, as h increases, the value of the corresponding beta will also increase to infinity. So as you can see here, at this value of h, we have a corresponding value of b. Okay? So when H increases, let's say it becomes at this value, this is a new Hs and beta will also increase with the same value. So I'll find that this linear relation or the ideal relation is found in air. So we can say is that Beta is equal to mu multiplied by edge, right? That what we have learned before, that beta equals mu H. This relation is valid in okay, or winds up. Permeability is constant. Okay? So this relation, you can see that the slope of the line is equal to mu naught. Now, the second type of Kerberos, which is the radial one or the actual one, is a non-linear curve is this one is found in nonlinear materials such as iron and other materials. Now you can find that at each value of x, there is a corresponding value of mu. So you will find that mu here is not constant. It is a changing all the time. However, here, mu is constant equal to mu naught. Now, if you look at this curve, you can see that we have a linear part, almost linear by linear part. Then we have a knee of the curve, then it will start getting into the saturation region. So what does this curve we mean? It means that as h increases, beta will increase. Okay? Well, let's start increasing. So as H increase, beta will also increase until we have a buoyant to call the saturation. Now what does the saturation means? It means it is the maximum value of beta or maximum value of the flux density. So after this point, let's say this is B, maximum, maximum value of the magnetic flux density. After this point, you will find that whatever the value of h as we increase edge, you will find that the flux density will become constant like this. A straight line like this, with its value is being max. That's why it's called saturation. The maximum value. In the nonlinear case, or in the second case, we don't use the reluctance equation. So we don't use an eye equal to flux multiplied boys or reluctance. We don't use this equation in the non-linear. Why is this? Because mu is not constant and that's the reluctance is dependent on Mu. So Mu is not constant, so reluctance is not constant. So we don't use this equation. We use instead in I equal to h multiplied by the lens. This one is valid in some linear materials. However, in that linear materials that we can use this equation or this equation. Okay? So you can see here we have the magnetisation curve or be a trigger for different materials such as sheet of steel, cast steel, and cast iron, as you can see here. Now, what happens exactly, let's say, or let's understand how to form as a magnetisation curve. And let's understand the meaning of the hysteresis loop. So forest you can see we have a ferromagnetic material or a magnetic material like this, formed of number of donors and we apply a current to it. Okay? So the current itself is equal to E divided by R. Plus the resistance of the coil. Okay? Let's say we have a DC supply. So we will neglect the inductance. Now, as we change this resistance, as we change this resistance, value of the current will change. Okay? So how does this even held by us? You'll know that n i. Okay, so we have a current going like this. So we have a flux coming out going from here to this point for more settles house. Now, as you know that n is equal to etch multiplied by a lens. So pi changing the current, we will it change edge. So as the current increase, etch will increase, and Peter will also increase. So by controlling the current, we control the flux or the field intensity, and from which we can control the magnetic flux density. Okay? So as you can see here, as, you can see, that ferromagnetic material, as that current increases, HA is proportional to the current. As we increase the current, the actual assault increase and Peter will start increasing till saturation point. So you can see we are starting from zero reaching the saturation point. Okay? So we, assuming that our magnetic material does not have any residual magnetism, does not have any intern. And magnetism is also remembers this point. We started from zero beta equals zero, h equals zero. Then we'll start supplying current. So we will have more edge leading to more pizza until saturation. This is the initial magnetisation curve. So what does that hysteresis loop mean? So first, if we start reducing the current back to zero, and then the ferromagnetic, ferromagnetic material will have some magnetism inside it. All that residual magnetism. So if you look at the curve here, let's start again. So we have the initial curve like this. We started increasing that current will increase until beta reach the saturation point. This point, the saturation point. Okay? So this curve as knowing as the initial magnetization, cough, okay. Now, what will happen if we start reducing the current back again? So remember that we form it's a forest occur with this curve is the initial magnetisation curve by increasing the current. So H0 increase until Peter reaches saturation point. Now what if we started decreasing the current like this? So actually started decreasing and the Beta will start decreasing until current equal to zero. It should be equal to zero. However, PII data will not be equal to zero. So you will find that we start like this initial Magnus retail saturation point. Now, if we started decreasing the current, we don't go on the same curve. We start to going into a different curve, this curve which is demagnetization curve, this curve. Okay, so Windsor current decreases towards start going like this until it actually becomes zero. So the value of that beta will be this value. So beta does not return it to zero. We will have some magnetism inside it called the residual magnetism. So let's understand what does the hysteresis loop means. So we have the initial magnetisation curve, which is this curve. So this curve, when we start from zero, like this, they'll maximum value P max. And the HM, HM, HM is the value of intensity at which we will have maximum, maximum pizza. Ok? So this is the initial curve until saturation. Now when we started decreasing the current again, so it starts to decrease, you will find that we start moving on this curve. Then we have h equal to zero at current equal to zero, which is called the residual magnetism. So let's understand what happens here. So the BH curve shows the initial magnetisation curve along with a curve known as the hysteresis loop. You can see this black line. This lobe is known as the hysteresis loop. And this line is the initial magnetisation curve, which are representing the magnetization or the initial magnetization of the ferromagnetic material. So the initial magnetization, so with the magnetic flux density, the tool result when increasing magnetic field is applied to an initially unmagnetized materials. So it is a material which does not have any magnetism. So it starts from zero. Then install this increase in glycolysis. And n magnetize the material is defined at the origin of the B-H curve. You can see at this point, salts from here at t equals zero, x equals zero, and the no net magnetic flux, given no applied field. And adds a magnetic field increases, which means H0 will increase the density or will increase until reaching a saturation point P M. If the magnetic field is in cycled between the saturation magnetic field, the value in the forward and the works directions, we will form the hysteresis loop. So let's understand this. So you can see we have this point, okay? So when we started decreasing, the current will flow through this line like this. They'll reaching this point. Now, let's say we have decreased as a current in the reverse direction. So the current becomes a negative value. And we started decreasing 18s and negative values. So you can see that current equal to negative means is that H wouldn't be also becoming negative in the reverse direction. So H0 will they increase in the reverse direction. So what happens to Beta? You will find that beta will start to decrease in glycolysis. Legs as flowing like this till a point at which beta will be equal to zero. Then it will keep decreasing, decreasing, decreasing until reaching that negative V max. So we have maximum saturation point in the positive direction and the maximum saturation point in the negative direction. So as we increase in, in that negative direction, we start flowing following this line, okay, until this point at which we will have this saturation in negative direction. Okay? So what if we increase again? If we start increasing edge again in the positive direction, we will follow this line. Lie exists like this, follow like this until reaching the maximum positive value. So you can see in the negative direction like this, in the bolster, the direction we follow this line. This big loop is known as the stresses loop. So that is bonds of any material, any applied field, the vents on the initial state of the material magnetization at that instant. So what does this mean? It means that if it is at a saturation point, it will follow this line if we are going in the negative direction. Okay? And if we are in this point, e.g. in czar, residual magnetism here or here, e.g. if we start increasing etch, it will follow this line. It will start decreasing edge, it will follow this line. Now, two important quantities found inside the curve. So the first quantity, or written devotee or PR, or the residual flux density and the coercivity HC or the corrosive force. You can see that we have, if we look at this figure, we have the point here is this point at which when h equal to zero, we will have some residual magnetism or residual value, residual flux density called the PR. Now you can see that in the negative direction, we have a certain value at which we will have zero beta. Despite having etch. This value is known as a corrosive force or Zach coercivity. So note that the written devotee is a measure of how much of the magnetic energy is retained. The pie is a material open removal of the applied magnetic field. So when we reduce the current to zero, it means that we are not applying any electric current or any magnetic field intensity. Now, there will be some residual flux inside the material. This this has measured the boy written. The hires are written activity relative to the saturation level. The more of the applied magnetic field is stored in the material. Okay, so the higher this value, it means more magnetic field or more magnetic energy is stored inside our inductor or in our coil. Corrosivity is related to the demagnetization of the material nodes as the smaller Zach corrosivity is a clause or this point to the point of the total demagnetization or the origin also be a trigger. So as you can see, if this point, if this value is lower, it will be in this here. This shows the curve would be something like this. Okay? So you can see it is much tighter curve. The materials was a low coercivity can take less energy to demagnetize. And sometimes we call them the soft magnetic materials. And the converse with with high preservatives are known as the hard magnetic material. Okay? So what does this mean? If you look at here, you can see that this value, the edge when we have this residual flux. And when we start from this point from h equal to zero to HUC, we take a certain, we need a certain value of h to make p equal to z. So the higher this value, the more it will be hard magnetic materials. So it is much harder to demagnetize. So and instead e.g. of having this point here, let's say e.g. here we have HCI like this. So you can see we need a larger or a bigger value of magnetic field intensity to demagnetize them bacteria. However, if it is at here, e.g. then we need very small energy to demagnetize the material. So you can see that materials was low. Coercivity is means is that it will take less energy to demagnetize or soft magnetic materials. And with high coercivity is known as the hard magnetic materials. So if you look at this figure, this will show you the one which I'm talking about. You can see how the magnetic material, big loop or wider hysteresis loop. However, if you look at this curve, which is a soft magnetic material, can see that c is very small. So you can see very tight curve. So this very tight curve is known as the soft magnetic material. And wider curve or a wider hysteresis loop is known as the hard magnetic materials. So how can we measure the magnetic field strength? Now citizen effect of goals, a hall effect, which means that the voltage is proportional to the field strength. The stronger the magnetic field and density, the more voltage we can produce. So you can see here, if we have a current source, e.g. and it's connected here to app e.g. play it e.g. okay. Now this current, we have a flux, of course, that flow with, throws us fluxes flowing through this material. The more flux or more magnetic density, the more voltage we can produce. So we have, using this Hall effect, UE was Hall effect a Gauss meters to measure the field strengths. So you can see here e.g. if you have a coil like this and we apply a current, so we will produce a flux. Now, if we add a blade like this, the more flux cutting this plate, the more magnetic field density. So we will connect this to a Gauss meter, which will show us the strength of the magnetic field. Okay? Now, how does this even work? As we have seen here, is a more flux cutting because it's played, the more voltage you produced. More voltage means that we have a stronger magnetic field. Okay? Now you will understand, in this course, you will understand AI-powered as a Faraday law. The Faraday law will help you understand how can we use magnetic field to produce voltage, which is important concept or the basic concept of the electrical generators. So don't worry, we will understand what is the relation between the voltage and the magnetic field in general. Okay? 11. Solved Example 5: Now let's have an example in order to understand how can we use the NI equal to h l relation in magnetic sockets. So let's say we have this figure we have going around this circular core or a core made of silicone cheat, steal. Remember core made of silicone sheet STR. Remember we need this, this core in the form of circular form. It has an outer diameter. Outer diameter of 20, 1 cm, diameter of mountain centimeter. You will find that we have here two coils surrounding this material or this code. You will see one core, one coil of I1 current i1, and another coil of current I2. Of course, both of them will produce a flux that will affect this material. Anyway, we have the value of the two currents. We have the number of turns of the two coils. And we have the area At which is our flux will cut the area. So you can see e.g. this one, we will have a flux of going upward using the right-hand rule. So this flux, so we'll cut a certain area. Certain area exists. This area is equal to 4 cm squared and it is equal to, Equal in the whole figure. Okay? Now what do we need to find? We need to find the magnetic flux density. We need to find the flux, and we need to find that relative permeability, permeability of this material. Okay, so let's start. So the first step in analyzing any magnetic circuit is that we need to convert this figure into a magnetic circuit or in the electric circuit form. So first you will find that we have a current I1 by exist, reducing the flux is going upward. Okay? So I will have by exist plus minus N1 or E1. Okay? So this is a first source, second source we have here i2, like this. Let's look at here. We have currently exists like this. Okay? So this current, if you apply the right-hand rule or the Maxwell ambient right-hand rule, you will find that the direction of the flux will be downwards. So it will be like this plus, minus. Because the flux coming out from it and fluxes from this one coming upward. This one will be an SN2 or E2. Okay? Okay. You can see this flux going like this and the flow is through the other ones. So both of them are in series. Okay? So they are in series like this. And we have a reluctance of the material itself. So we'll have our or, or, or, or whatever it is. It is a reluctance of the iron core or the silicon core, whatever it is. You can see we have two supplies and one reluctance of the material itself. So you can see the equivalent circuit in one i1 and i2, i2 flux and are all, okay. So you can see this two supplies are supporting each other like this. Okay, So let's produce a flux like this. And this one will produce a flux exists so both of them can be combined into one source. Okay? Okay. Now what does the next step we have N1 and N2 I2. Now what I would like to obtain is the value of R. However, we don't have mu are given, we don't have mu and we don't have the flux. So if you remember that we said, if we apply here, we have n, n1 i1 plus i2 i2 equal to the flux multiplied by our flux. I don t know the flux. And the ROI. We don t know that mu r, So we don't know. So what are we going to do? And instead of doing this, we are going to use the lens of the pores of the magnetic flux multiplied by h. Okay? So we can get H I and from it we can get the magnetic flux density. Okay. So you can see ROI equals NOI over mu i. Now, what is the value of the lens? Okay, So we have a flux coming like this. Remember it is flowing in the middle of the core, like this ligases. Okay? So you know that the outer diameter is 20, 1 cm, and the inner diameter is 19 cm. Okay? So what I need to find is the lens of this magnetic flux boss. Okay? So the lens of a circle in general, lens of any circuit as equal to two pi multiplied by the radius or pi multiplied by diameter. So Pi multiplied bys are timed. So what I need is the diameter of this figure. This damped. You can see we have the outer diameter and inner diameter. Their average will give us the diameter required or D average. So it will be equal to 21 plus 19/2 gives us 20 centimeter. So you can see that from here to here, it is 20 centimeter. Okay? So from here we can get the lens required, okay, By substituting in this equation. So now we are going to use the equation of KVL here. So you can see that here we have to use n equal to H L. So n, n1 I1 plus I2 equal to h a lie. Okay? So if you make sure, would like to make sure you can do a KVL like this. You can see negative n, n1, i1 and i2, i2 and the plus phi or I, or N1 I1 plus I1 i2, i2 equal to phi multiplied bys reluctance or H2 multiplied by isolates. So we have N1, we have I1, we have in i2, i2, we have the lens which we just obtained so we can get edge as required. So what we need in this problem, we need to find beta, value of beta. We need to find value of flux. And the Mu we obtained etch. How can I get beat? Now remember, we said before that there is a relation between H and beta, which is p H girl. Right? So if you'll look like this, we have a pediatric curve, the magnetic flux density and the field intensity for different materials, as you can see now, if you remember, we, each one of these materials are we using? We said that we are using silicone sheet steel, right? So we have HR equal to 575 and Berta to something in this point like this. If we go like this, 553, if we go up like this and go up, up, up. Okay, Going up until this point here, like here. So if we go like this, exist, you can see that the beta is approximately 1.25. So we talked 505, close to 500. If we go up like this, it will be 1.25. So you can see that beta from the pH curve of the silicone sheet steel, 1.25 Tesla. Okay, So we have bit and we can get a flux that the flux is equal to P multiplied by area. Area is given in the problem and the beta 1.25 tesla. So it will be the area which is given in the problem. Multiply it by beta, which is 1.25 desk. That'll give us y equal five multiplied by ten to the power negative for Weber. Now what do we need? Also, we need to find the z value of mu R or the relative permeability. So in order to get Etienne or that Beta is equal to mu multiplied by h. Okay? Remember, mu here is at a certain value. So at a different, other different value, we will have a different immune. Okay? So you can see this is a non-linear curve. So at each value we have a different mu or a different permeability. So beta equal to mu H or mu naught mu r H. We have beta equal to 1.20, 5.535, and the mu naught four pi multiplied by ten to the power negative seven. So we can get mu. Mu R will be equal to 1859. So you can see is that in the linear relation is a straight line. We have one mu which is equal to mu naught, or we can say a constant, the value of mu. In some non-linear material, which is the actual case, we have a nonlinear relationship. So the non-linear at each point we have a different immune. According to value of h, we have a corresponding value of beta and the corresponding value of mu. So in this lesson, we had another solvent, the example on the magnetic circuits. And we understand now how we can use the BH curve in magnetic circuits. 12. Inductance and Flux Linkage: Hey everyone. In this lesson, we are going to discuss two important concepts in electric circuits in general, or magnetic circuits. The first concept is called the flux linkage. So what does the flux linkage mean? The flunk success linkage of any coil assembly, an alternative term for the total flux. It is used for convenience in the engineering applications. So you can see that here. Let's say we have a coil like this with a certain number of turns N. Now, the current passes through each store, right? Okay, So if we have just one turn like this and the current passes through it, so we will have one flux. If we have another term like this, another term, then we have another flux. So the more tone as we have more flux, we will get the expression, expression of the total flux in a coil is called the flux linkage, which is the number of turns multiplied by the flux, which is n multiplied by beta multiplied by the area. Okay? So the flux linkage is the linking of the magnetic field with the conductors of a coil. When the magnetic field passes through the loops of the coil, expressed as a value. So you will find that the flux linkage, which we call it lambda, you will need to see lambda. It means the flux linkage equal to an n, or the number of turns multiplied bys or flux. Okay? So why? Because each photon here produces a flux. So more number of terms, it means more generated flux. Now what is the inductance of a coin? So we learned in electric n. Note electrical machines in electric circuits that are representing the inductance, right? Of inequality. Now, what is actually L? What is the value of L? Okay? So if we have a coil like this with the inductance L, So what does that value of inductance? So simply you will find that the inductance is the ratio between the flux linkage with respect to current, which is n multiplied by phi, which is flux linkage n phi divided by the current. And we know that the flux is equal to n divided bys or reluctance, NI divided by the reluctance. So if we take this and substitute in this equation here, we will have that the inductance equal to n square over r. So it will equal to number of turns squared divided by the reluctance of the medium of the magnetic field. Okay? So the value of one Henry or one millihenry came from here. It is number of turns square divided by reluctance. And as you can see, it depends on the geometry of that construction because our reluctance equal to learn some of the blood volume mu area. So it depends on the geometry such as area and the length of the magnetic box. And in addition to of course, the medium of the material itself. Okay? So in this lesson we are asked to give a small hint, or we learned about with that flux linkage and the inductance of a coin. 13. Faraday's Law of Induction and Lenz’s Law: Hey everyone. In this lesson we are going to talk about with the Faraday's law of induction and Lenz law. You have to understand that Faraday's law is really, really important because you will find it in every electrical machine. So Faraday's law of induction is used to help us understand how can we convert mechanical energy, mechanical energy, into electrical energy, into electrical energy. So find that this concept of four a day will help you understand how can we do this from mechanical to electrical or from electrical to mechanical, e.g. from mechanical to electrical, we are talking about electrical generators and the conversion of electrical to mechanical. We are talking about with electric motors. Okay? So let's understand what does this law states and what does it mean? For today's law of electromagnetic induction states that any change in a magnetic field, any change in a magnetic field will induce an electromotive force in a conductive coil that is directly proportional to the rate of a change in the inducing magnetic field. So what does this even mean? That's, let's continue for now and then we will understand everything. So it will induce an electromotive force, The call the EMF and the measured in volts, which will also create a current flow. And here is what does it mean? Okay? So first, the Faraday law says that any change in the magnetic field, so our magnetic field is measured or denoted by Phi. Phi is the magnetic flux, which you can represent the magnetic flux or Z lines of magnetic field. So the Faraday's law says that any change in a magnetic field, any change it change, any change, we represent it as a differentiation. So we'll say is that any change in the magnetic field, d phi over DT, or variation of magnetic field will induce an electromotive force. An electromotive force means E or a voltage. Okay? So any change in the magnetic field will lead to an electromotive force. The value of the electromotive force is directly proportional to the rate of change of a inducing a magnetic field. So what we learn here is that the voltage is produced is directly proportional to d phi over DT, or the rate of change of the flux. Okay? So we can remove this direct proportional to E equal to N d phi over d t, which is this low. Faraday is a positive sign. Okay? You will understand that there is a negative sign due to Lenz's law. Okay? So here E or the voltage are produced, or the electromotive force means the voltage are produced inside a coil, is equal to n, which is the number of turns of the coil. How many tones for this coin? D phi over d t is a variation of magnetic field. So it means that if there is no change in magnetic field, it means that there will be no voltage. Okay? So how can we understand this? Okay, you can see here we have a magnet. In a magnet produces magnetic field. This magnetic field is constant, okay? So this magnetic field, magnetic field is constant. Okay? So if we put a magnet like this besides a coil, okay? Is there any change in magnetic field? There is no change in magnetic field. D phi over d t is equal to zero. So no voltage is produced at the terminals of the coil. Why? Because the magnet itself is at, it's a place. It is, fix it, it produce a fix-it value of magnetic field. So the variation of magnetic field is equal to z. So there is no voltage between these two. However, however, if we take this magnet and the store to moving to the right or to the left, or move it to the right, you will find is that this coil, we will have an induced EMF. Why is this? Because the motion of the magnetic field, or motion of the magnet itself produces mixes, this coil sees the magnetic field as a variable feed. So in this case, you will find that we have a variation in magnetic field, which means that we will have a voltage. So let's see this figure to understand the idea. So if you look here, we have a magnet and then we have a coil like this, a coil like this one, which have two wires, two terminals, several coils. How many donors? 1234567. So we have n, which is the number of turns of the coil equal to seven. Now, if we keep this magnet as it is in this position, you will find that the voltage are produced at the two terminals is equal to zero. There is no variation in magnetic field. However, if you start moving this one like this, you will see that the voltage starts to be produced. Or if you move it like this in the other direction, you can see a positive, then gets back negative and so on. So you can see this motion of the magnet itself produces a voltage across the cohort, okay? If this magnitude is constant or standing in its place, it will not produce any voltage. So the Faraday's law say is that when we have a variation in magnetic field, we will have a voltage which will be produced as this voltage will produce an electric current. Okay? So let's see enormous opposition here as legs, as you can see here, that when we have a magnet like this, Okay, Let's see it. You can see when we move the magnet like this to the left and then stand still, you will find that the voltage is zero. When we start moving, you will find that the current is produced because we have an induced voltage, voltage which is produced at the terminals of the coil. Okay, so the current is formed only on the movement of the magnet itself because the magnetic field is changing with respect to this coin. The magnetic field as seen by this coil, is it changing? When we are becoming close to the coil, the magnetic field is increasing. More fluxes cutting is a coil. And the, when we start going away, the amount of flux cuttings or coil decreases. So you will see that this motion will lead to production of magnetic, production of electromotive force. When it is standard, still not moving, you will find that the voltage is zero. When we start moving, we will have and induced EMF. Okay? So the idea of Faraday's law is that when we have three elements, three elements, number one, when we have a magnetic fields, when we have a mechanical motion, mechanical motion we are moving left and right, left and right. So we have motion. When we have a wire which will take the output current. When we have this three elements, we can generate electricity. What we can do is that we can take an electric generator is, electric generator is formed of a rotor and stator. The rotor is rotating part. So when we add a magnet on the router and this rotor is rotating due to mechanical force. You will find that we will have a varying magnetic field, or a d phi over d t. And the stator is the one which will take the output voltage. We will see this in the synchronous generators and induction generators. Okay? So what about Lenz's Law? Lenz's Law is pretty, pretty simple. You will find that, that Lindsay Law states that when a changing magnetic field produces or induces a current in a conducting required. So what is the value of this current over? What is the direction of this current? Or why do we have a current? We have a current because this current will produce a magnetic field that opposes the induced magnetic field. But it's simply the induce, the current opposes the changing magnetic field, which is producing it, as shown in the figure we will see here. So as you can see, we have a magnet like this. Okay? Let's say it is in this position, North and South. So we have some flux lines here like this. Let's say it is reaching here until here. Okay? So let's say it is a standstill. So there will be no voltage here because there is no motion. Now, let's assume that we are moving from here to war this coin. What will happen is that if this magnet from this position becomes in this position, this position you will see that it cuts more of the coin. More magnetic flux will cut the coin. Okay? This motion will produce a varying d phi over DT, or a variation in magnetic flux, which will lead to production of voltage. Okay? So what do you think is phi or the amount of magnetic flux see him by the coil increasing or decreasing. Actually it is increasing because we are going close to this coin. So coming close, it means a more flux will cut this coin. So what does a solution now, I would like to produce a magnetic field that opposes this effect. So you can see magnetic field is increasing like this. We are coming close. So the magnetic field is affecting more and more zach coin. So the current will be produced the like this. Okay, So we will find that the current flowing like this, like this. Okay? So we'll find that when we use are all called Zap Fleming right-hand rule, you will find that this coil, due to the presence of a currently exists. It will produce a magnetic field in this direction, like this, north and south. So when does current flow is like this? It will produce North and South. Why is this? Because we have here north and south. North here means that it will pose, it pushes this one away, stay away from me. Okay? Now it's the same idea for this one. You see here we have north and south. Now if we have some flux cutting here like this. Now when this one moves in the other direction like this, you will find that e.g. it becomes in this position. So find that in this case you will find that it will cut like this. It will just the cost, e.g. here and here and here. The magnetic field seen by this coin is much lower, much lower. So what will happen is that a current will be produced like this. Like this by exist, I exist. Okay? According to the Fleming's right-hand rule, you will find that this one will produce a magnetic flux in this direction, like this, North and South. So what will happen is that we have this mega which is north and south. So this sounds will try to attract the snow, so it will oppose the effect. It will just try to get it back to its original position. So in the end, zach currently produced or the voltage produced in other direction produces a magnetic field in a direction that opposes the change. If this one tries to get closer and increases the magnetic field, the current will produce a magnetic field that opposes this effect. Stay away from me. If this one stays away and go away from the coil, the current will be produced here to attract it, please come back so it will produce a magnetic field in this direction to attract this magnet back again to its position. Okay? So Windsor North of the pole of the magnet in the figure above moves closer to or farther from the rope. And EMF will be produced to produce a current that will produce a magnetic field that opposes the changing magnetic field from the magnet. So here you can see this is the ID, exactly what happens. So here, when this one starts to come and get close to it, you will see that a current will be produced. The current will be produced another direction which will produce north and south. So if you have a current in this direction and this direction like this, okay? So we will have like this, okay? So the magnetic field will be like this. And we will have north and south. You can see when this one twice to come closer, a current will be produced the legs this. Why is this? Because you will see that the current Like this, like this, moving down, down, down. Which means that according to Fleming's right-hand rule, the magnetic field will be in this direction. Of course, if you don't know about Fleming's right-hand rule or all of this. You can get back to our goals of electrical machines, okay, in which we discussed in more details about magnetic flux and the magnetic circuits. So we have North and South, and this one is north and south. So as you can see, when this one tries to come closer to the coil, the current will be produced, will produce a magnetic field north and south, which opposes this magnet. When it starts going away from it, it will start reversing its direction to produce a magnetic field that will have as house and tunnels here, so it will attract this one. Please come back. So as you can see, when it comes closer, it produces a repulsion force. When it goes away, it produced an attraction force because it wants it to be in its own position, is the original position. Here is an example of the Fleming's right-hand rule. So as you can see here, here we have our code. Let's say it's a current going like this. Not like this. Let me have it in the other direction. We have positive here. So let's say the current is like this, going down like this, like this. So if you put your hand like this, you can see in the direction of the current, this hand is in the same direction of the current law exists. So we'll find that this, some of your own hand will produce the direction of magnetic field, which is in this direction. So this is the direction of current. This is the direction of magnetic fields. So the current up magnetic field on the right or the nodes, since it's the magnetic field that exists. So we have North and South. So by using this Fleming right-hand rule, you can apply it here to find the direction of the magnetic field. Here is more about eight. You can see we have a coil according to the direction of motion. This will happen. So you can see we have, this magnet is moving. So we have moving towards it. So it will produce a current that will produce a magnetic field that will oppose this motion. So e.g. in this one, it is moving like this, so it will produce north and south to oppose the effect, to tell it to go away. Here if the magnet is moving away. The same idea. This will produce North and South in order to attract it. Come back. Please come back here for this example, it's the same idea if we have North and South. But this one is the one which is moving the coil is the one which moves. This one is a stationary. So since this one is moving, it is also seeing this magnetic field as varying. Toilet try to attract it. So it will produce north and south to lead this one come to me. Okay? Same idea. If it is moving like this, it will produce also South and the North to attract this one. Okay? So in the end, it will try to keep the magnetic field is same as before. So what we learn from this, or what is the purpose of all of this, you will understand that in order to generate electricity in magnetic field, generate electricity in electrical machines, we need three elements. One, we need a mechanical force or motion. Number two, we need a magnetic field. Number three, we need a wire that will carry the output current or the wires that will have an induced voltage. So you can see here we have this magnet, which contains magnetic field, and it is moving left and right. So we have a mechanical force. Then we need the wires, the wires which will carry the output voltage or output current. Okay? So we have three elements that you will always find in every electrical machine. Okay, so let's go to the next lesson and start understanding the forest, the type which is a synchronous generators. By understanding the synchronous generators, you will be able to find disease three elements. You will find the mechanical force, magnetic field, and the wires. Okay? 14. Introduction to Electrical Transformers: Hi, and welcome everyone to this course, our course for transformers. In this course, we are going to talk about transformers. First, the electrical transformers, or what is the importance of electrical transformer? The transformer is an electrical device that transfers or transport the electrical energy from one circuit to another using the electro magnetic induction. Or sometimes it's called z transform or action. So what is a function of the electrical transformer? It is used it to step up or increase the voltage level or step down or decrease the voltage level. So the transformer is aesthetic machine. What does this mean? It means that this transformer does not have any rotating parts. As you can see in this figure here. This is our transformer or S three phase transformer, which is used in electrical power systems. This transformer does not have any rotating part, does not have any rotor. Such as in DC machines or induction machines or any type of electrical machines. It is aesthetic machine, non rotating machine. There are two types of transformers that will be discussed in this course. The first type of transformers is called the single phase transformer. The second part, which is important, the three phase transformers, such as this one, which is used in electrical power systems. So we now understand that the transformers are used to step up or increase the voltage, or step down or decrease the voltage. Now, I would like to understand why do we do this? Why do we step up the voltage? Step down the voltage in electrical power system. During the transmission of electrical power, the voltage is increased via a power transformer in order to reduce the transmitted current, which will reduce the total losses in the transmission system. So let's look at this figure. This figure representing as small representation of the electrical power system. So first we have the first stage, which is generation stage. We have our generator. It can be conventional power plant or renewable energy power plant, e.g. let's say e.g. f. Also for your will power plant, this fossil fuel power plant will produce S three phase power voltage, or the generated voltage at 11 kilovolts. This is a level of generation, the generation level. Now we will add here an intermediate stage, which is the step up transformer. This transformer which we are going to discuss. We'll take this 11 kilovolt and increase it up to 400 kilovolt as an example. Okay? It is not a constant. A value in the band is on the transmission system. It can be e.g. 110 kilovolt. It can be 220 kilovolt, it can be 500 kilo volt, and so on. It depends on the system itself. Okay? So we have our electrical power transmitted now through that transmission system at the high voltage of 400 kilovolt. When we are starting approaching transmission system as a distribution system, we will start stepping down the voltage or decreasing the voltage. As an example, we will take this 400 kilovolt here and reduce it back using a step-down transformer to the 33 kilo volt, or 60, 60 kilo volt or 11 kilovolts or whatever it is. Then we will have a distribution system. And then we will step down the voltage again until Zack consumer stage. Okay. So as you remember or as you understand that at our consumer e.g. me and you, or in our house, we have a voltage of voltage of 220 volt or a throw 180 volt, or 1,110 v, and so on. So we can see that we started with 11 kilovolt. Then using a transformer, we step up the voltage. Then we start reducing it as soon as we are approaching the consumer side. Until we will reach these levels of 220 volt. So hundred 80 volt, 80 volt, 110 depending on the country itself. Okay. Now why do we do this? This process of increasing the voltage will lead to reduction in the current in the transmission line. The current inside the transmission line will be much lower price stepping up this voltage, which means that the power losses in the resistors of air resistance of the transmission line, if you remember, I square multiplied by R, so that I squared multiplied by R, What does this mean? It means that, that losses are, losses in the transmission system will be reduced because the current is much lower. Okay? So by increasing the voltage, we will have much lower current, which will lead to lower power losses. In the next two lessons, we will learn why does the current is reduced or how does the transformer increase the voltage and reduce the current? We will learn about this in the principle of operation of the transformer. Then, as we have said, transformation increase the voltage for transmitting electrical power and adds the distribution of the electrical power to the consumer. The voltage is decreased, the ones more. Using a power transformer, it can be several times until voltage level suitable for power consumption. E.g. consumers through 180 volt to 220 v hundred and ten volt. For factories, e.g. the voltage is suitable for them is 11 kilo volt or service three kilovolt. It depends on the consumer itself. The same process here, as you can see, we have an electrical generator from any electrical power plant. Any electrical power plant. Here, 11 kilovolt here as an example, 30 kilovolts. This is a generation phase. We will start stepping up the voltage using an electrical transformer resists to this shape representing as transformer. This shape representing a transformer. This transformer will increase the voltage, e.g. 500 kilovolt for transfer transmission of electrical power. Then we will start reducing that voltage by using several transformers until we will reach our lute, 120 volt or any other voltage. As this stepping down of the voltage is at, called the Z distribution phase, or the distribution is stage. The last stage of electrical power system is that consumption of electrical power. So in this lesson, we talked about the electrical transformers and why do we need them in electrical power systems. 15. Construction and Operation of a Single Phase Transformer: Hey everyone. In this lesson, we will talk about the construction of a single phase transformer and the principle of operation of a single phase transformer. So first, you will see in this figure, this figure representing as single phase transformer. This transformer is consisting of three main parts. First part is our primary winding. Second part is that second rewinding. And the part is cool. So the first part is the primary winding. And secondary winding here is a primary winding is the whining at which we are going to connect our voltage source. And the second rewinding is the output voltage. It can be as a step-down voltage or the step-down voltage which will be connected to the lute. The two windings are connected together, not electrically, but magnetically, using an iron core. The iron core well connected between these two winding using the magnetic flux. So first, as you can see, primary winding connected to an AC supply. This winding has a number of turns, N1. So we have here a coil with number of donors N1. That secondary winding is a winding which is connected to the electrical load. This winding has a number of donors. And two. Then we have our iron core, which is made of iron. Pretty clear. I have no corn made of iron. In the form of laminations. You will see that this are in accord, is formed of laminations, as we will see right now, in order to reduce one of the types of the losses that we are going to discuss in the electrical transformers, which is the eddy losses, which will lead to enhancement of the efficiency of the system. So as you can see here, here you can see this iron core is similar to this one or this one. You can see that this is not a blocker, is not an iron block. However, it is made of laminated, is still cool. So you can see it's format of group of laminations above each other. Why do we do this in order to reduce the eddy currents which are forming inside the core itself. So due to the flow of electrical, due to the flow of magnetic flux inside our core. We will have induced the currents inside the core itself called the Eddy currents, which will lead to more losses in the electrical transformer. So when we make, is us from laminations, this current is highly reduced. So why do we need an iron core? Because this ionic core will act as oppose for the magnetic flux line. Okay, so let's see now how does an electrical transformer or a single phase transformer works. So we've talked now about single phase because we have only one source or one supply. So that operation of a single phase transformer. So as you can see here is the same figure. We have the primary winding. Secondary winding, we have the input voltage source V1. We have the output voltage which is going to dilute V2 number of turns N1 number of turns N two. So the primary winding is connected to an AC voltage source, V1. The first winding connected to the supply itself. Now what will happen when we have an AC supply connected to quiet? You will see that an AC current I1 will flow through the primary coil. We have a voltage source and we have a coil with a certain inductance or a certain reactants XL e.g. so e.g. it will be the current, I1 will be the voltage divided by the total that it sees. Okay? So we will have a current flowing through this coin. Since we have an AC current and AC current flowing through this coil, what will happen in this case, we will have a magnetic flux. So when I won flow is like this, through this coil, like this, we will have a generated magnetic flux. As we discussed, the forms are magnetic circuits. So this flux is called phi one. Now you will have to understand that this phi one will be divided into two parts. The one coming like this through air leakage flux, through air, flux like this, going like this, from north to south, like this through air. And this type of flux is called the leakage flux. This amount of flux, phi l, denoted by phi L, is the leakage flux, which is the flux going through air and coming back to the coin. This is just a very small portion of the total flux As which can be neglected. However, the major part of the Phi one or the flux goes through the iron cool like this and come back to the other. Okay, So the flux will goes through here from norse, coming back to cells. And we said before that the flux will do this. Most of the flux will go this because our reactants of the iron core is very small compared to the reactants in air. That's why most of the flux will flow through the iron core itself. Now sensors are cool, is our flux of the core is flowing through the coil like this. It will cut the two windings. It will cut. This winding is our primary winding, and it will cut all through that secondary winding. So when this AC flux, AC flux cuts both of these coils, we will have an induced the voltage E1 in the primary winding, and we will have an induced the voltage E2 enzymes secondly, wine. Okay? Now, as you remember that the induced EMF is equal to negative N d phi over d t. Induce the voltage across a coil is generated when we have number of donors. So we have here N1 and N2. And at the same time we have a varying flux, since our flux is AC flux, so that there will be a variation in the flux. So we will have induced the voltage here and here. So as you can see here, we have y1, which is a forest induced voltage equal to N1 number of turns on the primary winding, d phi over d t and the secondary winding E2 N2 d phi over d t. So pi, you're looking to these two equations of E1 and E2. If we divide them together, we can have this final relation. We can find that E2 over E1, or the induced voltage of the secondary, on the secondary winding, the terminal voltage, but the voltage across the coil itself. E2 over y1, is equal to number of turns into, divided by number of turns N1. So the ratio here, N2 over N1 is known as the a, or the tone is rich. So the tone is ratio of the transformer is a ratio between the number of turns on the secondary winding divided by the number of donors of the primary winding. This is our most well-known definition for the single phase transformers. Another definition you can find is that turns ratio of the transformer is the number of chromosomes are primary divided by the number of donors of the secondary. Number of donors of the transformer can be equal to primary over secondary. Or it can be also equal to, depends on the definition itself. It can be N2 over N1. However, resist one is the most widely used, the secondary divided by their primary. Okay, so let's continue. So here the winding with the higher number of turns is called Zara high voltage or the high tension winding. So let's say e.g. N1, N1 is greater than into as an assumption. So this one has a higher number of turns. So we call N1 is a high voltage or the high tension wine Nick. And we call N2 as low voltage or the low tension winding. So high number of doneness means high voltage means high tension. N is a lower number of donors, means low voltage or low tension whining. So depends on the turns ratio. A transformer can be a step-up transformer or a step-down transformer. As an example here you can see two types of transformers, assuming that our source, our AC source is here. Our AC source here is connected to the primary like this. And the secondary is connected to any loop like this connected to allude. And this one is connected to a loop that turns ratio. If you look at this transformer, we have the input voltage, 240 v. This is the input value, and the secondary has a value of 120 v. So it means that the voltage is decreased or step down. That's why this transformer is called a step-down transformer. If you look at the turns ratio a or the turns ratio equal to secondary divided bys a primary, as you can see here, equal to induce the voltage of the secondary itself, E2, which is 120 volt, divided by y1, which is a voltage of the primary. So it will give us 0.5. As you can see here. Same idea for this transformer. This transformer has E1, the primary voltage, hundred and 20 volt, and the secondary voltage, 240 volt. So the ratio between them will be equal to two. So what does this mean? It means the owners ratio, high turnover ratio means or greater than one. It means it is a step-up transformer. So you can see step-up transformer because our voltage increase the forearm hundred and 20 volt to 240 revoked. And this one is called as step down transformer because the voltage decreases from 240, 220 volt. So you now understand that how can that transformer, it changes the voltage. So if you remember in the previous lesson, we set as our transformer is used in the electrical system. So by controlling the number of turns of the primary, number of turns of the secondary, or the turns ratio, we can increase the voltage or decrease our voltage. Now what all the different types of the transformers? So we have three types of transformers as step-up transformer. When that secondary voltage is higher than the primary voltage, or the number of donors is greater than one. We have also step-down transformers when V2 is less than V1 or number of donors is less than one. Now when the tone is ratio becomes one, it means it is nicer. Step up transformer nor a step-down transformer. So in this case, we say that this transformer is called an isolating transformer. It is used to isolate between two electrical system using the transformer itself. Now why does this transformer isolated between electrical systems? Because as you can see, this winding and this whining are not connected electrically. They are connected using the flux or using the magnetic field. So they are isolated electrically from each other. That's why it's a transformer, can be used as an isolating transformer. So in this lesson, we talked about that transformer, Zach construction of the electrical transformer, or a single phase transformer. And we also talked about the different types of transformers and the operation or the principle of operation of a transformer. 16. Ideal Transformer: Hi, and welcome everyone to this lesson about transformers. In this lesson we will talk about with the ideal transformer. So the first type of transformers, which is the ideal transformer, and this type of transformer does not have any kind of losses. So the ideal transformer cannot be physically realized. However, that practical transformers, or the real life transformers have properties that approach very close to the ideal transformer. So sometimes we can treat our practical transformer similar to an ideal transformer. In this type of transformers, we don't have any leakage flux. So we, as you can see in this figure, we have the primary winding, secondary winding. And the county here produces the flux, core flux. And as you remember from the previous lesson, we said that zeros or leakage flux. Now in the ideal transformer, we will neglect this leakage flux. Second part of the ideal transformer is that we will neglect the winding resistance of the primary and the secondary coil. So if you look at this figure, we have a coil here, or the primary winding. And the secondary winding. These two windings have resistance. These two windings have resistance. We have the primary resistor. And we have the secondary resistor, which are representing the resistance of the winding itself. Since it is made of copper or any other material. In ZAP practically or in real life on an old rail transformers, they have resistance. However, since we are talking about the ideal transformer with no kind of losses, then we will neglect this resistance. So in this case, we assume that our coin is a pure inductance. That sold assumption here in the ideal transformer is that the permeability of the core is infinite. It means that the, or the resistance or reluctance of the magnetic circuit is equal to zero. It does not exist at all. Another type is that the cool losses or Amazon assumption is at the core losses, the hysteresis and eddy losses are negligible or they are not. They don't exist or are completely neglected. We will talk about the different types of losses in the electrical transformer in the next few lessons. So some of the types of losses, hours a hysteresis, losses and the losses. All they are defined as, or they are known as the core losses. So we will talk about the core losses are coupled losses and all of the different types of losses in Amazon Alexa. In this lesson we say is that we don't have any kind of losses. We have an ideal transformer with ideal properties. Now if you look at this transformer, you can see we have a coil here without any resistance zoster, the inductance of this coil. So if you look at this figure, or if you remember before we said that the total is ratio, or the ratio between the secondary induced voltage and the primary induced voltage equal to N2 divided by N1 equal to a or the turns ratio. So the ratio between this voltage and this voltage equal to N2 over N1 turns ratio. Now, as you can see here from this figure, since we don't have any kind of losses, we don't have a voltage drop across R resistance or any other elements. So that if you look at this circuit, you can see that the input voltage V1 is equal to as a magnitude equal to y1. And the induced voltage E2 is equal to V2. So the ratio between each of our E1, E2 over y1 equal to V2 over V1 equal to N2 over N1 equal to a or the turns ratio. So by controlling the tone is ratio, we can ideally control the ratio between the output voltage and the input voltage. We can increase the voltage or decrease it. Now, the most important part, which will help you understand why does an electrical transformer, when it increases the voltage, it will reduce the losses. Now, how does this occur? Now we'll look carefully at this equations. If you look at these two equations, these two S1 and S2, what does this represent? This rubbers and things that input apparent power and the output apparent power. So the input apparent power is of course equal to the voltage multiplied by the current. So we have here an AC supply. So multiplying this voltage by the current coming out of it, it will give us the apparent power S1. So V1 multiplied by I1 give us S1. For that secondary winding or the transformer S2. The output power going into solute. Here, this power will be equal to the voltage across the load multiplied by that current entering it. So it will be V2 multiplied by I2. Now, since we are talking about in this lesson, APA with an ideal transformer. Ideal transformer, it means it does not have any kind of losses. So in this case, all of the generated power or all justice antigen rated at Bear power will be equal to all of their consumed or the apparent power going to dilute. So in this case, S1 will be equal to S2 V1 over T1 equals V2 I2. So by looking at this equation, you will find that v2 over v1 will be inversely proportional to i1 and i2 equal to the tone is ratio. So what can we learn from here? What we can learn is that if this transformer is a step up transformer, it means that E2 over y1 greater than one. If it is a step up transformer. So let's say e.g. let's save, let's say, or V2 over V1 greater than one. Since we are talking here about ideal transform, Let's say e.g. this ratio is equal to 50, 50. So it means that the voltage using the number of donors, we increase the voltage by 50 times. Okay? Now, let's look at this here. V2 over V1 equal to 50, equal to I1 over I2. So from this equation, you will find that the secondary current is equal to 1/50. Okay? So what does this mean? It means that when we increase the voltage, when we stop the observed voltage, similar to that transmission system, if you'll remember from the previous lesson, 11 kilovolt. And when we stopped the observers to 500 kilovolt, what will happen to the current? The current. And instead of having i1 and i2, the current i2 won't be much, much lower than I1. Now, why is this due to the increase in voltage or the current is inversely proportional to the voltage. So when I2 becomes a very, very small, you will find that the power losses, power losses in the transmission line is equal to I square one to Budweiser resistor. When this current is very, very small, it means that the power losses will be reduced. That's why we step up our voltage. When we increase our voltage, the current will be reduced because we have the same power. Ideally the same power. So when this happens, you will find that the power losses will be reduced greatly. Okay? So in this lesson, we talked about with the ideal transformer, and now we understand why do we step up the voltage and how this will reduce our electrical current. 17. Phasor Diagram of an Ideal Transformer: Welcome everyone to this lesson. In this lesson we will talk about that Faisal diagram of an ideal transformer at the no load condition. So if you'll remember from the previous lesson when we had our Nucor with the primary winding and the secondary winding N1, N2. And then we have the voltage V1, V2, E1, and E2. Now, let's start step-by-step to understand how can we represent that Faisal diagram of an ideal transformer without any connected load. So it means this part is an open circuit. So let's start first. If you look at this one, this figure here represents our phasor diagram that we would like to get. The first step is that you can see that our flux, the core flux, which will produce the due to the magnetizing current. This flux is, the flux is at connectors between this winding and this one being magnetically. So we will use our flux or the magnetic flux as the reference value. So we are going to say is that flux Phi is our reference value, or a zero angle. And we will start to building our other elements or the voltages and currents and based on this flux. So the first step is that you will find that to add new node. The secondary is an open circuit or is open circuited, which means it is open circuit. We don't have any loads, so the current here is equal to z. And those under such conditions, you will find that the primary, again is a pure inductance. We don't have any resistor here, or because it is an ideal transformer. Now, you will find that when we take an hour apply a voltage V0, V1 applied to the primary, it will produce a magnetizing current, which we will go through this coil. What is the function of this magnetizing current? It will produce our flux Phi cool. Now, you have to understand that we have here our circuit, this part can be represented like this. We have an AC supply, V1. And do we have here our inductance which can, or our coil like this, our winding like this, with an inductance L. And we have the current I m, which will produce the magnetization inside the core or will produce the ICU. Now if you look at this circuit, we have a circuit with a pure inductance. So what does this mean? It means that our current will be lagging the voltage by 90 degrees. So that current will lag the voltage of Pauline 90 degrees because we have a pure inductive circuit. Now at the same time, you have to understand that this current or the magnetizing current will produce the Phi core. So you will have to understand that the Phi, Phi core is directly proportional to the I m. Or as the current increase, the flux will increase and at the same time they have the same angle. So in this case, I can add the current i m, choose a flux like this. Z are in-phase, have the same angle but with a different magnitude. As you can see. Now, v1 or the current legs, V1 by 90 degrees. So V1, V1, V1 leads. I am by 90 degrees. Or IE1 legs if V1 by 90 degrees. So we have here, I am, okay, I am. So V1 is leading by 90 degrees, like this, V1. As you can see here. Now, what about the flux? Now, you will find that the flux cuts both of these windings, this winding and this winding to produce E1 and E2. Now, you will learn in the next lesson in the EMF equation, EMF equation lesson, you will learn that E1 and E2 are leggings or flux by 90 degrees. So you will find that lagging, the flux lagging -90, the flux E1 and E2 lagging by 90 degrees. So we will draw here E1 and E2 are different in magnitude due to as the number of turns. Now what about the voltage V two? Okay, is that as the remaining parts? So V2, as you can see here, e2 is our source like this. So this will produce voltage that will be consumed inside our loop if we have a load, okay? So E2 is equal to v2, and that's why you can see e2 equal to v2 from KVL. So now we draw with our Faisal diagram for the ideal transformer. So as you can see, the alternating current produces a flux that is proportional to it and in phase with it. Phi core will link both windings and will induce voltage E1 in the primary and E2 in the secondary winding. And y1 at every instant is equal and opposite to V1 according to a lens alone, which we have discussed before in electric circuits or in magnetic circuits. When we said that E, or the induced voltage is equal to a negative N d phi d t. So why it is negative? Because it oboes us the supply. That's why v1 opposite to E1. Now E1 and D to lag behind Phi core by 90 degree, which will be proved in the next lesson. In this lesson, we talked about that phase diagram of an ideal transformer at no load condition. 18. E.M.F Equation of a Transformer: Hi, and welcome everyone to this lesson about transformers. In this lesson we will talk about that EMF equation or the electromotive force equation of a transformer. So let's just start first. Let's say that we have a voltage V1 over frequency f. This is a frequency of the supply, e.g. in electrical power system, it can be 50 hz or 60 hz, depending on the country itself. Now, since it is an alternating current, has a sinusoidal flux, will be produced the bicep primary. So we have V1 that will produce a current that will go through this coil and the producer flux. And this flux is alternating flux. Why? Because I M is our sine wave. So the flux will be also add a sine wave since they are proportional to each other. So you will see that phi or the flux, which is a flux of the core equal to phi max sine omega t because it is a sinusoidal flux. Now, what about the induced EMF, E1 or E2? So if you remember from the previous equations of the Faraday's law of induction and the Lenz law. We have said before that when we have an alternating flux cut, our winding, varying flux cut the winding is or the first winding or the primary winding or the secondary wine. We will have an induced EMF. We will have induced EMF Ea. The induced EMF is equal to negative d phi over d t. So here we are talking about the first two coil E1. So it will be negative N, N1 number of turns of that primary d phi d t, the variation or the derivative of the flux with respect to time. What flux is this flux, which is a core flux. D over d t phi max sine omega t, The derivative of sine omega t, derivative of sine is cosine omega t multiplied by the derivative of the angle with respect to time. So it will be omega, omega cosine omega t. You can see that negative one, negative one. And we have here cosine omega t and the volume x as it is because it is a constant value and Omega here. So it will be negative omega n, n1 prime x cosine Omega t. As you know, that Omega, or the angular frequency is equal to two pi multiplied by frequency N one phi max cosine omega t. Ok? Now you can, you can take this negative. So you can say is that negative cosine omega t. Take this part and replace it with sine omega t minus ninth degree. So sine Omega t -90 degrees is similar to negative cosine Omega t. So we replace this part with sine omega t -92 pi f n n1 phi max. Okay? So this representing what rubbers and things, the induced EMF equation, the induced EMF equation, E1 due to the flux Phi. Now let's look at these two equations, the flux and E one. You can see that the flux is sine omega t. So if we assume that the flux alike this zero angle, look at E1. E1 is sine Omega t minus nine. So it will be like this, negative 90 degree lagging by 90 degree like this. So we have here E one similar to what? Similar to this phasor diagram that we discussed before. This one, you can see E1 lagging by 90 degree and we have now proved this. Why is this happening? Now? What is the maximum value? So you can see y1 equal to maximum value two by F n n1 phi max multiplied bys out sinusoidal wave form. So this is a maximum value of the primary voltage. What about the secondary induced EMF E2, E2. The same idea. A2 will be like this. A2 will be negative n into d phi over d t. So it will be the same equation. What's the difference is that instead of using N1, we will use N2. Now what does that? So this is a maximum value. What is that root mean square value or the effective value of the primary EMF. Now, if you remember from the AC circuits, so we said that let's say e.g. we have V equals V-max cosine omega t. So this value is the maximum value. So what is the effective value or the root mean square value is the root mean square value, is that effective is the maximum value divided by root two. This will give us the root mean square value or the effective value of the induced voltage. You can see we took the maximum value divided by root two. It takes us one divided by root two. You will get 4.44 f n n1 phi max. Now the same, you will find that y1 is equal to E2. But the difference between them is that instead of using N1, we use n. So in this lesson, we talked about poets transformer or the EMF equation of the transformer. And we discussed, then, we are now understand why do we have a 90 degree lagging. The voltage E1 and E2 from the flux. 19. Polarity of Transformer Windings: Welcome everyone to this lesson in transformers course. In this lesson we will talk about with the polarity of transformer windings. So the windings of the transformer or other electrical machines are market to indicate that terminals of like polarity. So if you look at this figure, you will find this dot, this dot notation here. This one indicates that all stiff polarity of the transform, both stiff polarity of the transform. So you can see we have annotation here and another one here, which means that z is a terminal. And this terminal, terminal one and terminal three are identical to each other. And terminal to terminal for which does not have any notation or identical to each other. So 1.3 identical to each other, and 2.4 are identical to each. Awesome. Now we have to mention something before I continue their polarity of transformers. You can see this one representing the forest winding and the swan representing the second winding. You can see this battery line. Okay. What does this battery line mean? Better line means that this a core of the transformer is made of iron. So you, when you see this better lines, it means the core of the transformer, as you can see here, is made of iron, or it is an iron core types of transformers which you can find in my own course for high voltage, like this, accordion and another coil without any parallel line. What does this mean? It means it is an air cooled. It is used in some applications and instead of iron coal, we have air core. So when you see these two parallel line, it means that we have IR cool. In the opposite figure, as you can see here, 1.3 are identical. Now why is this, or why is this two terminals are identical? Because if the current end of these terminals, it will produce flux in the same direction in the core. So as you can see here, if I1 enters that notation here, or terminal one or three enter this notation or enters a current, i2 enters the terminal three. If the current enters here or here. If you look at here, you can see that when the current I1 enters the terminal one, you will see it will be like this. The current will flow like this. So it will produce a flux along axis going like this, like this through the core in the clockwise direction. Now let's see the same idea, but for the other current terminus three, when i2 enters that I exist here and here exists, it will form a flux. If you do the right-hand rule, you will find it is flowing like this, downwards, like this. So you can see this flux is also clockwise. So Wednesday current enters. When the current enters the stroke from terminal one or terminus ray, it will produce flux in the same direction. That's why we say is that terminal one and terminal three identical to each awesome. Similar to two and fall if the current enters here. For through to or through four, it will produce flux in the same direction. For the same reason, terminals at 2.4 are identical, are identical to each other. If these two wines are linked by a common time-varying flux, the voltage will be induced in these windings, such as that at a particular instant, potential or voltage of terminal one is positive with respect to two, and the same instant of terminal three will post it with respect to four. So what does this mean? As you can see here, let's say e.g. end current entering from here. It will produce a flux flowing through that ionic core itself. This flux will produce an induced EMF in the first coil. Plus minus like this. At the same time will produce another induced EMF in 3.4 legs. As you can see, we have the bolster terminal of the voltage here, and the positive terminal of the voltage here, one identical to three, so they have the same polarity. One important note here is that the polarities of the transformer windings must be connected together if they are, if they are connected in parallel. As an example, if you look at this figure here, we have the force transformer, this one. And we have another transformers, this one. You can see this transformer and this transformer that mutation positive. Negative, positive, negative, positive, negative polarities. So if you are going to connect these two transformers parallel to each other, which will supply electrical current or power to loot. They must have the same polarity. So as you can see, the old stuff, the forest or the primary winding is connected to Zappos div. Then negative is connected to negative. Here that secondary winding, positive connected with positive, negative connected with it. Is that, is that correct connection? However, if you don't connect to them, right, like this. If you look at the secondary, primary is connected correctly, however, the secondary winding is score is connected wrongly. Now why is this? Because if you look at here, the ball stuff connected with negative and positive connected with negative. Now what will happen in this case? If you look at this figure here. If you look at this figure here, you will see that here we have a supply and another supply. So as if they are in series, Z are in series. So we can represent them like this, like this. This one is one and this one is e to two. Okay? And as you can see between them here is a pollster has a short circuit here like this and connect it to the negative of A22 like this. So as you can see, we will have a circulating current or a short circuit current supply divided by the impedance of these wires. So it will be, there will be a circulating current here, and the current going into the load is very small. The problem of the circulating current is that it can damage the transformer. We have to connect them correctly. The ball step terminal with other bolster, the negative with the negative. Now, let's talk about the polarity of the turns ratio. So that relation between the primary voltage account with a secondary voltage and current is related by that dot notation as follows. If v1 and v2 are both eyes or ball step or negative as a bolted terminals, we will use both stiff turn insertion. Otherwise we would use negative tones, which if all you want to apply to both entering or both, both enter or both leaves adult determinants. We use negative terminals ratio. Otherwise we will use all stiff to earnings ratio. Let's have an example to understand these two statements here. So the first example you can see here we have this notation here. We have plus, minus, plus minus. So as you can see, let's look at V1 and V2. You can see that first, if v1 and v2 are positive or negative ads adult determinants. You can see here we have plus with the dotted point, and here we have plus with a total points. So z are both the same polarity. They have the same polarity, positive ads n notation here. So we will use both of donors ratio. So as an example, it will be V0, V1 over V2 will be n, n1 over n2. So what about the current? If i1 and i2 posts enter or leave the dotted terminals, we will use negative toners ratio, otherwise use poster. You can see all E1 entering is adopted and notation. However, i2 leaves the bolded notation. It means that they are, most of them are not leaving and entering at the same time. One enters and leaves. In this case, we will use a bold step turns ratio. So we can say i2 over I1 will be posted n, n1 over n2 because one entering and leaving. So as you can see, V2 over V1, n2 over n1, n2 over n1 and n1 over n. So that is that first example here. Another one here. Look at this one. You can see v1 and v2. Plus, minus, plus, minus. Both of them are positive, adds a dotted point. So both of them are post of like here. So they have a positive tone as ratio because both of them are posted. At the dotted terminals. So what about I1 and I2? I1 and I2. I1 entering is adequate buoyant. And i2 entering that dotted points. So both of their currents are entering. In this case we use negative toners ratio. Like this. You can see positive similar as here. However here negative and not like this, negative because both of them are entering the dotted point. Another example you can see here, this one. Now look carefully at this one, V1 and V2, V1. That boast of all, let's make it more clear. V1, that negative point, V2 is a bowl stiff at the dotted points, so both of them don't have the same sign. They have a different sign. In this case, we are going to use negative demonstration. What about i1 and i2? I2 entering the dotted point? What about I1? Now, look carefully at I1. I1 enters the law exists not true the total Boyne not true that dotted point, however, it goes like this and goes out like this. All you want Lexus, right? Goes like this and goes out. So i1 leaves that point. So IE1 leaving because adulthood point, i2 entering those point. So those, they don't have this. So not those most of them are entering or leaving. One enters, one leaves. In this case, we will use both stiff turns ratio like this. So for the voltage negative for the current, Boston, last example here, i1 and i2. All you want enters the dotted point. Now what about this one? Look at i2. I2 like this. Or E2 can be like this exists. So i2 n tosses a dotted point and I1 enters all those points. So in this case, we will use a negative turns ratio. Now what about the voltage? What about the voltage? Let's see the leads us. V1 is a boast of wisdom notation. A V2, the negative with the notation. In this case, we will use negative toners ratio because they don't have the same sign. So as you can see here, for the voltage negative, for the current negative. So these two rules will help you determine if the tone is ratio positive or negative. So in this lesson, we talked about with Zao, polarity of that tone is ratio of an electrical transformer. 20. Solved Questions: Hey everyone, In this lesson we will have some soul with examples or some questions on the transformers on what we have learned so far. The first equation here, question here, is that the two windings of a transformer are conductively link it inductively Lincoln, not Lincoln at all, or electrically link it. So the two windings are, transformers are primary and secondary. Okay? These two windings are, they can connected, electrically connected. Electric z are connected using wires. No, they are not electrically connected. I'll say conductively connected. Know, are they not link it at all? No, they are inductively Lincoln. Now, why is this? Because if you remember, they are related to each other using the magnetic induction or using the magnetic flux. So they are inductively link. So the answer is B. The second question here is that what will happen if the input supply voltage V1 is a DC voltage? So if you look at this figure, we have V1, which is the primary voltage, and I1 and V2 and I2, whatever the signs here, it doesn't matter. What is important for us is that we have all U1 and V1. Now what if V1 is a DC voltage? If V1 is a DC voltage, there will be no flux inside the machine. And use the math, there will be a DC flux. There will be a DC flux, not AC flux. So there will be no AC flux. So if you remember that the induced EMF here, E1, E1 is equal to negative N d phi d t, right? So if V1 is a DC voltage, it means that all E1 is also DC. Okay? So when i1 is a DC, it will produce a DC flux. So it means that our flux is a constant value. Will be, there, will be any variation in the flux. Know there will be no variation in electrical flux or in the magnetic flux nodes electric flux in the magnetic flux. So no variation in magnetic flux. That means that this part will be equal to zero. It means that there will be no induced EMF in some machine that transformer will not work because the transformer is based on the electromagnetic induction. Electromagnetic induction which requires AAC flux. Now when there is no E1, what about the value of current? What is the value of one? So if you look at here, you will find that from KVL voltage or the current I1 will be equal to supply V1 minus the induced EMF E1 divided by the total impedance of the system here, which is that inductance and resistance of the wire itself. Now, y1 is equal to zero, so V1 over V1, since E1 is pretty, pretty close to V, V1, when V1 does not exist or when one does not exist, you will find that the current is equal to V1 over z, which will be very, very large value, which can damage is that transformer. So everyone is a disease and current by one will be also DC current and the core flux is decreasing. The induced D1 and D2 will be zero because there is no variation in magnetic flux. That's why from the KVL equation, the current V1 minus y1 over that, it will be V1 over that, which is a very high current that can damage that transformer. That's why you show them connect the transformer with a DC source. Okay? Now the last question for this lesson. If we have an electrical transformer with this information on its, on its nameplate. We have attend kilovolt and bear 1,200 or 1,100, 110 v 60 hz. What are the meaning of these ratings? And what is the turns ratio of the electrical transformer? So the first equation, what does the question, what does this even mean for us to part ten kilovolt am here. Now, what does that give? Volt Ampere kilovolt and bear is a unit of the apparent power. So the ten kilovolt and bear representing water, representing the rated power of the electrical transformer, rated apparent power of the transformer. So that is the first part. This is a rated apparent power, or the maximum power that the transformer can produce or can transmit. The second part is at 1,200 or over oneself than ten. What does this represent? This representing the ratio between the high voltage with respect to the low voltage. So as you can see is that the rated voltage of the high-voltage windings. So we have two windings here. One which is the high voltage or the high tension, and the one which is a low tension or low voltage winding. So the first winding has a rated voltage of 1,100, 1,200 volt. And the secondary winding has a rated voltage of the low voltage winding hundred and ten volt. Lastly, we have 60 hz. What does this represent? This is representing them operating frequency of the transformer. The frequency of the supplies that will be connected to this transformer. Velocity question here is, what is the tone is ratio of this transformer assembly is acetone is ratio equal to a number of turns of secondary, divide the number of donors. Those are primary or V2 over V1. So it will be one. So I wasn't 100/1010, not, not like this. 110 secondary divided by 1010. Assuming of course, that this is a step-down transformer that will take 1,100 and step it down to 110 v. So as donors issue will be equal to 0.1, assuming that this is a step-down transformer, or voltage or reduction transformer. So in this lesson we had some solvent questions about electrical transformers. And the next two lessons we'll have some examples about electrical transformer. 21. Solved Examples on Ideal Transformer: Welcome everyone to this lesson. In this lesson, we will have some soul with examples, some mathematical solver examples on that transform. Or to be more specific or ideal transformer. So in this example, we have a transformer that is required to deliver one m bear current at the 12-volt from a 240 v supply voltage. So we have here transformers that will, will deliver 101 and bear at a 12-volt. So if we represent this, we have legs as a transformer like this. Okay? Of course. And we have Froma 240 v supply. So this is our supply voltage, 240 volt input voltage. And it will deliver to a load at a 12-volt. So this is the output voltage. Output voltage. And it will deliver one and bear the load here. They're connected load here will absorb one and bare legs us. The number of turns in the primary winding is 2000, so N1 equal to two. Now what do you like to get? The force requirement is that how many tones are required in the secondary winding? The forest apart. Here. As you can see, this is a step-down transformer. It takes that 140 volt and reduce this voltage to 12 volt. So let's represent our volts. So we can say is that V1 over V2 is equal to N1 over N2. From here we have N1 equal to 2000. N2 is required. This is the number of turns on the secondary. V1 is 240 volt and V2 is 12 0 volt. So by using this equation, we can get number of donors of the secondary. The second requirement is that what is the current in the primary winding? Current or yuan? So if you remember that all U1 over I2 ratio between the current of the primary with respect to secondary, or E1 with respect to second row, which is one and bear equal to what? Equal to N2 Over N1 z are inversely proportional to each us. So number of turns on the secondary is obtained from the first part and number of turns of the primary equal to 2000. So as you can see here, this is our, all of our given parameters inside our example. The ratio N1 over N2 equal to V1 over V2. And we substitute so we can get that the number of turns on the secondary is 100 tons. Them by using the ratios that I have discussed before. V1 over V2 equal I2 I1 or n, n1 over n2. So you can say, is that all E1 over I2 equal to N2 over N1 equal to V2 over V1. Or you can say i2 over I1 equal to n, n1 over n2 equal to V1 over V2. Same as here. So from here you can get that all U1 will be equal to 0.05 and bears. The second example here is that we have a single phase transformer with a primary number of donors for hundreds. So this is n, n1 and secondary winding 1,000 tons into. Now what does this mean? If you look at this, this number of donors, primary and secondary, you can see number of turns on. The secondary is higher than number of donors of the primary. So this transformer is a step up transformer. And then we have the cross sectional area of the course. The iron core itself is 60 centimeter square and the primary winding is connected to at 50 hz supply at the 520 volt. Find is that big value of flux density in the core. And number two, the voltage induced in the secondary winding. So let's start with the big value of the flux density in the core. So if you remember that from our previous equation that we obtained before, that E1 or the induced voltage. Owns a primary or E2, E1 or E2, whatever it is. Let's say E1. E1 is the induced, the voltage on the primary winding equal to 4.44 frequency and one B max area. So from this equation you can get them maximum or the big value of the flux density. So as you can see, this value is a big value of flux density. And a is the cross-sectional area which is 60 centimeter square, will be converted to meter square. And number of tunnels of the primary, which is $400, and the frequency, frequency, which is 50 hz, they induce the voltage. Here we are talking about the ideal transformer, which means that y1 equal to the supply voltage, which is 520 volt, like this. Now remember that 60 cm squared to convert this from centimeters squared to meter squared, you will need to multiply by ten to the power negative four. Like this. From this equation, you can get B max. So that maximum or the big value of the flux density is this value in weber per meter squared. Now, the second requirement is that we need to find, we need to find the voltage induced in the secondary winding. So we have number of donors of the primary, number of turns on the secondary, and we have the supply voltage, now we need E2. So if you remember that A1 over A2 or E2, E1, whatever it is, is equal to n, n1 over n2. Number of donors. Those are primary, which is 400 number of turns on the secondary, 1,000. Y1 equal to 520 volt and E can be obtained. So as you can see, E to E1 is the tone is ratio, which is N2 over N1. It is the same idea. As you can see, number of donors and N2 over N1, 2.5. It means that this transformer, this transformer will maximize or will increase. So voltage apply to 0.5 fact. As you can see, E2 will be 2.5 multiplied bys of supply. So it will give us 1,300 volt, which means that z is this transformer, is a step up transformer. The last example for this lesson is that we have a 25 kilo volt and pay a transformer, which is what does this represent? This is representing the S rated, rated apparent power of the transform. Has 500 turns on the primary winding and 50 tons on the secondary winding. So this representing N1 and this row representing n2. The primary one is connected to as results and two volt 50 hz supply. So this one is E1 or V1, whatever it is, 50 hz is our frequency. Neglect is a leaky two drops and the no-load primary current. Now this, what does this represent? This means is that our transformer is an ideal transform, which means that V1 is equal to y1. That first requirement is that fine desert full load primary current and full load secondary current. So the full load primary, Karen, how can we obtain it? Simply, you have the power and you have the voltage. So if you remember that S or the apparent power is equal to v multiplied by I. So you can take this rated power divided by is a voltage, you will get the primary current. So as you can see, S rated divided by V rated of the primary, it will give us 8.3. And bear. Now I would like to get this secondary current. How can I do this? Remember that i2 over I1 is equal to N1 over N2, which is one over the number of turns. Order one over that tone is one over the turns ratio. So in order to get E2, it will be E2 will be equal to one divided by, that. Lets the forest against the turns ratio, which is the ratio between secondary divided by xy prime money like this, turns ratio N2 divided by N1, which will be 50/500. It will give us 0.1. I2 will be primary current divided by a or the turns ratio. So you will get eight is 3.3 and bear. Now, as you can see that this transformer is a step-down transformer, primary 500s and secondary 50. So it means it will step down the voltage and the wireless step up the account. So as you can see, that current is increased by ten times or a factor of ten. Now the third requirement is a secondary EMF, so we need E2. It is pretty, pretty straightforward. Somebody, you can use a turns ratio. N, n1 over n2 is equal to V1 over V2 or E1 or E2. E2 is equal to earnings ratio, or the blood by E1. E1 is a given supply 3,000 volt and turns ratio is 0.1. So where did we get this? If you remember, E2 over y1 is equal to N2 over N1 and N2 over N1 is the turns ratio. So E2 will be y1 multiplied by the turns ratio. Like this, you will get 300 volt. Last requirement is the maximum flux in the core. So how can I get this from the e m f equation? So if you remember, we said that E1 or E2, whatever, most of them will give you the same solution. Y1 is equal to 4.44 frequency n n1 phi max. Remember here we are talking about the maximum flux, maximum flux density. Here we're talking about the flux. And the flux itself, if you remember, is beta max multiplied by area. For Imax equal to Beta Max multiplied by area. We have y1, which is 3,000. Frequency, 50 hz is number of turns, those are primary 500 and phi max is required. So as you can see, we can get that phi max, or the maximum flux in the core itself is 27 mentally Weber. So in this lesson we have some solving mathematical examples on the transformers or the ideal transformer. 22. Shifting Impedances in a Transformer: Hi, and welcome everyone to this lesson. In our course for transformers. In this lesson, we will talk about shifting of impedance in an electrical transformer. This is really, really important in the ideal transformer and in the approximate circuit or in the practical circuit of the electrical transformer. So this lesson will be very important as it will help you understand how can you treat this transformer as one electric socket? So first, let's look at this socket. So we have here our primary and secondary winding. Now, if we have an impedance that Guan, let's say that one, R1 and Z1 and Z2, R2 plus j X into. So we have an impedance as a primary end impedance at the secondary. And what I would like to do is that I would like to take this impedance, remove it from here and put it to the other side, or council this impedance and move it to the secondary winding. So how can I do something like this? Now we have the voltage v0, v1, y1, and voltage V2 and I2. Now, if you start analyze this electric socket, you'll find that that impedance, the equivalent impedance here, is equal to x1, which is impedance at one is equal to the supply divided by I1, V1 divided by R1. And the impedance at the secondary will be V2 divided by I2. Voltage divided by current gives you the impedance. Now, let's see the ratio between them, the ratio between the maintenance of the secondary to the primary. So if you look at here, you will find that z d2 divided by zed one. This equation divide is this one. It will be V2 over I2 divided by V1 over I1. So let's try it. V2 over I2 divided by V1 over T1. So it can be equal to V2 over I2 multiplied by the inverse of this one, which is one divided by V one. It will be V2 over V1, V2 over V1 multiplied by I1 over I2, I1 over I2. So let's hit Delete first all of this. So here we have this equation. So if you remember that V2 over V1, the ratio between the secondary voltage over the primary voltage gives us the turns ratio. And the ratio between I1 and I2, i1 and i2. It will give us also a ratio between V2 over V1 or equal to a i1 and i2 gives us a, a multiplied by E gives us a square, which is a tone as ratio is square. So Z2 over Z1 gives us a square. So it means that our secondary impedance is equal to the primary impedance about amplified by a square. So what does this mean? It means that if we would like to transfer the parameters of one winding from one to another, what I'm going to do is that if we have a resistance R1 in the primary, we have a resistance R1 in the parameters. So I can take this resistor and bought it and the secondary here by a value equal to what? Equal to r one a square. Okay? So the equivalent resistance here, Here's the equivalent resistance will be the primary resistor multiplied by a squared. And if I would like to take a resistor here, R2 and what it ends up primary. This resistor will be reduced by a square. So R1, the equivalent resistance here will be R2 divided by a square. Reactants. X1 in the primary will become a square X11 transferred to the secondary. So as you can see that here, if we take X1 and the voltage here, it will be X1 multiplied by a squared. If I take x2 from here and put it here, it will, its value will be x2 divided by S squared. So when transferring the voltage or current, we use only a or one turns ratio. However, in there, impedance we use a square. So it is similar to, it's similar to the voltage, similar to the voltages that impedance similar to the voltage about two ways, a square of the turns ratio. So if you remember, V2 over V1 is equal to turns ratio. However, now z2 over x0, x1 equal to the square of the turns ratio. So in the next lesson, we will learn how can we apply this in an electrical transformer and how it will help us. 23. Example on Shifting Impedances: Welcome everyone to this lesson. This lesson we will have a soul with example, on the shifting of the impedance of an electrical transformer and how it will help us in analyzing transformer. So here we have in this system, we have a single-phase power system. What does this mean? It means it is consisting of one AC supply. The supply is our voltage of 480 volt and the angle zero degree. And this generator, or this single-phase ball system provides electrical power to allude equal to four plus J3. Using a transmission line that the line of an impedance 0.18 plus j 0.24. So we have our generator that all provide an electrical power to, or electrical power to an electrical load using a transmission line. Now, the question is, if we don't have any electrical transformer, if we exhaust, connect this generator with a transmission line to the load directory, what will be the voltage at the load? What will be the v load or the voltage across the load, and what will be the transmission line losses. In the second case, if we added transformers t1, a step up transformer, then we added a step-down transformer. Choose a load. Similar tools up our system. If you remember, if we have 11 kilovolt and we step up this voltage to, let's say 500 kilovolt voltage of transmission then adds the end of transmission line. We will step down the voltage again to a voltage suitable to the lute. Same idea what we are going to do here. We have a step-up transformer, one to ten that will increase the losses, increase the voltage to reduce the losses in electrical transmission line. And then we have a step-down transformer to reduce the voltage to a level suitable for our loop. So let's discuss these two cases and you will understand now why, why using a transformer is important in electrical power system. So let's start with the first case. We have this system without any transformers. And I would like to find the voltage across the load. And of course, if you know that voltage across the load will be equal to assembly that glute multiplied by the current, current flowing through solute. So how can I get the count? We have Z load which is four plus J3. How can I get the current, current assembly equal to V supply voltage divided by the total, the total impedance of the system, which will be the line plus the glute, like this. So the current coming from the generator equal to the line, current going through the transmission line, equal to the current going through the loop, equal to the supply, divided by the total impedance, which is 0.18 plus four rail j, 0.24 plus three, the imaginary part. So you will have this value of k. Now what I would like to get is V, the voltage across the load. It will be the current multiplied by impedance. Like this. V root will be load multiplied by the load, the current multiplied by the impedance of the load itself. It will give us this value. As losses in transmission line. What does the losses in transmission line? It will be the resistor multiplied by current square. If you remember, P losses, losses in a resistor or an electrical transmission line will be I square multiplied by the resistor. The resistor, which is 0.18. And the square of the current will be this current square. Like this, I squared, which is the magnitude of the current line d square, multiplied by the resistor which is pointed in. It will give us 1482, 0.73. What? Now what we can learn from here, as you can see that the supply 480 v and voltage across the load is 453. So there is a reduction in voltage by how much? 480 minus 453. Approximately 27 volt losses or voltage drop across that transmission line. The voltage across the load is much lower than the supply voltage. Remember this value, 27 volt drop in the voltage. Now let's look at the losses in the transmission line. Power losses in the transmission line is equal to almost 1.5 kilo watt. Remember this value and this value or this value, 27 volt drop due to the presence of a transmission line with our transformers, and the loss is 1.5 kilowatt. Now let's look at the case of the transform. So what are we going to do first? In order to analyze this circuit or in order to get the voltage across the load or the losses in transmission line, we need the three currents. We need generator current, we need eyeline, and we need elute. First, we are going to get all your generator. And from a generator using that tone is ratio will get eyeline, and then we will get a load. So what are we going to do? First? We are going to take this route and the boat it here. And then we will take the total impedance here and the voltage here. We are transferring all of our impedance or shifting our, I think our impedance choose action rate or site. In order to have our generator with the total impedance, equivalent total impedance in order to find the generator current. So how can we do this simply using is a rule which we have discussed before. So first, we will take that glute and the bottom here using the tone is ratio. So referring says that the load from the secondary of transformer T2, those are primary of T2. So I would like to move it from here to here. Now as you can see it as a turns ratio of one to ten, where we have more number of turns, which means that our z will be amplified. So let's make it more clear. We have here one, let's say is that one ends into x1 over z2 will be equal to 10/1 or ten Z12 value. Or in order to get x1 is equivalent to x1. It will be that one. It will be ten multiplied bys into the impedances into two. When it is transferred to the primary, it will be multiplied by a or a square, a square here, the square of the ratio, square of the ratio. Like this. So as you can see, we have loot four plus J3 and we transfer it to the primary of T2. So we multiply it by ten square, the ratio square. So it will give us the equivalent impedance of the load here, will be 400 plus J 100 ω. So as if we cancel this part completely. And we now have an impedance series, was this one like this, 400.300. So these two impedance or series with each ours and now this part does not exist. Now, since they are in series, we can combine them together like this, 400 plus 0.1800 plus 0.24. Now, what does the next step? We are going to take this total impedance, which is the equivalent of all of this and transfer once more tools are primarily using this stone is ratio. So it will be 1/10 square like this. So let's delete all of this. That total impedance multiplied by E is a tone as ratio square you are going into here. So 1/10 squared. So the total impedance here will be 4.00, 18 plus j 3.00, 24 or so. We have total here, which are representing the total impedance of the system. And do we have here our supply? So we can get the generator current, like this. Generator will be supplied divided by the total equivalent impedance after being shifted several times. So now we have the rail generator current, which is nine to 5.9 447. This is a current coming from the generator. Now, this current which is coming from the electrical, the electrical generator, we are going to get aligned from it. Now as you can see, this is a step up transformer, one to ten. So the voltage will increase and the current will be reduced. So eyeline will be a generator divided by the turns ratio. So our generator divided by the tonnage or divided by ten. So as you can see that the current flowing through the transmission line is now reduced equal to 9.5 9447. Now, using this scatter and we can get some losses in transmission line. So that losses in transmission line will be the resistor 0.18 multiplied by secant square, line square, which is 9.59 squared. Total GFS give us 16.56. What? Remember, in the first case or in the radius without any transformer losses walls 1.5 kilowatt. Now, using an electrical transformer has all of this is 16.5. As you can see here. There are losses is much reduced using electrical transformer. Now, let's find out how can I get V load. You will need to take this current and unbelief for it. Again, you can see ten to one. It means that the voltage is reduced, but the current will increase. The current will be 9.59 multiplied by ten. So as you can see, that load current will be eyeline multiplied by ten. Why? Because the voltage is reduced due to this turns ratio and the current will increase, as you can see. So the voltage across the load, what is the value of the voltage? It will be this current multiplied by impedance, like this. Big current multiplied by impedance will give us 479. Now, as you can see, as you can see that the supply is 480 and the voltage across the load is 479.70, 0.3 volt. Voltage drop, very small voltage drop compared to what, compared to 23 volt without transform. So as you can see that transformative help us to reduce the losses in transmission line. And at the same time, it reduced as a voltage drop across the transmission lines. So that's the voltage across the load is now very close to zero generator voltage. So in this example, or is this solver the example we learned? Why do we need a transformer? And how it helps us to reduce losses and voltage drop in electrical power system. So as you can see that raising the transmission voltage of the power system radios does that transmission losses by 98.88 per cent? 24. Transformer Losses: Hi, and welcome everyone to this lesson. This lesson we will start talking about with z transform or losses. So the first type of losses that will occur in the electrical transformer is a copper losses. Now we discussed before is our ideal transformer. This one is an ideal transformer. And I would like to convert this ideal transformer into a practical one or non ideal transformer. A more realistic transformer, or a more practical transformer. So the first type that will occur in the transformer is a couple of losses due to the flow of electric current in the resistors of the primary and secondary winding. If you look at here, we have this windings are primary winding and secondary winding. Now since this one is made of copper, a conducting material, it means that this winding has a certain resistor, and this one has a certain resistor. So we have a resistor R1, which is a resistor of the primary, and which is a resistor of the secondary. Now when the current flows through this resistor, it will cause power losses. So we can say is that the primary winding resistor is denoted by R1 and secondary winding resistor is denoted by R two. Second type of losses that you will find in electrical transformer is the hysteresis losses. And it is one of the core losses. So we have two types of losses in the core occurring inside the iron core itself due to the presence of the magnetic flux. We have two types of losses. Historicist losses, hysteresis, losses. And then we have also the ED Eddy current losses, Eddy current losses. So these are the tool types of losses that occur inside the iron core itself. So let's start with the hysteresis losses due to the present history says nature of the iron core, that would be energy losses. And this hysteresis losses are proportional to the flux a frequency ends or magnetic flux density big value. These types of losses or this type of losses. But as a cover, losses as a hysteresis losses causes heating of the electrical transformer. So for the couple of losses, which is a loss occurring inside the winding, it will be I1 square multiplied by the resistor, which is a primary resistor, plus I2 squared multiplied bys a secondary resistor. This represent things are losses due to the flow of current inside the resistor of the primary and secondary winding. The hysteresis losses, remember from the magnetic circuits is that we have discussed before that due to the presence of the hysteresis loop BH curve, we have a hysteresis loop of the material itself. Due to the presence of this hysteresis loop, we have the hysteresis losses. That so the type of losses is the Eddy current losses. So the Eddy current losses are one of the core losses. Why? Because the iron core itself is a conducting material. Now, remember, remember we have when the current flows through a winding or the primary winding, which will produce a magnetic flux. Magnetic flux or the core flux, will cut the secondary winding and it will cut the primary wanting to induce E1 and E2. Now, this AC flux, it produced E1 and E2 because these two windings are conducting material. Now, the same idea sense. So we have here Nicole. Nicole, this iron core is a conducting material. So when the magnetic flux flows inside it, it will induce a voltage inside the iron core itself. So if we look at the iron core, we have one block of encore due to the presence of the flux, we will have eddy currents inside it. So we have induced the voltage due to the flow of magnetic flux inside the iron core itself. This magnetic flux will produce, induce the voltage E. This E will produce type of currents, call this the eddy currents. Currents inside the core itself. Therefore, currents will flow inside the encore, known as the eddy currents. Now how can we reduce or eliminate, or Jews or reduction of this type of losses simply by using laminations. So we said before in previous lessons that instead of having one Bulk core like this, in which our flux will flow, we will divide the score into group of laminations. Laminations. Now why do we do this in order to reduce the eddy losses? Now why is this? Because if you look at here, you can see that we have a big bulk material. The eddy current will be very large. However, when we divide this into several laminations, that current will be very small in each of these laminations. Now we will understand more. How does, how can we understand the difference between them in the equation of the eddy losses? And you will find that eddy losses are proportional to the frequency. So in order to understand that we need, in order to understand disease, we need as a two equations of hysteresis losses and the Eddy current losses. So the hysteresis loss or the power losses in what and AD losses in what also both of these type of losses. This is a equation of hysteresis losses. And this one is the equation of the Eddy current losses. Now let's look at these two equations here. For us today, hysteresis loss is equal to eta P max to the power n, all to the power ITA at lose power n multiplied by the frequency multiplied by u, v. Now what does this, each of these elements to represent forest ITA, what does eat or a process called Steinmetz historicist coefficient. So the spine met since Theresa's coefficient is the coefficient that depends on the type of the material of the core itself. Second part is beta m to the power n. Beta m is the magnetic flux density, maximum value of the magnetic flux density flowing inside the core itself. And n is a spine myths exponent which ranges from 1.522, 0.5, and it depends on the material itself. So this one should be n, not eat. So we have e to here, which is Steinmetz stressors coefficient and the Steinmetz exponent, which is between 1.25, 22.5, which is here, selected as 1.6. Then we have the frequency, which is frequency of the supply itself, or the frequency of the magnetic flux, which is volume of the material itself. Now the same idea for the Eddy current losses. You can see that we have K E, which is a eddy current loss coefficient. A coefficient eddy current constant, beta m, which is the maximum flux density, f, which is the frequency of the supply, t, which is a sickness of the illumination in meter. And we have V, which is the volume of the material. Now let's understand the how the laminations helps us to reduce the eddy losses. So let's consider e.g. R1, bulk cool like this. And we will consider laminations or like this, or like this, ten of it. Okay? So we have e.g. ten laminations. Okay? Then laminations. And we have one big iron Nucor. Let's look at the thickness of this one and this one. So let's take the eddy losses in this case, let's say e.g. this bulk call, this bulk core is e.g. ten meter. So the second is t is equal to 10 m. So the total eddy losses, it will be tan square, which is hundred multiplied by. The other factor is the k e, f square v and beta max squared. Let's say all of this is assaulting constant c. Let's say we are just considering the thickness of the core. We have ten meter, ten meter, ten square gives us 100. Now let's look at the lamination. So we have thin laminations. Each elimination will be 1 m. Then laminations each one is 1 m. So it will give us ten meter. So one laminations 111, summation of all of this will give us the same code. Now let's see the Eddy current losses. So the eddy current loss, it will be power, will be equal to that same constant c, which is k e beta max squared f squared. And we multiply it by ten because we have how many illuminations? 1234. And so we have ten laminations multiplied by the thickness of each elimination square. So we will have one square. So we will have ten multiplied by c. So as you can see, we have one Bulk core. Velocity is 100 multiplied by a certain constant c. However, when we divided it into ten laminations, we have now be equal to ten multiplied by sin, which means that we reduced the Eddy current losses probably 90% just by dividing this into laminations. That's why we divide our core into laminations of certain sickness. So in this lesson, we talked about Z, transform and losses. In the next lesson, we are going to start using these losses to represent our non ideal transformer. 25. Practical Transformer and Exact Equivalent Circuit: Now let's start by talking about the non ideal transformer or the practical transformer. So Windsor previous lesson, we talked about with the previous types of losses occurring in the electrical transformer. Now let's use these types of losses to represent our rail or practical transformer. So first, we said that we have copper losses or we have a resistance of the primary R1 and the resistance of secondary or two. Number two. In the ideal transformer, we neglected the leakage flux. Remember that we have two types of flux when the current flows through the winding, it will produce that Phi core. That main flux, or the measure flux, is the flux flowing through the core and very small part of the flux called the following leakage, or the leakage flux will flow through the air. Right? Now, this flux can be represented in our electric circuit. We're using reactants X1 and X2. What does x1 and x2 represent? It represents the z phi leakage you here and find leakage here. The leakage flux in the primary winding and leakage of flux in the secondary winding. So as you can see, we have resistance R1, resistance R two, and we have leakage flux here and leakage flux here. So we can represent them by adding them to our circuit in the form of X1 and X2 like this. So our circuit will be R1, j X1, and induced EMF E1, induced EMF E2, R2, and J x into and V two. So in the ideal transformer, we didn't have any R1 or x1. We didn't have R2 and we didn't have x2. However, since we are talking about the rail transformer or a practical transformer, we use R1 and DJ, X1 and X2 and j x two, we need to consider all types of losses in the transformer. So as you can see, x1 leakage reactance of the primary, secondary, leakage reactance of the secondary winding. So the primary winding impedance, we can say that it is R1 plus j x1 primary winding impedance, secondary winding maintenance is R2 plus j x2. Now as you can see from a KVL, we can say that the voltage supply voltage is equal to I1 multiplied by R1 plus j x1 plus y1. Since v1 is a source, it will supply voltage. So this one and this one, voltage drop and E1 for the secondary winding, you can see that E two here is our supply that will be divided into the voltage drop and the voltage going into solute. So in this case, E2 is equal to voltage drop I2 multiplied by T2 plus V2. Okay? So E2 is our sources that will provide voltage to that z2. And we do. So from this equation, we can say that V2 is equal to E2 minus i2, i2. So this representing that phasor equations or the equation of the primary and secondary windings. Now, let's add more elements to make our transformer more practical. So as you can see that these two reactants, j, Z1, and Z2, doesn't cause or don't cause any kind of power losses. Because the power losses is I squared multiplied by the resistor. However, due to the presence of our reactants, reactants itself, it will it change as a power factor, because power factor is real power divided by the apparent power. So the apparent power will it change due to the presence of the reactants? And at the same time there will be a voltage drop or a current multiplied by x on the reactant itself. So it will cause reduction in the voltage itself. Then practically in practical magnetic cool, we said before that the iron core in the ideal transformer. In the ideal transformer, we said that the iron core itself has infinite, has infinite permeability. As infinite permeability. However, in the practical or real transformer, we don't have infinite permeability. We have a finite permeability, which means that we need, we need the magnetizing current I m to produce a flux inside the core. This effect can be represented using our reactants called exam. So why do we use XM? Xm is used the two representing the magnetization effect inside there, nicole itself. So we need x m in order to establish or produce the magnetic flux inside. Cool. Also, if you remember, we said in the previous lesson we had iron core losses or the cool losses, which is a hysteresis losses and the losses. So we can represent this power losses in the form of a resistance R c, or the core resistance. So in the end you can have this final circuit. You can see this part, R1 j X1, R1, X1, r2, r2, r2 J x into V2 and V1, V1 and V2. And we have E1 and E2, E1 and E2. And we add an extra element, two elements to our circuit, which is cool representation. This part. You can see that we have our x1 and we have a current going into the transformer itself, which is representation for the current going into solute. At the same time, we have another part here, this part which is a parallel branch representing the RC, which is a core losses. And x m mature presenting them magnetization inside our electric transformer. So this circuit, you see here exactly. This circuit is our final representation of the transform. This circuit representing is a non ideal transformer. The practical transformer or the rail transformer. Considering all types of losses and effect is happening inside that transformer itself. You can see that our C and X M representing the new load circuit, a phase or some of both. Amanda, I see the current going through a cool losses or the resistor of the core. This RC or cold resistance representing what? Representing that losses, hysteresis and eddy losses occurring inside the core itself. And I m, which is the magnetizing current of the magnetic circuit itself or the transformer itself. So the summation of this current and this current, Faisal. Faisal not magnitude only magnitude and angle phase or summation of IRAC on Doyen gives us all a fall, which are representing the no load current. This will lead us to the exact equivalent circuit you can see here, as you can see, it's this one that we have discussed in the previous slide. Now we can also, we can also remove this part completely. How can we do this? Using the referring or the shifting of the impedance transformer can be moved. The twos are right or left by referring all the quantities to the primary or secondary site, respectively. The equivalent circuit, move the toes are primary is chosen, as you can see, what we did is that we keep this part as it is. And we started referring this, this elements to the primary. So we moved x2 becoming x two dash or to becoming R2 dash. And the load here becoming Z2 dash and v2 dash. And we eliminated the spot. So as you can see, x two dash, two dash, here is a leakage. Reactants. Dash, two dash, v2 dash. What does that mean? Means referred to as a primary. So we have moved all of these elements. Those are primary site. So now we have the exact equivalent circuit referred to the primary site. Okay, Now, this will help us to deal with our transformer with much less or much easier way by having one big circuit with all of these of each element. Now, also you can start shifting this elements from here. And instead of R1 X1 RC exam, you can start shifting them to the other side. So we'll have R1 dash, dash, dash or C dash and so on. But it is much easier to take the secondary and the boat it in the primary site. Okay, So we can start using this Referring methods that we have discussed it before. We can eliminate our transformer core. Now, various voltages and currents can be obtained by solving this electric shock. So if we have our UIView or supply, you have the load, you can get all of the other elements in a much easier way. So in this lesson, we discussed the exact equivalent circuit of the electrical transformer, considering all types of losses and voltage drop and cool losses and every St. 26. Approximate Equivalent Circuit: Hey everyone, In this lesson, we will talk about with the approximate equivalent circuit of a transformer. In the previous lesson, we reach in that exact equivalent circuit, which is referred to the primary, this one. Now how come I approximate this equivalent circuit to more simplified circuit? You will find that here we have our supply V1, and we have current or E1 going through the transformer. Part of this current, I1 is going through all the parts going to i2 dash or the referred second recount. Now, as you can see here, that the values of R1 and x1 are usually small. Or one index one. So the voltage drop across the primary impedance so that one is very small. That's why v1 is approximately equal to E one. If you remember that here, y1 is the voltage here, E1, the induced voltage, let's say V1 is equal to supply equal to I1 multiplied by x1 plus y1. Now, this voltage drop is very, very small compared to the induced EMF. So we can say V1 is approximately equal to y1. So how does this will help us simply, you can, you can take the branch composed of RC and x. M can be moved the total supply. How it looks like, like this. You can see, let's look at this circuit here. You can see here we have I1. So we have taken this branch and put it right here. You can see R1 and R2 dash R1 and R2 dash x l and x l2 dash here. And we have taken this branch and put it near as a supply. So we have V1 then the branch. Now why did we do this? Because the voltage drop here is very small. So we can say is that V1 is the voltage across this branch or the magnetization branch is approximately equal to the supply voltage V one. So this will help us simplify the computation of the currents. Because we can say is that this part, or the primary impedance and the secondary impedance or series with each other. So we can combine them together into one impedance because they have approximately the same current. Now, let's understand this statement more. So as you can see, we have current one. We have current or a fall. We have current I2 dash. So as you can see that I phi or the magnetization current or the core flux carrot or core current is equal to is or is. Its value is very, very small. So it is very, very small compared to R2 dash. So we can say is that most of the current of the transformer, or E1, the primary current, most of these current is going to become i2 dash. So we can say that i1 is approximately equal to i2 dash. So we can say is that this branch has a current I1. This branch has i2. So when both of them have newly or has no Liza same current, it means that these two impedances are in series with each other. They approximately have the same current. Now, as you see, is that the iPhone, all the exciting current, which is the summation of I m, the magnetizing current and the core current is a small percentage of the rated current of the transformer, less than five per cent. So let's say e.g. if IE1 is 100 and bears, so I2 dash or let's say the exciting current is less than five per cent, approximately e.g. five and bears. So if the primary I1 hundred and bear, this one will be five and bears. And the most of the current will be like e.g. nine to five years approximately, of course, because this is a phase or submission. So it is approximately, not exactly 95, but approximately, you can see all E1 and E2 are very, very close to each other. So we can say is that two branches, the primary impedance and secondary impedance, or series with each other. So we can also make more approximation to the equivalent circuit by removing the exciting branch completely from that circuit like this. So instead of having this one, so we have I1 and I2 dash nearly close to each other. And the current flowing here through this branch is very, very small. So we can neglect this branch like this. So we can have more approximation to the equivalent circuit. Why are you referring to the primary and removing this excitation branch? So the same idea, we can now combine both of i1 and i2 or not i1 and i2, that embed answered one and Z2. We can now combine them together as one equivalent impedance. So the first approximation is that Let's get back here. So the forest approximation is that we took this branch and put it here near the supply, or we took this branch and move it here. The second approximation is that we can neglect this branch as the current flowing here is very, very small compared to i2 dash. So in this lesson, we talked about the two approximations that we can do to the exact equivalent circuit. 27. Phasor Diagram of a Practical Transformer at No Load: Hey everyone, In this lesson, we will talk about with Zach Faisal diagrams of a practical transformer. In the case of the no load condition and in the case of the inductive load condition. So as you can see, this is our circuit. So we will start the buys a forest, a case in which we don't have any load condition. So what does this mean? It means that this part is an open circuit. It means that there is no current here, there is no load here. So means that i2 will be equal to zero. Which means that i2 dash is also equal to zero, no current going into the transformer to the loop. We will have only one current, which is a Phi, or the exciting current. So we have V1 that will supply R1, which is equal to Phi. So all of the current will go like this through the code itself. So we have no load current only because it is a no load condition. Now, also in this case, we will neglect is our winding resistance and leakage of flux. Now why did we do this? Because as you know that a voltage drop here is very, very small. We can neglect this part and say that the voltage V1 is equal to the voltage across the load part or that part. Or if you remember from the approximations that we took this part and put it here, the voltage V1 will be the voltage across this exciting part. Okay? Now what are we going to do first? As you know that we have our flux as our reference. So we use the flux as our reference because the flux, which is produced inside the cores or Phi core, is the fluxes that will go and produce E1 and E2. So we will use zero angle as our reference is our flux of folly. And as you know that E1 and E2 are shifted or lagging by 90 degrees from the flux. So you will see that 90 degrees lagging E1 and E2 from the flux. So E1 and E2 lagging this flux 0.90 degrees, as you can see here, E1 and E2 with different magnitudes depending on the tone is ratio. Now, the second part, if you look at this figure here, you can see that the flux itself is produced due to what current due to our m. So we have I fall, which is exciting current. It will be divided into two types of current. The first one which are representing the core losses, and second one which are representing is that magnetization of the core. When I am goals here, it will produce the flux that flows inside the code itself. So we say that the flux is directly proportional and in-phase with I M or the magnetizing current. So you can see withdraw with a vector, I am in phase with flux. And as you can see, the reactive component of current I m is small in amount and in the same direction of the flux. The leg is the supply voltage by 90 degrees. Now why is this? Because if you look here at this figure here, you can see v1, this part is completely neglected. We neglected the winding resistance and leakage flux. So if you look at here, you will find that the voltage V1 is equal to the voltage across this part. V1, which is a voltage across R c and voltage across Z are parallel to each other. So voltage across this part equal to V1. Voltage here. And you can see we have a current going through a pure inductive load. You can see a pure inductance. So what does this mean? It means that due to the presence of an inductance and we have a current here. This current will lag the voltage across it by 90 degrees. As you know that the inductance itself causes the lagging of current. So the current here will be lagging by 90 degrees from V1. So you can, all we can say is that V1 leads I M by 90 degrees. You can see legs or supply voltage by 90 degrees. You can see v1 and I am, you can see differences between them, 90 degrees shifted between them, v0, v1. And at the same time you can see that V1 is the voltage across the resistor RC. And we have current here. I see now, since we have here at BYU resistive load and v1. So it means that due to the presence of a view resistive load, it means that V1 and the ICR in phase. So you can see IC is drawn exactly above V1 because they are in phase. So what we can learn from here is that I am lagging V1 by 90 degrees. You can see lagging probably 90 degrees because we have here a pure inductance. And IC is in-phase with V1 because it has current, because it has a pure resistance. So they are in phase with each other. Now as you remember before, we said that all if I, if I is the summation of summation in what case? In phase or some mission phase or summation of I C and I am, or if all equal to I c plus I am as a phasor submission. You can see we have M here and do we have here IC? In order to add these two vectors, we will take this vector here, the voltage here at the end of the rows of the first vector. So we have IM, then we add the above it RAC with the same magnitude and same phase shift. Then we will connect this at the beginning and the end of these two vectors. It will give us all a phi. So as you can see here, you will have i m plus IC gives us all a phi. This RFI is lagging from the supply by a certain angle because we have here our solute. So you can see that v1 and all if y is the total current is lagging by a certain angle. Folly. Okay, Now, here, if you look at this figure we have here I am, we have I4. I see. And this part is. So you can see that we can say that sine Phi, sine Phi naught is equal to sign this angle is equal to opposite, which is m, divided by the hypotenuse here, which is RFI. So we can say is that I M is equal to sine phi naught multiplied by phi, which is this equation here. Second equation is that we can say is that cosine phi naught equal to adjacent over the hypotenuse. Adjacent here is all c. The hypotenuse here, which is all fine. So we can say is that IC is equal to I phi cosine phi. Note here using the cosine and sine loss. So in this lesson, we discussed the ZAB Faisal diagram of a practical transformer in the no-load condition. And when neglecting is a winding resistance and the leakage flux. 28. Phasor Diagram of a Practical Transformer at Inductive Load: Hi and welcome everyone. In this lesson, we will discuss as a phasor diagram of a practical transformer. But in this case, when we have an inductive load, and of course we neglected the winding resistance and leakage of flux. So we have here an inductive load. So we have a current here, a load like this, or not necessarily a pure inductive load. But we have r and that current is, we have inductive load, which means current is lagging. The voltage. I would like to draw the phasor diagram. So the festival diagram of this case will be something like this. So where did we get this phase diagram? It is really, really easy. We will just go step-by-step. So the first thing, as you know that at zero angle is our reference, the flux. The flux is zero and this flux is produced due to the magnetizing current, I m, I m. And the flux will be in phase with each other like this. We have IM and then we have the flux. Second step is that we know that this flux will produce E1 and E2. E1 and E2 are lagging by 90 degrees from the flux. So lagging by 90 degree from the flux. So we will have E1 and E2 here. And at the same time, E2 is equal to V2 because we don't have this. We neglected the winding resistance and the leakage flux. So E2 will be equal to V two, as you can see here. Okay? Now the next step, we have this part and we have this part. Now what is next? Here, as you can see, is that in case of the inductive load, which causes the secondary current two legs and secondary voltage V2 by an angle Phi two. You can see that we have here an inductive load and we have a current going through this load. So i2 will be lagging from V2 because it is an inductive load. So i2 lags if V2 by a certain angle called the phi two, depending on the load itself. So you can see we have V2 and I2 is lagging by angle phi two from it. Now as a primary current, I1 muscle supplies and no-load current I phi two means the iron losses in the transformer and provides a flux inside the code. So I1 will provide the current RFI and all provide I2 dash, which is the equivalent of i2. And it also must supply I2 dash, two dash in order to counter act as Z D magnetizing effect of the secondary current I2. So as you can see here, we have i2. I2 dash must be, must exist in order to counteract the magnetizing effect of the secondary i2. So you will find that i2 dash is equal to i2 multiplied by N2 over N1 is the number of turns of the secondary divided by number of turns of the primer. Now where did we get this? Because if you remember I2 dash, which is similar to previously i1, okay, with that core part, I2 dash, which is I1 divided by I2, is equal to N2 over N1. It is inversely proportional to the turns ratio. So I2 dash is equal to n over n naught multiplied by I2. As you can see here, it is 180 degree out of phase. So what we can learn from this, we can learn is that we have I2 dash, i2. We will have i2 dash opposite to it, 180 degrees from it. And at the same time has a magnitude equal to i2 multiplied by the turns ratio n2 over n. So we will have i2 dash. Now let's look at this figure here. We have IM, we have I am here, and we have here I2 dash. And then we have V1, which is opposite to v2. And what we would like to get, and as you can see, we would like to get r If I and I see, I see Assembly equal to IC is in-phase with what invades was V1. So I see will be like this IC. Okay? Now, if we take the vector IC and add it to IM, like this, I M plus IC, it will give us all a fine this vector. So let's delete this. So we have IM, edit to it. All I see which is in-phase with V1 but with a smaller magnitude, i c, which is equal to V0, V1 divided by RC. Like this. Adding these two vectors together similar to the previous case of no-load, we will have all a fine. We have now. We have only two dash. Remember I2 dash, which was equal to I2 multiplied by N2 over N1, but always it to 880 out of phase. Now, one which is the supply current is equal to I phi plus I2 dash. So we need to add this vector and this vector to get I1. So how can I do this? Okay, simply, just to take, we have i4 here. Take this vector and batteries, do it, bolt it right here at the end of this first vector. So we took this vector and put it here. Then we will connect the beginning and the end to produce IL-1. Or you can simply take all a foil like this. And the boat it right here at the end of that first I have four at the end of the vector I2 dash. Then connect the beginning with the end of the vector to produce our E1. Okay, So it is simply summation of vectors. So now we'll understand where did we get each of these vectors? Simply one, which is a flux I am in phases, I see is leading by 90 degrees or in-phase with v1, i2 lagging from V2 and I2 dash is opposite to i2 to counteract that the magnetizing effect of the secondary current I2. Remember that i2 is produced to produce a flux that will oppose the main flux. I2 dash is coming from the supply to counter act as this effect. So in this lesson, we discussed that phasor diagram of a practical transformer. In the case of the inductive load. 29. Solved Example 1 on Practical Transformers: Hey everyone, In this lesson we will have some soul with examples on the practical transformer. So first we have this transformer, this circuit, as you can see here, 2,200 slash 200 volt transformer. This transformer is a step-down transformer that will take that 2,200 volt and step it down to 200 volt rated values of the high voltage side, or the primary and rated value of the secondary winding, or a low voltage side, eight rows at no load, primary current of 0.6 and bear and absorb is 400 watts so that no load primary current, what does this mean? It means RFI. This is a new node can, and so it is equal to what? 0.6 and bear. So we can say RFI is equal to 0.6 and bear. And this new load current will absorb 400 watts. So we have our power consumption. Power consumption equal to 400 watt inside that core part. Okay? You can see no-load primary current of 0.6 and absorb is $400. What does it absorb? What absorbs 400? No load part. Now what we would like to get its findings and magnetizing and iron loss. So we need to find magnetizing current, which is i m. And then we need to find the iron loss current, which is IC. Ic or the coal loss. And neglect is a winding resistance and leakage reactants. So we will neglect this part. We will neglect this part. Okay? Now, what are we going to do? First? Let's look at inputs, and from it, we will can get these two currents. The first thing you can notice here is that the primary voltage is 2,200. So V1 is equal to 2,200 v. Since we don't have any voltage drop here, because these two are neglected, then it means that the voltage here across the no-load part is equal to V1 or 2202nd. Thing is that we can notice here is that we have a power losses inside the core for 400 watt. Now, if you look at this circuit, where are we losing this power? We are losing this amount of power inside the RC. X m does not cause any kind of power losses. It causes the reactive power, the presence of reactive power. However, RC is the source of power losses. So all of the power losses are occurring inside this resistor. We can say is that the power losses, which is a 400, What is equal to the current or AC, multiplied by the voltage across eight, which is V0, V1 or IC square multiplied by RC. So V1 is 2,200 v. Voltage across this resistor is a supply voltage. So we can say is that IC is equal to 400 divided the 0.2200 likes this equal to 0.182 and bear or the iron loss account. Now, if you look at that phase or diagram, or if you remember from the phasor diagram here, you can see that RFI is equal to IC as a phasor plus i m as a phase. Or the magnitude is the magnitude as a magnitude, or if I as a magnitude equal to root C square magnitude of the first account plus the magnitude of the secondary current square. Because from this vector i4 equal to I m square plus z square. Now we have already falling, which is the no-load current equal to 0.6. And we have IC which we obtained all 0.182. So from here we can get, you can see that from this equation, we can say is that I M is equal to root if I square minus IC square, like this, you can see I phi equal to as a magnitude, equal to magnitude, magnitude and the angle only magnitude equal to root IC square plus i m squared. Because the summation of two vectors, or from this equation we can get I M equal to root I phi squared minus IC square RFI, which is 0.6 IC, which is 0.182. We can get the I m, which is 0.572, or the magnetizing current. 30. Solved Example 2 on Practical Transformers: Hey everyone, In this lesson we will have another example on the practical transformer. So in this lesson, we have at 2,200 slash 250 volt transformer, or it is also a step-down transformers that takes that thousand 200 rated value and converts it into 250 v. It takes a 0.5 and bear at our power factor of 0.3 at no load condition, no load means I2 dash is equal to zero or i2 is equal to zero. That cannot absorb it. Here is the no load current, which is our folly. So 0.5 and bear is equal to 0.5 and bear with a power factor of 0.3 is the current iPhone. Now what we would like to get is the components of the no-load primary current. We need to find IC and I am the neglect is our winding resistance and leakage reactants. So how can I get this simply? You have a power factor of 0.3. So from here you can get the angle, angle phi naught. Power factor is the angle between voltage V1 and what N, the I phi. So if you look at the phase or V1 and the I phi angle between them, phi naught. So how can I get phi naught from the power factor cosine -1.3 negative. You can see that phi naught is equal to cosine -1.3, which is 72.542. Okay? Okay. Now, from this angle we can get IC and I am, how can I do this? I see is equal to I phi cosine phi naught. I m is equal to I phi sine phi node like this. So I am I Phi sine Phi naught and ICI phi cosine phi naught. Okay? So you will get 0.477 unpaired and 0.15 and bear these two currents. If you get the square of this current plus the square of this current, you will get the no-load current of 0.5 and bear. 31. Solved Example 3 on Practical Transformers: Now let's have another example. We have here. The transformer has a primary winding, N1 equal to 800 tones and secondary winding into 200 tons. When the load current on the secondary is HIM pair at 0.8, power factor lagging as our primary effect, primary current is 25 and bear at 0.707. Lagging, finds a no-load current of the transformer, and it's a phase or angle with respect to the primary voltage. Okay? This example is really, really easy. Photos, you can see that the load current on the secondary, which is i2, is equal to what? Equal to 80 and bears at an angle power factor of 0.8. So the angular will be negative, y negative because here we have legging and negative what cool design, -1.8. So I2 is equal to 80 negative cosine -1.8. Now we have the primary current 25, so we have our Y1 equal to 25 and bear. And the angle lagging means negative cosine -1.707. So we have current I1 and we have all E2. Now, what I would like to get is then no load current, I need a phi. So phi from this figure, I phi is equal to the supply current i1 minus two dash. So how can I get I2 dash? Simply I2 dash is I2, but this is multiplied by the turns ratio N2 over N1. So it is equal to I1 minus I2 multiplied by a, or the turns ratio N2 over N1. Like this. We have the turns ratio n2 over N2. N2 over N1 secondary divided by the primary 200/800 gives us 0.25. Here that i2 dash will be I2, which is this current multiplied by a, like this. So you can see here a multiplied by I2, which is 80 and bears and with the same angle, negative 6.29, negative 6.9 is negative. Cosine -1.8. So cosine -1.8 is the angle negative 6.9. So now we have this i2, i2 dash, two dash, which is I2 multiplied by eight, gives us this value. Now in order to get I4, it will be i1, which is 25, and the angle negative cosine -1.707 minus this value, like this. So you can see I phi will be equal to 25 negative, negative because it is lagging. Lagging means negative. Cosine -1.707, which is 45 degrees minus, which is a sign. That current I2 dash, which is a 20 angle negative 6.29. Remember here we are subtracting a phasors, not magnitude. V has a magnitude and angle, magnitude and the angle. So we subtract them from each other. We will get the no-load current, which is 5.2 914, and the angle negative 73.457 and bear. 32. Solved Example 4 on Practical Transformers: Now let's have one more example about the practical transformer. And this transformer, we neglected the load or the core apart. So we have the primary winding and secondary one. Now what we would like to do is that we have a transformer of 100 kilovolt ampere, which means S serrated or the rated appear on the power of this transformer is 100 kilovolt and bear with a turns ratio 1,100 slash 220. So it is a step-down transformer that takes is a high voltage and steps it down to the low voltage. 50 hz single phase transformer has an impedance of 0.1 plus j 0.4. For the high voltage winding, you can see the high voltage is the primary and the low voltage is a secondary. So it means that R1 plus j x1 is this part, 1.0, 0.06 plus j 0.00 15 on for that low voltage one, which means that to find is the equivalent to winding resistance reactants and impedance referred to the high voltage and low voltage, just like what does this mean? Then the equivalent means x1 plus x2. But when both of them are in one side, either on the high voltage side or in the low voltage side. So we will start the pie giving the turns ratio secondary divided by primary, which is 220/1010, which is V2 over V1 or N2 over N1. So to give acetone as ratio point to, that is a first step. Second step we will start referring. Let's just start by referring to the high voltage side. So what does this mean? It means I am going to take the reactants from here and the impedance, or reactants and the resistance or the secondary impedance Z2. And get it back here. Now, let me remind you how to do that. Referring. Remember that the di2 over x1 equal to a square. So what I'm going to do is that I would like to convert z chew into that one. I would like to move it from here to here. So what I need is the one that equivalent x1. So x1 will be equal to z2 divided by a square. So we will take this values, 0.06 plus 0.0, 15 divided by a squared or the square of the turns ratio to get the equivalent impedance on the primary. So we will get legs, as you can see that here we have for our two dash and x two dash, which is a reform, the values to the primary. It will be the value divided by a square. So as you can see here, let's say e.g. are two dash. First are two dash. Two dash, which is that x1, or the equivalent value of R1, or the equivalent value of the resistor. On the primary side, it will be z2 divided by a square or R2 divided by a square. So we have R2 is 0.06 divided by a squared. So what is a square? A square is a turns ratio square. So 220 divide the 0.100 square. So this will give us 0.06 multiplied by 1,100 squared divided by 220 square, as you can see here. So this is the inverse of the square of the turns ratio. So this part is one over a squared. This part. Okay? So we took the resistor and multiplied it by one over S squared to get the equivalent resistor on the primary. So instead of having R2, we get R two dash. Okay? So as if we took this and put it here. So we have the equivalent to resistance. It will be the primary resistance, which is 0.1 plus that secondary resistor referred to the primary. So by multiplying this, we referred it to the primer. So we have now are two dash. It will be 0.25 ω. Similar to the reactants, it will be X1, which is 0.4 plus extra two dash, which is referred to as a parameter. So as if we take this one and put it here, it will be exit two multiplied by one over a squared, x2 multiplied by one over r squared, which is 1100/220 all squared. It will give us this two values. Now, the equivalent impedance, that will be 0.25 plus j 0.775. Or as a magnitude, the square of the first plus the square of the second, all under the square root. Like this. The magnitude of the impedance or the equivalent impedance. Here we have equivalent resistance, equivalent reactants. And the equivalent impedance is a square of this part, square of this, all under the square root. 0.5 means all of them, all under the square root. So it will give us 0.814 3 ω. Now, we need the same idea, but referred to the low voltage side. We need to convert this part to here. So we will have R2 plus R1 dash R2 plus one out of the one that switches the referred the value of R1. So it will be R1 dash will be R1 multiplied by a square, like this. So you can see R2 plus R2 dash, which is therefore the value of the primary resistor, R1 dash. It will be the value of the resistor, which is 0.1 multiplied by a square, which is 0.2, 0.2 squared. So it will give us a 0.01. Same idea for x1. We need x1 dash. It will be 0.4 multiplied by the square of the turns ratio likes us. So it will give us 0.031 ω. In order to get the equivalent impedance, it will be root, root 0.01 squared plus 0.031 square, like this. So it will give us 0.03 to 8 ω. So now we have the values of the impedance equivalent even refer to that low voltage side and the values referred to the primary or the high voltage side. So assembly, don't forget that. One last. Singapore, this is that e.g. if I would like to take extra two and voted here, which is becoming like this, x C2 dash. Two dash is equal to Z2. X2 is in one side. What side? Zi2 dash is in on the primary side? On the primary side. So it will be multiplied by square root n, n1 over n2 Y, because X two dash is in the primary here. So I'm moving it from the secondary to the primary. So it will be extra two multiplied by the square of the turns ratio, turns ratio here. You are moving it from here to here. So you can say N1, that a number of turns at which I am going divided by n2. Same idea. If I would like to take this one and put it here. So I would like what X one dash, which means X1 moving to the secondary. So it will be equal to X1 multiplied by square number of donors at which I am going, I'm willing to, what? I'm going to the secondary, which is N2. So it will be N2 over N1. As you can see here, n over n, which is 0.2, it will be 0.2 square X1, X1, which is 0.4 multiplied by the square of the turns ratio. Same idea here. If you'll get back here. Okay? Here you are taking R2 and the voltage here are two dash equal to the original value multiplied by square. Where I'm going, I'm going to get to n, n1 or the primary. So it will be n, n1 over n2 squared. So you can see that if you look at here, we can have resistance R two dash equal to R2, R2 multiplied by n one over n into n, n1 over n2, N1 over N2, which is V2 over V1. Same idea, all squared. So according to where are you going? You will multiply this by the square of the tokenization. 33. Transformer Voltage Regulation: Hi, and welcome everyone to this lesson in that transformers goals. In this lesson we will talk about with the transformer voltage regulation. So what does the voltage regulation mean? The voltage regulation is a measure of how well our transformer can maintain a constant secondary voltage under varying conditions. The voltage or regulation of an electrical transformer is a percentage, a change in the output voltage from the anode condition to the full load condition. So as you can see here from this equation here, the voltage re-regulation is a percentage of the change in the output voltage from that no-load condition to the full load. A change in the output voltage with respect to two no-load output voltage. So what does this mean? So as you can see here, adds a terminal. Here. We have two conditions. The first condition is that we have no load condition. We have that full load condition. So that no load condition, it means that we don't have any load. So the current here will be equal to zero, which means we don't have any voltage drop. So V2, well-being, maximize the maximum value when we don't have any connected load. When we have a full load condition, our current will be maximum. Will we have the highest current? The full load current, which means that V2 is at its lowest values. So what we would like to get or we would like to obtain is that the voltage regulation is a difference in between the voltage at node loot minus the voltage at full load divided by the no-load voltage, as you can see here. Now as I lower this value, that much better is that transformer. Or what does this mean? It means that when the transformer, it changes from the no load condition, the load increases to the full load condition. That change in V2 is very, very small, which means it is a very good transformer. What we would like to obtain is that the voltage duration must be minimized, must be very small value in order to produce a very small change in V2. As you can see here from the equations, here. From the phasor equation, e2 is our supply and V2 is our output. So V2 is equal to E2 minus i2 divided multiplied by voltage drop. So V2 equal to e to minus i2. To. Now add the no-load condition, we don't have any load V2. No load value will be equal to E2, or the voltage induced on the secondary winding. Because the current is equal to zero. At full load condition when I taught at full load, V2 four add four load will be e2 minus i2 full load multiplied by impedance of the secondary. So as you can see that the maximum value of v2 is at the no load condition and the minimum value is at the full load condition. So what I would like to obtain is that the change in these two must be minimized. That change from no load to full load must be very small. So we say is that the voltage regulation, as you can see, V naught minus V followed divided by V newNode, similar to this equation. Now, in order to get the best transformer or best performance out of your own transformer, you need to have the lowest possible voltage regulation. So it means that the voltage across the load here at this part does not change much when we transfer, transfer from Zomato the state to the folded state. So we say is that we have a good transformer. When's the least value of the regulation of the transformer is in the order of plus minus five per cent. So what does this mean? It means that that change in the output voltage, a change between e2, e2 minus this value or vino load minus V4 load divided two or divide or with respect to v no-load is equal to 5%. Very small change in the voltage. 34. Transformer Efficiency: Hey everyone, In this lesson we will discuss is that transformer efficiency. So what does an efficiency mean, or what does an efficiency mean for us? Or why efficiency is important. Efficiency representing exact ratio between in any electrical machine is the ratio between output power, output, real power with respect to two input rails bar. So high efficiency means that the output power will be very, very close to in biopower or the losses will be very small. So let's understand what is the value of inefficiency in the electrical transformer. So here this is our transformer and this is the same representation. We have a supply coming out of it, currently only ones that will go to the coil that will produce a flux that will cut the secondary wine and produce E2 that will produce our elute, or i2 is the current to go into the load and the voltage across the load V2. So that efficiency, as we've also said, is equal to the output power divided by the input power. Now, what is the value of the output power and what is the value of input power in general? In general, the active power or the real power consumed or supplied is equal to V voltage multiplied by the current, multiplied by cosine phi voltage. Let's say e.g. if I'm talking about the supply power, supply, active power, it will be the voltage of the supply multiplied by Zach current of the supply coming out from the supply, multiplied by cosine phi or the S phase shifts between V and I. So as you can see for the input power here, the input voltage, which is V1, is our supply, multiplied by Zach currently coming out from it, which is I1, multiplied by cosine phi input, which is a phase shift between I1 and V1. Same for the power consumed. Here we're talking about the, our power. Our power, or consumed power will be equal to V2, which is a voltage across the load, multiplied by the current entering the load, which is I2, multiplied by cosine phi two, or the phase shift between V2 and I2. So as you can see here, power out is equal to V2, which is a voltage across that load, multiplied by I load. I looked similar to i2. I2 secondary current is similar to the current going into the loop. No difference in between them. Multiplied by cosine phi, phi L or phase shift of the load current, or PHI to whatever it is the same. What does they represent? The European wasn't as the phase shifted between V2 and I. So now you can see here that phi L phase, phase difference between V2 and IL or i2 Phi input, which is a phase shift between V1 and one. Now we can represent our efficiency in another way. So we have power output divided by input. So we have power output. And we can say input power. So the input power, input act of power over their electrical transformer is equal to the output power going into the load plus all of that real losses occurring inside the transformer. So we can say p input is equal to the output power going into that trend to the load itself, plus the loss is occurring inside the transformer itself. Now what is the type of losses that is occurring inside the transformer? We said before that we have two types of trends are two types of losses occurring inside there. Electrical transformer. The first type of losses is a couple of losses, which is produced due to the flow of electrical current through that resistor of the primary and secondary I square multiplied by R1 and i2 square multiplied by R2. So this is representing Zach copper losses occurring in such a transformer itself. Second type of losses that we have discussed is the core losses, which is the losses occurring inside the IR Nucor itself, which was divided into Eddy current losses and the hysteresis losses. So we can take this equation and substitute it here. So we will have V out over V out plus b, couple of losses plus b. Now, let's define something which is really, really important in transformers that will help us provide more realistic or more detailed equation for the efficiency. We have something which is called the X or the loading ratio or the loading factor. This sort of presenting the ratio between i2 or the load current with respect to the full load current. So if our transformer is fully loaded, it means that i2 here will be i2 full loot. And i2 divided by I2 for loot. It means that we will have one, which means 100% loading on the transform. Now, if i2 is lower value, it means that we will have x less than one. So i2 representing divided by I2 full load gives us x or the loading ratio, which are representing how much is our transformer is loaded from there rated value. So we can, we can, since we are talking about i2 divided by I2 full load, we can multiply this by V2, which is the voltage across the load, and multiplies this by V2. As you can see here. This will give us I2 multiplied by V2 is the apparent power. Apparent power, or the output is the output apparent power across the solute item for load multiplied by V2, it means is that full load power. So we can say that x or the loading ratio i2, i2 pollute or I would power, I would bear on the power to be more specific, divided by output full load power, apparent power. So x will be like this in the end. Now what are we going to do? Simply, you know, that power habits that we have said before is equal to V2 I2 cosine phi L V2. We can, we can take I2 here. We can take this equation. Let's type it V2 cosine phi L multiplied by I2. This part is similar to this one. Now, we can simply multiply by two for loot, divided by two for load. Did we do anything? No, we simply multiply and divide by the same value. So this equation is similar to this one. Now as you can see that i2 divided by I2 full load is equal to x. So let's type x and cosine phi L multiplied by. Now, we took the sport and added x cosine Phi, cosine Phi n. Now the remaining part is V2 multiplied by I2 absolute. So this multiplied by this, which is this part, gives us S for loop like this. So this equation, one transferred to x cosine phi L S a full load X as the volute cosine phi L. Now, what about the core losses? The losses are independent on this secondary or that load current value. So the cool losses itself is independent on the loading condition of the transformer. It is at constant value that depends on the volume of the transformer or volume of the iron core, the sickness of the illuminations, frequency of the supply, and so on. So it is independent on the loading condition or the secondary current. We say is that the goal losses R is a constant value, or the coal loss is occurring, or having a constant value. Now, what about just saw the time, which is copper losses? So remember that capital losses be cupboard. Symbol is equal to I square, the square of the current multiplied by the resistor, right? So we have I1 square multiplied by R1 plus R2 square multiplied by R2, and so on. Okay? Now we can, we can use the referring muscles in order to have one equivalent resistor. And one current is the primary current or secondary current, as we would like. Anyway, let's say we have reformed our transformer to the secondary part. And do we have I2 square multiplied by R equivalent representing the coupled losses occurring inside the transformer itself. Now the same idea you can see here, P is equal to R equivalent multiplied by two square. If we divide by I2 square root multiplied by I2 square at full load. Okay? So I2 square divided by two square full load gives us x squared, as you can see here. And our equivalent multiplied by I2 full load squared, I square full load multiplied by R equivalent is a copper losses at full load condition. So we transfer or we form it more clear equations for the efficiency. So we have power output, we have beaker, we have b cover. Now let us substitute with all of these values in the efficiency it will be like this. It's using all of these equations. We will have efficiency equal to this big equation as a function in what? As a function in x or the loading condition. So we have a certain loading condition that can produce maximum efficiency. So what we would like to do is that I would like to find the value of x that will produce maximum efficiency of the transformer. That will minimize the losses in the transformer and to produce maximum efficiency. So how can I do this? Simply, you have an equation, efficiency as a function in x. So if you get the derivative of the efficiency with respect to x, D efficiency with respect to dx. You will get and equate it with zero. You can get the value of x at which we will have maximum efficiency. This value is equal to x, equal to route B Corps divided b cupboard for loop. So the value of x is that will produce maximum efficiency in the transformer is this value. Now, if we take this value and substitute it here, we will have this final equation which are representing maximum efficiency of the transformer. Now, again, if you plot the relation between our power, our power, and efficiency, you will find at a certain value, we have the maximum efficiency. Remember that our power here is dependent on x, right? Depends on the loading conditions. So we have a certain loading condition at which we would have maximum value. So if you take here a line here, this line has a slope equal to zero, equal to zero, or the derivative of this part is equal to zero. Okay? So we obtain the maximum value by using the derivative, derivative of the function with respect to our variable x and equated with zero. To obtain this final form. Now you will have to undertake sensors are transformers, efficiency is usually or generally in the range of 95 to 99%. So as you can see, it has a very high efficiency. The efficiency can reach even 99.7 per cent for great power transformer with very low wastage. That transform a rating is expressed in kilo volt and bear not kilo. What? Now why is this? Because if you remember that that transformer has both Excel and has resistor. So it has p or act upon and at the same time contains inductance. So it means that the transform must be rated in kilovolt and bear. So in this lesson, we talked about the efficiency of the transformer. And what is the value of x or the loading ratio that will produce the maximum efficiency. 35. Notes About Transformers: Hi, and welcome everyone. In this lesson, we will have some notes about the transformers. The first to note here is that you will have to understand that in practice or in real life that transformers have very small losses. So the output power, power going to salute act about going to the load is approximately equal to the input power. Why? Because the losses inside the transformer, the core losses and the losses are usually very small. In other words, we can say is that as transformer has a very high efficiency. Also that transform, our action is based on the laws of electromagnetic induction. We know that the wind current goes through the winding of the transformer primary winding, it will produce flux that WorldCat the secondary winding using, using electromagnetic induction, it will produce the secondary voltage, as you know. And of course, we don't have any electrical connection between the primary and secondary windings. And we also know that the electrical power transferred from the primary or from the supply, choose allude using the magnetic flux. Magnetic flux caries this electrical power to the secondary winding using the magnetic field or the magnetic flux. And of course, there is no change in frequency. We don't have any rotating part. So the frequency of the supply is equal to the frequency of the current, equal to the frequency of the flux, equal to the frequency of the secondary windings. All of the system has the same frequency. Lost. Singapore was a transformer rating. Any transformer has cool losses and the copper losses. Losses itself, which is Eddy current losses and historicist losses are dependent on the input voltage. That frequency is a value and so on. Ends a couple of losses are dependent on the current running through the winding itself, throws up primary and secondary windings. Therefore, the total losses depend on the voltage in joining to the current, but not open the power factor. That's why we say that the rating of the transformer in kilovolt and bear or not in kilo, what it is expressed in kilovolt ampere because we have dependency of copper losses on the current and Carlos has dependency on the voltage. So we say that S or the input power V multiplied by I. So cool losses depends on the voltage and the couple of losses depends on the current. Multiplication gives us as apparent power. So they don't depend on the power factor, but they depend on voltage and the current. That's why we need to express our transformer in kilo volt and bear. In addition, of course, you know that the transform myself consisting of resistor and inductor and we have magnetization. Magnetization requires reactive power. So x, or the presence of x m or x leakage means we have a reactive power consumption. We can not just to say that the transformer in kilo watt. One final question before we end this lesson is that we have a transformer to 120 440 v 50 hz, five kilovolt and bear single-phase transformer operates on a 220 volt 40 hz supply with a secondary winding open circuit. Then in this case, you will find that eddy current and histories is decrease or increase. Or eddy current remains the same, but hysteresis losses increase. Ad losses increase what hysteresis losses remains the same. So let's understand what happens here. As you can see here, we have this as our transformer. This ratio to 120 slash 440 operates at 50 hz and apparent power five kilovolt. Now we connected our supply to 120 volt, similar to the original supply or the rated voltage. However, you can see that the frequency here, frequency of the supply connected, is much lower than the rated value or the 50 yd. The operating frequency in this case, is lower than, lower than the original or the operating frequency of the transformer. What do you think will happen to eddy current and the hysteresis loss, as we said before, that the core losses in general in the two equations of Eddy current losses, both of them depend on the frequency. As the frequency increase, the CO losses increase, hysteresis losses increase, eddy current increase. In this case, we are operating at a 40 hz lower frequency than the original frequency. So in this case, the eddy current and hysteresis losses will decrease. The correct answer is a. Both of the losses are proportional to the frequency. So the frequency decreased from 50 hz, 40 hz. So post of their AD and hysteresis losses are decreased. 36. Solved Example on Transformer Efficiency: Hi and welcome everyone to this lesson. This lesson we will have a soul with example on the transformer. Or to be more specific, the efficiency of the transformer. So we have our 5500 kilovolt and bear transformer with an efficiency 95 per cent at both the full load condition and at 60% of the full load condition. So at full load, when x or the loading ratio is equal to one, and add tickets to Bruce and two when x equal to 0.6 or the loading ratio equal to 0.6 is the efficiency in these two cases is 95% at UPF, which is unity power factor. So add up cosine phi equal to one. So the power factor is unity at 60% of the full load. And at 100 per cent of the full load. The forest requirement is separate out the transformer losses. We need to find that couple of losses. Value of copper losses alone, and value of coal losses alone, core losses. And defines the efficiency of the transformer when we have a 75 per cent full load. And you want to tip our effect, which means x equal to 0.75 is this is a second requirement. So let's start step-by-step. So first we have at x equal one and x equals 0.6, the efficiency of the transformer is nine to five per cent. Using this tool requirements, we can get the couple of losses and core losses. So let's start. So this is our given a full load there, rated power of the transformer, rated apparent power of the transformer, 500 kilovolt. And pair efficiency at x equal 1, h loading ratio equal one, equal 0.295. And the efficiency at x equals 0.6 equal to 0.95 and the power factor equal to cosine Phi equal to one. So for us, what are we going to do? We are going to substitute with our equation, equation for that efficiency using these values. First, let's start. Efficiency, as you know, is equal to x 0 followed cosine Phi. Cosine Phi plus x-squared be covered for load plus b Corps. This is the equation that we obtained before in the previous lesson for the efficiency of the transformer. Now what does an extra step? Next step is that we will start with x equal one. So the efficiency is equal to 0.95 when the loading ratio x equal to one. Cosine Phi. So power factor is unity equal to one. And S of all loads are rated. Power is 500 kilovolt ampere. Same idea here. X equal one is full load 500. Cosine phi equal one x one squared, which is one squared. Be cupboard full load plus b. Cool, like this. So the efficiency point line 5.1 by one by four multiplied by 500, 500 and same here, 500 plus b copper fluid plus b cool. So from here we can get the first equation. Summation of the copper losses or the full load cover losses plus the core loss is equal to 26.31 kilo watt. Now we need another equation, same idea, Wednesday efficiency x equal to 0.6 or their efficiency at loading ratio of 0.6 equal to 0.95. So we'll do the same idea here. Instead of x equal to one, we will have x equal to 0.6 x 0.6 here, 0.6 squared. And cosine Phi equal one here and here. So full load equal 500.500. And the same equation equal to 0.95, say efficiency equals 0.295 at loading ratio of 0.6. From here we can get a second equation that's representing the relation between Kabbalah, full loads of full load, couple of losses, and the core losses. So by solving these two equations, by any method we can get be coupled for load and the core. So the copper couple of losses at full load equal to 16.4 and the core losses will be 9.87. Now we would like also the second requirement is that we need the efficiency at loading ratio x equals 0.75. So simply, the efficiency will be equal to x, which is 0.750. 0.75 square root is 0.75 square S of a load which is 500. Cosine Phi, which is unity. It is given that it is unity at 0.75. And finally, copper for load, which is this value. And the core, and the core losses is this value. So we will have like this efficiency at x equal 0.75 by substitution with the values, we will get a nine to 5.15%. So this was solved with the example on how can you apply the equation of the efficiency of the transformer. 37. Open Circuit Test: Hi, and welcome everyone to this lesson. This lesson we will discuss how can you determine or the determination of the transformer parameters. What I mean Pi is a transform of parameters. It means I would like to know the value of R, the resistance of the winding itself, R1 and R2. I would like also to find the leakage reactance, XL one and Excel to leakage or axons of the primary and leakage reactance of the secondary. We would like also to get x M, which is that magnetization reactants of the core itself. And the RC is a resistance of the core. So how can I get these parameters of an electrical transformer? Simply, we are going to do two types of tests. The first test is open circuit test. Second, the test is a short circuit test. So let's start with the first type of test, which is the open circuit test. The open circuit test is used to determine x and our sea in order to determine the reactants, magnetization reactants and core resistor, we will use the open circuit test. What are we going to do is that one winding of the electrical transformer usually is a high-voltage winding, is left open, or it is an open circuit. And the other one, which is the low voltage side, is connected to supply with normal voltage and frequency. The open circuit test is usually or always perform it on the low voltage side of the transformer. Because if it is performing on the high volt sides at no load current will be very small. Ends applied voltage will be launched. So let's understand what does this mean. So as you know that we have a high voltage side and we have a low voltage side. Now, we are making the high voltage open circuit and we are applying the voltage V2 or the supply to the low voltage side. So if you know that high voltage has high voltage to low voltage has a low voltage. At the same time, the current of the high voltage side is very small because the voltage is high. However, the current in the low voltage is high. Okay? Now remember that the open circuit test is used or will provide, you note or no-load current. In the open circuit test, it will give us our node or the no-load current. So we are performing ends are on the low voltage side because I naught is already a small value. So we will need to maximize it using application of the voltage source to the low voltage side. Again, I naught is usually a small value. If we apply this as applied to high volt side, it will be much lower value. However, if we apply it to the low voltage side, that current will be higher, which means that we can measure this current and it will have a lower error, as we will see right now. So we will use are what meter, voltmeter and ammeter connected in that low voltage winding. With normal voltage applied, normal flux will be set up in the core, already have the core flux and therefore iron losses and will occur inside the core itself. However, we will have very small couple of losses in the primary winding, which will be recalled that buys or what meter. But since we are talking about open circuit test, which means that we have only the no-load current is this current will be very small current, usually two to 5% of the rated load current, which means a couple of losses in the primary is small and zero in the secondary. Which means we can, we can neglect the couple of losses occurring in the primary. And the answers are what meter reading when we're presenting a core losses under no-load. So let's understand what does this even mean. Okay, So here, as you can see, we have high voltages side, low voltage side. High voltage side is an open circuit. As you can see. And local side we have our supply and we have a voltmeter that will measure the supply. What meters that will measure the real power that will be consumed inside the transformer. And we have a meter that will measure the current coming out of the supply. Okay? So now let's see the equivalent circuit. This is our equivalent circuit. Remember that we had here R1, R1 and x1x2 dash, two dash here. Remember that we referred to as a secondary winding parameters. Choose a primary. So we will have one equivalent circuits. Okay? Now as a first step, as you can see that forest This part is open circuit sensor. We have an open circuit here. I2 will be equal to zero or i2 dash. When we refer to this parameters to the primary, it will be also zero, so we don't have any current going to the secondary winding. So it means that we don't have any couple of losses here. Coupled losses here of gunk inside the resistor is equal to zero. No copper losses because the current is equal to zero. Now we will have only one current. So the current coming out from the supply will go through R1, L1, then go to the core itself about we have zero current going into the secondary one. So all of our current I1 is equal to what? Equal to I naught the new load current. So we don't have any current going to the high-voltage winding or no I2 dash. So all of the current coming from the supply is the no-load current. Okay? Okay. Now with this new load, canon is a very, very small value, two to five per cent. So what does this mean? Since it is two to 5% of the rated current. Rated current. What does this mean? It means that the losses inside the resistor here is very, very small, which means it can be neglected completely. So in this case, what meter will only detect what kind of power it will detect as the core losses power. That's our power consumed inside the core itself. We will neglect it from here, since the current is very small, we will neglect good Zach current inside R1 or desire copper losses inside R1. So in the end is or what meter will give us the power consumed inside the core itself. Okay, I hope it's clear now, why did we neglect that copper losses? And since we have very small current, will neglect is a voltage drop here. So we say that E1, which is a voltage here across the core, we say is that E1 is approximately equal to V1, which is a supply. Okay? So we have voltmeter which measures v1 or the supply, which is a voltage across the core parameters are c and x m. And we have current or inode, which is the current that will be devoted to IC and the IM, okay? And then we have what metadata power, that is the power consumed inside or C. So what can we do? You'll see that the power measure the pie is or what meter or the new load power, is equal to voltage multiplied by current cosine phi V1 I-naught cosine phi voltage multiplied by the current, multiplied by cosine, the angle between them. Voltage, which is V1 current, which is the no-load current, and cosine the angle between them. So from here we have v1 naught and power from the measurements here, we can get that cosine angle. Okay, so what is next? Next is two, we can get IM or the magnetization current. How can I get magnetization current? Remember that R naught is equal to the two currents I, C and I am. So I naught can be like this, equal to or I m, I m equal to I naught, sine phi naught and c equal to I naught cosine. Note, where did we get this two equations from the phasor diagram that we discussed before. So I m equals I naught sine Phi, which is this equation here. So we will get the value of RAM. We have the current from the ammeter and sines angle from this part. From here, we can get x M. X M is equal to what? Reactants is equal to the voltage across it, divided by the current. Voltage across it, which is V0, V1 divided by the current which is i m. So V1 divided by m that we obtained. We get x M. Now how can I get r c? Same idea. You will get the current I C cosine phi, as you can see here. From here, RC is equal to, which is here equal to the voltage across it divided play IC. So from here we get RC, so we obtain x m and all see which is that no load parameters or the core parameters. Now another method we can do is that you can see that here, power at no load is equal to V1 I-naught cosine phi node, right? And also we can say, we can say is that the power, which is the power consumed inside the resistor here. So power at new load can be also equal to voltage is square divided by RC, a voltage across its square root, which is V1 square divided by the resistor. This equation is similar to this one, so that power losses here is v squared over RC. So from here you have V1 and you have been allowed so we can get our C. So in this lesson, we discussed is the open circuit test inside an electrical transformer. 38. Short Circuit Test: Hey everyone. In this lesson we will talk about with the short circuit test of that transformer. So this dust is performed with Pi, short circuiting. One winding usually is a low voltage winding and applying the rated current through the winding. As you can see this as a equivalent circuit boy, in the case of the short circuit condition, when we are shorting now with that low voltage winding, modal high-voltage winding buds are low volts one. And we are applying our voltage to the high-voltage winding. In this test, the applied voltage is zoster, a small percentage of the normal voltage. That's why you will find that the flux or the mutual flux or the core flux produced is also a small percentage of its normal value. Therefore, we all find that Zach cool losses are very small. Therefore, the meter reading, we'll just represent things that copper losses for the whole transformer. Primary and secondary coupled losses. So as you can see here, in this case, we have the voltage but with a small value. And we said before that transformer or not the transformer part, the eddy losses and the losses are dependent on the voltage of the transformer. So the higher the applied voltage, the higher these losses. But in our case here we are just applying a small portion of the voltage, which means that the coal losses are of a small value. So we can neglect it. And what meter reading will be that losses occurring inside the resistor of the primary and the resistor of the secondary. We can neglect the core itself because the current is very low. The losses are very low and all y1 is approximately equal to i2 dash. So from here we can get resistor R1 and we can get or the equivalent resistor and the equivalent leakage reactants. So as you can see here, that the power in the case of the short circuit here we have a short circuit current in the primary and the secondary and in the primary, which is equivalent to i2 dash and all E1 or E2 which is secondary current. When it is referred to the primary, we will have equivalent current, I2 dash, which is equal to one. Now anyway, we have the voltmeter, ammeter, and what meter? So the power measure, the boys are what meter is a power consumed inside the resistor? R1 and R2 dash. The power produced, or what Twitter is equal to the voltage multiplied by current. So it will be V1 I1 cosine Phi. So from this equation we can get cosine phi, which will be this value and the impedance or the impedance of the electrical transformer. Here you can see this is the equivalent circuits. You can see V1 divided by the current that gives us the z equivalent to z of all of the transformer. So z equal to V1 over y now are equivalent, will be equal to the R equivalent will be the real part of z and x equivalent will be the imaginary part of z. So it will be equal to cosine Phi sine Phi. Now, if you remember like this, we have our zipped and we have rail equivalent and x equivalent. The angle between a Z is equal to phi. Cool. So we have this part which is x equivalent. So cosine Phi will be equal to R equivalent over z. And sine Phi u will be x equivalent over that from the phasor diagram itself. So from using z that we obtained are equivalent and x equivalent now are equivalent is equal to what? R1 plus R2 dash. And x equivalent is X1, X L1 plus L2 dash. Now of course, we can say that R1 is equal to R2 dash equal to R equivalent over two. And x one equals x two dash equal to x equivalent of virtue. So using that short circuit test, we obtain this R resistance and inductance or the leakage reactance of the electrical transformer. In the next lesson, we will have a solvent example on the open circuit and short circuit test to understand how can we apply these equations. 39. Solved Example on Transformer Parameters: Hey everyone, In this lesson we will have a soul with example on the open circuit test and short sectors of the electrical transformer. So we have several tests that are performed on a single phase ten kilovolt and pair 2,200 slash 220 volt 60 host us to transform 60 hz transformer. The following results. Results were obtained. Finds a transformer parameters they referred to the high voltage and low voltage side. When we did the open circuit test, we made the high voltage side open circuit as we learned before. In the short circuit test, we made the low voltage side short circuit. The rating of the voltmeter ammeter, and what meter in each case is showing as here. Now, let's see what happens here or how can we get the parameters? So we want to start with the open circuit test. This is the equivalent circuit of the open circuit test that we discussed before. So the reading of the voltmeter, which is V1, which is the voltage across the core parameters, or C and X m equal to 220 volt. And the value of the ammeter is a current of diameter is 2.5 and bear. So this is a current or inode or the core current or i phi. We said before, I know no-load current. And sometimes we refer it to as I phi or the exciting. And we have also our meter, which is the power consumed inside the resistor of the core. So the first step is that we said before that the power of the open circuit test is equal to the voltage squared divided by the resistance. So we said V I cosine phi. And also we said before v square over RC. So voltage across the resistor, which is v1 squared divided by RC, gives us is our open circuit power because it is the power consumed inside the core. Okay? So we will substitute with a voltage to 120 v squared divided by RC, which is unknown equals to the power which is 100 watts. So from this equation, we get our C L equal to 220 square divided by 100 equal 48 4 ω. All CL means what means resistance of the core losses. Okay? Now we have the resistor, so we obtain the forest, the prompter second parameter required is x m. So how can I get x M Simply we know that. Okay? Like this. First you can see that the current, I see ACLs or current going here, is equal to what? Equal to the voltage divided by RC. So you have several muscles to get x M. First you have current flowing here is equal to voltage, which is 220, divided by the resistor, which is 484. So the current here will be 0.45 amperes. Okay? Now, I M itself. What is the value of volume I naught is equal to root I c square plus m square. I naught is equal to 2.5 and bear Zach given value of IC is equal to 0.45, 0.45. So we can get IM like this. So i m will be rude. I l square minus z square, which is 2.5 squared, -0.45 squared, all under the square root gives us 2.46 and bear. So we have the current i m, and then we have the voltage across that reactants x m, which is V1. So we can say V1 divided by 2.46 ampere gives us x m, like this. Okay? So x m will be 89.4. Now, remember, remember that we have now the values of RC. Value of x m refers to what side here, RC, which is a cool resistor. Here L doesn't, doesn't demean losses here. L means low voltage, means low voltage. So Zach, cool losses. The core resistor referred to the low voltage side. And XML means the magnetizing reactance referred to the low voltage side. Okay? So I would like to find these two values. Revert to what side? To the high voltage side. So how can I do this? Simply, if you remember that that said D2 over D1 or whatever r is equal to square of the turns ratio. So first, let's get that turns ratio. So where are we going here? Remember, this test is performed on what? On that low voltages site. Open circuit test. The high voltage side open circuit. So we are doing all of our measurements on the low voltage side, I would like to get. So I get RC and XM referred to low voltage side. Now, I would like to get these values at the high voltage side. So we are going to work going towards the high voltage. So it will be the turns ratio of the high voltage divided by turns ratio of the low-voltage. All square, which is this one. So a is the turns ratio. You are going to what side to the high voltage. So it will be voltage of the high voltage divided by voltage or low voltage. Or it will be done as ratio of the high voltage side divided by number of donors of the low voltage side. So anyways, the turns ratio when, while going to the high voltage side will be done. So simply we are going to take each of these values, 89.484 and multiply it by a square, like this. Square, RC L square XML. So it will give us RC, the cool resistor, refer to the high voltage side. X m. Magnetizing reactance referred to the high voltage side. So now we obtained the goal resistor and reactants, or the magnetizing reactance, referred to high voltage side and the low voltage side. Now, let's do that short circuit test. So remember, so sectors, low voltage aside, shorted. So it means that all of our measurement at the high voltage side, okay? So our equivalent is the equivalent to a resistor adds the high voltage side. And x equivalent is the equivalent reactants at the high voltage side. So simply we have V1, V1, V1, which is the voltage on the emitter. And the current coming going through these elements is 4.55 and bear. And the reading of ammeter is power consumed inside the equivalent resistor, R1 plus R2 dash. So we can get the R equivalent. A, very easy. How can we get it simply? You can see that the power is equal to current squared multiplied by R equivalent. Like this. You can see power at a short-circuit which is 215, What is equal to the current flowing through the resistor, the resistor or the equivalent resistor. So it will be I square 4.55 squared multiplied by the equivalent resistance. Remember, our equivalent edge means at the high voltage assigned, because all of these values are obtained as the high voltage side. So from here we can get our equivalent equal to the power 215 divided by square of this current. So talking about stem 0.4 ω. From this, we can get that, remember that z is equal to V over I. Voltage divided by current gives us the z, or the equivalent impedance hundred 50/4. 0.555 gives us the equivalent at the high voltage assigned. So you know that the equivalent is equal to root R equivalent square plus x equivalent square. So we can get x equivalent from the relation between r and x. X equivalent at high voltage side equal to root z square minus r squared. So that'll give us this value, this one. So we have our equivalent as the high voltage side. We have x equivalent adds a low voltage side. Now the last thing remaining is that we need to refer all of these values to the low voltage side. The corresponding parameters. How can we get simply, you can take this value divided by a square and take this one and divide by a square. Why? Because we are going to the low voltage side. So it will be like this, are equivalent at the low voltage side divided by the turns ratio square and x equivalent divided by the turns ratio square. Okay? So now we obtained are equivalent and x equivalent at both of the low voltage side and the high voltage side. Finally, we will have our two circuits referred to the low voltage side, referred to high both sides, the core parameters. And the primary or secondary winding resistance and inductance or reactants, or the R equivalent and x equivalent. You can see that at low voltage side, values of the resistor are very small. Combine the two, the high voltage side due to what? Due to the a squared or the square of the turns ratio. So in this lesson, we had a solvent example on the open circuit test and short circuit test of an electrical transformer. 40. Autotransformer: Hi and welcome everyone to this lesson. In this lesson we will discuss another type of electrical transformers, which is O2 transformer. You have to understand that in some cases, it changing the voltage level by only a small amount is desirable. So e.g. instead of e.g. a. Stepping up the voltage from, let's say e.g. they live in kilovolt to 500 kilovolt, we will use the traditional single-phase transformer. However, in some cases instead of 11 kilovolt, I would like to make this value e.g. like this, 11.2 e.g. I. Would like to change the voltage by a small value. So instead of using this traditional transformer and providing flexible change in voltage, we will use on a cell type called desert O2 transformer. So e.g. from 110, 220 volt or from certain point tools to 13.8 kilowatt. Very small change in voltage, step-up or step-down. We will use the auto transformer. In this transformer, common winding is mounted on a core and the secondary is taken from a tab on the winding. In contrast to that two-winding transformer, the primary and secondary of an auto transformer are physically connected. So let's look at these two figures. So as you can see here, this one windings, this one big one winding is called an auto transformer. So as you can see, we have the primary side and secondary side. So here's the primary side. You can see here we have tabs. This one is called at top. That's transformer itself or on the winding itself. So e.g. if I selected this tab and take it the secondary from here to here, this part only. Then the voltage will be a voltage induced on this winding. Only this part, only. If I select it, e.g. like this, this part, then the voltage will be from here to here. This amount. If I selected this tab, then it will be this voltage only. So pi, selecting which tab I am connecting, my own secondary, I will be able to control the voltage. Same figure here as you can see here. This double line means that we have an iron core and we have one big windings. So we have our supply here, our supply connected to the winding itself. And part of this winding will be connected to our loop. So by selecting at which point we will be able to control the voltage. Now, the basic principle of operation is the same as that of the two-winding transformer. Since all the Telenor's link is the same flux ends up transformer core. So let's understand what happens exactly in this type of transformer. So simply we have the primary site, okay, it's a primary site or our supply. Let's look at this figure, which is much more clear. So we have this AC supply or AC voltage connected to is this winding. So it will produce an AC current that will go through this winding. Now Windsor AC current goes through this winding, it will produce AC flux. Ac flux. So when this AC flux is produced, it will cut the hole, whining all of the lining. So there will be an induced voltage on the primary side and induce the voltage on the secondary side. Why due to the presence of ESA flux. So when's the current comes from the AC supply goes through this winding. It will produce magnetic field or AC flux. This AC flux will cut the hole winding producing induced EMF on the primary and induced EMF on the secondary. Of course, as you can see here, the primary is connected to the supply E, or the voltage source value of the induced EMF of the bones. The primer is equal to the supply. However, the secondary induced EMF depends on the number of donors of the secondary. So e.g. if we select this, this amount of Tony's, it will be higher voltage than selecting this tab. So the induced voltage depends on how much we are taking from the number of turns. So the auto transformer at least have three tabs. So at least have 12.3, at least where electrical connections are made. And as you can see, there is no insulation or isolation, electronic or electrical isolation between primary and secondary z are physically connected to each other. Unlike the traditional transformer in which they were separate from each other as they are, we'll link it using a magnetic field. However, here, the primary and secondary are physically connected with each other, electrically connected. The auto transformers have some advantages of being a smaller, lighter, and cheaper than the dual winding transform, which is a traditional transformer that we discussed before. You can see one winding, which is much smaller than using two windings, lighter and cheaper than the two windings. In addition to the lower leakage reactants, because we don't have two windings, we have just one winding. Lower losses, lower excitation current, and higher voltage rating for a given size and the mass for the same size and demands of an auto transformer. And traditional transformer, we can get higher voltage volt, MPR or higher rating from the auto transformer. Over the only problem, or the biggest problem of this type transformer is that there is no electrical isolation between the primary and secondary circuits. As you can see, it's a primary. Secondary sites are physically connected with each other, unlike the traditional transformer. So this one is that big advantage. So the isolation is important to avoid short circuit between the two windings. However, here is they are physically connected with each other, which you may cause some short circuit problems. Okay? However, that auto transformer has very good advantages of being smaller, cheaper, and so on. So as you can see, this one representing a small all to transform it. So you can see here from zero to hundred, each of these lions representing one tab. So you can see one tab, tab, tab supply selecting by rotating this wheel and selecting which, which tab we would like. We can control the output voltage of the transformer or the auto transformer. So as you can see here, this is a transformer, as you can see here, you can see has an input voltage hundred and 20 v. You can see what v hundred and 20 v and output voltage 0-140. So it is a step up transformer. Or we can also do the two functions, step up and step down, as we would like, according to the tabs which we select. So as you can see, we can control. So we have input voltage, 120 volt. Output is 0-100 v. So it can do step up and step down as we would like by controlling z, rotation of this wheel or selection of the top itself, we can control the output voltage. Here we can see is that auto transformer inside. You can see by rotating this wheel. This way, you can see we can select whichever tab of the transformer we would like. You can see that the two ones are physically connected to each other. Now, let's go and understand more equations about the all to transform. So as you can see here, we have V1 and V2 in both or the primary voltage. And secondary voltage, we have all y1, which is a primary current, I2, which is a secondary current, okay? Now a V1 produce i1 and i2 is the current going into the glute. Now, as you can see, number of terms in one here is defined as the whole number of tons that are whole winding, number of turns. All of this, n, n1. Okay? So we have i1 going like this and I2 going out. Now we have to understand some things that when one goes through this winding, it will produce magnetic flux. Magnetic flux that will cut the hole winding, reducing induced EMF on the primary and the induced EMF on the secondary. So if we look at the secondary itself, we have induced EMF Ea. So we have a current that will come from this winding that will increase this output voltage, output current. So as you can see, we have current I1 coming like this. We have current I2 going to salute and the current upcoming due to the induced EMF, the value of this current from KCL, you can see I1 plus this current is equal to i2 from TCL. So from here we can say that I is equal to i2 minus i1. As you can see here, i2 minus i1 going upwards, going to i2, supplying current to i2. Where did this come from? From the induced EMF itself. Okay? So you can see that we have two parts of the whole one. So we have this big winding, we have two parts of it. This part. And this part we say is that this part, which is the chair, the bar is our primary and secondary can see this part of the winding is connected to the secondary. And the same time this part is a part of the primary winding. So we say that this part is called the common section. The second part, which is not shared by the primary and secondary, or what portion of the winding that is part of the primary. This part is called disease C or is Section Series, section, section. It is series with supply or the primary. Now, you have to understand that the baritone is provided by the SEO section of the winding. So we have this part, we need to find the impertinence n. I remember that from the magnetic circuits and I will help us also in producing the magnetic flux. So let's say we would like to get the umbo tones of this part of the winding. So we have current I1, and then we have number of turns of this part only. So we have all winding N1 and this part into, so it will be N1 minus N2. This part of the winding. Okay? Now, here, as you can see here, this part, a number of turns in this part or in this equation here representing n, n1 over n2, number of terminals of the primary, over the number of turns of the secondary, okay, In this definition here. So as you can see here, if you take n one as a common factor, Let's take N1 as a common factor, will be one minus N2 over N1, N1, I1. So we took in one as a common factor. So it will be one minus N2 over N1, all multiplied by N1. Now, N2 over N1 is the inverse of the Umberto one over a. So this part is one over a. So we have this final equation. So this representing the importance of Zahn. See yours section. Now, the same idea for Zack comments sections as part. The umbrella tones of this part will be equal to number of donors of eight, which is n2 multiplied each current, which is i2 minus i1, i2 minus i1. Now this n2 is equal to n one over a is equal to n, n1 over n2. So we need to, so any two won't be equal to from this equation n one over a. As you can see, we have this two and belt on as one produced in the primary port and one in the secondary part, or the common section, or zeros section and the common section. Now, we have to have unpaired tone balance. These two forces. This to ampere tons must be equal to each other. If you take this equation and equate with this equation like this, you will get finally, that I1 over I2 equal to n over n, n1 equal to one over a, equal to V2 over V1. Okay? So Pi controlling the number of turns, N h over N1 number of turns on the secondary. And the primary, we will be able to control the currents i1 and i2, primary and secondary current. And the same time we can control the output voltage V two and V one. Now, the auto transform itself can be a step-down transformer and it can be a step up. You can see here we have the primary v0, v1 content consisting of this whole winding. And we just to take a small portion of the secondary, small portion of the winding folds as secondary. So it is a step-down transformer. Now, the same idea, you can reverse it if you bought the supplies to the smaller section or the common section and connected the output too, the whole winding, you will be able to step up the voltage. Again. How, when one goes here, we have a current induced here, right? We have a current induced here, which is I2 minus I1. This will produce a flux that will induce voltage on the whole winding, which leads to V2. So as you can see here, V2 over V1 equal to n over n, n1 equal to a or number of turns, and i2 over I one equal one over n. Now remember something here important that a or the turns ratio, it can be n, n1 over n2. Or it can be also defined as N2 over N1 depending on the example itself for as you would like, in the end, you, how you both this umbrella or toners, the band or the turns ratio, depending on the step-up or step-down transformer. So any way you can define it as N1 over N2 as we defined in the previous slide. As you can see here. You can see here a is equal to n one over n h2. Here we defined a as N2 over N1. So as you'd like, you can define it like this or like this. Okay. 41. Solved Example 1 on Autotransformer: Hi and welcome everyone. In this lesson, we will have the first solve the example. On the auto transformer. We have an auto transformer here of V0, V1 equal 1,250 volt and V2 equals 800 volt. V1, which is the supply voltage 1,215. And V2, which is a voltage across our load of 16 kilovolt ampere. This voltage is equal to 800 walked. And we have forest or a one, and we have current i2. And of course, our inode, which is i2 minus i1, as we have discussed before. So what we would like to get is the value of n, n1 and n2, the number of turns of the primary part and number of turns on the secondary, and all E1 or E2 and the I node. Now first we have to understand something which is really, really important. Here. When you see this sign n, n1 and n2, What does this mean? N1 representing the number of donors of Z C or is part of this winding, this section, or the zeros section. So n one representing this portion of the winding, only. Unlike what we have discussed before, that N1 was the whole winding. Here. When you see this two simple as above each other, it means that n n1 is the CRS portion or that C or section and n2 is a secondary part or the common section. What we can get from here is that V1 over V2, V1 over V2, well be equal to number of turns representing V1, which is a whole tones. Okay? Now remember, the whole tone is a summation of this winding, the sea or as section and the common section. So it will be n, n1 plus n2. N1 again is this part only, this part only. And n2 is this part only. So when I talk about V1, I talk about the whole winding N1 plus N2. And V2 will be n into this part of the winding and two legs. So as you can see, V1 over V2, n n1 plus n2 divided by n2 equal to V1, which is 1,250, and V2 which is 800. Okay? Now, you can assume that this is an assumption. You can assume that number of donors of secondary and n2 equal to 800. Assumption, you can assume any value would like that will satisfy this equation. So as an example, we will say is that n2 equal to 800. And when any 200, let's substitute here. We will get N1. So n n1 plus n2 equal 1,250. So n one will be 450. So this part only 450 and this part only is it hundred tones. Okay? Okay. So from here we obtained N1 and then it'll again, N1 is a part, this part only. Then two is the secondary port. Okay? Okay. Now we would like i1 and i2. Now remember same equation here. V1 over V2 equal to n, n1 plus n2 over any two equal to R2 over R1. Okay? Leave it now. And at the same time we have this load, S equal to V I. The magnitude of S equal to magnitude of voltage multiplied by the magnitude of z. Alpha power 16 kilovolt and pair. Okay? Equal to the voltage across it, which is V2. V2 is equal to 800, if you remember here. Okay, multiplied by the current which is going to the load, which is i2. So from here we can get I2 like this. You can see V2, I2, which is the power going to the load, which is 16 kilovolt and Beta equal to voltage which is 100 and all E2. So from here we can get the value of I2. Now we have the current I2, which is 20, and they're using that tone is ratio V1 over V2 equals I2 over I1, or 1,250 divided by a tundra equals I2 over I1. We can get the value of phi one. You can see it over I1 equal to 1,250. Here you can see all it over I1, I2, I1 equal one. So 250 is this equation here. So from here we can get a value of I1. So let's delete all of this. First one will be 120.8 and bear. Now we have I naught. From here, I2 is equal to I1, as we discussed before. Plus I naught. We have i1, which is 21 pair. We have i2, i2, which is equal to i2, which is this one is 20, and pair y1, which is 12.8. So we can get our inode like this. Okay? So as you can see, what we did again is that we simply use the turns ratio to get N1 and N2 or to get i1 and i2 and I naught. Now again, n, n1 over n2. What does this represent representing that portion here? N1 and N2 representing this spot. That's why we add this a summation because V1 is a whole winding voltage, V1 is the voltage across the whole whining. So it will be n one plus n two. V2 is only this part, so it will be n two. 42. Solved Example 2 on Autotransformer: Now let's have another example. Find the i1, i2 and dynode ends a complex power supply to the load. So we have this voltage source 120 and Engels salty. We have our load eight plus six. We have V2, which is a voltage across it, and V1, which is the supply voltage, i1, i2, and I naught. Now first thing you have to understand is that here in this example we have a complex power, complex equation, not just the magnitude, but magnitude and the angle. Now second the thing here you can see that we have V1, V1, 220, and angles, so two degrees. Okay? Now, we would like to see here you can see a two tones and 120. What does this mean? It means n, n1 over n2. N1 over N2. And this is a step up auto transformer. You can see here small windings and V2 is across the whole winding. So V1 over V2 equal to. Now, look carefully here, N1 and N2. What does N1 means? Here? Our supply is add this part of the winding. So this part is n, n1 and n2 is that part, or Zach common part, which is N d2. So again, 80.120 means n one over n into n one, which is the number of donors of the primary, which is this part. This is our one which is related to the primary. And n2 is the portion which is the common section. So in the end, these two turns, N1 and N2 representing one representing that common section, and the other representing zeros section. So V1 is corresponding to N1. And the V2, which is the whole winding V2, is volts across the whole one, which is 8,020, which is n, n1 plus n2. So I hope the idea is clear. So as you can see, it's a step up transformer, or is n n1 equals n2 equal hundred 20? You can see n, n1, 80 and then a 220. We can say is that V1 over V2 equal n one over n, n1 plus n2 one which is 80. And summation of the two turns, 80 plus 120 is 200. We have V1 which is 120 and angle certainty. So we can get to from this equation. So it will be zero hundred and the angle t volt. Okay, so let's delete all of this. So now we have a value of the voltage V2. And do we have here our loot? So can we get i2? I2 assembly equal to the voltage divider point is at Dell. Likes us. So to be V2 over the cell, it will give us salty and the angle negative 6.87 degrees and bear. Okay, so we have now current I2, now we have V1 and V2, and then we have current i2. So we can get from here, or U1, V1 over V2 is equal to i2 over I1. I1 over I2 equal to N1 plus N2 over N1 equal to 280, which is similar to, you can see here, N1 plus N2. The sport is equal to V2 over V1. This equation is similar to this one, but they exhaust reverse it. Okay? So from here we can get a value of value of the current or E1, like this. So I1 will be equal to 75 and angle negative 6.87 degrees. So now we have only one, we have i2 and we need or I naught will be i2 minus i1, as we learned before. So KCL here, you can see that I1 plus I1 equal to i2, which means I naught equal to I2 minus I1, as we did before in the previous example. Okay? Now we have the three currents. The only part is the complex power supply to the load, which is a power supply to this load. So the power in general is equal to voltage multiplied by the conjugate. Remember that here we are dealing with complex numbers. So since we are dealing with complex naught magnitude only, so it will be V and I conjugate. Or it can be magnitude of the current square multiplied by z. Okay, if you don't know this equations, return back to our course for electric circuits. As you can see, it's a complex power would be voltage multiplied by i conjugate, or the magnitude of the current squared multiplied by the impedance magnitude of the current. You can see i2 where as i2, i2 here, magnitude 30. So it will be sorted square. And the L, which is the impedance, this impedance. In Faisal, it will be done and the angles are 6.87. So it will give us this value in kilovolt and pair. Okay? 43. Solved Example 3 on Autotransformer: Now let's have another example. We have an auto transformer, has a coil with a different number of turns. It is really, really clear now that each turns, each turn is our given directly without any kind of confusion, you can see that AC, number of turns of AC is this tones, is hundred tones. You can see that a, B, this part is 50 tons, BD, Swifty tones, and so on. And DC, which is a whole winding 200 tons, which is the summation of all of these parts, a, C plus AB plus BD. Okay, So we have a supply 400 volt, and this auto transformer supplies power to several nodes or two parallel lines. You can see allude here 60 ω and another one for T ohms. Now what we would like to get in this example, we would like to get the current in the various parts of the circuit. So we need to find the supply current. We need to find the current here, and its direction is downwards or upwards. We need to find this current. This one is a current. Here in this part, we have several canons that we would like to get. Okay? So let's start step-by-step. So first step is that we first get the occurrence of each of these loads. Okay? So the current here will be the voltage across it divided 60 on current here will be voltage across it divided bys of voltage. So our goal here is to get a voltage across each of these loads. Okay? So let's start. So let's say we are talking about this one, this one first. So we have our supply and the corresponding number of turns, AAC. So we will say voltage 400 volt and corresponding number of donors, which is AC, and the corresponding number of tunnels, she is 100 tons. Now what we would like to get is the voltage across the second row, B, C. So we will say voltage B, C, voltage here. Vbc. And the number of turns of PCs are corresponding number of turns. All of this, so all of this will be BC, right? Which is number of turns of a B plus number of turns of AAC. So it will be hundred and 50. So from here we can get VBC. Okay? So let's start As you can see here, V supply divided by VBC. It will give us number of turns of AAC, this part, which is hundred, divided by n, b, c, This part, which is hundred plus 50, which is 150, as you can see here. So from here we can get VBC equal to 600 v. And when we take this voltage across as SS-20 600 volt divided by 60 own, we will get the value of the current. So current rules as 60, 0 will be 600/60 ohms will give us ten amperes. Now, same idea, same idea. You are going to apply it to their second load here. So we have V supply and the corresponding number of turns, which is hundred. This supply and corresponding number of turns. Here we would like to get this voltage. So it will be, is a voltage V d c, v d c. This voltage will have a number of tunnels equal to the summation of all of these tones. So VDC or any DC number of turns of DC, you can see equal to 200 mile from here we can get VDC. So as you can see, 400 divided by VDC equal to hundred divided by 200. So from here we can get Vdc. Now we have a voltage, VDC, which is the voltage across the four t. So if we take VDC and divided by 40, we will get that current going through that fall TO which is 20 amperes. Okay? So now we have current here to win and bears. And we have the current through 60, 0 here equal to ten and pears. So as you can see, it's really, really clear that if you would like to get this current, current here, will be devoted to this current. And the current going like this, like this, which is that when the ambient. So by KCL, the current flowing in the spot in the section only will be 10:00 A.M. pairs plus 20, which is subtlety. And bears. So certain birds are going up will be divided to this load and this load. Okay? So t amperes, okay. Now, we would like to get this current and this current. So let's start by supply current. How can I get the supply current? Look at this circuit, you will find that we have two loads, the security arm and forth TO. So if we get the total power consumed here, total power consumed, it will be equal to the supply power. From the supply power, we can get that supply curve. So as you can see, that total load here is equal to 20 square multiplied by 40 I square multiplied by r. This is a power consumed in such a resistor, 20 square multiplied by 40, square multiplied by 60. This summation will give us 22 kilovolt. This representing that total power going into the load, which is equal to supply power. Assuming that of course we don't have any kind of losses. So 22 volt is equal to the supply power. So we can get the current. So the current of the supply will be equal to the total power, total apparent power, which is 22 kilovolt. The word applies or supply voltage, which is 400 volt. So it will give us 55 and bear. So the current coming from the supply 55 amps here. As you can see here. So as you can see, we obtained 2,010.55, let's say sees a salty and bear. By applying KCL at B, we obtain the salty and pair, which is the current flowing here. The current is the current flowing here. How can I get this current? Simply Pi KCL in this spot at a. We will be able to get this current. So we have a 55 and bear supply and thirsty ampere going up and another current going down. So 55 and bear certainly am pair plus 25. So as you can see here by applying KCL at this 0.55 and pair divided into 32 when T5 ambient, so that 55 -30 gives us 25 embedded going down. So in the end, it will be like this, our circuit. So as you can see, 552,510.20. So this was another example, owns the O2 transform. 44. Core Type Transformers: Hi, and welcome everyone. In this lesson, we will talk about the two types of transformers. Or how can we place our electrical transformer windings in a transformer. So we have two types. We have the shell type transformers and we have the core type transformers. These two types of transformers representing the positioning or adding the windings in any electrical transformer. So first, if you look at the transformer, we have two types the shell type and the core type. This figure representing the core type transformer and this one representing the shell type transformer. So in the core type transformer, the windings are wound around the two legs of a magnetic core of a rectangular shape. So what does this mean? If you look at this shape, this is our iron core in which our flux will flow, the magnetic flux will flow inside this iron core. Now, if you look at here, we have in the construction of a transformer, we have this upper layer, this upper part, and this lower part, these two parts are known as the yoke of the transformer. The upper part or the horizontal part. Horizontal part of electrical transformer is known as the yoke of the transformer. The vertical part, the vertical part, this one and this one, here, for example, this one and this one. And this one are known as the legs of the transformer. And you will find that we have here this open area, you can see this open area here or in the shell type, this open area, here and here. Are known as the window of the transformer. So we have the upper part and lower part or the horizontal part, upper horizontal part and lower horizontal parts are known as the yoke of the transformer. And we have the vertical leg, vertical leg, vertical leg or the vertical part of the core of the transformer, which is a leg of the transformer. So the core type transformer, you can see that here the windings are wound around the two legs of the magnetic core of the rectangular shape. It is not necessarily a rectangular shape, but here as an example. Okay? Rectangular shape, of course, it is always rectangular shape for the core itself. Okay? For this, it is shown as rectangular. However, the leg itself can have different cross sectional area as we will see in the next two slide. In the shell type, the windings are wound around the center leg of a three legged magnetic core. So in the core type, we have two legs. In each leg, we have a part of the winding. As we will see in the next slide, we will understand which part of the windings. And for the shell type transformer, we have one, two, and three. We have three legs, and we have our winding in the middle leg of the transformer or the center leg of the transformer. Now let's talk first in this lesson about the core type transformer. So we use here L shaped laminations used for core type. So as you can see here, you can see the core. You can see we have L like this. Like this, here, like this, L L shaped, and another L like this, plu it like this. So by using two L shaped above each other, we will be able to form this rectangular core. So as you can see here, it is something like this, L and plu it another L. These two L shaped are put above each other in order to form the rectangular core. You can see L shaped plu it another L, and then another layer L and L until you will have multiple layers of L shaped laminations in order to form this rectangular core of the transformer. And we said before that these laminations are used to reduce or reduce the ID losses inside the electrical transformer. Now let's talk about again the core type. As you can see here, we have this big winding and another big winding. We said before that we have two inside the transformer. We said we have the low voltage winding and the high voltage winding. So how can we bless this inside the transformer? We have two options. The first option is that you will have the high voltage on one side and low voltage on another lamp or another leg of the transformer. So for example, this one will be the high voltage, and this one will be the low voltage as an example. Okay? So each winding on a separate leg. However, another configuration which is more common is that in each limp, we have half of the primary and half of the secondary. So as you can see here in this figure, instead of having this one representing half of the low voltage winding and this red one representing half of the high voltage winding. This one here will be half of the low voltage winding and this red one will be half of the high voltage winding. Here, for example, for the first configuration, for example, this one is the high voltage, and this one is a low voltage. In the end, the magnetic flux will flow inside the iron core, and this magnetic flux will cut both winding, the low voltage and high voltage. It is the same principle of operation. Nothing changed at all except that we divided the two windings on a separate legs, one which containing half of the primer or half of the low voltage or half of the high voltage, depending on the type of the transformer itself. So each lamb carries one half of the primary winding and one half of the secondary winding to reduce the leakage reactants to the minimum possible value. This is a function or why do we separate or form half of the winding above it the other half, or around it, the other half. So if you look carefully about it for this configuration or half of the high voltage and half of the low voltage, you can see that here, we have like this. We have our core, right? This core, which is considered as the pass for the magnetic flux. That will cut the low voltage winding and the high voltage winding. So let's start by the low voltage. You can see that we have the low voltage winding and around it, the high voltage winding. Of course, they are not touching each other because if these two windings are touching each other, it will lead to a short circuit. So what do we do? You can see that here in this figure, we have the high voltage. Then we have this is our high voltage. Then we have here an insulation, high voltage insulation to insulate or isolate between the high voltage winding and the low voltage winding. You can see we have here like this, for example, high voltage winding. Then we have an insulating material that will insulate between the high voltage and low voltage winding. This one is a low voltage winding. And then between the low voltage winding and the core itself, we have another insulation to insulate between the low voltage and the core of the transformer. Here we have here finally our core. So you can see we have high voltage winding. Then we have an, high voltage insulation to insulate between. Let's delete all of this to make it clear, high voltage, then high voltage insulation to insulate between high voltage and low voltage, and you can see low voltage winding. Then we have low voltage insulation, then our core. Now, as you can see in this figure, that the low voltage is inside and the high voltage is outside. Now, why is this happening? The low voltage is wound on the inside nearer to the core, while the high voltage winding is wound over the low voltage winding away from the core in order to reduce the amount of insulation materials required. So as you know that the insulation, the insulation required in any electric circuit, is directly proportional to the voltage. So the higher the voltage, more insulation required. So in order to insulate between low voltage winding and the core, we will need small insulation. However, if we add the high voltage, we will need large insulation between high voltage winding and the core itself or the core or the magnetic core itself. Okay? Now, we have in our core type transformer, we have different configuration for the core itself. So what I mean by this, the core can be rectangular shape. The cross sectional area of the core can be rectangular shape, or it can be square shaped, or it can be circular shaped. So here you can see that here. This one, if you look at this part, you can see that the core here is rectangular shape in the form of a rectangle. So when you are winding the winding itself or when you wind the winding of the transformer or the coil itself, we are putting it in the shape of a rectangular shape. Of course, not rectangular only can be rectangular or it can be square shaped or any other type. In general, we can have for this core, we can have rectangular core or rectangular cross sectional area. It can be a circular cross sectional area. It can be a square cross sectional area. Now, at the same time, when we want our coil, we can put this winding in the form of a rectangular form, square form or circular form, as you can see here in the different figures, you can see here. This part is our shape of the core and outside the shape of the coil itself. Okay? So the rectangular core requires more length of copper for the same number of tons as compared to the circular core. So the first problem of using rectangular or square is that the amount of copper or the length of copper required to form one term inside the rectangular core is much more higher than the circular core. So we will need more length of copper. So in this case, we usually use a circular core. Another benefit or advantage of using a circular core is that when we have a short circuit condition, when we have a short circuit condition on the winding itself, we will have a very high mechanical forces because as we remember that the forces or magnetic forces or mechanical forces are directly proportional to the amount of current flowing inside the winding itself. So since we have a short circuit, it means we have very large current which can deform the square or rectangular coil shape and damage the winding and the insulation itself. So you can see that we have mechanical forces on the circular core itself that will try to deform this shape here and also here. For the square coil, and for the rectangular coil. However, you have to understand that the circular coils are more preferable to the square or rectangular coils. This shape is more preferable than the square coil and the rectangular coil. Now, why is this? Because the round coil has more uniform stresses. You can see stresses which is radial like this in all directions. Okay. So the mechanical forces, the deformation inside the circular coil is much lower than the other type of coil such as the rectangular or the square coils. Why? Because in the square and the rectangular coils, we have the corners. These corners here. You can see these corners. These corners representing weak point or subjected to more stresses electrically and mechanically, especially under the fault condition. That's why the circular coil and rectangular coil are more subjected to deformation during a short circuit condition. So to summarize what I said is that the first problem is that for for the circular core, we need less amount of winding or less amount of copper for the same number of tones in the case of the rectangular cool and rectangular core and the square core. Also, the circular coil can withstand the deformation under short circ condition compared to the coil and the square coil. So in the end, what are we going to choose? We are going to choose a circular coil with a circular core. Like this. So we need a circular core, and around it, we will start adding our coil. However, what is the problem here? The problem here is that the core must be laminated. It cannot be one big bis. Okay? So in order to form a circular core, it is not practical. You cannot just form a practical with lamination like this elimination, another lamination. It is really, really difficult to do something like this. Okay, because there is a problem of securing them together. In order to attach them together in position, it's really, really difficult. And at the same time, you will need large number of different size lamination because each lamination like this and the next one will have a different radius, next one will have a different radius and so on. So it's really difficult to form laminations of circular core. So what are we going to do? In this case? We are going to form the circular core by approximating it into a stubbed core, having an infinite number of steps. So what does this mean? You can see that here, this is a circular form, right? So what are we going to do is that we will make one lamination like this, which is the first step, then another lamination, like this. Then another lamination like this. So here we can see we have one, two, three, below it, one, two, three. So this shape in the end will be close to a circular form. So this one is called the stebbed core. Okay, Stebbed core. Now, this one since we have one, two, three, or three different steps. So we say this one is a three stubbed core. If we look at this one, for example, you can see we have one, two, three, four steps. So this one is called the four stepped core. Okay? So the more steps we have, the closer we are to a circular four, which means we are getting closer to the circular core. So here we have the rectangular core. We have the square core. We have the croifm core. You can see in the form of the cross like this one, two or two stebbed core, and this one is a three stubbed crossiform core. So usually the small transformers may have a course of rectangular or square with a rectangular or circular coils. However, it is useless in the case of large capacity transformers and the large capacity transformers, we need to use the stepped or the stepped cruciform core with a circular cylindrical coils are used. So as you can see here, we have the three stubbed cruciform core here we see one, two, three steps. And this one here we have one, two, so we have two steps here. So this one is called the Crocifom. This one is called a three stubbed Crocifom core. Now, the cost of manufacturing such a cruciform core is much greater than, of course, the rectangular or the square cores. However, the circular cores are easier to went and provide more mechanical strength, as we said before, when a short circuit occurs, and the same times the amount of copper required will be much lower. As we said right now, that the Crociform cores are employed because of the reduced mean length of tons resulting in a reduced couple losses. So in the end, instead of using a circular core, we used a csim step core or a three step crossifom or a two step croiform depending on the cost we have, which will help us to reduce the amount of copper losses and reduce the amount of length of tours required or the cost of copper. So in this lesson, we talked about the core type transformers, and we understand now how can we design or select the form or the shape or the cross sectional area of a transformer, the shape of the cross sectional area. So we know that now it is a circular or a cruciform with a circular core. 45. Shell Type Transformers: Hey, everyone. In this lesson, we will take a poet the shell type transformers. So in this type of transformers, the cross sectional area of the central limp is twice that each of the side limbs or the side legs. So what does this mean? It means that you can see here this is a cross sectional area, this area of this part. The part and this one. You will see that the central limp or the central leg, the cross sectional area is double that of this one and this one. So the central limp since it takes all of the windings, its cross sectional area is twice that of the other side limbs. Also in the shill type transformers, we use the sandwich or the disk windings. So what does this mean? If you look at this figure here, you can see this is the central limp here, this part. So we have this side lamp, one, and the other side lamp or the side legs. This one and this one or this one and this one. The middle one or the middle or central leg, this part. Okay? This one. And you will see that the winding is around it. All of the windings around this central leg. Now, what does a sandwich or a disk windings mean? It means that we are putting our windings in the form of a sandwich layers. So what does this mean? You can see here. First, we have low voltage winding, as you can see, low voltage winding, this one and this one, which is winding like this around this core. Then we have the high voltage winding. Then we have low voltage winding, then high voltage, then low voltage. So as if you have a layer of sandwich, layers inside the sandwich, low voltage, then high voltage, then low voltage, then high voltage, and so on, like this. So as if they are layers above each other. So what does it mean? Or what we mean pie the sandwich windings. So here you can see that here, here, of course, the low voltage wind. Of course, we have here insulation between it and the yolk or the core itself. And of course, we have here insulation also here in the sport. If we have a low voltage, then we have low voltage insulation. If we have a high voltage, then we have high voltage insulation and so on. Okay? So here we are dividing our windings into in the form of sandwich layers. Now, this one, by doing this function, we will be able to reduce or reduce the leakage reactants inside the transformer by subdividing the low voltage and high voltage windings into mini sections or coils and arranging them alternately the high voltage and low voltage sections with the low voltage section nearer to the yoke. So similar to the core transformer, inside it, we had the low voltage near to the core. Here, we have the upper layer and the lowest layer, the highest layer and the lowest layer are low voltage, which is the one nearer to the yoke, which is a horizontal upper part, and as you can see, lower near to the lower lowest part. Low voltage near to the lowest part. So and alternating the high voltage and low volt section, you can see low voltage, then high voltage, then low voltage, then high voltage, and so on. So here is the shape of the transformer. You can see here, this one, here is the left leg, and this is the right leg and the middle leg here, which contains all of our windings or the shell transformer, which is in the sandwich form. Now, in order to form this type of transformers, we use E O and L shaped laminations. There are other types, but this is one which are commonly used. So as you can see here, you can see we have E, letter, E, like this, I reversed ET one E, which can be used for this part, E like this for this part, and the lost part, this part can be I this one is in the form of E shaped, and this one is I. By using E and I, we can form the shell type transformer. Another thing we can see, you can see here, E and I. Another thing is that you can use L shaped laminations. For example, this one can form L this one is L, and this one is also L above each other. This one can be also L like this. We have different forms that can help us form this cell type transformer. However, one important note here, as we said before, you can see here that the cross sectionary of this one and the s and the s. You can see that the middle one have a higher cross sectional area than the left leg and the right leg or having a higher cross sectional area than the other two limbs. Finally, let's talk about the transformer insulating material. So we said that we have insulating material that will insulate between high voltage and low voltage and between low voltage and the core or between the high voltage and the core itself, or low voltage and core itself. So according to IEC 85 standard, we have different classes for the material that will be used for insulation. Now, this material can be A plus A or E, B, F and H. So what does this mean? So that transformer windings are insulated by insulating material. The most important characteristics of the insulating material is its class. So the class of the insulation denotes the maximum temperature that it can withstand. So we know that this transformer has or this transformer or this type of transformer, the power transformers are used to convert large amount of electrical power. So when we are seeing large electrical power, we have a high voltage, and we have also large amount of currents. So this large amount of currents will lead to large heat energy. So we need insulating material that can withstand this high temperature. So here we can see that we have maximum ambient temperature. What does this mean? This is the maximum temperature of the surrounding. So if you are putting the transformer in a location with a maximum temperature 40 Celsius degree. So the temperature of the location of the transformer itself has a maximum temperature of 40 Celsius degree. Now, in addition to this, the winding itself will have this temperature temperature of the surrounding the same temperature of the surrounding, which is 40 Celsius degree as an example. Now, this winding its temperature can increase by a certain amount, increase or rise in the temperature. So as you can see, if we are using class A, then this insulating material can increase by an additional 60 degrees. So when we measure the temperature of this winding, it can reach 100 Celsius degree. Its maximum temperature. Similar to class E, which will have 40 degrees plus 75 degrees. So this one if the high voltage insulation is of class E, then it means that at ambient temperature of 40 Celsius degree, it can withstand up to 115 Celsius degree temperature rise in the insulating material itself. So when you measure the temperature, add the insulating material, it can reach up to 115. It can withstand up to 150. Okay, similar to B F and H, each one has its own permissb temperature rise. One important here is that each of these insulating classes have a thermal margin, additional withstanding temperature. So for example, that class A can have a temperature can increase by an additional 5 Celsius degree. E can increase by an additional 5 Celsius degree. So as you can see, class A, can reach up to 105 Celsius degree, can withstand up to 105 Celsius degree? E, up to 120. So what does this number represent? It representing the ambient temperature, plus the amount of permissible temperature rise, plus the thermal margin. So this insulating material of class A can withstand up to 105. Okay? So in the end, this depends on what depends on the ambient temperature, plus the class itself. Okay. So class A, E, B F and H, all of them are used in dry type transformers. And for oil immersed transformers, class A is used. So what does this mean? What does that dry transformer mean? And oil transformer mean? We will learn about them after learning about the three phase transformer. But for now, you have to understand that dry or air type transformers and oil immersed transformers, representing what representing the method of calling the winding of the transformer method of calling these windings. So we will learn about them after learning about the three phase transformers. 46. Comparison Between Shell and Core Type Transformers: Now let's compare between the shell type transformers and the core type transformers. So this comparison came from a website called the Engineering notes online website. So I like this comparison and I wanted to share it with you inside our course. So you can see here we have two types, which is a core type transformer. We have the shell type transformer. By definition, we said that the core type, the coils are wound around the two lengths of a rectangular magnetic core. So we said that here we have our winding itself. The winding itself or windings are wound around two limbs of the cook. However, here's the shell type are wound on the central limb of the three core transformer, right? Now, another thing here, you can see that here a rectangular magnetic core. However, it is not necessary, of course. You can see here that the cross section of the core itself can be rectangular or square or the cruciform, which we have discussed before and circular cylindrical coils. So what are we using? We are using the Crociform the Crociform type, the two stepped and three stepped is commonly used. And we said before, why do we use this type of transformers? We talked about it in the core type lesson. With a circular cindrical coils, the coils itself are cylindrical coils. However, in the shell type, we use a cross sectional area of the core is rectangular. Now, what about the copper? We said that here, the core type requires more copper. However, shell type requires less copper. Now, why is this? Because if you look at here, you can see here. The two windings, the low voltage, and high voltage are around each other. So we will need large amount of copper to form, you can see here. The more windings, the more turns, we will need larger amount of coils like this. This core you can see more Copper in order to form one turn. However, here we need a constant turn. You can see like this, then this one blew it, then this one blue it, and so on. The amount of copper required is much lower than this type. This type needs large cover in order to surround the two cores or surround the two windings or add turns around them. Here since they are separate, so we need less amount of copper. The minions we said before, this one can be L shaped and E and L or E and I or L. As we discussed before about the shapes or the alphabets, letters used for the core and shell types. This one has two lmps one, two. This one has three limbs as we discussed before. Design, this one is easier to design. However, this one is more complex because of course we need here, we are putting them in a Sandox form which is much more complex in design. The flux distribution equally distributes on the side lamps. You can see here, the whole flux moving here is the whole flux moving through the complete core. However, here you can see the whole flux like this, y, then it will be divided to 5/2 and 5/2. You can see the flux buses through the central limp like this, complete flux. Then it will be divided into the two parts. Now remember what you see here in the Shell type transformer is one of the types or one of the magnetic circuits that we talked about in the magnetic circuits part. So if you remember, we talked about the core type and shell type magnetic circuits before. However, we didn't say that they are core and shell types. Now, another thing, the insulation. Here, for the core type, it provides space for insulation, making capacity suitable for extra high voltage requirement. So for high voltage application, the core type gives us more space. You can see that the high volte wine is outside. However, here and you can see we can have more space. However, the shell t gives us less insulating or less insulation. So what does this mean? You can see here that we have a low voltage in high volts and low volts Between all of them, we need insulating here, insulation here, insulation here, insulation here, and here and here. And of course, between each winding and the core itself, you can see we need more insulation for the same voltage. So in higher voltage application, it is difficult to have a shell type transformer. Why? Because it doesn't give us much space, or we need to increase the size of the transformer. That's why the core type usually used for large applications. Now, what about the losses? For the core type, the losses are more than shell type. Why Because we have more couple, which means more couple losses. What about the mechanical strength? The mechanical strength here in the core type is lower than the shell type. Now, what about cooling? This core type has a better cooling because more surface are exposed to the external. You can see the high voltage is exposed to the external or the open air. However here in shell type, we use fans. Of course, when we are talking about large powered transformers of the shell type. The maintenance, this one is easy to repair, as assembly can be dismantled easily. We can separate the parts together, and we have the high voltage alone and low voltage alone, so we can separate them from each other. However, here you can see that in the shell tie, you can see we have a sandwich form, which is much more complex to separate from each other. That's why the core type is usually used for high voltage applications or extra high voltage applications, such as power transformers in electrical systems can be used as an auto transformer and high voltage insulation. Now, the shell type transformer can be used for low voltage applications like transformers in electronic circuit and small transformer. It can be used in small applications. Usually, the core type is more popular and much more widely used throughout the world. Because of the simplicity of the design of the core form power transformers. And since the core form transign is simple because we don't need sandwich form, they cost less than the shell type transformers, which have much more complex design. However, you have to understand that the shell power transformers are widely used in North America. So the type is usually used in the world wide because it has a simple design and easy to fix. And of course, it gives us more space for insulation compared to the shell type. However, shell type is much more popular in North America. Since or some of the main advantage of the shell form transformers are that they are more compact than core form transformers and have great mechanical strength and having great mechanical strength because it helps us in over current situation or short circuit that transform is less prone to being damaged. 47. Three-Phase Electrical System: Hi, and welcome everyone to this lesson. In the previous lessons, we talked about the single phase transformers. We talked about the core type transformer. We talked about the shell type transformer, and we also talked about the equations of the single phase transformer. Now in this section or this part of our course, we will start talking about the three phase transformer. So before we start talking about the three phase transformers, we need to remember first the three phase system. So in our electrical power system, we have a three phase system. We have the three phase A, BC, they can be named as A, P, C, and the neutral, or it can be red, yellow, blue, and the neutral. So we are supplying electrical power to our loads in electrical power system using this three phase system. And of course, as we know from electrical power system that the three phase, the red yellow blue are having the same magnitude, same magnitude, same maximum value of the voltage, this one, and this one and this one, same magnitude, and the three phase are shifted from each other by 120 degrees. So if you remember that V one will be equal to V max and angle the V two will be equal to V max. Here, for example, cita, it will be eta -120 degrees. V three will be equal to V maximum angle cita plus 120 degrees. So we have V one or VA, VB VC, V max VMX VMX same magnitude, and the phase shift between them. First one is eta. Second one is lagging by 120 degrees, third one leading by 120 degrees, which is a three phase system. Now, since we are dealing with a three phase system, we need a three phase transformer. So before we start going to the transformer, we need to understand that our three phase system can be connected or connected in the form of star connection and Delta connection. So we have a star connection and Delta connection. So what's the difference between them? The star connection, which is this one. We have red, yellow, blue, which are having the same magnitude and phase shift 120 degrees. This three has red, yellow, blue, and the neutral. So this is called the star connection. Here we have also the delta connection, red, blue and yellow. And we have the three terms, red, yellow, blue, and here we don't have a neutral point. So what's the difference between them in the star connection. In star connection, the magnitude of the line voltage is root three times the phase voltage. So what does this mean? It means that, for example, let's say VR the voltage between red and neutral, this voltage is called V phase. Okay, V phase voltage between blue and neutral, is called the V phase. Voltage between yellow and the neutral is called the Vphase. Now, the line to line voltage is a voltage between each two phases. For example, between R and D B, it's called V line. Between B and Y, is called the V line. Between red and yellow, is called the V line. Now, in the star connection, the phase voltage is different from line voltage. You'll find that V line is equal to the value of V phase, multiply it by root three, greater than it by root three, and at the same time, the angle will be cita, which is angle, or let's say, for example, V phase, this is a vector, so it will be plus 30 degrees. So in the star connection, the magnitude of the V line or the line voltage is greater than the phase voltage, P magnitude of root three. And at the same time, its angle will be leading the vector of phase voltage by 30 degrees. So what I mean by this, it means that, for example, if V phase, is equal to ten and angle ten degrees, for example. Then V line will be ten root three and angle ten plus 30 degrees. However, in the delta connection, the phase voltage, which is a voltage here is equal to the line voltage. V phase is equal to V line in the delta connection. In this lesson, we had a simple example on the three phase power system and the star and Delta connection. In the next lesson, we will start talking about the three phase transformers. 48. Three-Phase Core and Shell Type Transformers: So let's start by talking about the three phase transformers. So we have two types of transformers, which is a single phase transformers that we discussed before. Here, for example, this is a core type transformer. This is a single phase. If you remember that we had two windings, primary winding and secondary winding, or we had half of the high voltage, around it, half of the low voltage, and here, half of the high voltage and half of the low voltage. If you remember. Now, this is a single phase system, which means it takes one single supply, single AC voltage. In the three phase system, we need three phases or three windings. So we have here 14 phase A, phase B and for phase C. Now, each of these has its own primary winding and secondary winding. For phase A, we have two windings. We have winding for the primary and winding for the secondary. For B, we have another two winding and C two winding. This configuration is the core type transformer. Similar to this one, this is a core type transformer, takes three phase input and gives us three phase output. So the changing the voltage of this system, what I mean by this system, the three phase system in electrical power system can be done using a three phase transformer or using a single phase transformer. So we have two options. In order in electrical power system, in order to step up the voltage or step down the voltage, we need three phase transformer or multiple single phase transformer. The three phase transformer has one core with three sets of one. You can see. All of this configuration is one magnetic core. This magnetic core has three sets of windings. We have one, two, and three. The primary and secondary one are placed above each other or around each other. On top of the other on each of the three legs of the core as shown here, we will see more another figure that shows us this in detail. So as you can see here, we have two types of transformers, the shell type, transformer, three phase transformer, and three phase course type transformer. In the three phase transformers, the core type in each leg in each leg here, we have for example, this for phase A, this one for phase B, this one for phase C. For shell type here, we have phase A, phase B, and phase C. In A here, we have the high voltage and low voltage or the primary and secondary of A. We have primary and secondary of B, primary and secondary of C. Here is the same idea, primary and secondary of C, primary and secondary of B, and primary and secondary of A. Now, let's see this in more details. The three phase core type transformer. So this will help us understand. So we said we have A, B, and C, which is a three phase system. Now, A will be input like this. A has two windings. Two windings, which is the primary and secondary. You can see here, primary and secondary. F B, primary and secondary. F C primary and secondary. To windings for each of the phases. Similar to the single phase in single phase, we had primary and secondary. Now, since we have A, B, C, or three phase system, then we will need this three of the two, and three. Okay. So one, which is this part, two, which is this part, and three, which is this part. Okay. So let's delete those. So you will see it like this so you can see the high voltage winding, then high voltage insulation, similar to the single phase that we discussed before. High voltage then high voltage insulation, then low voltage winding, then low voltage insulation, similar to the other types. So we have here, for example, A, B, and C. So these two windings will be around each other. You can see low voltage and high voltage are pretty, pretty close to each other. Now the question is, why do we do this? Why do we make these two windings very close to each other? This will help us reduce the leakage reactants or the leakage reactants inside the transformer. When the two windings are really, really close to each other, this will help reduce the leakage reactants. In the end will reduce the voltage drop in the transformer and reduce the amount of Q inside the transformer. As you can see, this is the core type transformer. Now for the shell type, remember the single phase here, we have one, two, three, four, whatever the number of layers. If you remember it is in the sandwich form. The low voltage and high low volte high voltage are above each other. This is what for a single phase, right? So for the three phase, we are going to do this several times. So this form is like here. Let's say this one is A, A consisting of low voltage, high voltage, low voltage, high voltage, low volte, and so on. F B, same configuration here, for B, same this form, low voltage high voltage, and so on. F C, the same idea, this part. If you look at it more carefully, you will see like this the high voltage and low voltage, high voltage, low voltage, high voltage low voltae and so on. So as you can see, the low volt and di volte are below each other, below each other and in the sandwich form. And again, why do we do this? Why do we make these two winding the low voltage and high voltage very, very close to each other in order to reduce the leakage reactants inside the transformer. This will improve power factor. This will lead to lower voltage drop. So I hope the idea of the ahual type and co type of transformers are now clear for you. So if you look at here, you can see here. This one is A, B, and C, A, B, and C. For example, A, which is this part is consisting of low voltage, high voltage, low voltage. This is only for phase A. Then we have low voltage, high vol low volta, is for phase B, low voltage for phase C. Each ploug here representing low voltage and high voltage or primary and secondary winding of a single phase for each phase. Okay? 49. Three-Phase or Single-Phase Transformers: Okay, so the question is, why do we use a three phase transformer instead of three of a single phase transformer? Why do we use this form three phase arty for example. Instead of using this one, single phase, but three times. Of course, you can see that the three phase transformers are less expensive than three single phase transformers. Because as you can see in this figure that we require less total core material. As you can see here instead of having three of this, a core a block like this, three X of it, we will need just one big block like this, three legs. That takes the three winding. So instead of having this single phase three of this, this will lead to too much material. However, when you make this form, it is more compact and require less material. So less material required and the packaging cost is reduced. Also, we find that this one takes less space than three of this one. If you use three of this one, it will take more space. And of course, the three phase transformer here requires less external wiring. It is really easier. And of course, it is more efficient than a single phase transformer. That's why this configuration is compact, requires less material, less less core material, less packaging cost, less wiring, lighter requires less space, more efficient, and the best thing which is less expensive. Same idea, of course, for the shell type. Instead of using one big block like this, we use this one instead of three of this one. Okay, so you can see the shell type like this is much more efficient than using three of this. Let's delete this. Now, one important note about transformers or single phase and three phase transformers is that in the single phase transformer, we have one voltage ratio that agrees with the turns ratio. If you look at this one here or this one here, you will find that E one induced EMF on the primary over the induced DMF on the secondary is equal to N one over any two. So we have one, which is a turns ratio, A, Okay, Tn is ratio equal to E one over e two, very clear. However, in the three phase transformer, we have two definitions. We have the first one which is the pen ratio or the ratio between line to line voltage, V line of the primary divided by V line of secondary. Ratio between line to line voltage and another definition, which is a phase ratio. It is a ratio of the voltage in the coil which agrees with the turns ratio. What I mean by this V phase of the primary divided by V phase of the secondary, which will be equal to the urn is ratio A. So again, in the single phase, we have one definition E one over E two equal to N one over any two. However, in transformers, since we have a primary winding with a certain connection, it can be Delta connection or it can be a star connection, and the secondary can be also Delta connection or star connection. So since we have different connections here, we will have different voltages, not only voltage depending on the tones ratio, but also voltage due to the different in connections. Okay. So we have two definitions here ratio between bank ratio which is the ratio between line to line voltages, and we have phase ratio, the phase ratio, which is V phase primary divided by V phase secondary. This will give us the number of turns or turns ratio to be more specific. So in this lesson, we talked about the three phase shell type transformer and the three phase co type transformer. Now in the next lesson, we will discuss the different connections that we have in electrical transformers. 50. Three-Phase Transformers Connections: Hey, everyone in this lesson, we will talk about the different connections that we have in an electrical transformer or a three phase transformer. So we have four major connections in electrical transformer. There is more connections like this, other than this one like zigzag connection that we will discuss, maybe we can discuss in another lesson. But there are 43 phase transformer connections which are YY or star star connection. Delta Delta connection, Y Delta connection, and Delta Y connection. These are the four major three phase connections that you can find in electrical power system. So let's start and understand the benefit of each of these connections and if they are good or bad. The first one which is YY connection or star star connection. So we have the primary of the transformer is connected in the form of star, secondary is connected in the form of star, since it is YY connection. So the YY connection is rarely used. Now why is this? Because in the star connection, we have the problem of the third harmonics on the secondary lines. So what I mean by this, let's say we have here our loud. So we have here our supply, our generator, three phase generator connected to the primary, and the secondary will be connected, for example, to the loud as an example to our loud here. Okay? Now if this lute is using power electronic equipment, power electronic equipment, then this loud will absorb or take harmonics or will have harmonics, due to the presence of power electronic equipment. So the most important harmonic is the SOD harmonics. What I mean by SOD harmonic sOd harmonic which have a frequency equal to three times the supply frequency. So these harmonics are, for example, current harmonics. Okay, current with a frequency three times the supply frequency. Now, this harmonics causes overloading on transmission lines, causes more losses in electrical power system lead to reduction in power quality in electrical power system. So that Sod harmonics, we need to trap them or eliminate them. However, the currents, these currents which are at the allude site, they will be transformed to the primary site and cause issue in electrical power system. That's why YY connection is not helpful in this case, if we have a ud and the primary is from a generator or from transmission line. This transmission line will take the sod harmonic currents. So in this type of transformers, there is no phase shift between primary and secondary senses. They are Y Y transformers. Now, what is the ratio between voltage bank ratio, which is a line to line voltages, secondary line to line and primary line to line, which is line of secondary. Divided by V line of the primary. Now, if you remember that V line in a star is equal to root three V phase, right? And V line of the primary, V line here since it is Y connection, it will be root three Vhase. Root three will go with root three, so we will have V phase secondary over V phase primary, which is a turns ratio. Okay? So in the end, the ratio between line to line voltage or the bank ratio, ratio between secondary over the primary line to line voltage is equal to the phase ratio equal to the turns ratio. Since the are the same connection, YY connection. Now let's talk about Delta Delta connection. So in the Delta Delta connection, we have Delta in the primary and Delta in the secondary. Now, this connection does not have any no harmonic problem. Now, why is this? Because as we said before, if we have a load here, which consisting of load here, that takes this three phase power. If this one has harmonic currents like this, which have frequency three times the supply frequency, these currents will be inside the Delta. Now, without going into much details, you will find that using a Delta connection here, the harmonic currents will cancel each other. Okay, they will be trapped. They will not go back to the power system or not go to the transmission lines or the generator. They will be trapped inside the delta connection itself and they cancel each other. They will not flow to the electrical person. They will be trapped here inside the Delta form or Delta connection. That's why this type of connection does not have a harmonic problem. Another advantage of this one is that we can remove one phase of the transformer to be repaired, and the remaining two will keep delivering electrical power to the three phase system at a reduced rating of 58% of the original power. This is known as the open Delta or V connection. What does this even mean? Open Delta or V connection? Let's look at this one. Let's say I'm going to take this part for repair. We will remove this winding completely for repair. It will be like this, it will be like this A, A, going to this winding like this. Mm hmm. And we don't have here anything, then we have B, B, then we have this winding like this. Okay. Then we have C. So you can see, A, B, C, the three phase power will go like this, and it will give us electrical power to the other side. Okay? So we remove here and remove the same winding from here. So if we remove the A, we will remove it from here. Okay? So you will find that ABC will still provide electrical power. To the system. Okay? So as you can see, this one is known as open Delta because we took one of the winding, so the delta is now opened. And the same time it has or it's called V connection. So why it's called VN connection. If you look at this figure here, you can see it is in the form of V, as you can see here. That's why it's called V connection. So the question is, can we do this removing of one phase in the Y connection? No, we can't do this. If we get back here. Let's say, for example, you removed this one. This one here. So we will have A like this. Then we will have open circuit, open circuit, we have B, like this and C, like this. So you can see, B provides electrical power. C provides however, A is open circuit, so it cannot give any electrical power. So we cannot use this formation. So the delta is helpful in this function in giving electrical power at a reduced rating or reduced rating. The only problem with respect to Y connection is that the Delta class, the insulation class of the windings must be for the line to line instead of the line to neutral or the phase voltage. What I mean by this each of these phases has insulation, right insulation that can withstand the breakdown voltage. So if you look at the two, this formation or the delta, the insulation class must withstand line to line because the V line to line is equal to the phase voltage. Voltage across the phase is the line to line vote. So we need insulation that must withstand the line to line voltage, which is larger value than phase voltage, in Y connection. So if we get back to Y connection here, for example, let's lead first. So if you look at here, what is the voltage here? Voltage here is V phase, V phase, which is V line divided by root three. So the insulation required here is lower than the delta. Why? Because of phase voltage here is Vline divided by root three. So the voltage is lower, which means we need lower insulation. That's why here in the delta, the voltage the phase must withstand the line to line voltage, so it will need more insulation compared to the Y connection. Now, if we do the bank ratio, same idea. Bank ratio line to line, Vline VLAN is equal to V phase and Vfs equal to the tone is ratio, similar to Y Y. Okay? Now let's talk about the Delta Y connection and Y Delta connection. These two connections are really important. Now, we usually use Delta Y connection is commonly used to step up the voltage. What does this mean if we have a generator here? Usually, if we have a transformer that connects to the transmission line or transmission system, then we will need a step up transformer or increase the voltage. Y in order to step up the voltage in order to reduce or reduce the losses in electrical power system, as we discussed before. So if we have a generator connected to a transformer at the side of the generator, we will have the Delta connection. And the side of the transmission line, we will have the Y connection. So it is used to step up the voltage. Now when possible, Y is connected to the high voltage site. So why do we connect this one to the high volta site? Because it will require lower insulations than using Delta here. Remember, if we use the Delta, the voltage on the phase will be line to line, which means we need more insulation. However, here, the voltage across the phase is V line divided by root three. Okay. So we use Y at the transmission system and Delta at the generator because here we have the high voltage side, so we will require less insulation compared to delt. At the same time, we use Y Delta because if we have harmonics in this side, it will not be transferred to the generator. It will be trapped inside the delt. Okay? So any harmonic currents will be trapped here in south Delta and it will not go to the generate. So we do two functions here. Number one, we reduced the amount of insulation required, and at the same time, we help it in eliminating or removing the harmonics from the generator itself, preventing the harmonics from traveling to the generator. Another thing you have to understand that Delta Y connection can be used at the distribution system or at the end user. Remember that we need, so for example, it can be connected here to the transmission system. Then at this side, we will have our loot the low voltage system, which is 380 volt as a line to line or it can be changed from one country to another. So why do we do this? Because for the load, we sometimes we need also the neutral. So each load here or a single phase load, it will need phase plus the neutral, right? So since we need the neutral, Delta does not have in neutral. So in order to get the neutral, we will have a Y connection at the load side at the end of the distribution system or the utilization of the electrical power. Now the issue here is that secondary line to line of V primary. Remember here, V line of the secondary. Look at this shape. So V line of the secondary line of the secondary is equal to V phase, mata blood bi root three because it is a Y connection. For the primary, V line to line is equal to V phase. So it will be line equal phase. So you will find that the ratio between the bank ratio, which is the ratio between the line to line voltages is equal to root three multiplied by the turns ratio. The ratio between V phase and V phase here is A or the turns ratio. However, the ratio between V line to line and V line to line is root three multiplied by turns ratio. The last connection is Y Delta. This one is commonly used to step down the voltage or the high voltage to a lower voltage. We can use take here from the transformation line. Then we start stepping down this voltage to distribution network or lower voltages. Then another time we'll take this delta and we connect it to a Y transformer for utilizing the electrical power. It depends in the end on the structure of the electrical power system. The issue here, which is secondary line to line volts over the primary line to line voltage will be V line secondary over V line primary V line secondary, line secondary is equal to the phase because it is delta connection. However, V line of the primary is equal to V phase multiplied by root three. So it will be A over root three. In this lesson, we talked about the different connections that we have in electrical transformer or in electrical power system. 51. Solved Example 1 on Three-Phase Transformers: Hi, and welcome everyone. In this lesson, we will start having some solved examples on the three phase electrical transformers to understand how can we apply the previous connections. So we have a step down transformer. Again, step down transformer. Connected to an 11 kilovolt supply takes 6:00 A.M. Pair current, and the turn ratio is 11. Remember here, it is a step down transformer. First, determine the line voltage at the secondary side, the line current in the secondary coil and consider the Delta Y and Y Delta connections. So we would like to find the line voltage at the secondary site, line current in the secondary coil, when we have Delta Y connection, and when we have Y Delta connection. So let's start. So we have 11 kilovolt supply, 6:00 A.M. Pair inbot current, and the turns ratio is 11. Remember, it is a step down transformer. So the first connection that we would like to find is Delta Y connection. Delta Y connection. Okay. So 11 kilovolt supply, what does this mean? It means that always always when we have a certain value of the voltage, a given, it means the voltage is line to line, root mean square. So 11 kilovolt is line to line voltage, root mean square. So the line to line voltage of the delta here is 11 kilovolts. V line to line of the primary is equal to 11 kilovolt and as you can see from this figure or from the delta connection, you know that the phase voltage is equal to the line to line voltage. So this will be equal to V phase of the primary. And it takes six and pair as an input current. So the current input current here is six and pair. What does this mean? It means the line current input line current. Okay. Okay. So the six pair here is the line current. So what about the phase current? What is the value of the phase current? It will be six a pair, divided by root three, as we learned before. We said before that the value of the line to line current or line to line voltage is equal to V phase multiplied by root three. So if I would like the phase current, it will be the line current divided by root three. So what we would like to get if we get back here, we need to find the line voltage at secondary and line current in the secondary coil. So we need to find line to line here, and we need to find the line current, which is similar to the phase current. So let's start with V line to line. So we now have the line to line current or line to line voltage equal to the phase voltage, equal to 11 kilovolt. And this one is a step down transformer. 11 here A equal to 11 equal to the ratio between between the primary V phase, primary or V phase, secondary, right? Why? Because it is a step down transformer? So from here, the V phase here for the primary is what is 11 kilovolt. So from here, we can get the V phase of the secondary. So the V line line of the primary equal to V phase primary, equal to 11 kilo volt. From here, the phase voltage at the secondary side is equal to V phase. Of the primary, divided by the turns ratio which is 11, as you can see here. So it will be equal to 1,000 volt. Okay? So this is phase voltage, this voltage phase voltage of the secondary, but I would like to get the line to line voltage. So it will be the phase voltage multiplied by root three. Right? Because in the Y connection, the phase equal to line to line divided by root three or the line voltage, line to line voltage is equal to the phase voltage, multiplied by root three, as you can see here. Now, what about the current? We need this current. So first, let's get the phase current. So we know that the phase current here is equal to six divide by root three. So what about here it will be since it is a step down transformer, it means that the voltage decreases, right? So the current will increase. They are opposite to each other. So if I would like the current or phase of the secondary, it will be the phase current of the primary. Multiplied by 11. So as you can see here, here, we divide it by 11 since it is a step down transformer. However, for the current, it will be what will increase the current. So it will give us the I phase of the secondary. So as you can see here, you can see here that I phase for the primary is equal to six of root three, as we said, and the I phase of secondary which is equal to I line will be the primary multiplied by 11 as we did here. So let's delete all of this to make it clear. So the phase current in the primary I phase, the current here will be equal to the line current divided by root three, and the line current in secondary line current is equal to the phase current. So it will be equal to the number of tons or to ratio multiplied by the phase primary. To get I phase secondary, which is the line to line current or line current. Okay, so what about Y delta connection? The same idea. As you can see here, 11 kilovolt means that the line to line voltage is 11 kilovolt. And since we are dealing with a star connection, then the phase voltage will be 11 divided by root three. The line voltage as a prime is 11 kilovolt and the phase voltage at the primer is line to line, divided by root three. Which is this voltage. From this voltage, we can get the secondary voltage, which will be this value divided by the turns ratio, which is 11 because we are comparing phase with another phase. So it will be like this. V phase of the secondary will be V phase of the primary, divided by the turns ratio. So it will give us 577 volt. Okay? Now, V phase of the secondary is the line to line voltage required because it is a delta connection. In the delta connection, the line to line voltage is equal to the phase voltage. It will be like this, line voltage as a secondary will be equal to the phase voltage, equal to the same value. Okay, what about the current? We have six a pair, 6:00 A.M. Pair, which is a line current, which is similar to the phase current of the transformer or the Y connection. I phase of the primary equal to I line of the primary equal to six ampair. The line current is equal to the phase current. Okay? So that is the first part. Okay? Now, I would like to get the line to line here. So first, you will get the phase current, this current. Okay? So we will see what is the relation between the phase. It will be. This one is six and pair, so it will be six a pair, multiplied by ton is ratio. Six a pair, multiplod by tone is ratio. Why? Because it is a step down transformer. So the voltage is reduced by 11, so the current will increase by 11. So it is 11 multiplied by the phase current of the primary. So the phase current of the primary is six a pair. Multiplied by tonus ratio gives us the phase current of the second ring. Now, I need the line current. The line current will be phase current multiplied by root three. Okay. So in this solvit example, we learned how can we apply the Delta Y connection and Y Delta connection in order to obtain the voltages and currents in the secondary. So we now understand that it is similar to the similar to the single phase transformer, but the only difference is that there is a change due to the connection. The difference between star and Delta connection. 52. Solved Example 2 on Three-Phase Transformers: So now let's have another solvid example on the transformer. We have a three phase transformer, 50 Hurts three phase, 50 hertz transformer with a Delta connected primary and star connected secondary. The primary delta secondary is a star connection. The line voltage being 22 kilo volt and 400 volts. So the line to line voltage here 22 kilovolt and the line to line voltage here 400 volt. The secondary has a star connected balanced loud, so it has the same resistance and inductance or the same imbedance that this impedance equal to this one, equal to this one. This means it is a balanced loud. If these values are different from each other, it will be unbalanced loot. So it is secondary with a balanced loot at 0.8 power factor lagging. We will understand how can we use this later in the problem. The line current on the primary side is five and pair. So the line current here of the delta is five and pair. So the phase current will be five divided by root three. Okay, find the current in each coil of the primary and the secondary line, and what is the output of the transformer in kilowatt? So the first part which is the currents, we have the line current equal 5:00 A.M. Pair of the primary and the phase current of the primary will be five a pair divided by root three, right? So the phase voltage on the primary side is equal to 22 kilo volt, 22 kilovolts is equal to the line to line voltage of the primary. You can see line to line, equal to the phase voltage. And for the secondary here, we have the line to line voltage equal to 400 volt, which means that the phase voltage here will be equal to 400 divided by root three, as we learned. So from these two values, 22 kilovolt phase voltage of the primary and 400 divided by root three, which is a phase volta secondary, we can get the turn is rich. Okay, so the phase voltage on the secondary 400, divided by root three. So from here, we can get the turns rich. You can see any 2/1, A two over N one. So it will be like this. A two, 400, divided by root three. And 400, this is divided by 22. It will be like this multiplied by 22 kilovolt. In summary, it will be 400, divided by 22 kilovolt, multiplied by root three. I will give us this value. You can see here that the definition of turns ratio changes from one reference to another. So we have some reference says that the tones ratio is equal to N one over N two. And in this problem, for example, it is the tons ratio which is denoted by K K here representing the tones ratio from another reference. It is equal to N two over N one or V two over V one. So it depends on the reference itself. Okay? We have this tons ratio. Now, how can we use this tons ratio? First, we will get the primary phase current. The primary phase current is this current here. So the phase secondary current, what's the value of the phase, secondary current, which is the secondary line current. They are similar to each other. The second phase current I phase two will be equal to the primary phase current five divided by root three, This is a phase of the primary I phase one divided by what divided by the tone is ratio K divided by K. Why? Because here as you can see, this ratio is N two over N one, right? So in order to get the secondary voltage, it will be primary multiplied by this ratio. However, for the current, it will be the primary current or the phase primary current, divided by the turns ratio. So it will give us finally like this. So you can see five or three divided by K. Give us 275 and par. As you can see in order to make sure that you are solving the problem correctly, you will see that. If you look here carefully, that we started with 22 kilo volt as a phase voltage. Then since this one is a step down transformer, you will find that the phase voltage became 400, divided by root three, so the voltage is reduced or reduced. So the current should increase, since we have the same power. You will see that we started with five of root three and pair for the phase current. Now at the secondary side, we have 275 pairs, so the current increased. So we are solving the problem correctly. Okay. So what is the next step? So we obtain the primary phase current, secondary phase current, which is similar to the line to line current. Now we need to find the last thing which is power. You can see secondary line current, similar to the phase currency are similar to each other. Line current and phase current. Now, let's get the output power in in what unit kill what. Remember, kill what. Power in general, power in general is equal to three multiplo by V phase, multiplo by I phase, Okay. This gives us the apparent powers. However, we need the active power. So we multilize this Pi the power factor. So you will have three V phase, I phase, power factor. Or you can do another thing, which is power is equal to root three, V line to line, I line to line. But the blood Pi is a power factor which is also known as cosine Pi. So as you can see, we use the second one root three, V line to line, I line cosine Phi. So root three, Vline which is a line to line voltage, 400 volt, I line, which is similar to the phase current, which is 275 and cosine phi, which is the power factor given in the problem, which is 0.8. If you get back to the beginning, you can see 0.8 power factor length. This is a power factor of our loot. Okay. So this finally gives us the output power, absorb it or output active power absorbed by the load is equal to 15.24 kilo watt. So this was another solved example on the connections or Delta Y connections or Y Delta connections in the electrical transformer. 53. Vector Group and Nameplate of a Three-Phase Transformer: Hi, and welcome everyone to this lesson in our course for transformers. In this lesson, we will talk about a very important topic in electrical transformer or three phase transformers, which is a vector group. So what is the vector group? The vector group is related to the IAC method of categorizing the high voltage windings and the low voltage winding configurations of the three phase transformers. And what is the IIC, it is, of course, well known standard, the IAC standard, the IE standard, the NEC standard, the IEC which is abbreviation for International Electrotechnical Commission. So the IEC helps us to identify the high voltage winding, connection, the low voltage winding, connection, and the phase shift between them. So this will help us find the winding configuration or indicate the configurations, and at the same time will help us to identify the phase shift between them. As an example for the vector group that you will see on the three phase transformers, DYN 11, Y ND, Y ND, 11, and so on. So what does this even mean? So first, where can we find this vector group? We can find it on the name plate of the electrical transformer. As an example, this is an electrical transformer from APP. So let's look at this nameplate and understand more about it. So the first thing that you will see here is that this APP ran three phase transformer has number one, a rated power of 100 kilo volt and pair. This is a rated output power input power and output because the transformer has a very high efficiency. Number of phases three. So this is a three phase transformer. You can see this is a standard IIC standard at which this transformer falls or the standard that the transformer follows. We have here the rated voltage. You can see high voltage and low voltage. You can see 11 kilovolt and the low voltage is 415 volt. Okay? So it can be a step up transformer or a step down transformer depending on the application. Okay, you'll find here plus minus two multiplied by 2.5%. So what does this mean? You can see at the high voltage site, this transformer is with a high probability. This transformer is a low or a step down transformer. This transformer takes the 11 kilo volt and steps it down to 415 volt. So what does this part mean? This part is related to something which is called the type changer. A function that we will learn about in electrical transformer. So you'll see that this is a high voltage site, and this is a low voltage site, high voltage winding and low voltage winding. You will see that here, this transformer has tabs plus or minus two multipled by 2.5%. So what does this mean? You will see that here. There's five tabs. Because we have plus minus two multipled by 2.5%, so we have. It can be plus 2.5%. Or plus two multiplied by 2.5%. It can be zero. It can be can be -2.5%. It can be minus two multiplied by 2.5%. So what does this mean? It means that we can control the rated inbut voltage. We can increase it or decrease it or keeping it at the 11 kilovolt. So you can see here that. For example, at the tab number three, we will have this amount of winding. This amount is equivalent to number of tons that will give us 11 kilovolt. If, for example, I would like to increase 11 kilovolt to greater value, I can connect it to, for example, 0.2. So we will have more number of tours, or I connect it to one to have more number of tours, the whole tons. This increase in tours will be equivalent to increase in voltage by 2.5%. Here, increase by two meta blate by 2.5, which is 5%. So here will give us an increase in voltage by 5% from the 11 kilovolt. The same idea if you go here upward, if you connect it here, you will decrease the amount of windings by this amount. You will remove this winding. If you go here, you will remove 5% from the 11 kilovolt. So this type changer is helpful in different loadings of the transformer. So you can see here this is the tab changer part. Now, another thing here you can see the current, the current at the high volt site, the rated current at the high volta site, and rated current at the low voltage site. Okay? So let's use Okay, let's use this one. Okay. Here you'll find another thing insulation level. So what does this mean? Insulation level for the high voltage and low voltage? You can see for high voltage, this part, and for the low voltage, this part. So what does this mean? You have to understand that the high voltage side in the electrical substation, since our transformers are in electrical substations. So the high voltage site is coming from that transmission line. So we have our transmission line. Like this, which are exposed to air. These lines will go to the transformer like this. These lines will go to the transformer like this. Okay? So this part is exposed to air, okay? And exposed to the lighting itself, okay, lightning from the sky. So we should make the high voltage part. Should withstand the effect of lightning on it. Okay? So we need to have some sort of more insulation level or higher insulation level. So it should withstand this high voltage due to the lighting itself. So you can see here that the insulation level, you can see here LI means lighting. Okay? And 75 means what means 75 kilovolt. So this one has an insulation level that can withstand a voltage from lightning up to 75 kilovolt for a very short time. And it can also, you can see here, AC 28, AC which means the normal power frequency. So voltage, increase in voltage at power frequency can withstand up to 28 kilovolt. Okay, so let's delete this like this. You can see Li 75 means that the 11 kilovolt transformer, high voltage winding. We are talking about high voltage which is 11 kilovolt normally. Can withstand a lightning impulse up to 75 kilovolt for a very short time. And at the power frequency, which is 50 Hearts or 60 hortis, can withstand up to 28? This part relate to AC 28 at the power frequency. Li 75 lighting impulse up to 75 kilovolt. For the low volt, since the low voltage is 415 is going into the underground cables, it will not be exposed to lighting. You'll find that it has only one protection, which is or not protection, an extra. Insulation level, the insulation level itself of the windings can withstand up to AC What means at power frequency three kilovolt. This is the insulation level. Of the low voltage winds. You can see it is normally 415 volt for the short circuit case, not the short circuit for over voltage case, the insulation level can withstand up to three kilo volt. That means AC. Now, another thing here, you can see the ambient temperature. The temperature surrounding the transformer is normally 40 Celsius degrees. The allowable temperature rise of the winding itself is 60. What does 60 K mean? Sext Celsius degree, and not Kelvin. Sexty Celsius degree, the oil, which is a cooling part inside the transformer itself, this is a transformer oil transformer. As we will discuss later inside the course. This oil transformer has a temperature rise of 55 Celsius degree. Now, another thing here, you can see total mass and so on. Noload losses, the losses without connecting any load. If you remember at the nad losses is due to RC here, the resistance inside the core itself and the winding resistance of the primary. Okay? So this losses is very, very small, 145 watt, very small n load losses. That's why it has a high efficiency. And when we have a load connected, it will have a losses of 1.7 kilo watt, which is very, very small compared to the 100 kilo volta empire. The total mass of the transformer itself is 463 kilogram. The mass of the active part is 279. What is the active part in the transformer? The active part is the mass of the windings plus the iron core. We have some extra configurations or extra information about the oil inside the transformer itself. You can see here the core material, this is made of steel. This is the material of the core itself and the mass of the core. This representing the ratings or the values of the transformer. Another important part in the transformer, which is the rated frequency, operational frequency, which is 50 Hertz. You'll find also the short circuit imbedance in percentage. This representing the representing the z as a percentage of the transformer. Z of the transformer, which is a resistance and inductance but in per unit system in per unit system. The transformer itself that itself is divided by that percentage is divided by the base value, the base. So that actual of the transformer we divided by Z pairs, multiplied by 100%. Okay? So this is the meaning of short circuit embed the embedance of the transformer itself. So if you don't understand what does a pair unit system mean, you have to go to our course for power system, in which we explained in details about the pair unit system. Los in the details, we have the cooling method and the connection symbol. So the cooling method is ON AN. What does this mean? It means oil, natural, air natural. So the heat energy inside the components or the windings of the transformer is transferred to the oil first. Then the oil will transfer this heat to air naturally. That's why it's called oil, natural air natural. We will discuss the cooling method, of course, inside the construction of the three phase transformer in the next lessons, don't worry about this. Now the point which we are talking about in this lesson, which is a vector group, which is DYN 11. You can see this one. This will help us to understand the connection of the high voltage, connection of the low voltage, and the phase shift between them. So before we end this lesson, let's understand the victor group. So DY N one, what does this mean? The first letter, which is D Delta. So this representing the connection of the high voltage winding, high voltage wind not primary, but high voltage winding. So the high voltage winding here is a Delta connected. Second letter is a low voltage winding. Low voltage winding here is a Y or a star connection. N means that the neutral exists inside the Y connection. So sometimes we have Y and the neutral does not have any wire. And if this neutral has a wire, it will be Y N, since if it has a wire. Okay? So the neutral exists. Now the last point here, which is one, what does one mean? It is a phase shift between the low voltage winding and the high voltage winding. Okay. So how can we translate one into degrees? Okay, we would like to transfer this one into degrees. So it will be like this. Here, what are we going to do? We will start by having our clock here. You can see this clock here. This will help us to draw the transformer and the connection or the winding of the transformer, as we will see in the next lessons. So we have two arrows here inside any clock. We have one, the longest one, which is this blue one for the minutes. Okay. And we have the shorter one which is for the hours, right? So the longer one, which is a minute is our reference one, or our reference value. So 12:00 means zero degrees. Okay? One means negative 30 degrees. Okay, negative 30 degrees. Two means negative 60 degrees. Three means negative 90 degrees. Four means negative 120 degrees and so on. So here, this will help us to draw the phase shift between the two connections. So as you can see, one here means one, what does one mean? It means negative 30 degrees, negative 30 degrees. So what does this mean? It means that the secondary, not the secondary. The low voltage has a negative 30 degrees from the high voltage or the low voltage winding is lagging by a 30 degrees from the high voltage winding. Okay? So first, what are we going to do? Number one, the blue line or the minute arrow will be constant. It will not move at all. It will be at its place the whole time. So that 12:00 is our reference, zero degrees. As you can see, zero degrees, zero degrees, our reference. This blue line representing the high voltage. First line or the minutes arrow representing the high voltage. The shorter hour which moves, which is the hour representing what representing the low voltage winding. So as you can see, the red one is the one which moves the whole time. So as you can see, red one here representing at one means negative 30 degrees. However, at 11, it will be plus 30 degrees. Okay. At six will be 180 degrees. Why? Because as you can see, here, negative certy negative 90, negative hundred negative cert, negative 60, negative 90, negative 120, negative 150, 180, negative 200 and negative 210, 200 and negative 240, negative 270, negative 200 300, negative 330. Okay, and then zero. So here, this direction is negative. Okay? So as you can see in the end, 11 is negative through 130, which is equivalent to what equivalent to plus 30 degrees, right from mathematics. Add to it through 160 degrees. So it will be plus 30 degrees phase shift. Okay? So as you can see here, we have zero negative 30. Whatever the number here, it will help us identify if the winding, leading or lagging p certain ang, okay? So remember that the rotation in this part, the postive rotation is anticlockwise. So the normal rotation is like this, which is representing the positive value. So here you can see both of them are above each other, so it is zero degrees. Here you can see for the positive rotation, anticlockwise, that 12 is leading one. That's why we say that one is lagging by negative 30 degrees because our direction is anticlockwise. Here in this one, you can see this arrow for the low voltage is leading the blue one since our direction is anticlockwise by how much 30 degrees only. So it will be plus 30 degrees. Here it is a phase shift 180 or negative 180, they are the same. So one means 30 degrees lagging, low voltage, legs, high voltage with 30 degrees. 11 means round and 30 degree lagging or 30 degrees leading. So the low voltage leads the high voltage with 30 degrees. So in the next lesson, we will start talking or giving an example or several examples on the vector group. 54. Drawing Connection of Dyn11 of a Three-Phase Transformer: Okay, so let's have the first example on the drawing connection of the DYN 11. So we have DYN 11. Okay. Okay, so DYN 11, what does this mean? It means? D means Delta, which is a high voltage. YN means the low voltage. Okay. And 11 here means what means the phase shift between low voltage and high voltage. And we said before that the line like this, this is the first one here. This is a reference value, which is a high voltage, and the low voltage is here 11 11. So it means that the low voltage leads the Delta by 30 degrees. Since it's leading here by 30 degrees. Okay, this is for our knowledge. Usually this type of connection is used in the distribution transformer or the step down transformer at the end of the power system network, DYN 11. Okay, so let's understand how this will help us to draw the connection. We need the connection that will achieve 30 degrees shift leading for the low voltage. This one is the high voltage, and this one are the three phase low voltage wind, three phase high voltage, three phase low voltage, and our clock. So let's start step by step, okay? So we have first delta. Okay? So our Delta starts at the 12. Okay? Starts like this at 12. Now, this is a zero degrees. Okay? Now, remember that for A, B, C system, A is our reference. Let's say Sta angle theta. Let's make it zero. Okay? Let's make it zero angle. Now B what about B? B is lagging by negative 120 degrees. Okay. C, leading by 120 degrees. So let's identify this point. So the first 0.12 means zero degrees. Okay. Second point is negative 120 degrees. So since we are talking negative, it means in the clockwise direction. So this point is negative 30, negative 60, negative 90, negative 120. So this is the second point here. Okay? And C plus 120 degrees from A, so it will be plus 30 plus 60 plus 90 plus 120 degrees. So this is a third point, like this. So what are we going to do? Okay, we are just going to connect our delt, like Okay. And the last one like this. So this is a high voltage high voltage connection or the high voltage drawing on the clock, which is the first connection. Okay? Okay. What about Y and 11? Okay? So the second connection is Y with the neutral. So this point representing our neutral, what it like this. Neutral. Okay, so this Y starts at 11. Okay? Starts at 11, like this. Okay. This is the first point here. Let's say this one is A. Okay. So 11 is the first one. What about B? B is lagging by negative 120 degrees from A. So here, this is our A. So we have 30 then we have Sekisty negative sexisty, then negative 90, then negative 120. So this is our B at this location B because it is 120 degrees from A, which is at 11. Remember, our reference here for the star is at 11. So B will be at three. Okay? What about C? C will be leading by 120 degrees. Okay, so it will be plus 30 plus 16 plus 90 plus 120 degrees. It will be like this at this point. So this will be our C. A then B, then C. Okay, A, B, C. Now remember, all of the currents are going out from the neutron. A will be like this, B like this, and C like this, A, B, and C. Now, what is the next step? You will find that this line, this line of A is parallel to this line. So our first winding, this is our first winding, the low voltage winding A. So this one will be H one. Since it is the first letter A, this one will be H one, and it will have the same direction of A like this. Look at B, B like this, which is parallel to this one. So this one will be the H two and have the same parallel direction. What about C, C is like this, parallel to this line and same direction. So it will be like this, the final figure. So as you can see, X one, X two, X three or ABC this one is H one, H three. Since it is parallel to C, this one is H three. Okay, and H two. So as you can see, white is important because this direction will be important in the connection diagram. So I hope the idea is clear. First, we draw with the delta, which is reference at zero degrees, zero, 120, 120. Then we draw it our Y, starting from 11 and first shift 120, past shift, 120, and all of the currents going outwards. So we have X one, X two, X three. Now, X one parallel to this line. This one will be H one with the same direction. This line, barrel to this one in the same direction. This line, barrel to this one in the same direction, and so on. This will help us in drawing. How it will help us. Let's start with the easiest one, which is X one, X two, and acces three. You can see they are having one common point. All of the currents going outward, X one, X two, access three, X one, x2x3. All of them are going out from the neutral. All of this point will be the neutral. Very easy. Then we'll have X one, X two and access three, we'll have X one, X two and excess three, which is a three phase input. That's three phase terminals. Like this. Very easy. What about H one, H two, H three? You will understand the importance of this part. So we have H one like this, then H three, then H two. Let's start, for example, for H one. Look at H one. The end of H one here, this is a start, and this is the end. End of H one is the beginning of H three, right. So H one starts from here and ends here. The end to point of H one is the start of H three. Okay. So the end point of H one is the start of H three, so it will be like this. Like this. Why? Because H one then H three. H one then H three. Look at H three, end of H three is the beginning of H two. End of H three is the beginning of H two. It will be connected like this. End of H three is the beginning of H two and the end of H two is the beginning of H one. End of H two is the beginning of H one, so it will be like this. Then we will have the three phase terminal. It will be like this. As you can see, H one, beginning of H one is the end of H one is the beginning of H three. Beginning of H one is beginning of H three, end of H one, beginning of H three, H one to H two, H one to H two, h2h3, and so on so we have a PC. And for this one, the neutral, then A, B, C. Okay? So I hope now it's clear how can this connection, as you can see here, form it a 30 degree shift between the star and delt in which the star is leading by 30 degrees. Okay? How did we do this by doing the clock? Which helped us to draw this connection? In the next lesson, we will have another example. 55. Drawing Connection of YNd11 of a Three-Phase Transformer: So now let's have another example. We have Y ND 11, which means that the high voltage is a star connection and the low voltage is Delta and the first shift is 11. So we have the high voltage, winding and low voltage winding. Let's start by the low voltage with a high voltage winding. Y ND, YN is a high voltage. This one will be our reference 12, four, and eight because the phase shift between them is 120 degrees. Now the first one is Y, it will be like this. Mm hmm. Like this, and like this. Okay, high voltage H one, H two, H three, it will be H one, H two, and H three, like this. And all the currents going outward. Very good. Okay? This is our neutral Okay. So again, star starting from the reference, which is 12, which is zero degrees minus -120 degrees plus 120 degrees. Okay. Then we have the Delta starting from 11. So we have here 11. Then we are looking for the second point. We have 30, sexist, 90, 120, so this is the second point. Then 30, sete, 120, 30, 60, 90, hundred 20, so this is the second point. Then we will draw our Delta like this, like like now let's look at the parallel. You can see that this line parallel to this line. So the direction is upward, so the direction here will be also upward. Okay? This one will be X one. Why X one? Because this one is H one. So this one which is parallel to it is X one. Now, what about h2h2 here is parallel to this line. So it has this direction. So this one will be the same direction. H two, so this one will be X two. This one is parallel to this one. This one is H three, which is parallel to this one, which is X three. Okay, so the final figure will be like this, as you can see here, X two, X one, X three, as you can see, H one, h2h3, same as we just drawing. Now, let's draw the connection. The star is the easiest one. You can see H one, h2h3. So let's draw the star. So we have one neutral point like this and all of the currents going out from the neutral. So it will be first terminal, second terminal, and third terminal. X1x2 and X three, let's start with X one. The X one end of X one, which is this point, end of X one, you can see going upward, going upward. So this point is the end, right? Connected to the beginning of X two, connected to the beginning of X two, like this. X two, Ed is connected to the beginning of X three. X two, can see going upward, going upward, this point, connected to the beginning of X three. So it will be like this. Then end of X three, which is this point, connected to the beginning of X one. So it will be like this and we will have one, two, and three, like this. So as you can see, like this. Uh huh. As you can see, all of them give us the final four. So this was another example on the drawing the connection of the Y NED 11. 56. Drawing Connection of Dyn1 of a Three-Phase Transformer: Now let's have another example. Let's draw the connection of DYN one. DYN one means Delta for the high voltage. YN is low voltage which is star connection, low voltage with a neutral, and one is angle of low voltage which is negative 30 degrees, lagging by ty degrees from the high voltage wind. Now, one important mood here you have to understand is that the first letter is always capital. This title is capital all of it, it is not clear this part. So the first letter for the high voltage is capital D or YN like this. Second letter for the low voltage is small, so it will be like this Y N one. Small. Here, if it is D, it will be like this D one. So the first one is capital representing the high voltage, and second letter is small, which representing the low voltage. Okay? Okay, so let's start. First, we have Delta at our reference, which is 12, four and eight. It's really clear now. Okay, 120, 120, and 120. Okay. So let's not draw H one, H two, three now because we don't know their directions in the delta. When we draw the star, we will know this. Then we have Y and one. Y, which is a star at one. So the first point here, which is a zero angle for the Y is X one, X one. Now, there is a phase shift, 120 degrees, 120 degrees. Okay, so 30, 60, minty, 120 this point. Then 30, 60, 90, 120, like this. So this one is a star. This is our neutral. So we will have like this one, two, and three. So this one will be X one, X two, X, three, all the currents going out from the neutral, line like this, like this, and like this. Now, let's start with X one, X one like this going upward this line parallel to it, it will be the same direction. This one is X one, so this one will be H one, then let's see X two. This X two is parallel to this line like this. This one is xi two, so this one will be H two. This line parallel to access, like this. So it will be H three. So the final draw, you can see X three, parallel to H three. This one is H three, of course, H two, parallel to X two and same direction, X one, parallel to H one. Now, why do we do this? Of course, because each winding, if you remember, in the three phase transformer, each one are surrounding each other. So they are parallel to each other. The high voltage and low vol winding are parallel to each other. So they have the same direction. Okay? Okay, so let's draw the connection. Okay. Let's start with the easiest one, which is the star, again, X one, X two and X three, one neutral point, and one, two, three, and the neutral, of course. H one, H one, end is the beginning of H two. End is the beginning of H two. End of H two is the beginning of H, beginning of H three, like this. End of H two. Okay, sorry, here, this one is not correct. H one, end of H one is the beginning of H two, like this. End of H two is the beginning of H three. End of H two is the beginning of H three. Then end of H three is the beginning of H one, so this will be like this. We'll have one, two, three, and here we will have also one, two, three. This is all what we have, and this is a neutral, and we have one, two, and three, and neutral. So it will be like this. You can see this is a final phone. Okay. Now, we had now three examples on the Victor group. Now, in general, if you would like to see other examples, you can use this figure. You can draw them by yourself and try getting the same configuration. You can see here Y Y zero, DD zero, YD one, DY one, weeded Y D 11, and DY 11. You can start doing them by yourself and see the results. Okay? So now I hope the idea of the vector group is clear for you and you now understand the importance of vector group in three phase transformers. 57. K-Factor of a Transformer: Hi, and welcome, everyone. In this lesson, we will talk about an important factor or important definition in transformers, which is called the K factor. So what does that K factor mean? It is a weighting of the harmonic loud currants according to their effects on the transformer heating and they are drifted from the NC alterable EC 5,710. It is a representation of how much the harmonic load currents can affect our transformer. The K factor representing the weighting of the harmonic load currents. We will see what does this mean right now. So if we have a K factor of one, it means we have a linear load, a linear load without any kind of harmonics. It means it is resistance plus inductance only. JXL or XLJ whatever it is, resistance and inductance or reactants. We don't have any kind of non linear loads. And what I mean by non linear loads is a presence of power electronics, power electronics, such as the rectifiers, DC shoppers or AC shoppers, and so on. So K factor of one means we have a linear load without any kind of harmonics. As this K factor increase, it means our load is having more and more harmonics. The higher the K factor, the greater the harmonic heating effects on the transformer. When a non linear load is supplied from an electrical transformer, this will help us understand what is a problem here. It is sometimes necessary to derate the transformer capacity to avoid overheating and insulation failure inside the transformer. Now why this happens due to the harmonics of the non linear load, this will lead to increase in eddy currents inside the transformer leading to more transformer losses and more generation of heat energy inside the transformer, which means we have a higher temperature rise of the electrical transformer. So let's delete all of this. Now, also the root mean square lot current can be much higher than the transformer reading. So what I mean by this, you will find that our current in normal operation is at a certain frequency, 50 hurts, or 60 hots depending on the frequency of operation of the electrical system. Now, when we have harmonics, we don't have only the 50 hots. We have multiples or multiplication of this frequency. For example, we will have three times the frequency. We can have five times the frequency, seven times the frequency. These are the harmonics which are generated due to the presence of the nonlinear root. In this case, instead of having IRMs of the fundamental only, the IRMs, the root means square current in this case will be root of the I square of the three times the frequency, plus I square, five times the frequency, plus I seven times the frequency, plus the fundamental component. IRMS fundamentals. You will see that it is a square of the summation of all of the currents. In this case, this current can exceed the transformer rating, the rated current of the transformer. That's why we need to derate the transformer, reduce the loading of the transformer to avoid the overloading and avoid the transformer losses. Okay, so how much we are going to de rate our transformer. You can see a transformer rated for the expected load will have insufficient capacity. If we have a non linear load, the presence of harmonic can lead to presence of harmonics can lead to overloading of the electrical transformer. So as you can see here, for example, this is the capacity of the transformer, how much we should load our transformer. However, as you can see here according to the ANC code here, from I E, as you can see here, as the K factor, the K factor of the load itself. The higher the K factor, the more harmonics inside the lot. The higher the K factor, the more harmonics inside the load, which will lead to greater harmonic heating effects. Okay? So what will happen is that as the loot K factor increase, the more harmonics inside the root, what are we going to do? We will start decreasing the rating of the transformer or we will start de rating the transformer. So when we have, for example, at one you can see we can reach up to 100% of the transformer. K factor of one means we don't have any kind of harmonics. However, if we have a loud with a K factor five, it means we will go up here and you can see it is approximately 90%. So in this case, we can only use 90% of the capacity of the transformer. If it has 20, for example, K factor 20 is a loud itself, it means we cannot exceed about 65% of the capacity. So that's why in order to stay away from this, or let's be more clear. Let's say, for example, I have a K factor of 20 K factor of 20, it means that I can only load my own transformer with only 65%. Okay? So in order to have a transformer that will be loaded by 65%, the new rating or the transformer that I will need will be the original power rating divided by 65%. This will give us a higher value that will be loaded, a new power rating of the transformer that will be loaded by 65%, and it will be suitable for this nonlinear load. So what does this mean? It means that we are now oversizing our transformer. We are increasing the size of the transformer to be able to supply this kind of load. Now instead of doing this, there is another method. The other method is that there are special transformers, which are called the K factor transformers. They are having an additional thermal capacity of no limits. The K factor transformers are designed to supply electrical power to non linear loads. So the transformers you can have can be a K factor transformer of four, nine, 13, 20, and so on. This is the k factors of these transformers. Now, as you can see, if our load is 0% electronic, we don't have any power electronic equipment or zero harmonics and 100% electrical. And what I mean by electrical resistance and inductance, it means we are going to choose a transformer with a K factor one. Which is a standard value, similar to the noma transformers that we discussed before. However, if this transformer or the load itself, if the load is 25% electronic and 75% of it electrical, then we are going to choose a K four transformer that will be able to supply electrical power to this load. If it is 50, 50 K nine, if it is 75, 25, then we will use K 13. And as you can see here, we have other types of transformers, other types of loads. So you can see how can I know the K factor of the load? You can see the loads have a K factor of one. This type of loads have a K factor of core and so on. So for example, if I'm supplying electrical power to the loads, then I'm going to choose a transformer with K factor one. If we have a transformer that will supply electrical power to the loads, then we will choose K four and so on. The K factor is important when the transformer is supplying electrical power to non linear loads. As you can see, if we have 100% electronic and 0% electrical, then we will use K 20 rated transformer. 58. Per-Unit Impedance of a Transformer: Hey, everyone, let's talk about an important definition in electrical power system, which is the per unit imbedance of an electrical transformer. If you look at any electrical transformer, you will find on the name plate of the transformer, 5%, you'll find 60% and so on. What does this mean? This means the per unit impedance of an electrical transformer. If we look at this electrical power system, for example, this is a single line diagram for electrical substance, electrical system. If you haven't seen this type of diagrams, I advise going to our course for fault analysis. You will understand how can we get the pair unit impedance of any electrical component, and you will understand what does per unit mean in the system and how can we obtain the short circuit in an electrical system. As you can see, we have a generator, then we have a transformer, a step up transformer. You can see T one, takes the 22 kilovolt of the generator and converts it into 220 kilowatts. It is a step up transformer that will supply electrical power through this transmission line. Then we have a T two transformer, which is, as you can see, a step down transformer, takes 220 of the transmission line and converts it into 11 kilovolt for the motor itself. Similar to here, T three is a step up transformer, takes a 22 kilovolt of the generator and converts it to 110 kilovolt. T four takes 110 kilovolt and converts it into 11 kilovolt. So what I would like to learn from this. What I would like you to learn is that you see here, power rating, you see the voltage, and you will see X per unit. And you'll see which is the reactants in per unit system. And for the four transformers, t1t2, T three, T four, you can see X per unit equal 0.1, Xb 0.06, X 0.064, 0.8, and so on. So the per unit system is very, very helpful in electrical power system. I advise that you go to our course for fault analysis to understand what is the meaning of peri unit system and how it can help us. Now, let's get back to the per unit imbedance in a transformer. What does it mean? The per unit imbedance describes the percentage of the rated voltage required to produce the full load current while the transformer output is short circuit. So as you can see, we have our three phase transformer. Here we have the three phase input, and we have this three phase out with the neutral. Now, when we make a short circuit here and we start supplying electrical power, we will have a short circuit current here, right? So the value of the short circuit current depends on the supply voltage. So when I say percent imbedance 4%, the period imbedance of the transformer is 4%. What does this mean? It means that if I apply 4% of the V rated of the transformer, if I apply 4% of the voltage at the primary site, the current here which is produced will be equal to or the short circuit will be equal to the rated current of the transformer. So the per unit imbedant describes the percentage of the rated voltage required to produce the full load current while the transformer out is short circuit. 4% means applying 4% of the voltage will lead to the rated current at the out. Also, for example, the per unit is 60%, it means if I apply 60% of the supply voltage, we will have the rated current at the out. This is what is meant by per unit imbedance. And at the same time, the per unit imbedance is also representing per unit is equal to the actual imbedance of an electrical transformer divided something which is called base, the base value. This you will learn in the course of fault analysis. Okay? Because it will take lots of lecture to understand the benefit of the per unit system in analyzing electrical system, okay? So you'll find that the lower the impedance, the lower the voltage required to produce the full load current. Now, how can the per unit help us? Or how can we understand that the lower impedance leads to higher short circuit current. So as you can see, lower impedance of the transformer have higher fault current. Now, let's understand this. So I will show, let's say, for example, we have a short circuit here at this point, okay? So we have our generator which is 22 kilo volt and as you can see, X per unit, the per unit imbedance is 0.18, and here we have the imbedance of the transformer. You can see 0.1 X per unit 0.1. For example, 22 here is equivalent to one per unit of voltage. So if I would like to find the short circuit current, it will be the one per unit, divided by 0.1 plus 0.18, 0.1 plus 0.18. This will give us a value, which is a short circuit in per unit system. So the lower the imbedance of T one of the transformer, the higher the short circuit. Now measuring imbedans in units of percentage greatly simplifies the calculation of currents and voltures in a power system. Of course, we can use the absolute mbedance absolute imbedance which is measured in OMs. However, it will complicate the calculations. Now why is this? Because if you look at any electrical transformer, we have the primary site and we have secondary site, and this primary site has its own voltage and its own current. And here we have our own voltage and current here, the same idea. So the problem is that this complicates the calculation, for example, of a short circuit I I would like to get the short circuit here, it will be really complicated because you would like to take this imbedance here, then the total imbedance will be referred here. You are going to do the referring several times in order to get this current. Which is very difficult. However, when you are using the per unit system, you are taking T one as if we have only an imbedance like this and we have another imbedance like this. Without thinking about the transformer, you replace the transformer with an X like this. Okay? So you can get the current very easily, okay? Now one important note here is that we said per unit impedance. Now, you have to understand that the per unit impedance of an electric transformer is approximately equal to X per unit of the transformer. Why? Because the resistance of the transformer is very, very low compared to X. That's why the imbedance of the transformer approximately equal to X per unit. That's why you can see here in T one, T two, three, and instead of using, we use Xpunit. Okay? Now, according to IIC, what is the value of the transformer imbedance according to its rating. You can see the stable helps you understand this point. You can see the short circuit impedance at rated current. So this one representing that percentage of an electrical transformer, the per unit impedance. You can see that for rated power, 630 kilovoltapre, from zero up to 660 630 kilovoltapre. Of course, there is no zero voltage, but as you know, anything less than 630. So up to 630, the short circuit imbedance the minimum value is 4%. From this to this, 5% and so on. So the higher the rating of the transformer, the higher the short circuit imbedance. Okay? That's why the distribution transformers have lower impedance than then the power transformers. Power transformers have a very high power rating, which is equivalent to higher imbedance or that. In this lesson, we talked about the transformer imbedance or the per unit imbedance of an electrical transformer. 59. Construction of Three-Phase Transformer: Hi, and welcome everyone. In this part of our course for transformers, we will start talking about the practical construction of a three phase transformer, the components inside the three phase transformers. So if you remember that the transformer is an electrical device, as we learned before, that transfers electrical energy from one circuit to another using the electromagnetic induction and also known as the transformer action. And we said that the most important function of the three phase transformers is that they step up and step down the voltage in the electrical system. And we said before that we step up the voltage in order to reduce the losses in the transmission lines. So here's the image of our transformer, the practical transformer. This one is a three phase transformer. What we would like to learn in this part of the course is that we would like to learn the components of the three phase transformer. We need to identify the conservator, the pushing, the winding, the once, and so on. So what are the components of the transformer that will be discussed? Number one, we will talk about the laminated core, the windings of the transformer, the insulating materials, the transformer oil. If we are talking here about the oil transformer. There are two types oil transformers and dry transformers. So if we are talking about the oil transformer, then we have the transformer oil, the pushings, the tab changer, conservator, breather, cooling tubes, the booklsRlay explosion vent and more about the transformers. So in the next lesson, we will start with the iron core of the transformer or the laminated core. 60. Iron Core of the Transformer: So in this lesson, we will start with the incre of the transformer. We talked about the once before when we discussed the construction of the electrical transformer and the principle of operation. We talked about the once, and this once provides the pass for the magnetic flux. So as you can see, we have a practical transformer, a practical three phase transformer, the high voltage and low voltage winding. Same idea for this three phase system, as you can see here. Now inside here, we have the iron nucre. So let's look at this, you can see this is the iron nucre, right? So in practical situation, it will be looking like this. You can see laminations blow each other. You can see one, two, three, four, five, six, and so on. Several laminations below each other. So the onnucle you can see this is the leg of the transformer. Also this is another leg and the leg. The three legs, one, two, three, you can see they are completely laminate format of laminations. Okay. Similar to it, the yoke, which is the upper part, you can see the upper part, the yoke. You can see that the yoke, of course, here we will have more material here. Here we will have the yoke here, material too. In this part, we will also have laminations. So first thing is that what's the function of the core? The core is used to support the winding transformer. It carries the winding of the electrical transformer. It also provides a low reluctance pass to the flow of magnetic flux because it has a high permeability, it allows the flow of magnetic flux through it. It has a permeability greater than air Pi several times. Now the construction of the core itself, the core itself is made of several laminations and silicon steel laminations. Why did we form the transformer from laminations as we discussed before, in order to reduce the Ed current losses and the hysteresis losses inside the transformer. The thickness of each lamination, each lamination, this one is elimination. The thickness of this lamination is usually in the transformers between 0.25 millimeter to 0.5 millimeter. This depends on the design of the electrical transformer itself. Now, what is the material used with it, Sun silicon steel laminations. Now, if you would like the exact material, it will be called rolled, grain oriented, silicon steel or abbreviate as CRGO. If you see this, this is the material of the lamination itself. It is made of steel. However, it is a cold, ruled, grain oriented steel. Now, what is the function of silicon here? Silicon here first, the steel, the steel. Why do we use steel information informing this core? We use the steel because it provides a high permeability for the magnetic flux, which will enhance the transformer efficiency. We will have lower losses in the magnetic field. Also the silicon, why do you use? Silicon is used to insulate between the laminations. So you can see this lamination and the next lamination, and so on all of these laminations under each other, there is an insulating material between them. Okay? This insulation between these layers is the silicone. Okay? So the material itself of the iron core or the core of the transformer is the steel itself. Steel is the material. And the insulating material between these laminations is the silicon itself, okay? Now in electrical transformer, the magnetic flux density inside the core is between 1.5 to 1.8. Again, this depends on the design of the transformer. However, you should not exceed the maximum flux density inside the transformer. Now, why is this? Because if you increase the flux density more than the design, for example, if this transformer has a maximum flux density of 1.5, Tesla, if you increase the flux density or the Peter magnetic flux density greater than 1.5, then you are going to go to the saturation region. The problem of the saturation region is that it leads to formation of harmonics in the electrical transformer, which will lead to reduction in the efficiency. So as you can see again another image, here we have the transformer, and you can see here the upper part and lower part, which is the yoke of the transformer itself. Okay? Now, as you can see here, it's form of lamination. You can see this shape. If you remember when we discuss different shapes for the iron core, we said we have a rectangular circular shape, and so on. And we said that circular shape is the best shape for the core of the transformer. However, it is difficult to form this shape. So we said before that we make the shape almost circular, close to circular shape by using the Crocifm shape. If you remember, we had a circular shape, and we said we did lamination like this. First layer, then second layer, then third layer. Format of steps, if you remember, four steps or five steps depending on the transformer design itself, if you remember. So this is the same process. You can see it is steps, smaller than larger layer, the larger lamination, and so on. So this will give us an almost circular shape. As you can see, almost circular. It's not circular, but it's very close to circular. This shape is known as the Crocifm shape. Now, an important note here is that any internal and external parts such as the yk and the iron core must be set. So what I mean by this is that this iron core should be set, erst. The yolk itself is also erst. All of these components are except what except the winding. The winding take the input and output. Okay? So the most important but is any other thing other than the winding should be set. Why? Because all of these on materials, such as the yoke or steel, such as iron core, itself, all of them suffer from huge magnetic and electric field stresses. You remember that the magnetic flux is flowing inside them. So all of these material are suffering from magnetic flux, strong magnetic fields, and at the same time, since we have high voltage winding, this high volte form is large stress on the insulating material inside the transformer. So if we leave these stresses, it can lead to breakdown of the insulating material between the illuminations. Okay, that's why we need to earth to reduce the stresses on the iron core and the yolk of the transformer. 61. Eddy Losses and Saturation Phenomena: Now let's talk a little bit or a little bit more about the Dylosis. If you remember that we said before that we form these laminations in order to reduce the Dylosis. So why does this help in reducing the dylosis Because the laminations increases the total resistance of the iron core leading to a reduction in eddy currents. So as you can see here, when we have a solid core, with a larger area, large area, it will lead to high eddy currents. However, when we have laminations with a smaller area, each lamination has a small area. Or a small sickness. So if you remember from the Onslo or the basics of resistance, you remember that resistance is equal to raw over area. The density multiplied by lens, divided by the area, the cross sectional area. So when we have a small cross sectional area, as you can see here, small cross sectional area, we will have large resistance. That's why the ED currents will be small in case of the laminated core. Another explanation for this part is that if you remember that the equation of the ED current loss as equal to KE, BM squared squared T squared V. We discussed this before, as I remember, in the magnetic circuits. So if you remember or the beginning of the transformer, as I remember. So if you remember this, you will see that we have a term called the sickness, which is the sickness of the lamination itself. So as the sickness decreases as the sickness decreases, the Eddy current loss will decrease. That's why we form smaller laminations to reduce the diloss. Now, another thing is that what happens during the saturation of the transformer. So if you remember the BH curve for the transformer, you'll find that the transformer, at the beginning, the transformer core is made of the ferro magnetic material, which is steel here that will get saturated at a certain magnetic flux dense. When Peta reaches a certain value, the transformer core will start going into the saturation region. Now what will happen is that when we start increasing the MMF or the magnetic motive force, which is NI, number of tons, multi blood by the current or to be more specific, increase in MMF means that we are increasing the current going to the windings, which means we are trying to increase the magnetic flux. However, when we reach the magnetic the saturation case, we will not be able to have any increase in the magnetic flux. So what I mean by this? So if you remember that when we had our winding and we have number of turns N and current I. So when I increase in I, which is the MMF, okay, the magnetic mood force for the magnetic circuit. So as the current increases, the supply current increases, more magnetic flux will be produced, right? So we have our supply, our EC supply. So when this EC supply increases, the current will increase, which means we will have further increase in the flux. However, however, when our magnetic flux density Beta is at the saturation region, the ion core is saturated with magnetic flux. What will happen in this case? In this case, when you increase the current, the flux will remain constant. It will not change. Why? Because we are in the saturation region. Now, someone will ask me what is the problem in this you will find that when the primary winding has excessive applied volts, we applied more voltage to produce more current in order to produce more flux. However, you will find that the flux may reach saturation levers during the peak moments of the AC canoe during the peak moments. So what will happen in this case, you will find that the voltage induced in the secondary will not remain sinusoidal anymore, which will lead to formation of the harmonics in the secondary wind. So as you can see, when our flux or magnetic flux density reaches saturation level, Okay. If you remember here, let's look at this curve. You can see when we reach the saturation region, you can see as we increase the voltage, which will lead to increase in the current, it will lead to increase in the magnetic flux density, more flux until we reach a point at which will have saturation, which means that whatever the increase in voltage or current, the flux density will remain constant. Now, we will have this part saturation region. This region will lead to formation in harmonics in the secondary winding. So what I mean by this, we always had the input as a sine wave, and the output will be also a sine wave, either having a higher voltage or lower value depending on the tones ratio. However, when we have the saturation region, it can be like something like this. Okay? It will not be a pure sine wave. It will be a sine wave, but it is distorted. What I mean by distorted, it means that this wave is no longer a pure sine wave. We have harmonics, due to the increase of the magnetic flux at to the saturation region, okay? Okay, so the effect of the harmonics will lead to overheating in transformer, power losses, reduced efficiency, and shortening of the lifespan of the transformer of all the devices inside that transformer. Okay? So this is the effect of both of the saturation, and we also discuss the effect of ED currents or how can we reduce the ED currents. 62. Windings of the Transformer: Hi, and welcome everyone. In this lesson, we will talk about the windings of an electrical transformer. So we have this winding, which are group of windings with several number of turns. Now, windings are wound over the transformer core, which we discussed in the previous lesson. And these windings are insulated from each other. You can see this turn and this turn and this turn. All of the turns must be insulated from each other, or they will be considered as one complete turn, right? So they are insulated from each other, insulated from the core, and insulated between the high voltage and low voltage. So the winding consists of several turns of copper coils that are bundled together and each bundle is connected in series to form a winding. As you can see, this winding for example, like this, like this. All of them are connected in series. They are insulated from each other, but they are in series at the same time insulated. What I mean, there is a gap between them, so we can have turns. If they are one unit, complete unit, very close to each other, then it will mean that they are one turn. Now, why do we use car? Cover has a high conductivity, which means it will minimize losses, as well as the amount of cobo needed for the winding will be lower, which means that the volume and weight of the winding will be reduced compared to something like aluminum. Aluminum, for example, has a lower conductivity than cover, which means we will need more aluminum to carry the same current, which means we will have a larger weight of the winding. Also the capper has a high ductility, which means it is easy to bend the conductors into tight windings around the transformer core. So you can see it is really real tight here, which will lead to minimization of the amount of caber needed. Also, it will reduce the overall volume of the wind. Now, what are the different classifications of the windings? First, we have the input output supply classification, which means we have the primary windings and we have also the secondary windings. So primary windings means that our windings at which we will have our input. The primary at which we will have our input supply as we discussed in the course and secondly, which are connected to the load are the winding that have the output voltage that will be connected to our load. Okay? Now, what about the voltage range? So we have a primary winding and secondary and primary means we have our input, and secondary means we have our output. Now we have also high voltage and low voltage. High voltage winding, it means that this is a winding, which have a high voltage and high voltage and low current. So you can see that the number of tones is a multiple of the number of tones in the low voltage winding. It has high number of tons, high number of tons to produce the high voltage site. So if you remember that V one over V two is equal to one over any two. So the higher number of turns, the higher the voltage. The higher the voltage here. So high voltage winding has a corresponding number of tons, great number of turns compared to the secondary winding. And you'll find that the copper coils are sinner than those of the low voltage winding. Why? Because here, if you remember, the high voltage winding has a corresponding low current. Slow current means that we will need a sinar cross sectional area or sinar coils. Why? Because it doesn't need to because it has a low current and does not need to withstand high currents. It is a sin wires, because it is a low current. However, in the low voltage winding, we have lower number of turns because we have a lower voltage at same time, the coils itself are sick coils, very sick coils or sicker than the high voltage winding. Why? Because the low voltage winding has high current. Means we need sick wires, very sick wires. Let's make it like this. Very sick wires. In order to withstand the high currents. Because as you can see here, that the current in the low voltage winding is higher than that of the high voltage wind. Now, the transformer can be supplied from low voltage site or high volte depending on the requirement. If we make our input, the low voltage and output high voltage, it means we have a step up transformer. If we put our input to the high voltage site and the outt from the low voltage site, it means we have a step down transformer, as we discussed before. 63. Types of Transformer Windings: Now let's talk about the different winds or different windings inside the transformer. What I mean by different windings, the different configurations for installing the winding on the iron core or the transformer core. The first type is the helical winding, which you can see in this figure, the helical winding. As you can see the helical winding consisting of a few more than 100 insulated strandus wound in parallel along the length of the cylinder. With spaces inserted between the turn or the dsks to minimize the circulating current between the parallel strengths. As you can see here, you can see between this big turn, we can see ask, dusk, another desk, another desk. Between them, you can see here, this is the spacing or spacers you can see the part let's read this. You can see this part. This part is called the spacer. You can see there is a spacing between the group of windings or turns. Be wise because it will help in minimizing the design of the transformer in this form. It will help in minimizing the circulating currents between them. Now this type of windings when we do this formation, when we have a large or high currents. So when we have a low voltage high currents, or high currents, we will need to use this formation or the helical winding formation. Why helical winding? Because it is easy to manufacture with high mechanical strength. Only the biggest problem of this formation or the helical winding is that we will have a large transformer, large volume because we have spacers here, which will lead to increasing increasing the size of the transformer. So if you look at here, you can see this part, the part, which is the spacers inside the transformer between each group of windings. Here is another shape, as you can see here, the core of the transformer and the three phase as a high voltage or low voltage winding, high voltage, and then low voltage, you can see here spacers. As you can see the sport, the sport, the spaces between group of wins or group of strengths of winding. Similar as here. You can see here and here, spaces between them, spaces between them. The second formation is called the disk one as if we have group of disks around that transformer core. Now, this one is used with high power rating transformers. It is used when we have a transformer that has a large number of windings or large number of tones and low current or to be more specific, low current high voltage loads, greater than 25 kilovolt value. High voltage, 25 kilovolt. And you'll find here insulators are here between or are between the desk layers. You can see between each layers between these disk layers, there is an insulating material that insulates between the group of dsks. What you need to know is that this formation or the disk winding is used when we have a high voltage or greater than 25 kilovolt. The third formation is called the layer or parallel winding. Now, as you can see, this is a parallel parallel winding or the layer winding. This formation is used in the tap changer transformer or the loud tabchanger transformer. The transformer with tap changing function or tab changer function. You can see this part, the spot that will go outside the transformer, this representing what This representing the tabs of the transformer, you can see one, two, three, four and five, five tabs in this transformer. And you said that the tabihanger will be used to change the number of turns of the transformer. Now we will understand the tabu changer in another lesson inside this course. Now, the layer winding is one of the simplest of winding in which the insulated conductors are wound directly next to each other. Now, several layers can be wind on top of one another and the layers are separated by solid insulation, ducts or a combination of insulation and ducts. Now, what is the benefit of ducts? Now in oil transformers, we would like the oil to go through the winding to be inside this winding. So we have ducts between them, between these layers to allow the flow of oil. Now, what will be the function of oil here? It will be help in cooling this winding. Since they will have a high amount of heat energy, the flowing of the oil through the winding will lead to cool down of the transformer. Also this type gives us the tabs that will be used in the type changer as we just said. Now, the last one which we will discuss is called the pancake one. As you can see, it is giving us the shape of the pancake. Now, the arrangements of conductors here are formed in disks. We have disks above each other. This will form in the end the shape of the pancake. This type is used exclusively in the shell type transformers. In this lesson, we talked about different formations that you will find in the construction of the windings of the transformers. 64. Insulating Materials in Transformer: Hey, everyone. In this lesson, we will talk about the different insulating materials that we are using inside the electrical transformer. We talked before about different insulating materials, and we said before that the insulating material is used to insulate between the high voltage and low voltages, low voltage, and high voltage winding. And it also it is used to insulate between the low voltage and the core of the transformer. So what are the different types of insulating material? You will find that the first type which is commonly used is called the electrical grade paper or craft paper. It is one of the cheapest and best insulation materials that are used in transformers. As you can see, this is a craft paper that is used and this one has a high dielectric strength, which means it can help in insulating between the high voltage and low voltage and insulating between the low voltage and the core which is ect. This dielectric material should be free from any conducting particles because it will reduce its insulating strengths. Now this craft paper is not only used in electrical transformer, it is used also in insulating the high voltage operators such as the transformers, the capasors and cables. And you can see here where we can find this. You can see the paper here. As you can see here, this one and all of the wirings coming out from the transformer itself, you can see all of them are surrounded with this craft paper. Also the insulation between high voltage and low voltage is also craft paper. Why in order to insulate between all of these materials? You can see here another form when the transformer was being prepared, we had also this craft paper. It is also used to insulate between the tours of the transformer. Now let's talk about other materials. We are not going to talk about each of these materials, but in general, we have this table. If you remember we talked about the insulation class before. We said before in order to insulate between high voltage, low voltage, the core of the transformer. We need insulating materials. We talked about several classes PCEF, and as you remember, and we each of these classes have its own temperature rise, and in the end, it has its own temperature limit. So as you can see here, we have the insulating class, Y A PCEF H. Each one of these has its own temperature limit. You can see Y, for example, is 90 degrees Celsius, A, 105 degrees Celsius, and so on. So each one has its own temperature limit. The maximum temperature temperature it can reach. Also for the insulating material, each class representing one type of insulating material. For example, Y representing cotton. And why also representing silk, paper, and wood without ipignation. However, here we can see class A, representing wood, cotton, silk, and so on, but they are when they are in brignt or having impregnation with natural resins or insulating oil. So we having our insulating material. And in addition to something else such as natural resins, or to be more specific in electrical transformers, the insulating oil. So paper plus oil leads to higher insulating level and higher temperature limit or temperature limit. Okay? And so on you will find here, glass with silicon resins and so on different materials, which is not important for us, but in the end, what's important for us is that each class which is on the nameplate of the transformer will lead to a specific temperature limit, okay? So in this lesson, we talk about the insulating materials inside the electrical transformer. 65. Bushings of the Transformer: Hey, everyone. In this lesson, we will talk about the pushings inside an electrical transformer. As you can see here, we have our transformer, and you can see we have the three phase with the yuk here b and lower yoke, the per yoke and lower yoke. And all of these transformers or the three phase concentric windings are placed inside this tank. You can see this tank, this metallic tank. This one is used to contain all of the three windings, iron core, insulating material, and so on. Now, as you can see above the transformer here, you'll find this part. Okay? So the wiring itself, it will go like this, go like this, like this, like this and the high voltage like this. So what does this represent this part representing the pushing of the transformer. This part is the pushing of the transformer, this part pushing pushing. So what does the function of the pushing inside the transformer. So pushing is an insulated device that connects between the internal transformer windings and the external circuit through the transformer tank. So as you can see, this is our tank here. Okay? And we have the internal transformer winding here, internal transformer wind. And the external circuit between, let's say, for example, we will take from here and connect it to a cable or an overhead transmission line like this. Okay. So in order to connect between the internal winding and the external circuit, we use this pushing here, external and the internal of the transfer. Okay, I hope it's clear now. Okay, so what is the difference between these two? As you can see, we have one, two, three, four, which means we have a three phase and a neutral, which means that this part is a star connection, right? One, two, three, four, the three phase, and the neutral. Now, on the other side, as you can see here, we have one, two, three, we have three pushings which means it is a delta connection, delta connection. Now, how can I know if this one is a high voltage site or this one is the high voltage site? Now, the larger the pushing, larger pushing indicates the higher voltage site. So as you can see, if you look at this pushing here, this pushing is a big pushing compared to this one, small pushing. So what does this mean? This pushing is higher. It means that this part is the high voltage site. And here, this part is a low voltage site. So it means that we have a Delta star transformer in which a high voltage coming from transmission line connected to the delta and the low voltage site is a star connection which is going to the lute. It means that this transformer is a step down transformer, takes the high voltage delta connection voltage and transform it into lower voltage or a star connection for the lute. Okay? Okay, so we know that now this is an insulating material that will connect between the inner windings and the external circuit. Now the question is, why don't we connect these two directly? Why don't I connect it directly? You'll find that this pushing is made of a porcelain material. This pushing here is made of a porcelain material to provide insulation, o voltage insulation. And you'll find here that the wavy shape surface, the wavy shape of the surface here, you can see this is a wave like this. You can see this is a wavy shape. Okay? Now, why is this important? Because it will help minimize or maximize the surface pass length and minimize the surface leakage, the corona effect, and preventing the eventual arcing from exposure to dust, air pollution, and so on. So let's understand this point. Okay, so if the high voltage, this will help you understand now the function of this poshing. If the high voltage is connected directly inside the cable box of the transformer, connected directly to the winding of the transformer, what will happen is that at the terminal point at the point of connection, you'll find that the insulating material between the body of the transformer, and the high voltage is only air, which have a low dielectric strength, which means that this large magnetic field or electric field produced by the high voltage will lead to breakdown of this air and providing a liqage pass through the body of the transformer to the ground. Okay. So what does this even mean? Let's understand this point more clearly. Let's say, for example, you have here, this is that transformer here, the winding at this point, and we connected the high voltage like this at this point. Okay, here. Okay, let's say, for example, it is like this. Let's show it in another way. Let's say the windings here at this point, and we connected the high voltage at this point. Okay? So they are above the transformer. Now, this one is a high volt. Let's say, for example, 11 kilovolt. Okay? Now, as you remember, as you remember that the body of the transformer itself, we said the iron core. The body of the transformer are set. So this part is connected to the ground, right? What will happen is that at the point of connection, we have a high voltage of 11 kilovolt or six kilovolt or whatever the voltage. What will happen if you remember that the air itself have a low dielectric strength. It is not a strong insulating material or insulating medium. What will happen is that the high voltage here will break through air and go to the body of the transformer to the ground. The insulating or the high voltage here will break through air and go to the ground. Okay, because the body of the transformer is air set. So in order to prevent this phenomena, we add this pushing. So if we have the high voltage here, in order to break through air to the body of the transformer, it will need very large voltage, not just 11 kilovolt. It will need higher voltage. So it will not break down through air. And sometimes this pushing providing if the high voltage wants to break through the pushing, it will need also higher voltage. So the pushing here acts as insulating material between the high voltage and the body of the transformer. So it will prevent the breakdown of air through them because we have a higher pushing. Now, as you can see, this is a smaller poshing because we have here 440 volt, which is 400, not 440 380 volt line to line voltage, depending on the country. This voltage is very, very weak to break through air to the body of the transformer. We have a smaller poshing the size of this poshing will increase depending on the voltage of the output or the input of the transformer or the voltage coming from the transmission lines. Okay? Again, it acts as insulation between the high voltage or low voltage and the body of the transformer. Okay. Now, why do we have this shape, this way the shape? Now what will happen is that sometimes in the location or in the open area, let's say if for example, we have an air substation in which it is exposed to the external outbut what will happen is that if we have rain, if we have rain or accumulation of dust on this pushing, what will happen is that dust will help in conducting electrical current. What will happen is that there will be a leakage current that will flow through like this. Through the pushing. Why due to the presence of dust and any other particles that will lead to a conduction of electrical current, which leads to weaking this insulating material. So instead of instead of having one pushing like this, like this, so that any accumulation of dust will lead to likage flux like this. We use this wavy form like this. Like this. Why we doing like this? Because it makes the pass of the current very large. You can see you need to move all of these distance instead of one direct distance, you need to move all of this. So this will increase the total insulating resistance of this insulating material. Okay? So as you can see here, the wavy shape, maximize the surface pass lenses and minimize several pomon such as the leakage current and corona effect due to the air pollution and dust. Now, as you can see the pushings, let's see it more closely, as you can see here. This is a body of the transformer, and you can see we have this pushing and we connect here the external circuit. As you can see here, the high voltage, one, two, three, here this is the high voltage site and you can see here we have our low voltage. We take from here, going to our circuit, the star connection to our circuit, here and here, this is coming from the transmission line. And of course, we have different shapes and size depending on the current and depending on the voltage utilized. Now you will find that inside the insulator itself. If you look more closely about the pushing of the transformer, you'll find here that this is a terminal at which we will connect our cable here, terminal of the pushing. You'll see that here we have this couple that's coming from the terminals of the transformer. Coming from the transform let's say phase A. As you can see, the current will move through this scupper going to the terminal. However, you will find that here we have a small air gap around it. Okay, it is not directly connected to this pushing, but there is an air gap between them. Now the problem is that if this one has a high voltage, it can break through the air and through the pushing and go to the ground like this. Okay? Instead of breaking from here and going through all of this distance, it has a shorter distance like this and break like this. So how can we solve this problem? What we do is that we fill this gap here with insulating oil, mineral oil, similar to that inside the transformer here and here. This oil will increase the dielectric strength of this medium here and prevent the breakdown through it and to the ground. Okay? The function of this oil, it will help in preventing the breakdown to rs. So the high voltage should break like this. However, since it's coming from the transformer like this, it can break like this. To prevent this breakdown, we added this oil, which increased the dielectric strength of air. As I remember, I'm not sure as I remember that the dielectric strength of air was 30 kilovolt per centimeter. And for oil, as I remember, 80 kilovolt per centimeter. Okay? So in order to break down through air, we need 30 kilovolt for each 1 centimeter of air. And to break through air, we need 80 kilovolt per centimeters. That's why we add oil that will increase the dielectric strength and prevent the breakdown. Okay? Now, as you can see in this figure, you will find something interesting here. You will see the two horns, arcing horn. What does this king horn do? We will find out in the next lesson. 66. Arching Horn and Surge Arrester: Now let's talk about in this lesson, we will start talking about the arc horns inside the pushing of the transformer and also the surge arrestor. So first, you will find here this is our pushing as we discussed in the previous lesson, and we have here the arcing horn, the spot, and the spot, and between them, there is an air gap. Okay, so what happens exactly? The arcing horn inexpensive and inexpensive form of the over voltage protection. They are employed merely as a lightning protection. Their function is to prevent the damage to the equipment caused by high voltage levels by providing an independent path for that voltage to ERs. Furthermore, they must allow the equipment to resume the normal operation once the high voltage event is dissipated. Okay, so what does this even mean? So we have here our high voltage coming like this, high voltage, and this poshing acts as insulation between it and the Earth's tank, right? That's what we talked about in the previous lesson. Now what will happen if we have a transformer that is in an air substation, an air substation. It means that this transformer will be exposed to lighting effect or lightning phenomena. So what will happen if we have a lightning strike hitting this high voltage or the pushing itself, it will lead to break down through the pushing to the ground. Okay, so the lightning strike, the lightning strike will have a very high voltage that will break down through the porcelain or the pushing and go to the ground. Now, this pushing cannot withstand lightning several times. After hitting or hitting it several times, it will lead to weaken this insulating level of this pushing. So what we can do in this case, instead of letting this lighting, breaking through the pushing, we will give it an alternate path, which is easier to break than the pushing. So normally we have this Rc and this c and between them and air gap. So the high vol the normal high volts will not be able to break through this air gap to this arcing wire. This wire is going to the arcing wire. So the high volt will not be able to break through air gap to the ground in the normal operation. However, in the lightening case, it will be able to go like this. And break through the air gap, then go to the ground. So in this case, we protected our pushing from the lighting effect, and we provided an alternate path to go to the ground. Now this phenomena happens during the lighting and during the switching surge. When we switch on and off some loads, we will have an over voltage phenomena, especially when we reduce our loads. You will find that this overvolte during switching will lead to breakdown through the pushing. Instead of letting this, we will give it the alternate path to the ground. This is a function of the arcing hon inside the transformer. Now, most of the larger power transformers use the surge arrestors instead of king horns. So what does the surge arrestor mean? So let's go here. The surge arrestor protects the system equipment, such as the transformer, transmission lines from excessive voltage or any other voltage caused by lightning or switching surges. So as you can see, this part, which is looking like the pushing, but this one is different from the pushing. This what you see here in this figure is what we call the surge arrestor. So what does this do? It protects the equipment such as transformer and transmission lines from the lightning or any excessive voltages. Now, you will find that at higher voltages, you will see that this we have rings. You see the rings. You see these rings, what does these rings do? There is a phenomena in high voltage transmission lines, which is called the corona effect, the corona effect. Now, these rings are used to protect the system from the corona effect. That's what we all need to know. Now let's see the search arrestors in real life. As you can see here, we have our transformer. This one is a big power transformer. You can see the pushings which is going to the transmission line. Let's say, for example, this is a generating substation with a transformer, a step up transformer. This transformer will go to the transmission lines. As you can see, you can see the size of the pushing very large pushings. You can see the larger the pushing, the higher the voltage. As you can see this pushing very large pushing here, you can see this is a terminal going out, going out, and going out. Three phase system. This is a delta connection. So as you can see here, we have the pushing of the transformer and the output wires. Now, as you can see this going to the transmission line, going to transmission line, and going to transmission line. But you will find something here which is interesting. You will find that we have this large construction here or equipment, which is a surge arrestor. This one is a surge arrestor, surge arrestor, and there is one is a blue one surge arrestor. You can see the R connected in parallel. You can see the R connected close and in parallel with the equipment to be protected. So we would like to protect the transform. The surge arrestor, they are very close to the transformer and parallel to it. Transformers and surge arrestors parallel to it. Now, the search arrestors will protect the transformer against the lightening effect. You can see here three phase pushings and you'll find here that surge arrestor that will help in protecting the transformer against the lightning effect. The purpose is to safely divert the surge to the ground and prevent damage to the insulation of the associated voltage as pushing of the transformer from the effect of over voltage. So what happens exactly? You'll find that we have here this large pushing, right? Okay? And inside it, we have a nonlinear resistor, nonlinear resistor inside this pushing. Okay? At normal voltage, let's say, for example, we are operating at 400 kilovolt. Okay? This is a normal voltage. So the pushing here prevents the breakdown due to the 400 kilovolt, okay? Inside it, we have a large resistor, non linear resistor, a nonlinear resistor. Now, what will happen exactly is that when we have the 400 kilovolt. This nonlinear resistor will be very high, which prevents any flow of current to the ground. However, when we have a larger voltage, due to switching surges or due to lightning protection, this nonlinear resistor will start to decrease leading to flow of current through it to the ground. Again, at 400 kilovolts, the nonlinear resistor will be very large. At any other voltage, let's say, for example, 800 kilovolt due to the lightening effect, this nonlinear resistor will be very, very small compared to the original value. It will allow the current to flow through it to the ground. Okay, so that is a function of surge. It gives a pass to the surge to go to the ground instead of breaking through the pushing or going through the pushing to the ground. Okay? So it will help in protecting our electrical system. 67. Dry and Hermetic Transformers: Hi, and welcome everyone. In this lesson, we will classify our electrical transformers into other types, not just by the voltage rating or the power rating, but this time we will talk a poet commonly used names for the transformers, the dry transformer, the hermetic transformer, and the oil transformer with conservator. Let's start with dry transformer and understand what does this even mean? So what you can see in this figure is a dry transformer. You can see here we have the three phase, the three cores. You can see here this is the shape, here the upper part, the yoke and lower part the yoke. And we have one, two, three legs, and in each leg, we have the primary and secondary winding, primary and secondary winding, and the primary of the and secondary winding. And we also have here phase A, for example, phase B and phase C. Okay, similar to what we discussed before. But the difference is that this one is called dry transformer. Why it's called a dry transformer because it does not have any liquid. So as you can see here, there is no liquid that provides installation and cooling to this transformer. This transformer is completely dry. So as you can see, a dry type transformer does not use a liquid cooling agent. So it is called pi Air. So as you can see, this transformer is completely opened, as you can see, and the heat energy coming from the windings and the flux inside the core, all of this is called naturally pi air. And it does not have any liquids such as oil. And you will see that instead of oil, such as in other types as we will see, circulating air protected the coils, windings and insulation from overheating. All of the heat energy is radiated from this transformer and provided to air. Now we have to understand this type of transformers has a low rating. Why? Because the higher rating transformers have more heat energy or higher rating transformers have large amount of heat energy. So we need a type of cooling liquid that will absorb all of these heat energy and provide it into air. So for example, we will start using something like the oil transformers. So what we need to understand about dry transform, it is a cast resin cast resin transformers. As you can see here, this cast resin, what's the function of this part. It prevents any moisture or air from going to the windings. They are completely sealed from the external air. As you can see here, if we look inside this, you can see here one, two, three, three phase transformer with the insulating material. Okay. Now, as you can see here, another shape for the dry transformer, as you can see here, you will find that here. If we look at here, you can see phase A, phase B, phase C. As you can see here on the other side, you will see one, two, three. You can see here three phase here and another three phase here. And then there can be the neutral also. Anyway, as you can see here, A, B, and C, what you will see here is that this connection here that is provided is Delta connection. So as you can see here, we have phase A, like this and phase B and phase C. You can see the terminals of this winding is here and here, for B, the one and this one, this one, and this one. And we have A, B, C. Now, how this connection is Delta. As you can see here, we have A, B, C, which is coming A, B, C, as you can see here, let's start with A, for example. As you can see here, A, the internal one is connected to the output of B. You can see connected from here to here. Now, let's look at here. You can see here. A is connected to B. A is connected to B, as you can see here. C, as you can see here, B one, which is the first point, connected to C two, as you can see here, connected to C and going out, which is part. As you can see, C is connected to A, C is connected to A. So this form, as you can see here, this connection is adult connection. This is what is called the dry transform. It has a low power rating due to the heat energy. We cannot increase the rating above a certain level because it does not have a large cooling method. As you can see here, another type of transform, which is the hermetic transformers. The hermetic transformers are the hermetically sealed transformer is a transformer design that has no conservator, and we will understand what does the conservator mean in the nexxt lesson? When we go to the conservative part of the transformer. Now, the hermetically sealed is what you see here. Similar to the dry transformer, but we have here a large tank, which contains a three phase input three phase, and three phase out of the transformer, similar to what we have seen previously in the previous lessons. However, this part, which is our tank which contains iron core and the windings of the transformer, it contains inside it oil. Or to be more sefic mineral oil or hydrocarbon oil. Now, what's the benefit of this coil? It is used for calling the transformer winding and increasing the insulation level of the transformer. As you can see here, the di electric insulating fluid inside the transformer tank is completely sealed, as you can see, it's completely closed and not exposed to air and has zero contact with atmosphere. As you can see, this is completely sealed closed away from air to prevent the entrance of any moisture or any particles from air. So as you can see here, if you look at here, you can see this part, three phase here. However, we have a large tank that contains a three phase one without the cast resin, without this part, only the windings and the insulating paper, for example, the craft paper that we discussed before, and we have the insulating liquid inside which provide cooling and insulation. Now, this design avoids the air in the transformer tank, thereby avoiding the sludging and oxidation of the dielectric fluid. Here's dielectric fluid, which is a hydrocarbon. Now, as you can see, this is a transformer. You can see inside it, we have the three phase windings. Now, you will find this one. You can see this portal here. So what is the function of this part? This part in which we are going to add our oil. So we can open this one and add the oil to the transformer. Okay. Now, another part here you can see this here, this fence this part is called the radiator of the transformer and its function is used to radiate the heat energy coming from the oil to air. This fence increase the total area of the transformer to provide heat energy coming from the transformer to air. Now, another thing you can see here inside the transformer here, all of the details, and you can see here we have these two points, this part. And on the other side, you will find another one like it. Those are used to lift up the transformer using a crane. If you'd like to move the transformer from one location to another, then we are connecting it from this point and here and here to hold up the transformer. Now, what about this oil which is inside the transform. So as you can see, we have the iron core with the three phase inside this completely sealed tank. And so that we will have our oil that is surrounding the iron core and all of our three phase windings, the primary and secondary windings. So what's the function of oil inside the transformer? The oil is used as an insulating material. So it's used to insulate between the windings and at the same time cooling. So as you can see, it has two main functions, which is cooling of the transformer and insulating between the windings of the transformer. Okay. So what happens exactly? So as you can see here that the transformer core and windings are completely immersed in oil. You'll find that this type of oil is hydrocarbon mineral oils. 95% of the times is one which is used as a transformer oil. You'll find that other function which is reducing the oxidation of the components in the transformer and helping in detecting internal faults inside the transformer. What happens exactly is that the heat energy due to the flow of current inside the winding of the transformer and these windings have a certain resistance R. When current flow is through a resistor, which is a resistance of the windings itself, it will lead to production of heat energy. So this heat energy inside the windings will be transformed to the oil surrounding it. So the oil will absorb all of the heat energy due to losses inside the core and inside the windings. So it will absorb all of this heat energy. Then this oil is with complete interaction with the body of the transformer. So the oil will transfer its heat energy to the tank of the transformer and tank will radiate this amount of heat energy into air. So in the next lesson, we will talk about the calling methods in the transformer. 68. Cooling Fins and Tubes: So let's talk about the calling methods or not the calling methods, an example on how can we call our transformer. So we talked before that we have the three phase winding and we have the oil surrounding them. Now, the heat energy coming from the windings, the core of the transformer will be transferred to oil, and then oil is with a contact of contact is in contact with the tank of the transformer. So it will radiate this heat energy. The first part is the cooling fans inside the transformer. You can see this part. This each one of these plates is called the fin or calling fan. What is the benefit of this? This fence is added to the transformer enclosures to increase the service area and improve the calling efficiency. The heat energy will be transferred to the tank itself and from tank, it will go to this fence, which will increase the total area exposed to air, which will lead to cooling of the transformer. Second thing that we have is calling tubes. So you will find that the transformer itself, higher rating of the transformers, oil transformers can have tubes surrounding it. Now, what's the function of these tubes? Now, we said before that we have oil which is surrounding the core of the transformer, right? So this core gives large heat energy to the oil. So what will happen is that when the oil takes the heat energy from the core. It will start, its temperature will increase and its density will start to decrease and start going up. The oil itself will start going up after taking heat energy from the core of the transformer. Now, then what will happen is that it will go through the tube Okay, and radiate all of the heat energy it has to air. Okay? This part, this tube is called the radiator tube. After radiating all of its heat energy to air, it will start cooling down, which means its density will start increasing again and start going down again. And this cycle keeps repeating. Same idea in the larger transformer, you can see here the radiator panko or radiator tubes. What will happen is that here, it will go up. Then it will go through this tube, and it will go through this tube here. You will see these two tubes in the Nx slide. Then it will start going through each of these tubes, smaller tubes, and radiates its heat energy to air. Then it will go down through the other tube and get back to the transformer. So again, again, the cooling tubes are used to cool the transformer oil, cooling, cool. It's really clear as you see. The transformer oil is circulated through the cooling tubes. As you can see, circulating going up in circles. The circulation of the oil may be either natural or forcet. What I mean by natural facet, natural, it means that when this oil is heated, it will go up and go through the stube naturally due to the temperature rise of the oil and its density will start decreasing, so it will go up. Another type of cooling, it will be forcet as you will see in the types of cooling lesson. What I mean by forcet the oil itself is forced by pumps. We use pumps in order to force the oil to move to the tubes. So the pumps will push with pumps or motors will push this oil through the radiator tubes. It will push it through the radiator tubes down and push it up. So it is forcet. Not naturally it force it, but this forsotype will increase the cooling power of the transformer. Okay? In natural circulation, as we said when the temperature of the oil rises, the hot oil natural rises to the top and the cold oil sins downward as we see go up and going downward. Thus, the oil naturally circulates through the tubes. In forced circulation, we said that we have an external pump that will circulate the oil by force. As you can see here, if you would like to see the tubes, you can see the upper and lower tubes, you can see here this transformer, and you can see all of this radiator part with fins, and at the same time, it will allow oil to go through them. So as you can see, we have the upper tube here. Tube, as you can see here, and we have the lower tube, as you can see here. Similar to this figure, lower and upper tubes. And as you can see in this part, we have an additional cooling method, which is air. So we have fans that will operate and force the air to go through this transformer and cool it down. Don't worry, we will talk about the different types of cooling methods in the transformer. Okay, we will talk about oil, natural, oil, forced, and so on in another lesson. In this lesson, we talked about the cooling method or the cooling effens and cooling tubes inside an electrical transformer. 69. Conservator Transformer: Okay, so let's start talking about another type of transformers, which is a conservative transformer. So what's the difference between a conservator transformer and hermetic transformer? The same idea similar to the hermetic transformer. However, this type of transformers has an additional conservator part. This part is called the conservator of the transformer. So now what we have learned till now is that we have three times. We have dry transformers and we have oil transformers that are classified into hematic transformers and conservator transformers. Okay? So the function of the conservator here. The conservator conserves. You can see conservator and conserves transformer oil. So as you can see in this tank, you will find an additional oil. So if the oil level inside the transformer due to any kind of reasons starts going down, it will start taking additional oil from this conservator and it will go through the tank. Through a tube here with something which is called the Pockels relay. The Pockels array which we will discuss in another lesson. Anyway, the oil will go from here and go down. Let's say, for example, one of the reasons is that if the temperature decreases, what will happen to the oil? The oil will start to contract. So when it contracts, its level will start going down. So it will take some of the oil and go to the transformer. Now if the temperature increases due to any reason, the oil will start expanding the excess oil will go through this tube and go here and this level will start increasing. Again, this conservator is an air tight, metallic cylindrical drum that's fitted above the transformer. The conservator tank is vented to the atmosphere at the top and the normal oil level is approximately in the middle of the conservator to allow the oil to expand and contract as the temperature varies. So as you can see here, the conservator tank is connected to air. How it's connected to air, you can see this part is our tank or the conservator tank. What will happen, you can see here? There is a part here called the press or here connecting to something which is called the Silica jal. These two we will discuss in the next lesson. But for now, let's focus on the conservator. Let's say, for example, if you can see the level, normally at the middle. Half of the conservator is oil and the other half is air. So what will happen when the oil expands? When the oil expands, it will go here and the level will start increasing, and it will push the air through the breather and go to the atmosphere. Okay? So when the oil expands, this level will start increasing, pushing the air here through the preser to the atmosphere. Okay? Now, when this part when the oil starts to contract, so the level will start decreasing, right? So the level will become like here, for example. So we need air to replace this oil. So the air will go from the atmosphere through the presser and to the tank. So the presser here with a silicael will act as a tube or act as a way to absorb the air and let out air. Okay? So here, this conservator allows the expansion and contraction of oil. And as you can see the conservator is connected to the main tank inside the transformer, as you can see conservator and the main tank is connected through a pipe, which is filled with oil through a pipeline, filled with oil through this pipeline, which contains something which is called the Pockels relay which we will discuss. Now, as you can see here, for example, if the oil level starts to decrease, oil level starts to decrease. If it contracts, you will see that the oil will go from the conservator to the tank itself, right? So it will take air from the atmosphere through the freezer and it will replace this oil. So when the oil starts to contract, this level will start decreasing as you can see here, and the air will come from outside to replace this empty space, like through the freezer and the silica jot. Okay? Now, again, what's its function, I compensates for the variation oil volume due to temperature changes. It is also an effective barrier between air or the atmosphere and oil. It also provides protection against humidity, and as you will see or moisture, as you will see how can we do this using the silica gel, which we will discuss in the next lesson. And it also helps in elimination of the gas bubbles for meting oil. All of the gas bubbles here are going to the air here. This space. 70. Oil Level Gauge and Dehydrating Breather: Now let's talk about another equipment or another tool that is used inside the transformer. So we talked about the conservator and said it will help in expansion and contraction of oil inside the main tank. Here we have on the conservator, something which is called oil level gauge or sometimes it's called the magnetic oil gauge. So what does it do? You can see here, this will give us the level of oil. Okay. So we can know if the oil, you can see that the oil is normally at the middle, you can see here at the level, normally at the metal. Now, when the oil expansion expands during or due to heat energy or due to temperature rise, what will happen is that the oil level will start increasing when it expands. So when it expands, the temperature will increase, so the level will increase, indicating increase in the temperature or in the temperature of the oil. So the oil level here is represented by the temperature of oil. Okay. So as the temperature increase, you will see plus 85 Celsius degree, which indicates that the temperature, this is the maximum level here. You can see this gives us the temperature or the level of the oil, which means it's a dangerous level at 85 Celsius degree of the oil. Now, when the oil starts to contract, you will find that the level will start decreasing till the minimum level of the tank. Okay? So here it is an indicator of the oil level in the conservative tank in the form of temperature. The 20 degrees here is a reference for the oil level at this temperature. For example, at a temperature of 20 Celsius degree, the oil will be at this level at this level of the whole tank. Here is another part. You can see empty and full for this conserved tank of oil and you'll find that behind it, we will have here a floater. When the oil expands, this floater will be pushed upwards, indicating that this level will go like this. And when the oil level starts to decrease, this floater will go downwards and the pointer will start moving to the empty part. So this floater moves with the movement of oil inside the conseror, okay? Now let's talk about the dehydrating preser inside an oil transformer. We said before that we have the main oil tank and we have the conservator, which is at the middle of it. The oil level is at the middle. What will happen is that due to expansion and contraction of oil, this level will start going up and down depending on the expansion and contraction of oil. Now, what is a function of the dehydrating preser or the preser inside the transformer? The preser controls the moisture level in the transformer. The moisture can arise when the temperature variation cause expansion and contraction of the insulating oil. So due to changing in the temperature of the oil inside the transformer, this leads to expansion and contraction, which will lead to change in the pressure inside the conservator, which is the sport. The pressure changes are balanced by a flow of atmospheric air in and out of the conservator, which is how moisture can enter the system. So we have here our air, okay? Now let's say the oil level contracts or the oil itself contracts, which means that the oil level will start decreasing. Let's say the oil level becomes at here as an example. So what will happen in this case? In this case, the air will go through the presser here and it will replace this space, so the air will be here exactly in replacement of the oil itself. So as you can see, when the main tank oil starts to decrease, the air will come from outside go through the preser and replace the space inside the conservator. So this is how moisture enter the system. When air goes from outside and replace this air gap here or the gap here due to the decreasing level of oil. So here, when air goes from outside, it will cause here the presence of moisture. That's why we have this preser here. So the problem of the moisture is that if the insulating oil encounters the moisture, it will lead to affecting the paper insulation, such as a craft paper, which is used as an insulating material for the winding of the transformer between it and the core and the windings itself, which will lead to weak points inside the oil transformer or inside the winding of the transformer leading to internal faults. That's why the air coming from outside, entering the tank must be free from moisture. So what will happen is that we have this part of the preser which contains silica gel. Usually silicazle material or 90% of the times or 95% of the times, it is silica gel. Now what does this do? When the atmospheric air passes through the silica gel of the preser, their's moisture is absorbed by the silica crystals. So this silica gol absorbs all of the moisture from air. So the air going through the conservator is free from moisture. So the breather has two functions. It acts as an air filter which filters all of the particles or filters the air coming from outside. Make sure it is clear from any particles and at the same time absorbs any moisture from it. That is a function of the breather inside the transformer. Now let's talk a little bit more about the silica gel. This is a part of the breaser which is consisting of silica gel. This silicagol is the sport as you can see here. You can see inside the silicazle crystals can be orange orange crystals, or it can be blue crystals. So again, it can be blue crystal blue silicazleO it can be orange silicagol. There are two types. So the air goes through the silicajle and the moisture is absorbed by the silica gel. So as you can see that the silicagel has an orange crystalline appearance. As we absorb the moisture, the color will change to colorless. So we make this one. Silicagle has a color because it will help us to understand if this silica gel is useful now or can absorb moisture or should be replaced. So if this color is orange, as you can see here, it means that it is completely fine and it will absorb all moisture. As time passes, you will find that the orange silica gel will start changing its color from orange to colorless, as you can see here, white or colorless color, starting from the bottom, going to outwards. So the air entering, it will be absorbed here. And as time passes, it will change completely from downwards to upwards to colorless color. This means what this means that if this silicale the orange, silicagle became colorless, it means we need to change it. Okay? Same idea for the silicale with a blue color. There is a silicagle with a blue color. As time passes, when the silicazal color it changes from blue to pink, it means we need to change it. As you can see here, silicazle can be blue and they turn to pink color when they absorb moisture which indicates that the crystals must be replaced. So that's the benefit of the color here. So it can be orange converting to colorless or it can be blue converting into pink crystals. 71. Buchholz Relay: Hi, and welcome everyone. In this lesson, we will talk about an important device inside the electrical transformer, which is BocelsRlay. You can see this one, which is our BocelsRlay. So we have here our transformer tank. And if you remember, we talked about the conservator in the previous lesson and wind them, we have our buckles relay. So what's the function of buckles relay? Let's talk about it first. So the buccal relay is a protective device, container housed over the connecting pipe. You can see this connecting pipe from the main tank which contains the iron core, the windings and the oil of the transformer to the conservator tank. So it is in the middle in this pipe. It is used to its function is used to sense the faults occurring inside an electrical transformer. It is a very simple relay that operates by gases emitted due to the decomposition of transformer oil during internal faults. It helps in sensing and protecting the transformer from internal faults. Now let's talk about how does this buck relay work? As you can see, we have this pipe, this one, which is going to the transformer tank. And we have this pit, which is going to the conservator. And between them, we have our device, which is Pockels relay. Now, what happens exactly? I'll just explain it very easy. Then we are going to see it in the slides. So first, when we have an internal fault, what I mean by an internal fault, let's say, for example, a minor internal fault, a very small internal fault, which occurs between windings of the transformer short circuit, for example. Okay very small short circuit. Now what happens exactly is that? Will be here due to this short circuit. I will lead to generation of heat energy. This heat energy, this heat energy will lead to decomposition of the oil of the transformer. So that decomposition of oil will lead to formation of gases. This gas will go here like this. And it will go up here in this space. You can see the sport here. And you will find that in the Pockels relay, we have two switches. You see the one and this one. So what will happen during minor internal faults, very small internal volts. The gases will go here in this space and push this upper switch downward. So instead of being in this position, it will go in this position due to the gases emitted due to the decomposition of oil. So it will push this switch downward. And when the switch is closed, it will lead to activation of an alarm. I will not trip the transformer, but it will give us an alarm that there is an internal fault or a minor internal fault inside this transformer. Now, very important thing that during minor internal faults, the gas is not enough to push this switch. It has only enough power in order to push this upper switch downward. Okay, or upper floater downward and activating the alarm switch. Now, when we have a measure, when we have a major fault, what will happen is that we will have a very large generation of gases because it is a very large fault. So this very large amount of gases will push this lower floater and activate this switch. So it will activate the lower switch and also activate the upper switch because we will have here a large internal fault, which is corresponding to large amount of gases, which will push this floater and activate this switch. So in the end, this switch when it is opened or when it is closed closed and activated, this switch will lead to tripping of the transformer, I will turn off the transformer. Okay? So in lower faults or in minor faults, the upper floater will activate a switch, which will give us an alarm. In a large fault, both of the upper and lower switches will be activated. It will give an alarm, and at the same time it will trip the transformer. So that is a function of the pocosary. It protects the transformer against internal faults and external faults. So let's see when we have a minor fault that occurs inside the transformer, the heat generated due to this small fault in the transformer will lead to decomposition of the transformer oil. And you'll find that we will have a gas bubble produced due to the decomposition of this oil. This gas power bubble will flow upwards direction and get collected inside the pocos relay. The collected gas will displace the oil in the buckles relay and displacement is equivalent to the volume of gas calculator. As you can see, this gas will go here will be accumulated here and it will displace this oil pushing it downwards, this floater will go downward. The displacement of oil causes the upper float, which is this one to close the upper switch, which is connected to an alarm circuit. Hence, when a minor fault occurs, the connected alarm will be activated and the collected amount of gas indicates the severity of this fault. So how much gas is here, this will be equivalent to the severity of this fault. So during minor faults, this amount of gas are not large enough to move the lower float. It is only enough to displace or move the upper float downwards. Only be able to activate an alarm. Over the lower float is uneffected. Now, during major floats like a phase to earth short circuit, or phase to phase short circuit, the he gen rate since it is a short circuit, it will be very large and large amount of gas will be produced this amount of gas will similarly flow upwards, but its motion is high enough to tilt the lower flow. So it is very fast, and it will push this switch with the floater, pushing it like this downwards, leading to activation of the switch, leading to activation of the switch. So you will see that we have a tilted part here. You can see this tilted part. When the large gas go here and push this one, it will lead to activation of the switch. And at the same time, this floater, when the oil starts to decrease, this floater will be moving downwards, leading to operation of the switch. So as you can see here, let's explain this point again. So we have this upper switch. You can see per float. Swing is open with a high gas level. So when we have lots of trapped gases due to the decomposition of oil, it will move this floater downward. Okay? So it will activate an allow. In the lower part here, you will see here pale swings open with oil so you can see this part here. Okay? So when we have very strong gases, it will push this part to this position. When it is moved to this position, it will activate the switch. Leading to tripping the transformer. Now, another floater unlike this one, we have this floater and we have this one. This floater here, which you see here, its function. Was its function? Is function is that the lower floater swings open with low oil level. So what I mean when the oil level starts to decrease beyond a certain level, you will find that this floater will start going down, which indicates that the oil in the transformer is very, very low and it is a dangerous position. That's why this switch will be also activated due to this floater. So we have three parts here, the upper floater due to minor faults. This puddle swings. This one will be activated when we have a large fault that will push it and activate a switch, and we have this lower floater that will be operated when the oil level is low. So you'll find that in this case, the lower float will trip the transformer from the supply. So in this lesson, we talked about the apocalzlay function inside an electrical transformer. 72. Methods of Cooling: Now let's talk about the different methods of calling the electrical transformer. So we talked before about the different components that we have in electrical transformer, and we need to understand more about the calling methods ins the transformer. That will help in defining the power rating of an electrical transformer. So the first method, which is simplest method is called the air natural. Calling is used in the Troy self cooled transformer. You can see we talked about the Troy transformer and we said that it is called Pi air. So we say that we have air natural. It means that it is called by air. The cooling medium is air and is called naturally due to the natural circulation of air. So as you can see here, all of the heat energy will be dissipated to air. In this method, the natural circulation of the surrounding area of the surrounding air is used for calling the transformer. The natural method, this method, what you see here is used for low voltage, small transformers up to 20 kilovolt and pair. The second method is that we will have also the dry transformer, but in this case, we have air forcet. What I mean by this, we have the cooling medium, which is air, but this cooling medium is forcet. What I mean by this, it means that we have here in this method. We have a continuous plaster of filtered cool air is forced with the help of a fan through the core and winding of the transformer for cooling. You'll see this fans will provide forced air through this transformer. This will, of course, enhance the cooling of the transformer compared to the air natural method. Air natural due to the natural circulation. In the air faucet, we have a fan that will force the air. So the air plast or the air faucet are used for transformers up to 50 kilovolt and pair. So the method is that we will have an oil transformer. In this type of transformer, we have oil natural, air natural cooling method. So the first part here, representing the cooling medium or the insulating medium inside the transformer. You can see here oil natural, you can see we have an oil transformer. So the oil is used to take heat energy from the windings and cool of the transformer. And then it will transfer it to the tank of the transformer, which will be cooled by air naturally. That's why it's called oil natural air natural. We don't have any pumps. We don't have any fans. So the oil air natural cooling is used in the oil immersed type transformers. You'll find that most of the medium and large rating transformers have their core and one immersed in di electric oil or the mineral oil or the hydrocarbon oil, which acts as a cooling medium and insulting medium at the same time. This type of transformers is used for 50 kilovolt and part up to ten megavolt and pair. So as you can see, the better the cooling, the higher the power rating. Now the next method is called oil natural, but this time is air forcet. Oil natural means that the transformer is cooled by using the insulating oil, which will move upwards when it is heated and provides its heat energy to the body or the tank of the transformer. And then this heat energy will go to air. However, this time we have not air natural, but air forcet, which means that we are forcing air to cool the transformer. So we have here in this method we have fans. So in the previous one, we had oil natural and air natural, which means we didn't have any pumps and fans. In this case, we have air force. We are forcing air using fans. In the oil natural effocet cooling of the transformer, the heat generated by the cool and winding of the transformer is transferred to the walls of the tank and to the radiator, which is a radiator fence through the natural circulation of oil, similar to what we discussed in the hematic transformers and in the oil transformer or the conservator transformer. Now this time since we have air facet, the faucet air is directed over the cooling elements of the transformer. Hence the transformer is cooled by the natural circulation of oil and the plast of air. Of course, this one, this type, oil natural and air faucet has a higher power rating than oil natural air natural. The next method is called the oil facet air forcet. Now, as you can see, facet and facet, it means airforcet, it means that we have fans that will force the air to cool the transformer. And we have oil forcet. It means we are forcing the oil using pumps. So you can see we are pushing the oil through heat exchanger using pumps and getting it back using pumps. So you can see in this method of cooling the heated oil, is circulated from the top of the transformer tank to a heat exchanger. You can see the heated oil or the higher temperature oil will go outward. It will be pushed by a pump to a heat exchanger. The plast of air is forced through the heat exchanger by turning on a fan, you can see this fans will push air to this heat exchanger to its heat exchange the heat from oil to air or transfer oil or transfer heat from oil to air. Then the coal oil is returned to the bottom of the transformer tank. This method of cooling is used again for higher rating transformer, other than oil natural and air natural. And this time we have oil force. So we are forcing the oil using bombs. So this method is used for higher power ratings of transformers that are used in electrical substations, large electrical substations, and generating stations. Now the last method is called the oil, facet, water faucet cooling. In this case, instead of having air, we have this time water, which means it will provide higher cooling for the oil. So as you can see here, in the oil force water force cooling method, the heated oil is circulated from the top of the transformer tank to a heat exchanger, so it is provided to a heat exchanger. But this time instead of having air with a fan that will cool the oil, this time we will have water that will be provided to this heat exchanger and exchange the heat energy from the oil to the water, where the pressurized water is used to separate the heat from the oil. The coal oil is returning to the bottom of the transformer. As you can see, we have pump that will return back or force the oil, the coal oil back to the transformer. Now, this type of cooling is used for very large transformers, generating station. As I remember, it can exceed or reach up to 600 megavolta beer as I remember, very large ratings of the transformer. In this lesson, we talked about the different methods of cooling the electrical transformer. 73. Tap Changer in Electrical Transformers: Hi, and welcome everyone. In this lesson, we will talk about a very important component inside the electrical transformer, which is the tape changer. You can see this device is our type changer. So what does it do? You'll find that the output voltage which is going to our load or the output voltage of the transformer, the secondary winding may change depending on the input voltage to the primary winding of the transformer and due to the loud, the variation inside the load. So during the loaded conditions, the voltage on the output terminals will start decreasing, whereas during off load conditions, output voltage will increase. So in order to balance the voltage variations, the type changers are used. The type changes can be either on load type changers or off load type changes or flouid type changers. What does this mean? All load type changers, it means we can change the number of terms during the operation of the transformer without isolating the transformer from the supply. However, off load tibi changer, it means that we need to disconnect the ad or turn of our transformer before changing the number of turns. The tabihanger function is that it changes the number of turns to provide constant voltage to the load. And there are, of course, automatic tab changers which are found in large transformer or transformers in the generating power stations, which are, of course, on load tabihangers. Now let's understand this ID. So let's look at this. We have this transformer, a step down transformer. We have the high voltage side and we have the low volt side. The nominal rating of the transformer is hundred 13,200 volt 480 volt. So this is the nominal rating, which you can see on the transformer. So the voltage here 13 200. And the out is 480 volt. So we have here our out for 180 volt. Now, let's say, for example, that at the end in the end we have here our load our load here, we have here our cable here and here. This is our cable. Okay. So what will happen is that usually when I have a 480 volt, for example, I would like the voltage at the end user, for example, 400 volt, as an example. Assuming that 480, it will reach 400 volt at the end user. Now, the difference between them, which is the 80 volt, where does the 80 volt goes? It goes as a voltage drop on the cable. The voltage drop on the cable is equal to the current absorbed by the load, multiplied by Z, which is the imbedance of the cable itself. Now, let's say that our load starts to decrease, starts to decrease. So what will happen here? What will happen is that when our load starts decreasing, the current absorbed by the load will decrease, okay? So when the cnn starts to decrease, the voltage group will also decrease, right? So instead of reaching or instead of having a voltage of 400 volta at the end user, we will have, for example, a 410, a higher voltage. Now, what is the problem here? The problem is that the voltage here it changed at the end user. It is higher than what the equipment can withstand, which can lead to other voltage issues. Another case is that if the load amount of load increased it means that the current will increase leading to higher voltage drop, leading to since we have here, higher voltage drop, then the voltage here can be, for example, 160, which is lower than what is required by the load, which can lead to under voltage issue. In the end, what can we do in this case? What we have to do is that we need to have a constant value, Let's say I would like to keep a voltage of 400 volta at the end user. So in order to do this, I need to change the number of terms here to change the input voltage here. Now, how does this even happen? Now, if you remember that V two is equal to V one, multiplied P A two over N one, number of turns of the secondary, divided by number of turns of the primary, multiplo by V one. If I would like to change V to the voltage here, to keep the 400 volta at the end user. What can I do? I can change N one or change in two or change V one. You can see we have how many options, one, two, three. Now you have to understand that we don't do the change of the number of turns at the secondary. Why? Because at the low voltage side, we have a very large current, which will lead to very large current surges when switching from one turn to another or switching the types of the transform so we are not going to change we are not going to change any two, okay? So what are we going to do? We have two options. Either to change the supply voltage, it is coming from the electrical substation. This we don't have any options. It's coming from the electrical substation. Okay? So our only option is to change N one. By changing number of turns of N one, we can have a constant output voltage, okay? So let's say, for example, let's say here, let's just delete all of this. Okay? So we have V two equal to V one, N two over N one. Okay? Now we have at this side, we have plus -480 volt. Okay? And we have here the original one, let's say, zero thousand 200 volt. Okay. Now, what will happen is that let's say, for example, that the voltage here, let's say the loud decreased, loud decreased, which means we have a lower voltage drop, which means we need to decrease this voltage. So how can I decrease this voltage by increasing number of turns? So as in one increase, V to start decreasing. So as in one increase, V tool start decreasing, which means instead of having 480 volt, we can have, for example, 440, which will lead in the end to 400 volt. Okay. So how can I increase number of turns instead of having at this position? I will put the taving at this position here. So we will have this large number of turners. So N one increased, so we will start decaying. Same idea. Let's say, for example, if the load voltage increased, let's say it reaches 360 volt, the load increased, so the voltage drop increased, leading to a final voltage of 360 volt. So I need here at this point, I need, for example, to increase the voltage to 500 volt. So in order to increase the voltage here, we will decrease the number of turners. So we have a lower number of turns. So in the end, by controlling in one, I will be able to control the voltage here to make the voltage at the end user for 100 volt. Or even if the end user without any voltage drop is here, and if the load increased and decreased, it will lead to a different voltage drop and leading to a different voltage. Okay, so by controlling these tabs, we can have this function. This is one of the functions of the tab changer. But let's have another more function which is useful for Tabithanger, which is also well known and it is used a lot. You can see we have niner rating, 3,200 volt, 13, 500, 13, 800, 12, 800, 12, 500. So as you can see what will happen here. So let's say if the supply coming is 3,200, then I will put it, for example, at position two. If the voltage coming from the substation is 3,530, then what I'm going to do is that I'm going to put it into tab number one. So I increase the number of terms in order to keep the output voltage constant. So depending on the voltage coming from the substation, I will choose what tab should I select. I will select my own tab, depending on the input voltage. Now what does plus 5%? 2.5% mean? It means that 2.5% of the total number of urns, plus 5% of the total number of urns. -2.5% means I'm decreasing the total number of turns by 2.5%. I'm decreasing the total number of turns by 5%. So the taps, as you can see, they are on the high voltage side because as you can see, number of turns is very high, which means we have a better accuracy and adjustment of voltage is possible. You can save very small number of turns. So if I'm going to do some taps, it will be very hard. Unlike this one, you can see we can have a very large accuracy because we have large number of turns. Second reason is that the current in high voltage winding is lower. So when I switch from here to here, the current surge will be lower or the switching surges will be lower because switching on lower currents is easier and the spark will be smaller. Okay? So the lower current surges here. However, if I am going to the high volide, there will be higher voltage, higher current surges. Why? Because if you remember, at the low volide we had a very large current, and in the high volt side, we had a very small current. Now, as you can see, how can I do this? How can I do this in real life? So we have an Exca transformer, a step down transformer. You can see high voltage side, low volt site. This one is A one B one, C one, which is a delta connection. And as you can see here, A one B one is small, and you can see then neutral of the Y or the star connection. You can see this one is a star connection at the low volt site, and Delta connection at the high voltage site. Now you can see that this high voltage have a different voltages. Depending on the inbot voltage, I will select the tab. Let's say, for example, if our inbot voltage is 3,300 or 33,000, 33,000, it means that I'm going to connect these tabs or the position number three. What does this even mean? You can see here we have five, six, four, seven, three, eight, two, nine. This four C one, B one, and A one for the different phase. Let's say, for example, if my own input is a 33 kilovolt. Then I'm going to use four and seven or position three. So how can I do this? Simply, it's really easy. You just select four and seven connect them together, four and seven connect them together, four and seven connect them together. Then you will be in position three. And you will be able to connect 33 kilovolta supply. And depending on position on what voltage is the input, you can, for example, if you have this input voltage, then you connect two and eight. You can see two and eight connect them together, two and eight connect them together, 28 and connect them Of course, there is no other connections, only the one seen here. So what I mean by this, if, for example, I have this one, then I will connect to only four and 64 and six only together. Okay. Nothing else. We will be in position number two. As you can see here, by connecting them, we can change a number of turns, and we will have a constant output voltage. Now, as you can see here, we have this type, which is the unload tab changer. This one is an offload taphanger. The offload type changer, as you can see, we have this wheel. When rotating this wheel, we will be able to change number of turns and change or changing the tabs and changing number of turners. Similar here, we can change number of turns inside an unload tabchanger. Now, since it's unload, it is usually done automatically. Okay, because the transformer is very dangerous, you cannot just go close to it. Okay? It is done automatically using automatic tab changers. The load tab changer is used in power transformers, and this type of tabihangers have a 17 taps or more and also has a special oil inside it for eliminating the spark during switching. So when we switch from one tap to another, there will be a spark. This spark is killed or eliminated by using a special oil, not the oil of the transformer, a special oil. The offload type changer is used in distribution transformers with only three or five taps. You can see 17 tabs for the large transformer, onload type changer at the generating station. However, the offload is used in distribution transformer at the end user distribution network. So the power transformer at the beginning of the system at the generating power station and distribution at the end of the customer at the customer or at the end user with only three or five tabs, and here we use the oil transformer during switching. Since it is switched when the transformer is switched off. Remember that off load type changer, we disconnect the loud or isolate the transformer from the loud. So we don't need a special type of oil for eliminating the spark because there is no spark because it is turned off. In this lesson, we talked about the different types of tape changers or the type changers inside an electrical transformer. 74. Explosion Vent: Hi, and welcome, everyone. In this lesson, we will talk about another component inside the electrical transformers, which is the explosion vent. So where is the explosion vent exactly, you will find it here in this figure. You can see this part, the pipe which is connected to the tank of the transformer, and in the end, this part is called the explosion vent. So what's this function? The explosion vent is used to expel the boiling oil in the transformer during heavy internal faults in order to avoid the explosion of the transformer. What I mean poses during heavy internal faults, such as, for example, short circuit. During short circuit, we will have a very high temperature, very high temperature of oil due to the generation of heat energy due to the short circuit itself. The temperature of oil will increase very much leading to expansion of oil. Okay, beyond the space we have here in the conservator. So what will happen is that if we don't allow this expanding oil to have more space or giving it space to expel this boiling oil, this transformer can be exploded or explosion can happen inside the transformer because this oil which would like to expand does not have any remaining space. So instead of this, we have this explosion vent in which would has a small glass. So when the oil becomes expanding very, very much, you'll find that the boiling oil will go through here and release all of the pressure using this explosion vent. Okay? So during heavy faults, the oil rushes out of the vent. And the level of the explosion vent is normally maintained above the level of the conservatory tank. Why? Because, of course, all of the oil will go through the conservator or the conservator, and this one will be at a high level, so it will allow it to be the last place it will go to. So it will go normally to the conservator tank and lastly to the explosion vent. 75. Temperature Monitoring and Control Box: Now let's talk about another thing inside the transformer, which is temperature monitoring inside the transformer. If I would like to monitor the transformer winding temperature, such as here, you can see winding temperature. And we have here oil temperature. We can measure the temperature of oil and winding temperature. Why is the indicator that will help us to make sure that our transformer is at a good state? We should make sure that this transformer does not exceed its temperature does not exceed a certain limit. Now, as you can see, we have two needles here, there's one black needle and red needle. So what do they indicate? Red needle indicates the highest temperature that the oil reached in one day. And the red needle here for the winding brature it means the highest temperature that the winding reach it in one day and the black needle representing the current temperature. Okay? So we have the highest temperature, which we reach it in one day and this one representing the current temperature of the transformer winding or the oil. Now, as you can see here, we have four other parts here or four temperature indicators. What do they indicate? These are used to select the temperature at which we are going to start. For example, the motor pump forcing the oil. Also, it will help us too, starting another cooling method such as fans. And at the same time, it will give us an alarm and trip the transformer. So each one of these temperature has a certain function according to what we would like. As an example, if the temperature of the winding reached, for example, 80 Celsius degree. I would like the fans to operate. So I will select here a temperature of 80 Celsius degree. It will be going to give the signal to the fans. Now, if I would like the pump motor pump to force or make the oil force it to a heat exchanger, then I will, for example, make this at 100 Celsius degree. And at the same time here, if I would like the alarm to be given, when temperature reaches 80 or 100 or any value, I will select it here and the out will be connected to an alarm. Here is the same idea. If temperature reaches a certain value, it will give a signal to circuit breaker to trap the transform. So that is a function of this part, giving the temperature monitoring, and at the same time, gives us signals to our protection devices and cooling methods. So the black needle here, as you can see, this one, so is the current winding temperature, the current. What I mean by current at this instant. At the time we are looking at this temperature monitoring, we will know what is the temperature of the winding itself. However, the red needle shows the highest winding temperature, reach it for a particular day. And here we are in this spot when I'm talking about winding temperature and highest winding temperature, I'm talking about this one. You can see winding. Okay, so the black representing the current winding temperature, temperature, and red representing the highest winding temperature. For the oil, it will be the same black representing the current oil temperature, and the red representing the highest oil temperature in one day. And you have to note that the red needle must be reset manually. So after looking at it, we can reset it again manually. Now let's talk about another thing inside the transformer, which is a control box or panel, which can be found beside this electrical transformer. What does this control panel contain or what does it do? You will find this control box or control panel. It houses that transformers monitoring devices, terminals. So for example, it can contain the temperature monitoring devices. It can contain the auxiliary device such as, for example, the terminals of the pushing current transformers and the calling fans. All of this can be inside. In addition to the indicators of the tab changer connections. Okay. So what I mean by pushing current transformers, you have to know that we add here current transformers around the pushing of the transformer in higher rating transformers in order to measure the three phase current. It's going to a protection system, going to a relay that will be activated if a certain condition met. For example, if, for example, we need these currents for the differential protection or other current protection, any kind of protection of an electrical transformer. So since we are talking about different types of protection, differential protection over counter protection, and so on, I advise that you go to our course for electrical protection, which you will find it as a part of power electronics course. You will find inside it the differential, the overcter protection, and other types of protection device. Okay? 76. Power and Distribution Transformers: Now let's talk about the power and distribution transformers. So we talked about the different types of transformers, such as dry transformers, the oil transformers, such as hermetic transformers and conservator transformers. So let's talk about another definition which is power transformers and distribution transformers. They are similar to each other. There is no difference in construction. The only difference is their power rating and their location in the electrical power system. So let's look at a comparison between them. The distribution transformer is used for the low voltage distribution system. Then 33 kilo volt in the industrial applications and 380 volts 220 volt or any other values depending on the country itself for the domestic purposes and as a step down transformer. The distribution transformer is used to supply electrical power. It is used to step down the high voltage to low voltage for supplying the consumers or the end customer demand. Okay. So it is used as a step down transformer to supply electrical power to the end of the system, electrical power system or the distribution network. However, the power transformers are used at the beginning of the transmission system and throughout the electrical power system. They are used in generating stations as a step up transformer and in transmission substations as a step down. For example, taking the step up means it will take, for example, 11 kilovolt of the generating substation and convert it to 220 kilovolt or 500 kilovolt or any other transmission value. Then throughout that transmission system, it will start stepping down this voltage. It will take, for example, the 500 kilovolt, convert it, for example, to 66 kilovolt, and again, take the 66 kilovolt and convert it to 33 or 11 or 22 kilovolt, whatever, the value depending on the country code itself and the design of the system itself. So it is used to increase the level of voltage to higher value for transmission of electrical power over the long distance. So as you can see, distribution only a step down transformer. Power transformer step up at the generating stations and start stepping down the voltage throughout the electrical system. And we said before, why do we step up the voltage in electrical transformers in order to reduce the losses in the electrical system? Now, their location, the distribution transformer is installed near the load centers or at the consumer's end or at the customer's end. However, the power transformers are installed at the generating station and along the transmission system or the transmission substation, the transmission section of the electrical power system. Now, as you can see, since the distribution system at the end user and power transformer at the beginning, you will find that, of course, the distribution transformer are smaller in size and power transformer are larger inside because this type has a low power power rating, and this one has a high power rating. Their maximum efficiency are given at 60 to 70% of the rated load Z, that is the value at which it will be loaded. However, the power transformers are having the maximum efficiency at full load condition. They are at full load all the time. If they are at no load state, they will be turned off. However, the distribution transformer can be loaded from, for example, 20% to hundred percent, depending on the current state. Also, what about the flux density, which is Peta Beta in distribution transformer is low flux density compared to the power transformer, which has a high flux density. What about the protection system? So you can see that since the distribution transformer or a low rating transformers, they have low protection devices. What I mean by this, they have a high HRC fuse or high rupturing capacity fuse, which is used to protect against short circuit. If you don't know about the HRC fuse or any other protection systems, you can go also to our course for electrical design. Another thing here you can see, we have the over current to protection, Pockels relay which we discussed, restricted ERS volt to protection, which is against leakage current to the Earth. We discussed this in our course for electrical design and protection systems for larger transformer larger than 500 kilovolt and pair. So if we have a transformer less than 500 kilovolta and pair, we use only the HRC fuse. If we have a higher than this, then we will start adding more protection component. However, the power transformer is really, really important, so we will start adding more protection to it, such as a pocalzla the explosion vent pressure relief that we discussed before, temperature indicators that we have seen oil gauge or the magnetic oil gauge oil level gauge that we discussed before, the lighting arrestor or here. I think here lighting, not lighting. Arrestors they are used to protect against the surge or the lighting effect. And we talked about it before. In the previous lessons, in addition to differential protection over current over flux, combination of lots of protection device. Why? Because this type of transformer provides very large amount of electrical power and it is really, really important compared to the distribution transformer which has a lower rating. 77. Assembly of a Three-Phase Transformer: Now, everyone, before we end the transformers part, we will talk about the assembly of the transformer. Let's look out how distribution transformer, for example, is format. Let's look at this video, I will help us understand the different components inside ctrigal transform. So as you can see, we have the three legs of the transformer and the lower yolk of the transformer. So let's go down. You can see we put the first winding, which is internal winding. What I mean by the internal winding, which is the primary or the low voltage, and you can see we are surrounding now the high voltage winding. So we put the low voltage. Then we put the high voltage as you have seen right now. Then we have the upper part, which is the yoke of the transformer, the upper yoke and we have the lower yoke here as you can see here. Then we added the tank. We now closing the tank of the transformer. As you can see with the conservator, you can see this is the upper part of the transformer. Now, this part is the tab changer. We have seen an image for the tape changer, this part. By rotating this wheel, you can see there is numbers here. By rotating this wheels, we can change the position of Tabithanger and we can change this tab. Of course, this is a distribution transformer which operates at load, not at no load condition, but when we are isolating our transformer, we need to disconnect our transformer, then we will start changing the tab of the transformer. And as you can see, they are adding now the part of the transformer, this part here. Let's get back here. As you can see this part, which is pushing of the transformers, as we learned before about them, as you can see the low voltage and high voltage pushings. Then they are connecting everything, welding everything, as you can see here. And then finally, we have our transformer, as you can see here. Okay? That's all for this video, as you can see here. This was the assembly of the electrical transformer, as you have seen the different parts which we have discussed before in the construction of an electrical transformer. 78. Principle of Operation of a DC Motor: Hi, and welcome everyone to our course for DC machines, the ultimate DC Machines course. In this course, we are going to start discussing the DC machines that operates on DC supply, either to generate DC supply or takes DC supply to convert it into mechanical power. So in our first lesson, we will discuss the principle of operation of a DC motor. So how can we use a DC supply and and convert it into mechanical power? So in order to understand this principle of electrical to mechanical, we need some ingredients that you will find inside our conversion systems to electrical to mechanical and vice versa. So in order to convert electrical energy, for example, in this example, we have our DC supply. This is our supply. Okay? DC source, as you can see a DC source, or for example here, we have a battery, DC source or DC supply battery. I would like to convert this DC source or electrical power into this rotation or this mechanical power. So in order to understand that, we start with a very simple rectangular form, which you can see, you can see this rectangular loop like this. Okay. This rectangular loop, we would like to rotate it. Okay? So in order to do this, we need three ingredients. Number one, we need magnetic field, magnetic field, which as you can see here north and thus, right, north and south. Okay? Between them, we will have this magnetic field like this, going from north to thus like this. Magnetic field like this. Okay. Great. Number two, we need an electrical power source. Our source here is our battery, as you can see, a DC supply. In our case for DC motor. Number three, we need a conducting wire. So what I mean by conducting wire, not this actual wire. What we are concerned with the wire, which we would like to rotate. This one, I would like to rotate it. So I will need an electrical current to flow through it. So as you can see here, as you can see here, I would like an electrical current to flow. So what we do is that we connect the supply like this, that's draw it. So we will have our supply positive and negative, and we connect it like this. For simplicity, we will just assume that this does not exist, so that we can understand the concept. So we have our north like this, South, like this, and we have magnetic field between them, like this. This battery will lead to flow of electrical current, like this currenty goes from positive to negative like this, go through it like this. Okay? Like this. Now, we have number one, magnetic field north and south, okay? We have electrical source, DC battery. We have our conducting wire, as you can see, all of this conducting one. Now, how can I rotate this? If you have these three ingredients, then you will have a torque generated. Now, someone will say, how can we even get a torque? Okay, this is based on the principle of flaming left hand rule. So if you look at the flaming left hand rule, let's draw it. Flaming left hand root say that if you have number one magnetic field, you have an electric current inside and you have a conducting wire, then this wire or this lobe will start rotating. So let's get back and see how. So what you can see here is that you have three directions. You have direction of magnetic field. So our magnetic field in this direction like this. So we will take this thumb here and put it like this. Okay. In this direction. What about the direction of current current is in the upper direction. So this as if it is on the other side. So as if we have our hand like this for magnetic field, for the direction of the current, it will be like this, and this thumb or this part or this finger will be pointing downward. So it means that we will have a torque generated downward like this. Based on this principle. So we will have on this side, current flowing like this, direction of magnetic field like this. So according to flaming left hand rule that we discussed in magnetic circuits, you will find that we have a direction of torque going down, or the force going down like this. Okay? For the other side, we have the same direction we have from north to south north to south like this. We have current in this direction in this direction like this, same direction of this finger. So our force will be up. So our force will be up like this. So what does this mean, you'll see that we have a force like this, force going up, so they are opposing each other means that our loop rotate like this. So it will start rotating. Okay? This is how a motor works. Very easy, right. All we have to do that due to presence of current and magnetic field, conducting wire will have a force on it based on the principle of lemming left hand rule. Okay? So we'll have two opposing forces that will lead to rotation or a torque produced. Similarly, as you can see here, the same principle. We have north and those like this, north and thus, magnetic field like this in this direction, North, and let's type it with a pencil, make it easier north and thus between them like this. Okay. And we have our current flowing down like this, perpendicular in this direction. So it will be here in this direction. So here like this, and this is like this. So the force will be upward. So you can see that the force is upward. Similarly, this one will be the force downward leading to rotation to the other side. So what you can see here is that we rotate based on the direction of the current. So if the current is like this, then we rotate clockwise. If it is inversed by inversing as a supply, then we will rotate from the other side or anticlockwise, okay? Okay, so again, we have this thumb here representing the motion, first finger representing direction of magnetic field and current. So if we just take our hand, put our direction of the field like this and let's say current like this, current current going in, so not like this, it will be on the other side, like this. So this finger will be on the other side, it will be like this. So this finger will be downward. Okay? So our torque will be anticlockwise. Similarly, this one will be clockwise. So that is the principle of motor. Okay, so let's see this one from Jared Owen channel. This gives us a nice animation to understand this principle. So let's go to this. So let's see from this minute exactly. As you can see here that we have our supply current coming in, and this is the other side at which the current will go out. This rings, these two rings that we use called commutator rings. Okay? What the benefit of them, we will understand right now. You can see that there is a gap between them. They are insulated from each other. Okay? So we have this section or this side is connected to this commutator ring, and this one is connected to this commutator ring. Okay, so they are separated from each other. Each ring is connected to one supply, okay? So what happens exactly? So as you can see here that these these are called pushes. Carbon process. What the benefit of them, they are used to take this electrical current and energize this ring. So for example, if we have our current like this I going like this, it will go through this carbon process. Then are in contact in always contact with this commutator ring. So it will energize it with an incoming current. So the current will go like this. Okay. The other side, it will go all the way like this. Then the erg so the current will go like this and go out. Okay? So simply, we have two polarities, positive and negative. These carbon processes are always in contact with these rings, and you'll find that since we are rotating, then we would like to keep this carbon process in contact. We have inside here a spring that keeps this process in contact with the commutator rings. So let's continue like this. So you can see that it rotates. We are supplying a current. So let's say it rotates in the clockwise direction, okay? Now, the most important question, okay, is that, how can we have a unidirectional? So what you can see that when we rotating like this and like this, in the vertical position in the vertical position, we will have zero torque. We will have zero torque. Now, if I would like to keep it rotating in the same direction, you can see that when we are in the vertical position and due to the inertia, it will keep rotating in clockwise. However, when it rotates, I would like it to keep the same direction. So what you can see that it switches to the second one like this. You can see that here, we are giving here a current. Let's just delete this. You can see that we are giving current, okay? Like, look carefully at this one. So we have an entering current. Let's say it rotates like this, for example, rotates in this direction. Now, this site will go all the way to the other one. So let's go like this. Okay, like this. As you can see that when we take this side goes all the way to this side, I would like the torque to be in the same direction. So I'm going to switch from giving current, positive current to this one, I will give it to the second side that came here. So you can see that we always giving current to the same side. I would like to give the current to the side here so that it keeps rotating in the same direction. So as you can see, we rotate, and then when this side came here, I give it the current so that it will keep rotating in the same direction. Okay? Like this. So that is the benefit of the commutator rings that when our side, when the side came here, the one here will always take a positive current or always take a negative current. Okay? We also have another problem that we will see right now that when we are dealing with like this one loop back this, you can see Like this irregular motion, regular motion problem. Now, why do we have this irregular motion? Because when we are in the vertical position, we will have zero torque, Okay, in the vertical position. So this zero torque problem makes an irregular motion of the machine. So how can we solve this by adding more windings. You can see that this winding has two commuted rings. So let's look at this. You'll see that this winding has two commuted rings, one and two. We add another winding with this commuted ring and this commuted to ring. When this one is in the vertical position at zero torque, this one will have the maximum torque because all of the flex line are cutting it. When this one has a zero torque, this one will have a maximum torque leading to continuous motion like this. As you can see here. So when this one in the negative position, this process switches to this one. Okay, before reaching the so you can see that this switches to this one, before this one reaches the zero torque. So that this one keeps giving us more momentum and more rotation like this. Okay. Now, in order to make this machine more smooth, we add more windings. Okay? Instead of just one coil, this one which we call one rectangular loop or one coil, we add more and more like this. So we will have lots of rectangular loops, which you can see right now. Each one is connected to two commuter rings. So you can see that now more, our machine became more complex. We have one, two, three, four, five, six, et cetera. You can see one commuter to ring, two, three, four, and, et cetera. And all of this keeps switching between these two process. Like this. So our machine will be moving more smoothly as we can see. Now, not only this, these winding are placed inside an armiature core. This one which is made of steel or laminated steel. This is a core at which we install our windings. These openings, which you can see here inside this core is called the slots of our machine. This slots of the machine. We add inside them the windings of our electrical machines or these rectangular loops. So that it provides a better interaction between these two pools north and south and provides better magnetic flux interaction between these pools and these windings, like this. Okay. And of course, when we are generating electrical mechanical motion, we would like to have a shaft in which we are going to install what we would like to provide mechanical power to it. So this is our shaft here. Now, of course, as we said before, these are carbon process which are in contact with commutator rings. They always have a spring in sodium to keep the contact with the commutator rings. Okay as you can see here. Okay, great. Now let's continue. If I would like to build up, similar as the previous lesson, you can see that we have only one loop. So when we add more and more like this, you can see that it switches like this. The problem is that at this position, we have a zero torque. So it will lead to a regular motion, as you can see, so we add more and more rectangular loops, as you can see here. In order to make it rotate, as you can see. So this one will have a more position, then it switches to the second one like this, giving it the current so that it will start rotating. This one will be not energized. T will be energized like this, et cetera. So it will keep switching so that we will have a smooth motion of our electrical machine. And as we said before, we will add more and more rectangular loops or more and more windings in order to make it much smoother. You can see that here, keeps switching between them so that our machine keeps rotating, as you can see right now. Okay. As you can see, now, of course, our loop, to be more specific, our loop is consisting of or this rectangular loop is called a coil, okay? Made of conducting wires or a conducting material. These loops can be multi turn with what I mean by this, more than one. You can see how many wires, one, two, three, four, five, six, and seven, et cetera. Mini wires. These wires makes the torque much higher and better electrical motor. Okay? And we said that it's placed inside the slots and keeps rotating as you can see. And in reality, it will be something like this for a toy, very small one, and for an electrical motor, you can see that we have the same configuration see. These are the commutators. This is our shaft, and you can see all of this our slots at which we bought our wining. Now, don't worry. We will discuss in details in the next lessons, more about the DC motors. We will discuss more clearly about the DC motor or DC machine construction and its components. 79. Principle of Operation of a DC Generator: Hey, guys, and welcome to another lesson in our course for DC machines. And this one we will discuss the principle of operation of a DC generator. So again, how can we produce electricity? Again, the same principle of the motor, we said we have three ingredients inside our motor. We set for a motor. We need number one. We need a conducting wires, wires, we need magnetic field. And we need a DC supply. What if I would like to change motor into a generator? In order to do this, very easy just replace DC supply with a mechanical power. That's all. You will have a generate the same construction exactly. In order to have this rotating and you can see this is a galvanometer which measure the current, you can see that the currency fluctuates between zero and maximum value like this. Okay. Now, as you can see, we take this rectangle loop and provide for a mechanical power, that makes it rotate. Okay? And we have our conducting wire and the magnetic field. Then when we have these three ingredients, you will have a generated current. That's all. Now, as you can see here, here, we have two rings for this rectangular loop, as you can see, and on this axis of rotation, we provide a mechanical power or a torque in order to rotate this loop inside a magnetic field. Okay? Now, again, using the flaming left hand rule, you can get the current. So for example, if you have force like this, torque of rotation like this, torque like this. It means that this force will be downward like this. This force will be upward, direction of magnetic field. You have direction of magnetic field. You have direction of force going downward. So you can using this two, you can find the current using flaming left hand role. And as you can see that this current is unidirectional or DC. Why? Because we are putting it in this principle. Okay? Someone will say why DC Because as you can see here that this side is always connected to the coil facing north. So let's say this coil goes here at the beginning, let's say that the current is positive, current like this, generated current generated current like this, I. During the first principle, we have at the first position, we will be like this vertical, zero generated power. Okay, when we are in the horizontal, we will have maximum generated voltage or generated current. Why? Because at the vertical position, we have a zero magnetic flux interacting with our loop. However, in the horizontal position, all of our magnetic flux is cutting this rectangular loop. Okay? We will see this in the next slides. So we have here our current in this riction so in this riction like this, like this. So when it goes from here from maximum to let's say this vertical position like this, it will be from here to here. Okay? I will show you in each ofsion in the next slides. Okay? Don't worry. Now, when this one goes to the other side and this one goes here, you will find that this side will now take the same direction of current, and this blue one will also be connected to this commutator ring. So it will always take the same current. So this configuration makes that this brush is always in contact with the site here. Okay? Is our blue or green, whatever blue or red? Whatever it is, the side on here. This one is always in contact with the one on the south. That's why the current will always have a unidirectional. You can see that unidirectional. Now, in the AC AC electricity generation, instead of having this configuration, we will have 22 rings like this, and this red one will be always connected to this one, and this blue one will be always connected to this one. So let's see this in order to understand. So we have this configuration to help us understand DC electricogens. Let's say we are rotating in this direction. Okay? So we will start in this vertical position. In this vertical position, as you can see here, you'll see that the flux will not cut the conductors. So we will have zero generated volte. In the vertical position, remember vertical position, zero voltage, horizontal position, maximum voltage. Great. In the vertical position, we have 00 flux cutting our conductor loops. So our current will be zero. Now, as this one we are rotating clockwise as we are rotating, let's draw it here. As we are rotating like this, let's say our loop will be like this in this part. Okay? Inclined a little bit. When it is inclined a little bit, more flux will start cutting it. So our voltage will start increasing like this. Until we reach maximum voltage at the horizontal posit. So this side, let's say we rotate and this side became here. Okay? For example. Now let's look at the current. So when we have this position, you will see that nose like this. So our field north and south right like this in this direction. This is similar to as this and this. Now we have rotation clockwise or going down here and going up here that we will have rotation like this, this is going down. Let's say, for example, I'm talking about this loop, talking about this one. Force is up, force is up, you can see that magnetic field in the same direction of this finger, force is up similar to this one. So where our current, our current will be like this, right, like this. So our current will be going down like this. Based on the flaming left handles, you can see the current like this, exactly the same, but it is opposite to it like this. Okay? Okay, great. Now let's look carefully. Our current will flow like this. Okay, go like this. You can see this ring is in contact with our push here, this ring connected to our push here. Okay, great. So the current will go like this and like this. So we will have a maximum positive current. Okay? Remember the direction of current. This is very important. Okay? So our curt like this. Okay, great. Now, what will happen when we keep rotating when we rotate in this direction, the same of the toque direction, we will go back to the vertical position. So as we rotate like this, this will go up and this will go down. So our magnetic interaction or how much flux cutting how many flux lines, cutting our loop is now decreasing. So this will lead to this position. So we are going all the way up and take this one all the way down. So we will have, again, vertical position with a zero voltage. So we had this peak value. And as we go to vertical position again, our current will start going down like this going down. So we draw it the first half cycle, half cycle, right? Let's continue. Now, when we start again, continue rotating like this, you'll find that as we rotate like this until the horizontal position, flux our voltage will start increasing once more until peak value at the horizontal position. Now, when we are at the horizontal position, again, this one will have a current in this direction and this one will have a current in this direction. This one is connected to this ring, so the current will go like this. Right? So as you can see, even it doesn't matter which side on the left or on the right. Always the one on the left is connected to this brush, and always the one on the right is connected to this brush, leading us to a unidirectional generated power or a generated voltage, or a generated current, as you can see here. I hope you understand now the principle. So it doesn't matter which one of these here and here. Always the one on the left is connected to this one, always the one on the right, connected to this one. So you will always have current in the same direction. Now this principle, you will find that it is different in AC. In EC, we will have positive and negative, positive and negative. Now, how can we do this? You can see that they are away from each other. Each side, each side is always connected to one ring. Remember, remember here. This doesn't matter which side. The side on the left is connected to this one. The side on the right is connected to this one. It doesn't matter which one. They are switching depending on their position. Over here, the left side is always connected to this one. The right side is connected to this one. So it leads it to AC generation. Like this, you can see that this side let me explain it like this. You can see that here. Let's say this position. Okay? You can see that this site, this north and south exactly like this, you can see that we have this rectangle, right? Let's make it like this. Okay? So what you can see that this site is connected to this ring. Okay, this ring. And this pros is always connected to this one. You can see look carefully. Always connected to it, right, like this. So this one sometimes has a positive current when it is here, and when it goes to the other side, it will be a negative current. So this one will take positive current and the negative current. This figure is exactly this one. You can see that this side is connected to this ring and this side connected to this ring. So when this side, this is very easy now. So when the site is here, let's say the current will be like this, for example, okay? When this side is here, okay? On the left beside the nose, it will be positive, okay? So it will be like this. Okay. And when the side goes to the other side becomes here when it rotates and becomes here. Now look carefully. This side is always connected to the sprush? Always connected. So in this position, we will have a positive current. Okay? Now, when this site rotates and becomes opposite to south, the current will be reversed. So instead of having current, this one will be here. Instead of having positive current, it will be negative current like this. This negative current will be translated into negative current on the same brush. So it will be like this. So we will have when this side here, we will have positive current. When it is here, we will have negative current. Because why? Because this brush is always connected to this one which will have a varying current. Positive and negative. This one, same idea, connected to South sometimes. And when this one goes here, it will be opposite to North, so the current will be reversed. So we will have AC current. However, in the DC, we eliminate this problem by having this configuration in which this brush, sometimes connected to this loop and sometimes connected to this one. I hope the idea is clear for you. Like this, you can see here AC generation, as you can see here, one commuted ring connected to this brush and another commuted ring connected to this brush. You'll see that this side, this commuted ring is always connected to this one, which is sometimes here and sometimes here, leading to positive and negative. You can also apply the flaming right hand rule here and here you'll find that the current is a changing was time, AC generated wave four. And you can see here that at each position, you can do this. You can see that AB, when it is at the vertical position is equal to zero. When it goes into the horizontal position, it is maximum. However, maximum, but let's look at which side. For example, this one is here. Facing the south. Okay? So we will find that the current will be positive. Now, when it keeps rotating, here, zero again. And then when it continues rotating, it will be on the opposite to nose. So the current will be reversed. Okay? Because our commutator ring is always connected to one site. Now on the vertical position, we have zero flux because you can see that if you look at the rectangular, you'll see that these are our conductors, no flux lines cutting it. So we will have minimum EMF. When it is in the horizontal position, all four magnetic flux is cutting, so we will have maximum EMF, like this vertical zero EMF, horizontal maximum EMF. I hope the idea of EC electricity generation is now clear for you. 80. Construction of a DC Machine: Good morning, everyone. In today's lesson, we will start taking a pet the construction of a DC machine. So we talked before in the previous lessons about DC machines. We talked also about how can we generate electricity in the EC form or in the DC form. Now, let's go much deeper into understanding the construction of DC machines. So if you look at our DC machine, which you can see in this figure, this is a practical DC machine. This DC machine can do two functions. So we have either DC machine, which can be used as with the same construction, of course, it can be used as a DC motor, DC motor, which is used to convert electrical energy or electrical power into mechanical energy or mechanical power or mechanical output. So electrical to mechanical. If we would like to convert mechanical to electrical, then we will have a DC generator. That is only the difference between these two. Now, let's go onto the construction. So as you can see, any DC machine is consisting of two main parts. Number one, which we call the stater the stator of the machine. This outer frame is called the stator. This part of the machine does not move and normally the outer frame of the machine. What we say that if you look carefully about the name of this part, you can see it's called stator. If you look at here is Sator coming from the word stationary. Right? It means it is static, not moving. This part is our stator, fixed part that does not move. This is the first part. Second part is the router. This router here is the rotationary part. That's why it's called router. This part of the machine is free to move and normally the inner part of the machine. You can see this part here is called the router. The outer frame is called the stator. Now let's go and understand more. You can see that this part, which is a stationary part called the stator and this is a rotationary part called the rotor. When we combine them together, we will have the DC machine. Let's discuss more about each part. So starting with the stator which we call it the yoke. So the stator here, this outer frame called the ok. So the yoke is simply, which is like this. What is it exactly or the frame? It is simply the outer frame or the yoke provides mechanical support for the pools. So in this yoke, we will install our pools, magnetic pols that produce magnetic flux, right, and also acts as a protective cover for the whole machine. It also carries the magnetic flux produced by the pool. So as you can see here, this is the outer frame called the yoke on this yoke, you can see these magnetic pools. As you can see here, all of these magnetic pools are installed on the yoke. Similarly on this inner side, we will install our magnetic pools. Here, we will also install our magnetic pools. In a small generator, the yoke is usually made of cast iron because we are concerned more with the cheapness rather than the weight. Number two, in larger machines, we usually use cast steel or rolled steel is employed. Now, looking at the type of windings, if we look at our machine, we have two types of winding. One which is usually installed on the stator part or the static part. This one is called the field winding. Field winding which is concerned with the production of magnetic flux. We have here on the router this is called the armature winding. Armature winding. This is a wind at which it is connected to the commutator rings at which we will have generated current or we provide current for the DC motor. So number one, the winding in which we will have a generated voltage or induced voltage is called the armature winding, which is this one. The second one, the winding through which a current is passed to produce the primary source of flux or magnetic flux is called field winding, which is this one. Now, someone will say, however, we have seen in the previous lessons that we have our machine like this, North and South, right, large magnetic pools. In reality, you can use these type of pools, which is called permanent magnets, or you can use windings and the flow and provide for a DC current to produce magnetic flux. 81. Field Winding of a DC Machine: So let's look at this. So we have two types of magnets, permanent magnet, which is used usually in a very small DC machines, permanent magnet like this, two separate pools, or we will have the electro magnet, which means we provide electricity to get magnetic flux. What I mean by this, if you remember when we provide a current like this goes like this, this current will produce for us a magnetic flux. By using the right hand rule, the flux will be like this, right? If you remember, that is exactly what we are doing. By providing DC electric power, we will produce magnetic flux. Why do we use this type? Because we can control the field flux or the field magnetic flux? This helps us to have more control on the speed of the machine and other properties regarding the electrical machine, as we will see in the next lessons of our course. So we have two large pools north and south, which we call the permanent magnets like this. And of course, this is a constant field. This one, of course, has degradation or has a lower amount of flux as time goes pi, right? After years, these pools lose their ability to provide enough flux. That's why when you have the type of flux, this winding, which is called the electromagnet windings, when we have a winding, we can control them without the problem of wear width time. So what you can see here is that when we have a large electrical machine, we usually don't have just north and south. Okay? We have more than two pools. We can have several north and south, as you can see here right here. This is a DC machine. You can see this outer part, the yuk, as you can see here and you can see these pools magnetic pools are fitted on this stator or the yuk you can see this is armature winding on the armature core. This is a rotationary part, similar to the rotationary part here for the DC machine. Now, as you can see, we have how many poles, one, two, three, and four north, south, north and south. How can we do this? It is very easy. You have a field supply or this one like this. A battery like this, positive and negative. Okay? We can control it by having a variable resistance. For example, if we have a resistance here like this, by controlling the value of this resistance, we can control the value of current, so we can control amount of flux. Very easy. Now, let's see why this is a north, south, north and south. Very easy. Look at here. So the current goes out from the supply like this, right, goes like this. Okay, so it goes like this, goes like this. Now, if we use if we use the right hand rule, the curl right hand rule by using this, put your hand here, you will find that this thumb show that the current or the direction or the direction of the magnetic field will be going out like this, right? Direction of current. If you take this part, your hand and put it here, fingers here, you'll find that your thumb is pointing in this direction. Okay? So this is a direction of the magnetic flux. Now, as you can see that the current will go and continue like this to this one goes from down like this. So it will be like this. The current or the wire itself or the winding itself goes behind and comes like this goes all the way around this pool. Now, you will find that the current will flow like this. If you use the cur right hand rule, you'll find that the magnetic flux will be inside, going inside like this. Similarly for this, going outside by how you are going to fit this wind inside. So if the flux going out like this, then we will have the north. If the flux going in, it will be south. If the flux going out north, if it's going in south. That's why by how we add this winding or connect these windings, we will be able to control which one is north and which one is south, okay? And then finally, the wire, all of these field windings are in series. As you can see, all of them are in series, and then we will take the wire to the negative of the supply. So the current goes here through all of this and then get out from here. Okay? The best thing about this is that we can control flux of all of these pools by controlling the current by using variable resistance. As you can see here, this field winding you can see here are like this. You can see this is one pool, another one, another one, another one, and this is a router or the rotational part of the machine, which we fit it inside this machine. Now, another figure here, you can see that this, you can see this one and this one and this one and this one. These are the main pools. These are this and this and this. Now, what you can see here, these are enter pools. Leave them for now. We will understand them later inside the course and why do we need them. Okay? So there are other types of pools, smaller pools called the enter pools, leave them for now. Usually, we are now concerned in this lesson with the main pools. Now, if you look at these main pools, you can see that we have this winding around pool core. So we have pull core. At which we will install our windings or wand our windings around it. You'll find that we have this shape here, this part here. This is called the pull pull ho. Okay. So let's understand this. So what you can see that any pool here, you'll find that like this one, you'll see that it's consisting of the pool core, pull core, like this at which we will add or wound our field winding, and then we have this part, this one, which we call pull chow. Okay? Now, you'll find that our pool is laminated or divided into laminations. I will explain why right now. So we have a field magnet consists of pull cores and pull shoes. So the pull core, which is at which we will add our winding and the shoe provides larger area. So the pull shoes spread out the flux in the air gap and being of a larger cross sectional area, reduce the reluctance of the magnetic path. So what I mean by this, you can see that when we add our windings here, the flux, let's say look at this figure. We added our windings here like this. So the flux will be like this right. However, remember that the reluctance, which we discussed in the magnetic circuits is dependent on the area. So you can see that when we have a large pulled shoe like this, the flux will be distributed along larger area. This larger area will reduce the magnetic reluctance. If you don't remember it, the reluctance will be equal to the length of the magnetic path divided by u, permeability of the medium multiploid by area. So as you can see when we have a larger area, as you can see, larger area, length multiplied by width like this, the lens itself is much longer, means that the area is higher, meaning that the reluctance is lower, so the magnetic flux is much higher. That's the benefit of having pulso. Now why our pull cool laminated? Because when the current flow through the armature winding armature winding. This armature winding, we will have something which we call armature reaction, which we will discuss later in the course. This armature reaction, it means that when the current flowth through the armature winding, it produces a flux because a current flows through a conductor so when it flows through the armature windings, it will produce a flux that will cut the magnetic core or this pool, which means that we would like to induced voltage will be produced here. So we will use laminations to reduce Ed currents, okay? Okay, now field winding, as you can see here, we have our pull cho. As you can see the choose here of the pools, as you can see here, choose. Okay. And you can see this is our winding. Now, as you can see another example here, pull core around eight armature winding. And this is around eight field winding, and this is our armature part. 82. Armature Core and Magnetic Path: Now let's understand the armature core, which is related to the rotationary part or the router. You can see this is a router or the rotationary part, and we install it inside our machine. Now, this armature core, this one is called the armature core. What does it mean? Armature core is the one which houses or or contains the slots at which we are going to install these windings. So as you can see, this is what we call rmiture core, and you can see also made of laminations. You can see that the core itself, the rotation report, consisting of openings. This one, which is a slot, slots, slots, slots, mini slots here at which we are going to install our windings. So remember that when we had a rectangular shape like this, we are going to install it like this. So you take it like this, goes here like this. Okay? Or to be more specific, it has two terminals, and it will continue like this. So anyway, these slots at which we are going to install our windings, which you can see right now. Okay? Now, what you can see that armature or this armature core is made of laminations. You can see one and two, three, four laminations. Between them, there is an insulation. Why do we use laminations again as we discussed in magnetic circuits to avoid the eddy currents? So the function of the armature core is the one which hosts or takes houses, the armature conductors or coils and cause them to rotate. So it is here this opening here, which we connect our shaft. As you can see, this shaft is connected to this opening which helps this armature core to rotate. And when these windings rotate inside the magnetic field, we will have induced voltage. So it helps them to rotate and cut the magnetic flux of the field winding, leading to field magnets or field windings in order to generate electricity. Also provides a path of a very low reluctance to the flux through the arm share core from N pull to an pull. So when the flux goes you know that the flux goes from north to south, right? So when it goes from north to south, it will pass through the armature core. Since it is made of very low reluctance material, it helps to make the magnetic flux strong and doesn't lose much energy. Now, we will see this in this figure exactly as you see. So for example, you can see we have North and South, right? So the flux will go out from north to the south like this, like this. Like this North 2000. Not only this, but it will go from this north to the south from north 2000, like this. Similarly, this will go through here and here. Now, as you can see, the magnetic flux goes from here to here, goes from north to south like this and continue like this. Continue like this, because it goes from north, south, a cycle or a loop. Similarly here, it will go from north south like this. Don't worry. I will show you the magnetic flux or the magnetic path flow inside this machine. Anyway, what the benefit of this luck you can see that then goes from north to thus the magnetic flux. So it passes through air, this small gap. Let's make it much clearer by magnifying. You can see it goes from north to south like this, like this, right. Now, when it goes from north, okay, this is made of good reluctance or a very low reluctance material. No problem at all. Now, when it goes, you can see there is a very small air gap. I can't make this air gap zero. Why? Because I would like because this is a rotationary part, and this is a static part or a stature. So we need a small gap between them to provide some clearance between them, clearance between these two, between North or the pools and the rotationary part. And also, these small gaps help to provide cooling for the machine. So we have a small air gap so that we have a small reluctance and at the same time, we will have a clearance between our machine, our rotation report and the ascetic part. So it goes from north like this to south. So it passes through the Armiture core. So we have to make this armiature core made of a good reluctance or a very low reluctance material or a good material with a high permeability in order to prevent losses inside our flux. Okay, so it will go through this machine and get back like this, okay? Okay. Now, this is as you can see, it has a cylindrical shape and it is made of circular circularul laminations here. Each lamination here, let's just zoom in is made of about 0.5 millimeter sex. If you go like this, you can see this one and two and three, and four between these, there is an insulation which we call the mica insulation, mica insulation between these, Mica insulation in order to insulate between these layers. And it's key to the shaft, as you can see, they are connected to the shaft, as you can see here. Now, these laminations, as you can see, we have some holes here. These holes are used to allow air duct or allow air to flow through them, for cooling of our electrical machine. Now, why do we divide this into laminations? If we remember about the Eddy current, if we have bulk, one bulk core, like this, we will have large eddy currents, and ED currents is simply Eddy means circular. So Eddy currents ED is translated into circular currents. When we have a large core like this, one bulk core, we will have large eddy currents which will lead to high ED losses, which means we will have high heat losses or heat energy dissipated inside our core. Now, when we divide it into laminations like this, Eddy currents will be much lower leading to lower losses. Now, someone will say why this happened? Because when we divide it into laminations with an insulation between these layers, remember, there is an insulation between them. The magnetic flux itself flowing through here is much lower due to the presence of these insulations, okay? And not only this, when you divide it into laminations with a small thickness, this helps to have a smaller ED loss. Now, if you remember our equation, this equation here, Eddy current loss equal to this equation here. And inside this equation, you'll find that we have thickness of lamination, T square. So when we have a small thickness, someone will say, when we have a small thickness, we will have smaller dilosis. Now, someone will say, Okay, but if this sickness, let's say this is a sickness of T equal to four. And when you did into sickness, let's say one and one, one, and one. Let's say this part from here, to here. So we take the bulk one and vote it into T equal one, T equal one, one, someone will say the total thickness is the same, so it should have the same Dlosis. Now, let's compare these two cases. So for example, for the first one, EDloss will be, let's say this and this and this and this are a constant. Let's say constant K. Multi blod by T square. So what is our sickness? Well, it's the sickness will be four square. So that is the Dlosis in the first one. And the second one Dilosis will be this, plus this, plus this, plus this, or separate. So it will be E equal to. The same constant here, multiblod by the sickness square. Thickness of each layer. First one is one, so it will be one square plus second layer, K, one square, third layer. Fourth layer. So what you can see that the total will be four K. However, here it will be 16 K. So what you can see that by having laminations, we divided AD losses, and we will have four K instead of 16 K in one large pulk. Okay? Now, let's see the magnetic path inside the DC machines. So this is very easy, as you can see here. This one will be like this. As we said before, let's just zoom in. North to South like this, North going south, north going south, north going south, and it goes like this through the core and back. So it have this looks you go like this. You can see that the core, we have north thous north and south. You can see that the flux lines goes from north like this through this armature core like this goes all the way to thousand and get back like this. Similarly here goes from north like this, 2000 and get back like this. Again, north goes to thousand and get back, North going to thousand and get back. That is how the magnetic path looks like in a DC machine. 83. Commutator and Brushes: Now let's talk about the commutator commutator or commutator rings. As we said before, in the commutators simply use it to clt the currents here this ring, commutator ring or this part. This is commutators divided into several parts. You can see that this is a commutator rings, one, two, three, four, it can be rings like this, or it can be a wedge like this. There's wedges like this. As you can see here, they are insulated by mica insulation, as you can see here, to insulate these layers of commutator from each other. So as we said before, this commutator function is to facilitate the collection of current from the armature conductors to the outer circuit. So for example, if we have a generated current here, current generated here and here and here, all of this is collected by the commutators, which will be connected to process that will provide current to the external circuit. If we are talking about a generator, if we are talking about a motor, the commutator rings take current from the external circuit or from the process and provide it to the armature core or mature conductors to help in producing the torque. The commutator is used to convert the alternating current induced in the armature conductors into a unidirectional current. So remember that this configuration here is used when we have a unidirectional. If we have each brush connected to a certain ring, it will be an AC as we discussed before in the previous lessons, the difference between the commutator and the process in the AC generator and DC generator. It is made of a copper cylindrical structure, as you can see, cylindrical structure, as you can see here, and build up of wedge shaped segments. As you can see a small segments here, as you can see, with the wedge shape. And they are insulate from each other by thin layers of mica. Now, each commutator segment, each, each of these segments is connected to an armature conductor. As we will see in the next lessons of the lab and wave windings, we will understand how are we going to connect or how are we going to install these armature conductors on the slots. So it will be dependent on the type of windings. We have lab windings and wave we will understand the difference between them. How can we install them, and when do we use each type? As you can see here, we have a closer look up the commutator. You can see that we have an insulation between them, the mica insulation. We have these segments, and between them, there is this one. Between them, there is a mica insulation between segments, and each one is the copper segment or the winding segments or the commutator segments. And you can see that the arm chart conductor, you can see it goes all the way to the mica insulation. Similarly, here you can see that each one is connected to the commutator. Remember these armitu coils or these rectangular loops, all of them are connected. Each one is connected to a segment here. This will lead us to the next or the last component, which is a process. Process is simply connected to these commutators, and it can be two process and it can be more than two processes, depending on what, depending on type of the winding used, is it a lab winding or is it a wave winding, as we will see in the next lessons? So the brushes inside them, we have connected to a spring inside this box here. These boxes, we have a spring that keeps the process in contact with the commutator. As you can see here, this process can be has two functions. Number one, if we are talking about a generator, so it collects the current from the armature, from the commutator, takes the current from the commutator like this and provide it to the external circuit. So we have here our terminal box at which we are going to install our loud. We can install any type of loads, any type of loads that require DC machine. These loads is connected to process process connected to commuter, so they collect a current from this to an outor in a DC generator. In a DC motor, we connect here a battery or a DC supply, which is connected to process that provide current to the wine. So either take current or provide current like this, depending on the type of the DC machine. So it collects a current or provide current to the commutator they are made of carbon or graphite, and their shape is rectangular, as you can see here, rectangular shape. These processes are housed in brush holders like this. You can see this is a brush holders, which is usually of the box type variety. As you can see here, inside here, we can have this spring or it can be flexible cbar wire or big tail like this one. And this is a carbon brush closer look for the carbon brush. Here again, as you can see the process connected to the commutator and here another figure. Now, what is the problem of the process inside DC machines? Now, of course, in synchronous machines, we don't have brushes. In synchronous machines or AC generators, we don't have process, which is a big advantage for AC machines. For process here, the disadvantage of using process in DC machines is number one. This process requires periodic maintenance, because they are always in contact with commutator. So as time passes, they wear. Right? The wear or the wear of the process happens due to the contact with the commutator so that we're not wearing wear of the carbon process happen due to the dictum. They are always in a contact with each other. This is a rotationary part and this process are stationary, so they are always in a contact leading to the wear of the carbon process means that it needs periodic maintenance or we need to change them as time paths. Now, of course, in this one, in larger machines, specifically in larger machines, we will have large currents. Now, this contact can lead to sparks inside the electrical machine. Okay? Spark here happening when we have specifically large currents. 84. Turn, Coil, and Winding: Hey, guys, and welcome to another lesson in our course for electrical machines or DC machines to be specific. In this lesson, we will discuss the definitions for the armature components. And this one, we will start discussing some definitions which will help us in understanding the different types of armature windings and how are we going to draw our windings or how are we going to install our windings inside our DC machine? So first, we will start discussing three terms. Number one, turn, coil and winding. So number one, this is our turn. What does a turn mean? Simply, if you remember from our previous lessons, when we draw the basic north and Tuo, the basic generator or motor, whatever it is, remember that we had a rectangular lobe like this, right? One rectangular loop. You will see that one of the loop here, which you can see here, this loop is called a turn like this one. You can see it's consisting of two sides, one, the site, and the site. These two sides. Okay? So this is what we call a one turn or we call it also a coil. It is called one turn, as you can see here, one turn since we go from here all the way here, one turn or coil. This coil or any coil like this one, is consisting of two sides. You can see that or two conductors. To be more specific, you can see, one conductor here and another one here. One conductor here and another one here. And we try when we are designing our electrical machines, we try to put one of our conductors under the north and the other one under the south, under different pools, we don't install them on the same polarity. Why don't we do this? Because if we install them on the same polarity, we will have zero EMF or zero generated voltage. Ses because if you remember when we had north and south, let's say we are rotating in any direction, we will have a current flowing like this and another one like this right north current going in this direction and this one going in this direction or we have EMF generated E due to under the north in this direction and EMF. Opposite EMF on the other side in this direction, so we will have a current flowing dix. The total EMF generated to E, one opposite to another because we have a north here and thus here. Okay? Now, if you have the similarity, let's say, north and north like this, then what will happen in this case? In this case, we will find that the current will be like this and the other current will be also like this. The same direction, generated voltage in the same direction because they have the same polarity. You'll see that the current generated in this direction will ose the current generated in this direction or EMF generated here opposite to this one. So the total EMF is equal to zero, right? That's why we put one side on one pool and the other one on a different pool. Okay? Now, we will understand more about this in the next slides. So a turn consists of two conductors, one which we usually install under north and the other under the thous. Now, usually when we have one turn, we can call it a coil, okay? And if it can consisting of more than one turn, you can see here one, two, three. You can see one, two, three, three turns, and then we have the two terminals. So this coil consisting of one, two, and three turns, right? So the three turn is here, multiple turn coil. Okay? So this one is called a coil and this one is also called a coil, but this is a coil with one turn. This one is a coil with a multiple turn. Okay? So with two ends, start and finish, okay? Now, if we take several coils like this one, this one or this one, usually in electrical machines, we have a multi turn. Okay. Let's say we have this one, and we connected it with several other turns or several other coils. So we have one, two, three coils. So we connected the finish of this one to the start of the next one, connect the finish of this one, to the sort of this one, et cetera. So we are connecting them in a specific way. In this case, we will have what we call the armature winding. So the winding is formed by connecting several coils in series. Okay? Now we will understand how we are going to connect them using the lab and wave windings in the next lessons, okay? 85. Mechanical and Electrical Angles: So let's now discuss an important part which you will find in every electrical machine, okay? Mechanical angle and electrical angle. Okay, so let's understand what does this even mean? So in any electrical machine especially the large electrical machines, we have more than two pools. For example, when we have a stator of a DC machine with four pools, two P equal to four. Now, this is very important. Again, when we are dealing with electrical machines, you will find that there are some references, electrical machines, references, o? One, which can be used like this, I can say that number of pulls, number of pulls will be equal to how many pools we have is equal to two P. And how many pull pair will be equal to P. So this is the one which I'm working with in this course. To P means how many pulls we have. For example, if we have like this, like this, like this and like this. So we have North, South, North and South, like this. How many pulls we have, number of pulls or two P, one, two, three, and four. So we have four pulls. This is called a four pull machine. How many pull pair pull pair means north and south. So we have one pair, two pairs. So how many pairs in the machines we have two P equal to two, P pull pair. Okay? This is very important. So let's look at an electrical machine, DC machine with the four pulls machine, as you can see here. Now, let's look at number one. If we go around the air gap, AirgapOs, what I mean by this if we start from north here, and we completed one complete site. Let's say I rotated all of this, we started from here, and we rotated all like this, all like this. Until we reach the starting points, we rotated one complete cycle, one complete loop. Okay? This complete loop is in mechanical form. Mechanically, it is 360 degrees, right? 360 degrees. This 360 degrees is called the mechanical angle. Mechanical angle. In radians, it will be two Pi. Okay? So one mechanical angle cycle, two Pi is called the mechanical angle Theta is a shift. Now, when we have one complete cycle, we will have two cycles of variation of the flux density distributions are encountered. That's called the electrical angle Theta E. What does this even mean? So we understand now the mechanical part. When we have one complete loop, we will have one complete loop. We will have 160 or two Pi. Now let's understand why when we have one complete cycle, we will have two cycles of variation of flux. Let's understand this. If we draw like this, like this, Peter, flux density with let's say angle or with time. Let's make it with time. So as you can see, let's say we started from here, for simplicity, from here. Now, you will find that this one, magnetic flux Pita is maximum from here to here, maximum positive. So we will have this positive. This is N. Let's call this one N one, a one N two, and a two, four simplicity, okay? So N one under N one, we have maximum positive flux. Okay? Under S one, under a S one, we will have maximum as one, maximum negative flux. Then we have N two, N two, maximum positive flux, then a two, maximum negative flux. Let's just try to delete this one. If I just delete this like this. Let's do it again, draw like this. All the way like this. Okay? So we have maximum flux maximum Pita magnetic flux density at maximum negative value at a one, maximum at any two. So we have maximum negative here, maximum positive, maximum negative, maximum positive. Okay? Now, as we go, as we go from north from here, as we go all the way to here, we have maximum positive, and this point is maximum negative. As we go from here to here, we are going like this. Right from north 2000. Now, when we go from maximum negative here to maximum positive here from here, from here to here, right, so we are going like this. And then from maximum positive to maximum negative, again, maximum positive to maximum negative like this. And then from here to N one, so we have here again in one and like this. So this part will be exactly similar like this. Okay? So we have what you can see right now is that when we completed one mechanical cycle, two Pi mechanical cycle, you will find that how much we passed from here we started from let's say we started from this point for simplisting. Let's say let's make it from here, to make it easier from here, okay? Like here. You'll find that if I go from all the way back to here, so I started from here and ended here. Now, if you look at this area or this distance here, you'll find that we have one and two. So how many cycles we have passed through. We have passed through two cycles. Of electrical, electrical, because we have a change in flux, right, positive to negative, positive to negative. So when we completed one mechanical cycle, we had two cycles of electrical. That's why when you draw it like this, we can delete this. Yours is a Pita with Theta, no time, Theta or the electrical variation. And this is a mechanical one complete cycle of two Pi mechanical cycle. You'll find that for our magnetic flux from north, south, north through South, right? So we have four Pi, two Pi, and another two Pi. Okay. Great. So we can find that we observed that the relation between Theta electrical and Theta mechanical is equal to Pi, multiblod by Theta mechanical. Remember that our here in this example, we have Theta Theta, electrical four Pi. And Theta mechanical is two Pi. Between them, how many pairs, pull pairs. We have one and two, multiplied by two. What we got that if we take Theta mechanical, multiplied Pi, pull pairs, we will get Theta electrical, okay? Great. Now, another definition which we will find that the distance between the centers of two adjacent pools centers of two adjacent pools. For example, if I'm talking about center between this north and the south or between the south and this north or between this North and the South. This is the adjacent pulls. This distance, which we call is called the pull pitch. Pull patch here, which is abbreviated as Tao Is simple is taus equal to 180 degrees. Very simple. You can see that here from North, center of the North and center to the south, center of North and center of the south like this distance between them pull pitch. If you measure this electrically, if you measure it, you'll find that the distance from here to here is equal to poi. This is a constant value pole pitch between two pools. Okay? This distance here as similar as this distance from here to here. Okay. Great. Now, we can also in another view, we can express the pull patch as distance measured in terms of armature slots. So what I mean by this, remember that our armature here, the rotation report has slots inside it like this at which we are going to install our windings right here. Now, if we would like to know the distance from here to here between these centers, it can be we can get it simply like this. We can say that the total number of slots here, how many slots we have, divided by the total number of pools will give us approximately how many slots per pool, right. So if we divide S total number of slots, by the total number of pools to B, we can say that the pool patch t is equal to S over P. Right? So we will get how many slots per pool. So what does this mean if we get how many slots here, you'll find that this number of slots is actually similar to the number of slots from here to here from north to south. Okay? That's why it's called the pole pitch. Okay? So to equal to S over two P. 86. Pole, Coil, Full, and Short Pitch: This will lead us to pull coil, full and short patch. So we have pull patch, coil patch, full patch, short patch. We would like to understand the difference between these three. Number one, we understand already pull patch from the previous lesson. Now, I would like to know the coil patch. Now, as we know that, as we said before in the previous lessons, we said that our coil is consisting of two sides, right, two conductors, like this connected together, two sides. We said that one side under the north and the other side under the south, right? Now, the distance between these two coils, remember that this one is installed in one slot and this one is installed in a different slot. The distance between them is called the coil pitch. Which is a distance between the two sides of the coil. Okay? So the distance between two sides of equal is called the coil patch. Okay, like this, these two sides, if you remember. Now this is very important. What's the difference between full and short pitch. The difference between them is very easy. If the distance from this side to this side equal to the pull pitch like this from here to here, these side, the distance between them is equal to pull pitch to. If these are equal, then it is called a full pitch coil. If it is not equal to this one, let's say, for example, if we have north and south like this and the two coils like this, sN. So here, this is our tw, right? And this is the first side and this is a coil pitch here. Coil pitch. Okay? If it is santo, then it's called a fractional pitch or a short pitch, like this. So let's lead this. This is a full pitch. As you can see, two sides, one under the north and under the thou, as we said before, they have two opposite currents because they are under two different pools, okay? So this is a full patch, and if it is less than one pull patch, it's called a short or a fractional patch. Like this, you can see distance between them, less than the pull patch. Okay? Now, the DC armature winding is made of a full patch coils, okay? Now, what you will find that, how can we do this if we divide S or the number of slots, divided by two P, which is a pull patch. If you find that pul patch here is not an integer value, not an integer value. In this case, we are not going to use the full page. We are going to use a fractional patch. So fractional patch is used when S over two P is not an integer. If it is an integer, then we use full page. So again, full patch is used when pulpatg is an integer value. If pulpa is not an integer, it is a fractional value, then we are going to use a fractional patch, okay? 87. Single and Double Layer: Now we have two types or layers, which we call single and double layer. What does this even mean? Inside the slot itself, we can have one layer, one layer, we can install just one conductor, or we can have double layer, we can install two conductors or two sides. That is the difference between them. So in a single layer, a winding in which one coil side is placed into inside each armature slot. This one is rarely used because it doesn't make use of the electrical machine well. We need more than one coil, which will be subjected to the same pool at the same time. So as you can see here, this is an example. You can see slot one, two, three, four, five and six. For example, this coil is installed in slot number one and slot number five, the first side under one, second side under five. And similarly, B under three and six. You can see that there are no other armature coils or no other side, just one side in each slot. That's why it's called a single layer. In a double layer, we will have two coils side bay slot, arrange it in two layers. So the coil side of one coil is placed in the upper layer of one slot, which is usually represented by a solid line, while the coil side is placed in the lower layer, represented by a dashed line of another slot. Okay, what does this even mean? Let's first under Sanders. So a double layer and instead of having just one side in this one, you will see that we have two coils, one, two, three, and four, five and six. Okay, so this is a slot consisting of two sides. This one is called consisting of two sides, two sides. Remember that these are insulated from each other electrically, okay? They are not in contact with each other. They are insulated, okay? So for example, this one can be one coil, and this one is a side of another different coil. So they are not the same. So for example, one connected to five. So one here like this, one connected like this, 25. Another one, which is two from behind like this, connected to, let's say number six. For example, we will understand how are we going to do this in lab and wave windings. Okay. Now, what you will see that we have upper layer and the lower layer. Upper layer is this one, one, three, and five. This is the upper part of each slot, upper part, upper part, upper part. The lower layer two, four and six. So we have upper and lower. Okay? Now, usually when we are dealing with upper layer, we draw it as a solid line. So let's say if we are saying we are having a connection 1-6. Okay? For example, so upper layer is represented by a solid line and the lower layer is represented by a dash to line. So how does this even happen? You can see that. Let's say this is upper layer one, upper layer one, like this, and this is lower layer number six. So we will have solid coil like this, coil slide going all the way like this and we will go like this and make it dashed. So the dash line representing a lower side or a lower layer like this, number six, for example, and solid line, das line lower layer, and solid line represented an upper layer. Usually, we install one on an upper layer and one on the other side in a lower layer, okay? So for example, you can see here that you can see one, two, three, and four, five, six, seven, eight, nine, ten, et cetera. Remember, this is our slots, and this is our commutator. This is a different two different parts of course. Now, as you can see that here, we have upper and lower, upper and lower, upper and lower, et cetera. One side can be installed in the upper layer and go all the way and be installed in a lower layer. Okay, et cetera. Now, in each slot like this, you can see that how many, how many coils, you can see that we have two sides, right? One, two, two sides, three, four sides, five and six, six sides. All of the six sides, okay? So I would like to know how many coils Pi logic, pi logic. The number of coils is equal to half. So Pi logic, let's type it. So this is our slots here. Inside it, we have our conductors as you can see here, okay? If I would like to know how many coils, so I know that coils is equal to half number of coil sides, right? Because you can see that we have one and two, two sites. Okay? Forget about tons. For now, we are talking about a single term, single term for simplest. So you can see half of number of coil sites. So if we have, you can see this one, one and two, making us one coil. So half of the number of sites will give us the total number of coils. So how can I get number of coil sites, number of coil sites? Number of coil sites is simply equal to how many conductors, how many conductors, pair slot, or how many coil sides, coil sides, pair slot, right? So multiplied by number of slots to get the total size. Okay, let's make it easy and type. So we have a definition called, which is how many coil sides per slot, which is always an even. It can be two, four, six, et cetera. Okay. So you can see we have two coil sides here. Two cool sides here, two co sides here, et cetera. Let's delete this. So for example, if U equal to two, so we have two coil sits up a layer, lower layer, upper layer lower layer, et cetera. Okay? If you equal four, it means that we have four coil sites or four dactors in each slot, as you can see here. Okay? Now, great. Number two, we have C, which is number of coils and equal to number of slots. So C or how many coils we have will be half of S, which is how many slots we have, multiplied by U, which is how many coal sites per slot. So if I make this easy for you, U assembly how many coil sides, pair slot, right. So if I would like to get the total coil sites, I will just multiply by number of slots, and that is what we do. We take U, which is how many coal sites per slot, multiplied by S. This will give us total coil site. If I multiply it by half, I will get how many coils I have. Last one, you'll see that in the upper layer, equal to odd numbers, one, three, five, seven, nine. Similarly here, you can see one, three, five, seven, nine, 11, et cetera. In the lower layer, we will have even numbers two, four, six, eight, ten, two, four, six, eight, ten, 12, et cetera. So we use odd numbers to indicate the upper layers, and we use even numbers to indicate the lower layers. 88. Example 1: Now let's have our first example on the DC motors or Shunt DC motors. So we have the Sant DC motor. The speed of 500 volt, hunt mean 500 volt, and mot it means this is our input supply, which means V terminal equal to 500 volt. We need to increase its speed from 700 RBM to 1,000 by using field weakening. So this is N one, and this is N two. The total torque unchanged means that torque one in the first case, equal to torque two. The armature and chant feed resistance are 0.8 and 750. Armature resistance, resistance of the armature is 0.8 oms and 750 or F equal to 750 oms. The supply current at lower speed is 12 and bear at the lower speed, supply current, I supply equal to 12 and bear. Remember, I supply one in the first case. What do you need? Well, I would like to know the additional Shante field resistance required. Remember that we use the field weakening to increase its speed 700-1 thousand. So field weakening means we increase our resistance to take I field down. So I would like what additional resistance do we have? Okay, so how can I get this? You can get it very easy. How you know that we have two relations. We have E equal to Ki Omega and torque equal to Ki armature. So what you can see that E one, will be pi one omega one, or you can say also directly f one omega one. Let's make it K omega one, and E two equal to k52 omega two, right? So if you divide these two together, you will have E one over E two equal to 51 Omega 1/52 Omega two. And the flux is directly proportional to field current, so I can say I field one over I field two because we changed our field N one over N two. So number one, do you have N one, and I have N two? I need field the current, and I need induced MF. Okay? Number two, we have four torque. For torque, we have T one, equal two, K, i one, I mature one. And toque number two, equal to K f two, I armature two because armature cart changes, flux change. If you divide these two, you will have T one over T two, equal two, f one over f two, multiplod by IA one over Ia two. Again, f one over a two is IF one over IF two, multiplied by R armature one over I Rmture two. Now, T one over T two is equal to one. Okay? So we have this relation. And we have this relation. What we need to get the Sand field resistance is that we need to find value of IF two. Okay? So what I need now is I armature one, I armature two, I field one, okay? And we need induced MMF E one and induced MMF two. Okay? And using these two equations, we will get finally our values needed. Okay? So let's get step by step. So V urnal here is 500 volt. Okay? Can I get I field one? Well, I field one very easy equal to the V terminal 500 divided by the resistance of the shunt, which is 750. Okay. What about I armature? I armature I can get a y? Because we have supply current 12 and pair. We have I field from here. Okay, I field one, so I can get I armature one will be I supply minus I field. Okay, so I can get the first armature current. So let's see I field one equal VTN over RF one, equal to 0.67 500/750, and the current equal to subtraction, 11.331. Okay. Can you get the first induced EMF? Yes, applying QVL or as you know that EBC in a motor equal to Vterminal minus I armature or RmatureO and one. EB one will be V terminal minus I armature, or armature equal to this value. We have the first induced EMF. We have first armature current, and we have IF one. Now remember that torque is equal to constant, and as I said before, T one over T two equal IA one over IA two, IF one over IF two, equal one, I armature one given 11.33, IF 10.67 I armature two and IF two, I don't know them. So I will take one as a relation with the other. Ia two from this equation equal to 7.6 over IF two. Again, BMF, the second BMF will be terminal voltage, 500 minus Irmature two A, I armature two or A. I armature two, I already obtained a relation for 7.6 over IF two. So we obtained the second EMF as a function of the field current. Now we know that the ratio between E one over E two, as I just explained, equal to IF one over IF two over N one over N two. E one is equal to 490. E two, I just obtain a relation for it. We have Omega one IF one over IF two or Omegon over Omega to, which is N one over N two, 700/1000. If 111.0 0.67 and IF two is unknown. So we have one large equation unknown in IF two. By solving this equation, you will get IF two equal to 0.465 and pairs. Now, how can I get the new resistance? As you can see that IF two is simply equal to V terminal over RF two, the new resistance after adding a resistance. So RF two will be 500/0 0.465. We have the current and we have terminal 500. We can get the resistance 1075. So this is the new resistance. What is the additional shunter resistance? Our resistance was 750 ms now 1075. So the difference between them is our additional resistance, resistance which we add. 89. Types of Armature Winding: Good afternoon, everyone. In today's lesson, we will start discussing types of armature windings. So what are the types of armature windings? We have two types of armature windings. We have lab winding and the wave winding. So what does armature winding even mean or types of armature windings, which we are discussing in this lesson? The arrangement of conductors of our conductors in a systematic manner or in a systematic way. This is what we call an armature winding. Now, depending on these conductor connections, the armature winding can be classified as two types. The first one called lab winding. Number two, we have wave winding. These are the two types we have for amature windings. So what I mean by this, remember that when I discussed in the previous lessons, we said that we need two conductors. One side of our coil. So if you remember, we said that we have two coil sides like this. Right? And I said before that these coil sides, of course, they are not connected, but anyway, these sides one would be under North and one under South, right. So each one will be under a different pool. So in order to do this, we need to put this one in one slot and this one in a different slot, in a slot away from it. Okay? For example, as you can see here, this is our router, right. Now, these are our slots, one, two, three, four, five, et cetera. Now, if I put my coil side, the first side here, under the north like this and go all the way to slot number four, we will put the other side. Our system, if I take this rotational part and expand it, make it flat like this. You will see we have our North, this one, similar at this one. And we take this rotationary part and we just expand it like slot one, two, three, four, five, et cetera. Like this, you can see slot one, two, three, four, five, and et cetera. You'll find that we have some windings, some slots under the norse like this, some slots here, under the snores and some slots under the south and between them, empty slots, okay? Okay, or not empty slots, but slots in between in the neutral zone. This is what we call neutral zone at which we don't have south honors like here. Okay? Okay, now what you can see that we have one coil here under this slot and the other side under this slot. So this is what we do in order to produce two different EMF. So the generated EMF here, for example, can be like this equal to E, and the generated EMF here will be opposite to it because it is under different polarity. So the total EMF will be two E, or this one will give us a current in this direction, and this one will generate a current in this direction. They are the same current, but this current is due to two opposite EMFs, okay? Okay, great. So you can see we bought it in one slot and another. How can I define this distance? This distance can be defined using the type of armature winding configuration? Are we using lab winding, or are we using wave winding? Now, this is a single turn, as you can see here. If we have several tons like this, you can see several sides of the same coil. Okay. Then it's called multiton as we discussed before. Okay, so as you can see here, we put one in one side and the other in another slot, and we connect between them like this. Okay? And here also, we connect between them, et cetera. So what is the difference between lab winding and wave winding? So lab winding is used or armature wine. Our armature wine is divided into several parallel paths, which is denoted by A, how many parallel path as you can see. This is always equal to the number of pools or two P and the number of processes inside our machine. So what I mean by this if we have four pull machine, so let's stop it four pools. In lab winding in lab winding, we will need how many processes, we need four process. And we will have four perl paths. So number of pulls equal to number of processes required, number of perl paths. Okay? These process will be divided into two positive process. And the other half will be two negative pushes. Okay? We will see this right now. The wave winding on the other hand is an armature winding, divided into just two parallel paths independent on the type of number of pools. So in wave winding in wave winding, we have two parallel paths, okay? And we have two pushes. Okay, two brushes and two per bus, one positive brush, and one negative brush, like this. Now, regardless of the number of pools inside our electrical machine. Okay? So that is the difference between them. Now, why do we do this? We will understand this later that when we have for example, in lab winding, when we have several parallel passes, we can generate larger current, but lower voltage. However, when we have in wave winding, we connect lots of windings, lots of coils in series, leading to large voltage and low current. So anyway, we will see this right now. So in a four pull machine, you'll find that we have four parallel paths for the lab winding. This is a lab winding. You can see here positive push and negative push, we can have two of positive and two negative as we will see when we draw these windings. So in general, we have four parallel pas. Each one will generate a current. So as you can see, more parallel pauses, more current. However, in wave winding, we have just two parle pas. You can see that many, many windings are in series or many coils, not windings, many coils are in series, like this. Each one will generate E right like this. Let's say pause a negative E, pause the negative E, E, et cetera. So many, many coils in series means we will have large voltage Okay. Here we have lower amount of coils in series means lower voltage. However, we have many parallel passes, each one will give us current. Let's say I, I, I and I, let's say it will give us for I. Here, it will generate just two I. So usually, usually, when we would like to get large amount of current in some applications, we need large amount of current. In this case, we will use lab winding because it generates large current. If we have an application that requires large voltage, then in this case, we will use wave winding, okay? Here is in reality what the difference between them. You can see that this one, this is what we call lab winding, and this one is what we call wave winding. You can see two side. Let's say the coil, you can see the first side goes all the way to another slot connected to under the south pool, right, north and south. Similarly here in wave north and south north and south, et cetera. The difference between them, we will discuss this in the next lessons. We will discuss each one in details. 90. Lap Winding: So starting with the lab winding, what is exactly winding Lab winding, as we have seen that the number of parallel passes is equal to number of number of pools, right? More pools, more parallel passes means more brushes. That's why since we have many, many parallel passes, that's why what we call it a parallel winding. We call this sype a parallel winding. Okay? So what exactly is lab wine? Or how can we draw lab wine? Okay, so lab winding is simply finish end of one coil is connected to a commutator segment, and to the start end of the adjacent coil, stewed under the same pool, and similarly all coils are connected. What does this even mean? So as you can see, this is the first coil coil number one. As you can see, this is the first commutator segment. Remember, slots are different from commutator segment. In the first segment here, we go all the way and we connect it to the first side of our coil. So we have here. Let's draw it like this. Okay. So this is our first side. Let's say, for example, it is in slot number one. Okay? And then we go to the front of our electrical machine like this, all the way and go. And if you remember, we said that one is on the upper layer and the second one in the lower layer. That's why this one is solid line. And this one is dotted line. Let's say this is at slot, let's say, number seven. For example, we will see how we are going to do this. So we go all the way like this, like this, and we go to which commuter or segment to commuter segment number two. So we started at one and draw our first coil like this and then go to coil number two. Okay? So this is our first coil. Now, as you can see, this is a start and this is the end. Okay. The distance between them is one. And you'll find this in lab winding, the distance between start and end as a commutator segments or the start of the next one, distance between them is just one segment, okay? Okay, great. So as you can see, in lab winding, finish end of one kind. So this is a finish end. So we draw our first coil. This is a finish end is connected to a commutator segment, this segment number two, and to the start end of the adjacent coil under the same pool. You can see that after drawing the first one, the second one will start from the same point. You can see it finished here. The second coil will start like this, go to under the Norse, second coil, go all the way back, and again, dotted, go to segment number three. Then number four will be like this, go all the way like this. Under Norse, go like this and like this and go to segment number four, et cetera. So what you can see here is that they are overlapping each other, right? So you can see it goes like this. Second one overlaps it, right? That's why the name lab came from. So since the successive coils overlap each other, as you can see, overlapping each other and hence the name lab winding. Now here for a larger machine, as you can see here, we have north, south, north and south. You can see the first committed to segment number one. We have our first coil like this, goes all the way to slot number six, get back to two. And then from two, we draw the next one like this to three and continue like this. You can see we are continuing what we are doing right now. What you can see here is that how many This is a single layer, okay? This one is a single layer. Now you can see coils, some coil sides under the north and some coil sites under the south. When we are drawing this diagram, which we call the developed developed diagram, when we are doing this, you will find that we have some coil sites under North, some coil sites under South, North and South, okay? When we are doing each of these, we assume a certain current. So for example, when we are having the north, we assume that the current going down in the lower direction. You can see down like this, means that the current goes in this direction. For south it will be oust, it will be going up. Remember that in some references, they use current going up, and in others, they assume going down. It doesn't matter in the end, okay you will draw the same thing, okay? Okay, great. Now, you can see how many how many slots we have. We have actually 16 slots. How many pools we have four posts we have here equal to 16, 16 conductors. How many pools or two P is equal to four, right? So you will find that how many conductors, pair pull conductors, pair pool, it will be 16/4, which means four conductors under each pool, right? So you can see that we have one, two, three, and four under South, under North. Okay, South, as you can see, one, two, three, four, one, two, three, four, one, two, three, four, et cetera. Okay? Now, this is important why these directions are important because we are going to know how are we going to blaze the process? Number one, you will find that our process equal to number of pools in lab winding. So how many processes here, one, two, three, and four? Where are we going to install this process? Now, look at these currents at these points at each commutator. We're going to put each brush at a commutator segment. Now let's look. This one, current goes down like this. This side, current goes down. So you can see current is going down, going down, and it is getting the sum of these two currents going down. So in this case, we can take current from here, right. From this point, we can take current. So we have here a positive brush that will take a current going to our load. Okay, that is number one. Let's look at the second segment. Look at this one. You will see that the current going down. This one under thousand going up like this. So what do you mean by this? It means that the current goes from north like this to thus. No current will go here. So we don't need any kind of brush because the current goes from here, from this coil to the second one. Similarly, for this one, what you will see that we have current going up, and here, current going up. So it means that it is opposite to this brush going in. So we will say this one is connected to a negative brush, providing current. Now the next one here you will see that this one currently going up, this one currently going down, so the current will go from this coesite to here, no current will pass here, so we don't need any kind of brushes. Similarly here, you'll find that the current going down and here going down. So we will need a positive brush here as the same current going up and current going up, so we need a negative brush, and we will connect the negative negative and positive was positive to have the final four. Now, how can we get one? Which one should we connect these segments or these coils or these conductors? One here is connected to number six. How can I know this? The distance between them is what we call YPA, Y PAC. How I'm going to do this when we learn about the different types of pictures inside the electrical machines. Don't worry. I'm going to discuss this in the next lessons. So as we remember, number of parallel passes, equal to number of pools, equal to number four processes, four pools. How many purposes if you look at the circuit here, you'll find that if we divide this or draw the diagram, you'll find that we will have four parallel pass. Now, as you can see, two pull machines, two P pulls the machines and the mature conductors, there will be two P parallel passes per pass depending on how many pools we have, and each pass will contain Z over two P conductors in series. So what we do that we have like this one, two, three, and four, four parallel pass. So we have four puros. So our conductors, our Z is divided into two Divided by two P or two A, they are the same. So each one, each side will have Z over two P, right, over two B because we have four parallel pass or whatever it is, depending on number of pools we have. So each pass we take total conductors and divide it by how many paths we have or how many pools we have. So what we have seen in this figure, this is what we call developed diagram. So developed diagram is simply obtained by imagining the cylindrical surface of the armature to be cut by an axial plane and then flattened out. So as you can see that, we just take the rotational machine or router and we flatten it out. Note that the full lines represents the top coils sides or conductors and dotted represent the bottom coil sides or conductor. So if you remember that we said before that in each slot, we have an upper layer and lower layer, upper layer and lower layer, et cetera. That is what we are talking about right now. So when we have, let's magnify this is a developed diagram, this one, okay? And this is a ring diagram, this one ring diagram, this one is developed diagram. So what you can see here, here, this is a first slot, slot number one, slot number two, three, and four. Okay? Now, what you can see that we have here in each slot, we have two a layer and lower layer. In A layer, we have full conductor or not a full conductor, a solid conductor. In the lower layer, we have dotted conduct. And we said before we connect layer conductor to a lower layer conduct. You can see that one solid going get 212, which is dotted, okay? Great. And this is what we call the develop. You can see one goes all the way like this and then get back to commute it to number two and then continue like this, et cetera. And here we have four processs we have four pools. And what does this even exactly? What is this? You see that here, number one, commuted to segment number one. So this is the first segment number one. It is connected to. After developing this, you will find that one connected to one and ten right 1-10, so you can see here 1-10, right? Now, what you can see that one going all the way connected to 12. So one connect to 12. So as you can see, one connect all the way to 12. And then from 12, here we go to commutator segment two. From 12, we go to commutator segment two. And then found committed or Sigma number two, we go to third conductor like this, et cetera. So this is what we call ring diagram. Simply we just take we followed all of the diagram after drawing it. And then the location of brushes here is similar as the location of brushes here. Okay? Great. So this is, again, the lab winding four process and the same diagram or another one. You can see that we have four processes. Now, when you draw this, you will find that positive, positive, negative, and negative. Now, you will see that how many parallel passes we have, we have four parallel passes. So you can see that if we draw the equivalent circuit between positive, connected to a negative and negative using two parallel passes, you can see positive, connected to negative using one and two. Right? And the other positive is connected to this one and this one using again, so connected to this one here and this one here. So you can see we have four parallel paths. Okay? So this is what we call lab winding. 91. Wave Winding: Now let's understand the wave winding. So the wave winding, what we call series winding, remember that we have only two parallel paths, as we said before. In the lab winding, we call it the parallel winding. So in this type of winding, the coil site is not connected back, but progresses forward to another coil site. Remember that in the lab winding, we go like this and then get back overlapping each other like this keeps overlapping. Over in this wave winding, we go like this and go to the next one, keep moving forward. So that's why it's called progresses forward or moves forward. In this way, the winding progresses, passing successfully every N pole and S poltrotan to the coil side from where it started. So let's see what I mean by this. The name wave wind came from the wavy shape. So let's see this. You can see this is a wave winding. So what you can see that we started at this soil. Okay, you can see here, goes all the way back to the lower layer. Okay? Now, what happens exactly that we continue, we don't just get back like this. And overlap. No, we don't get back. We keep moving forward. So you can see that like this, and then it's connected to a commutator segment away from the very beginning, not after one, but away from it. And then we continue like this and like this. You can see this wave. This shape is a wavy shape. That's why it's called wave winding, okay? This is a lab winding which we discussed before. You can see they are overlapping each other. However, here we are moving forward. We are progressing forward. That's what's called wave wine. Now, the conductors here are split into two parallel paths. Each pass has a z over two conductors. Since we have two parle pass, each one will take half of the conductors we have. So we have mini conductors in series, which means we have a large voltage. The number of processes here is equal to two, equal to number of parallel passes, which is two. Now, this is again, wave one. You can see we have one under north thus north and south. Number two, you will find that one on the solid line, which means upper layer, lower layer, upper layer, lower layer, et cetera. This is a wave winding. You can see that let's zoom in like this. Okay. What you can see here is that let's say conductor number one. This is the first conductor. Okay? Forget about the first point at which you start? Forget about it. Now look carefully. Conductor one goes all the way back to slot number six, okay, like this. And then it goes down. So let's just let's draw it. So we can simply draw it first, and then we will zoom in. So we have here conductor one, as you can see here, goes all the way like this pack and reaching the dotted line here goes like this. Then it goes to this very far commutator segment, and then it goes like this, goes like this, goes like this. As you can see here. So what you can see, we are progressing forward. You can see we are moving forward like this. Let's just zoom in, magnify. What you can see, we are progressing forward. Okay, different from wave winding different from lab winding. You can see at 17, we reach a seven from seven, we went to 18 and et cetera. You keep doing this until we draw the full diagram. We will know the distance here. When we reach the different type of patches here and set this course to get, how are we going to draw it? Now, as you can see, we have, again, the same currents going down, up, down and up as you would like. You can assume it going down or assume it going up as you want. Now what you can see, how can we blaze this process? Again, we have, if we look carefully at this diagram, you will see that at this point. Number one, for example, you can see one connected here, this one. Let's just first lead, clear all, magnify like this. So you can see number one is connected here to this one. So what is even this one? This one is related to south. So as you can see here one at the south side, so the current is going up and as you can see here for this one goes to K. If we go here and look at K, K is at the side here, which is also related to this slot. This one and this one are related to each other, goes up like thus. So we have a current going up and current going up. So this one is a negative brush. Now, looking at this one, this one or this one, you'll find that they are the same. Currents are going in. So let's see, for example, this one under the Norse going in, this one under the north also going in. So current coming in and the current coming in here. So here, a positive brush. Similarly, this one will be entering and will be a positive brush, negative brush, and positive end, et cetera. However, you can see that inside, if we draw the diagram, the same shape, you'll find that it is different from lab winding. So if you get back to lab winding here, you'll find that there is each parallel pass or have quarter of the conductors, right? Quarter of the conductors, quarter, quarter, and quarter. Now, here it is different. You can see that here. They are very, very close to each other between them, just one coil or one conductor. In this case, we can actually eliminate one brush. We can simply delete, cancel this one and this one. We just have only two brushes, one positive and one negative between them, one conductor, and another conductor. We will have positive, negative brush, one conductor, or a whole series of coils. And series coils. Okay? It's like this one and two. Okay? Since they are very, very close to each other, we can actually remove one of them. That's why in wave winding, we call it the series winding. So in reality, you can keep this brush only or this brush, similarly for negative, or this one or this one. Okay. Now again, for the armchair windings here, again, this illustration can see this is a wave, as you can see, we are progressing forward, as you can see here. This is a lab, as you can see, we go all the way and they get back to commute Segment two and then go forward like this. Now, if you look at it in the rotational form, you'll find that this is our slots upper and lower, upper and lower, as you can see here. Okay. In each slot, different pools, and you can see that in the lab winding, we have four process, two negative and two positive. And in wave winding, we have two process only. And this is how it looks like when we add them in a slot, when we connect each side to a slot, as you can see, for example, in this one, one connected to the commutator, A or the first segment, five dash connected to the segment, as we will see in this diagram, if you get back here, you will see, for example, you can see three committed or Segment three is connected to this one, which is eight and connected to one dash, which is a lower layer. So by knowing these two connections, we can connect them here. Okay, we can like this one and five dash, for example, okay? Similarly here for the lab winding, when we know each commutator is connected to which sides we connect them like this. Okay? So we discussed lab and wave winding as a general form in order to understand the difference between them and how they look like. We will discuss some definitions related to type of pitches inside the electrical machines, which help us understand how can we draw lab and wave windings. 92. Types of Pitch in Windings: Hey, everyone. In today's lesson, we will start discussing types of patch windings or patch inside the electrical machines. So the types of patch is very helpful in understanding how are we going to draw our lab and wave windings, okay? So starting with number one, looking at this figure, here we have two figures, one representing lab winding and the other one representing wave winding. Now, as you can see, in order to move from this to this one, from this side to the other side, there is a certain distance between them. This distance is measured in how many segments or how many coil sites, okay? So the distance between them here is Y P, and you can see we have Y F, YR, and et cetera similar here for this one. So let's understand each of these terms. So number one, let's look at this. We have pack pitch. Back patch here or Y P, what does this represent? This representing the distance between the two coil sides of one coil, and it must be an odd number. This is very important in your own design. So what I mean by this, as you can see here, let's say, for example, this one, let's use this one pen. Okay, let's go here. In this part, you can see here that this one is slot number one. Okay? So I'm going to take it from here and go all the way back to reach the other side, the other side. Okay, this one, let's say at slot number three, Slotnumber four, not three, slot number four. Now remember that we said before that our winding inside the slots, we have upper layer, lower layer, upper layer, lower layer, upper layer to lower layer in double layers. You can see that the upper layer is one, three, five, odd number, and the lower layer two, four, six, et cetera. Now, remember that we have one side. Remember we said one side on upper layer, the other side in the lower layer. So one here, on one, for example, and the second one in four. One in upper layer, solid line, one in the lower layer, dashed line. Now, as you can see the distance between them, how many slots between them, four minus one equal to three, right? So in order to change from upper winding, upper layer to lower layer or from lower layer to upper layer again, we need we need what we need an odd number. That's why the distance between these two is odd number. So here you can see four minus one is three. This one representing PEGPH, okay? Y P. Okay. Great. So you can see that when we are designing, let's say we started at slot number one, in order to know where I'm going to connect the other side, I will say, let's say, at one plus YPAC which we will get its own equations. Okay? So as you can see here, Y PAC. Why is called YPAC because we are connecting them, we are going from this side to this side through the back of the electrical machine. Pack of the electrical machine. What I mean by this? Look at this figure here. For lab winding. As you can see, we have this site and this site. I'm connecting between them how I'm going like this through the back of the electrical machine, this pack. Okay? That's why it's called PAG pitch, ok. Similarly for wave winding, we have this winding here and the other side, and we are connecting them pack. That's why you can see the site and the other side, why pack between them? Okay? So the distance between two sides. The second definition called front patch, front patch or Y F is a distance between mature conductors which connected in the same commutator segment. So as you can see here, we connected the first winding. Now remember that we go back to commutator segment, and then we go to the next coil, right? So this is our first coil, and then we draw the second coil. Now, the distance between the last or the second second coil site to the next winding that are connected in the same commutator. So let's say, for example, I draw it, this one, added this one, like this. And then I know Y PAC equal to whatever is the number like this. Let's say it is equal to four. Now, I would like to know where I'm going to draw the next one. Is it at slot number two, three, four? What is it exactly? Now, the distance between these two, the next coil is called Y f. So for example, if Y f is equal to, and of course, again, it must be an odd number. Okay, it must be an odd number. So let's say this one is six, for simplicity, and let's say Y f, equal to three. Y F equal to three. So I'm going to the next coil, go back three slots. So I'm going from six minus three. So I'm in slot number six, I'm going all the way back to slot number three or layer number three, whatever it is, as we know that each one has an upper and lower layer. So we are going to number three, right? Six minus three. So I'm going all the way back to this one so if this one installed in one, this one will be installed in three. So YPAC helps us to go forward to the next coil side, and from here, we can use Y forward to go to the next coil, or the next winding next to coil side we are dealing with. You can see they are connected in the same commutator segment. Now in lab and winding, we have equations for Y F and YB to help us decide where are we exactly going to install these coil sites, okay? Okay, so let's read this. This is for lab winding YBC and Y forward. For this same here between two sides, YB similar as here. And since we are progressing forward, you can see at the same commutator segment, we connect this one to this commutator segment. Okay. And then I would like to know the next position of the next to coil, between them again, YF. Similar to here, between them YF. Okay? Now there is also commutator patch YC distance between the commutator segments to which the two ends of a coil are connected. So what you can see here, look at this one. Here you can see this is a first coil first coil side. Number one, connected to this commutator segment. Let's say, call it one. Segment two, Segment three, et cetera. So I would like to know this is a first decoil, right? The second decoil this one, this second decoil, where are we going to connect it? Okay? Where are we going to connect the distance between them called YC. Okay? So the forest coil in commuted or segment one, second decoil in commuted or segment two. In reality, in reality in lab winding in lab winding, the YC equal to one. Positive or negative. If we are moving forward or moving backward, as we will see in the nextll slide, can be positive or negative. Now, for our wave winding, you can see that the first decil this is our first coil. Okay, assuming it is connected to this commutator segment, number one. Now, you can see goes all the way like this to the second site and connected where connected here, right? At this one, you can see one, two, three, four, five, and six. So at 0.6, we connected the second connected the second coal site at this commutator segment, and from the same point, we start the next one. The distance between the beginning and end is Y C as you can see here. Right? In the wave winding, it is not equal to one. We have an equation for this type, for wave winding. Okay? Now, there is also a Y resultant or resultant pitch winding pitch with distance between the beginning of one coil and the beginning of the neck coil to which it is connected. So what I mean by this, let's delete this Beginning of the coil and the beginning of the next coil. You can see this is the first coil, beginning of first coil, beginning of second coll, distance between them YR or end of the first coil and end of the second coil, distance between them also YR. Similarly, you can see beginning of the first coil, beginning of the second coil, distance between them YR. Okay? Now, also if you draw the rest or the second side, then the distance between this side and this side is also YR. The equation of YR is simply like this in YR or Y. They are the same. In here, as you can see that there is a YBC and this is Y forward. This is YR you can see that YPC is equal to Y forward plus YR. So YR itself or Y is equal to YPck minus Y forward like this YP minus Y foward lab winding. In the wave winding like here, you can see that YR is simply submission of Y P plus YF like this. Okay? Now, for commutator patch, we said before that this one YC is equal to one in lab winding and we have an equation for it for wave winding. Now, there is a very important part in lab winding, it can be one or negative one. It can be one. So it means that the first side here, and we connect this second site in the after one like this after one, if it is positive. If it is negative, then I'm going to take this side and go all the way back here. Now, you will say, what does this even mean? You'll see right now. If commutator patch is equal to positive one, it's called progressive lab winding. If it is negative one, it's called retrogressive lab winding. Now, let's see the difference. Progressive, the same one which I discussed right now. You can see we started at slot number one here. So this is the first coil goes all the way to number two. YC here is equal to positive one. Now, from this side, we will go all the way like this and go to number three and then go all the way like this and continue as with it. We are progressive forward or moving to the right, progressive that's one. In the retrogressive, it is different. We are getting to the back. What I mean by this, look carefully here. So you can see that we have this at let's say this is number one, and this is number two, for simplicity, okay? You can see we started at two, like this. Okay? And then this coil side will be connected all the way back. So you can see that this is a beginning and this is the end. So you can see that YC, in this case is negative one. We are getting to the pack, not forward, but retrogressive, getting to the opposite direction. Okay, so you can see we connected here and then we draw the next one. So as if we are moving in the opposite side. Okay? Most of our windings are progressive lab winding, okay? Like this, you can see that this is a progressive. You can see we started at one, go all the way to commutator number two, then we draw the next one like this to commutator three and then go to number four. So we are moving forward. YC a positive value. If we have a retrogressive, for example, let's start from three to understand this. You can see that three all the way like this, and get back to commutative segment number two. From commutative segment number two, we will go all the way back like this to commutative segment one. So we are moving in from right to left right here we are moving from left to right. Okay? That is the difference between progressive and retrogressive. Now there is a factor here which is important. It's called multiplicity or multiplication of parallel paths. So if I would like to increase number of parallel paths inside, the lab winding, we have a factor which we can use, which is M. What I mean by M? Now, remember that YC or the commutator pitch is inside. The lab winding is equal to positive one or negative one, right? Positive one, if we have a progressive negative one if we have retrogressive, right? That is what we call. One is called simplex winding, just one step, simplex winding. If we have YC instead of being one, being two, if we make YC here, this one, make it YC equal to two. Instead of going like this, going from one, go all the way like this, all the way like this and connecting it to, no, I'm going to connect to number three. Okay? So the distance between the beginning and the end is two. Okay? That is what we call Dublx. You can see here plus two for progressive Dublx winding, negative two for retrogressive Dublx wind. If we have three steps, three steps from one going all the way to number four. So three steps forward or backward, then we will have a triplex. Okay, let's see it plus three for progressive triplex winding and negative three for retrogressive triplex winding. So you can see simple or single double and triple. Okay, Simplex one, double x two, triplex three. And as you can see here, we are progressing forward like this when we draw our electrical our developed diagram, developed winding diagram, you can see that we started at one, go all the way to let's say number ten, to number ten and then get back to number three and keep progressing forward. You can see that one, go all the way here like this to number three. And then from number three, we go all the way back here to number five. So what you can see here, let magnify this. You can see that we started at one, right? You can see that here, segment one. Okay. Then go all the way like this, go all the way like this, and you can see that it goes to which segment or commutative segment number three. So we started at one and we finished at three. So it means that this is a Doblx lab wining. Look carefully started at three, like this, go all the way like this. And we reach it five. So we started at three and dead at five. So this is also a YC equal to two, which is Doblxd progressive winding. As you can see, we are moving in this direction, right? So it means that since we are drawing in this direction, which is progressive, this is the direction of rotation or direction of motion. Okay? We are moving in this direction. How I'm going to move like this if you take this machine and draw it in the circular form like this, like this. If you say this is a commuted or segment, let's say, one, two, three, four, five, six, seven, like the stake, this part, and make it rotational. You'll see that we are moving from one progressive in this direction for one, two, three, four. So our direction of flotation, one, two, three, four, like this. So our direction of rotation will be like this. Okay. Now, if we have four, it will be quadruplx quadroublx too much plex in this lesson, plus four quadrublx and minus four for retrogressive quadruplx wining. Okay, so what are the equations which we are going to use in drawing our developed diagram? Number one, for YPAC YPAC in lab winding. Remember in this one. YPAC is equal to C, which is the Z. Remember C is number of coils. To C means that we are talking about the total number of conductors we have to C Z. Z over two P, which is a total number of pools plus M M is our multiplicity factor. If it is one, it means we are talking about simplex, two doublx, three troublx et cetera. Now for Y forward, it will be the same equation, but with a negative sign, negative. Now before we go to lab winding, as you can see here that when Y back, if it is a progressive progressive simplx Okay. Then M equal to one, right? So here plus one, and this is minus one. As you can see in this case, in progressive, Y PEC will be greater than Y forward. As you can see, Y PAC, we moved all the way from here to here. And Y forward we get like this, but with a small part, with a small value. Okay, so we move forward larger distance, then we get then getting pack. Okay? So in this case, you can see that we are moving forward, right, because we are not getting so far away. However, if it is a retrogressive Simplex, it means it will be minus one. So Yb will be minus one. Y forward will be plus one because negative one and negative gives us positive one. So Y back and Y forward. Now, as you can see here, as you can see here, YP and Y forward, you will see that Y forward greater than YB. So it means that if we move a certain distance here, Okay. Let's say five. Then in this case, I'm going to Y forward will be seven. So I'm going to get back like this seven steps because the difference between them between these two is two, right? Minus one plus one, difference is plus two. So going forward, going back. So as you can see, we are going to get all the way back. Similarly, go forward Y back, and then Y forward will get us back again. And so you can see that the direction of rotation or motion will be to the left, okay? Okay, this is for lab wining. I lost a point before getting to this one. We said B patch because we have we are connecting through the pack of the machine, right? This is from this coil peck similarly here, Peck of the machine. Why it is called front? Because you can see from this side to this side, we are connecting like this from the forward of the electrical machine. You can see that here from this side to this side, we are having their connection at the front of the electrical machine. That's why it's called front pitch. Similarly here, as you can see in this one, you can see that we have this coil and we go all the way and connect to the next side from the front. So this one is called Y front because we are at the front of the machine, YPAC because we are connecting at the back of the machine, for your own knowledge. Let's continue. We discussed the lab one. Now what about equations for wave winding? In wave winding number one, as we said before, YPAC and Y forward are odd numbers in order to switch between upper layer and the lower layer, okay? It is possible when we have odd numbers. Now, they can be in wave winding similar to each other or can be different by two. Now, how can we get them? In case of being equal, then YB will be Y fold, equal to Y average. So what is Y average? Exactly y average is Yb plus Y fold over two, or we are going to this equation here. So this is representing number of conductors, plus or minus two divided by number of pools. Okay? So we can have two solutions, one solution, which, for example, can be let's say eight and let's say difference between them, let's say five. Whatever the value, for simplicity. So if the answer is eight, okay, which is an even number, what we can do in this case if Y average equal to eight, which is an even number. Remember that Y PAC and Y Ford are odd numbers, and they can be equal if they are odd numbers or differ by two. So what I'm going to do is that I'm going to choose two numbers, two odd numbers close to eight and differ by two. In this example, we can choose five and seven, two odd numbers separated by two and very close to eight. So we can say this one is Y forward, and this is Y back. Or you can do the reverse. You can say five is Y back and seven is Y forward. One of these will give you a progressive or movement in a certain direction, and the other one will give you an opposite rotational direction. That is the difference between these two. These solutions, both of them are acceptable. Okay? Number two, if we choose five why average, equal to five. Then I'm going to use this equation here. Y average equal to Y B equal to Y forward. So we are going to choose Y equal Y forward, equal to five. This is when we are solving the winding diagrams. As you can see here, case of the differ by two, I average is an even number, then it will be YB plus one, Y forward minus one, as you would like, can do the reverse, but we generally use this. And remember that YC or the distance between two commuted or segment, equal to Y average, equal to one plus or minus one. Remember in simplex, I simplex, YC is equal to plus or minus one. Now, in the wave winding, distance from here to here, YC commutator distance, commutator or segment distance, distance between them is Y average, which is this equation. So if Y average, is equal to eight, for example, then YC will be equal to eight, distance from here, one, eight segments, it will be nine. Okay. So we learn it. How can we get Y P Y forward dependent on the value of Y average and YC or the commutator segment distance will be equal to value of Y average. Okay? So I hope in this lesson you understand now the different type of pictures inside the DC machine, and now we can be able or we can draw our winding or developed diagrams for lab and wave windings. 93. Dummy Coils and Equalizer Rings: Hey, guys, and welcome to another lesson. In today's lesson, we will discuss the dummy coils and equalizer rings. So what are these exactly, and why do we need them? So number one, dummy coils. Dummy coils are found in wave winding configuration, not in lab winding, but in wave winding configuration. So in wave winding of DC machines, dummi coils are used when the available number of rmi tu slots does not meet the requirement of the winding. This situation arises when the available number of slots is greater than the required number of conductors. So what does this even mean? Before we understand this figure, let me explain this. So let's say you have in your electrical machine, let's say you have four slots, four and Blest, okay? There are no machine with four slots, but let's say four slots. So four slots means our conductors, Z will be it, right? So we have in our electrical machines, four slots like this, okay? Okay, so our conductors will be it. Now, let me ask you what is the Y average? Y average, which we discussed before is equal to number of conductors plus or minus two divided by number of pools. So let's say we have four slots, and this is a four pull machine. Okay. So number of conductors will be eight conductors plus or minus two divided by number of pools. Number of pools is equal to four, so divided by four. So this number will be 10/4 or 6/4, right? So what you can see that is Y average. In any case, it is not integer. Okay? So it is not possible to have wave winding using this configuration. If we have four slots and eight conductors, we cannot use wave winding. So what I'm going to do is that instead of using eight conductors in these four slots, we will use six conductors. So let's say that will be equal to six. So what you can see that we have four slots that can take eight conductors. However, eight conductors is not possible because it does not give us an integer value. So let's say we reduced the number of conductors and we used six conductors instead of eight. So if you use six instead of eight, you'll find that Y average will be equal to six, which is number of conductors plus or minus two divided by number of pools. So it will be 8/4, or it can be 4/2. So in this case, 8/4, which means two or here two. Okay, here we have four. So this one will be one. Okay? So why average can be two or one, which means integer value. And since we have integer value, we can use wave winding in this case, okay? So I can use six conductors. In these slots, so I will add, let's say, one like this, another one here, or let's add two here and two here and one here and another one here. Okay? So what you can see that we have four slots. These four slots can take eight conductors. However, I used only six conductors. The usage of number of conductors, less than number of available slots or number of available sources is more than required the number of conductors. This will lead to unbalance inside our electrical machine because these windings, you can see we have some conductors in some slots and empty slots. In order to balance our rooter here in the electrical machine, we need to add some coils, some coils which are not connected to any commutator, just the same coils but without any kind of connection. Why these coils are used to balance our root. Okay? These coils are called dummy coils, coils, which you can see here, dummy coils, which are installed used just to balance our rooter without any kind of connection. So the dummy coils are like any other coils, except that their ends are cut, short, and tap. They don't connect with the commutator powers and used only to provide mechanical balance for the router only. So this is in wave winding, one of the problems of wavewinding. Now, going to lab windings and see the equalizer rings. Here we have a problem in lab windings. This problem arises when we have different pools or what I mean exactly that these polls are not identical. Since they are not identical, then we will have different flux from these pools. So you can see that all conductors in any parallel pass lie under one pair of pools. So what I mean by this, what I mean, you can see north, south, north and south. So what I mean is one brush here under the norse, another positive push under the norse. The negative brush here under the south, negative push here under the south. What I mean by this, for example, you will see that for this one, one, let's say N one, as one, N two, and a two. So this is the first two brushes, pair of brushes, positive and negative, these brushes or these windings here, let's say lie under one pair, N one and a one under a certain moment, of course, okay? These two windings or these two parallel puss lie under N two and S two. Okay. Now, if you look at this configuration, you'll find that each parallel pass lie under a certain pair of pools, okay? And one is one and n two is two. Okay? They don't pass. So these coils do not they are not under two different pools. They are one pair of poles, one a certain north and a certain south. Okay? Okay, so what's the problem here? The problem is that since each of these parallel paths lie under different pair of pools, you'll find that if these fluxes, flux coming from north, going south are the same, then the EMF induced in each parallel path is the same, is exactly the same. Hence, they will carry the same current. What I mean by this, let's look at this one. Let's say it has a generated EMF, let's call it E, and this one have the same generated EMF, E. Why? Because the flexi coming from north number two and north number one and going to south and south is exactly the same. Okay? So the generated EMF across the terminus of these windings or these coils are exactly the same. So you will find that the current will go out from the positive like this and go all the way out, right, and get back from the negative. Now, is there any current here in this loop no, why? Because if we apply KVL, you will find that if we apply a QVL, let's say this is a current I one, and this is a current I two. So if we apply KVL like this, then you will find that negative E plus I multiplied by resistance R, since this coil will have a certain resistance and the current flowing through it to the voltage drop I one, multiplied by R. And if we go all the way like this, you will find that plus here, I two multiplied by R with a negative sine with a negative sign because we are opposite to the direction of this current N plus E. A simple civial so you'll find that negative E will go with the positive E. And since these two currents are identical to each other, since we have same fluxes, so this one will go with this one. So it will be equal to zero, no circulating current. However, if you find that in reality, there are inequalities in flux due to slight variations in air gap length, wear of parings or any other condition. So all of this can lead to inequalities in flux. An one does not produce the same flux as any two. And this will lead to different EMF. E one will not be equal to E two. So due to different EMF, we will have a circulating current flowing here, a current flowing from here to going like this, going like this, like this. Or we can think of this, or we can see like this. Let's draw it in a different way. Let's say the soil, the swan, and the swan. Okay? So you can see that the current will flow like this, like this. All the way back like this, keeps flowing like this. You will find out the problem. What is the problem exactly. The problem is that it will pass through these process. The current will flow through these brushes. So what does it What is the problem? The problem is that it will lead to overloading of our process due to this circulating current. So instead of making the current flow like this, through these brushes, I will make it flow in a different way. I'm going to connect like this, add a connection here. Like this so that if we have a circulating current like this, add more than one connection like this. So if we have a circulating current, it will flow like this. Due to different EMF between coil sides, it will flow like this instead of going through these brushes. What is this connection? Exactly. This connection is what we call equalizer ring. This equalizer ring connects between points under the same pool so that it allows the circulating current to flow through it. So the problem of this process will lead to overloading due to circulating current leading to overheating problem in the armature. So let's see the equalizer rings. These equalizer rings are known as commutating or compensating windings. They are additional coils or rings, coils or rings, added to a certain segments of the armature in DC machines employing the lab winding. So let's look at this. You can see this electrical machine, here, the stator and the router. On the router itself, we have this equalizer ring. So if you look carefully here, Look at this equalizer ring. We have several equalizer rings. One, two, three. Look at these equalizer rings. You will see that here, this equalizer ring, this one is connected to mature winding here under the south Okay. And the same ring here, if you go all the way down here, you'll find that it's connected to the armature under the same south. So if there is a potential difference, an EMF difference between the coil under the south here and the coil on the south here, then the circulating current will flow from here from this armature, go through the ring to the second one. And instead of flowing through the process, okay? Now, the second one here, you can see that for this ring, for example, you can see it's connected at this point and connected here to the same point. After the north a little bit, we can see it is in approximately close to the neutral point here, the same point. Similarly, you can see the ring connected to this part. Close to the north exactly similar here as you can see. Now, let's look at this in the diagram. So they are connected in parallel with the armiture coils, and they are designed to improve commutation and prevent the circulating current through the process. So what you can see here, let's look at this figure. You will see how are we going to connect it? We connect it at a certain points of our electrical machine. So you can see that we have one, two, three, and four. Now you can see that we have under the norse here, under the nors, I'm going to connect the coil under the snors here and similarly under the other norse I'm going to connect st the same equalizer ring. If we have different in voltage or a potential difference, the current will flow from here like this and go like this. Instead of flowing from here through the process and go all the way back. Okay, I flows through this equalizer ring from here. Similarly, you can see that the south connected to the thus at the same point, the neutral point between North and South, also the same neutral point here between To and north here, the same point here, connected together, thousand thousand neutral point, neutral point, et cetera. So we connect several points so that if any potential difference between them, the current will flow through the equalizer ring instead of our process. Finally, we have a comparison between lab and wave winding before we draw them. Lab winding is called parallel winding, as we said before, because it has a high current, lots of parallel paths, high current, low voltage. This one is called parallel series winding because it has a high voltage, low current. Now in lab winding, we can see that we connect them in a form in which we are overlapping each other. In wave winding, we are progressive or moving forward, traveling forward. In lab winding, number of parallel passes equal to a number of bolls, equal to four. In wave winding, number of parallel pulses is equal to two. Lab winding is used for high current low voltage applications. Wave winding used for high voltage, low current applications. Again, the same point here, okay? 94. Example 2: Now let's have the first example, example number two, in order to understand how to draw the lab winding. So in order to draw the lab winding, number one, this example, we have a developed diagram of a two layer simplex lab wind. So two layer means double layer. Simplex means M equal to one. M equal to one, right, so let's go here, M equal to one. Right, for a four pool generator with 16 slots. So number of slots, number of slots equal to a number of coils, equal to 16, number of conductors Z will be double number of codes 32, right? How many pools to B equal to four. Now, since we are talking about lab winding and simplex M equal to one, it means that YC commutator segment space is equal to one or commutator pH equal to one. Okay? Now, two layer, if you remember, one, two, three, four, five, six, okay? So what we do is that we connect one in double layer. One in the lower layer, one in the upper layer, and one in the lower layer, et cetera. So let's start by getting YP, Y forward, and other values. Number one, the ratio between Z over two B, Z over two B is equal to a number of co, number of conductors, 32 divided by number of pools, we have how many pools, we have four pools in this equation. Or in this problem, we have eight ratio between how many conductors per pole, eight conductors per pool. Okay. Number two, to get YB and Y forward, remember the two equations. We take this ratio to C over two P, which is eight and at YP plus M, M here, sm blex which means one and subtract one. So eight plus one equals nine, eight minus one equal seven. So this is our YP Y forward, nine and seven. Now we will draw the winding table. That is very important. You can see that we have back connections and front connections. Back connections here through the back using Y B and we have front connections, which means from here to here, connection from the front. Now, let's see how are we going to do this. So let's say number one, Number one, we started at what slot slot number one. So let's go from slot number one to the Nexo slot. We have a distance YPG YPEPEgneton with the value Y PEG. So the first slot, go here, slot number one, two to which slot distance Yb, YbC equal to nine. So we will say one plus nine, one, two, what slot ten? I'm going to go from one to slot number ten. And then we have a front connection getting here. So ten front connection. So from ten here, I'm going to the left, buy a value of Y F, right? So I'm going to the left by Y f how much YF is seven. So here I'm here at ten, so I will subtract seven to go all the way back here. So it will be ten minus seven. It will give us three. Now, similarly, take slot number three. Which is this one and add to it Y back to go to the next coil. So three plus nine gives us 12. Then get back, get to the front 12 minus seven, et cetera. Keep doing all of this, all of this in order to know the connection of all windings, okay? Now there is a very important part here. Now, as we go, how many slots we have, we have how many conductors, how many conductors, we have 32 conductors. This is very important. As you go all the way, you'll find that in one location we have certitO we can exceed the certitude, like this, you can see 25. Then the next one we will add nine, 25 plus nine. Why back? Gives us 34. However, we have only 32 coils. So what does this mean? It means that the 25 is going to connect to, which 134, subtract from it the maximum number of conductors, 32. So 34 -32 gives us two. So 25 is going to be connected to the conductor number two, in the back connection. We will see this in the diagram. Okay? Now, when you are going to the forward, you are going to take the original value, not the last value, but the original one and subtract from 87. So from two, going to 27, 34 minus seven. Again, if you have any value exceeding 32, just subtract 32 from it like this. In the end, you will have your own complete table. Now, how can I know if I completed the diagram? We started at one, and we finish at one. Okay? Now, let's see this. This is our diagram. Let's look carefully here. So number one, how many per pool? How many conductors per pool? We have eight conductors per pool. Let's look here at north, thous, north and south. Okay? So let's say, one, two, three, four, five, six, seven, eight. So there are eight conductors under the norse. We assume that the current will go down and the sous will go up as you would like, you can assume this up and this is down as you would like, okay? So we assume that the current going down under the nose. You can see that this is the first slot, upper layer, and lower layer one and two. And as you can see, slots, the upper and lower layer are very close to each other. So this is a slot number one, up a layer, lower slope number two, up layer low layer. Number three, upper and lower, upper and lower, et cetera. So you can see eight conductors with the same polarity going down, this one also going down, for which one for which one for under the north, right? For south, you can see one slot, two, three, and four, four slots with upward direction. Okay? Four slots. Each one has two conductors, it means we have eight. Similarly, here eight conductors, eight conductors. Okay? That's the first step. So we have commutator one, go all the way, connected to first one, right? First coil. Now, 11 goes to ten. So you can see that we connected one goes all the way to ten. From ten, we go to which one, go to commutator segment number two. Why? Because YC in a win is equal to one. Now, from here, from ten, front connection, from ten going all the way to three. Okay, from ten, go all the way to three. And then from three, go to 12, from three, go all the way to 12, from 12, go all the way to five from 12, go to commit to three and go to number five, et cetera. Keep doing all of this until you finish. Now, let's look at these windings here, too. So 31 coin number 31. Okay, let's see 31 31 where 31 here, 31, going all the way to eight. So you'll see that 31, go all the way to eight. So you'll see that number eight here. Here, this is eight. You can see that here, eight coming from 31. So eight to 31. Similarly, you can see here from six going to 31, from six here, going to 31. So here from six here, going all the way to 31, and et cetera. Okay, so this is a diagram. Now, this back connection on the front, you can see ten to three, 12 to five. Let's see it. Ten, going to three, three to 12. Okay, three to 12, 12 to five, 12 to five, et cetera. This is a ring diagram, exactly similar to this one, okay? Now where I'm going to do the process, look at the currents. If let's zoom in again like this, as you can see here, you can see that at commutator one, you can see current, this is on the north, current going down, and this one on the north current going down. Current entering, current entering, so I can add a positive process to take the current from here. Now, what about commutator two? You can see that commutator two connected to this one, currenty coming down and the other one going out. You can see under the south, so it goes down. So it means that the currenty coming from here goes all the way here. So no current is taken from here. The current here goes like this. Four, three like this, four, like this. Four or five, look at it. Five is connected to nine. Going out and connected to 16, which is also going out. The cant going out from here, different polarity from this one. I will add a negative brush because current going out, current going in. Similarly, for nine, current coming in, 413 current coming out. Then we will connect two negative processes and two positive brushes. You will see also that one brush under north, one under thousand north and thousand four process equal to number of pools we have. Okay? Okay, great. Now, if we look at our electrical machine, you will find how many slots. So we have 16 slots, one, two, three, four, five, six, seven, eight, nine, ten. We are going to put at axis one, two, three, four, five, six, seven, eight, 910, et cetera. Now, what you can see here is that this is a direction of rotation. Why? Because you can see that we are going progressive in this direction from one, two, three, four, one, two, three, four, so in this direction, as I explained Now, if I would like to draw the equivalent ring diagram, equivalent ring winding, let's look at it. You can see that we have how many parables, one, two, three, and four. You can see that this are two process to positive process to negative process. Now, let me explain this. You can see that between if we look at this diagram, which will help us understand. You can see at let's say A is 1-8, right? So let's look at it 8-1. So here, just one correction here that the current going down. This arrow should be going down, not up but down. For D, you can see current going out for D, current going out 25-3232 and 25. Four B current going in, four B current going from 24 and 16 from 24 and 17, let's see here, 24 and from 17. Okay, sort of from 17, not 16, from 17. Like this, going down, going up, this is going down, up, okay? Now, you can see between, let's say, here push number connected to nine and one. 24 and 17. This number is a commuted or segment nine and one. You can see one and nine. A. Okay, so A, between A and C, commutator one, here, the first one, the positive brush, eight, six, four, two, 25. Let's look at it. Brush number A from here, eight, one, ten, three, 12, five, et cetera. So where exactly one, three, one, ten, three, 12, five, 14, one, ten, three, 12, okay? One, ten, three, and 12. Okay? So here we have the brush here. This brrush is exactly here. You can see the two direction is downward. This is a wrong direction. So our A is here. Okay? Between it and C, there is this winding, the loza until 16, between it and C. So you can see between it and C. C is number five, as you can see, Okay. The second parallel one, if you look at A, connected also to D 831, six, 8316 between it and 13 13, which is D, like this D. Okay. Similarly for the other winding are connected to g. So find have one, two, three, and four. If we have a current or mature current of IA, it will be divided by two. Each pros give us half of the current and each approach has two parallel paths, one, two, one, two. Each one takes the quarter of the current. You can see I over four, I over four, the submission I over two, their submission I over two and submission equal to I ort. 95. Example 3: Hey, everyone. In today's lesson, we will discuss the Zod example, example number three, which will help us in understanding. How can we draw the wave winding? So we would like to draw a developed diagram for a two layer. Again, double layer two layers, Simplex wave winding, which means M equal to one. For a four pool generator, two P equal to four and 30 armature windings, we have 30 armature windings. So how can I do this? Now, remember the equation. For Y average, we said that Y average equal to a number of conductors to see double the coils, how many conductors we have? We have 30 armature windings, which means 30 conductors, okay? Plus or minus two, divided by number of poles, which is four. Now, given that Y average will be 30 rmiture inductors plus or minus two, divided by number of poles which is four. This will give us two solution, either eight or seven. So why average equal to eight or y average equal to seven? Now, if we selected the odd number, why average equal to seven? Y average equal to seven. We know that Y B and Y forwards are odd numbers. And as we said before in the previous lessons, we will choose them the same value of Y average if it is odd number seven, like this. That is what we are going to solve in this problem. Y B equal Y four equals seven, Y average equals seven, which means that Y C equal to seven. Okay? Now, what if we selected eight? If you select the solution, eight, Y average will be equal to eight, equal to Y C. Okay? What about YB YB will be eight plus one, which is nine, and Y forward will be eight minus one, which will be seven. Okay, or you can do the reverse, Y back can be equal to seven and Y forward equal to nine. We can do the inverse. The difference between these two is that one of the solution will give us progressive or rotation in a certain direction, and one will give us a rotation in the opposite direction. That's the difference between these two. You can see that if we select eight, then the patches will be YP equal mine, YF equal seven, or the inverse like this. Y equal YC which is seven as we selected here. If we select the other solution, YC equal eight, it will be rotating in the opposite direction. So YA and YC, depending on them, one of them will give us a rotation in the clockwise direction, and the other one will give us a rotation in the opposite direction. Okay? Okay, so let's see our solution. Again, we collected everything. Y equal seven and Y equal I fold equals seven. Now, let's start by typing our winding table. So we have back connections again and front connection. What are we going to do? That we are in a progressive direction. So what I mean by this if we started here at one, then we go all the way to eight, and then we go all the way to 15 and et cetera. So we don't subtract anything we are in the forward direction, okay? Now we will start at one. So let's zoom NS number one, and we know YP equal Y four, equals seven. So we will start at slot number one. Then we add plus seven for the back connection. So plus seven, it will be eight. Now, from this 0.8, I'm going to go front pitch like this to the nexus slot front patch of how many of 72, right? So it will be eight plus seven, like this eight plus seven, eight plus seven gives us 15. So we will go 1-8 and eight to 15. So from one, to eight and 8-15, et cetera. Now, you will continue as 15 plus a plus seven, gives us 22 plus 729 plus 736. Now, this is very important, okay? When you are dealing with a value greater than the number of conductors, remember, we have 30 armature conductors. 36 is greater than this. What we are going to do that we will subtract search six from 30. We will go all back to six and in the next one, we don't start with search six, because we are just it doesn't matter if you let's say, make it like this. If you say six plus seven gives us 13, write the last value. If you use the original value of Sirt six, it will be Sirt six plus seven gives us 40. 43, and then you will find that this value is greater than 30. We will subtract 30. It will give us 13, the same value. Even if you take this value or this one, it doesn't matter. It will lead you to the same value of 13. Now magnify continue 13 plus seven, 2020 plus seven, 27, et cetera. You will keep doing this until you will find that we started at one and we ended at one. Our winding is finished. So this is our table. Now let's see our diagram. Now, what you will see here, let's magnify like this, you'll see how many pols one, two, three, and four, four pools. Now, what are we going to do? Let's type it. We have 30. Let's type it where exactly here 30 conductors, right? So how many slots? 30/2. We have 15 coils or 15 slots, right? Now, what I would like to do, I would like to divide these slots under the bools. So we have 15 slots, divided by how many pools divided by four pools. So this will give us, if I remember 3.25, okay? Three and a little bit. Okay? So what we can do is that I can say that we have four pulls, I can say here, the first one will take three slots, second one will take four, four, and four. So what you will see that four plus four plus four, 12, 12 plus three equal to 15. That is my own design. You can make it four, three, four, four. You can make it four, four, three, four, whatever it is. Since they are not divisible by number of poles, we can exchange or make some slots under north and other under Toth. Okay? Now, if we translate this, you can see that here you can see Ts here, one slot, two, three, and four, this slot this slot is exactly this one. Okay. So remember, this one is not under the north. This is under the thus, okay? This is This is one, and this is here also one. Okay, so don't worry about this. This is exactly the same coil. So this is related to this thus. So we have one, two, three, and four. North, one, two, three, and four. One, two, three, and four. For this north, it has three, one, two, and three. Okay? Now let's start. You can see these currents are dependent on which one under north and which one is under South, right? Okay. We started at one goes to eight. So as you can see, one goes all the way to eight. And eight goes all the way to 15, so we can see eight go all the way to 15. Okay? Now, someone will say, Where is our start? Here we assume that you can number these slots as you would like. You can make this one, one, two, three, four, whatever it is. This is according to an electrical machines reference, and it selected this commutator numbering as he would like. This is his own selection. You can make it one, two, three, four, or whatever you would like. Anyway, you can see that number one started at this segment. This segment is number three. Segment number three, as you can see here, one, One. This segment is three. Let's just type it so that we can don't forget it, magnify like this. This is started at number three. Now, goes all the way and where I'm going to connect it, I connect it at seven. Why at seven? Because if you remember, y average here in this example, y average equal to seven, Y B equals seven, why forward equal to seven. We said that y average, Y C equal to Y average, equal two. In this example, Y average is seven. Okay. So what we are going to do is that the distance between two commutator sites, two R cogal sites is seven. So as you can see, if we started at three here, we will go three plus seven gives us ten. So as all the way to ten, so you can see that we go like this to number ten. If I would like to add to the next segment, so this one goes after what? 10-17, right? One, two, three, four, until 17. We don't have 17, we have until 15. So we will subtract 17 -15 gives us a slot number two. So if you look like here, ten goes all the way like this. Two slot number two, because the distance between them is seven. Now let's continue. So what you can see, one goes to eight and eight goes to 15. Eight goes to 15. 15 goes to 22. So let's see. So 15 here 15 goes to 22, you can see here 22, 22 goes all the way to 29. 22 goes all the way to 29, et cetera. So you keep doing this, you will draw the wave winding. Okay? Okay, great. Now, the same diagram here, you can draw it at the ring diagram equivalent ring diagram, as you can see Okay. Now, let's get to the most important part, most important part in the wave winding, which is always confusing. Always confusing. Now let's look at the brushes. Where are we going to place our brush Remember that we only need two brushes inside our DC machine or our DC machine with a wave winding, okay? So I will show you where are we going to do this process? So what you can see that if we look at all of this figure, you can see that current goes out and the current goes out here, right? So we will have our negative terminal here. Very easy, right? Now, let's look at the rest of this diagram. Okay? Forget about this process. Let's look. Current goes in, goes out. No brush in out, in out here in and out in and out, in and out, in and out, in and out, in and out, et cetera, you'll find that actually, there is no process here. There is no process because we don't have any two outgoing currents or two incoming currents. So how did we place these process these process? Okay, let me explain this. Okay, look carefully here. Now, since we don't have any connection here, you will find that actually, actually, the location of push is behind here. We should put a brush here. What do you mean by this? I will show you exactly. Look at this one. At this point here, this point, look at this. You can see this point, current going out and current going out. So how is this possible, you can see that current going out and the current going out, right? So it means that I need to collect the current at this point. I need to collect this current current going like this and the current going like this. So this one should have a brush. However, I can't add brush here because this is the back of the machine. I can't add any brush. I can only add this on this side. So what we are going to do is that I'm going to look to the nearest two commutators. So look carefully here. So what you can see this one, right? This is the one which we are talking about. You can see that go like this, go like this. Looking to the second one like this, like this and go all the way down. Okay, to currents like this. Now, let's zoom in. You'll see that the current going in current going in, right? So by logic, two, this is I should put a brush here. However, the nearest two commutators, this one and this one. So I have two options, either to add a positive brush at 11 connected here or a positive brush connected at three. This is my only choice. I can add it here or here. This diagram shows two process. However, you can select what brush as you would like three or 11. Similarly for the negative, if you look carefully at the negative, let me show you here. You'll see that this one, look carefully at here, currently going up like this, all the way, like this. Okay. And the current also goes up here, holds away like this. So you can see that the current here going up and here going up. So we need also a brush at this point, right. So if you look carefully here, current going in, current going in for this point. So I'm going to put a brush at the nearest two commutators, this commutator, and this one. So you can add a negative brush here for current entering or a negative brush here for the current entering here or here. Okay. So this is optional. You can select this brush or this one for negative and for positive, this or this. Okay? I hope it's clear right now. So if you zoom in like this, when you look at the same diagram, you can see this point has two entering currents, so we can put a brush here or a brush here. Similarly, for this point, two currents going out, so we have to put a brush here or the nearest 21 since we can't add any process here. Okay? I hope you understand. Now, where did we put this process? Now if we now draw our diagram, you can see we have two, one positive and negative current going out, since we have a generator ct going in. Now, we selected the two points P, which is connected to 17, and we selected R, which is connected to two and nine. Whereas R, we selected this one, two, and nine. This is our negative brush, right? Going out two and nine. Negative brush, two and nine, you can see here, two, and nine. And then the connection of the rest, you can see two is connected to. If we go all the way connected to 25, two connected to 25, et cetera. Similarly, for nine, connected to 16, so nine connected to 16 and et cetera. Then you'll find that we have only two parallel paths here. As you can see, and the positive brush, which is located at here, you can see ten and 17 17 and ten Push at community to 11. And you'll find that it is connected like this and like this. So we have only two parallel path. So this is how you can draw the wave winding of an electrical machine. I hope you now understand it and understand exactly how can we add our brushes. 96. Induced E.M.F Equation: Hi, and welcome everyone. In today's lesson, we will discuss the induced EMF equation. So if we remember before that each conductor under a different pool generates EMF right or generate an induced voltage due to the motion of our conductors inside the magnetic field. So we would like to know the value of this EMF. So we have some definitions here. Number one, we know that to B is a number of pools in the field, of course, in the field, not like this, filled field systems. And flux is how much flux pair pool, flux produced by each pool in whippers. So what I mean by this, we have north like this and thus. So the flux like this, amount of flux coming out of the north or entering the South is called the Phi. Each one has a flux called Phi. So this is a flux for each pool. Then we have N, which is a speed of the armature. The speed of the router itself, how many revolutions per minute, how many cycles or how many complete revolution? Let's type it. Let's say if it completes 10 hundred and 60 degrees or 12 Pi cycle mechanical angle, this is what we call one revolution. How many revolutions it do in each minute called RPM revolutions per minute? Which is a speed of the armature. That is a total number of conductors as before, which is number of conductors. Multiblod multilodPi how many slots? How many conductors per slot? I don't know why this reference keeps inversing everything. This is from a certain another electrical machines reference. So I do inverse many things as you can see here. Anyway, A, which is parallel paths. For lab winding, we know that number of parallel paths is equal to number of pools. Again, this reference uses B as number. Of pulls. However, I forgot to change it. I changed this one to two B, which is number of pulls, which we always use. In other reference, they can use B as number of pulls. Okay? I will change this in the slides when you have it, okay? So anyway, let's continue. So number one, according to Faraday's law, the rate of a change of a conductors cuts by a magnetic field. The EMF induced on this conductor will be as follows. It will be like this. Induced EMF is directly proportional to defy over DT. Now, where did we get this? Remember that from faro Days law, we said that E is equal to N, defy by DT and we have the negative sign, which is from lens law as we discussed in magnetic circuits. So induce the math on a conductor on a coil on a conductor for simplicity is equal to how many tons multiplied by the variation of flex with time. Okay? Great. So since we are talking about just one conductor, we will say N equal one for now, four simplicity, okay? N equal one, since we are talking about just one conductor. Now remember that our conductors our coil is consisting of two conductors, one under the norse and one under the south. So one under the norse will have a generated voltage E, and under the south it will have an inverse generated voltage like this, okay? So the total voltage will be plus or minus two e four, coil under two different pools. Okay? So we are seeing now that each pool has a flux, either a positive flux going out or a negative flux going in. Okay, and each one has its own effect on the conductors. Okay. Now, what we would like to do is get DFI and DT. So DFI, which is a variation of flux, for one complete cycle. So the flux affecting our coil, our conductor for one complete cycle is equal to the total number of pools multiplied by flux of each pole. Now, where did we get this? Now, let's say we have our machine like this, North, To North and Tous. Okay. So when our machine completes one complete cycle like this, it will be any conductor. Any conductor will be subjected to flux from north or thus or north and thus. It will be subjected to all of these fluxes. Okay? That's why in one complete cycle, the flux defi is equal to two P, which is number of pools. Here, for example, four pools. Number of pols multiplied by flux, contributed by each of these pulse, so that we get all the total flux affecting this conductor when it completes one revolution. Okay, so it is two P Multiblte five, which is flux per pool. Now, DT, this is a time. I would like to know since we have one complete cycle with this flux, I would like to know the time taken for one complete cycle. Now, as you can see, we have N, which is a bit of the armature. N is how many revolutions, how many complete cycles per minute. Number one, if I would like to convert it into second, I will say N divided by 60 gives us how many revolutions. Pair second, right? So what does this mean? It means that for each 1 second, each 1 second, it will do N over 60 revolutions, right? So for each 1 second, it will make N over 60 revolutions. Now, I would like to know the time of just one revolution. So the time T of what exactly one revolution. Okay, so how can I get this simply by cross multiplication? This multiplied by this, and this multiplied by this. So what you will find that is one, this multiplication equal to T multiplied by N over 60. So the time taken for one cycle will take this to the other side. It will be 60 over N. So again, we took revolutions per minute, convert into revolutions per second. So this is how many revolution it do in just 1 second. All what I need is just one revolution, since this is a flux for one revolution. So one revolution and time T by cross multiplications, we got the time T equals 60 over N. So let's see it. It will be like this Dt 60 over N. So we have DFI, we have Dt, divide them together. So induced EMF, pay conductor. Remember that N df vertity. N is equal to one, one conductor we have, Divi vertity take this one divided by this. You will get this equation here. So finally, you will find that this, let's type it, go here p2p, phi, but multiplo by N divided by 60. This is induced EMF for each conductor like this. Now remember that remember. How many remember that. Let's say we are talking about wave winding, for simplicity. So we have one, two, three, et cetera, one, two, three, et cetera. So we have two parallel paths right. In each one, it has an FE. Thus EMF E is equal to EMF of one conductor, multiploid EMF of one conductor, multiblo by Z in this parallel path. So that the Z of this parle pass is equal to Z over a number of parallel paths. Again, remember that if we have two parallel passes, then I'm going to take the total number of conductors and divide it into two parallel paths. Or if we have Z parallel paths inside like in lab winding, then z divided by each path will have number of conductors divided by a. So we simply have, for example, here it will be z over two and this one z over two. Half of the conductors will be here. So this is the number of conductors in each path, right? They are parallel to each other. And if I take these conductors and multiply by the induced MF of each one, we will get the total E. So for example, if we have this value equal to three, let's say we have one, two, three, and one, two, and three, like this. The total EMF of this generator will be how many one, two, three, it will be three conductors multiplied by the induced EMF of each one. So what you can see that we took this equation and multiblo it by how many conductors per path. It will be over A, like the two P, Phi, the N divided by stA. This is a final equation, how many conductors pass and the induced MMF of our generator. Now, this is a very important part. Another point here is that you will find that usually, we say that E, which is the induced MMF of the armature equal to K N Pi where FI is the flux per pool N the revolution per minute, how many evolution bin and dec is the conistance we have. What I mean by this, it is exactly Z K will be z to be over 60 A, like this. So this is just a conisant to replace several values here and just multiplied by N Pi. Okay? This is important when we discuss the control of a DC machine, speed control of a DC machine. 97. Example 1: So let's have the first example on induced MMF. A 400 volt, it pool 600 RPM, DC machine has 100 slot. Each slot contains 40 conductors. Zaloxe per pool is 0.01 whipper. Find the type of winding used. Okay, how can I do this? How can I know the type of winding? Now, if you have voltage and several other factors, by using the induced EMF equation, you can get how many parallel paths. So if I know how many parallel paths we have, we can get the generate the type of winding. So we are going to use the EMF equation. Remember that E equal to pz N to P over 60. Now, flux here, this is a flux spare pool. You can see flux per pool is 0.01 member. So this is 0.01 multiplied by Z, number of conductors. Now, as you can see, we have 100 slots, S, and each one contains 40. So we have 40 conductors per slot. So if I would like to get the total number of conductors, it will be simply number of slots, multiplied by number of conductors in each one, which is 4,000. So this one will be 100 multiplied by 40. Multiplied by two P which is number of pools, eight pulso, divided by 60 A, 60, multiplod by A, which is the number of parallel paths which we don't know yet. Now, E, the total induced MMF of our generator. Our induced MF is 400. Remember that here we have Z over A, which means we are getting the total EMF, not the MF of just one conductor, the total EMF of our generator. So what you can see here is that the equation will be like this. By getting A, you'll find that A equal to A. Now, what you can see that the parallel pathos here is equal to number of pools, eight parallel pathos, eight pulls, which means that we have lab winding. Since number of parallel paths equal number of pulls, then we have lab winding. 98. Example 2: Let's have another one. So in this example, example number two, we have a DC generator that generates an EMF of 520 volt. It has 2000 armature conductors, flexi per pull of 0.13 whipper, speed of 1,200 RBM. And the rmitre has four parallel paths. Okay, great. Find the number of bools. Okay? So since we have EMF and other factors, we can get the number of pools to be using the equation we know. Okay, right? However, without even using the EMF, I can tell you how many pulls we have. The answer will be four puls. Without doing anything. Now, how did I know even that it is four pulls, I will tell you right now. Remember that in the parallel paths, we have only two options. We have parallel paths equal to two parallel paths in wave winding, right, and we have A equal to two, P in lab winding. Now since our parallel paths is four, it means that we are not dealing with wave winding. We are dealing with lab winding. And since we are dealing with lab winding, then number of parallel paths equal to a number of poles. That's why four parallel paths will be equal to a number of poles which is four poles and a point. That is the answer, okay? The answer with equations will be like this. We use the EMF equation once more. EMF is 520 volt. Flux per pool is 0.0 13 grade, multiplied by number of conductors, 2000 armature conductors, 2000 mature conductors, N number of speed, how many revolutions per minute, 1,200 RPM. Multiplied by two P, which we don't know yet. 60 a parallel path is four. As you can see here, you can see the same substitution down here. Now, what you can see here is that after we substitute, two B will be equal to four as I just predicted because this is a lab winding. 99. Example 3: Let's have another example. In example number three, we have a 12 pool DC generator has a simplex wave armature containing 144 coils of ten tons each. The resistance of each turn is 0.11. The flux per pool is 0.5 weber. And running at a speed of 200 RPM, find the induced voltage and the armature resistance of this machine. Okay, so number one, how many pools, 12, et cetera. So in order to get induced voltage, we need the equation E equal to viz and two P over 60. Let's start step by step. So we need E. What is a flux per pool? Actually flux per pull, 0.05. So let's type it. So flux per pool or 0.05. How many conductors we have? This is very important. How many conductors, as you can see, we have 144 coils. Each one has a turn turn. So like this, it will be. So we have the first coil side and the second coil side, one and two. Now, what we do that we keep doing like this one, two, and three until we go down here. So several turns, and then we go down. So what does this even mean? So our conductors will be, how many coils we have actually have 144 coils. Each one is repeated ten times, ten tons ten times, so we will multiply by ten. And so this will give us total number of coils. Okay? So if we multiply by two, since we have two coil sides or two conductors in each coil, we will get total number of conductors. So again, 144 coils repeated ten turns or has a ten tons, repeated itself, ten tons, okay? So ten turns multiplied by how many coils we have will get us the total number of turns, total number of turns or total number of coils. So the total number of coils will be 144 multiblie by ten. And since each coil has two sides, it will be multiplied by two. So it will give us total number of conductors. So here, that will be 244 multiplied by ten, multiplied by two. Okay, the speed of the generator 200 RPM, number of poles, 12 pool machine. A, which is a number of parallel paths, how many parapath we have, it doesn't see it gives us this value. However, you can see that it is simplic wave armature. And we know that in wave, parallel paths equal to, so A will be equal to. By substituting this equation here, as you can see, you will get the induced F equal to 2,880 volt. Great. Now, we would like to know the armature resistance of this machine, okay? So how can I get resistance? So let's say first, we know that this is a wave winding, right? So we have two parallel paths like this one and two, right? So our conductors, our conductors z is divided by two. So this one takes z over two, and this one takes z over two. Okay? So first, let's see what is the number of conductors, z over two. So our conductors here and this path will be conductors Pair paths will be equal to. Z over two like this, which will be equal to how many conductors, 144 multiplied by ten, turn multiplied by two, divided by two. Why multi blood by two? Because each coil has two sides and we have ten turns. So this is a number of conductors per path in each path. Now, it's resistance, as you can see here, the resistance of each turn. Okay, remember, each turn each, this is one turn. Each turn consists of two conductors. In series, of course, this one and this one in series. Now, the resistance of one turn R turn will be equal to two multiplied by R of the conductor. Right, double the resistance of one conductor because they are in series. Now, R turn is given as 0.11. So the resistance of one conductor is half of this value. So in order to get resistance pair half, it will be this value like this, 144 multiblo by ten and multiply it by the resistance of the turn, which is 0.11. And divide it by two. Why divide by two? Because each turn consisting of two conductors. The resistance of just one conductor is zero point 11/2. This is the resistance of one path. 1044 multiplied by ten, multiplied by 0.11, divided by two. So we can see that this is a resistance of each bass. You can use this equation, which is resistance of each turn, multiplied by how many tons, this will give us the total number of the resistance of the total turns, multiplied by number of coils, resistance of the total coils and divided by A to get the resistance of each path. So this is a final equation exactly this steps, exactly similar to this. They will give you the same answer. Except that the difference is that I used here, how many conductors in each path and then multiplied by the resistance of each conductor, which is half of the resistance of the turn. Or you can simply get the total number of turns, multiplied by number of coils and multiply it by the resistance of just one turn. Then divide it by two because we have two parallel paths. Now, as you can see, the resistance, it will be like this. Of each one, 7.92, 7.92. And since parallel to each other, then R total will be R over two because they are the same resistance. However, they are similar however we have two parallel paths, so it will be R over two. If we have a parallel paths, then the total resistance will be R over A. In general. So here it will be 7.92 divided between because we have two parallel paths. So the total resistance equivalent resistance will be half of one of these resistors. 100. Example 4: Let's have our final example on the DC generator for the induced EMF equation. A four pool machine running at 1,500 RPM, has an armature with 90 slots and six conductors per slot. Flux per pool is ten milli whipper. Calculate the terminal EMF, the coils are lab connected. If the current per conductor is 100 and pairs, find the electrical power. So our solution, number one, we need total EMF. We use our equation E. Number one, flux per pool is ten milli whipper. So ten milli means ten to zero negative three. So it will give us 0.01 whipper. So the flux 0.01. How many conductors, as you can see, we have 90 slots, 60 conductors in each of slots. So the total conductors will be 90 multiplied by six, 90, multiplied by six. How many what is the speed or RPM, RBM, 1,500 RBM. Multiplod by two B or the number of pools, four pools. Okay? And how many parallel paths? As you can see that we have what type of machine lab connected. So A equal to two B. Number of parallel pathos, equal to number of pools. So A will be similar to two B, which is four. By substituting like this, you can see 0.01 90 multi blod by 61500 RBM, 464. Okay? So it will give us inducing math of 135 volt. Great. Now the next requirement that we need if we have the current for each conductor is 100 and pre, find the electrical power. Now, as we know that the power of any electrical machine is equal to power equal to volt, multiblod by current, right? Okay. Let's look at our machine. So this machine is for lab connected for parallel paths. So our machine will be like this right one, two, three, and four, right? Great. Four parallel paths. Each one, each one or each conductor, had a current of 100 ampairs. So this one, 100 ampairs, 100 am pairs, 100 am pairs, 100 ambers, current flowing in each conductor. And the terminal EMF, the generated EMF of this equivalent circuit, as we said before, all of them are parallel so they have the same voltage, 135. So this is our E. So the current here, the total current is 400, right, 100 plus 100 plus 100 plus 100. So the total current of the electrical machine 400. Voltage of the electrical machine is 165. So the power will be voltage 135, multiplied by the current 400 like this. So it will be power 135 multiplied by 400 gives us 54 kilo W. Okay. 101. Types of DC Generators: Everyone, in this part of our course, we will start discussing the different types of generators that are used in our electrical machines. So how can we classify our generators? It is very easy actually. So we have different types of DC generators. We have separately excited DC generator, self excited DC generator. Under it, we have the hunt wound DC generator, serious DC generator. We have compound, short generator, and long compound generator. Now someone will say, what is the difference between all of this? Let me make it clear for you. The difference between all of this is the connection between the armature armature winding, and the field winding. What do I mean by this? If the armature circuit is separate from the field circuit, we have a circuit for field winding and another circuit for armature winding. So this is what we say separately excited. Our excitation. And when we say excitation, we are talking about magnetic field. So our excitation is used using a separate DC source. And our armature circuit, you can see the two terminals of our armature are connected to our load in case we have a generate. In case we are talking about sont DC generator, what does this even mean? SNT generator means that the field winding is parallel to the armature winding. So the two terminals of the field windings are parallel to the two terminals of the armature. So it will be connected like this and we don't have any supply here. So our circuit will be like this. You can see that our shunt is parallel to the armature itself. Okay? They are par to each other. Series, it means that we take the field winding and we connected it in series with our armature winding, and then we connect our loot. In the short compound generator, what does even mean? Compound here means that it means that we are combining two types of generators. We have series and a shunt. So what you can see here in this form in these two figures, one which we have a shunt, parallel to our armature, and also we have a series field one. So we have a series to this configuration, and we have one parallel to our armature. That's why it's called compound because it combines two different types series and shunt. For the long shunt, we have instead of having this combination of armature and field in both of them parallel and their final configuration is series with a serious field winding. And this configuration, we have armature, series with a series field winding, and both of them are parallel to one long shunt. That's why we say it long shunt because you can see long shunt, parallel to a series field and armature. Here is a short hunt because we have only armature, parallel to shunt feet. That is the difference between these types, okay? For example, as you can see here, this is a chant decisenertor, armature barrel to field oneing. So how can we understand this? You can see here in this figure here. You can see we have two terminals. For our deci generator, it has two terminals. These are the brushes, one positive brush, and one negative brush. The two terminals. Now, from these two terminals, you can see connected to one terminal of the field oneing and the other terminal is connected to the other part or the other terminal of the armature circuit. You can see one terminal, the first terminal of the field winding, and the second terminal of the field one, one connected to this part of the generator and the other like this. You can see that these two are parallel to each other. Hence, we have our chant generator. And this is the two final two terminals. These two terminals which are going to be connected to our loud. Now, let's get back here. This one here is the same idea. You can see here that we have two processes, one positive poach. You can see these two are positive process and two negative pros or vis Werth, as you can see here. You can see two processes here and two processes here. These two are connected together. These two are connected together as you can see here. We have one negative brush, one positive brush. You can see the two terminals as you can see here. From these two terminals, one positive and one negative, one connected to the first terminal of the field, and the other connected to the other part of the field. You can see that one terminal connected to the first terminal of the field and the second terminal connected to the second terminal of our field winding. We have field al start. We will talk about this later inside our course. You can see here this is a series wound DC generator. You can see that we have the two terminals. One terminal is connected to the field winding and all the way like this, and the end of the field one is connected to our load and then get back to the generator. So if you try to draw this, it is very simple. You can see that we have two terminals of the generator like this, negative and positive. You can see that one connected to the field winding, Okay, connected to the field winding. Going all the way all the way, all the way, and the final terminal of the field winding, the second terminal of the field winding here is connected to our loud connected to the loud like this. And then get back to the pulsive terminal. Get back to the pulsive terminus. You can see that the field winding in series with the armature winding. Okay? So, or this is an overview about the different types of DC generators. We will start discussing each of these generators in details inside the next lessons. 102. Separately Excited DC Generator: So let's start with the separately excited DC generator. So separately excited DC generator, what does this mean? It means that the field winding or the field circuit is separate form the armature winding circuit. So we have two separate circuits. So we have a DC generator who's field winding or the field coil is energized by a separate or an external DC source. Hence, it is called a separately excited DC generator. As you can see, the field winding itself is energized by an external DC source. So we have a DC source like a battery, providing the required excitation or the required current to produce flux or the field that we need. Okay? Now, you can see that the field winding is independent from the armature circuit. It doesn't require this generator to produce current in order to produce field or flux, okay? The flux produced by the pulse depends on the field current within the unsaturated region of the magnetic material of the pole. Flux is directly proportional to the field current. What does this even mean? As you remember before, that when we had the pH curve, pH curve like this, which we discussed before in the part of our magnetic circuit, right? Now, remember that we have one linear region here, linear region, and we have a part at which we are going to be constant or the magnetic flux density becomes constant, which is called the depth saturation region, saturation region, right? Now, during what we are talking about, we usually for the field winding or the excitation, we are operating in this linear region. In which we etch here, remember that edge is directly proportional to field the current. This is a field current IF. So as IF increase, the amount of flux produced also increases, right? So as you can see here, more field current, more magnetic flux or more magnetic flux density. Okay? Pita starts to increase, okay? In this linear region. And this is what we call the unsaturated region, the linear or unsaturated region. This is a region at which we are working with. The flux magnetic flux increases as I field increase. Now, the saturated region when the saturated region IF increases, Beta or the flux is still constant. Okay? So we don't operate in this region, we operate in the linear region. Okay? In the saturation region, as we said, right now, the flux remains constant. Reostt is normally included in the circuit of the field win as you can see here. Why? In order to control the field current, therefore, we can vary the field MMF. What does this even mean? As you remember, if you look at the circuit here, let's call this as VF and we have here a current IF, as you can see here. So by logic, VF or not VF. If the current flowing is equal to from KVL, equal to the supply VF divided by the total resistance, which is Rf plus R rheostat or R variable. Let's call it variable, variable resistance. So by changing this resistance, by increasing it or decreasing it, hence we can change the field current. So we can control the excitation or the flux of the electrical machine by controlling IF, through the usage of a variable resistance. Now, you will find that by changing the flux, you can change the induced EMF, and you can also change the speed of the machine, as we will see in the nexxt lessons of our course, okay? Now we have two options for excitation. We can use a DC source, as you can see, with a field winding, as you can see right now, and this provides us with a variable flux dependent on the selected resistance. However, we can also use a permanent magnet. Permanent magnet usually used in small DC motors in toys and small applications, okay? Okay. But however, the problem of the permanent magnet is that it provides a constant flux. We cannot control the excitation. That's why enlarge DC generators or DC machines or DC motors, we use the field excitation using field winding, not using a permanent magnet to have more control on the flux. Now looking at this circuit, remember the equation which we discussed before that they induced EMF, the generated EMF here, as we remember equal to pi, and P over 60 A, as we discussed from the previous lessons. Now, what I would like to do is that I would like to make this one in a simpler form. What do I mean by this? I would like to do something like this, multiply by two Pi and divide by two Pi. You will understand why I'm doing this right now. So if I multiply by two pi, we will have this and divide by two Pi, we will have this. The same equation right now. Now, what you'll see that is two Pi in over 60 equal to omega. Remember that N, how many revolutions per minute. If I would like to convert this into revolutions per second, simply divide by 60, right? If I would like to convert a revolution, in each revolution, we have two Pi, right? So if I multiply this by two Pi, I will get how many radients per second, which is our omega, right? Okay, rotational speed. So as you can see here, two pi and over 60, which is omega. So we can take this part and substitute with Omega. So you can see that we have Omega. Now, what we will have remaining? We have flux. Let's put it outside like this, and we will have two Pi, Z over two Pi, two pi, Z, over two pi, and a right. Like this. Let's delete all of this. So what you can see is that we have speed of the generator. Let's keep it right now. And we have here the angular, of course, the angular speed, keep it like this. And we have the flux produced by the field winding. Keep it like this. We have two Pi z over two pie for a specific machine, for any electrical machine. We have a constant number of pools, constant number of conductors and constant number of parallel paths depending on the type of winding, right? So it means that this part can be a constant part. So we can take all of this and make it KA. It can be K or K armature, or whatever, a certain constant. Multiplied by flux, flux is not constant. Why? Because we can change it using a resistance. Omega, as we will see in the next lessons, is also constant when we talk about the torque speed characteristics of our electrical machine. So our final form or our final equation is EA or the induced IMF in the armature, equal to a certain constant multiplied by flux, multiplod by radiance per second or angular velocity, or angular speed. So we will have this form. Remember this because it is very important. Okay, great. Now, in our electrical machine, we have something which we call developed torque. What does this even mean? Now in a DC generator, a developed torque reverse to the twisting force produced by the generator when it is the load and generating electrical power. Now, when a mechanical energy is applied to the generator's shaft shaft, the interaction interaction of the magnetic fields within the generator induces an E math in the armature winding, resulting in the generation of electrical power, very very clear and very simple. Now remember that we have our generator connected to the armature circuit like this. Now this one rotates with a certain torque torque, mechanical torque produced by the motor itself. That drives the shaft of this generator. Now remember that when it rotates in a magnetic field, there will be an induced induced MFE, and when it's connected to a ad like this, like this, let's make it resistance, EA, and it will take a current A armature current IA, so we have this one rotates the electrical machine electrical motor, electrical generator, rotor, and when it rotates it inside the magnetic field, electricity is generated. Now, this electricity generated here, this electricity generated, what its power power? Equal to EAA. This is a generated electrical power at the terminals of our armor sect. Now, how can I convert this? Now, remember that we have a motor here, a certain motor that drives provides mechanical or mechanical torque. This is a torque produced by the motor to rotate the shaft. Now, since it rotates the shaft, we have a developed electrical power. Now, this developed electrical power is considered as a loud, right? Loud for our motor. So this load itself or the electrical load is like this. Opposite to the direction of the motor. It opposes the rotation of this generator. So this motor rotates the generate, let's say anticlockwise. The produced EMF produces a torque that opposes this one or it's considered as a load. We can represent it as a torque in the opposite direction. So we will have a torque. Electric electrical torque mechanical produced by the mot. Okay, so that we will have a steady state, right? So since this rotate this direction, the induced DMF produces a torque in the opposite direction, right? So how can I get this torque electrical, what we call the developed torque? We can get it from this equation. Remember that power is equal to torque multiplied by Omega, right? So we can convert the electrical torque. We can get the electrical torque using this equation. So we can say the torque electrical, equal to EA IA over Omega. Okay. So the developed torque from here, EA over Omega mechanical or the Omega rotational or the rotational speed of our shaft, okay? Okay, so as you can see here, that and we remember from the previous slide, we said that EA equal KA pi omega. So I can take this and substitute it here in this equation. So if you take this and subsiute have torque. Equal to K phi Omega A divided by Omega, right? So if we take Omega with Omega, we will have K phi A, like this. So what we can learn from the torque, of course, in Newton meter. What we can learn from this. What we can learn is that the E or the induced EMF, the generated EMF is directly proportional to the flux and the speed. The higher the speed, the higher the flux, more generated MF. For the torque, it will be another case. As you can see here, more flux, more torque produced, if the armature current increases, the torque also produced developed torque increases. So as you can see here, the flux and flux armature current, and the omega affects our MF and our developed torque. As you can see right now. So what we can see that inj generator that developed torque opposes rotation, right? Remember that remember, if you remember from the very beginning, the very beginning at when we discussed the magnetic circuits. When we said that when we have a certain, let's say, a wire moving in a magnetic field, the generated EMF is used to provide a force that opposes the original force. The effect or the generated EMF here is used to provide a torque opposite to the original torque because it would like to return to the steady state or return to the previous position. That's why in wind generator, this developed torque opposes the rotation provided by the motor itself. However, in the DC motor, the reverse will happen. In the DC motor, when we give electrical power or energy to the armature, we will have a torque that will lead to a certain direction. That's why we say that the developed torque in motor helps us rotate because we give it power. However, in generator we take power and leading to a torque opposes the rotation. In any DC machine, the torque produced by the motor itself that rotates the shaft is equal to the developed electrical torque. Okay? Okay. Now, let's talk about the separately exited DC generator equations. So we have here our circuit, and I would like to see this equation. Equations are very simple. Now, as you can see, we have VF voltage of the field circuit. We have the resistance of the field winding. We have a variable resistance here. For the rheostat here to change the field current IF and we have the induced FEA. Resistance of the armature is in series, of course, in series, we have current generated armature going to our load which is RL. Now, the voltage at the two terminals of our load called Vternal and the current is called terminal. Very easy. Now, by applying simple KVL and KCL, you can get these equations here. The F voltage of the field is equal to IF multiplied by the total resistance or F multiplied by IF. That resistance is, of course, the field winding plus the variable resistance. The induced DMF sense we are a generator, EMFE is equal to terminal voltage plus any drop happening. Our induced EMF equal to terminal voltage plus I armture multiplied by resistance, voltage or drop. Okay and from the same equation, we can get Vterminal and E is equal to K phi Omega, as we learned in the previous slides, Vterminal is simply equal to I terminal multiplied by RL, and I armature here in this case is equal to I terminal, the same current flowing through our loot. 103. Characteristics of a Separately Excited DC Generator: Now let's discuss the characteristics of a separately excited decision narrator. We have three types of characteristics that we will see in these different types of decision rators. We will see the open circuit characteristics. This one representing the relation between induced EMF or generated EMF. And the field winding at a certain speed. The second curve is called internal characteristics which are representing the effect of the rmiture current on the induced MF or on the machine itself, EMF and rmiture current. We have external characteristics which is related to the lute thus representing the relation between V terminal and the lot current. Okay? Three curves. Let's start discussing each of these curves. Number one, we have the open circuit characteristics. Open circuit characteris is exactly called magnetization curve of a separately excited. So let's see this curve. Now, remember that this circuit is exactly this one. However, when we say the first characteristics, open circuit characteristics. What does open circuit mean? It means that we don't have any load. No load is connected. So it will be open circuit like this, okay? No current is flowing, right? Or armature, equal to zero. Okay? So open circuit, this means open circuit characteristics. And I said this is a relation between E and I field. So what does this mean? I would like to see what will happen to the generated EMF as we change field current. Okay? So in this case, in the open circuit characteristic, you will see that Vterminal is equal to EG because I armature is equal to zero. So when I armature is equal to zero, you will find that V terminal equal to induced EMF, right like this. Now let's see the open characteristic, the relation between E and the field current. So as you can see, E is directly proportional to I field right. So what does this mean? I can draw it without any issues like this? You can see that the generated EMF with respect to IF, which is open circuit characteristics. You can see that as the field current increases, the induced EMF or generated F starts increasing until we reach the saturation region in which whatever the current of IF, the flux will still be constant. Remember that E is directly proportional to flux or direct proportional to I field in this region. As we reach this region, you will find that E is constant. Even if IF starts to increase, why? Because we reach the saturation region. That's what happens exactly. As you can see here, EA and IF, you can see we start as IF increases, induced DMF starts to increase until we reach a saturation region. You can see it like this. You can see we have linear region, IF as IF increase, induced DMF also increases until we reach a constant, which is called saturation. This curve at a certain speed. Okay. Now, you will ask me why did we start at a certain value called residual? Why did we start at a certain value? Why didn't we start at zero? Now, this will be clear when we discuss the self excited DC generators. Okay? But anyway, for simplicity, when you when you provide when current flows through field winding or any coil, flux is produced, right? Even if you remove this supply, there will be still some flux, very small amount of flux. This is what we call the residual flux, a small remaining flux inside the DC machine. Due to the small remaining flux, this one, you will see that even if I field is equal to zero, we can generate a small EMF because there is still some residual flux inside the electrical machine. Okay? This flux is very helpful in the self excited DC machines. Now at a different speed, we can have these curves. You can see we start at the same point. What you can see as I field increase, the curve starts to increase or go up as a speed increase. Why is this? Because as you can see, E is equal to K Phi Omega. And Omega itself is two Pi N over 60. So what you can see is that E is directly proportional to N. So as speed of the generator goes up and used DMF goes up so you can see that this is a curve for bid number one is bid number two, speed number three. As speed increases, the generated EMF, nload voltage or EMF, starts to go up. And why did we say no load voltage? Because if you remember, open circuit means that we have these two terminals opened, which means V terminal equal to EA, which is no load voltage, E. Okay? So as speed increases, the curve goes up, which means we have more generated EMF. So what we can learn from this is that in any electrical machine, for any fixed excitation, which means a flux is constant, which means the field current is constant. What we can see that E equal to K Phi omega. So what we can see that if we say E one, Omega one, E two, K phi omega two, remember that flux here is constant. We assumed fixed excitation. If we divide these two equation, we will find E one over E two, equal to omega one over omega two, which means N one over N two. Now, this is healv because it will help us to get the relation between the induced MF at a different speeds. The second characteristics or the two other characteristics, the internal and external characteristics. So let's see these characteristics. What happens exactly? Now, let's look at these characteristics. If you remember that we said that the characteristics is simply the relation between terminal voltage and the loot current or the terminal Let's get back here. All the way back, you can see that the internal characteristics representing the induced MF and armature current, and V terminal and loud for the external characteristics. Number one, you will find that. Number one, you'll find that the lot current in the separately excited I Lot is I armature. Okay? Same current. So we have internal and external, internal E with respect to armature. And V terminal with respect to I armature too, because a lot current is exactly similar to I armature. Now, I would like to plot these curves, internal and external characteristics. Now, let's get back step by step. Okay. So the first curve here, A, B, the curve is the relation between. Let's get back here. One, E, this is induced MF, with respect to I armature. Okay? Now, the first curve is called the internal characteristics, the effect of the armature current on the generator itself. So I would like to know what will happen when we have I armature. I would like to know the effect of it on the generator itself. Now, what you will find that due to the flow of current armature, through the coils, we have our coils like this, if you remember, we have a current flowing through. When the current flows through a coil, it will produce what it will produce a flux, right? So the armature itself has a flux because current flows through a coil. Now, this flux here opposes the flux from the field. So we have when the armature current increase, more flux coming from it that opposes the main field, the field that's coming from our pools, right, leading to so phi resultant will be five field minus foi armature. The resultant flux will start going down as armature current increases, flux from armature increases, opposing field current leading to lower resultant flux. What is the problem of this? The problem is that the resultant flux will lead to a reduction in MMF. As I armature increases, the EMF will start going down as you can see here going down. Okay, due to what effect exactly, due to the internal effect of the generator, internal characteristics. This effect which you can see right now is called the armature reaction drop or the rmiature reaction in the DC machines. The effect of the armature on the main flux, okay? That's why without anything without considering voltage drop or anything, this one is called internal characteristics. This blue line, internal characteristics, as you can see here. Now, when we start adding the other effect of our loot, remember that the second curve is Vterminal with respect to I loud or I armature here. So what will happen when I armature increase? What happened to V Vurnal equal to induced MF minus RAA. As I armature increase, the voltage drop voltage drop increases, leading to Vtermal becoming less and less. We have a third curve here, which is called the external characteristics. This curve is lower than the previous one. Why? Because we have armature reaction leading to EA going down. And we have another drop due to the voltage drop on the resistance or armature resistance. Giving us the last curve here, which we call the external characteristics. Okay? So we have one internal due to effect of the armature current on the flux itself, armature reaction, and we have external characteristics, effect of loot current on the terminal voltage. And this effect is represented by voltage drop, okay? Now the question is, how can I know the operating point of an electrical machine? So we have Vterminal and we have I terminal, I terminal or I loud, which is similar to Irmage. Now the question is, I would like to know if I have a load here with a certain resistance, RL, let's say, RL equal to Ms. I would like to know what is the operating point? What will be Vtermal and what will be Ormat. This is very easy. How it is easy, I will tell you right now. RL is simply V terminal over armature, V terminal over armature, equal to two. The two OMs is represented like this by a line, which you can see here right now. This line representing V terminal over armature or loud. The division of these two at any point gives us the two Ms. Okay. So this gives us this line which you can see, which is a load line. So at any value of armature here, I one or I load, you go up here, you'll find we have the equivalent Vterm right? At any current, we have Vterm. Now, this is a final characteristics of our machine, external characteristics. Now, the intersection between our load which we connect resistance, which you can see right now, the intersection point between them gives us the operating point. So at this point exactly if we go down here, you'll find we have a certain current, and if you go like this, we have here a certain voltage. This is the operating voltage. Now, of course, as resistance change, this line will change. It can be like this. It can be like this. To summarize what I have said, volt drop on armature resistance as armature current increase, volt drop increase, you can see armature current increase. You will see that volt drop or AIE starts to increase. The armature reaction is due to the flow of arantin armature winding, which produces a flux that opposes the main flux of the field winding. This reduces the total flux and decreases the generated IMF. The intersection between external characteristics and the loot characteristics here gives us the operating point. And we said that this line is represented by the resistance of our lot. 104. Example 5: Hey, everyone. In today's lesson, we will start taking some examples on the separately excited DC generator. Example number five is the continuous example for this section. We have a separately excited generator. When running at 1,000 RBM, supply 200 pairs at 125. The amature resistance is 0.4 and brush drop to volt. Find the dilute current when the speed drops to 800 RBM. If the field current is unchanged. Okay, so we have here two parts of this problem. We have at the beginning, we have the first speed and one, and this speed drops to 802. Now when we say supplies current at 125, what does this even mean? It means that this is a lot current, the lot current, reach to the lot which is 200 amps. And as we know in a separately excited lot current is exactly equal to armature current. And at 125, it means that this is a terminal voltage VT equal to 125. So we supply 200 amber to the lot at a voltage of 125. RA armature resistance, 0.04, and voltage drop on the process push, equal to volt. What does this even mean? Our process itself causes a voltage drop. So we will take this into consideration when we are getting our values. What we need is the loud current. I need the second lute current IL two. Well, let's say IL one, I armature one, IL two or I armature two, they are similar to each other. When the bit is like this and field current is unchanged, it means that IF one equal to IF two equal to a certain constant. Now let's combine this in this figure. We have our field circuit, and we have our armature circuit. Now in the mature circuit, number one, we have Rmture current, 200 pairs, 200 ambers supplied to our load at 125, as you can see here. Now, the first step that we can do from this givens, we can get the resistance of our load, right? We can get RL. RL is simply equal to the voltage divided by the current. So the load resistance equal to 125 terminal voltage divided by the current or divided by the current, which is 200 ampirs, okay? Giving us 0.625 oms. Why did I get the loud resistance? Because we will need it in the second part. Okay, now, step next step that we have in this circuit, we have the terminal voltage. Let's draw it. We have V terminal. Let's go here. As you can see here, Vurnal. And we have I mature, and we have drop due to the brushes, which is two volt, as you can see here. Now, how can I get generator Curt? I need E one. Why do I need E one in the first case? Because as you can see, we have two speeds, and we remember that E equal to K I N. So I need a ratio between E one over E two equal to 1/52, and the flux is constant. If one equal IF two and change it. So it will be N one over N two. So I have n11 thousand RBM, 800 RBM. So I will get E one to get E two. Okay? And through E two, we can get the armature count. Okay, the second lute count. So I need E one, so E one, is equal to Vterminal plus I armature or armature one plus plus voltage drop on process, right, because we have a drop on our process given us two volt. So by using this equation, you will see that Vterminal 125 plus I armature or armature, as we just said, 200 and bear multiplied by the resistance of the armature itself, 0.04. Drop on process plus two, gives us 135 volt. So this is our E one. Now the second thing is that we have this ratio, E one over E two equal N one over N. So our E two will be equal to 108 volt, right in one over N two, E one over E two, E one, 135 E two, the one which we are looking for. Now, we know that E two itself is equal to VterminalO armature or armature plus drop on process, right so V terminal equal to 108, which is the new voltage induced EMF, 108 minus I armature, which I need right now. Okay, Multi blood by resistance, which is 0.04 minus drop on process. Okay? What about Vtermal value of Vterm. Now remember that here, we have Vtermal Vterminal will it change? Why it will it change? Because the induced DMF itself it changes, right? So since induced DMF change it, I armitar will it change and Vterminal will it change. So Vterminal in general, Vterminal in general is R L multiplied by armature, or I lute. So RL is the one which we already obtained day before, and I armature is unknown. So I can say, equal to like this I armature R. This is our Vtermal we have a Vterminal here, which is this part 106 -0.04 armature. By solving this or equating this together, we can get I mature as 159 point 4:00 A.M. Pairs. Now, as you can see, speed, drop 1000-800 lead to a drop in E generated 135-108. Okay? So this is the solution for our example. 105. Example 6: Let's have another example on the separately excited DC generator. We have a four pool 900 RBMDC machine with a terminal voltage of 220 volt and induced voltage of 240 volt. Now, we need to know the armature resistance is 0.2. Is the machine operating at a generator or as a motor? Number two, find the armature current number of armature coils. If air gap flux per pole is ten milli whippers and the armature turns per coil is eight. And the armature is a wave wound. So let's go step by step. Number one, you have here the first equation is a machine operating as a generator or as a motor. Now, very easy. How can I know if the machine is a generator or a motor? Look at the E generated and terminal voltage. So we look at E generated and V turn. If E generated greater than Vterminal, by logic, it means that this is our source. So our generator gives electrical power to reach outlod. In this case, it will be a generator. If EG less than Vterminal, it means that V terminal is our supply giving current to and produced EMF, right, induced EMF. So in this case, we will have a motor. Now, in our case here, the terminal voltage, 220 volt here and induced EMF is 240 volta. It means that the generated voltage higher than terminal voltage, which means we have a generator, right? Okay. Number two, find the armature current. Very easy. How can I get armature current? We have our E generated, we know that E generated equal to Vternal plus I armature or armature. R armature is giving us what as if we go here, 0.2, 0.2. Vterminal was the value of 220 volt. And induce the MF to 140, as you can see. From here, we can get the value of current. Our current will be equal to 100 and pairs. Okay. Great. Number two, find the number of armature coils. If the air gap flux equal to ten milliwipers, Ormature turn spare coil or eight and the armature is wave bond. Now, number one, since we have an armature is a wave bond, it means that a parallel paths equal to two, right. Here we have four pool, which means to be equal to four. The speed N equal to 900 RBM how can I get and flux per pool FI equal to ten milliwipers. How can I get the How can I get a number of armature coils? Very easy. All you have to do is to get the number of conductors, right? If you remember that we have induced MF equal to K and FI, and this K is some constancy, if you remember. So we can use this equation, EG, fi Z N to B over 60 A. So we can say that generate DMF, 240 volt, equal to flux, ten meleber, ten to the power multiplied by ten to power, negative three. And we have that number of conductors which I need speed 100 RPM, two p four pools, and 60 a 60 multiplied by number of parallel paths, which is two. From this equation, we can get a number of conductors, right. Now, how many coils? As you can see that the armiturs bear coil or eight. So what are you going to do? You are going to divide this number by 16. Why 16? Because we have. We have Let's type it here. We have 800 conductors. Now, if I divide this by two, I get a number of coils, right? Great. However, each coil is consisting of how many turns eight turns. So I need to divide this also by eight. So eight armituturns multiplied by two. Since we have two sides, if we take 800 and wide by this, you will get the number of coils. So 800/16 gives us 50 coils. Again, we have eight turns in one coil, and if I get 800/2, I get how many coils and how many turns we have in each coil, we have eight turns. So if I divide by eight, I will get also the number of conductors. 106. Example 7: Now let's have another example on the separately excited. We have a separately excited DC gen rated at 125, rated at 125, and one pair at 1,200 RPM. When the loot is disconnected, the terminal voltage rises to 130 volts. Find at rated conditions. Number one, armature current, voltage regulation, the armiture resistance, and the internet torque when supplying the rated loot. Let's get it step by step. Number one, separately excited decision, rated at this and this at this apt. What does this even mean? This rated value means that we have it gives at its two terminals at the final two terminals at which we are going to connect our loot at. Let's draw the circuit. It means that at the terminals, these are the two terminals after subtracting voltage drop on the armature. The I armature and we term them when we are connecting our load at rated conditions. I armature will be 1:00 A.M. Pair, and terminal voltage will be 125. Okay? So this is a solution of the first part armature current will be equal to 1:00 A.M. Pair, right? This is the current at rated conditions. Okay? Now, when the load is disconnected, the terminal voltage rises to 130 volt. What does this even mean? So when you disconnect the load, if you remember, let's draw our circuit like this, we have here our E, and we have armature resistance or A, and I armature. And at these two terminals, we connect our load right here. Now, when you connected the loud at rated conditions, you had one and Bar and 125 volt four V, right. Now, when the load disconnected, it means that we have open circuit. What does this mean? It means that the current equal to zero, right, I or Mature equal to zero. So Vtermal in this case, what the value of Vtermal Vtermal will be equal to the induced EMF E, right? So it means that and what's the value given? Terminal voltage, 130 volt. So Val in this case, 130 volt. So what can I learn from this? I can learn that our induced EMF originally is equal to 130 volt. We obtained it from the open circuit condition. When I armature equal to zero, V will be equal to the induced MMF, and it is given as 130 volts. Okay? The requirement here is voltage regulation. What does this mean? I would like to see how the volta will change from the no loot condition to compare to the full loot condition. So the voltage regulation and re general equal to the induced AMF which is at no load condition minus full loot conditions, divided by not conditions. So you are comparing the change in voltage with respect to the rated conditions, okay? Well, with respect to no load condition, the highest voltage. So E is equal to 130 as we just obtained, minus V terminal, which is 125, as you can see, divided by 130 gives us 3.846%. So it means that there's a voltage. It changed by about 4% compared to its rated compared to its no load voltage condition. Okay? Now the third requirement armature resistance. Now we have induced FE, 130 volt. We have terminal voltage, which is 125. We have the current which is one and pair, so we can get the resistance by applying civil, right. So our resistance will be equal to change in voltage divided by the resistance. E minus VT divided by armature gives us five forms. If you don't know where did we get this, remember that E, equal to V terminal plus A or armature. If you take this to the other side, E minus Vt will be equal to I armature or armature. If you divide this by armature here and I armature here, you will get RA like this. Same equation. Okay. The final requirement internal torque when supplying rated uid. If you remember, we said that the torque is equal to EA, A divided by Omega. Omega two Pi N over 60, and our N here 1,200 RBM, I armature, one pair, induced DMF is 130. You will get the torque, as you can see right now, two Pi N over 60, 160 mota by one gives us 1.0 345 Newton meat. 107. Example 8: Now let's have another one about separately excited. In this example, we have a separately excited DC generator rated at 125, one and pay at 1,200 RBM. The generated EMF is 130 volt, and the armiture resistance is five m. This is exactly the previous example, okay? However, I would like in this time two things or several things or several requirements. In the first part, we increased speed of the generate. Our speed was 1,200 and I increased it up to 2000 RBM. I would like to know the at current after increasing speed, the terminal voltage and the mechanical power convert it to electrical power. Okay. So let's go step by step. So the first requirement is the lot current. I would like to know the new out current. In order to get the new lute current, I need the induced EMF, right, the new induced EMF. Okay. And not only that, I also need the resistance of the loot so that I can bot it in an equation. Let's go step by step. So the first step that we have E one over E two equal to N one over N two, right, since we changed our speed at a constant field. We didn't change the field, so we will keep it constant. So E one over E two equal N one over n2n1, 1,200 RBM, N two, 2000 to RBM, E one, 130 volt, and I need E two. So E two equal to 216.7, which is equal to V terminal plus I armature or armature, R armature is given as five Ms, right? Now, V terminal itself, what's the value V terminal? 125 no. Why? Because we already changed the speed, right? We changed the speed. So V terminal, in this case, we have to get the new value. Vternal is simply equal to I armature or L. So how can I get the loud resistance? We can get it from the first condition. Loud resistance or L equal Vternal over I armature, which is 125 divided by I armature, which is one pair gives us 125 Ms. So by using this equation, we have only one unknown which is I armature. So RL, as you can see, equal to 125 as I just obtained. So by using the equation, R metre will be equal to induced MF, divided by RA plus RL. From this one, you can see IA as a common factor, it will be IA RL plus RA, equal to 216. 216 divided by the total resistance. Five plus 125 gives us 1.67 and pair. Now, I need terminal voltage, V terminal equal to RMture Nu, multiplied by the 125. Like this, New current multiplied by the resistance of our loot, giving us 208.75. Final requirement mechanical power converted to electrical power. Mechanically converted to electrical, simply, it is the electrical power power equal to E a IA induced F is a new one, which is 2,160.7 I armature is the new armature current, 1.67. So this will give us the developed bower, which is simply the mechanical converted to electrical. Like this 216, multiplied by 1.67 gives us zero hundred and 61, what? 108. Shunt DC Generator: Good evening, everyone. In today's lesson, we are going to start discussing the shunt DC generator or another type of generators, which is the shunt DC generator. So what is exactly DC shunt generator? Simply the field winding. As we said before, in the beginning of this section, the field winding is connected in parallel with the armitu conductor. We have the Armitre circuit, parallel with it the shunt field, and the two terms of our rmiture circuit is also connected to our load. So what we can learn from this field winding, parallel with the armature, parallel with the lute. This type of machine is called a self excited DC machine. White's called self exoted DC machine. If we look at the previous one, separately exoted DC machine, we remember that our electrical machine separately exoted the field winding, let's just draw this quickly. If you remember, field winding was excited by an external DC source, right? And this is the armature wind. So they are excited separately from the armature circuit. So we need a DC supply in order to reduce our field or excitation, right. However, in the Shuntage generator, you can see we don't have any DC source. We have armature circuit parallel to shunt generator. This type does not need any external supply for the field winding because the induced EMF itself will give us required the current for the field. What I mean by this? Remember that our generator here produces a current armature. Part of this current will go to our load IL, and another part of this current will go to the field winding, which is shunt current. When this current flows through our field winding, we will generate flux. That will lead to excite our electrical machine and produce more induced EMF. So if we look at our circuit here, what are the equation? We see that this is a generator, so I armature equal to the current going to our loot IL plus the Shante current or the field current IF, submission of two currents, KCL. Then also we have here Vterminal by applying KVL terminal here. By applying KVL here, you will see that Vterminal equal to our supply, which is the induced F minus the voltage drop, which is I armature. Here we have a resistance R. Or A multiplied by IA, the Lutkar generated induced EMF minus the voltage drop. Another equation that we have here the Shanti current. How can I identify shanti current? Thus field winding has a certain resistance called RF Let's type it here, RF. If I get voltage across it here, VF I can get the current simply I shunt or I field equal to the voltage across the sante field which is Vf, divided by the resistance of the field or F. However, as you can see here that the two terminals here, the external and this one here, these two terminals are exactly the two terminals here, this one and this one. What exactly is a voltage here, plus or minus Vterminal Vterminal here, voltage between these two points is exactly the voltage between these two points, which means that our field voltage here, voltage here is equal to Vtermal what we can learn is that If field current equal to the terminal voltage divided by R field or R chant. Now, looking at our circuit in a different way, the same circuit here, you can see that we have armature induced EMF with the armature resistance in series with it, and we have here our RL, our loud and our field resistance. And all of this is parallel to each. Okay. Now, what's the difference exactly between motor and generator? The difference is that only only that we replace the load by a DC source. That's all. You can see that here, for example, for a motor and shunt generator, you can see that armature, barrel to field winding here. You can also see in the generator armature, parallel to shunt winding, right? Okay. However, at the two terminals here, at this terminals here between this and this, in case of a generator, we are giving electrical current. So we are going to connect here a certain loud, a resistance or whatever it is. Okay? So this is supplying electrical current to our load. In a motor, we are giving energy electrical energy in order to have mechanical output power, right? So we give electrical energy by removing this load and add a DC source, as you can see here. So we have a DC source that gives current to field current field winding and to the armature in order to generate a torque in order to rotate our electrical machine, okay? So we have some conditions. In order to have our Shante decision rat in order to work, remember that our decisenator here, Shante generator is a self excited. So in order to work as a self excited decision rator, it has some conditions. The residual magnetism must be present in the machine. What does this even mean? We will understand this in the next slide? Number two, the field winding MMF should add the residual magnetism. Also the field circuit resistance must be them the critical resistance. So what does this even mean? Okay, let's go to the theory of operation of a DC generator to understand what I'm talking about. When I have a DC generator, like shunt, okay? No separately excited, separately excited has its own excitation by having a DC source. When I have a completely new electrical machine, a DC shunt generator, you will find that the field here when current is equal to zero, flux is equal to zero. Flux equal to zero. We don't have any magnetic field inside the electrical machine. Because it is a completely new electrical machine. Now, what will happen if I supply to this? You remember that this rotor is connected to a shaft shaft connected to a motor that drives the rotor of our generator. The armature itself rotates it, right? However, in order to generate electrical power, this rotation must occur inside the magnetic field, right? However, our magnetic field is equal to zero, so we are not going to generate any electrical power, right? Why? Because there is no magnetic flux. So we are rotating in nothing less. We don't have any magnetic flux. So what can I do in this case? At the very beginning when we have a completely new machine, what we do that we operate the DC generator as a DC motor. How can I do? Simply I disconnected this load and add a DC supply like this. At the very beginning when it is a completely new electrical machine, this will give us current that will go to here and here. So it will start at the beginning as a motor. Why I'm going to do this, you will understand right now. So we are giving a current to field winding, so we will have some flux inside our electrical machine, and we will generate torque, right. Here I'm talking about. We add D supply, so we are talking about a motor. Okay? Okay, so what's the benefit of doing this? When I disconnect this DC supply, when I disconnect the supply, the currents are equal to zero, right? I armature and shunt are equal to zero. However, however, what you will find that the flux is not equal to zero. I shan't equal to zero. Yes, exactly. However, the flux is not equal to zero. There will be flux, some remaining flux inside the field winding. So flux. This flux is called the residual Flux. The residual or residual magnetism, with some flux remaining inside our electrical machine. So how does this flux will help us? This flux will help us when we are connecting our load and we are operating as a generator. So the benefit of connecting an external supply is that when we remove it, we will have some flux inside our electrical machine called the residual flux. The machine will still have some flux called the residual flux. When we turn on the machine again, this residual flux, this small flux will cause some induced EMF in the machine. We have some flux here, and we connected our loot how we started rotating by giving some torque using a motor, we rotate the armature. We rotate the armature in a very small amount of flux, the residual flux. So we have small magnetic field and we have rotation, mechanical power. This will lead in the end in generation of induced EMF, right? Which we call ER or the residual EMF. Now, what will happen exactly when we have ER? By logic, when we have ER, we will generate current armature. Part of it will go to our lot, and the other part will go to the magnetic field. So I chant now is not equal to zero. Now has a certain small value. This current when it goes through the field winding, it will generate another magnetic flux. So we have flux, residual flux. Plus some generated flux due to flow of current, right after having induced EMF, this will lead to increase Pi resultant will start increasing. Right, since we have these two, and this leads us to the second decondition. The current here must aid must be helpful for us, aid there the original residual flux. Okay? Because if it is in the opposite direction, instead of having plus, it can be negative and it can destroy our residual flux. Okay? That's why if you get back here to the second decondition, residual magnetism must be present in the machine, and we said that by adding DC supply, the field winding MF should aid the residual magnetism by having a current when it goes through this. It will produce a flux that helps the residual flux. Okay? The celtic condition we will talk about later, okay? Now, let's just continue. So as you can see here, this EMF generated produces current that leads to increase in flux. This flux will lead to higher amount EMF, right, more EMF generated. So this EMF leads to higher current Increase flux, higher MF, increased current, increase flux, higher EMF, and et cetera until reaching the operating point. Okay? So let's see this. Look at this figure. Let's magnify it. So you can see that we have at the very beginning, we have I field current is equal to zero, right? Now, this is the field resistance line. Look at this one, field resistance line, okay? This one. And this is the relation between induced EMF and I field, right? It is like this the characteristics that we talked about before, open circuit characteristics. Okay. So what you can see that when the I field equal to zero, we will have small amount of induced DMF ER or the residual armature induced EMF, some residual MMF here, okay? This EMF will lead to generation of a current, right? What is the value of current if you put a horizontal line here at this point, horizontal line, you will see that this induced EMF will lead to a current called IF one, the field the current. And when we have a certain current I field, the induced EMF will increase to what value exactly you go to the open circuit characteristics. So it will lead to increase in the field of the induced EMF to EA one. And this EA one will lead to generation of a current, I field two. How can I get it if I extend a horizontal line until the field resistance. You'll find that we have I field two. I field two will lead to generation of EA two and EA two will generate If three. If three will generate ESE will lead to I four, and keep going up and up up until the intersection between field resistant line and RF and the induced EMF. The intersection between these two gives us the operating point, the induced EMF and the field current. Very easy, right? Now, the question is, why do we have EA and IF or this line field resistance is drawn like this field resistance. If you remember here from this figure, you'll find that here, Let's F equal to Vtermal over terminal voltage over the terminal voltage over what exactly over I F, F equal Vtermal over I, which is Vterminal which is E minus I armature or RmtureO IF. Okay. Now, as you can see, here, the voltage drop here is considered as very small value compared to E. So we can say that this is approximately equal to E over F. That's why the field resistance here, which is RF can be drawn at a relation between E, E over IF because we approximate this relation. Okay? So this is exactly the series of operation of some decision rate. You can see that induced DMF lead to more field de current, more field de current lead to higher induced IMF, higher induced DMF, more field de current, et cetera. Okay? That's why this is called a self excited decision rator by having some residual magnetism inside the electrical machine. We don't need any external supply to operate it. So as you can see, field current increases due to the induced EMF leading to increasing the total generated EMF of the machine. This process continue until the field characteristics and the open circuit characters intersect with each other. 109. Characteristics of a Shunt DC Generator: Hey, everyone. In this lesson, we will start discussing the characteristics of a shunt DC generator. The characteristics which we talked about before, open circuit, internal characteristics, and external characteristics. So number one, remember that we had a condition called field resistance, right? We said that the field resistance must be less than the critical resistance. So let's see what happens exactly. As we will see right now that as RF increases, the resistance line is shifted more to the upper left until the critical point, which is the tangent, which gives us the maximum allowable field resistance. If RF increased beyond this value, the machine will not operate. Now let's see this and understand what do I mean by this? Look carefully here. Now, SRF F here, you can see this is a field circuit resistance, and this is the open circuit. You can see this is open circuit characteristics, open circuit characteristics, like this, and the intersection is operating point. Okay, great. Now look carefully here. Now, let's say I'm now, this is a resistance line RF. If I increase the resistance, it will be shifted more to the upper left, more to the upper left, as you can see here, going like this, going like this, you can see that this is a resistance, resistance or F two, or F three. As the resistance increase, we go all the way to the left. Why this, I will tell you right now very easy. Remember that RF approximately, approximately, approximately, okay? E over F. So as RF RF increase, E will increase with respect to IF, right? So instead of having this line, we will have it like this. We will have it like this. Or you can say that the slope of the line slope of the line starts to increase all the way like this, okay? Okay, now let's look at carefully here. So you can see that when we are having this resistance, this is the operating point, great. Now, this is a tangent. You can see this is exactly tangent to it, tangent to this open set characteristic. So it will operate at the intersecting point here. This is the operating point. Okay? Now, as you can see, as you can see that originally we had high induced EMF. High field current. Now, when we increased the resistance, the operating point was now lower. What I mean by lower, low amount of field, low induced meth. Why? Because by logic, as we increase resistance, the shanti current will decrease, meaning that we have lower amount of flux, right? Current, lower due to increase in resistance. Okay, what if the resistance becomes very, very large? You can see there is no intersection between it and open circuit characteristics. So it means that there is no operating point. It means that the resistance is very high, making a field current very small and the machine cannot start. Okay. Why? Because the field resistance is very high, making field current very small, making induced MMF very small, and the machine cannot build up. Okay? Okay, great. Now, in this case, this is a resistance at which this is what we call critical resistance. This is a maximum allowable resistance. We cannot increase beyond it. If we increase beyond it, then our machine will not build up the voltage. Okay? It will not be able to generate electricity. Okay? We cannot increase beyond the residual magnetism, okay? Okay. Now, what is the effect of speed? Again, as we learned from before, as speed goes down, characteristics goes down, and as a speed increase, the characteristic goes up. Now, remember that E equal to Ki Omega, and we said that Omega is speed, more angular speed, more induced MF, lower Omega, lower induced MMF. So the open circuit characteristics, as we said before. Let's look at it. You can see that here, we have this is open circuit characteristics. Right? Now, as speed goes down, you can see N three, lower than two, lower than any one, you can see in three lower than two, lower than no. As speed decreases goes down, you can see curve go down, goes down. And what's the problem of this? You can see that there is a speed which we call it the critical speed at which the field resistance will be tangent also to our open circuit characteristics, as you can see here. If we go below this speed, the machine will not operate and the voltage will not build up. Okay. So as you can see here. Now, similarly, if you get back here, you can see that as we increase resistance, intersection, this is a critical resistance and the intersection does not happen between them or intersect at a very small point, which means that the machine will not start operating will not give us amount of induced MF or not build up. Exactly the same option here, but instead of changing the resistance of the field, we change this bit. If this bit goes down, you can see that if it goes below this, you can see the intersection will be at a very small point. Making the machine will not even build up. That's why we have a critical speed at which the field resistance tangent to it, we should not even go lower than this. Okay? Now, someone will say, why do we have these characteristics or the effect of resistance, field resistance, and speed? And we didn't discuss this when we are talking about separately excited. Why? Because separately excited, it has its own excitation from a separate DC source. So whatever happening in some a machine, it will not affect the field winding or the field flux. However, speed and everything here is affecting our operation of the self excited machine. That's why we have to consider the speed and the speed and the field resistance when we are talking about chant machine. Let's talk about internal and external characteristics. Now, let's start again. Similarly as separately excited for the open circuit characteristics or open circuit characteristics. It is exactly the same. However, we have a small additional voltage drop due to decrease in load voltage. Let's see this and we will understand this. You will find that as the loot current increases, voltage drop on the armature increase leading to reduction in terminal voltage. And hence this terminal voltage will lead to reduction in field current, leading to reduction of the induced MMF. What does this even mean? Okay, let's look at the characteristics here. So you can see that we have, if you remember open circuit characteristics, we draw it in the previous slide. This one, open circuit characteristics, right? Okay. Now let's see the internal internal is the relation between induced EMF, induced MF and the rmiture current, right? Induced EMF and rmiture current. Let's just type it induced EMF. And armature current. Theoretically, when the armature current increase, it should be constant. Like this is EA, which is constant dependent on the rmiture current. However, this is not reality. Number one, we have two effects. First effect as rmiture current increase, as armature current increase, what will happen exactly more armature reaction. This armature will produce a flux, which opposes the field flux, hence leading to reduction in the generated EMF. What you can see that E, when I increases, as you can see when I increases, it goes down as the current increases Y due to the armature reaction which you talked about before. This one, this curve here, is the internal characteristics, right, because this is the effect of the machine on itself. Okay? Great. The third curve that we would like to see is the external characteristics, effect of the relation between V Lute or terminal voltage and IL or lute. Now, as you can see that we started at when we have zero current, V terminal will be equal to E or the induced DMF. Let's remember, V terminal equal to E minus I armature or armature from KVL here. Now, I'm drawing the relation between V terminal or VLud and I terminal and Ilute. This is the cert characteristics, which is our external characteristics. What happened? Before I say what happened I armature here, the current of the armature equal to I Lute plus chant, can I say lute plus Isend? Okay. Great. Now, what I would like to see number one at zero current when this current is equal to zero, when it's equal to zero. What we will see that the voltage drop here equal to zero, which means Vterminal equal to induced DMF. So we are operating at this point. Vtermal equal to induced DMF at a zero current. Okay, zero current. Okay, great. Now what will happen exactly? Now, what we will see here at that as I loot increase as the loot current increase. As the lot current increase, what will happen? Here this term will go up leading to reduction in Vtern. So as you can see, this is the original one, internal characteristics. We go down due to the ometre reaction, and we have an additional voltage drop, which is external characteristics. Here due to IaRa, this term here, right, as I load increase, I armature increase leading to reduction in Vitermal because of the voltage drop. Okay? Is it over? No, we have an additional voltage drop due to decrease in load terminal voltage. What do I mean by this? Now, look carefully at this circuit. You can see that Vterminal here? And look at the sont circuit here. You'll see that from these two terminals are the same. We remember that I field equal to V field over RF or V terminal over RF. So what we can see here is that we have this effect. We are blotting VL with respect to oil, and we see that as oil increase, it goes down. So as you can see that it goes down already, Vtermal goes down. So when Vterminal goes down, you will find that oil field goes down, meaning that flux goes down, means that another effect induced MMF goes down. So it means that we have another drop due to decrease in flux. Right? So we have more drop in the shunt due to decrease in flux, due to decrease in the terminal voltage. So again, when we have when I armature increase or I load increase, I armature increase, voltage drop increase, V terminal goes down. And when Vterminal goes down, the shunt field itself or the current here goes down. And when the current goes down, the induced MF goes down, so E goes down, so V terminal goes down once more. Okay? Now, what you will find that we will have a certain condition. When the current start going up, the loot current goes up, and this will lead to drop in Vitermal, drop in E, which will lead to high drop in Viterma. So instead of having this, our Vitera can be like this can go very low like this. Why due to reduction in E like this. If we look at the characteristics, you can see that we have. Internal characteristics due to our mature reaction. And then we have the external characteristics, which is due to a voltage drop and drop due to decrease in flux, due to decrease in terminal voltage, and we find that there is a point, a breaking point when currenty becomes very large, leading to very large voltage drop and very large reduction in termer, which will lead to reduction in flux and reduction induced in meth, leading to reduction again in Vtern leading us to a breaking point like this going all the way down. Or we can say the destruction of our machine. Destruction is a very complex word. We can say that a short circuit or our machine is not working anymore, okay? So these are the characteristics of our Sound DC generator. 110. Example 9: Hey, everyone in this lesson, we will start discussing some examples regarding the DC shunt generators. In this example, we have a shunt generator that delivers 40 5:00 A.M. Pairs at 230 volt. When we say delivers, it means 40 5:00 A.M. Pairs to the loot at 230, this is a terminal voltage. It means that we have here. 230 volt and the current going to it is 45 and pairs. The resistance of the shunt and the armature are 500.03. So we have here armature. Let's type it or Rmture A equal to 0.03, and resistance of the field, F equal to 50 OMs, find the generated EMF. How can I get EMF? Our EMF here, our MMF here, we can get a applying QVL. You can see that induced M equal to VternalPlus I armature, or armature, Vternal plus the drop on the armature resistance. So Vternal equal to 230 volt plus our current armature equal to I ut plus I shunt, I ut plus I shunt. And our armature here, resistance of the armature, 0.03 or 0.03, multiplo 0.03. What is the value of lute current ut current 45 and pairs? I need shant in order to get the induced MF. I need the current here. Now, as you can see, these two terminals are exactly the two terminals here. The voltage here is equal to 230 volt the terminal voltage. So shant equal to V terminal divided by F, which is 230 divided by the resistance 50 ms and you substitute it here, you get induced EMF, as you can see here. I field, 230/50, then total current, IL plus on 45 plus on 4.6 gives us a total current. Induced EMF will be equal to A or A plus V terminal, as you can see here. 111. Example 10: Now let's have another example. In this example, we have an eight pool decision generator. So eight pool means number one, two, B equal to eight. Okay, with 7778 wave connected armature conductors. So our Z conductor 778. Okay? And the wave connected means that the parallel path is equal to two, okay? Running at 500 RBM, our speed 500 RBM, supplies a load of 12.5 s at 250 volts. 0250 volt here. Okay? At 12.5, the resistance R L equal to 12.5 s. Okay? The armature resistance 0.24. Okay? So we have the resistanc here. Equal to A, equal 2.24 ms. Field resistance to 150. Field the resistance field equal two to 150 ms. What do I need? Number one, armature current, induced EMF, flux purple. Great. Number one, what can I get? I need rmiture current. Armiture current from here, I armature, equal to I field plus lute. I field field current here equal to terminal voltage, 250, divided by the resistance of the field, 250, plus I lot lot current. What is the lot current Lute current? Simply, the current flowing through the lot is equal to the terminal voltage or load voltage divided by the loud resistance. 250 V terminal, divided by the loud resistance 12.5. And from here, you can get a mature equal two to 21:00 A.M. Pairs. Okay. Great. Let's read this here, read all of this. Okay. So we will leave some space. Okay. Let's get back to the pen. Okay. Now, the second requirement induce MFE, buy a blank EVL, E equal to V terminal plus I armature or armature, or Rmture equal to 0.24, as you can see here given us, I armature. We just obtained 21 and V terminal equal to 250, 250. Like this hundred 50 plus 21 metal lot by open 24 gives us 255 volts. Okay. The only remaining part is flux per pool. Very easy. How can I get flux per pool? We have all of our requirements. We can use our equation of EMF. We know that E, equal to some constant like this, equal to that over A, two P, 60, multibloid B, N, multibloid B two by N, Z over A, 60, A, multiblod by flux. Okay? If I remember correctly. Okay, so you can see that E induced DMF, equal to two P, number of pools, multiplad by N O speed, multiplied by Z, number of conductors, flux, which we need 60 A. So in used in math here, 255, flux which we need to get that equal to 778, speed, 500 RBM, number of walls, eight, 60 a parallel paths equal to two. Like the SR flux will be 9.83 milli whipper. 112. Series Wound DC Generator: Hey, everyone. In today's lesson, we will start talking about the series one DC generator. So the series DC generator is very easy. All you have to do is that you take the field winding in series with our armature and our lute. Like this, you can see that the field winding series with our armature, and the final two terminals is connected to our lute. In case of a generator, in case of the motor, all what we have to do is that we add a DC supply so that it will operate as a motor. A. Great. Our equations here in this figure very easy. You can see that V terminal here, you can see that we have. Number one, this is a generated EF. We have Rmture resistance. Remember A, and we have field resistance or F, and we have here V terminal. Okay. Now, number one, as you can see, that the armature current, armature is exactly equal to the field current, right? So I armature equal to I field because the current coming from the armature is a current flowing through the field, and it is exactly current flowing through our loot, so it's equal to I loot Okay. Number two, induced DMF, this is our supply. Our supply equal to terminal voltage, V terminal minus I armature or IL or IF, all of them are the same. Okay, multiplied by the total resistance that we have or E plus or F or A plus F, right? So from here, this exact plus, of course, plus not minus because this is our supply, our supply giving to Viternal and the drop. Okay? If I would like Viternal, all I have to do is take this equation to the other side as we did before. Developed bower, as we said before, how much power is developed on the armature itself, it is equal to induced DF, multiplied by I armature, exactly as we said before. Output power here, it means that the power at the terminals of loot at the terminals. So the output power after subtracting losses in the armature, the resistance losses, or power losses. We will have output power here, output power, power equal to volta, multiplied by current. So it will be V terminal, multiplied by terminal, which is armitu. So it will be Vterminal multiplied by O armitu. Okay. Now in this type, we have the field winding connected in series with the armature conductors. This is different from the DC Shanta generator because the field wine is directly connected to the load. As you can see, connected to the load. Why is this important? Because in this case, you will have to design the field winding or the cross sectional area of the wires of the series field winding must be large enough in order to carry the load current. Okay, so as you know that as the cross sectional area of the cable increases, it can take more current. And since it here holds the lot current, it means that this one must have a large cross sectional area in order to hold the loot current, which means it will lead to more expensive wind. Characteristics. Okay, let's look at the characteristics right now. So the three characteristics, open circuit characteristics, the internal characteristics and the terminal or the external characteristics. Okay. So let's start by the internal characteristics and open circuit characteristics. Open circuit characteristics, as we learned before, is simply equal to the relation between induced MMF and I field. Right? And remember, I field here is equal to RM armature, equal to I Lute, okay? So we can draw the relation between E and any current I armature or I lute, okay? So what we can see here is that as the current increase as the current increases, more induced meth we will generate, right? Okay. And of course, we start with the residual flux because we can connect the first ADC supply in order to operate as a motor exactly as we did in the Santa generator, remember that the series is also self excited, okay? So by adding a supply, we can have some residual flux inside the series field. Okay. And when we move it, we will have some induced IMF due to this remaining flux inside our electrical machines. You can see the characteristics between induced MMF and the loud current or the fielded current. So you can see it increases until saturation point, right? Okay. Great. Number two, what you will see that here. So this is the first characteristic, the open circuit characteristics. Second, the characteristic is the relation between induced EMF, and I armature. Exactly the same. E is the same E. I field is the same as I armature, it should be the same exact curves. You can see that here, this is the first curve and this is a second d curve, exactly the same curve except that we add the rmiture reaction. Since we are looking at the effect of rmiture current on the induced MF, the Rmitu reaction. This one, instead of having this curve, it will go down due to armature reaction. That's all. You can see it is exactly the same curve characteristics with the armitu reaction. The third one is between V terminal and the I loud, right? So what you can see that this is our V terminal, right, and this is our loot current. Now, as you can see that as loud current increase as load current increase, the voltage drop here increases, right? So we have not only E grated, armature reaction drop and armature reaction drop. We have, in addition to it, a drop due to the reasons of a resistance resistance here and see that goes down. Now, as you can see that as armature current increases, voltage drop increase, voltage drop increase, rmiture reaction increase. And at the same time induce the Mth increase by a little bit, so E increase. However, in general, will start going down. You can see that this is after armitureaction, voltage increase, as I load increases because E increase. Okay? So let's just explain this in another way. So we have equal to E minus I A or A plus S. You can see of this as the same curve of E by adding however, subtracted from it, armature reaction and omic drop, like this. So as you can see, as loot current increase, V terminal should go down, right. However, induce the MF at the same time increase, compensating for the increase in current or increase in drop, leading to an overall increase in V. That's why V or terminal voltage increase as loot current increase, as you can see here, Okay. However, there is a breaking point here, a point at which the reverse will happen. Which point exactly? At this point, we will see that we are going into saturation region. In saturation region after saturation as current increase beyond from here, let's say from here, start increasing, I start increasing, induced MF is constant, is constant. Why? Because we are now in the saturation region. And since this one is constant, so we can say a constant minus an increasing value. This will lead to V going down. That's why after in starting incestorrati region you can see that we are going down like this. Why? Because E is constant and the volt rob start increasing leading to going down? This is very important in understanding the series DC generator. Okay? That's why we call this external characteristics, internal characteristics, and open circuit characteristics. And how can I define exactly the operating point depending on the resistance of the load, right? So if we draw Vterminal and I terminal, we have a Vterminal versus I terminal like this, and this is a load resistance. We have this characteristics, which we just obtained right now, this characteristics. And when we draw our resistance, the intersecting point is the voltage and the current which we are operating at exactly as we did in the previous lessons. 113. Efficiency of a DC Generator: Hey, guys, and welcome to another lesson. And today's lesson, we will discuss the efficiency of a DC generator. So in order to understand the efficiency of any DC machine or any machine in general, we need to get the llation between, or if you would like to say efficiency, in general, any application is output power over input power, multipla by 100 to convert it into percentage. So output power divided by input power. If I would like to find the difference between them, the difference between B input. And B output is simply our losses, right? Losses occurring in our electrical machine. Okay, so let's see what our losses that we have in a DC generator. So the total losses are divided into. Number one, couple losses due to the presence of resistance, armature couple losses, shunt couple losses, series caballos, depending on what type of electrical machine or DC generator we are talking about. So for example, couple losses exist in DC generator, series exists in series DC generator, and armature exists in every type of generators. Armiture couple losses in couple losses is simply equal to current, square multiplied by resistance. So if I'm talking about armature, it will be I armature square or armature. If I'm talking about chant, then it will be shant square multiplied by R shunt. If series or S multiplied by S. This is the first type of losses. Number two, we have losses, losses occurring in our armature specifically, which we call the historic losses and I cant these losses which we discussed before in the electrical transformers. Losses, he stresses, and current. You can get back to transformers if you don't remember them. They have the same formula in DC generators. The third type, which is mechanical losses called friction and windage. So the frictional losses is due to the friction between the mechanical parts inside the DC generator, and windagelosis is due to the resistance of air. So let's just summarize what I said. Wendiglosis is due to the resistance encountered by the generators, rotating parts, and they move through the surrounding air. This resistance leads to energy dissipation in the form of heat. Now frictional losses on the other hand results from the mechanical friction between various moving parts of the generate like parings process commutators. These parts rub against each other during operation. Some of the mechanical energy is dissipated into heat leading to energy losses. So these are the two types windage and friction. And we have ionloses. If we combine, usually we combine these two together, on losses and mechanical losses and calling them rotational losses. Or stray losses, stray losses or rotational losses. This is a magnetic losses, mechanical loss. Now we have also two classifications here for these losses. It can be constant losses, which does not change independent on the loud, and we have variable losses. The losses in constant, which is regarded as a constant losis is number one, iron losses, mechanical losses. These are considered constant loss. In addition, which are the stray or rotational losses. In addition to them, we have the Chante field loses. We assume that the practically, they are considered constant. Why they are considered constant Because the variation in current variation in field decurrent is not much variation in current. We assume that this field current is almost or the losses related to field decurrent is almost constant. Remember that the field current in chant is equal to V terminal over RF. So when V terminal changes, the currenty changes. However, the current does not change much because the variation in vitamin is much not much change, because we have a voltage regulation, if you remember. That's why we say that the change in feed is not much or not significant, meaning that the feed decabolosis is almost constant. Okay. Now, the variable losses here, the losses which change with the lot, independent on the loot are called the variable losses. The variable losses in DC generators are number one Rmitre losses, couple losses in armature winding, Ia squared, multipla by RA and series field winding I series square or series depending on the type of the generator, okay? So if you look at the bower stages in a decis genero number one, we provide mechanical power, right? We give mechanical input power to our shaft, the driving engine for our shaft. That rotates our armature. Now, this mechanical power suffers from some losses, which is iron losses and friction losses or what we call the rotational losses or stray losses, right? After this, after subtracting these losses, we will have degenerated electricity developed power in the armature itself. Which is the induced, induced, induced MF, multiplied by the armature current. Then this developed power suffers from couple losses on the armature and on chant and series winding depending on what type of generator, leading to our output power at the two terminals of the generate, which is V terminal or terminal. Okay. Great. Now, looking at this, we have three stages, right? We convert mechanical power to electrical developed power, and from electrical developed power to electrical out power. So we have A B, and C. Now we have number one efficiency. This is mechanical losses. So we call the sport mechanical efficiency, which is the relation between output power over input power, B over A. B is the electrical developed power, generated power, and A the input mechanical power, input mechanical power generated E multibloodO Omiton. Then we have the second losses, which is related to electrical that's why we call it electrical efficiency, a ratio between output, C and B, C over B. So C over B, but power, which reaches the loud circuit or reaches our lute, divided by the total generate total generated wattage. So but I divided by this one which is a generated electricity. The developed electricity. Now, in general, we have a combination which combines these two together called the overall efficiency or the commercial efficiency. Overall efficiency is the relation between C over A. Or simply if you look at this equation, it is simply equal to efficiency of the mechanical efficiency, multiplod by the electrical efficiency. This multiplied by this gives us COA, which is output power at the loud divided by the input mechanical power. As you can see here, for good generators, it can be as high as 95%. Now, the question is, when do we have the maximum efficiency in our generator? In order to do this, we need an equation for the output power, an equation for the input power. So we know that generator output is V terminal multi blood by terminal, and we know that generator input power equal to output power plus losses, right output power, plus some losses. Great. So input equal to this output Vi plus the losses occurring in our electrical machine. And we have just learned that we have output Vi and losses. Let's say we are talking about, for example, for this condition, let's say we are talking about assont generator. So in a shunt generator, we have losses. Let's just draw it Like this, E, our armature, and here our field, and we have here our loud, right? So the currenty going to the loud is, currenty going here is I shunt, and we have armature. So we have VI which is output power and losses. These losses are divided into constant losses, WC, constant losses, which include shunt losses. And rotational losses or stray losses, right? So here we include the losses, WC. What losses we are having or remaining the losses on this armature resistance, I square multi blood by array, I square multi blood by array. And we know that the armature current is equal to sont plus I like this. Okay. Now, if we look carefully here, we know that the current, the current of armature is approximately equal to I lute. Okay? I shant is very small in general. That's why I armature is approximately equal to the lot current. We can neglect shunt. Like this. Compared to the Lod current. I arms are equal to I approximately. Okay? Now, what about efficiency? Efficiency put power, Vi, divided by the generator input power, which is losses, but plus losses, output, which is Vi plus I since we neglected I shot it will be I squared R A, I squared R A plus WC, like this. Okay. Now, what else? We have this equation, right? Let's divide by Vi and Vi, here, Vi and here VI. If you divide up and down numerator and denominator by I, you will get 1/1 plus IRA over V, WC over Vi. Okay? Now, what I would like to do is maximum efficiency. I would like to maximize this one. Order to maximize efficiency, this one is constant. R one, I can't do anything about this. However, this term, I can play with it. I can reduce it. So if I make this one, minimum, I will maximize efficiency. So how can I minimize any function? To minimize this, simply get the derivative. Remember the derivative of a function with respect to our variable here, which is a current loot current for this function, Okay. F of I o, and equate it to zero. So get the derivative of a function and equated to zero, you get the minimum, right? So as you can see, get the derivative of this function with respect to the current, and equate it with zero. So the derivative of this function with respect to current derivative of the first is RA over V. Derivative of second, we have one of our I. Is derivative is negative one of I squared, right? Negative one over I square equal to zero. Okay? So from this equation, you'll find that I square A equal to WC. This is a condition in order to have maximum efficiency. So what we can learn from this, this is a variable losses, and this is a constant losses. So in general, the maximum efficiency occurs when the variable losses equal to constant losses. From this, you can get value of the root current at which we will have maximum efficiency, which is like this I will be root WCA. If we blot the efficiency with respect to current, you'll find that efficiency increase as current increases like this until maximum value, which is at I equal root WA and then starts to drop. 114. Example 11: Now let's have an example in order to understand the efficiency of a generator. So we have a generator like this delivers 180 5:00 A.M. Pair at a terminal voltage of 250 volt. So it delivers 190 5:00 A.M. Pairs at a terminal voltage of 250 volt. Armature resistance or mature resistance is 0.020 0.02 or a Ohms and field resistance, 50 oms the resistance here, F equal to 50 oms. The ion and frictional losses equal to mi hundred and 50, which is rotational losses. 950 what? Remember here, it doesn't include the Shana resistance. It is only the rotational or stray losses. So this is WC. Okay? Find the IMF generated, couple losses out of the pri motor, commercial, mechanical and electrical efficiency. Okay. Very easy. First, we need E. From this, we know that E, let's type it. Let's make it here. Go down here, E, and use them f equal to V terminal, plus drop on the armature resistance from KVL. V terminal equal to 250 plus I armature or armature. What is the resistance 0.02? I need I armature because I don't know it. So I armature equal to I field plus lute. I lute given as 190 5:00 A.M. Pairs. I field, how can I get the current of the field? It will be terminal voltage, terminal voltage to 115 divided by the resistance which is 50 os. So we can get armature leading to induced EMF, like this. So 250, as you can see, 0.02 multiblod by I armature, 200 and pairs, I loud plus IF. If we term 250/50, as you can see here. Okay. Now, what we need also couple losses. So couple losses is simply I is square, multi blot by RA plus It square, multi blot by R shunt or R F. You can see IF square or F, couple losses in field winding, couple losses in armature winding wind this, giving us 2050 what? Find the output of the prime mode. What does this mean? What does it mean out of the re mode? It means that I would like to know prime motor is the one that drives the shaft of the armchu. So we need the outt of the rotor means the input mechanical power to the generator, input mechanical power. So the input mechanical power is simply equal to output power so input mechanical power, let's type it here. Input. Mechanical power, which is output of our prime mover or our prime motor, it will be equal to output power. Plus losses occurring, right? We have What is at power? Out power will be Vterminalblood by terminal, Vterminal 250 I terminal 195. Plus losses, constant tolosi or rotational losses to be more certain 150 plus that 2050, which is a couple losses. 2015, like this. So developed power plus losses, you can see that EAI A plus the stray losses. Okay, so why this. You can see we obtained it in a different way here in the slide. So you can have two options output, output power, plus all losses gives you input mechanical power, this equation, o or you can say that if you have the developed power here at this part d plus the rotational losses. So we can say developed power, EAI A, here, multi blood I plus the stray losses or rotational losses gives us input mechanical power, which is 51, 750. This equation here or this final value, and this one will give you the same result. If you use this or this, you will get the same result 51, 750. Okay? The solution here, I took out power and added all losses. And the solution, take the developed bower here and add the rotational losses. Okay? Both of them will lead to the same solution. Okay, what about the commercial mechanical and electrical efficiency? Okay? So number one, as we said before, we have several equations. If we type number one, mechanical efficiency, it will be develop the power, develop the power, divided by the input mechanical power. We have developed power, EIA, we have induced MMF 254. Multiblod by the armature current, which is 200 and pairs, divided by input mechanical power, input power provided to this generator, 51, 750. Gives us 98% mechanical efficiency. Electrical efficiency is the ratio between output power here, which is V terminal terminal, divided by the developed electrical power. Like this 2050, multipled by 195-20-5250, multiplied by 195, divided by Abu developed electrical power, E AIA, which is this value. If you multiply these two together, you will get the overall efficiency, which is a commercial efficiency, 94.19%. 115. Example 12: Now let's have another example on the efficiency of a generator. We have this time a series. Tin kilowatt series generator. What does Tinkilwat mean? Since we have a generator and it is called, and it is denoted by or given as ten kilowatt, it means the abut power Out power at the loot site here. P outbut will be equal to ten kilowatt, delivered to the loot. Have an armature circuit resistance of 0.75 and field resistance of 1.25. They are in theories, right? So our armature and our field 1.20 50.75. So they are in series. So our total equal to 2.75 plus 1.25 gives us two OMs. Okay? That is a total resistance. Gives us a terminal voltage of 250 volt at full loads of the terminal voltage here. Terminal equal to 250 volt. Find the efficiency of the generator at full loot assuming iron and friction and windaloss to be 600 what? So number one, we know that efficiency equal to output power. Divided by input power. Now, out given in the problem, output power, ten kilowatt. The input power is the input power coming from the generate. Ten kilowatt, input power is equal to abut power plus all losses in the generator. The abut is ten kilowatt, two. Losses, we have two losses. We have W, C, which is constant loses, 600, what, or the stray losses. We need to add to it. Any other type of losses, which is what kind of losses we have. We have losses on the resistance, which is I armchon square multiplied by the total resistance and the R in series R total. R total two s, we need Rmture, right? So how can I get armature? Now, look at this here. You'll see that our load here takes ten kilowatt, and the voltage across the load is 250. Can we get the current? Yes, we can get the current P but, equal to V terminal, I terminal, which is armature, so I armature, equal to but power. Which is ten kilowatt, right, divided by V terminal, which is 250. So from this, we can get I armature, as you can see, load electrical power over input like this and input power plus couple losses, plus stray losses. So we have ten kilowatt, as you can see, ten kilowatt plus 600 plus I armature square multiplied by total resistance, which is RA plus R F. IA will be power divided by V, as you can see here, giving us 40 and pair. So substituting here, we can get input power, 113,800 what? And we can substitute here, you can get efficiency as 72.46%. 116. Compound Wound DC Generator: Hey, guys, and welcome to another lesson. In today's lesson, we will discuss the compound wound DC generator. So the compound wound, DC generator is simply a combination of the shunt and series. So the generator has both shunt and series fields called the compound wound generator. If the magnetic flux produced by the series winding assists or helps flux, our shunt flux, then the machine is set to be a cumulative compound generator. If the series flux opposes the shunt field flux, then the machine is called a differential compound generator. So let's understand this. Or before we understand this, let's continue these two sentence. Okay, it is connected in two ways, as you can see here. One which is a long shunt, as you can see, this one is a long shunt, and another one is a short hunt. So what's the exactly the difference? If the shunt is connected in parallel with the armature alone, as you can see a shunt, parallel to armature and their combination in series with a series winding. In this case, we have a short shunt. You can see that the shunt itself is short compared to this case. In the long shunt, if the shunt is connected in series with the armature, then it's called long shunt. So as you can see here, armature, series with another field winding series field winding, okay? So we have a series field winding here and here. One with the combination of the shunt and armature, and the other one is in series with the armature winding, okay? So in both cases, number one, it takes lot current here, lute flowing through the series field winding. Since it flows through a series winding, it has flux and we have FIF. Similarly here, we have the series winding. In this case, I armature flows through it. So we will have also another flux against or with our Santa flux. So if this flux or this current produces a flux, that helps our F. It increases it, it's called cumulative. If it opposes it opposes our flux, then it's called differential, okay? So where are we going to install our series field. So we have our pools, as you can see here, our pools, and we added our shanty field, right? The field winding shanty field. Now, on the sample, we add another serious field, another series field, here and here. Now, this series field will produce a flux. When current series flows through it, it can be Ii armature or loud depending on type of the compound wound, DC generator long or short shunt. When the current flow through it, you'll find that it produces a flux. If it helps our shunt, five total equal five Shanta plus five series, then it's called the cumulative. If it opposes opposes our shunt field, then it's called the differentia because it decreases the total flux. And in this equation, we have phi total, total flux, phi Shont shunt field, and series field winding flux. So what are the characteristics for a compound wound DC generator? So let's look at them. So we have different characteristics. We have over compound, level compound, under coompound and differential compound. So looking at these characteristics, we have the over compound level and under here we are talking about the external characteristics, the relation between V output or V ternal and the loot current. Now, you can see these three types here are under the cumulative, under the cumulative. It means that the series winding five series helps our five flux, or aids our five flux. Here, this one is the only one which is differential. Now, let's understand what's the difference between these four, okay? The three cumulative and one differential. So number one, as IL increases as the loud current increase I loud increase, let's say this one Iot, to make it more clear as I load increase. What happened exactly I armature and I series increase this I armature, and I series are exactly the same. Series, the current flowing through the series field winding, when the load current increases, I armature increases as we learned before. So when the current flows through, I series increase flow through the series field winding, f increases, five series increases. So it produces more flux. Okay? But at the same time, we have. So we have one factor, Vitern, one factor that increases Viternal. Okay? What is this factor? I series. So when I load, increase, I load increase, I series increase, pi series increase, leading to increase in Vtermal. However, at the same time, we have two factors that lead to Vtermal goes down, which is voltage drop, armature reaction, and drop voltage drop, of course, on the armature RA plus R series, right? Because we have here volt drop, if you apply KVL here, you will find that V terminal equal to E minus IA, or A plus series, we have volt drop and armchre reaction. Okay. And also, of course, when Vtamin drops, we have a drop in our load in the voltage across the shunt leading to reduction in flux or current first, then the field flux and reduction in E. If you remember from the characteristics of the shunt DC generators, okay? Now what are we going to compare with? We are going to compare the effect of five series, increasing loud current on five series with respect to all of this. So we have one positive effect, which is when I load increases, when I load increases, f series increase leading to Vtermal increase and also when I load increase, drop increases in addition to mitre reaction, right? So I would like to compare these two factors. So you have several conditions. If this drop, if this drop is higher than the effect of this one of the five series, which helps us, then we call this is when we call this generator, is an undermpounded generate undercmpounded generator. Which has this characteristics, this one. You can see it drops but not drops too much. In the shunt, it was dropping like this. Okay? So here we are having more flux, flux produced by piss, which makes the Viternal higher. Okay? Okay, great. So this one is undercmpound it. Why? Because it drops in nature, as you can see here, because the piss effect is lower than the effect of volop. However, it is much better than the shant Dcgenerate, okay? What if the effect or what if the five series effect higher than the volt drop? What will happen in this case, if the drop in Vterminal is less than the increase in Vtermal due to increase in flux from the series winding. Then we call this generator over compounded, which has this characteristics, which is all see like this. This is over compounded. Why you can see that this is a nullad voltage, E, the induced MMF at Nolut. You can see that as I load increase, you can see that the voltage starts to go up up up up, right? That's why you call it over compounded, too much, right, because we are increasing the induced EMF too much or the terminal voltage is higher than the induced EMF. Okay, you can see converted to no load condition. You see goes up up up. Okay? Okay, great. So we have over compounded, too much Viternal and under compounded, too less or less or lower than E or lower than the no lluod induced mF. Okay? Now, between them, we have the level. What do I mean by level compound? When the effect of the two Two, one which increases Vitermal which is oysters and one which decreases Vitermal which is the armature reaction drops and everything. Then in this case, if they are neutralizing each other, then the generator is called a flat compounded or a level compounded. Like this, you can see that this is a level. You can see that this one is called level compounded when they are neutralizing each other. Now, someone will say, but it increases above and goes down. Why do we call this level compound and this is an over compound? The difference is very easy. All you have to do is to look at voltage V terminal at the rated current. As you can see here that at the rated current you can see that the value of voltage here is equal to nu load voltage, right? This one is exactly equal to the nuload volte. So that's why we call it flat. At the rated current, it is exactly the induced EMF. Okay? However, if you look at the over compound, you can see it is above the induced nload EMF, under compound lower than E. So this one is flat because it gives us the nud condition as if nothing happened as if there is no voltage drop or armature reaction, okay? So these are the three types. The force one which is a differential. The differential, of course, you know that now we have voltage drop, Vterminal goes down due to armature reaction and voltage drop on series winding and the armature winding. Not only this in the differential, we will have five series opposes Phi shunt, right? So it also helps the vitama to go down. That's why you have these weird characteristics. You can see that it goes too much down. If this is a shunt, normal shunt like this, then this is a characteristic of differential goes all the way down. Why? Because now we have everything opposes our opposes our field wind or our Vtermal makes it going down all the time. Okay? So we have resultant flux reduces due to the presence of IL as Ilod increase. This showed almost constant. However, IC is increase as IR Mature goes up. So it means that the flux or the differential flux increase. Making resultant flux goes down in addition to armature resistance, serious field resistance, armiture reaction, which helps the terminal votes to drop further, right? That road goes all the way like this down. Okay? Making it even goes to a breaking point when the current becomes too much. Okay, because in this case, the flux will be very small, leading to induced MMF becoming very small compared to what we are having. So vitamL starts to go down or the current starts to go down. Okay, so what are the applications of DC generators? So in general, since we discussed all types of generators, we have some applications for you. Number one, separately excited DC generator is used as an accurate supply for testing labs. It is used in Word nard speed control systems, word speed control systems, and this one is very simple application. If you would like to have a control on your own motor, a very large control from zero to rated value or even beyond, all you have to do is that you can use the word Leonard speed control systems. What is this method exactly? Simply, we have an induction motor, which we will discuss in the induction machines part. Anyway, assume that this is an AC motor takes a three phase supply and provides mechanical power that rotates a DC generator. So we have a DC generator operated by an AC mode. Okay? This DC generator produces a terminal voltage that is used as an input for a DC motor. So we have an induction machine, DC generator, and DC motor. So the DC generator acts as a supply for DC mode. Now what happens exactly, you can see that we can control our motor by controlling field winding here and by controlling V turn. We can control Vtermal by controlling the flux here and also the speed of the three phase induction motor. All of this makes us have a high control or a precise control on our DC motor. Now, why Ifield and Vrmal can control our DC shunt motor, we will learn this in our part or in our course for not our course in the next section of our types of DC motors and torque speed characteristics. So we will discuss this later. For a series generator, it can be used as an arc welding in arc welding supplies used in incandescent lighting, used as a serious booster for increasing the voltage. Hunter generator, on the other hand, power supply, lighting, battery charging for the compound generator. It can be used in heavy surface railways, a line volt pooster for DC systems and arc welding. Now remember that these two are related to DC traction system. We discussed the usage of line volte pooster and thus inside our course for electric traction. And of course, lighting as the previous applications. For the compound wound DC motor, this is a final thing in this lesson. For the compound wound DC motor, it is simply like this long shunt compound motor and short chant exactly similar as we did before long shunt when they are in series with Armitu and shorthand when it is series with the combination of the two here. Now, when do we use this or why do we use a compound wound DC motor? Compound DC motor is a combination of shunt and series, right? Now, as we will see from the torque speed characteristics, which we will see in the DC motors part, we will find that shunt has a very good speed regulation characteristics. We can say that this is an almost constant speed motor. While series one, the DC motor has a high starting torque. By combining them together, we can get something which have a good speed regulation characteristics and at the same time has a high starting torque. The cumulative compound is one of the most common DC motors. Why? Because it gives us high starting torque and good speed regulations at high speed. 117. Example 13: Now let's have an example on the compound DC generator. So we have a short chant compound generator that delivers a lute current of 30 amperes. So we have 820 20 volt. So it means that our elute equal to 30 pairs, and V terminal equal to 220 volt. And as an armature, series field and hunt field resistance of 0.05, 0.3 and 200. So it means that armature resistance or armature, 0.05 ms and and series field are series, equal to 0.3 ms and the chant field or field are shunt equal to 200 oms. Find the induced MF and the armature current allow 1 volt per brush for contact draw. So let's first draw our circuits. We have iude, V terminal, and the resistance, and chant means that we have hunt parallel to armature and their combination, we have a series winding like this. So what you can see here as you can see, we have sum parallel to arcture and their combination in series with them, the series winding. And we have our lots. You can see our lot 220 volt, the lute current 30 and pairs. This is a resistance of R series. Let's call this series or series. And the R Mature resistance A equal to 0.5, as seen here. And 200 OMs this is chant equal to 200 OMs. Okay? Now, we need induced EMF. Now, what you can see that how can I get induced EMF? Very easy. What do you mean very easy? All you have to do here's armature, here's lute. All you have to do is appli civil in the loop. You'll find that the generated voltage equal to Vternl drop on the armature, I armature, or armiturePlus the drop on the series resistance. So it will be Ilde multiplied by our series, because the current flowing through it is in the lot current, 30 pairs. What else do everything? No, you can see 1 volt, pair push. So you can see that we have two pushes in general, two pushes, in this figure. So it will be plus, two multiplied by 1 volt. Okay? V terminal, 220 I armature equal to, where is our armature armature, I don't know I armature, right? Not given. Leave it for now, and lute, lute, given a armature 0.05, lute, the lute current 30 pairs, R series 0.3, so we have everything except I armature, right? Okay, so how can I get the shant current? Okay, we need shant current, and we need the lot current. Why? Because I armature. Assembly equal to IL plus I shunt. Okay? So from here, I shunt, Ilude is given as 30 pairs. Now, the only thing remaining is I shunt. Okay? So how can I get this? You can employ a large Kevl here. Kevl like this all the way like this. And look carefully at this ivial, okay? So we have echan entering here. Okay? So our voltage drop here will be like this. Okay? Look carefully at the kevial. So look carefully. So we are in the clockwise direction. So you can see we have a negative, negative the resistance shunt, multiplied by hand. Y negative because you can see that we are in the clockwise direction going in this direction. However, the hand go in the opposite direction. So we have a negative sign. Now we go all the way like this. You can see volt drop here, positive and negative, so it will be IL, multiplied by 0.3 plus L, multiplied by R series. Plus -20 20. So if we go all the way like this, positive first. It will be positive Van equal to zero. We have everything you can get R shunt. So you can see negative hand 200 Ms, 30 metablat by 0.3, which is our IL metablot by R series, plus Vterna equal to zero. Then the shant will be 1.145. So I Rmture will be L plus hantthirty plus this value. Then the induced MF, Vurnal plus series drop, I armature or armature, armature or armature, here, and series drop IL or series, L or series, as you can see, and the plus drop two multiplied by one. So this will give us 262.56 volt. And we already obtained the armature current, as you can see here, armature equal to 31.1, four, five amp. 118. Example 14: Now let's have another example. In this example, we have a long shunt compound generator delivers a lot current of 50 ampere at 500 volt. And as an armature series field and shunt field resistance of 0.05, 0.03, and 250 ohms respectively. Calculate the generated current, generated voltage, and armature current, and allow one voltable pros for the contact drop. So how can I solve this? All you have to do first draw the long shot. If we draw our long shot, we will have the circuit shunt, armature, armature resistance, and series field wine and our lute. First, we have long shan delivers a out current of 50 ampers lute current, 50 ampairs at a 500 volt, at a 500 volt, 50 ampairs. The armature resistance, rmture resistance is 0.05. Series field resistance, 0.03, as you can see, 250 oms chant field, as you can see. Okay, so how can I get these values? Okay, so the first thing we need generated voltage and armature current. So very easy. All you have to do that number one, get armature current, I armature, equal to I field, plus I I field, which is a shunt plus Ilude. Now, what about Ilude? I load equal 50 a pairs. What about I field? I field is equal to field current equal to voltage divided by resistance, voltage divided by resistance. So you can get I armiture. What about induced EMF? You can get it by applying KVL here, right? So induced EMF, E will be terminal voltage, V terminal, plus drop on armature, I armature, and we have 0.03 series was 0.05, so we can say RA plus R series. That's it. So I shunt first 5500/250, which is the loud voltage divided by R field. Okay? I armature would be submission, 52 pairs. And EG is Vternal plus I armature. Whereas I armature series drop, which is armature, multiplied by RA plus R series, you can see armature, 52 pairs, multiplied by the submission of two resistance, 0.05 plus 0.03, two resistance E. Now one thing here is that we have 1 volt a pair brush. We have two process here, so it will be plus two multiplied by one. I give us 506.16 volt. 119. Armature Reaction in DC Machines: Hey, everyone. In this lesson, we will start talking about the rmiture reaction in DC machines. We said before that the armature reaction is a result of the flow of current inside our armiture conductors and it produces a flux that opposes our main flux, right? So we would like to discuss this in more details. So the armitre reaction represented the impact of the armature flux on the main field flux. The armiture field is produced by the armature conductor when the generated current flows through them, and the main field is produced by the magnetic pools. Now, the armiture flux here has two effects on the main flux. It distorts the main flux and at the same time reduces the magnitude of the main field flux. So let's understand what happens exactly. So let's first before we do anything, let's just draw some figures. First, we have this one. This one representing this is our armature, okay? And this is our two pools north and south. Okay. So the current so the flux goes from north to south like this through the armature itself like this. Okay? So this representing the main flux. Now what about these conductors? I would like to see the flux of the armature. So the second figure here armature flux. You can see each one has a flux around it from the flaming right hand rule or from using the right hand rule, right? So each one has a flux around it. Each current has a flux around it. So if this one clockwise, this one will be opposite anti clockwise, okay? Because one is under the north, one under the south, okay? Now let's look carefully at this magnetic flux. You can see that here, flux is clockwise like this. Let's add arrows here and here like this, and here like this. Okay? Similarly, for this one, goes here like this and like this. Okay, you will understand why I'm doing this. Now look carefully at this area. Okay? Lo carefully at this area first. So we have our magnetic field magnetic flux going like this, right. Now, what you will see right here is that we have our flux produced by this armature, itself, going up, right, going up, opposite to its direction. So it means that a magnetic field here, flux, magnetic flux will be less. You can see if you look at here, you'll find that the magnetic field here is now weaker. It reduces the magnetic field flux, in this region here. Okay, here. Now, let's look on the other side. On the other side, we have here and this side, we have magnetic field going like this, right? Magnetic flux going down. And the armature flux here also goes down. So it means that it helps or aids our main flux, right. So this one helps this one. So what you will see that as a result, their submission will be a thicker area. More thick area. So we have a lighter area and thicker area, more flux, less flux here, and more flux here. You can see there is a distortion right now, right, because one area has a thick flux and the other has low amount of flux. Same idea here for this one. You can see that for this area, you can see flux going down and here flux going down. So this area is thick. Looking at this one, you can see at this area, flux going down, flux going up, so it will be less. So what you can see that as a result, you will see that we have a thick area like this and thicker areas and lighter areas or thinner areas. Okay? This one leads to distortion in our magnetic field and also reduction in the magnetic field flux. Another thing that you will notice here that remember that this point this axis here. Now, remember that when we said we have north and south and when the rectangular coil, if you remember, from the very beginning, we said at this area, the induced EMF is equal to zero. This is a transition from north to south or from south to north depending on the direction of rotation. So at this side here or at this region here, we have zero flux, right, or no induced emf. That's why we usually or in electrical machines, we put our process here. Like this. Why? Because this is a point at which we are shifting from one coil to another. Okay? So when we are shifting this axis here, we don't have any induced EMF. That's why no sparks will occur on this process. Okay, when it shifts from one to another, because we don't have any flux in this region or this is a neutral axis, as we will see in the next slide, okay? However, due to this distortion which you see here, now this axis in reality, the zero flux x will be shifted like this. So we should move our process from this location here to another location like this. At which we will not have any sparks. You can see that it's shifted by an angle phi or Theta depending on what reference are using. Okay? Okay, great. Now, so this is the first problem. If I keep the process here, there will be sparks as there will be induced MMF here because the magnetic neutral axis is now shifted. Okay? Now, another problem here is that what is the problem of just shifting the process all the time. The problem is that this angle is dependent on what load we are connecting on the load connected. So this shift will change dependent on what current we are or what current that our load is taking, okay? That's why in this case, you have to find another solution. Okay? Zusty shifting process all the time is not a practical solution. Okay, so let's look again. So we have here our magnetic pools. We have flux from the armature, and as you can see, one helping and one opposing, you will see that the resultant will be thick like this and it will be like this. So the neutral axis, magnetic neutral axis will be shifted from the original position. So this is a original position, and this is a shifted position. So we have two axis inside our electrical machines called D axis and Q axis. So what's the difference between these two? Direct axis and quadrature axis. The difference between them is that a direct axis is the direction of field Okay. And axis is the direction of torque, a blight or torque generated depending on a motor or generator we are talking about. So this is a direction of torque, direction of field. And if you remember before, from the flaming left hand rule, we know that the flux and the torque have 90 degrees between them, right, like this. So in this case, we have direct axis from north south, this is our direct axis, and the quadrature axis is perpendicular to it, leading by nine degree. Okay, so the direct axis x, which is the flux is produced by the field winding in this direction. And the quadrature axis is the x on which we have a produced torque. By convention, usually you will find or all of the time or the electrical machines, Q axis is spare perpendicular leading by 90 degrees from Dx electrically. Now we have a geometrical neutral axis, which is along the qua quadratal axis of the DC machine, as you can see here, and we have the magnetic neutral axis which is perpendicular to the axis of the resultant. The geometrical is the one which divides the machine geometrically. So it is the axis of the machine itself. The magnetic neutral axis is the one, which is perpendicular to the direct axis or the resultant flux, which is this one here. GNA cosides with MNA, as you can see here, magnetic neutral X at which we will not have any generated EMF or zero flux. Now, when we don't have any loads like here, you'll find that MNA cosides with GNA. However, when we have a loud, you'll find that the GNA, and this is a new MNA MNA starts shifting from GNA, okay? So what are the equations for armiture reaction? So we know that it is shifted like this. So we have this axis here in the middle. Let's just draw it. You can see here. This ax is here in the middle, which is GNA, and this is a new MNE shifted by an angle theta. Okay? Now, you will find that we have two effects for armiture reaction, which we said, reduction and distortion. The reduction is called the demagnetizing effect. As you can see that nors to thus like this, and we have magnetic flux that opposes it. Part of this rmitre reaction opposes it. So that's what we call FD or demagnetizing effect. So this is our magnetic field direction, and this is a distortion effect or not distortion, demagnetization effect or reduction in field. It opposes the main field. The second one which is called cross magnetizing Cross magnetizing is in this direction, we have a field flux in this direction like this. And like this here, you can see one like this, one like this, and one like this. This is a demagnetizing effect, and the one is a cross. What does it do? It leads to what we call cross magnetizing leads to distortion. How it distorts it, you will see like this. You'll see that north and south are like this, goes like this. However, this one also has a part that goes down. Right? So we have a field like this and cross magnetizing field going down FC. So find that the resultant will be like this, F resultant, right? Shifting for our magnetic field. Even if it's a small part converted to magnetic flux, it will be also shifted. Okay? So if we draw it like this, you will find that the resultant will be like this, right? The resultant 90 degrees from it, as we learned before. That's why you will see that it is drawn like this, because the field like this and the resultant MNE in this direction. Okay, so what you can see here again, we have FD and FC, the two effect demagnetizing and cross magnetizing. There summon gives us the armature reaction, okay? So what are the equations for demagnetizing and cross magnetization? Again, demagnetizing reduces the flux. Cross magnetizing distorts the flux as cross magnetizing plus the main flux leads to shifting of our flux. Shifting of our magnetic neutral axis. The demagnetizing, how many apaurns pair pool is equal to I multiplied by Theta, mechanical the leading angle here, mechanical angle, mechanical shift. Over 360 degrees. Cross magnetizing the I 1/2 P minus Theta, mechanical over 3,360 degrees. These are the equations for cross magnetizing and and the demagnetization effect. What are the effects of mature reaction? Again, demagnetization or weakened the flux. It distorts the mean flux or cross magnetization effect and decreases the efficiency of the machine. Also due to the shifting, as we said before, the process must be shifted or there will be sparks at process. Why? Because there will be a generated EMF at the terminals of the armature itself, at the terminals of the process. Okay, it reduces the induced MMF as we have a flux opposes the main flux. Now, how can we solve this number one? We can place our process along the M&A to avoid sparking because as we know that the reversal of current when we switch from north to south occurs along this axis, right? Or this is called also the axis of commutation. Also, this is not a practical solution. We can do we have another solution is that we can use a compensating winding, which is added on the main pole so. So this compensating winding is used to take the same rmitre current in order to produce a magnetic flux that opposes the magnetic flux produced by the rmitre reaction. So let's see what about the compensating winding. So if you look at our machine, we have this armature, and this is our two pools right with their field flux. Now, you can see that one current X here means that the current is entering into beach, entering entering into beach, and that means current is going out. So since we have a current entering, we have a flux produced in a certain direction. So what I'm going to do that I'm going to add here winding here, compensating winding. Which take the same current of armature, but in the opposite direction. So instead of we take the same current. You can see current entering. I will connect it in a certain way in order to have the current going out so that it will produce a flux that opposes this flux or neutralizes its effect. Similarly, I can add another one here, compensating one on the other pool. The current direction will be opposite to this one. If it is this one going out, this one will be entering, so that it will oppose it too. Similarly here, you can see that we have the main flux, and you can see that current going out, here, entering, going out, here entering in order to oppose the main flux. So it is added on the pull shoe itself, okay? Similarly, what you can see that let's get back. So as you can see here, you can see that we have armature, and we have our pools north north here, South, North and South. What you can see that we have the two terminals, we take the current and bout it here and so the compensating wind go all the way to South, all the way to North, all the way to South. And as you can see, okay? And as you can see, also, we have the second terminal here, one from here, and one from our compensating one because armature winding will be in series with the compensating one, similar to the series field winding, okay? Now, as you can see, we add our current to be entering in a certain way in order to produce a flux that opposes the armature flux, similarly here, similarly here, okay? 120. Example 15: So let's have an example on the Armit reaction to understand what happens exactly. So a four pool DC generator to B equal to four, let's type it to B equal to four, supply is a current of 140 am pairs. This is a armature current, and pairs. It has a 480 armiture conductor, so Z equal to 480, wave connected A equal to. The brushes are given an actual lead of ten mechanical degrees, our processes are shifted due to the armitureaction by ten mechanical degrees. So it means the Theta mechanical equal to ten degrees. Find the demagnetizing and cross magnetizing and perten pair pole. In order to get this, we have the two equations that I but blood by theta mechanical over 360, that I 1/2 P minus Theta mechanical over 160. That number of conductors, 480, Theta mechanical ten degrees, that 480, number of bools, four, Theta mechanical ten degrees. The only one which is current, someone will say, Hey, the current is 140 am pairs. No, this is completely wrong. Why? Because the current we are looking for is the current of each conductor. Current I equal to current of the conductor. Okay? Now, what it will change, you will see right now. Remember that here, our machine is wave connected two parallel paths. So we have our conductors like this. Like this. So the total current is 140 am pairs. So each conductor will take 70 am pair or each path will take 70 am pairs. So I one equal to 70 ampere, I two equals 70 am pairs, right? Okay. So our current will be 70 because this is a current flowing through each conductor. So 70 am pairs and through the demagnetizing effect, pi substituting, as you can see here, ten degrees, 7,480 gives us how many hundred and 33 ampair turns. And the cross magnetizing effect will be 7,466.67 a pair terms. 121. Interpoles in DC Machines: Hey, everyone. In this lesson, we will discuss another solution for the rmture reaction, which is the inter pools. So what are the interpools in DC machine? So look at this one. You can see that in this figure, we have our compensating winding two pols north and south, and we added two windings that opposes the main flux. Okay? Now, what are we going to do? In interpols we are going to add some. Remember that we can add some inter pools and other pools here, smaller pools in the neutral axis region, or in the magnetic neutral axis region. So what you can see that we have north and south, right? And this is our root. Now, what I'm going to do that I'm going to add another pull like this and another pull like this, and it will take the same current from the armature itself. It can take the current from the armature itself. Now, why are we going to do this? You will understand right now. So the interpols are small and placed between the main pools of the yoke or the region, usually, or they are placed in the region at which we have zero EMF, or theoretically, we have a zero EMF when we don't have armiture reaction. So this region here, as you can see, we have here north and south, you can see this region here. This is a newt MNA. At no load, right? So this is supposedly should have zero induced EMF, zero flux. So we add this due to rmitre reaction, we will have induced EMF here, right in these coils. So I'm going to add these pools, which you can see north and south and we will understand how are we going to select them in order to produce a flux that oboses this flux and neutralizes it. Okay? That's why we add them in the interpoolar region or in the region between these two pools. Like compensating wining the interpols are series with the armature winding so that the MMMF produced by them oppose the MMF produced by the armature conductor in the interpolar region. This region between pools is called the interpolar region. We add our poles here. It produces a counterflux on the coil, which is undergoing commutation, counterflux undergoing commutation to nullify the reactance voltage. What does this even mean? Now, remember that we have a coil here. This coil is of course, an inductance or an inductor. Since it is a coil, it means it is an inductor. So we will have a reactant voltage or a voltage on the l to be more specific, L or our inductance, right? So this is our reactants. Since we are having here an EC voltage, remember that this is rotationary and we have an AC voltage. When we add process, we convert it into DC. However, it is originally an AC current, an AC voltage and AC current, and we convert into DC Pi adding process. Okay. So since it is originally AC and we have coil, then we will have a reactance voltage. This reactant voltage will lead to sparks at the process. Since we have a voltage here at this, coils at the coils here in the interpolar region, then we will have sparks between it and the pressure. Remember that we put process here in the interpolar region or in the MNA region. Since we have induced EMF or actans voltage, we will have to nullify it by using an interpolar that produce flux that kills this induced EMF. Okay. And also it nullifies the armiture flux in the interpool region automatically. So any flux coming here, it will be canceled by using these pools. Okay. So what happens exactly from the interpool or not interpool In general, when we are our coil, when it transforms from the north, 2000, right? I transforms from north 2000. So it has the maximum positive current. And when it transfers from here to here, it goes all the way to the most negative. So in the developed diagram here, when the coil passes through the brush, its currenty changes direction, because it transferred from north to thousand, right? Now, this ideally, ideally, the current when it changes from north to south, using the process, of course, this is a commutation time, which is very small. When it transfers from norse to thousand during commutation period, you'll find that it is ideally goes linearly from maximum positive to maximum negative, right, because the currenty changes. If you remember, or if you let me explain this, remember that when we had a coil like this, we have North and South, right? So the currenter we have in this direction and in this direction, right? So when this coil rotates from most of South, it changes from big value, and when it reaches South, it will be most negative, right? So during this period, it goes from maximum positive to goes all the way down to maximum negative, right? However, this transfer here is not ideal. This transfer from north to south is not ideal. Due to the presence of inductance or the coil inductance, this will lead to lagging in current, delay in current. So you can see that instead of going all the way down directly to most negative, it will be delayed like this. You see delayed like this. So what will happen is that when it reaches the south, it doesn't reach the most negative. It has a lower current. The current will be one and this will be I two. So this is our I two. So when it transfers from idly like this, when it reaches thus, when it rotates and reaches south, it will be most negative. However, here, due to coil inductance, it will not reach most negative. It will reach a lower current I one, not the most negative current I two. Now, the difference between these two currents or the current will go suddenly a sour go suddenly from this to this from lower value to most negative. This transition, this faster transition leads to a spark inside our process. Because it jumps to full value almost instantaneously, this will cause sparks. That's why we add a small pool called interpool or commutation pool. This one will take the rmiture current and produce a flux oppose the Q axis current produced by rmiture current. Q axis because in this region, we will have a flux like this. So we have a flux going like this. So we need a flux that opposes this flux, from the coil itself at the interpool or interpolar region. Okay? So simply interpools what do Z do? They cancel the flux produced by the armature, or by the armature ct. As a result, the net flux in the interpolar region is almost zero. So in this case, we don't have any kind of sparks. Now, as you can see that when we are looking at this figure, this one is exactly this one but stretched out, okay? So as you can see here in this region, we have currents, as you can see entering and this one current leaving, on the north on the south. And these are the process which are placed in the MNA at which we don't have any induced MF, right? So another problem here is that what you will see that during this transition when the process moves, it will have a short circuit between two coils, one in the interpolar region, and one in the interpolar region. Okay? Remember that the process is about let's read this. It is about the size of the commutator like this. So in a certain position, this brush can touch two commutators at the same time. So it can have a short circuit between two coils, right, when it touches them together. However, due to the design of the electrical machine, these two coils will be at a position at the interpolar region. We don't have any induced EMF. However, if due to the armitre reaction, we will have induced the meth here and the current flowing here, which means we will have a short circuit. This is another solution or another way another thing. Why do we use an interpool in a DC machine? In order to neutralize any generated reactant voltage here, any reactant voltage generated in the interpoolar reach to prevent short circuit ls. The interpolar polarity is equal to, how can we select a similarity equal to the polarity of the incoming ball in case of the generator and vice versa in the motor. So what you can see here like this, you can see that our generator here rotates in this direction. So we have north north and going to thus. So the interpolar polarity is equal to polarity of the incoming ball. So we go from north south. What is our incoming? Well, our incoming is south, so I will both here south. Here I'm rotating like this. What is my own incoming ball or incoming ball north, so I will put here north. That's it. In the motor, it will be the reverse instead of having not the incoming, but the opposite of the incoming. So it will be North and South, in case of the motor. Here, the same idea. You can see that here, direction of rotation clockwise. So I'm going north, 2000. I'm going 2000, so I'm going to add what pool I'm going to add a South pool. Okay? Going from south to north, what is my own incoming? My on incoming is north, so I will add a North pool. Our incoming south, I will add South pool and et cetera. Okay? So this is how you add interpools inside DC machines. 122. Shunt DC Motor – Torque-Speed Characteristics: Hey, everyone. In today's lesson, we will start discussing the characteristics for our DC motors. We are going to discuss the characteristics for the Shunt DC motor and the series DC motor in addition to a small hint about the cumulative and differential shunt motors. Okay? Now, we are not going to discuss the separately excited because it is not widely used. The one which is widely used is the Shunt DC motor and the series DC motor. So what are the characteristics which we can learn about? So we have three characteristics. The first one, which is a torque, arm and the armature current, the relation between the torque generated in our motor and the armiture current OA. This is known as the electrical characteristics. We have also a characteristics which is a speed and armiture current relation between N and O armature. We can also combine these two torque and speed, and we have speed torque characteristics, which is called the mechanical characteristics. So we can have a relation between torque, armature current, speed, armature current, and speed and torque. Let's discuss the shant DC motor torque speed characteristics. How can I get the relation between torque and speed? This is actually very simple. Number one, we need to draw the Shante DC motor. If you remember we have field winding or the Shante field parallel to our armature or A and the armature itself, right? However, we are talking about a motor, not a generator. In case of our generator, if you remember, our generator gives electrical power to an external load. However, right now, we are talking about a motor in which we are going to connect. We are connecting an external supply with a value of VtermT is a DC supply. DC supply. Giving current to our motor, part of the current will go to the field winding to provide excitation. And another part we'll go through the armature conductors. Now, as you can see, we have field excitation plus conductors rmiture conductors, carrying current, carrying carrying current. R mature, R mature carrying current. Okay? So we have conductors, carrying current inside the magnetic field. What will happen exactly a torque will be generated, right? So we are going to connect to our shaft for our motor. We will connect any mechanical loads. We have here our mechanical out. Okay? Now, remember something which is very important. Our here, our armature is rotating due to this production of torque, it rotates inside the magnetic field, right? Since it rotates itself inside the magnetic field, there will be an induced mF EPAC. As a result of rotation inside the magnetic field. This induced EMF or BMF according to lens law, will oppose our original supply. So we have a BMF generated that opposes V turner, okay? So the induced EMF in the armature always act in the opposite direction of the supply voltage. This is according to nslo if you remember E, equal to negative N dpi by DT. This is from Faraday's law, and this is from lenslo. It means that negative because it opposes the action or the cause to oppose the cause producing it. So the EMF opposes the supply voltage. It's called the BMF EPC. Now let's look at the relation. Number one, we have our supply current, IL coming from the supply, IL equal to IA plus IF, the current coming from our Vtern giving current to our field and the currenty going through the arm ture. So I L equal to I plus IF. Remember, this is our supply in the motor. In the generator, this was our supply. Now, looking at these two terminals EPAC what about ViternalO EB? EBC will be equal to Viternal minus armature or armature. Now, how can I do this or how can I know this? Very easy. You can see that the current entering the resistance from here, right? Plus or minus. So our voltage drop is in this direction going down, positive and negative sense the current going from this terminal. Now, if I apply AVL here, like this, let's apply QL, go here like this negative Vterminal negative V terminal, go all the way like this and positive, IAA positive, IAA, and then go all the way down, positive Eb positive EB equal to zero from a QVL. Vterminal will be equal to EBAC plus IAA. So EBAC itself will be Vterminal minus IAR R Mig. Okay? Now, if you don't know how to apply KVL and all of this stuff or don't understand it, you have to get our course for electric circuits before this course of electrical machines. Okay? So we start with electric circuits first, then electrical machines. Okay? Okay, great. So we have our EBC, and our torque will be EB, IA over Omega. Where did we get this? Remember that our power our power equal to torque, multi blod by Omega or EBC, multi ploid by I mitre developed power. Okay? So from this equation, the torque will be equal to EBC IA over omic like this. Okay, now, remember that also that EBAC itself is equal to K Phi Omega, and the torque, K PiiA right from what we learned in the beginning of our course for DC machines. Okay. Now, what I'm going to do is that I would like to get our Omega. So our Omega here from this equation here, our Omega equal to EBC divided by Ki, EBC over Kfi. And we know that EBC itself is Vterminal minus A or Rmture. So it will be like this Vterminal minus I or armature. So it will be V terminal over Ki, minus IAA over Ki. Okay. Now not only this, we will take Kfi, we will take I armature and replace it with the torque let's explain this, this will be equal to V terminal over Kfi minus I ARA, over Kfi, right? Okay. Now, we know that I armature itself, I armature from this equation equal to torque, divided by Kfi. So let's substitute this here. So it will be equal to Vtermal over Kfi minus RA over Kfi. Now, the current itself is torque divided by Ki, torque, divided by Kfi. So we will have Vternal over Kfi minus RTA a TA, divided by K Kf, which is K five square, as you can see. Why did I do all of this to get a relation between or torque speed characteristics, relation between speed and torque? Now if I'm going to blot this figure Omega with respect to torque, as you can see that as torque increases, the negative value increases leading to reduction in Omega. What you can see that we start at a certain point as torque increases, Omega goes down. As you can see here, as torque increase, the bid goes down. This is a characteristics. Now leave V terminal for now as we will discuss this in the next slides. 123. Speed Control of the Shunt DC Motor: Okay, so how can I control my Shante DC motor? I would like to control its speed? How can I do this? If we look at our relation here for Omega, you can see we have different options. We can control Vternal. By changing Vternal, I can change Omega. Also, you can change Phi or the magnetic flux by controlling the resistance. If you control resistance, you can control the field current, which means you can control the excitation. You can also change the resistance of the armature, which will lead to change in omega. These are the three Armiture voltage control field control and armiture resistance control. Now, as you can see that as V terminal increase, Omega will increase. As the field increase, magnetic flux increase, Omega itself will start going down. As field increase, it speed will go down. As also the resistance increase, the negative sign increases means that Omega will drop down. As resistance of the armature increase, its bid goes down. Now let's look again at each option and draw the figures. So control the terminal voltage as the terminal voltage can be controlled by several methods. How can I control Vterm? How can I change it? You can number one, add a potential divider, which of course is a bad idea because it leads to power losses. Now, what I mean by potential divider? So let's say we have a DC source. VDC. These are the two terminals of our supply. Instead of connecting it directly to our supply, we can add a resistance here like this, like this. So by changing this value of the resistance, we can change the V terminal across our motor. However, the problem of this idea is that when you add a resistance, you have power losses, right? Okay. Another option is that you can add another decision rate. Remember that when we said the word Lenard method in the previous section for our decis generators, we said that we can add decision tor, a decision ator driven by an induction motor, and by controlling the out of the decis generator, we can control V terminal of our motor, and hence we can control speed of our motor. Of course, this is an expensive method because you will need a decis generator and an induction motor. The third method is that using rectifier. What I mean by rectifier rectifier, which we will learn in our course for power electronics, assembly a inversion from AC alternating current, similar to the one which you found in your own house into DC or like the one which we need here in our DC machine. Okay, so this is a rectifier. AC to DC converter, it can be a three phase rectifier or a single phase rectifier. All of this discussed in our course for power electronics. Okay, great. Now, another thing that we can do that we can use something which we call DC shoppers. What does DC shoppers do? They convert a DC from one value into another value of DC. It can be a step up, step down DC shoppers. Also, we have another type which is called PAC converter, post converter, and PAC Post converters. All of these are in our course for power electronics. Okay? So if you would like to learn about these types, you can go to our course for Power Electronics. Okay? Okay, so let's get back here first. As you can see that at zero torque, this is very important. So we plotted one curve like this, terminal, like this. Okay? And we have a certain value at Omega at torque equal to zero. This is very important. Torque equal to zero. Omega will be Vterminal over Kfi. So as terminal increase, Omega will increase or the 00 point here will go up like this. So you can see the whole curve shifted upwards like this. Okay? So as V terminal increase, it will be like this. Go So this one Vitamin one greater than Vitamin two. And you can see that the zero torque point shifted upward. This is important as you will see another type at which it will not change. Okay? Now, the other method is controlling field flux. By controlling field, you can control speed. But before we see the field flux, how can I know the operating point? So this is a torque speed characteristics. Let's say this one for simplicity. This is a torque speed characteristics for our sont mode. Okay? The intersection of our shunt motor torque speed characteristics with the torquispeed characteristics of our connected loot, the intersection between them gives us the operating point. So this intersection here, this is a point, the torque and the speed at which we are working with, okay? What about field flux? As you can see that the more field we have, the lower the curve. So as you can see as flux increase, Omega will drop down. Even at a zero torque, you can see that as flux increase, Omega goes down. That's why you can see this is a first curve. As we increase flux, IF two greater than IF three or increase field current, you can see that the curve goes down. If one, IF two, IF three. Okay, great. Now there is a very important part here regarding this type. Now, look at this figure here, this equation here for the field control. Now, let's say we are not connecting any kind of load. The torque equal to zero. We don't have any kind of load here. Okay, great. We don't have any load. Okay. What will happen is that our equation will be like this will be Omega equal Vitermal over Ki. Omega equal Vitermal over Kfi or KfiF depending on changing or substituting pi with current. It is exactly the same, but a different constant. What's the problem here? The problem is that at zero torque, no load connected. And at the same time, if we suddenly make IF equal to zero, we make it an open circuit for any kind of reason. What will happen in that Omega will go to infinity or be very, very large. So you can see that anything divided by zero gives us infinity. So you can see that turn over zero gives us infinity, which is a very dangerous situation. Why? Because this very large can damage the mechanical bearing. And since also we don't have any induced MF, the armature current will be very high. I armature in the motor will be V terminal minus I E over R. V since it is our supply minus E over R Rm. If the field is open circuit means F equal to zero. It means that there is no inducedmF equal to zero, so E equal to zero. This will lead to Van RF, which means very, very high current or extremely high current. Our armature would be very large, which can damage our armature conductors. That's why it's very important in shunt generator that we have to connect ut and at the same time, we don't make the field circuit open circuit because this will lead to this dangerous situation. Now we have armature resistance control, the last method or a controlling armature. As you can see that as we increase resistance, the omega will go down. So as we increase resistance, as we add more resistance, as you can see here, you will find that the curve will start going down, or armature increases, curve going down. But you will find something here which is different. You can see that they are not as before, if you remember the previous figure, Omega and torque, it was like this, like this. However, for our armature, we start at one significant one specific point. So it will be like this, go down, go down here, go up, down, whatever it is. So at the same point. Why at the same point? Because as you can see that when torque equal to zero, Omega M will be V terminal over Kfi. Now, as you can see in this equation, we don't have any or right So the zero torque point is constant regardless of the value of RA. If you increase armature or drop it down at a zero torque, it will be the same point, right? The same exact point. That's why the curve changes starting after torque equal to a certain value. Okay, it drops down, but as you can see, drops down, but it starts at the same point. However, in the other curves we had like this, this point change it because as you can see, we have V terminal here and we have flux, which will change the zero torque point. I hope it's clear for you. The problem again, of any resistance method that we will have efficiency or the efficiency will start decreasing due to power losses in the resistance. Last point for shant DC motor that the rmitre reaction effect. Now, as we know that there is a very good thing about armitre reaction here in the Shante DC motor. Now, as you can see that as torque increase, as the torque increase, Omega will drop down right like this. Like this, we have our omega and torque, so it goes down like this, like this. However, due to the presence of rmitre reaction, remember what does the armiture reaction do when IA increase due to increase in our loot. What happens exactly? What happens exactly that when I armature increase, torque increase, right? And at the same time when I armature increase, armature reaction increases means that the flux from the armature increases leading to Fi resultant will go down or the field flux will decrease. So what will happen in this case? In our characteristics, our speed goes down with torque? However, due to miture reaction, it will lead to reduction in FOI. Meaning that this reduction will lead to Omega going up. Okay. That's why instead of having this curve with no armitureaction, it will be a little bit higher with armature reaction. That's why you can see that the speed does not change much with the change of torque. That's why we call this type of machines, the Shunt motor as a constant speed motor because its speed does not change much. The armiture reaction and at the same time by controlling field flux, we can have constant speed for our generator for our motor. 124. Speed Control Beyond Rated Speed: Now, how can I control our speed beyond the tidy speed? Okay? So let's look at the stages for our controlling our shunt mood. In general, we have two stages. Number one, we have reds omega base, which is a rated speed. From zero to rated speed, we control it by controlling the terminal voltage. Beyond the rated speed, we use something which we call field weakening. What does it mean? It means that we control field current in order to increase our speed. Okay, so let's understand this. So first, we have our power supply power equal to V terminal I armature. This is a power given by our terminal DC supply. V terminal let's type it. So here, power, V terminal I armature, and V terminal itself is equal to E minus plus I armature since we are talking about a moton modulated by Rmture. And since the voltage drop is small compared to the induced EMF, so what does this even mean? So we can neglect the sport. So it will be approximately equal to inducing FA, which is our developed power, developed power. Okay? So our developed power is equal to E A, which is equal to the torque multiplied by Omega, right? Okay? So as you can see, power, approximately EIA and the power is equal to torque equal to E IA. So let's just delete all of this and keep this part E IA. Okay. So what do you would like to say? What I would like to say is that you can see that our power here in this range, this point is rated power. When we supply V terminal rating, give us the maximum rated terminal voltage multiblo IA rate. During this period, here we are drawing power with respect to Omega. So what we can do as I increase power, I increase speed, right? As I increase power, I increase speed. Why? Because I'm controlling Vtermal? So the power increases by increasing. Remember, this one is Vtermal or arm approximately. So as I increase Vternal I increase power supply to the motor, I will increase the speed. As you can see from here, you can see that as I increase power, and say this is power as power increase, the speed increase. In this reason here, we call it Vternal control because we are controlling our terminal voltage by giving more current using arctifier, using a potential divider, whatever the method used to change V urnal we control Viterm and this will control power. As Viterm increase again from here, Omega will increase, right? So our speed will go up until reaching a certain point. This point is a rated power. I cannot increase beyond that. We have V rated rated at which we will have Omega rated, right? So on this point, what I'm going to do that I'm going to in order to increase is bed beyond the maximum speed. What I'm going to do that V terminal will be constant, which means power will be constant. Okay. However, at the same time, I'm going to use field weakening. I'm going to reduce our field by increasing R F. By increasing the field resistance, I will reduce the flux, meaning that our speed will start going up, right? So in this range, our speed will go up at a constant power. Why? Because we fix it now V terminal and the Armitu current. Okay, great. We fix the Vurmal so our power is constant. This is a relation between power and Omega. What about our torque? Our torque will change like this. Look carefully here. So our power is constant, right? Our power is constant, or not constant right now. Let's say this. Let's talk about this region first this region at which power increases. So power equal torque Omeka. So in this region, power increases leading to increasing Omega. Turkey itself is constant. Nothing changed. That's why Turkey in this region is constant. Okay? Starting from here to here, power constant, power constant. And our speed increases, our speed increases despite power being constant. So in order to keep this power constant, the torque must go down. That's why the torque at this part starts to go down as a speed increase. So all of this related to the relation between power, torque and Omega. Let's summarize what I just explained. Is bit control from zero to maximum or a base bit is usually obtained by miture volte control. As I change V terminal, I increase Omega, and as Val increase, power increase, as you can see here. What about torque? Torque doesn't change. It is constant in this region. Beyond the Omega Base is obtained by decreasing the field one. That's what's called field weakening. By reducing flux, Omega will increase beyond the maximum speed or the rated speed. At the same time, since power is constant and we increase Omega, then the torque must be reduced like this. So at the base bid, here at this point, the rmi char terminal voltage is at rated value. If the current is not to exceed its rated value, speed control beyond the base bit is restricted to a constant power, known as the constant power operation, as you can see here, because if I would like to keep torque constant, I have to increase the current, right, in order to give the same torque. Or increase the armature terminal voltage. That's why since our power is constant, then the torque will decrease with the speed increase in the field weakening region. You can also think of this as follows. You can think of this as Omega increase, torque increase, decrease from this equation. 125. Series DC Motor – Torque-Speed Characteristics: Hey, everyone. In this lesson, we will start discussing the series DC motor, the torque speed characteristics. How can I get the torque speed characteristics for a series DC motor? This is very simple, as you can see. The same as we did before, we have V terminal, giving us I armature, which is the field current at the same time series field with our armature, leading to production of induced IMF here, EBA Okay? So what we can see that I load or I load here means ternal. It should be term because we don't have any load here. It should be ternal or I supply, equal to armature current, equal to field current, right? Because all of them are series with each other. However, EBC will be terminal voltage minus the voltage drop here. So it will be Vterminal minus I armature, or series plus R E plus A. What does this even mean? Series, the field resistance, R A or Mature resistance, R E is the external added resistance, the resistance which we add, to control our motor. As we will see right now. So again, what we are going to do is that we get the two equations, E B equal to Ki Omega or Omega, if you are talking about the American accent, torque equal to KfiOOrmchu. Now, what I would like to do that I'm going to type Omega. Omega will be Eb over Kfi. Eb over Kfi but before this, we can do a little trick here. What are the trick exactly? As you can see that the armature current, in this case, all of this are series with each other. So it means that a Irmture increase our flux increase, because I armature is exactly I field. Okay. And if we assume that so I armature or flux directly proportional to I armature. So we can see that Phi is a constant, let's say K one, I armature, right? Constant modular. Let's say, of course, we are talking about the magnetic linearities assumed. What I mean by this, remember that the pH curve, when we are operating in the linear region, this is a linear region. This is a magnetic linearity in which the current increase, flux increase. So what else? I'm going to take this and substitute it here. It will be E equal to K, which is the first constant, F, which is KA, KA, Omega M, and exactly the torque will be K K one IA, KA, multiplied by IA, multiplied by IA. So it will give us E equal to. You can see we have a constant multiplied by another constant. So I will say that it is K series, and constant, IA Omega M and the torque. Will be the same constant K series, I is square, I is square. It will be like this. K series I Omega and K series I is square, right. What else? I'm going to type Omega with respect to EBC. Omega will be EBC over K series I armch. Okay. So Omega from this equation here, Omega will be EBAC divided by K series Rmiton. And we know that EBC itself from this equation is Vterm minus IA series plus or E plus or Omega will be the same value divided by Ks IA, which is this equation here. Okay? Then as you can see that we can divide this into Omega M equal to V terminal over K EIA minusA. Let's say, our total for now for simplicity, KsiA. Now, we know that from this equation that IA from here will be root, torque, over KsE, right. So what I'm going to that. What I'm going to do that I will substitute with this here. Okay. So our ViternalO course, sorry, IA will go as IA here. So we have R total over Ks. Okay? Okay, leave this for now. This is just a constant negative R over Ks E. For this part, we have KsErmature. SEOrmature is root, TA over Ks, root TA over KsE, right? So this is exactly V terminal over root torque, multiplied by KsE divided by half KC gives us root K. So very simple, just mathematical simplification. You can see there's a total resistance divided by K, as you can see here, and this one is Vterminal divided by root KsE root torque of the armature. A. Great. So what you can see here that we have now the relation between Omega and root torque. By simplification, you can simply say that Omega is inversely proportional to root torque. So the relation if you block this figure or before plotting, let's just say this is a very important part regarding the serious DC motor, that if we don't have any kind of flute, which means torque equal to zero, it means that Vtermal over zero gives us infinity, which means Omega will be very, very large if we don't have any loot. That's why for a serious DC motor, it never be started without any kind of louts. I must be connected with a lot. That's why you will find that serious DC motor is used in electrical or in electric traction systems. Now, if we block this relation Omega and root TA, it will be like this inversely proportional. As torque increase, Omega will go down as you can see here. And at zero torque, Omega is going to infinity. And also, as you can see, as Omega equal to zero, torque torque is almost infinity, very large torque. So what does this mean? It means that at a zero speed, it gives us large torque. Why it is very helpful for us because our electric traction system, we need a motor that will start with a large load. In electric traction system, we have people and other entering our train, and I would like to start our train with a large torque presented. At OmiO zero at zero speed when it is in a station, it can start with a large torque can handle this large road. That's why serious DC motor is very helpful in electric traction systems. Now what will happen if I increase Vterminal by changing vitamin, it will be like this. It will go up like this, as vitamin increase, Omega will go up. What about resistance as resistance increase, our variable resistance increase. Omega will go down, so it will be opposite direction like this. As you can see that by increasing resistance, our curve will go down and also by increasing Viternal you will see that it will go up. They are the same curve, but the difference is what? That if I would like to know, again, the operating point, simply we intersect these two, the torque of our loud with the characteristics. This is our operating point or this or this. Now, of course, increasing term by increasing Viteral the characteristics will go up like this. Okay? Now the series motors are used where large starting tokes are required, which is in automobile starters, attraction, crans, locomotives, et cetera. The torque speed characters of various DC motors. So we have seen the shunt and we have seen our friend, the series DC motor. For other types, it will be like this is for shunt, almost constant characteristics due to arm reaction and the voltage regulation for this type of motors. For the series, it is inverse. Omega torque, it is an inverse regulation, as you can see here. What about differential and cumulative? Now, the problem of differential and cumulative. Now remember that in cumulative, we increase our flux. We provide more flux. And in differential, we have lower field, once we have more field, it means that we let's get back. If you remember from the torque speed characteristics, Omega was inversely like this Pi square as flux increase, the Omega will go down. That's why in cumulative, this is a shunt and in cumulative, we have more flux leading to fast reduction in speed. That's why if this is a shunt, then cumulative will also go more down. Okay? In the differential field weakening, we have lower field than shunt. This will lead to higher speed. That's why it will go up. Okay? That is only the difference between these three types. So what are the applications of DC motors? We have a shunt motor. It is considered as a constant speed motor used in applications, various applications like pumps, flowers, and fans. It's also for the series motor. It can be used as a variable speed motor, high starting torque, and it's used in elevators, electric tractions, vacuum cleaners, et cetera. The combined motor differentially is not used, rarely used, but the cumulative used in process and other applications. 126. Example 1: Now let's have our first example on the DC motors or Shunt DC motors. So we have the Sant DC motor. The speed of 500 volt, hunt mean 500 volt, and mot it means this is our input supply, which means V terminal equal to 500 volt. We need to increase its speed from 700 RBM to 1,000 by using field weakening. So this is N one, and this is N two. The total torque unchanged means that torque one in the first case, equal to torque two. The armature and chant feed resistance are 0.8 and 750. Armature resistance, resistance of the armature is 0.8 oms and 750 or F equal to 750 oms. The supply current at lower speed is 12 and bear at the lower speed, supply current, I supply equal to 12 and bear. Remember, I supply one in the first case. What do you need? Well, I would like to know the additional Shante field resistance required. Remember that we use the field weakening to increase its speed 700-1 thousand. So field weakening means we increase our resistance to take I field down. So I would like what additional resistance do we have? Okay, so how can I get this? You can get it very easy. How you know that we have two relations. We have E equal to Ki Omega and torque equal to Ki armature. So what you can see that E one, will be pi one omega one, or you can say also directly f one omega one. Let's make it K omega one, and E two equal to k52 omega two, right? So if you divide these two together, you will have E one over E two equal to 51 Omega 1/52 Omega two. And the flux is directly proportional to field current, so I can say I field one over I field two because we changed our field N one over N two. So number one, do you have N one, and I have N two? I need field the current, and I need induced MF. Okay? Number two, we have four torque. For torque, we have T one, equal two, K, i one, I mature one. And toque number two, equal to K f two, I armature two because armature cart changes, flux change. If you divide these two, you will have T one over T two, equal two, f one over f two, multiplod by IA one over Ia two. Again, f one over a two is IF one over IF two, multiplied by R armature one over I Rmture two. Now, T one over T two is equal to one. Okay? So we have this relation. And we have this relation. What we need to get the Sand field resistance is that we need to find value of IF two. Okay? So what I need now is I armature one, I armature two, I field one, okay? And we need induced MMF E one and induced MMF two. Okay? And using these two equations, we will get finally our values needed. Okay? So let's get step by step. So V urnal here is 500 volt. Okay? Can I get I field one? Well, I field one very easy equal to the V terminal 500 divided by the resistance of the shunt, which is 750. Okay. What about I armature? I armature I can get a y? Because we have supply current 12 and pair. We have I field from here. Okay, I field one, so I can get I armature one will be I supply minus I field. Okay, so I can get the first armature current. So let's see I field one equal VTN over RF one, equal to 0.67 500/750, and the current equal to subtraction, 11.331. Okay. Can you get the first induced EMF? Yes, applying QVL or as you know that EBC in a motor equal to Vterminal minus I armature or RmatureO and one. EB one will be V terminal minus I armature, or armature equal to this value. We have the first induced EMF. We have first armature current, and we have IF one. Now remember that torque is equal to constant, and as I said before, T one over T two equal IA one over IA two, IF one over IF two, equal one, I armature one given 11.33, IF 10.67 I armature two and IF two, I don't know them. So I will take one as a relation with the other. Ia two from this equation equal to 7.6 over IF two. Again, BMF, the second BMF will be terminal voltage, 500 minus Irmature two A, I armature two or A. I armature two, I already obtained a relation for 7.6 over IF two. So we obtained the second EMF as a function of the field current. Now we know that the ratio between E one over E two, as I just explained, equal to IF one over IF two over N one over N two. E one is equal to 490. E two, I just obtain a relation for it. We have Omega one IF one over IF two or Omegon over Omega to, which is N one over N two, 700/1000. If 111.0 0.67 and IF two is unknown. So we have one large equation unknown in IF two. By solving this equation, you will get IF two equal to 0.465 and pairs. Now, how can I get the new resistance? As you can see that IF two is simply equal to V terminal over RF two, the new resistance after adding a resistance. So RF two will be 500/0 0.465. We have the current and we have terminal 500. We can get the resistance 1075. So this is the new resistance. What is the additional shunter resistance? Our resistance was 750 ms now 1075. So the difference between them is our additional resistance, resistance which we add. 127. Example 2: Now let's have another example. In this example, we have a series field motor or a DC series motor connected to a 440 volt supply so en equal to 440 volt, runs at 600 RBM when taking a current of 50 a pairs. Our current Rmtar. Let's say one because we are going to change it equal 50 am pairs, and in one equal to 600 RBM, great. Find the value of seress we need to add a series resistance, which inserted in series the motor to reduce its speed to 400 beam. So the second new speed and 2400 RBM. The gross torque is half its previous value. T two equal to half T one. We reduced our torque at the cost of reducing the bit two by adding a resistance. The sulfur resistance of the motor which means the total resistance is 0.2 ms. What do you need? I need the new additional resistance. That will lead to new additional resistance. That will lead to a reduction of this bit. So remember that the relations of our DC series motor like this, right? So what we can see that we can say E one, over e equal to K, K, and I armature one, Omega one, K I armature two, Omega two, which will be equal to I armature one and one, armature two N two, right? So we have E one over E two, equal to I armature one and one over N two. Okay? The second relation which we have is torque T one over T two, equal to K a one square, K, Ia two square from this one, right? So it will be a one square over Ia two square. T one over t two. So you can see that T one over T two equal half. So this will be equal to half. Now we know that the first current Ia one is equal to 50 and pairs, right? So we have 50 square divided by I armature two, equal to half, so we can get I armature two. That is the first step. So we have I armature one, we have I armature two. We have N one, 600. We have N two equal to 400 RBM. Now I need E one and E two. So E one assembly equal to terminal voltage minus the drop, which is our current 50 and bears, multiplied by the armature current, which is multiplied by the total resistance 0.2. This is our E one. By solving this, by using this here, you will get E two and we'll see what are we going to do? As you can see, T one over T two equal to half Sorry, it will be equal to two because the torque number two is reduced to half. Okay? So if I would like through this, is equal to two, not half. Okay. Why? Because as you can see, T one over T two equal to one over half. So T one over T two, T one over Tito is equal to one over half, gives us two. Okay? That's why T one over Tito equal to two. I armature one square over I armature two square equal to first 150 square over I armature two. From here, we can get armature 35.3 6:00 A.M. Pairs. And then what are we going to do that we are going to get E one, E one as I just explained, 440 -50. What about by 0.2, gives us 430 volt. Okay? Now, we substitute in this equation here, E one over e two, IA one in one, IA 22, like this. So E one over E two, IA one, omega one over omegatorN one over N two. E one, 430 as was obtained and E two, we can obtain it, and then we can obtain the new resistance. So if we get E two, let's say we got E two without this, E two equal Vterm minus I armature two multiplied by the new resistance because we add the resistance in the second case. Vternal 500 I armature two, we already obtained it here, so we can get the new resistance. So by solving this equation, we can E two. We can substitute with this or we get E two, and then we get RA two. So the new resistance will be 6.7. Now, if I would like to add the value of the series resistance, which is inserted in serosm so we have 0.2, and I added another resistance. So I will have to subtract from this 0.2 to get the added or the extra resistance. 128. Starting of DC Machines: Hey, guys and welcome to another lesson. In today's lesson, we will discuss an important topic which is the starting of our DC machines. So what I mean by starting of DC machines? Well, you will find that when we start our DC machine, at the very beginning, the electrical machines take very large amount of current, which can exceed even the rated current. Now, why is this happening? Now, remember that we have E or the BMF. Equal to five Z N P over a right XTA. At the very beginning of our electrical machine, DC motor, we have our supply, V terminal. That gives us a current. One current goes to the armature and one goes to the shunt to provide excitation. At the very beginning of DC motors, the speed of this motor is equal to zero, right? So it means that at the very beginning when N equal to zero, the BMF equal to zero. So what is the problem of this. You'll find that at the very beginning that the equation of current is equal to V minus EB right from QVL here, from QVL here, divided by our armature. So when EB or at the very beginning, EB equal to zero, it will be armature will be V terminal over R armature. Now, this value can reach six to eight times the value of the rated current, which is a very large amount of current. So this is actually a problem in starting of DC machines. So at starting of the motor, the motor is stationary, so the speed is equal to zero, Ebike equal to zero. V over RA is very large. This high starting current has some issues. Number one, it can cause the burning of the armature due to excessive heating. Number two, why excessive heating? Because the heating is as a result of IA square multiplied by R armature. The power loss is very high at the very beginning. Damage of commutator and the process because they cannot withstand this amount of large current. In addition to excessive voltage drop, you can see that voltage drop here, IA multi blood by the resistance. Since I is very large, then voltage drop on the armature is very large. So in order to avoid this starting effect, we add a variable resistance in series with our armature. This variable resistance is known as the starting resistance. Okay? So this resistance is variable. We add it at the very beginning of our electrical machine. So when we add an additional resistance, or starting, current this resistance will increase leading to current going down, okay? Now, as you will see that this resistance is variable. It is not a constant resistance. We change it as it is reduced as the motor gains speed, and it cuts out completely after the motor gains its own full speed, okay? So what you can see that this is a configuration that you will find in many electrical machines. We have our terminal voltage. We have our field winding here or F and the inductance of the field. This is our field winding and we have our induced EMF or the rmiture circuit. Now in series of the armature circuit, we will have our variable resistance, the starting resistance. Okay? So what you can see that at the beginning, when the motor is off, this is open circuit, okay? We don't have any kind of supply. Okay? Now, when the motor starts when the motor starts, as you can see here, when the connected Dicim was to be started, the, the lever here turn it gradually to the right. So it starts at the first position of like this. So we'll have all of this resistance or all of this added in series, which makes, so it will be plus R a one or R one, whatever it is. Okay? So the current will be limited. Instead of having six times or eight times or whatever, it will be reduced to the specific value that I need. Let's say, for example, maximum two times the rated current. Okay, so when liver touches 0.1, the field winding is connected to, as you can see, connected to the supply, and the armature winding gets connected with resistance R one to R five. So we have one, two, three, four, five, five resistance in series. Now, during starting at which we will have zero B F, the full resistance is added in series with the armature winding. Okay? So what you will find that the speed of the motor starts going up, so as the speed of motors went N, instead of being zero, it will start going up. So what does this mean? EBA also will start going up? Okay? So EBC will start going up. So what I'm going to do if I keep everything, if I keep this resistance, the current will start going down more. So what I'm going to do that I will start removing resistance. So instead of having this large resistance, I will have a smaller one, this only. Okay, by removing this and connecting to number two. So we will have smaller resistance making current going up again, et cetera. As the speed reach the rated speed, we cut this resistance completely from the armature circuit. And in this case, we are going to be connected at the position, this position, which is the run position using an electromagnet. Okay. So what you can see that here, this position will be our final position. You can see that the current from the supply will go like this, part of it will go to the field, and the other part will go like this through the armchu. So we will not have any kind of resistance at the run position. And this electromagnet keeps holding the position at run until we disconnect our supply. So this will return back to the off position automatically when there is no supply voltage. 129. Example 3: Now let's have an example, number three, in order to understand how are we going to do the starting method. So, number one, we have a DC machine of a ten kilowatt, 1,000 RBM and an armature resistance of 0.1. Connected to 100 volt DC supply. So our supply here, 100 volt and the resistance of the armature 0.1. Determine the starting current if no starting resistance is uplied and the rated current of the machine, find the value of RE E to limit the current to double its rated value, the starting current to limit the current to double its rated value and find the value of resistance steps and number of steps to limit the current between 100% to 100% of the rated v. This is basically the design of starting of the machine. Okay, so let's start step by step. Number one, we need starting current. We know that from KVL that I armature equal to V terminal minus EBC over armature. Now at starting, E BAC is equal to zero. So our mature at starting will be Vternal over RA. Vtermal 100 volt dishes app R armature 0.1. So this is the first solution. I start without any starting resistance equal to 1,000 ampirs. Okay? What about the ritt current of the machine? Okay, how can I get it very easy? As you can see that we have ten kilowatt. So we have power equal to ten kilowatt. And we have our voltage equal to 100 volt. So we can say that the starting current will be or the rated current of the machine is 10/100 volt. So ten kilowatt divided by 100 gives us 100 hundred am pairs. Okay? Great. What we can see here right now is that the starting current compared to rated current, starting current is ten times I rated. Right? So very large amount of current that can damage our windings or our machine, commutators, process everything. So what I'm going to do is that I need a resistance to be added to limit the current to double its value. So double its value, it means that the current will be two multi blood by rated, which means 200 and B. That is the current I need maximum current at starting. Okay? So our current equal to V terminal over R armature plus the additional resistance R E one, okay? So our current 200 pairs, V terminal, 100 volt, and RA plus RE, RAE. Okay? Okay, so armature 0.1, and you can get RE. So as you can see here, equal to 200 and pairs, V terminal over the new resistance plus the armature resistance. This gives us the starting resistance to P 0.4. So what this resistance, exactly all of this. R one equal to 0.4 s in series with the Rmitre resistance of 0.1 s. Okay? Now, what I'm going to do or the next requirement that I need to know the value of resistance steps and the number of steps to limit currenty 100-200. I need to know how many steps we have and the resistance of each step. So how can I do this? Let's understand what I need exactly. So here, as you can see, that we need to limit our current between 100 and pair, which is the rated to double rated value. So at starting, since we added EE at starting at the very beginning, all of our resistance here, all of our resistance, our current at the very beginning when EB equal to zero, at the beginning, the current will be 200 and pairs, right? And we know that and we know that as the speed goes up with this motor, EBA will go up. As EBA go up, I armature will start going down. Here we still have the resistance. We still have R one, as speed increase, the EPAC increase, I armature will start going down. As you can see, it will start going down. Until reaching the hundred am pairs. If I don't do anything, if I don't do or remove the resistance, any part of the resistance, then the current will start going down like this. Be EBAC increase at the same resistance, I armature will keep going down. So I don't need this. I want it to fluctuate 100-200, 100-200. So at this point, I will prevent it from going down. How can I prevent it from going down by removing some resistance to make it go up to 200 am pairs once more. Okay. So at this point, at this point when it drops down to 100 am pairs, I I will remove part of the resistance, make the new resistance R E two, remove this one and make new resistance R E two. So when the resistance goes down, the current will start going up once more to the 200 am pairs point. And then after EBAC increases once more, current will start dropping again, right? And then when it reaches 100 am pairs, I will remove another resistance, this one, so we will have R E and et cetera. So let's see what are we going to do exactly, okay? So number one, I have here RE one equal 0.4, the whole resistance. I would like to know when the current drops down to 100 am pairs, when I A equal to 100 am pairs, what is the EBC generated? So we have RA plus R E one. This is 0.4, this is 100 volt. This one is 0.1. And I would like to know the new EBAC when the current drops down to 100 pairs. The EPAC that makes it goes all the way down to 100 am pairs. So like this, so EBC will be I armature or armature, V minus I armature or arm, V minus I armature or mg. So we have 100 volt or supply -100 ampers at this point, minus the total resistance, which is 0.1 plus 0.4. So it means that in order for our curret to go 200-100, we need 50 volt generated as a EBC. Okay? Very nice. Now I would like to at this specific point when we have EBC equal 50, I would like to make the current go up again to 200 and bears. In order for the current so the current will be V minus EBAC divided by the resistance. So I will get the new resistance right now. So our E, our current will go 100-200 by removing a resistance. So I would like to know at this point, what is the new R. What is R E two, this resistance. So I don't like the resistance, and I know that the current will be 200 and pairs, at the same EBC 50 volt, with the same supply 100 volt. So what about the new resistance? So again, here, it will be 100 -50/200 gives us the new resistance. So in order for the current to go up again, we need the resistance to drop down from 0.4, okay? No 0.4 only. Okay? Remember that the total resistance for this equation, this total originally is R one plus R R metre. Okay? This is our total resistance. Okay, which was originally 0.4 plus 0.1 gives us 0.5. Okay. Now, here the new resistance will be 0.25. Okay, the new resistance will be 0.25. So what is our resistance right now or what is our drop right now? So our resistance was originally 0.5. It will be now 0.25, which is R E two, which is this resistance. The new resistance 0.25 is R two plus the armature resistance, right? This is a resistant to resistance that will make it 200 and pairs once more. So in order to get RE two only, I will subtract from this value RMatar value. So it will be 0.25 -0.1, which is the Rmture resistance, gives us 0.15 ms. So again, if you don't understand it, let's repeat this. So we have originally a resistance of 0.4. Which is a total starting resistance plus 0.1, which is armature resistance, which is 0.5. Now, in order to make the current it goes from 100 and pairs to 200 pairs, the resistance will go half half its value, which is 0.25, right? So the new resistance here of this armature at this position, for example, it will be this resistance plus armature resistance. So I would like to know this is step only. This step only, the part only is 0.15 ms after subtracting our niche. Now, what again, I'm going to wait for the current to go down due to increase in EBAG. So I would like to know new EBC, so the hundred am pairs at this point, when the resistance will be R armor plus R E two, right at the new resistance, which is all of this is 0.25 and terminal 100 volt. Now, get the new E back so EPAC will be V terminal minus IAR a two, which is the 0.15 plus 0.1, which is 0.25. This will give us a new back EMF 75. Now I will remove another resistance. To get E, I will remove a resistance. So we are going to step number three to raise the current once more to 200 and pair. Okay? So to raise it again to 200 and pair, it will be V minus EBC over 200 pairs, V minus EBC over 200 pairs, which will be 0.125. Now remember, this resistance here, the new resistance is the variable resistance R plus R RMture. In order to get only Re three, I will remove 0.21, which is the resistance of the armature. Gives us this step of 0.0 25s. So we have RE one RE two and Re, right? Okay. Now what? Now, I would like to know the next step. To get the next step, simply, we have. At this point, current goes down to 100 pairs. So at 100 pairs, I would like to know EBC at the new resistance, the new resistance, which is 0.125. Okay, and the back 100 like this. So the new EBA will be 100 minus I armature 100 multiplied by 0.125, gives us 87.5. Similarly, I would like to know what will happen next. I would like to know at a 200 and pair. What will be our resistance? So RA to increase the current, 200 pairs will be V terminal, which is 100 minus the new EBAC divided by the current 200 pairs. So it gives us the new resistance 0.062. So for the current to go from here to here, we should have a resistance of 0.0 625. This resistance is R armature plus R E four, right? However, as you can see, our armature itself alone is 0.1, which means it is not possible. Which means this one is the last point for us. How can I know this? If you subtract 0.1, which is the resistance of the armature, then what will be RE four? RE four will be a negative value, which is rejected, right? We can add a negative resistance. So in this case, we will have only like this we have resistance 1-2, resistance 2-3, right? And then we will have the run position. So how many steps do you have? We have one, two, and three, right? Resistance, R E one, E two, and three. Three like this. So what are the resistance that we have? Or the value of the resistance. How many, how many or the value of the resistance or one or two or three, R one will be this resistance, this resistance will be RE one minus R E two. R two will be R E two minus R three, three e three minus RE four, like this. Now, of course, we don't accept R one and R two because we don't have RY because R is three minus Re four and R four is a negative value. So we don't have this step here. So we only have two resistance R one and R two. So it will be like this. As if we have so let me draw it for you, these steps, we have one, two, and we have one, two, three, and the run position. Run, right, like here, one, two, three, four, five, and between it and the run, there is a resistance. Okay? So this is our starting. So one, first resistance will be 0.25. Second resistance will be 0.125 ms, Okay? And the last one is this one, Ret which is 0.025. Now, as you can see, at the very beginning, we take all of this R, which will be if you sum all of this, it will be 0.4 s. In the second deposition like this, we will have all of this resistance, which will be 0.25, right? 0.15, right? RE two, 0.15, all of this. Then on the last addition or step three, we will have 0.025. And then after this, we will go to the run position. Okay? So this is how you design the starting of a DC machine. 130. DC Motor Simulation Using Simscape in MATLAB: Hi everyone. In this video we would like to learn how to add a DC motor, doozy Simulink and simulate this DC motor. Previously, we just did DC model for the DC motor or a model for the DC motor in science, I simulate anchor by obtaining the electrical and mechanical equations and the electromechanical conversion between them. Now in this video we are going to get an actual DC motor using that power library inside Z MATLAB and do some simulation on this DC machine. So first we are going to New, now using Z 2019 MATLAB. Before I was using it at 2015 and I am now using that winter 19. Show you the difference between them. You will find that there are 2019 have more features of courses in 2015, but not a big difference. Store by clicking on new Zen Simulink model. Xin gong to choose a blank model, create a model. Okay, so now we opened the window for Z model, which you are going to add to it. Then we're going to use the Simulink library similar as before. Now, when we open our window, now we would like to get a DC machine. Dc machine. Now we have our DC machine, as you'll see here is this is our DC machine in the library of Simscape, since it is an actual or physical component and not z model of the DC machine. So we'll find that when we point at it, you will find that power library, machines, dc machine. So this forums power library. Now right-click and add block those the model untitled go into here and maximize it like this. This is our DC machine. You will find that a plus a minus this representing z are Mitchell, zap positive terminal of the armature and the negative terminal of the armature where we bought our in what DC supply. And you'll find f of positive and negative, this representing dizzy field winding of the DC machine. And then we have two terminals here. One here for z measurement. M means the measurement where we can display our values or measure our varies using the school. We have TL or the load torque where it is input to our machine. Now, we need at first as Z MBO DC supply. So let's open our Simulink library, then add a voltage source. Now we will find here a lot of voltage source. As an example, you will find that this one is power library, electrical sources, DC volt source. So this one is the one which show will be able to add it to the block. Why? Because it is from z power library. Let's maximize. So if you dig this one here, it will be connected normally. And if we connect it to the other terminal here, it will be connected normally. Why? Because this one is from DePaul Library and this one also from Zippo library. So RZ are from the same section or the same board of Z library. Now, as an example, you will find here when I click voltage source, let us see another one, such as this one. You will find that this is from E library. So add the block like this, this voltage source. Let's see if we can add it or not. By taking this terminal here. The field, you will find that it is not accepted. Why? Because this one is from a different library, Zan and xhat DC machine itself. There is this one exists. Going back again. We have another DC voltage source, this one. And we have another one way. Are we aware this battery, for example. Then close. If we selected CSA battery or this DC voltage or exists, it will not be accepted. Why? Because it is not from the same library. If we're connected this one here, it cannot be accepted. Why? Because this one and this one are from the frontal hypothyroidism. If we go back. This one, this is from E library. This one is from FL library. And this one is from e-library, but this one is from the power library, Zippo library, similar to the DC machine. So if we get back to the DC machine, DC machine, like this, you, if we look at it, you will find that it is power library machines, DC machine. We have to select the components from the same library. We have our DC voltage elastic Control and drag to copy it. The Control R to rotate like this. This is the input DC voltage or supply DC voltages to our machine. And here's a field winding, so connected this one here exists. And the negative term now we see a negative term. I will find the year f of positive and negative. If we double-click on the DC machine, you will find that we can choose our model. You'll have a different types of Z motors here available in MATLAB, 250 old superpower dollars, twenty five and so on with a different air rated RPM, or the speed, the speed of the machine. 500 voltage here representing the z in both DC voltage set of 100 volt DC, representing a z field voltage going up here. And as an example, we are going to choose 240 volt or 150 volts. 240 volts as an input DC voltage or armature voltage. And 150 volts affords a field winding. Selected this one, and click on. Okay. So we have the input 240. We have the output, which is 150. This is not the output but the field winding. Okay? What is the remaining single number one, Z load torque. Load torque. We will assume that it is a step function. We are boating our load from 0 up to the maximum value in an instant. Step. Going like this, choosing this one. Let's see, it is, this one is Simulink sources a step. So this one is used for every block diagrams, ad block to the model untitled. Come here. Select this one here. Like this. This is a step input for our torque load, or ETL. This one is z in both DC voltage. Now, this one is here. In both field voltage. We have the load. This is the load which is applied to our motors. This is the input DC voltage, input field winding. And we need some measurements. So we would need two things here. Number one, we need the scope, okay, school, school. Enter the block to the model untitled. And we need also that display. And I will tell you now why. Display and enter the block to the model untitled. We have that display. What does that this belay do. It shows us Z values of Z motor during the simulation and after the simulation as if it was a display in the actual or real life. You will see now the difference between them. Okay, now adding the scope like this, and then we have our scope, these blades z in PyTorch and every single. Now let's run that simulation. You will find that here an error. Showing his commands though cannot be evaluated. What is the error of this one? Without thinking, you will find that z power go, we, you block does not exist. So we have to go to z power, z power block to the model entitled this one is, this block is very important. Han, always give me yours. If I didn't talk about it, then rotten again. Now we will find that z Simulink program. Both lie exists. Our program now for Simulink shows us the output values such as the speed, the current Z omega, or as r Omega, or the angular velocity, the current, the torque, and so on. Some values which is related to the DC machine. Now if we open our score, you will find that here, our program. So always us z variation in z value such as here, going from the yellow one, for example, going up and going down until reaching 1093 as I think from here. Another value here, going up. Okay, let's see. Let's zoom in. Plus. Kayla exists. Now, choosing x0 will find you. Is this, is that yellow? I think I zoomed in very much. Okay, but anyway, going up and Xin reaching its steady state. Now for the other values here, for the blue and green values, you will find here starting from high-value exists and going down until reaching steady-state value. Here for Zim. Finds that weekend zoom in and out from here. You will find here his own Zoom x is on, y, zoom out and zoom in. So we clicked zoom out. Like this. We can choose a Zoom Out tool. You can find the diagram more clearly. Now I would like to show you on as our sink here inside the program for Z MATLAB 2019, the front from 2015. You will find that when we right-click, we can restore view. We can. Let's just delete this one right-click and you'll find here are different configurations different from before. Before when I click on right-click it, select the Z autoscale. But now in this program I cannot right-click and selecting or scaling or funds that the program automatically gives you the most appropriate view for Z simulation. Now on, as I was saying you a few click here. You'll find here is a configuration properties or right-click configuration properties. You will find here is that I have the option open adds as a mutation and stored. So if I click selected as a swan and apply. So by selecting this, you will find that z simulation. We'll start automatically after clicking on zeros and bottom. Another thing is that in the display case, sometimes if you don't see this graph inside the program, you will find that the problem is that I selected that limit data points to the last 5 thousand. Now if I click on this one, you will find that sometimes the program will give you starting from line, for example, yours finds that all of the previous values does not exist. Only this part, only. When you find that this part only exists. You have two unmarked because this one, because it will limit z data points to Z lost 5 thousand. So clicking on Okay, now it has no limit. I can draw all of the fever. The last equation is that what is this values? This value is number one is from the 4s as beat omega or rotationally speed in radians per second for the motor. The second value is the value of the armature current. Value is the value of z field, the current, and the lost value is the output torque. Okay? So those are the values which are output from our DC mode. And the weeds blades is values on our school. As an example, all of these values, you will find all of them except Z, Z, omega. This is only single, does not show here you will find that all of the virus, such as the field, the current, armature current and the electromagnetic torque appears here. Z lost evaluate, which is for z bid or Z omega is on the higher value. So if we zoom out it exists. You will find here is that now this value of which is representing the speed now appear starting from 0, going up and reaching a steady state. In this video, we learned how to add a DC motor and simulate it using Simulink in MATLAB. 131. Construction And Principle Of Operation Of Synchronous Generator: Hi. Everyone in this part for the course who are going toe discusses easing Chronos machines. So first in this video, we are going to discuss the importance off these in Cronus Machine and Z construction off synchronous machines. So the importance off synchronous machines, the number ones they are Azizi. Chronic generators are the dominant, the type off electric generators in power system. You will find that nearly more than 90% off the generators inside the power system are synchro nous generators. Okay, so there's Syncronys generators are really important to understand. Zen number two was that's in krone generators. Unlike see, induction generators which we are going to discuss in the induction and machines part have the capability to produce active power and the active power. You know that the power or the electric power generated boy generators is equal to S s is the apparent power or the power generated by a machine. It is measured in a kilo vault And there this power is divided in tow, the actor power being and the reactive power Q. Okay. Zp is measured in kill what? And the Q is measured in kilo vote. Okay, so the electrical power generated by synchronous generator are divided in tow. ZB or the actor Power and the Q. The reactive power zippy or the active power is used. Toe does Eos for work and side seam machines, for example, Z insides, for example. The lambs it produces e light required okay? Or the losses inside the resistance. Thank you! Is the power or the reactor power, which does not do any useful work, is this. Q is required for the induct ance. Inside the power system they are required in order to produce is a magnet ization for Z machines itself, so the machines absorb posts. Q and B Okay, is the machines which I am discussing is the machines or, like the induction motors, okay, and the inductions in aerators that cannot reduce reactive power. They produce actor power only. Okay, you'll find as a deduction generator requires magnetron ization, same as e. D. C. Machines. As you remember, DC machines in separately. Excited, we had the separate polls connected to a separate D C supply toe produces the magnetic field there quart or the flux it required. Similarly, in the induction generators, we will need several missiles in orderto reduce is a magnet ization inside seeing machine these are by connecting is the inductions in the retort to Sigrid or the power system. So it absorbs sick you, which is required before the magnetism ation for the machine. Or it is a self excited induction generator. And in this case, who will need capacitors? Okay, so in any case, is the induction generator only produce active power. But this in Corona genetic, as we will discuss in this part off the course you will find it can produce Xabi, which is the active power, and the produces a Q which is a reactive power. They have armature on the state, or so as you remember that inside that d C machines we had the armature on seeing as on the rotor and we had communicator and the process. Okay, but in synchronous machines, we can put the armature on the state or or on zero. Okay, but enlarging machines we prefer towboat ZR measure on the state in orderto collective power is me from it without with the usage off any process or communicators. So it is easy to collect apart from them and they can be designed for high voltage. Okay, because in this case, there would be no spark us. Since it is only the state. Or which means it is a stationary, they remain a synchronized whizzed Oppa's what does mean same organization. We will understand this in the on this part. OK, but in another lecture and synchronized, always honors are alternators, and they have common working frequency and one common Walt it. So just to give you some information about sink organization, as they have the same voltage, they say frequency the same phase shift and so on. So that is what is meant by synchronization. Okay, so that empower systems, as in Qana generators when they are connected to regret all of them have the same frequency , and all of them have the same terminal Voltage. Now we would like to discuss is equal misdirection off that messing coolness machine. This includes machine consisting off three main parts. Number one is the state or your funding, or the state or and you'll find here, consisting off slots where we put the state or winding, or the armature winding and second part, which is rotor, and you'll find it consisting off balls or it is used to produce the flux connected toe A. D. C. Supply and the between the state and rotor, as all types off machine we have is the air game now, Was he staedel? It is made off silicon sheet. This stato is made off a grove off Sercan sheets and it is laminated again. Why? Or divided in tow, A group of sheets or eliminations? Why, in orderto reduce the tickets for the old, For your knowledge, you know that as the lamination means that I'm dividing into in tow sheets. Okay, one sheet, better toe. Let's make it like this one sheet like this and parallel to it on us off sheet. And but I do it on another sheet and so on. So the state or consisting off a grope off sheets. Okay. Okay. Like this. That sheet itself increases the daughter resistance. Okay. Off the court so that eddy currents will be limited their eliminations or dividing it into sheets reduces the eddy currents inside the state Since it is exposed, Atos the flux off the road. It is off course cylindrical and slowed it from its and our surface. You'll find a consistent off a group off slots. Where we bought is a state of wine now, the most important Bart. It carries the armature winding. Okay, so we have your inside, the slots armature winding and it consisting off as three wine ings shifted by 120 degree in space. So why remember that? Which is very important for you that the synchro nous generators produce a three phase power or a three phase out with power? That's three phase power is the identical message off generation off electricity. So it's a three phase we have Empower system. We have city face for example, A and B and C or RST radio blow or whatever. And we have here the three phase that's Reef is a voltage V, a, VB and DVC. So we would like toe is generate. From that, I think Rana generator as three phase like this, consisting off of all TGV. All of them have the same value V, but the angle is different. Is science sine wave or may get team and the other one is signed Omega T but Shifted Boy 120 degree minus 120 and does he lost one is also sign Omega T minus or plus 200. Minus 240 or plus 120 or plus 100 and 20. Okay, so we have a three phase. We have V A V V V screen. The three phase are put off the Syncronys generator V A V v V C as I ve is Venus sine omega team. Same maximum value V v V. This one is assigned with sine omega T with a zero shift. The 2nd 1 is sine omega T minus 120. This means that B is lagging from a boy 120 degree. Okay, so be shifted from a by 120 degree and see shifted from B by another 120 degree. So minus 214 can be written as last 120 because, as you know, that sign Sita or set up plus 360 degree, A similar toe sign seat. Okay, So adding as 360 degree does not change the sign. So we need to produce a three phase voltage shifted by 120 degree. So we have in the state or which is considered as the arable off the synchronous generator . See why endings shifted by 100 to integrate, for example, a will be like this, then shifted by 100 lei being then shifted by Another 100. Agree, See, And you'll find that for example, Z is entering from here and going here We have a and a dash. One of them is the winding entering and the other is leaving. Okay, When we of course one dizzy wrote or around dizzy armature. We should have the entering and we have the living and the B and B dash. Okay, one off them is the one entering and the other part winner where its is leaving and sees he dish. Okay, so we have a B and C are shifted by 120 degree the angle from here to here 120 end from here to here. Another 120. Okay, so in this case, that shift in the winding will help us to produce Z three phase out would vaulted shifted by 120 degree. It consists off slots which can be open or semi closed or closed whatever. There is a different configurations for the slots itself. This is the case off the design off that sink Rama's machine. But in real life, this information is not really important for an electrical power engineer unless you're off course working in the design off machines now is the rotor consisting off. It carries that field winding of the machine. Remember that we said that inside. See, as in Cronos Machine, we need city parts. We need number one Z generation off, as he, of course, number ones in mechanical power. Is the movement off the rotor? Number two. We said that we need excitation and doing it conductors. So we have here the conductors, which is a state or armature winding. And we have the magnetism ation representing a boys if it's the winding on the photo and this rotor is rotating, so we have mechanical power so we can generate electricity so it carries the feed one off the machine. It can be easy or a civilian or non salient. Cylindrical rotor or non segment is a cylindrical, so the rotor has two times one, which is called dizzy, Syrian to type, and the other which is called a non salient time. Now we need toe camber between the store rotors. Okay, so at first we have a roto here, which is a cylindrical or non salient. And we have here is a Silien Marotta, which is salient aboard rotor. That difference between Samuel finds it here. It's consisting off and armature winding. Okay, the feed one is in the form off armature winding. But the field here is consists off off a group off bulls, okay. And the state, Or as it is off course. So the Syrian topo rotor number one it consists off bores as a separate parts. Fix it so zero or fund. Here we have a born and we have another one here. And another one here and another one here. So each off this bone isf exito the rotor and separate from each other. The field one off. The polls are connected in serious as you remember that when we talked about that d c machines state, or we said that it consistent off a group of wars, and they have a winding connecting between all of them. Why toe have the same current to produce the same flux It has high number off boards, which means slow generators. So it finds that is that Cillian to pull type, which means that we have high number off boards. Salient means high number off wars, which means a slow generates and will understand now Why? Because the speed off synchronous machine is given point. Okay, there is a relation between the speed off that's in Cronus. Machine in rpm was respected. Toe the frequency and dizzy number off yours. So n or the speed off the synchronous machine equal toe sacristy F which is a frequency over the number off pool players members that we are talking here about full pair, not Z bulls, not the total number off bulls. Now, if we look at this machine, for example, is this machine for examine? You will see that we have one toe. 34 We have four pools and we have to pull pair. You will find that end north and south, representing one pull beer and another N s, which represent another will bear. So the total number off full bears in this figure is to pull pairs. So it finds that Wednesday number off bulls increase or pull pair increases. Zs in Chronos is weed off that generator air off the machine or the generator is reduced. Okay, that's why having high number of balls means slow generators, and this happens inside the salient type. So Z this type off generators or the salient a poor rotor is used in hydro generators where the speed off the water is slow. Convert toe other times. So we use hydro generators, which have high number off pores. So it means that the speed off the generator is low. But for the non salient to type this time it consisting off number one it is used the with Hizb e generators. Why? Because it has a low number off bulls. It has a low number of boards, which means high is beat it consisting off one solid steel block to withstand high centrifugal force. Remember that we have here one block. You see that here as a one block and you'll find that this you'll find that this one is a dot and this one is X X and a lot representing what representing exit means that Z whining is entering like this. Okay, Z one is entering NZ current is entering and docked means that the current is leaving out of page coming out from the beach. So that means that it is entering and Theo X means entering on dot means leaving. Okay, so we'll find that the flux will be in this direction. So this party representing the North and this part of resembling this house in the cylindrical router or the non salient rotor it consisting off one look like this it consisting for separate part. Why one block means that it can withstand the high centrifugal force and gets off high is beat. And, of course, it has lost to carry the field one slots, same as the armature wine. The last part off this machine is called the Air Gap, as we discussed before that clearance between the stool, the state or an zero, or the state or and field whining it representing and mechanical clearance between water and state of so that the rotor can rotate without off course, a fraction off the state. It is used, of course, for calling off the machine, and, of course, energy conversion takes place here. Mechanical to electrical or vice versa. Remember that Wednesay Roto dates with the flux. It's a flux of cuts of the state or and a produce electric energy. Now we would like to understand. Is the principal off operation off the cinchona generator? Now we have that Strief is winding on the state of this one for his number one phase number two and phase number three now is this reef is winding. We would like toa breed yours electricity inside them. So as you remember that in order to produce electricity, we need that E or the induced A meth inside Z machine, is it? What? Tonegative and defy over DT. Okay, we're in representing is the number off the onus off the one? Okay, so the three phase winding here are equivalent to each other. Does he have the same number off Turness? Same reluctance, same area. Reactant seem resistance. And we would like toa have defy but it e what does defy by that? He means we need variation off flocks. So how we can go there. Variation in flux. Simply We connected the rotor which representing a field which is connected to a D. C. Supply somebody. Is this representing a flux? For example, in this direct constant magnitude flux Ferrari is constant. Okay, so if we just about it like this, then no, A meth will be produced. Why? Because there's no variation in flux. So in order, Tobe reduces the variation in flux. What we are going to do. We're going toe. Rotate this. I feel so by rotating this field, The flux seen by each off this whining is the varying was time so enthused a meth will be generated inside this face and this freeze industries, and it will be shifted by 120 degree senses. The Serie phase are shifted in space, so that's in chronic generator works on the principle off for a day. Lows off electromagnetic induction in order to generate electricity is the three face winding. We need variation or flux or variation in a war of tennis. Remember that in order to reduce an image, we need a defy body tea or we need variation in and why? Because in that privation off this law in the beginning off and use the math there waas or consisting off two parts one which is a Fluxus constant and the variation off number off Turness. Always time okay, plus another induced The meth do toe constant the number off terminus and defy by DT. So usually we don't use that the end over DT or the variation off number off Turness was time. We always that defy by duties. That's why this part is zero, since the number off Turness is constant with time number of turns off each off this phases , it's constant. So the end over DT is zero, so we usually use that endures. The meth is defy over DT, so we use the rotation off DC Flux remembers that field winding here is connected. Toa d C supply toe produce a constant DC flux so that this influx in Air Gap actors as a varying infield when we rotate it. That state of winding C is a friend. As a varying field, not a constant field. The invitation of the sea flux appears as a varying. The field does a three phase winding, so the MF will be also generated inside the three phase winding Do does A relative motion between the conductor and the field induces the image and sides you conduct the rotation, he instances be zero and this one has a specific is beat. So this one at Piers or that field the year appears rotating was respected. Toe the state or so the relative motion between them causes that endures the man. But in order to understand, what does this mean if you rotate the state? Or was an example as beat cold, omega and zero toe with a speed cold omega xenzai relative speed between the rule and state , or is equal to zero? This have the same speed. So what does it mean? It means that the endures the my fear will be equal to zero because there is no relative is meat that in Memphis generated will be shifted by 120 degree do told displacement by 120 degree in the space between wine. So the Albert Power will be a three phase shifted boy 120 degree the soft offseason rate or here or the soft off the road, or can be connected toe Hydropower plant can be connected toe a sermon power plant like steam in orderto rotate Z as the rotor, and so on. Okay, according tools, the type off that generate. Now we will have to understand that the induced the image inside Z winding itself Have this relation. Four points 44 Casey, Katie Flux. Frequency defeats defense. Is the number off? Turness off each off this faith number of turns off this face frequency representing Z frequency off the hour. Vaulted with sediments. Off course. Owns this bead off the road. Okay, It's a frequency. Depends on the road or itself. The flux off course. The flux which got zem comes from Z rotor, which cuts the state or wine. Casey and the Katie are a constant, depending on the distribution off the wine. Okay. Depends on the distribution off the winding itself. Certain constants. Okay, 4.4 is on a sort. Of course. OK, we don't want toe goto the proof off this equation, but just a for knowledge, which is not important. Of course, Joseph Owners toe know that the effects is a function in flux. Frequency entity face. So what are the applications off that syncronys generator? That's three facing chronic Juanito hours. Dominant type of generators used a generation off power system off electrical power in power system, transmission off electrical power and distribution off power. So we use the city phase configuration is this city appears so produces a three phase power which is used in generation transmission and distribution off electrical power. So have to understand that think coordinators are really important. Syncronys genitals are used in the nuclear sermon and the hydropower system for generating Z voltage. The vaulted to produce the biasing corona genital is synchronized with the rotational speed off the generator. What doesn't mean? It means that the frequency off the voltage remember that we said for examined V air is a quest toe V sign. Okay, Sigh in omega team. And you know Xanthi Omega is to play effort to boy boy the bad buys he frequents. So the voltage here depends on the frequency. And is the frequency off the thief Abbott, the Bendis on that rotational is beat off the generator. Remember, that end is equal toe sacristy off over being, say, Christie F over B. So that frequency depends on the rotation and his beat. And they are synchronized with each other. The frequency, it was that easy. This frequency changes with us. We'd off the prime mover. This is the case when it's not connected to the infinite pass or cigarette. What does mean this means that when we are not connecting, our generator does regret. Then Z frequency would depend on that. Traditional is beat. Okay, When you are just preparing our machine, Toby synchronized with the infinite bus. By changing the end, we can changes the frequency. Okay, which changed, then it'll just calibrate Z frequency. Okay? Or when we are connecting our generator to a load inside our home as an example, not connected toe a gret. The frequency will change with this beat off the generator. But Wednesay on wins a synchronous generator connected toe the power system. What will happen? The frequency is constant. Frequency is gonna stumped. And that becomes independent on end. Okay, so whatever this beat off, the prime members of frequents would remain Afghanistan, depending on the grid itself. Okay, so the the after connecting the secret originator to regret what will happen when we grease the speed, we can increase the injected power or ejected active power toe zag rate. As will understand in the next lectures the back up. They are used as a back up or stand up stand by generators. They supply electrical power during outage due to homes, businesses and industry. Zack three phase power is transmitted and distributed off course, more economical than single Facebook. They found that the three face is the most efficient way off transmitting electrical power , and it's much more economical than using the single phase power. So in this video, waits cause disease in kroner, generators, deconstruction, importance and applications. And, of course, the weeds caused how does that sequence generator works? 132. Principle Of Operation Of Synchronous Motor: now in this video, we would like to discuss Z, as in Chronos Motors and the principal off operation off this increments motor. So before we discuss Azizi, Cronus Motor, we need to understand a very important concept inside season Cronos machine. So we said before that we had our state or consisting off a three phase winding. ABC shifted by 120 degree and they said we have zero toe, which is considered as if he'd winding, providing the flux required. So we said that A and B and C are shifted by 120 dignity. So the power generated or seapower intertoto the three phase in kids, as in cross motor, would have the following way forms. We said that A, for example, at this instant and this innocent young zero. So it will be a sign or me getting and B will be shifted by 120 degree form A as you see and this thing will be shifted by 120 degrees from B. So that's three phase winding shifted from a Chaucer by 120 degree and in an instant, a or this is seen by a plus, A and B will give us zero or the three phase winding or the submission off the three phase voltage at any instant at this one, for example, will give us zero at here will give us zero at here, Give us zero a and B and sees a submission off them. Zero, as you know that that sine omega t plus sign on me getting minus 120 Blust sine omega team Last 120 degree. The submission off the three phase is always zero. Now the question is that And what is that? Or rotating a field inside us in Conus machine? Okay, the the cutting off Sam they field wining off the or the flux off the field one off the rotor reduces and induced in meth inside the three face. But the induced the meth Francis three face is actually not only is this sign with OK or not only the fundamental frequency, which is f, it's consisting off different frequencies at a different values. So see that here, for example, is the imam meth or the flux reduced by a Remember that this flux cuts disaster relief is producing a city phase voltage induces as 3/5 car. OK, it's a three phase current, which is similar in guests off the Z motor or thank yous Officer generate. So the three faced currents here produces each off them produces field that feed off each off them, which you're representing the armature reaction. Remember that we said that the flux inside the D C machines cut zero toe, which produces current in science. The armature winding Zen's armature winding currents reduces flux, which produces armature action. Now, similarly, here, the total cuts is a three phase winding in the state of producing as three face flux each off this mmf or the magnetic Motive force, or the flux off each off them, Having this equations of three equations here. OK, we are not going to discuss that derivation off these equations because it is really complicated okay, and is not important at all. But for now, what is important for us, you will find that it is our function in they're a cosine Omega T design Omega T minus 220 cause I know Omega T plus 100. And doing this representing is the phase shift in currents okay or in the face, Shift in voltage by 120 degree. Another shift which is signed in the Sita. Flying in the seat A minus 120. Sign any Sita. Plus 120. This free shift is produced to do Does a three phase shift in space A and B and C are shifted by 120 degree in space. Okay. Or mechanic? Any shifted by 120 degree. So there is a two shift one. Do you dozy shift mechanically and the other one shift electrically boy Z currents. Now, if we took the three phase flexes, that's a mission. Off the three fistful axis, we will have the MMF or the magnetic Motive Force off the city fears. Well, give us three over tow for maximum or that four of our boy if a maximum science et minus omega team. So this is a some mission off the three face full access. Okay, you'll find it is a maximum value sign. See the minus omega T. Now we will find it is a function in CDA or space and the function in Omega T or the electrical ANC. Now What does it mean? It means that now let's see it step by step. Now, at the beginning, we're assuming that at an instant off Omega T cords. You okay? We assume at this point where a zero at here. Okay, Z Omega teen is equal to equal to zero. Okay, so it finds that the mmf equal maximum value Science eater sign seat. Okay. At what at omega T equals he adds a time equal to zero. So if we draw the mmf as this innocent, it will be like this. Okay. As a function off, what? As a function off cedars. So Sita with same MF Okay, At what? At omega t equals zero. So it means that at a zero time the flux will change with the mechanical seat. So if we draws a mechanical seat assuming that starting from here, this is at an innocent seat. Alexis okay, is this is our angle seat? Ok, assuming starting from a tow any instant, the angle here is called the seat. So you will find that this wave is applied here at a time off zero. The wave will be like this. Going ally exists is in line exists and legs this. Okay, So, for example, the flux here is zero flux. Here at this Sita is maximum flux here and sissy, that zero flux here at this sita is negative. Maximum. Okay, so this is, at a time equal to zero. Okay, so the flux year will be the front from here. The front from here, As you see here, maximum. They are negative. Maximum 00 Okay, now, if we talk on other instant, for example, at omega T equal to 60. Okay. So what happened in this case, you will find that simply that this reform will be shifted. Okay, See it? Ah, minus 60. What does mean? It means that we are lagging boy and anger equal to 60. So this, for example, representing Omega team equal to 60 degree. Okay, so this is at Omega Tick or 60? It'll be drawn. Likes is now how we can apply it to our machine. It will be at this example. Citic. Well, 60 at omega T 60. Sorry. Omega t Quite 60. You'll find that the voltage will be like this. Okay. If it continues that way for much is sign and Sita. It will be like this gay like this. So we'll find that the maximum at omega t zero. It'll make it equal zero waas at here. Okay, Adds this ankle now is the maximum shifted like here. So as the omega T or time passes, the way form itself is shifted exists. And at another instant, it would be like assist. Another instant will be law exists. And another instant will be Alexis. So find it as if we have a wave and the moving along the Z machine this way for or this wave, what does it represent? Representing the total image off the three face. And it's called the rotating field inside a synchronous machine. Your fund, it is rotating along is a machine with a constant maximum value. As if we are moving this way form from here to here to here to here as time boss. Okay, Now, again, the F or the mmf off the three face with respect to toe seat or the angle at the Omega T equals zero, it will be thrown like this. Okay, continuing. It likes us at another Omega T equal 60 degree, it will be shifted. Boy, a 60 likes us and at another angle shifted and an extended shifted and so on. So this reform is like it is moving, so it's called a rotating magnetic field. So the three phase here at any instant Omega T here equals zero here, equals zero, Then moving, moving, moving the values or omega T is increasing. And you're finds here that this reform is rotating as time bosses is the way form or the flux. The total image meth or the result on the flux is rotating. So this is called inside the machine. A rotating defeat now at an instant, for example, at here, OK, at instant, for example. Let's remove all of this to understand. For example, at Omega T equals zero, we said it will be like this. OK, so we have this part is maximum voltage, and this part is maximum negative. This can be representing a north, and this representing s house and this North is moving along is a machine since it is a rotating field, so find that it is rotating. The North is rotating okay, along with this house, so sometimes the North will seize this house, and sometimes the North will seize the North remembers that we said that the field is rotating So at another incentive seen also will be here at another innocently and also will be here at another. Innocent will be here and so on. So sometimes the North Caesar Sau was off zero toe. Sometimes this house sees sometimes in north sees a Norse and so on. Okay, we are talking here about this in Chronos mode. Now this part is stationary and we have a rotating field seeing the different pulls off the road. So we need to understand the principle off operation off the synchronous motor. So we have these synchronous motors are audibly excited machine What does it mean? It means that we need to excitation or more Flux is one from the rotor which provides at D C flux and the other from the three feet supply which provides that rotating If he in this type of mortars, we apply three fairs supply toe the state or and D C supply 202 at starting. We have a stationary feed off total. Okay, since we need, as in Chronos Motor, which means we need mechanical power. So this one is a stationary does not move and produce a stationary flux of, like this one north and south. And we have the three phase rotating. If we said that moves are like here, sometimes on was here, north year at another instant Morsi year. Another innocents North Sea year another instead, Ramos here, another instant north here. So what does it mean at a particular instant at certain Omega team, the rotor and state of port Z state or balls which are represented by rotating the field and state or polls as a row Torture presented by S and the N and Dizzy state or which is a rotating field? Sometimes it have a similar bright and in or S s north seas on other north at here north, this is on north and that another innocent it can be north seeing the South's or this house off the rotating. If he'd see, is this house all this house off the rotating feed seasonals. So sometimes when they are equal because our repulsion force and the tunnels are innocent, they are in s which because an attraction force or attractive force. So the due to the presence off inertia off zero toe the motor will not be affected or the rotor will not be affected by the attraction forces or the movement or there forces produced by the attraction forces. So that rotor or that synchronous motor will not be able to rotate in any direction. Dude Oh, that attractive or repulsive force. So what does it mean? It means that these in Chronos Motor is not a cell for starting now. So this is why is that? Synchronous motor is not widely used because it does not. I or it is not a self starting are like the induction machine which is a cell for starting induction or in self starting motor, and also can control. It's his beat. But the synchronous motor speed depends on the frequency off the supply. Okay, so it has one constant is beat or we need to change the frequency. So we need NZ beginning some mechanical coupling toe rotate Z rotor at the beginning, in the same direction as a magnetic field. That was a speed Carlos does us increments his beat. So we need toe rotate zero toe with an external Dr such as D C machine or induction motor. Until Sami magnetic looking Coker's. So we rotate sea route or at a speed close towards us in grants beat or and when a shaving possessing crosses with the magnetic looking occurs, it means that the North sees the south's and looks with it, and the rotating field causes the rotor to rotate with it. Okay, then, after this weekend removes the external mechanical public. So in this case, we need message off. Starting off synchronous motor number one weekend started the motor by external prime over , for example, we have here our synchronous machine okay, giving it the three phase winding or the three piece in both supply. And we've and we have here Z for example z DC motor or induction motor this motor and rotating it or causing it toe was in supplies. Is the mechanical power required? The tour rotates a synchronous motor or start disease in Qana Small. So is this. Synchronous motors are mechanically coupled with another. This motor can be a three phase induction mortal or a DC motor. We don't apply that D c excitation initially, what does it mean? This excitation which means that we don't we don't provide the a d c supplying toe the field. The one off zero. Okay, we provide it when we reach is as big close towards us in Chronos is being so by rotating at a speed very close to us in Chronos is beat will give that d c excitation. Then, when the magnetic locking takes place between the rotating defeat and zero toe the supply toes extending motor is cut off so we can remove our extended. Another message off starting zest synchronous motors is using or something which is called Zied amber whining the number winding as asynchronous motor which is a silly in bold type number whining is placed in the motor pool fees. So we have here the balls off the Syrian type machine and doing both here are winding or damper parts. Okay, group off parts made off covers and fitted inside the pool itself. Okay, so when the rotor is not rotating, there is a relative speed between that number whining and the rotating Kerrigan flux. We said that we have a rotating the magnetic field moving inside Z air again. Kayla exists reduced from that state. Now that we're dating the magnetic cleaned here cuts Z damper powers here. Kay Cutts is them. So this number bars will have inducing meth. An image is reduced inside it, so the inducing meth here will produce that required starting to work for the machine. Okay, so that rotating if you flux cut zero tone reducing in used a meth which causes the machine to start Toto rotate as the speed approaches Easing Chronos is with the IMF and the talk are reduced. Okay, Senses He induced the meth Here the benders owns the relatives big between the state or and zero toe. So as this beat or that speed reaches asking crosses beat that I m f and the torque is reduced or are reduced. When magnetic looking takes a place, the talk is will be reduced to zero. Why? Because there will be no relative speed between the state and wrote or so the Tambor bars were Cesar state or or the rotating feel as a stationary feet. So the number buzz will have no induced a meth. So the torque will be equal to zero and the magnetic looking will be occurred between says bars in this case is asking gross motor first runs as three phase induction motor using additional whining and finally a distinct reminds, with the frequency now synchronized with the frequency off the supply itself and initially at as a three phase induction motor because the three phase induction motor needs at the three faced supply, which will produce their rotating field. And we have a three phase on the rotor which produces another rotating the field, and the interaction between this toe produces a talk we will discuss. Is the induction motors alone in another part of this course? So what is the features off the What are the features off the synchronous motors? Number one synchronous motors are not self for starting, so they require an extended means or extended mechanical covering. Toe brings air speed. Close a synchronous bid before the are synchronized. There's beat off operation off. Its is in synchronize Moza supply frequency and as equals. So 60 f or what a bean. So the depend on frequency off the supplies. They are synchronized with it at the constant supply frequency. They behave as a constant speed motor irrespective off the road. The frequency is constant so that speed is constant and independent on the road conditions . The motor has the unique characteristics off operating at any electrical power fact So it is used in electrical power factor improvement. Well, yours s in cross Moto at no Lord connected to regret to improve the perfect toe supplies era active power by varying Zia DC excitation off the motor The power factor off the motor can be very we can change is equal Zain fry of the motor Okay, by controlling that VC excitation also the over excited saying Chronos motives operate at a leading about factor since they are all what excited means that their current will be leading dizzy voltage And we have a leading bar factor, so provide a reactive kill of our like a pastor's Okay, we will understand this when we discuss Z Syrian and the monsignor According to the Faisel diagram, it will be more clear for you the applications off the synchronous motors Number one running at no load will help in injection off reactive power toe cigarette We use a synchronous motor running at no Lord and it is over excited so we it will provide a legging reactive power required the Boise induction motors and so on so secret. So it is used impor system in situation where zika best als You know, that said investors are used to provide que ilovar which is it acquired the policy in doctors inside the power system. So the capacitors and sometimes be expensive. So we use instead, as in Chronos motor at no load don't provide that required the king of our. In this case, it's called the S and grown ass condenser, or complaints it at the very high power. The cost and the weight off induction machines is very large convertido synchronous motor. So as an example, we need a power at 2.5 megawatt or a mechanical power at 2.5 megawatt. So at this large power and instead off using induction machine was started was existing Chronos Motors. It is used aware high power at the low speed is required, such as the Rolling Mills, mixers, bombers and compress. So in this video with Scott Dizzy Cross Motors is the rotating field and the principal off operation off the synchronous motors 133. Equivalent Circuit And Phasor Diagram Of Non Salient Synchronous Machine: now in this video we would like to discuss is the equivalent circuit off the non salient synchronous machine and the equations inside it. So first we have the equivalent circuit assembly. We remember that we have zero toe, which is consisting off a D C. Supply provided toe feel the winding. So we have a variable resistance toe, change the excitation or change the flux produced by zero toe and the current. I feed the current off defeat now for the state, or it's very simple. We have the e A or the induced A meth inside the armature. Okay, we are talking kid eyes, a single face circuit or thus the circuit off. One feels we have induced they may e which waas 4.44 certain Afghanistan. And we have that resistance R s or the resistance off the synchronous machine and X ir or the armature reactant and the leakage reactions leakage attractants and representing zero actors off the machine itself and x a r which representing the Z armature action resistance . So all of this produces the X, s or Z, as in Cronus, induct ance or the synchronously act IMS. So the equivalent circuit is e A or is our measure in use the voltage and excess? Or that a synchro mus in doctors and zem as the resistance can be neglected inside zing synchronous machine? Why? Because the resistance is very low. Convert toe the in doctors. So this is our equivalent sucked and we have plus minus V terminal in case off as the Power Albert or in gets off the water, it will be important. So the current off course is an and easy current. So current and angle sita. So if it is a motors NZ current is entering, if it is a generator resents the current will be leaving. So Rs is low compared toa access. So it is neglected excess or dancing dramas in doctors or reactors consisting off XKR or the armature reaction in doctrines and the liquids or self inducted, except now the equation off the armature in case off their generator and the moto and gets over generator then this one is a power is the one which supplies power so V terminal or C terminal voltage will be equal to eat a minus Z current motor blood by J excess. Okay, the minus I Z current armature Current motto Blood by Z A reactant X and the Multiplied by J Remember that in case off a C circuits, the induct Ince's is represented by E J excess. Okay, this is off course in case off a C and off course case off DC, then the excess will be quite cozy. Remembers that the induct ance a store at door by if and so at a zero frequency or at D. C. This one is not existing and only the or ists. And guess off a C excesses Very large combated tow rs o. R s is neglected. So we have excess j excess Xavi Terminal E a minor J excess now gets off the motors, and this one is the imports of eternal is equal toe e a Blust. Always easy access. We changed on Leah's design since it is a Now, if we draw that phase or diagram off non salience in Cronos machine, what does a fizzle diagram represent? If you don't understand, what is the meaning off official diagram, The federal diagram simply. We draw each off our component here is the e Z Karen, and determine all of them Withdraw it with their own magnitude and the egg. We draw him, we draw them as a victim. Okay, so we draws the victor e with Rosie. Victor, determine with Rosie Victor. Current E. Okay, so in case off a generate Oh, okay. Where With a leg bar factor. When the current is lagging from the terminal. Voltage, then how we can draw it. We have years. Evey Turman. We always represented the terminal voltage off the machine as a value and with an angle Equal toe zero. So withdraw 80 and horizontal line. Representing is E V term a victor horizontal with a zero angle representing our terminal watch. And we have a leg bar factor. What does it mean? It means that Z current is lagging by ass. An angle for or sita from the terminal Voltage. So we have re terminal and the armature current legging. Goodbye. An angle foi. Now we would like to find the Z E and gives off a generator. We said that e is equal toe i j x s plus vita So we need to add toe Bitterman j i excess. So how we can draw g I excess. Okay, assembly. Excess is a value. Okay, So assembly I x s assembly like thus increasing the lens off the victim I a excess legs is now. What does a J means? J means that adding lying to degree, toe this magnitude. So we have the victor I a legs. This I excess is the extension like this? Okay, the same line. But we increase the sea magnitude by excess. Now we would like to draw Jay I excess j I exists means that we take this victor and the ad mind to degree. Tow it. So by adding go 90 degree to it, it will be like this J R excess j oh x s okay with a 90 degree like this. So this vector of this new victims, this one is leading a by an angle 90 degrees from this victor from this one. So we think this line and added it. Take apparel line. And at the Jovita Jr excess Soviet Erman Ballas j i x s give us the total induced them f e . Okay, so he is the beginning off veteran and the end off giant. Since we are summing two vectors in mathematics, then the submission off them is the beginning off the first, the victor and the end off the second victim. So we have here eat and the angle between V terminal and the scold Delta. Okay. Delta is known as the power angle off the machine. So you will find that in this case when Z current is lagging what does this mean? It means that our machine is over excited. OK, why it's called over excited since is the key here is larger sends of eternal. Okay, you will find that this victor is longer sends his victim. So why it's called a generator senses he delta or the power angle is a postive. When's the power angle is postive then the machine actors as as united. Now we would like to see that lead perfect. Okay, here is the A graters and vitamin and the schooled over excited machine. Now what will happen if the current is leading? We have again. Vitre likes us. This is our written and I eat yours armature current leg leading by an angle phi Okay, leading by an angle for So this is I E. Now I would like to draw I a access toe added toe eternal. So J R E excess means that we are adding a mind to degree tothis victor. So 90 degree leading means that this victor will be like this j all a excess. So zj representing at angle or in angle added off 90 degrees is is a 90 degree. So she i excess. We will take it in barrel with a lion as a line starting from me. This line this line is parallel toe this line. Okay, so we talk this magnitude and added it here. So v terminal blasts g I a excess. Give us Z beginning and the end to give us e and will find again that power angle here Delta is a full step bank. So we're dizzy. Anger is postive and here is the Angeles Boston So the generator What does it mean? You will find that e is leading from V terminal breaded in a lagging and the leading perfect. Now we will find something is really which is really interesting that when we add determinant with J I excess what will happen you will find that e or the induce. The myth is lower than Vitre. Okay, so by Ed we adding here, not magnitude. But we add Victor's okay, we add victims. So the addition off to Victor's give us a lower victor in the case off lead and ah, higher victor in case off leg. So in this case, we say that when e graters and determine we say that the machine is over excited and when the lowers and eternal we say that the machine is under excited. But in case off the motor, we have that Bitterman is equal Toe e plus j xie or e. They used to make his V minus J x I Now we would like toa draw in case off leg bar factor and lead Perfect. Now, in case off a leg bar factor will find determine is a horizontal line and dizzy I is lagging to buy an angle Phi Now we would like to draw negative J xie. So first, let's a draw, Jay Exciting J x. I is a victor in this direction, leading by an angle 90 degree from this one. Okay, J I X Okay, same as before, leading by an angle 90 greens direction. But we need to find the a e a guest Offseason Comus Motor here in case off a motor is Vitre Man my in us J. Xie. So we need to draw negative zero x I so negative off a victor is Victor with the same magnitude but in the opposite direction like this. This is negative J oy X So we take Ze Negative z i X and added to of eternal Soviet ERM not taking g i X here starting from in going here This is negatively I X and added them together Give us Z e or the inducing myth and the angle here is delta and you'll find here in case off the motor the delta is negative or the e is lagging from Xavi Turn now In this case, you're finds that e is lower than determine which means that the machine is under excited. Now let's see the lead more factor in case off I need part factor. We have eternal here and we have armature current leading by an angle. Fine. And we need negatively Xie So J x I is this direction j exciting So negative, Jake. So you will be like this. Okay. The orbit is opposite off the victor So take this victor and the summit toes Evita So v terminal blast Negative zero i X, give us Z e and again Z Delta is negative. So e is lagging from Vita Now we will find that in the case off leading the bar factor is immortal. You will find that Z e is greater than V terminal which means that the machine is over excited. So what does under excited, mean and over excited mean in case off our motor and generator under excited means that it will take Z as a cue or the act of power from secret. Zack, you or that active power required the foursome organization off the machine from cigarette . But over excited means that it will provide the reactive power to cigarette provided skew. Okay, so we can use the motor at no Lord. Okay. And at leading apart factor to reduce and over excited case to provide que toe cigarette. You remember that? We said in a previous video. That's the thing Chronos motile is used in in improving bar factor by providing a Q or acting as a capacitor at no loot. So we use the a synchronous motor at a leading the perfecter toe. Provide que toe cigarette. Now, how does the power factor correction OK, so assembly and gets off that leading a bar factor. We operates that synchronous motor at normal. This is the first step Second steps us means that delta or the power angle is equal to zero . No active power is absorbent. No b is absorbed but so the delta is equal to zero. So what does it mean? It means that the Viet Urman is in phase with the f that to get back Wednesday. Power angry is equal to zero, which means that it is acting at no load. You will understand later. How does the power Z power angle effective Z reactive power? But for now, we assume that at no load the delta will be equal to zero. So when's this angle? Zero Then re terminal will coincide with e. Both of them will be on each other like this. Now we said that e is equal toe Vitre non minus g I e excess. Now we have G I X X games. This one is J I access. Okay, now I would like to draw I only so we need to draw another victor, which is lagging by 90 degrees. This is our a excess, okay? And J I excesses simply adding the mind to degree toe this victor. So 90 degrees with this vector Give us this victor. So I excess giving us z current in the end, leading by a 90 degree from Z v term. So in this case, since it is leading by 90 degree from the voltage, then it acts as a capacitor, so as if he'd excitation increases inside zero toe that induce them f e increases. So the difference between V terminal and the F J I excess between v, Turner and and vitamin A and the F is G Asia access. So this part increases as the excitation increases. Okay, we said that we have an over excited machine, right? So e f here is larger than vitre. Okay, in case off the over excited by increasing the excitation, we increased the e Toby beyond Dizzy Vitre. Okay, so e as a value greater than return. So the difference between them, which is this part, is J I access. So as we increase excitation, you will be increased the like this So here zj excess will increase. So the current leading a by a 90 degree as increases the current increases and the machine is over Excited when he is great as m V. At this case e graters envy. Since the current is leading by a 90 degree from voltage, it acts as a cabestan. Remember that the Kabah store provide is that Z current is leading about a 90 degree from the voltage. Okay, so here is the current is leading violent degree from the voltage. So in this case it acts as a capacitor and provides power toe cigarette provide is reactive power to cigarette and in this case at school Dassin, Chronos, Condenser or compensate or aka best. So what are the laws used in non salience in Cronus machine? We said that we have in our circuit we have the voltage V terminal and we have the current legging Goodbye an angle foi And this this current By ending a 90 degree toe it will will have j excess dozens of submission off them Give us Z e or the end used a myth and this angle is delta. This one is for now. Let's notice something which is really important if we made an extension here on the cut the real part and imaginary port. Now we will find something here as this angle is 90 degree. OK, since this is I and this is Jay I excess. So this is 90 degree. So this angle is 90 minus phi okay. And from geometry, this angle is equal toe this angle from where? From z vertically opposite anger in mathematics, this angle equals does this anger. So since we bought here an extension for 90 degree dozens this angle 90 dignity this angle is 90 minus foi Therefore then this angle is for Okay, so this anger is fine so we can get the component off G I access in the imaginary direction and in rail Dykes now is the active power off the machine is equal toe V on the blood by I cosigned fi, right? So v, I cosigned fly and sick. You'll is V I sign phi. Now if we divide this part by X and amount of light downward my ex multiply by x and divide by X multiplied by X and divide by x Ok, that's what we did So what will happen? We will have something which is really interesting. What is it you're finding is that this component can be in this direction? Okay, Like this is Jay is I is the magnitude Force I X cause I in the anger Go Zion folly! We talk this component and get the projection off it. In this direction from mathematics again is I X cosigned the angle between the horizontal and this line required to get it's a project. So it is. I accept design fight. And this one is what is I X sign for our X sign? Feli Salyan. Fine. Now this is a projection in case off in the direction of the imaginary port. And this is a prediction inside the rail part now is the some measure or the square root off this The square off this plus the square of this. Give us our X. Okay, now I accept. Was I in for here? Ok, I execute sine phi What is similar to if we exist e exist e And we have the angle year we have here 90 degree so we can take the and the projected here and presented here. Ok, e in this direction and in the direction off the aerial part So e will be projected here will be What All of this when he becomes here, Ines Abbas, this direction will be e cosigned the e go Zion that ok all of this part since we take he and rejected it here and the toxicity and projected it here it will be science that okay so easily in Delta and we have equals I that now we'll find something which is really interesting that I excuse I employ is equal toe e sign Delta this victor, this distance is equal toe this distance so we can replace I execute sign for you by any sign that I X cause I'm find Bye. He designed it. So the equation off the actor power produced by the machine is e multiplied by V sign Delta over X e v Sign Delta Over exist is a very important equation, even over X assigned it. This is representing the relation between the active power, produced the boys of machine and gets off on incident. Was respect to tow the power angle dealt. So find that at zero part bar active power Z Delta will be equal to zero. Okay, that is the explanation for that leading about factor in moment. Okay. When we said that we would like Toa operates us in Chronos Motor at no load in this case is a delta is now for the reactive power. Similarly, I exercise for what was I excited for? I exciting flight is this part and this part is equal to V And all of this is e cosigned. So e cosigned Delta which all of this cosigned Delta minus V or this part give us I exercising for so we can take all of this and substituted here in a set off my ex assigned so equals under the miners we multiplied by V over X so e v off our extra co sign Delta E V over execution Delta minus the square of Rx. Okay, so this is assembly Z Q off there machine in case off a salient type. So this are too important. Laws is short, but it in your own mind now we'll find something which is really important that z machine here. When delta that they can change from 0 to 90 degrees. This is a stable. The reason for Delta. So when does the zero no power is absorbed? Window his nineties and the maximum active power from the machine is given. Now, is that you or that active power? You will find that at cosigned zero, we will have the maximum reactive power provided. But at a dealt off 90 degree, then secu will be negative. So what does it mean? It means that the machine will absorb a cue from cigarette Okay, in order to supply the excitation. Now, if we'd rosa relation between the power and dizzy Delta, you will find that zip our increases as Delta increases until 90 degree and after this it will start to decrease. This region is on a stable region and this region is a stable region. According toe, the mechanical power provided to the machine the intersection off mechanical Bauer with the curve them per section off the mechanical power provided to was the rotor with the curve at this point representing the operating point or the operating delta at which you are working . So as we increase the mechanical power, the power generated will increase now from Z fizzled by Come here, we can have some important equations we have that you is equal tothis part or squares This part We said that i x cause I infi all square I x goes I'm five square plus all of this part which is V plus i x sci fi or square wien plus I x sign for all square this off course in gates off the generator. Now, in case off the motor assembly that the current sense in case off a generator dizzy current is going out off the machine in case off the moto Guzzi current is entering. So simply boat each Ari boy a negative oy So you will be quite toe wrote In case of's immortal Remind us I accessed since I becomes a negative I excess sign for all square plus i excess cuisine for negative I was square becomes I excess cosigned for okay, so in case off defy equal post of then it is lagging. The fire here is measured from here. Okay, this is for when it is positive it means that the Vietor is leading the boys this angle or the current is lagging from Vitter and the fine negative means that it is The current is leading now is the delta. From here you will find that delta here from 10 low. It is equal toe tens. This part over all of this okay, is the opposite Over the high NZ adjacent. So the opposite is I excess co sign Phi I access cause I'm fine And the adjacent is via Plus I excess sign V plus I excess sign for So this is our delta from Z 10 law. And this is a value off e from the Faisel diagram. So this law is important. This one is important and this laws are important. So let's have some examines on scene on salience in Coronas machine 134. Solved Example 1 On Non Salient Machine: Now, let's have an example on za Non Sadie into machine. So we have ass in Chronos generator with a state or reactant or the excess off 190 or And the internally mef E at open circuit is equal toe 35 kilovolt A but line to line. So this representing Z induced them f e at open circuit. What does it mean? It means at no load where e will be equal to O V term. The machine is connected to an infinite bus off a 35 kilovolt lying toe line. So this is the infinite bus. Voltage or the voltage off the grand off V. V. Turman or Thea Terminal Voltage is 35 kilovolt. Find Izzie. Maximum active power generated by Z machine. We need to be maximum generated. So how we can does assembly, we will get 1st 0 off the maximum power. Remember that first, that any is given as 35 kilovolt as a lying toe line. Voltage. So the phase voltage assembly or the E s for his Walter, since we are dealing with the face circuits. So the phase voltage is equal to 35 over the road city so 35 overwrought Sereni rotisserie is equivalent to 1.73 Give us that. The inducing myth for the internally MEP is equal toe 20 pointed toe kilovolt. Now, from the given, you will find that we bus or the terminal voltage is 35 kilovolt, but as a lying toe lion voltage! So again, we needs if he's voltage So 35 over the route City, give us 20 point door Gila vote Now we have the induced him f e off the machine and we have the pass Zavala off the bus so we can get the power generated boys a machine. How we know that the power is equal to three e v over X sign Delta. Okay, remember before when we prove this equation, we said that the power is evey over x signed built this in the case when you are dealing with the pair unit system Wednesay given is E in Bari on it value and the voltage in berry on it. If you don't understand what is the meaning off very on it, you can get So the video's off the as symmetrical power system fault. It's in my own YouTube channel. Okay, you can find the berry on it system and its explanation. So in case off the berry on it system, we we say evey over exercise. But in case we are talking about actual values such as 35 kilovolt like this Z, we will have a city. Why? Since we have a city face system so City V over excitement the maximum power occurs as we said before the maximum active power or occurs at a delta off 90 degree. So the maximum power generated assembly three a V over x three. Monta blood buys in your them f e What? The blood by the voltage over X, which is 190 home. This will give us a maximum power off the machine off 6.45 megawatt Now the second the requirement is if the angle that became our become a 45 degree okay finds the outward active power. So somebody we have the maximum power here, which is three evey off our X now at a delta, not 90 but 45 degree. So we'll take the maximum power here and the multiplied by sine 45 degree. So be maximum So in Delta, which is and Delta equal 45 degree. So the power and this case will be 6.45 which is the maximum power city. Evey over X signed 45 degree give us 4.56 mango. So this was a simple example on the non salient to machine. 135. Solved Example 2 On Non Salient Machine: another example on Z non salient machine, as in Chronos is in a little. So we have here Generator is supplying power toe a larger system with its a field the current adjusted so that the armature current legs, the terminal voltage. So what does it mean? It means that we're having as in krone generator, we have years of e tournament, okay? And dizzy field current is adjusted. So we controlled the field, the winding or the excitation off the field in the photo In orderto make the armature current lagging is the terminal voltage. So the armature current here I a lagging by an angle, Floyd. Okay, is this angle is for so the I excess will be like this I e for my excess g i e excess g i e s And does he totally and use them? I e will be like this. Okay, since we have a generator Soviet German plus I excess And this angle is dealt now, our Mitchell resistance may be neglected. Okay, Now is the field. The current is now increased by 10%. So we increase. Does he feel the car without changing the driving torque off the prime over. So what does it mean? It means that when we are saying that the driving talk off the prime mover is constant not to change it What does it mean? It means that the active power produced by the machine is a constant. So as you remember that the active power in the machine it's City V. I cosigned foi Or we can say that this part Okay, this part this vertical part is this part which is we have here angle phi. So cause I infi which is I a excess Go Zain Fi that are presenting is the active power off the machine. Okay, I excess Ghazanfar is similar to V I cosigned fi So the vertical partiers This part And here is this vertical part Representing is the active power off the machine so senses he driving torque is constant so this part should be consistent. We increased dizzy feel the current What does it mean? It means that we increase the Z excitation. Now we need to know what a changeable Okay in the power output the our part off the machine in magnitude and the face off the armature current easy value off the face current A and dizzy phase ANC and the magnitude off the torque angle torque angle is representing A By dealt now is this is the first requirement and let you see it. So we have here the voltage. We have the current leg by angle Phi and Delta and I X design five We said that this part this vertical part representing Z active power. So the torque inside that driving torque or the one which rotates the machine is a constant . So what does it mean? It means that the active power should be constant. So the locus or the allocation off a constant power is representing the boy horizontal line at this intersection. So we'll find that at this point at this this is the power and at another location, for example, here we will have the same power at another location. Here we will have the same power. So this is representing the locus or the allocation off, Zeke, honest and power. Now, since we are saying that Z feel the current increased so the excitation off the machine increase the source that end used, MFP will increase. So we draw the case off the increasing off the excitation current is this a new e is greater than this all the now If we decrease the excitation, it will be like this. Okay, that he will be lowers and isi so increasing the excitation means that we are increasing Zealand's off the excitation e Now, at this point is a new e So this representing Zanu J I X. Okay, Okay, I exit equivalent or I excess Now if we want to toe get Z current the current itself So we have B I X So the current will be lagging from this line by a 90 degree like this. This is a new current. This is a 90 degree between them lagging the pie 90 degree from J I X. So the current here will be like this taking a parallel line. This is a new car and this is representing is and unify. You will find a lot of things. Number one that as I feed increases, they induce them f inside the machine would increase. He will increase e increased as you see here. Since his exaltation increased the armature current well increase you'll find that e increased Readerman is a constant. So as e increases J I x will increase, So the armature current increased. So the new current will be something like this. Okay, Why? Since E is re Blust i g i x So when he increases at a constant davey, therefore see current will increase. So the armature current increased the power factor orders if I z power factor angle for increased. So as for increase, the perfecto decreased. Why? Because the power factor is cosigning fry and the design off an increased the angle means that a lower value off the out lower power factor. You will find that the new Delta is this angle. So delta is reduced. Okay, this is all the delta and this is the new dealt reduced the debt. So Delta is reduced now for the second the case instead off a changing the field, the current the driving talk off the prime mover is increases So increased the active power or the torque off the photo. What will it change inside the machine? So looking at here, that's really all of this. Now we have here I and we have V e and I X orgy I X. Now what does a constant excitation mean means that e will be constant. The excitation Constance means that you will be constant. So we draw here a curve starting from here we draw a curve at this instant, for example, Will gives us in me at here at this point will give us the same me. So at any point on this location, we will have a constant E or a constant excitation. So now Z as the power or the act of power increases. So this is our old active power. Now the new active power increased. So the new actor power will be I execute Sign for is a new I execution fight. So they knew we will be this part okay again we Afghanistan which events on the grant now is this one representing the new active power? This is the old actor power at this e And this is a new actor power When we increased it, boys, the effect off the increasing off talk. So the new e This is a new e. Okay, now this part representing I Xs and Ys cognisant and devious constant And this is I excess . Now if we would like to draw the current itself, it will be lagging by a 90 degree. So this is an your current, okay? And this is a new if I so we'll find. And this is a new delta. So we'll find that the power I am both increased. Okay, with our changing citation or the torque off, the rotor increased. So the active power increased. Now is excitation is gonna stand senses the field. The current is constant, the armature current increased. Why? Because you will find that e is constant and V is constant and dizzy. Power increased so power increase desist part increased. So I excess all because I invite all of it increase. So the armature current increased if I is reduced So cause I am fi increased. So the power factor increased. The new delta is higher. Why? Because we provided more active power. So this wasa symbol example on understanding the variation or the effect or variation off the field and variation off the Z have talk or the power on the death front of parameters off the machine 136. Solved Example 3 On Non Salient Machine: Now let's have another example A certain 0.8 kilovolt, then mega volt ampere 60 Hurtis, toe born. Why Connected steam turbine generators. Okay, so that we have year, as in Krajina, NATO with an s or the apparent power 10 Mega Volt and bear and Zeevi line to line Zeevi terminal as Aliant Linus certain 0.8. This is the maximum Razzie for Lord s or Z for load apparent the power off the machine and we have excesses easing Promus reactant equal 18 home and armature resistance off to own. Now we'll find that 18 is ah lot tires and toe. So we neglect Z armature Resistance decision Letter is operating a parent with a large power system or the infinite bus. Infinite bus means that it will not be affected. Boys a generator. It have a constant voltage. Kanis and the frequency and does not change Wednesday generator is connected to it as we will understand in the synchronization off the generators. So what is that magnitude off? He adds aerated conditions. We would like to find e at rated conditions, so we know that we have Zillow off E in case off the steam turbine steam turbine assembly and and unseeing into machine and another proof is forcing for the steam. That it is a non salient is that number off balls year is to a very low number of pores, which means that we are dealing with fast inter pine or we are dealing with a non salient machine. Now what is the value off e at rated conditions? Where will yours alone, which we discussed before that e phase is road refits plus I excess sci fi Blust since eighties as generator plus I excess cause I infi zipper factory is opened it It was not included in the problem but it is one for one off the givens. So cause I infi is point a lagging the excess given as 18 the re phase is 13.18 volt over the road three ze sign Phi Assembly. Is that because I minus one off point they give us is If I then fi is in? Sign off this angle. Give us sign for okay from mathematics, the current or the armature. Canada Assembly is the apparent power s 10 mega volt and bear, then mega volt and bear over route relying tow line or three V face. Okay, pose off them are similar to each other. So Route three relying tow line. So we have years, the armature current. Now, after substituting, we can get that it is a certain point. It at 63 or the airline. Tolan is 24 killed. Vault Now the second requirement. What is the torque angle of the generator? So same busy talk angle or the Delta assembly from the law off. Dan minus one. The Dell ties equal to 10 minus one. I excess cosigned Frye over the phase, plus I excess sine phi. So the angle pie substituting was All of the event is given. We will get it as 25.76 Or we can get it from here from zero off the Mansilla into machine . We sent that. The power is three. I phase. We face off excess sign Delta. So delta is unknown. Ive phase is now attend 13.863 re phases known excesses known and is the active power off the machine is Z s goes I employ. Then multiply it by 0.8. Okay, the portion off the actor power is s cosigned for now is he served the requirement? If the field the current ISC honest and so he is constant. What is the maximum power possible out of this generator and how much reserve a power or the torque decision rate or have at full load? So first we need is a maximum possible power. So the maximum possible Bauer assembly, Serie A V E V, over access. So we said that's the maximum power. Is that at angle or a delta off 90 degree. So three he faces, we face off excess. So I'm 19. Give us 18.4 megawatt. This is the maximum theoretical power off the machine at the power. Of course. Now the reserve off the machine we have here, This is the power at full load. OK, this is the power at full load and this is the maximum possible power. So we can subtract is a maximum power forms the rated active power, which is 0.8 multiplied by 10 0.8, which is co sign for Mata blood by s, which is then give us eight megawatt. So then point for Megan is considered as the reserve before the machine. Okay? Now the lost the requirement at the absolute maximum power possible. What is the reactive power? Was a generator be supplying or consuming? So somebody we would have that Zillow off Q or the actor Power assembly for 23 since you are dealing with a three face system and do not appear unit system. So three a V off our X s cosigned delta minus B squared over excess. Now is the delta at maximum possible maximum power is 90 degree. So this part is equal to zero because I 90 0 so sick you provided by his A generator is negative three V square for excess. So the Q is negative. What does it mean? It means that our generator in this case will absorb react. The power from the grid will consume. React the power from the grid if secure, Woz boasted, then it means that it provide is reactive power toe, cigarette 137. Solved Example 4 On Non Salient Machine: now let's have another example. Are 480 volt six a bolt synchronous model draws are 50 and bear from the line at a unity power factor and the full load Assuming that the motor is lossless, answer the following questions. What must be done to change the power factor? Toe opened a leading so have eternal and we have is the old the current which was like this in phase with the bitter at unity power factor means that the anger between them is here Now I would like to change his e power factor toe 0.8 leading increasing the card So how we can do this? How we can increase the current toe make it leading somebody as you remember before we said that investing Chronos Motor we can increase exploitation by increasing the excitation. We can increase the power factor or improves Ivar Factor And the Mexican aren't leading until 90 degree so it acts as a capacitor. So similar he's our answer for this question is simply increasing the excitation off the machine will make zipper factor off the machine leading. So we have Here is the voltage we have the anyone Are you one and all The X okay, in the synchronous machine is an synchronous motor. We have e plus I x s give us is the voltage okay when we add for this j So it will be a J i excess. Now if we increases excitation at a constant power same as before This is the location off a constant power Then this is the one this is e to and this is a new J i excess. So I excess alone will be like this i excess So the new current will bill exists. So this waas all the current This is a new current. So by increasing the excitation, we increase dizzy power factor or Mad Menzie power factor leading so simply by increasing the exploitation will make the power factor leading. So what is the magnitude off the lying current? The I A or the armature current If the power factor is adjusted toe 0.8 leading. So we need to find the new current now in this case, what did we change? We change it on Li Z field or the excitation about Z load itself. We said here we have the full load and the Lord connected doses in Chronos Moto is as it is . So in this case the power old will be equal to the new power. Okay, ZB one or the old power will be equal to the new new power and the sea power is three V 11 cause I if I won city veto I talk because I am fighting is the act of power. So the voltage here did not a change The terminal vaulted which is connected to a cigarette . We want a similar to veto and history goes, 03 So we have I want because I if I won equal I too because I am fighting and I want is equal to 50 and bear and the design fi one is equal to one bar factor one cause I infighter is 0.8 and I told is unknown so that new current would be equal to 50. What? The blood by one which is a unity power factor Oversee cosigned fighter which is 10.8. So the new current will be 62.5 and there 138. Solved Example 5 On Non Salient Machine: Now let's have another example in this example we have at 2700 vault 100 horsepower, 60 Hertha's eight full. Why connected synchronous motor and has a rated perfect off 0.85 leading at four loads. The efficiency off the machine is 85%. There are Mitchell, resistance is 1.1, and synchro nous wrecked. Ince's 20 or so they are Mitchell Resistance would be neglected while I'm goingto one convert to toe 20 is very low, finds the following quantities for the machine when it's operating at full load. So the first requirement is the album talk. We need that talk out off the machine. When I was at the talk out off the machine is equal toe the power over Omega. Now is the power off the machine here when we're talking about a synchronous motor, the 300 horsepower representing the rated output power. So the Power Albert off sitter or the torque out? What is the power? Our overall Megan Mechanical. The output power is 100 horsepower motor brought by 746 to convert it from horsepower toe. What so this representing the wattage off the power out the Omega is told by end over 60 or to buy f Overbey. Remember that Z, as in Chronos is beat and as equal toe 16 f over being so to buy n over 60 and over 16 is equal to f over being so to buy and over 60 similar toe to buy f Overbey. So we have the frequency given as a six stewardess and to be which is the number off bull bear. Let's get back. Number of prepare is four pools. Okay, it bull is a total number of pores and to be here is a number off Paul pair. So we have here for soc torque out off the machine will be 791.5 Syrian your 10 meter now the second The requirement is the simple power toes a machine we provide inboard power as they know we'll have the 100 horsepower as the out. So simply we have the efficiency which representing the power Albert oversee power in boot so assembly week and gets in both power Impulse power is equal to Z our power off the machine over the efficiency off the machine. So the Albert power is 100 multiplied by 746 over the efficiency which is 85%. So the import power to the machine is 78.76 Kill what? Z sir, The requirement is the armature current or armature. So assembly We have Z re terminal here. 2700 vault, which is that terminal voltage. And we have the power Albert and we have also see a power factor Z m But power anti bar fact So assembly We can get the current I armature or the power in both a three v phase I phase cause I'm fine. So the current is equal to the power in Bata Chose obtained its 7.76 equal What power? In photos and machine over 33 phases a voltage import was a machine three multiply 2700 over three This value is our lyinto line. So we Indians a phase and divided by rote city cause I infi is given as a rated perfecter is all 0.8 lead So the face current will be 25.29 toe And there now is the force. That requirement is the or then do the math. Remember that e we have the lawyer off it inside. That non silent is our walk off brought off the face, plus i excess sine phi. Plus I access cosigned Fine, but we said that we have here a mortar here, so this one should be negative since the current is should is the negative so they can't is negative inside the motor, But you will find here that's the power factor here is leading. So what does it mean? It means that is if I in case off legging was like this. It was a postive ANC, but in gets off leading the fire will be in this anger, which is a negative value because the fi measured in this direction as opposed to value and in this direction is a negative value. So they fly is negative, so sign and negative angle will give us and negative sign. So we have here a negative from this one and ending the from Z current and some mission off them is Apple Steph site. So by substituting, we will have e face off 1660.5 to vote the lost. The requirement is that mechanical power plus score blas astray. What does this Representing Representing Izzy losses inside the machine. We know that the power losses in signs that machine is equal to the import minus the out. But so I 15% difference in that efficiency, representing the losses so we can get Zillow says Vice up, directing the import power minus out with power. Now this losses is equal to what equal toe the mechanical or additional losses. The goal losses, the stray losses. And we have also Z couple losses are a couple losses. When's the armature? So the submission off before give us Z power losses. Now we need this three without the cover. So that's three off. This equals e power losses minus Z cabal losses. Okay, we talk this one and what it in the other side. So the power losses as the losses be mechanical losses called losses and Cirillo's equals e power losses, which is powering both minus powerboat mine us the couple losses. The kabbalah is city you since we have a city fear system I square or on Mitchell by square is obtained before and the resistance are a assembly 1.1. So we will have an Z losses inside the machine. This saree losses are equal to 1.9 kilo. What 139. Solved Example 6 On Non Salient Machine: Now let's have another example on Z Non salient the machine. We have our 440 volt three phase. Why connected? Syncronys generator has, as in Chronos Attractants excess off 1.5 all. And the field. The current has beena Joseph so that the torque angle is delta a certainty green when the power supplied by the generator is 90 kill What? So we have Delta 30 degree. We have the power supplied by generators nine tickle what excess? And we have the Reliant Line. So what is the magnitude off the Internet generated Voltage e in this machine? Very simple. We have the actor power. We have Delta so we can get so in Delta and we have e alone. We have TV and we have excess. So simply we can get that the power which is not to kill What quarto three e vase the vase over excess Sign Delta Delta is given as a certain degree. The three phase is a 440. Walt overrode sitting. Okay, this is 440. All should be changed inside the program as the problem itself or by 480. Whatever. We need. The concept more Zanzi Calculated numbers. So excess given as 1.5 own. So we can get e face as 354. 54.25 Which is great, Tarzan. The phase voltage off C terminal here. Okay, returns them 440 over roots three, which means that our machine is over Excited. So what is the magnitude and the angle of the armature current? In this case, we need the current I armature in this case. So I know that the current symbol equal to or not the current will see that he then does the math is equal toe the eternal plus j all right excess. So somebody we can get from here is the current current is equal toe e minus V over J access. So the current is equal toe e, which is e and its angle is delta. It's anger is delta in phase one, and Davey has an angle off zero and excess have a gene, so it will have an angle of mind to degree. So by substituting in faisel diagram or price of suiting in complex, for we will have the current and it's anger. It's angle cosigned. This angle will give us Z a power factor if they feel the current remains a constant. So the excitation is a constant. What is the absolute maximum power off the generator? So simply we know that the maximum power assembly three e phase we fears over access. So the maximum power is three e phase V face over excess and we have signed 90 which is one so we can get the maximum power off the months againt degenerate. 140. Equivalent Circuit And Phasor Diagram Of Salient Synchronous Machine: Now, in this video, we would like to discuss the second the type off, as in Chronos machines, which is a Silien pipe machine. But in this lecture would like to discuss the equivalent circuit. So here is our equivalent circuit. We have Z three phase on the state or and we have our water which in the form off a boat. Okay, Now what is the problem with the Cillian machine? Camembert two toes on on salient machine. You'll find that Z zero tore itself is made of pools. So it provide flax going out from the north. So like this Okay, and it rotates. Now we'll find something which is really interesting Is that the flux? Here at this point, is the maximum flux produced and going A to Z right or going it was the left until year. Is this direction you will find that the flux becomes zero. OK, so this part add sentences, directions, influx become zero and the year in this directions influx is maximum. So we have in the machine tool directions one which is called the director excess. And at a 90 degree from it, Zeke would reach our access. The direct X at which is the maximum flux occurs and this direction is the here, the direction off the maximum flux. And we know that e is equal toe negative n defy over ditty. Okay, so this representing is the maximum flux A produced this representing the minimum flux or zero flux. Okay, direct access and quad ritual X. The direct access representing busy maximum flux. Okay. And all finds that they induce the meth is equal to negative and identify what the team. So if this flocks is a a sine wave or a design wave, for example, cosigned with cause I infi then negative d five oddity or the differentiation off a design wave Give us a sign with K sine Omega team Omega getting on this one. Omega Getting so again, every flux is a cosigning wave. Then the Hindus them f will be assigned with. So there is a phase shift between them. There is a mind to degree difference. Okay, this is a design, and this is a sign. So if the maximum flux things direction since I induce the meth will be in this direction E So they induced the meth inside the machine is represented by Isaac You access. And if Lux inside the machine is represented by Z direct access. Okay, this is a very important concept. So we have fly and we have e or have d access. And do we have Q access? Now we will find another thing that this part rotates. So we have here at different air gaps. Why is this distance OK? Which is the direction off the director? Access is different from this air gap. For this will get Toby more subservient. This air gap if we are looking at a pool so this distance or the air gap in the direct access is a smaller sends the air gap in the direction off you excess. So the silly Intertype machine have a two reactors, one which is called Dizzy Exit E or the director Acton's and the other one goal dizzy execute for the quad ritual reactions. So that reluctance year is lower than this reluctance so that X city or the inductive is here in the direct access is lower than the induct INTs in the ACU access. So in the civilian Topol rotor that direct access is a long people's will find years are direct access is along the people in the election, off the maximum flux, and Zeke would ritual exes along the inter cola region. Interpol a means at a 90 degree from it. This is a quad Richard X at which is the minimum flux or the euro flux. And this direction is representing easy. Why, since E is equal to negative energy five over DT from the for a day law. And if Fluxus cosigned, then in you will be signed. So there is a phase shift off a 90 degree between them. Air has more reluctant than I are or silicone steel. Of course, as we discussed in magnetic circuits and you access Zeke, you access here is this part. The air gap is more than the air gapped off that he access, so their reluctance is greater. So they reluctance is a magnetic equivalent off the resistance. As we discussed in Z and magnetic circuits part Therefore, Zack, you accessory Acting's is greater. Sandzak their reactors off the d access their execute is greater than Exit E. But in case off the cylindrical roto or the non salient type, you will find that we had a rotor like this, and we have the state would like this. So the air gap here in the d and ink in that direction off you are similar to each other since we have a cylindrical four. So the air gap is uniforms, so Exit E was equal toe execute. That's why's that machine was represented by one ECU. It one x called X City or whatever. Okay, one in doctors or one reactors. But in the psyllium to type, we have two different air gaps. So we have a tool at two impedance okay? Or are to worry actors. Now if you look at the equivalent circuit off the machine, we have induced them f e. And we have the armature current, which you can be I d or like you. And we have directives which can be exiting or execute and our army. Okay, they are mature resistance. What? She can be neglected. As we said before, it was low and the veto. So the difference here is that we can have i d or I Q and X City or execute. I accuse execute and ideas Exit E. Now the question is how we can get the equation off you e is a function in I. D X City and I Q execute armature and Dizzy V Terminal. Now we will find that the current idea is the same in the same direction off that the access and I Q is in the same direction off Q access. So if we would like to get the for example, we have V Terminal and we have the armature current, which is consisting off I. D and I Q. Consisting off two components I Q, which is in the same direction off Q access. And we said, Que access representing Z induce them f e So we hav here Q access and direct access at a 90 degree from it. So cue exes, which is in the same direction off E f at the 90 degree from it, we have the D access. So we have our i d. And we have, like you, like you in the same direction off the end. Use them. F e and I D is at a 90 degree from it. The submission off these two vectors give us all are mentioned now with the Walt Ege here, which is every terminal, and I are matures. The difference between them is the angle Phi as before and dizzy angle between e f and G V is simply delta as before, since it is this phase or representing busy generator at the legging bar factor and is the angle between Z armature current and dizzy e f Okay, the armature current and e f A end is induced The myth which is this angle scold if soy upside is the anger between e and I are mature now I would like toe get Z e f from Xavi eternal soave eternal we add to it I our armature ie which is this one I our armature are in the air parallel to each other since, as they are, they have a zero angle. So I armature are a assembly equal to barrel to I A Now after this, we need to add i d exit e and I like you execute So it's and so we have to worry actresses in the machine. So Z I Q here we need to add to it or the i d. First we need to add to it. Jay x d i d. So a j exit e I d assemblies the I D. But added to it, mind to degree. So this one batteries do it is a line like this are lying like this. This is I I D And we added toyed jx city which means that we were rotated by 90 degree. So rotation off it. Mind the degree, Give us a sense victor Mind to degree idea exiting. And I like you execute what simply will be like you and that you it is a I as a x Q Okay, which means at a 90 degree from it. So it will be affected like this. So v plus I armature armature which is usually neglected plus idea axity as a i d Xidan plus J like you execute your give us they induce the meth e inside the machine. So we find that this is a difference as different from before. Before we had only one excess. Or that's in Chronos reactors, which is X'd. But now we have to react Ince's or are to the front of Victor's soul finds that this are two different victims and you have to understand something that the equivalent the circuit we cannot say exit e Parenteau execute or exited Plus execute knows they are two different vectors and appear at a different time. So in the end, we can get e by doing this Faisel by Graham Now we need to understand the front cases off Z a generator and is Emoto and their equivalent Faisel diagram. So in case off the generator was a legging power factor, it is the case which we exhausted discussed it. Now we have the e f which isn't the direction off Q and that a 90 degree from it that the access or i d some mission off them I the voltage A plus i r A And remember that the voltage is at a zero angle. This is really important. It's angle zero. So we have the voltage I i r a and add to it I dx dy you like you execute, Give us is in use them f e now in science of problems itself we need to find is the angle Delta In order to get I r a i the exit e r q execute okay in order to get the e in the end . So in order to get the angle Delta. We have to get a value on the locus off the E. Okay. On here on this line. Okay. So I we can do this. We have the voltage V and I are a Or can we can neglect at whatever we can get By adding I execute a point here which is representing a value with an angle dealt so simply we can get Z current the total current or the armature current and that do it j execute. So, Jay, execute moments that mind to degree from this one mind today getting from it. So mind to degree from it like this g I execute. So she I execute will intersect with the locus off e f giving us a value called e or B. Okay. Lets you delete all of this. We have e all be this value is a value which has and have no physical meaning. Okay, it has no physical meaning and at the same time, this value give us an angle off delta. So we attend the e o p toe get zida as we'll see inside this hole. That example So e o p equal to was the voltage or the V term none plus j the total armature current execute. So when we add this to assess will give us a point on the allocation off E f or a point on Zach you access which will give us E O. P, which has no physical meaning, but it will give us is the angle delta required. Now I cume and I d r faceoffs. Okay, Both of them are phasers. They are not a constant a value. So we find that our hue here is this current assembly Quito's All of this is a ploy. Okay, This angle is if soy the angle between the armature current and the induced them f e so, parent cause I nips I give us like you and Zakarin sign EPPS. I give us I d the angle between some 90 degree So Zain, it's I sign upside so I could sign It's I give us like you and I signed up So I give us i d . Now we have the magnitude we need to get the angle So the angle off like you a symbol equal to what from V V is our zero anger. So the angle between I Q and V is equal to Delta and is the angle between I D and Z Voltage ? What is this? This angle this angle is symbolic will toe the 90 degree minus dealt. So let's read all of this. So this is 90 degree. So this angle this angle between our I d and D V, which is our reference. This angle is equal toe mind to degree minus dealt minding minus that. But remember that since we are going in tow the clockwise direction, this direction so the angle is a negative. So it is negative. Mind to minors, death and dizzy. Anti clockwise direction is the postive ANC so e or that generated the meth is equal to V plus i d Exit e J Idea City plus G I Q executed J I Q x secure J I d. Exiting. So this is our induced Smith andal neglect. I armature ir a as the the armature resistance since it is very small now in gets off the visionary, it always a leading bar fact. So we have Zeevi terminal, okay, and we have the m f e since it is a generator. So it is leading by an angle Delta. And yet, if is in the same direction or having the direction off. Q. Okay, now we have the current I leading our The anger between it and the F is upside. And the angle off I and V terminal is if soy it's fine, this angle is fine. So I and every terminal between them for I and the I and the F is the angle between them is if soy so in orderto get the component off. I simply we have the current in the direction off you access and at a 90 degree from it is the current in the D access. So this is I d. And this one is our cue. Submission off two currents is the total armature current. Now we need to find the e symbolical toe eternal Blust I dx dy plus like you execute So I d we need to add it 90 degree so I d will be 90 degree like this is this is Jay I d So, jay, i d x city Is this victor added to determine and dizzy I Q, which is in this direction at a 90 degree. It will be like exists So this is Jay like you execute Jay, I like you Execute the submission. Vitre Idec City Like you Except you. Q. Give us Z and use them F e so z finally we get e v bloody I Q X. If you're Jay, I d accident. Now again, we have E O P which is needed to get the Delta. Why Delta is required Because we need Delta in orderto get the I Q and I d. Since they are function in Delta. So we need Delta. So we got and meaningless value. But with an angle Delta don't get Z Delta value. Now here you will find this is a ploy and this is Delta and this is far I, which is the angle between the current and determine a voltage so far is equal toe excite blas Delta or size for I minus Delta for I minus that like you. So we have here I Q. Which is in this direction is equal toe equals NFC and I d is I Zaynab site r equals I nips I and always I nips I this value, which is I Q. Is always having the angle dirt okay or having the same angle off e since they are on the same day in the same direction I d angle, what is it between it and give eternal all of this anger. So all of this angle is simply equal to Delta this mind degree plus delta, since it is from V to I d in the anti clockwise direction. So it is a postive angle. So it's equal toe delta last 90 Delta plus 90. So we can get from here the induced a meth e Now, in case off seem water with a lagging a power factor. Okay, If you understand one off these phase or diagrams, you can get all of the other fees or diagrams. So we have the voltage V and we have induced they may be at an angle that leg in the Bible . Okay, Why? Since you are talking about and we have a current legging by an angle phi from being angle fine from V and is the angle between E and I is simply if site this angle is it side. So we have the current I and I need the I Q and idea assembly like you is I resign if site and ideas I sign if side like your design him sigh always I name side the angle off I d assembly from v terman is negative Mind too Blas Delta This anger all of this angle is 90 plus Delta my auntie plus Delta about Since we are in the clockwise direction it will be a negative anger The i Q itself Is this like you was? This one is at an angle negative Delta from V this anger this is our i Q and this is V and angle between them is delta. So it is at a negative delta from V that induce them F e in this case is equal toe de miners York, you execute my nausea, I d exiting. So the question is why it is negatives. And so we have mortal, as we said before, So that is equal to B minus the drop. Now we need to draw nectar. Gee, I Q x Q and negatives ai dx dy Now as just a focus with me, I d is in this direction. So the J I d j I d is in this direction. We add on 90 degree tow it So in this direction is J I d And we need negative Gee, I d so negative means that we will reverses effect. It will be in this direction. This is negative. J i d. So a negative J i d x city which is exit the assembly value added So a negative zero RDX city which is in this direction will be like, this is the negative g i d Xidan. And we have negative like you execute we need it. We have I Q and at two a. Jay. So, Jay, this is J R. Q. But we need negative. So negative zero i Q is in this direction. So this representing negative J like you execute negative j like you execute so v minus j like you execute your minus. J i. D Xidan, Give us Z okay if you'll start off course if you'll start to his negatives here Idexx idiot . Well below this negative G i d x city minus negative g r like you execute, give us is the same answer Just adding in off the victims at the beginning will give off. They say in value now is the EP soy here This size, equal toe a negative for minus delta. Okay. Or if so, you just as a magnitude This soy as a magnitude isf r e minus dealt for I minus dealt. Now we have all of the values which is required to solve any problem. Now the elastic case If we have a mortal with a leading power factor So we have the voltage V and we have e lagging by an angle delta since it is our motor, so it is lagging by death. So this is other direction off Thank you access which is the same direction off the induced MFP. So at a 90 degree from it Z d access now is the current which is this one? This is our current will be one in Zach you access and another one in the D excess. The current having an angle phi between it envies This is fried between the current and V and angle upside between I Andy all of this is if soy So in the end we have is that the I Q assembly Quito, I or Zane? If sigh and idea is our sighing upside I q equal I resign if signed, will find it is in all of the cases here and the idea is a questo. Always sign upside. You'll find that this anger, the angle of this one, is simply quite to this angle. So this angle is equal toe mine. T this all of this 90 miners dealt mind, Your Highness dealt and I Q is legging from V boy and anger negative delta this negative delta And if so, I hear is equal to five plus delta for my pasta and E or being assembly as before, equal toe B minus zero I execute here in the case off the motor is negative in case off a generator is posted seminal here in case off the motor negative. But in case Holmes, the generator is Boston E Similarly, as before Now again, if you didn't understand the previous Faisel diagram, you'll understand this one. Now, I Q is in this direction, so we need J. Thank you. J i Q means that we are adding 90 degree toe. The victim So 90 degree does this Victor is in this direction. This is Jay. I like you, but we need negative G i Q So the negativity like you is in this direction. Negative. G I Q So a negative zero i q x secure will be added to V and the direction So this is negative Jr like you execute Now we need to add i d exit e So I d by ending our 90 degree to wait, it will be in this direction and negative J i rd it will be in this direction. This is I D. This is Jay. I d on this one is negative. G i t so negative. Zero idea added negative G i d X city in this direction. So this is the induced the math required. So now we discussed Dizzy four cases off our silly Intertype machine. Now we need to find the power off the silly and the machine with Scott Xena and silly into machine before their face or their equivalent circuit and the power out. Now we need to find the power Albert for the Syrian the machine. So we will assume a generator with a lagging apart factor. Having I q equal. I cosigned upside Delta idea. I sign it. Sign negative 19. When is it does? This is what we proved right now. So we know that the three phase power or the escort apparent the power off a three phase machine is equal to three V i or three V I conjugated Okay, this is from the fares or diagrams. And so we have a serene if a system. If you have Z. If you would like the magnitude, then we'll say is three v I. If we would like the magnitude as the Z power or the active power value and C reactive power values and we will use the Faizo So City V V is a V and angle deal value and its angle zeros is connected toes the power system So three V as it is now, is the current itself consisting off like you and idea and I Q is a victor. Ideas honors our victor, so I d and I q all of them are Contact it. Okay, if you understand the contract from mathematic if you don't understand the complex numbers at all, then goto my own course. Four complex numbers now City V the idea itself. The idea itself is a vector. Okay, having I d here is a victor having a maximum vendors say that this one is I d i d Which is I sign up soy and this one is having a magnitude like you so we can get Z three rail part and imaginary part the rail part of for I de is idee cause I negative nine to minus dealt So I d cause I negative mind tomorrow minus Delta is similar toe i d find out okay, cause I 90 miners Delta Similar toe sign dealt and the imaginary port is I d signed. Negative mind to minus delta, which is similar to negative since we have signed negative 90 So the negative will go outside and know it will be equal to negative sign 90 minus delta, which is negative. I d cosigned. And this is the imaginary port and this is a really part. Similarly again, the rail Bart off like you is like you design death and see machinery. Bart is easy. Like you sign Delta are like you will find that all of this is a contract it. So what does a Contra gate mean? If you don't understand it right now country, it means that we were reversed each jay by a negative G So I designed Delta Negatively becomes most of GE like you except like you call sign Delta Luxury becomes negative zero I co signed Delta So we have here in this case we have a Stevie and we have rial part This one is a rail This one is a rail and this one is a complex or imaginary This one is an imaginary So if we take the imaginary tourism and dizzy serial port whether we can get the b and Q But before this we need to find i d and like you i d We said it is I cause I nips I and I Q as I sign if site or from phase or I d So we have year. We need I d i d Xidan, is this value okay? And if you look at the face or itself like this, is this boss representing all I d Xidan? OK, And if we just to get a projection off this one off the voltage, it will be the design dealt us with this Vinnie design that so v cosigned delta And this this part representing I armature I our armature rejected here. And who said that we would negative I our armature so as this as if this space does not exist. OK, as if we shifted, It does the right does he left. So I assume that all of this is because I am dealt when the armature current is as the armature resistance is here and we have all of this distance is e f so the i d simply went toe e minus Vico Zain Delta over exit E E minus vehicles on delta over exiting. Okay, Why? Since the projection off this gave us v cosigned delta which is all of this distance from here. So here at zero r Mitchell Resistance and this distance representing I d x city and there's some mission vehicles signed that plus i d x city Give us e f now the like you how to get i Q If you look again I to execute, which is this vertical part? This vertical part. If we get the projection off V here on this part, it will be v sign Delta Okay, at zero armature resistance it will be the V will be at this point or view will be extended or the I Q or this victim will be shifted outward. Whatever this value, all of this will be a resigned that which is equal toe like you execute. So the I Q is visa and dealt over Execute, Resign Delta over execute. So by getting all of the rail power together and emotionally part together we will have finally that this imaginary part or rail active power and the Madonna report is Q So rail port, is he active power and imaginary part is acute. So we'll have Finally. Is this to laws for the city int machine? Seapower is equal to three e V over Exit E. Signed out blustery V Square over to one of our execute minus one of our exit designed to death and the cures three e V over exit E Cosigned delta minus three. The square Sign square Dealt our execute Blasco Zain, Score Delta over 60. Now you will not something that when exiting equal execute which is the case off the Syrian machine and non salient machine, you will find that one of our execute minus one of our exit e will be equal to what? In the non salient, this part will be equal to zero, which will give us a V off our excess. In Chronos for Xidan, sign Delta, which is the case off that mon salient the machine power que S three e V over exit equal sandals minus three V square and gets off the non salient exit You will be equal to execute . So science score Delta Blasco Zain Square that the over X give us one of our X Okay, so we'll have negative three V square over X, which is similar towards the case off the non salient the machine. So in this video, we discussed dizzy equivalent circuit off the sink. Rama's salient the machine, the equations and different cases off the motor and generate 141. Solved Example 1 On Salient Machine: in this video. We are going tohave. An example owns a civilian machine before we have an exam it on the salient machine. I would like toa correct something I said before. I said, That's the Xidan. His grace is listens. Execute Okay, but actually X Ding Xidan is great Tarzan Zach execute Why, As we remember, that forms the magnetic circuits that the induct ins is equal toe end square over our this representing Z inducts as the reluctance which is resistance off the game. So l is equal toe and square over our So here is that resistance or the reluctance off air is low. So the inductive is higher and years the gap is higher so they reluctance is higher. So the inductive is lower, So X city is actually greater than execute. Okay, we reverse it It so this waas the correction. Now let's ago and get our first example on the salient machine. So we have a civilian divorcing krone generator has an exit equal 1.2 and execute equal opening date and you'll see that accident, as you said now is greater than execute its supplying one per unit power toe an infinite bus at 4.8 Power factor leg. OK, so determines the load angle, which is Delta and dizzy IMF and used e sold angle, which is delta or the torque angle delta or whatever, or the power angle. All of them are the same and then use the Melfi. So first we are going toe applies the steps inside this face on like mam. This is official diagram off as Incarnation Reiter with a lagging perfect 4.8. Perfect or legging. So we have here that step number one, which is getting the E or B e or being so first e or B, which is our value, which is meaningless but having an angle. Delta is equal to a C voltage plus the total current J I execute so V which is having the voltage which is here in the very on it system. Okay, we are dealing with the very own system and dizzy infinite parts of voltage is one okay, one very on it and its angle zeal plus Z current, which is I, and you'll find that it's anger is negative cause I minus one perfect. Why senses the negative? Because the current is legging. Okay, you will find here that Phi is equal toe because I minus 1.8 and it is legging boy and negative for you saw the angle will be negative cause I'm on a somber fact multiplied by J Execute J execute executes given as 0.8 and J now we will find that negative cause I'm minus one z pointed. Give us negative 36.8 degree. The current itself is equal dozy power or s over the vaulted. Okay, we have a synchronous generator. It's Albert. Power is one very on it. And it's a voltage, which is the output Voltage will be equal to one. And you'll find here something you will find you that it is supplying one very wanted power . This power meant is the theater of power. Okay, so it will be be over V cosigned design. Fine. OK, here in the problem. One per unit is meant to Toby is the active bar. Okay, so now that the power is equal to the voltage was about by the current, because I am fine. Okay. So, uh, so cause I'm finds given as 10.8 and dizzy power heroes after power is one very on it. So we can get They can't. Okay, now we have the current and its anger, native, cause I'm in a swamp or factor J execute and dizzy Voltage. Now we can get Z yeop and its angle GOP will be 1.78 which is a meaningless value. But its angle, which is the delta, is the one which is required. Now we got the delta. The second step is substituting in our laws for this Faisel diagram, we have a ploy equal Delta plus five here, this soy equal Tau Delta plus five. So Delta, which is 26.56 And if I which is 36.8. Okay, remember that if I is a posted is measured from here is our post their value off 36.8. So see if soy is a Quito seconds to 3.6 degree the i d symbol equal toe I sign employed and like you are because I name sign. So we have i d given as one point 1/12 and I q 4.55 Now step number three. We need to find e f e f symbolical toes The voltage blast idea as a victor JX idiot plus like you a j execute. So we have the voltage or the terminal voltage off the infinite bus. This is a general value is one and it's angry zero once pretty on it. And dizzy Rhoda Green and our house. I think before we continue this, I would like Toa tell you that the power here is in pre on it. Okay, so power per unit is equal to the voltage on the blood. Bisi current very own it. V Barry on it multiplied by hyper unit because I'm for But if you are talking capper with an actual value as an example Z power, for example 10 mega What? The voltages 10 kilovolt, the current 100 bear or whatever, as his values are actual value, So the power will be equal Toe city V. I cosigned fine. So that's three years when we're talking about actual values. And three, this appears when we are saying we have a very on it system. So the i d is here as 1.12 and I q 4.55 one pointed wealth and point by five and D J Exit E J pointed it, and they one point toe j 1.2 and is a 0.8. Now we have the anger for dizzy I D and anger for I Q. From the federal diagrams at the I D year, it's angle is 0.2 degree here between, like your between I Q and idea 90 degree here. And we need to find the angle between the voltage and I D. So this angle will be mind to degree minus Delta, but in a negative value. So 90 degree minus delta. So we have years. It'll touches to win 6.56 mine T minus delta. This value will give us a 63.4, and since it is measured in that clockwise direction or a negative, it will be negative. 63.4 is The idea is lagging from the voltage Now for the I. Q. Was said that like you have the same angle, which is Delta do in 6.56 Okay, is this angle so the final valuable always something. All of this will give us talk going 24 at and an angle off two in 6.5 you will find here two things. Number one, That's the angle. Here is Delta, which is similar to yours, isn't this is the first to check. Second, the chick is that that z voltage e f toe born 24 is off course larger than 1.78 which is e o. P. Since e o. P. Is this value and e f is all of this so e f should be greater sends a meaningless value e o . P. And the anger delta or the torque angle or load angle is should be equal to the angle off your pee. So this was a symbol example on the salient machine. 142. Solved Example 2 On Salient Machine: now another example here. What percent off its aerated for Albert will a silly in the polls in Chronos Motor. So we have asking Chronos Motor Assailant Wolsey Thomas Motor mortar deliver without the loss off synchronization Wednesay which you are going to discuss later. But now just to concentrate with this problem When the applied voltage is Mormon and excitation, field or field expectation is zero. So I feel dizzy. Get wound needs us If X city is equal toe point it and executes 0.5 finds a value off the armature. Current adds a maximum So the first thing we would like Toa find dizzy rated I would power Wednesay Excitation feed excitation is equal to zero. So what does that mean? Feed excitation is zero feel the excitation zero means that the e is equal to zero or the induced The meth is equal to zero. Okay, as we discussed before. So e is equal to zero and is the voltage off course since it's connected. So the infinite bus it will be one perry on it and we have extra de we have execute. So the power off the machine is equal toe evey over x design Delta Blust V squared over 21 execution minus one of our exit de signed to death. And guess again off Very on a system we don't add the see here and here. Okay, city when we are saying we have actual values but since we are using very on it So that's three is not available now at the zero excitation or E equals zero, this part is gone. So we have the square over to one of our exit Your minus one of our exit de signed to Delk . So we need to find a Z rated power or the maximum power when we have no excitation. So the maximum power here when we drove scientist Delta it will be like this r sine wave, but its maximum value at a 45 degree. Why? Because if we substitute in the power with 45 degree, then two multiplied by 45 give us mind to degree. So sign 90 is he recalled. The one or the maximum value. So see power maximum will be quite toe attic zero excitation and dealt equal 45 degree, which is the maximum power. Give us the square of our tool one of our execute. Minus one of what? Exiting. So this were won over to one of our executing. One of what? Exit the exit. You as point thrive, exit e is pointed, so we'll have or points 375 bearing on it. Now, when it'll find sick, you'll okay, Since we need to find the rated ABA power, which means S s, which is equal to P plus, Jake, you or the square rode off. Be square as a magnitude, of course, plus que square. So we need to find Z P and Q So be it Sponsoring 75 carry on it and take you as add zero excitation negatively square and dealt a 45 degree X'd 450.8 execute 0.5. So we'll have a negative 1.625 pretty on it. So what does it mean? It means that the machine, since it is negative, it absorb this react apart from the grant and here it supplies act apart from secret. So we'll find something which is really interesting here that add zero excitation is a machine Orza Silien machine is a still providing power. Okay, at zero excitation, but a non salient machine at zero Excitation will provide zero power. So this is called the Saliency Inside us in Chronos machine civilians or civilian power or Silien See, power is the power provided by the city Anti machine at zero. Excited. Now we need the armature current. You know that the current is equal. Tow us over being V is one putting on it and dizzy s as a magnitude is the root. Be square plus Q square or people shake you will give us is the current as a magnitude and the face or whatever. So the, uh, the value off s is acquittal would be square, prosecute square be. It's all points 37 5 30 on it. Que is negative. 1.625 Carry on it. So we will have our current Fine. Okay, so where you will find the needs armature current at maximum problems. So maximum power here means that the maximum active power okay which occurs at 45 degree and s is the total apparent 143. Solved Example 3 On Salient Machine: Now let's have another example. We have the s, which is a parent power in Syria and the machine if all 15 mega, volt and bear and the voltage here is 13.8 Gil Walt. So this values are not happily on it values they are actual venues. And remember that just for you, if you don't understand until now, is the preeminent or what? You didn't go to my own YouTube videos. You can say that very own it. Assembly the value off for exam ity. Voltage as a unit is the voltage at in instant over Z rated value, the rated Very. Okay, So it's simply represented the value off the voltage with respect to its rated value Or, for example, Esperion. It means that the raise the value off s with respected toe its rated value zari show between them. Okay, so they generate Oh, the rivers 80% off rifle loot. The protector is open to it leg x equal or point at five and execute your 50.6 Now, please find easy e and finds adult. So the first thing that Z s here is given and the bar factor is given so as much blood supplies. The power factor we can get is the act of power being. And we have V and we have the exit e we have execute. So by using them, we can get a Z e. Okay, simply again, we have that E and Delta can be obtained from here E o p as they went through the voltage bluster. Gee, I execute from the face or itself as we discussed before. So v is equal toe 13.8 off our roads. Three. Okay, certain pointed senses is value is lying toe line. So are going to use that phase Voltage off 13.8 over certain 0.8 kilovolts over roots three plus j. I excuse We have executed 0.6 per unit and we have years Easy the value off the current Now the problem is here something which you can Those This mistake Okay, there is a mistake here. You can do What is this mistake? That first thing here if you notice and science. The problem is that this values are actual values 15 mega volt And there certain point Aitken vault is actual values about the exit D is given Asbury on it and execute your is very on it. So we have to change the ex city to actual values. Toe asset in OEM executing arm. All we can say is that we have Z s and dizzy voltage as a periodic values. Okay, we can say that those values is one video on it, Okay, As if this value it is aerated value or it's connected to the infinite bus. And this is the rated s okay, as one very on it. OK, but there is a very important thing here is that it's a is as a generator delivers 80% off for lewd. Okay, so the current here is 80% off its full load value. The full knot current I for load here in a very on. It, of course, is equal Toe s over. We s which is one pretty on it over V, which is one per unit, which he gives us one perry on it as a rated current. Now, since it delivers 80% off Eiffel, Load is NZ. I hear will be 0.8. Okay. Why? Because this is the eye for lewd, but we have 18% off it. So the current will be 180.8 Z or 0.8 per unit and its angle assembly since four point tonight. Leg so it will be negative was I am minus one point tonight. This is because I minus one z power factor, which is legging going tonight. So we have our current as a unit execute given Asbury on it, and the voltage is one periodic so you can get E O. P. As a pity on it. One point to 28 its angle Delta is 19.58 now from the face, or we can get that it's I equal fight. Plus, Delta Phi is 25.8 and the 19.58 give us 45.42 so we can get like you and I d As I put it on it. I cause I nips, I I signed up size. This one is Delta negative mind to minus Delta. So can get like you and I do. As Austin, by direct substitution now is induced. Their meth voltage is ee and size a machine. It will o v plus G i d execute x'd ai de exit e plus Jacque, you execute, which will give us 1.24 and an angle 19.6. So finds that this Delta similar to this dealt and this value is larger, sense his value. So the answer is correct. So this Waas that Forrester requirement E ended the second. The requirement is the excitation power and the reluctance power. So the excitation power assembly quite to forget those that question off the power, you will find that this is the part off the excitation. And this part is the part off the reluctance or the Cillian C inside the machine. So this is called the Excitation bar, and this is our reluctance or saliency power. So submission off them give us the daughter power. So the excitation power in this case will be E, which is 1.4 V, which is one point and exit given as or point it 85 to get back or point at five and sign what sign? Delta, which you are operating at 19.58 So we'll have 4.55 carry on it now is the reluctance. Power is equal to the square over to one of our X secure, minus one of our exit e signed to death, which will give us or point of team pre on it. So the total power off the machine is a submission off the excitation which events on the field, the current or the excitation off the machine and another power which depends on the grant or by absorbing cue from it. So we'll have a total power off 0.7. Okay, We can check if this power correct or not, by knowing that be at very own it. System is the voltage amount of blood by current multiplied by co sign for now is the voltage here symbol equal to what? The voltage is one body on it. And the current here is pointed since we are loading our machine poi 80%. So it will be 0.8 and co sign. Fry is given as opening tonight, so we'll have a power off 0.7. So this is the power which is equivalent to total submission off these two powers. The last requirement is excitation. Current is not a change, which means that E s constant. He is constant, but the power import does. The prime over is increased by 20% so the new power increased by 20%. Flying is a new delta. So simply by equating the new power with the equation off TV often exodus on Delta plus B squared over to one of our execute minus one of our expertise, Sorrento Delta will give us, then you Delta. So the new power is one point toe Be old. And the new power is 0.84 Okay, one moment, toe office, the old the value which waas 10.7. So the new power here, or 0.84 is equal toe evey over X design Delta nu plus the square of our to one of our execute minus one of our exit designed to death. All of this is constant. And all of this is constant, which are representing eloquence and the value off even over. X city is 1.64 and every square over to one of our execute minus one of our x League of us or 10.24 5 Signed Tau Delta Nu. And so until 10 You Now you will find that then you Nothing in this case is 23.6. Why assembly? We increased our power generated So increasing support in it means that we will have Ah, higher death. Okay, higher delta means higher output power. So those waas our examples on the salient machine 144. Parallel Operation Of Two Generators: Now, in this video, we would like to discuss Z barrel operations off at or generators. So if we have toes generators operating in barrel, what is the hour? What is the Albert power off Z generator? According to Z frequency. So we have toe started first, dizzy as a relation between the frequency and dizzy power characteristics off a generator. So here is that characteristic offer generator. We have the frequency off the generator versus the power generator. So we'll find that as the power generated increases is NZ frequency at which is a generator which you can operate well, decrease. Okay, more power. Absorb it from the generator means that lower frequency or lower operating frequency. So find that at noon. Would we have a frequency at Nolan which representing isas, beat off the generator at no Lord and at rated output power, we will have another. A speed called F one Orza rated is beat. That slope off this line is called are or considered as this slope off this curve and measured in what bear hurts now is the power Abu offer generator is related. So this frequency relation the power generated equal tow us or the stop off the curve in what they're hurt. Us multiplied my effort at no Lord minus effort System F at Knollwood means that the frequency at no load and therefore system means that the operating frequency off the system . So where did we get this relation? Simply we have here effort toe and for example, if one is operating frequency over system frequency, so know that this is the initial value off power, which is zero at effort. And this is the final off power be generated at frequency F one. So know that from mathematics Y minus y one over x minus X one equal to why to minus Why one why toe minus y one. Over exit tomb minus X one. Okay, this is the relation which relates that straight line itself So that why here is a frequency. For example, we have we need the power generated here. So our why will be a form. So this is F one minus z initial value. Why one the initial value. Why one which is, for example, if it'll over Z a power generated which our XB, minus X one x one is the theme. The power a minus X one x one, which is at it if it'll if it'll is at X one, which is zero. Okay, so the power generated will be equal toe F one, which is the frequency at as a generated power, or see if at as a system. And if it'll which is representing Z at no load. Now here you will find that F one be generated. Okay? And excess be. Now. If we get this to the other side, we will have the slope off the line here. Which is why to why, Tom, which is fun if one minus y one y one, which is if it'll ski over X, it'll minus X one Exito is zero and x one is be generated. Be generated. So this a slope is negative value. Okay, this value is negative. So a Z if we took Z power here, be here and we talk this part here, Then we will have a foreign miners. If a tour over one off the slope one over this club and we have already that the slope is negative, so it will be reverse it. So from the equation, we can get that sea power generated is equal toe SB Fono Lord miners every system and you'll find that year one over the slope You will find that this club is her to spare. What? Okay, hurt is But what Hurtis bear What senses The upper part is F one minus effort which is hurt us. And this one is the lower part. In what? So if we talk this toe the other side, it will be what over hurts, which is our recipe. So this is a relation off. The power generated off one off one generator at a constant torque. Now we will find something here that the power generated here is the electrical power. Okay, the electrical Z machine itself or the generator itself that are pine which rotates zero toe. It's provided in this care of Afghanistan. Talk okay, will provide it Afghanistan to power or Afghanistan to talk. So the power is equal toe talk multiplied by omega. So Omega, representing the rotational is beat and she talk representing the Albert electrical power. Okay, so if we would like to increase the output electrical power, then we will declares the speed at a constant power. So the power given so that our prime itself or the rotor is divided toe the electrical torque generated or developed the talk or develop the power and that speed which rotates the roto itself. So more power required means lower is beat. Okay, Now in this, if we would like to increase that no lord frequency or no load speed or make a parallel lines like this one increase their characteristics, we or something in power system, we opens evolve which produces or provide us more esteem toes after pine, so more esteem. So the turbine means higher is being at no load and increases are generated power. So we would like to discuss if true generators are operated in barren like this and we have a note. Okay, I have a load here and I would like Toa know what is the power off each generator and is a frequency at which they were will be operating. OK, they are not connected to the power system. They are off grid generators. Now we have this characteristics for this first regional later, and the Charest Characteristics force a congenital or this one is the precision aerator. And this one is the second generation zero frequency with the power and the frequency was the power. So this one have a frequency at no Lord, if in a low too. And this one has another frequency at normal. Now you will find that the power off the road is a certain power. Equal toe that power generated from the generator number one and BG to okay. This power depends on the characteristics off the toe generators as rural scenes. I example. So the power taken from Jena to number one and power taken from genital number two depends on the frequency at which our system will open it. So if we're right at this frequency, then the power bi G two and visual. If we operate at higher frequency or a lower frequency, then the power taken from genital number one is this power and power taken from generator number two. Is this power? So in the end, according to the frequency, we will know what is the power generated? And the frequency depends on the characteristics off your generators. Now, what will happen if we connected toe the generator Tosi power system or an infinite boss? So what does it mean? An infinite boss. Infinite boss is a definition representing sigret, which have ah, high number off generators. We have genital number one, 2345 All of them are connected together. Do an infinite bus. Okay, so this large a power system is not affected by this. A small generator wins. This generator is connected. Toe this system. It's a frequency off. The generator will be the same frequency off the infinite passes the infant bus, which contains a large number of generators which are synchronized with each other as well discuss in the next lecture. All of them have the same frequency. So they wins. Arjuna connected to it. Zack generator is force it, Toby. Like them now, These this is that characteristics off the generators. And this is the characteristics off the infinite bus Infinite bus. Which means a large number of generators means that theoretically, we can take any amount of power. This is the frequency off the grid. Example. 50 hearts. Okay, so when we connected the infinite bus with a generator and we salute so the Lord will take the power from the infinite paths which are represented by a large number of generators and our generate. You'll find that as the power taken from the infinite boss increases that infinite bus characteristics is a still a straight line as the hour or a horizontal straight line. So the horizontal line means that whatever the power taken from cigarette, it will theoretically will not be affected or the frequency will not be dropped. This is a characteristics off the generator, which means that when we increase the power generated means that the frequency will be reduced. Now we will find that the frequency, which is 50 artists representing boy store IT line, is this. Spirit lines means that the intersection here means that this is a power taken from the generator regime and dizzy remaining power for the Lou. This is representing the power required by zero would part of it from our small genital and zero from the infinite Bus. So simple is this is what is meant by as the barrel operation off Atos Generators Anjanette to connect it to an infinite boss. Now let's see an example. We have a generator number one with a frequency at Nollywood 6 to 1.5 Hurtis, and it's B or the slope off the line is one megawatt Their hearts. Zach Generator number two is the frequency at Knollwood is 6 to 1. Hurtis the slope off the line number one mega What? Their hurts zeroed itself required. A tow provided by that generators is the road is equal to 2.5 megawatt. The power factor is point it liking now determines e the frequency off the system at which is this toe generators will operate and the power taken from generator number one and the power taken from generator number toe. So how we can do this simply We know that the power off the road will be equal to Z. Some measure off powers in a little number two plus power generated by number one. And we know that. See, fortunate Number one is equal toe smp is my air motor blood boys a frequency at no loot minus the frequency of the system. Similarly busy toe. So if we look at the 1st 1 the power off the road, which is 2.5 megawatt equally cozy powers in it. Number one blast number two Number one is equipped with a slope number one if a new lord minus for system Similarly number two. The slope off number one is one slope number two is one. And is the frequency at Nollywood off? The 1st 1 is 6 to 1.5 Hurtis minus the frequency off the system at which this tool will be operating. I don't know it. Plus one multiplied by frequency at Norwood off second generator, which is 61 minus the frequency off the system. So this is an equation. Symbol equation in one unknown. So the frequency off the system will be sacristy. Hurtis. Now we would like to get busy one and division toe, simply busy. One is smp one effin lord minus effort system. So take this sexist artists and substitute Here it will be one about the blood by 6 to 1.5 minus 60 which is 1.5 megawatt and is the second generator simply equal toe one multiplied by 6 to 1, minus 60 hertz. So this is the second. The power generated and our friends is some mission is the 2.5 megawatt. And if we draw our system, it will have the 1st 1 will have 6 to 1.25 at no load and 2nd 1 61 at new loot. And this is the frequency at which the system will operate. 60 Artist, This is the power taken from the NATO number two And this is the power taken from generator number one. The second the requirement is one megawatt is added to our loot. Find the new F system busy one and Butto. So we added one mega. What means that our new power will be 2.5 plus one, which is 3.5 and the same steps as that? No point number one. So the new powers 3.53 point five equal to same as before. Now the frequency system is not 59.5. Previously, it waas sickest artist now 59.5. So the frequency is reduced. Why? Because more power is required. So senses Elwood increased means that more power is absorb it so the frequency of system will be reduced. Now is the power generated from number one would be told megawatt and the 2nd 11.5 from here, or force from this tour equations. Now, these are the requirement is what if f a no load number to increase it to 6 to 1.5 Hurtis. So instead off having if a load 61 hurt us, we increased it. So 6 to 1.5 finds a new emphasis. 10 busy one and a busy toe. So what does it mean? It means that in our case, instead off having this characteristics, we will have another one parallel to it starting from 6 to 1.5. So we did this hell in power system. We can do this by providing more steam to the turbine. So more esteem toes after pine means that the Albert Power will be increased. Okay, So the omega and is the hour power will or being trees together. Okay, so now let's see Number three. So in number three, here we have that you on 6 to 1.5 and is unique characteristics. And this one is a new characteristics. Now 3.5 in our new loot, one take storm 10.5 and this one is 6 to 1.5. Instead, off 61. Now we will find that they knew or frequency of the system is actually 59.75 which is high resents of previous value or 59.5. Why senses in power or the characteristic is shifted up means that I can take more power at the same frequency. So that frequency increased the senses. E curve shifted up. Now we'll find that the characteristics off this one is similar to this one. So the power donated number one would be Quito innovated number two equal 1.75 megawatt. So in this video we discussed dizzy parallel operation off a two generators I generated connected toe the infinite boss and an example on the barren over age. 145. Synchronization Of Machine With Grid: now, in this lecture we would like to discuss is the synchronization off machine with a great. So we said before we had the infinite bus connecting a large number of generators 12345 A large number of generators, all of them, are operating at the same frequent 16 artists or 50 years or whatever. And I would like to add a news generator toe this set or to the infinite bus. So that addition off a new new generator toes the infinite bus it's called Is there synchronization off a generator with the infinite bus. Now, what is the definition off that synchronization in an A C system alternating current electrical power system. The synchronization is the process off matching Xas beat and the frequency over generator or other source to are running network. So we have here we matches the frequency off this generator with the frequency off the infinite bus and ISI generator cannot deliver power to Onek electoral Great unless it is running at the same frequency as the network. And we have some conditions for connecting the generator. So the great So what are the conditions Off sync organization off our generator wizig rent number one. That generator showed how should have the same voltage. The same terminal voltage off the generator should be equal toes, a terminal voltage off cigarette or the voltage off the grant. Number two, it should have the same way for the hour. But was a great way for is off course Assign a Saudi a wave So the generator should also produce so you'll live. It should not be off course and would be a square wave like the one which comes from an inverter or at two level inverter, for example. It should be a sign with Number City. It should have the same frequency. If the frequency off the Glad it's 50 hurt us, then the frequency off the generator should be 50 hertz. If it's Sechrest is in the generator should have the same frequency off 60 Hearts number four the same face sequence. They should have the same first sequence. Okay, what does it mean? It means that ABC or the sequence off them, so be the same. So, for example, if z every a every B and V scene, okay, and we have three terminals off more system this term on for example, a And this one is being and this one is C So Z's, this is the hour it off the generator. Okay, so that fits. A should be connected with Fizzy and Bisbee should connected. Frisbee and Facey should be connected with. See? Okay, so they should have the same face sequence. This is an angle zero, This is Ah, minus 120 is plus 220. So this one should be the same. Ah, zero minus 220. Plus 120. You should not reverse any off the tour at tournaments. Okay, is he should have the same sequence. They should have the same initial angle or for shift. In case off, we have re eight equal v sine omega T plus five science. Oh, man, get team los fine. So usually v sine omega t plus phi. So use one easy fi, or that phase shift is usually zero, and the fish shift occurs in this phase. Shift in that generator should be similar to was a fair shift in the grant. If any of these conditions is not satisfied, a large circulating current will flow inside the machine or a short circuit will. Okay, so it is off course not allow it to not having any off this conditions. Satisfied in orderto does that synchronization and make sure that all of these conditions are satisfied. We are going to use a miss Would called the top right one door Clamber missing. And there is Amazon. Mr Gold's a Sridhar. Clamber, miss. So what happens here? We have a lamp. We have the three tenors a one be one NC one. Those are the terminal officer generator and we have a two be toe and see toe those hours eternal off the power system. We connected the first time between a one and a two and the lumber number two between B one C two and to see one beetle. Now in orderto does that synchronization First, we need to adjust the frequency off the generator toe matches he get or the network frequency. How? By changing this week off. Generator remembers at the end equal to 60 f over being. So by changing the speed off the generator, we can. It changes a frequency off the generator itself. Now the second thing is that the way for Miss similar as generator and both of them are signed. Soldier the voltage or they're relying Tow line Voltage is adjusted by varying Z field. The current So by changing is I feel the current we can change the induced them f e which in turn will it change the V line to line or the terminal voltage off the machine? So we can It changes the voltage until Z voltage here matches e a great voltage. The face sequence is adjusted buys a surreal amba mess on three dark lamp, a message or top right $1 clamp And this missile which in which showing in the figure number one the three lambs are connected between the generator terminals and system tournaments one between a one a two us around between B one, C two and C one b two The correct moment which means that this saree phase are synchronized with the three phase here is or was a correct a moment off. Closing this which or connecting is a generator. Wizig red is when that lambie here this lamp is dark. Okay, wins a straight connected lamp is dark and this to Lambert's are having the same brightness . So what does it mean? Okay, if z fizzy one equals V sign Omega T and the V sign Omega team, then connecting at Lambeau between two phases Having the same voltage means that the voltage here will be zero. Okay, This one, for example, provides a current in this direction. And this one provides a current in the opposite direction. The artist seem supplying. So the voltage here across the lamb will be zero or the slam will be dark. Now be one is different from Cito and DB two different from C one. So if Zee Lamm here, this lamp will be operated and Islam will be operated if the brightness off the stamp equals So this lamp this means that we won. The difference between B one and C two is equal to the difference between C one and to be toe OK z or have the same voltage. So in this case, this lamb will have the same brightness which means that be one is similar to be toe and see one similar to Sito. But what will happen if xylem is no dark or is a city lamps or dark? What will happen in this case in this case, the face sequence will be incorrect. Okay. And in this case, we need to switch between two or phase. So why does this? Lamb will be dark simply if this one b one. Okay, so I know Omega T minus 120 this one is B two sine omega T minus 220. Zen's a sequence is correct. But if this one is sine omega team minus 120 and this one is sine omega T minus 100 went to tow this one is Beato in a set off Sito. So in this case, the voltage across the Lambo will be zero. So the lamb will be dark and this one would be also see once Ito, which means it will be dark. So the basic once is wrong. So in this case, we will switch between two faces. We were replaced. Be one with C one, and in this case, the office sick ones would be correct. The three dark missile assembly we will have three like this three lamb bus. And this is a three face off Asian or later and three face off the great and will have first Elam like this and second lamb and serve them. We close that switch. That switch between the three terminals wins the three lamps or dark. Okay, wins this voltage equal to this and this, Walter equal to this and this one equal to this. So in this case, that's three face will be synchronized with cigarette. So in this video, we discussed disease synchronization and how to do it and how to the state in left. 146. Simulation of Synchronous Machine Connected to Small Power System : Hi everyone. In this video, we would like to simulate the asynchronous generator in power system and having a transmission line, having another swing bus or swing generator. We have a city phase fault. We need to know what is the effect of happening over there three-phase and after reaching steady-state condition. So all of this we would see now how we can simulate it inside the MATLAB. First thing we are going to click on new Zen Simulink model. We will choose a blank model. Now, starting here with our Simulink model, for a single, we need a synchronous generator. So we are going to the Simulink library as always. Then we will type synchronous machine. And we'll find here is the synchronous machine. You'll find here type which is the cilia and the machine. And the machine will see here is that we have a synchronous machine in Betty on it values, fundamental better unit values. And do we have here a synchronous machine barrier on standard? And we have a synchronous machine in Z or iSCSI or units or the fundamental SI units. So in this system we are dealing with power system. We need here to use that barely on it venues. So in order to use that better unit values already chose that synchronous machine, baryonic fundamental. Right-click and add block to the module on title. We have here our synchronous machine. Let's maximize it a little bit. So we have here our synchronous machine, and you'll notice that this synchronous machine will be generated. So ABC is the output of the generator or the three-phase output of the generator. M is the measurement board. We have BM or Zen mechanical input power to the machine. And do we have Vf or the excitation voltage enter Tuesday machine. For the synchronous machine itself, we would need to add here Z, mechanical input power and that field voltage. We can make the VL, the voltage you can understand and makes them mechanical power constant. But two are not going to do those as well, going to do something the front inside this video, we are going to use our control system, such as a hydraulic turbine for the generator itself? Or does that Bob mechanical in willpower? And we'll use for z field, we will use an excitation control system. We would use here a different thing. We need a closed loop in order to control or controls the excitation and the control Z mechanical in both those degenerate. Going back to Simulink. First, we need the excitation excitation system. It will Control Z field voltage, will find the excitation system. Okay, So this one or this one, whatever, right-click Add block to the model on tightened. This is the excitation system. This one is excitation system, which provides that field the voltages to our generator. Now, we need that buy-in or hydraulic turbine. High. Draw lick, lick data by right-click and add block. Does the model on tight. Okay, so we'll have here our mechanical in biopower, which is in-between generator, synchronous generator, and we have Z control or excitation system, whichever provide this field, the voltage to 0 synchronous machine. Now we will find here we need an omega France be a reference omega E z electrical power or electrical power generated. And d omega is our variation in z is omega is that bid outwards is bit of xij generator or speed of the generator itself and radian per second. We're reference, reference voltage for their excitation system, 3D and V-Q. And as a voltage stabilizer, if we have a stabilizer, then we will add here. We will have stabilizer and connect it to 0 supplies. We don't have one, so we'll use our ground. And then choose any one. Which one, which one that says Add link. Adds a block to the model entitled. Let's see if it will work or not. Selecting this one. Like this. And entering here. So if we don't have a voltage stabilizer, which you know is it is something which is called Z power system stabilizer. If you have it, then you would add a block for it and connect it to here. If you don't have it, then you will make it 0 by connecting it to the ground. Now we need to dereference omega reference and the reference. So we need a constant. Right-click and add block does the model on titled tags, this one here. We'll make 123 blocks. Connect this one here. Double-click this one here, and click on it. This one here. Collect on it. We have z, omega France, Francis bead embedded unit system be a reference embedded on it. And we reference these values is used at two megs. A control loop or Zach laws the lobe to reach a steady-state faster. According to the Simulink program itself. If you look at the MATLAB going to MathWorks website, you will find that that beer reference default value is 0.75. I will tell you now something if you make it one, if you'll make it 0.75, whatever, you will find that z-value of the abbot will be the same. It is just the **** bit to reach a steady-state first. Now, we need omega e be mechanical, mechanical power or electrical power. And z omega. How we can get these values and IVD and V-Q video and the VQ is direct excess voltage. V q is q axis voltage. Remember that this one is a hydraulic turbine. Since it is a hydraulic turbine, then it is salient machine. Double-click here it is at salient type machine. Why? Because the hydraulic system have lowest bid. So we use salient, the type synchronous machine and z round or z non salient is used for Z faster generators such as the diesel generator. How we can get this value simply by using the boss selector, bus. Select. First time we will add block to the model on title bus selector. This one. Let's make it bigger like this. Take it here and control. Control. You will find that control plus I use the total flip X0 block, get z measurement ear, and both adhere to the bus. Now what is the value is needed? Omega0, b, dW, Vdb Q. So double-click, delete the signals, select all and delete. Then first thing we need z omega AB. Okay? Let's choose all of our values. First, we need the DQ components. Let's see dq components, which is V D and V Q. Going here, VD select stator voltage V-Q component of VD, and the component of VQ is required the Ford is excitation system. In order to reach a steady-state for Zack laws, the loop. We need heat says speed. So speed is related to the mechanical. We need BE, which is electrical tower. Select. We need that d w and omega e. Omega e, which is rotary speed. Select the we need that variation in being DW. Select. So we have 123123 and we need VD week. We have v dv, dq. We can add another thing for ourselves, which is a load angle. Here we need the B naught means is that I would act a bar. Note here that Z electrical power. We find that it is b0 and b0 all which means that our robot or related to the Albert active plot, since we need only the act about for this lobe. So we will select it. And select is, is one where it is it mechanical electrical power. Delete it. This is the one which is required for 0 B0 all or the mega electrical output active power. And do we need load angle in order to see what happened to the load angle delta Forza generator itself. Going up here, we need also the stator current. Let's see, whereas the stator current here select to see, for example, Z sets or current IA, what will happen to it due to the presence of fault and the reaching steady-state. The first one is stator voltage V d. So take it here, V d, like this. Second one is a state of voltage V-Q. So take here, this one here, V Q. Or you can just go to here, stand at it with the mouse. You'll find that the one is mechanical rotor speed omega m, omega m. This one. Here is the number for z d w, dw. Number five is the load angle lift. Okay. Leave it now. I would ask the power p-naught, okay, tags, I'd be out with B naught here. Now we need to seize delta and the dizzy guarantee. We will use a scope, scope block to the model on titled Zen control and drag. Now we will connect this first one to z Delta. This one is z load angle. This is a scope for Z stator current. Okay. Now we're provided feedback obviously Albert from z measurement back to Z, Z hydraulic turbine controller, which is the governor. And here z excitation system, control for the excitation system giving feedback from the measurement board. Now we need a, B, C and the output connected to add transformer. We will assume that we have of our system. So that power generated here will be connected to a transformer. Transformer connected to our transmission line, then TO another generator and embedded with eight Z load and z three phase fault. Now going back here, we need Z transmission line or the transformer first transformer, transformer transform. Now what the type of the transform menu do? We need a three-phase transformer? We need a primary and secondary. That's all what we need. So it is a two winding, primary and secondary. You will find the three-phase transformer, three windings, one primary and two secondary. Transformer winding owns Primary and seconds. This one is that one needed ad block the OSI model untitled like this. This one here. They exist one here. And the final is this one. This is a three-phase transformer. Now if we double-click on Z generator itself, you will find here is our parameters for the synchronous machine, such as the power generated involved and bear the rated power and the line-to-line voltage in RMS. And the line to line ends or frequency of operation, which is 60 hertz. Now here's a line to line voltage of the power generated is 13.8 kilo volt, or 13,800 kilovolts, 1300 kilo voltage, only certain 0.8 kilo volts. So this is the voltage generated and this is a frequency generic, okay? We will make this one delta delta star connection to rule, but reduce that delta connection. This one will be a delta and this one would be his star. This is a step-up transformer. Now Z parameters, we need the inward voltage. This is nominal power frequencies. We need the voltage of the primary to be 13.8 kilo volt. We have here a bar three, which means ten power three. We need is a primary to be similar to the generator. So 13.8, so this representing z0 is 13.8 multiplied by ten power three, representing z kilo volt in both two. Transformer itself. And the output of the transformer, we will assume it is at 230 kilovolt. 230 kilo volt mix up on uncertainty kilovolt. We have here I delta star connection, delta star connection transformer. We need now our transmission line. Here, transmission line, transmission line. You'll notice that zeros are different configuration for the transmission line. For example, you are going to z bimodal. So as you're bimodal, which is similar USDA for this library, which is the power Library, is a three-phase. Since we have here as three-phase system. Like this, three-phase in both three-phase out, we need as three-phase bimodal. This one, three-phase bisexual multiple ad block to the module on titled exist. They exist one here, this one here, and this one here. Now what is Z? Next step, we need to add Z load and we need to add as three-phase generate. So z naught will be load. The load. Let's go down and see as three-phase node. Three-phase, see it as are a lesson. We're going to add a block to the model and tightened like this. We need also a three phase fault. Fault. Fault. Why is the fault in order to seize the response of the power system to Z fault having as three phase fault. Right-click Add block to the model on Python. They get here. Then control, I, control our first Zen control. I flip the block like this. Now we need finally voltage source. Voltage source. Now, the voltage associated used is a three phase source. Right-click Add block to the model on titled. We are here simulating a power system as if we are dealing with a power system, having guy, synchronous generator, transformer, transmission line load. We have another generator inside our Grid and z, three phase fault or getting here. And we need to see the response of our system. It takes this one here, control or he likes this. Now connect this one here, a to B to C to C By exists and connect the a, B. C is fault a, B and C. In addition to this, we will add a load here, Control and drag care air exist one here, a, B, and C. Now let's see all of our components here. For example, if we look at x0 bimodal, yours is that here we can see is a frequency used stimuli artist. And you'll find here as 0 sequence positive, negative z lying lands in kilometer. All of these values is available here in order to change it as you would like. Now looking at our load, load configuration is why connected load and grounded. And the nominal phase to phase voltage or line-to-line voltage is one hundred, ten hundred. Here, Z line to line voltage, as we'll see. The secondary, this is a primary. Secondary is 230 kilo volt. So we will make this 130 kilovolts. Where is it here? 213 kilo volt. We can make it ie, sitting, okay, 230 kilovolt apply. We can make capacitive reactive power 0. And that after Board 0, assuming the resistive load here we are going to do is the same, but the voltage here is 13.83. Because here z voltage at the primary here is 13.8 volt line to line voltage makes this 10 and this one z. We have here a load at the generator and we have another load I have towards Z transmission line. Now let's see is that three phase fault. You will find here different parameters such as default or resistance. The ground that resistance, resistance, capacitance. And you can change these values as you would like. Number two, you can find yours at Z fault here. Short-circuit here is occurring between phase a, phase B, phase C, and the ground. So this is a three-phase symmetrical fault with the ground. If we make it remove this one and this one, then it will be between phase a and the ground, which means at line to ground fault. If it is like this, then between two phases and the ground, so it is line to line to ground. Will make it like this. Then it will be line to line to line as three phase fault or getting between the three phases only without the ground. But the most severe one is three-phase with the ground. Now we will find it on other things, switching times. What does this represent? Representing z? First, the innocence of applying Z fault and the innocent of openings default. So at one of our 60-second, Z fault will be connected to this line as if we have a pdfs fault. And at the time of five over 60 seconds, Z fault is cleared or remote from our system. We will assume app buoyant one. And assume buoyant to. Now what this is, this is our swing phase, the phase to phase voltage. And let's make it also. What is the value that we choose to wonder uncertain as I remember, 200 and under uncertainty kilo volt, okay? So 230. Okay. We chose that face-to-face voltage apply. Then. Okay. What does this do? This is if you look at the load flow, is this is a swing degenerate. What is that swing generator? It means that it is the largest generator in our power system. It supplies the remaining load, and it is the largest generator in the system. We'll find here is that this one supplies to supplies the loads, this one and this one. And this generator also chairs with a certain power. Now we revert our power system. The only thing remaining is z power GUI block. Again, what is the benefit of z power block? Ebola goal we go II block is usually to analyze our system or sold with z equations in our system. The ODE or z differential equations in our system. Okay? Linear or nonlinear equations. In order to finally see z final values in the scope after and before the fault and during transient conditions. So here if we apply as a continuous starting run, you will see that here it will take a longer time in doing the analysis, you will find the look as the tongue itself TO 0.55 multiplied by ten power negative cities, Sarah, and 0%. So it will take longer time in solving our spar system. In this case, what does the MATLAB do? Let's see now what does the MATLAB say? Go here. You will find that here. You will find that we, as it has a method called is a phase or simulation method, is this method is used the two studies, electro-mechanical oscillations of power systems consisting of larger than haters and the motors. So as an example of this message is a simulation of a multi machine in a three-phase system. So in order to study is that electro-mechanical oscillations when a photo or a variation in the load angle delta in assist him having largest generators, group of generators and motors. In this case, we'll use that phase or solution. Let's get back here. What is the phase of social and how we can do this simply by going to zap continuous double-click. And you will find here in block, you will find the results or solver type is called continuous time. If you click on it, you will find that this grid and vasopressors are three different methods of solving our system. This grid simply takes samples of time, funding or assembled time if we make it 0.1. What does this do? It simply Apply and Okay, and I will show you what. It will happen if we choose this option. Now, if we open any scope like this one, look what will happen. You will find here at every instance of 0.1.1.1 will find that after solving it, it will give us this value for which one load angle that add 0, it has this value at 0.1, it goes down to is this value. Then add another o after 0.1, it will go to another value after 0.1 goes to owners or value and so on. So basically here what happens? It divided Z system and towards a solution into discrete or steps. It's always the steps, as he told, was the Apollo system in steps. It's always at 0.1.2.3. Then we connect them together as a step function. This is not a continuous solution. In this case. We use z solution which is called design phase or solution. The frequency is 60 hertz. Now someone may tell me now, when I double-click on z power GUI, I can't change this one from continuous to any other values. It is constant and they cannot change it. So how can I open this one? You can go to the settings or right-click and configuration parameters. Then go to this over here. And you will find here is that we have the solver. You will find here we have a different the types of solver for the ODE order differential equations. Here, different methods. You can choose any of them and you can read about each of them to understand when to use them or which one we should use. So as an example, weekend use this one. This one which is called dizzy Vygotsky champagne. Okay. I think I pronounce it correctly. This is one of the methods of solving ODE. This door burst together one and he's a student, Vygotsky and champagne. I think. I don't know how to pronounce it any way you can choose, for example, this one. And you'll find that when you select this one is different from this one and you'll find different solutions. So for example, we choose this one and Apply and Okay. You will find that when you double-click, you can now change it from continuous to any value. I'm talking about with previous versions of Z MATLAB program. Now click on, Okay. Now let's see if we start the simulation. Let's make it 30, for example. And start is as simulation at 630, similar to the previous values, you will find the exact simulation is now faster than before. Now the simulation finished. Let's see the values. We apply default at 0.1 and declare date at 0.2. So the first one here, let's see this one is the load angle that Double-click. This is the load angle delta and its variation with time. So Z, load angle at first, except breast, transient condition and very high frequency oscillations due to the presence of fault. And afterwards the fault is cleared, you will find that z power system is going to do that steady-state condition. Now let us see almost one. This one is a stator current, double-click. Like this. You will find here adds up beginning. It was too high frequency oscillations. And the higher value, you will see that 55 means five per unit, which means five times its rated value. Find very high currents, very high frequency and high currents due to what? Due to a business or fault and then clearing this fold. This will cause high frequency oscillations. Xunzi current starts to go into the steady-state and finally becomes steady. So this is the load angle and this one is z current. Now as an example to show you is that if I change this one too, for example, one Xin run. Let's see what will happen to our system or winnings there. Load angular scope, nothing to change. It is the same. The current is less than one video on it. Lesson one body on it. This is how to simulate a power system in MATLAB. Now, let's see another thing here. Now. If we change the silhouette, for example, this load is ten power t multiplied by t bar three. This one is also ten multiplied by Tibor City, which is totally 20 kilo watt bulbs. Those are synchronous machine parameters. You will find that z nominal power of the machine itself is 187 multiplied by ten power six, which means 187 mega volt and bear 107 mega volt embryo. So if I change it, for example, Z ten kilowatt kilowatt. And mix this one, ih bar six. It's 100. Done by Tim bar six. We have here 200 mega volt and bear, since we have no L AND Q and Randy know capacitance, we can say is that the volt and better would be similar to Z kilowatt. We have 200 mega volt and bear, and our machine is 107 mega volt and bear. So this machine cannot supply these two nodes. Let's see what would happen before that simulation. And I will tell you what will happen. What will happen is that z values obviously current and Z load angle will not change. Let's see why. Look at this one. For example, you will find that z city-state omega or does the load angle delta is nearly the same as before? The Z current itself is less than one video on it, again, did not exchange. This byte is changing absolute. Why? Because in the end, this one is the largest, largest degenerate or inside that system. This one is a swing and design main generator. It is on which will provide his most of the power. Let us see what will happen if we remove the legs AS select this and select this. And lit. We have 200 megawatt and beta, which is greater than the capacity of z as generator itself now run. Now let's see the current and delta delta. You will find that the delta is going down. Why it is going down? Because it cannot supplies his power like this. And see, Let's see if the current is the current heat absorbed with buys. That generator itself is nearly greater than one video on it, which means that the generator now is over loaded by this load. Overloaded more than its capacity. So let's see if we decreased it to, for example, its capacity 100 mega volt and bear. And this one, Let's make it for example. Not 87. I will tell you now why. Let's make it tick esteem. Why 60? Because remember that the Z transmission line itself having add x to power and the power losses, the submission of losses plus this, plus this load should be within the range of Z capacity of that generator. Now run again. Let's see what will happen after this. Double-click on Z load angle, z load angle and nearly reach it as steady state value. And disease current. The current is less than one body on it. Okay, Let's see, make it more. For example, 80, not 80, make it 85. Run. Because of course is the power here is not to mega volt and bear. 0 says here, of course. Let's see again, nearly equal 20. The current nearly equal to one per unit or a little bit over loaded, a little bit overload. You will find these at the values of the current and is the angle theta it change it when we're remote swing generator or the main genetic. So we see now is that effect of the three phase fault with the basis of our swing generator. And who's our this January. I hope you benefit from this lecture and small power system simulation with the presence of a synchronous machine, transformer transmission line. And finally, loot. 147. Construction And Theory Of Operation Of Induction Machines: hi, everyone in this part off the course, we would like to discuss Izzy induction machines. So in our first lecture we would like to discuss is the importance off induction machines and is equal instruction off induction machines. So, first, what is the importance off induction machines? The induction machines are one draught or type, or that wound roto. Mortal times are suitable for loads requiring high starting torque and a law starting current. So simply there are two types off induction machines, which were won't discuss. In this video, we have something which is called the one daughter or the Slow Bring and another type called the Squirrel Cage so that Wanda wrote or typed mortals can we can obtain from them high starting torque and low starting current as well. Learn Inside Z course. The induction motors that can be used The foresee in loads that require speed control will find that induction machines or induction motors, which is the widely was motors. You will find that we use it for loads that require speed control. We have different methods off his speed control inside the induction motors, which are going off course towards cuss. The induction motors are used in Crans bombs, innovators and compressors. The induction generators can be used with wind turbines because we have a variable frequency or a variable is bid, so we use with them induction generator. The induction regenerator have or require less maintenance because if it's a row, post construction or, for example, if you are talking about these kids, as we would see, it does not require any maintenance because it does not contain brushes. Unlike that day. C'mon, Ze s query Cajun motor is used as induction generator as is. Also, it is shaped in comparison with the Wando. And of course, it required less maintenance and will understand why in their construction itself, the inductions and a little also does not require any synchronization. Conditions are like that synchronous motor and synchronous generator, because the induction generator itself take their excitation from sigret. Okay, so that great or the excitation is provided from sigret, so their induction generator automatically synchronize with the grant. Also, our oneto discusses the induction, generate the induction generator. As we said, it is used to in when farms or when the turbines in order to generate electricity. So the induction machines in general or the induction motors subsequently used the four loads that require is beat control. Why this beat control methods? The induction motors are used off course in case off requiring high starting torque and low starting current by using Z one roto or C s like bring types and the induction genital used the inside. See wind farms which have a census, he went have a variable speed. So we use the induction generator from orderto reduce the voltage or the outward voltage as him as a great okay. But if we use as in chronic generator, it will produce a variable frequency output, which is off course, not acceptable. That's why variable is beat, but I was being Source is used with induction generate. So in order to understand about, see where the induction machine, we need to understand the construction off induction machines, the induction machines, similar toes, a previous machines contesting off state or roto and their game Okay. Three men Bart's same as e synchronous machine. We have the field wining and the armature one in D. C machines and we have in another type. Which is he? As in Chronos machines, Of course estatal rotor and air gap similar to each other. All of them are based on the same principle off electromagnetic induction. So first, let's understand the stato a state or first Izzy a part here which contains a Z winding or the three phase winding. Okay, the state or three phase winding so simply it has at surrender ical shape, you'll find it is on form off. Slender. Okay, number two, it is laminated off course. Ato reduce the Eddie losses as we said before in the D C machines and it carries a three phase. Palin said winding will find that here we have a e being and see OK, three phase winding A, B and C and A for example, It will be like this going in like this and be going like this. Okay, we'll find that we have input and output off course and see, for example, like this. Okay, going into was the postal or going to toes e c days. Okay, whatever it is. So the city phase winding are shifted by ah, 120 degree electrical in his space. So what I mean by this you will find that the angle between A and B and the angle between B and C Anger between seeing and a are 120 degree. Okay, between this angle is 120. Degree is this angle is 120 degree. This angle is 120 degree, and this one have C is our phase winding B is another phase, and see is another face because you know that in electrical power system we use as freeing face system Okay, there are, of course, single face induction machines about now, in this course we discusses as three phase induction machines which require, of course, high power the state or can be connected in Delta or store. So that winding itself it can be in the form off Delta, for example, like this. Okay, the delta connection. This is a SRI phase winding or can be in a store connection like this. Okay, we will also discuss the equivalent circuit in the next video like this. It can be a star connection where we have ABC ABC XYZ three face import supply and sniff is input supply. So in case off Z motor, we supplies that three phase voltage does the state okay and gets off. What? In case we are talking about induction motor in case off a motorway provides a three phase here in case offers generate all we take the power from the three face off the state. So the state or acted as if it is the armature winding in the D C machines. Second thing off course is there is air gapped air gap. This is zero toe and this is the state of between the state or and rotor off course. We have air gap. And as as we said before, this arrogant is responsible for a few functions. Number one, a very small, clear answer toe allows the rotor to rotate. OK, because if there is no air gaps and this rotor will have a friction with the state or and of course, this is not allowable. So we need a small air gap or us more clearance toe. Have a small X or the small and reactant in the equivalent circuit. So this small gap allows zero toto rotate. Another thing is that air gap allows for electromechanical conversion or the electromagnetic conversion. They convert easy electrical energy into Magnetics and magnetic too. The man electrical here, magnetic toe electrical owns the rotors. Enza rotor or the electrical power will be converted toe mechanical, whatever it is used, the four conversion or the conversion off electric power or the energy occurs inside this off course. It is responsible for calling Z machine. Now. The third component is the rotor zero Tohir air consisting off number one. It is cylindrical and eliminated. OK, cylindrical. Same air zing state. Okay. Laminated toe in orderto reduce Ziadie losses. It carries zero tour winding. So this rotor carries a three phase winding or it can be copper pours. This is the bending gone type off Roader as we will discuss now So it can be The rotor itself can contain a three phase or can contain copper powers. The rotor can have two types one which is you want to type or the slip bring time and the other type is called the square kitsch. Now is the forest the type off the rotors? It's called dizzy wound rotor or the sleeping. You will find that want What does I want to mean? It means that it is wanted. Okay, I'll see that here The wires is wanted around, Dizzy wrote. So this one is a story phase winding. You will find that it carries the rotor winding, which in this case as three phase winding, same as the state. Okay, so we have in induction machine this state, or is a stray if a state or city phase winding shifted by 120 degree in space, and the import supply also shifted by 120 degree electrica. So it has two characteristics. That first thing is that is the state or shifted by 120 degrees as any space or mechanically and 120 degree electrical according to's a supply hair. The winding is also a sniff is winding in case off the one daughter or asleep bring and this winding czar shifted by 120 degree also in space, so it has as three phase winding, shifted by 120 degree. It can, of course, be star or death, but in general they use a star. The rotor wanting short circuit by means off asleep brings so the three phase import supply or the state or is not a soul circuit. It is provided by a power or connected toe, a three face supply. Or we take it the Albert in case off the induction generate but in gets off the rotor, the rotor winding a short circuit by means off slipped, brings and process so far, and here we have that three phase winding our short circuit together. All of them are connected together as a short circuit buys a mean off, asleep brings and the process since zero toe is rotating, so we have a process in orderto hair toe connect, the whizzing slip brings. So let's look at here. You'll find years. This one is this one is a rink. This one is an ink, and this one is a rink and you'll find Here's the process one and two and three. Okay, so we have three process connected tours hearing, which is rotating each off the string, representing one of the faces. So by connecting and light exists, the are short circuit two is okay. Now, see, advantages off this type off slip brings is that we can adhere. Have variable resistance. Okay, So what is the benefit off this resistance? This resistance is helpful in a speed control and starting off machine, as we will discuss in the next two lectures off the starting A message. And this bead controlled the rotor winding as well said, now is accessible, which means that we can end resistance for his beat control and starting off them machine. The second, the type off the rotor is a squirrel cage. You will find that it looks like this. This is our road. Our rotor is consisting off are conducting. Bars are placed in the rotor slots, so this is considered as the slots inside zero toe and don't find here. Copper parts are inserted into the slots. This one is rotating. You'll find that it's called a square kids, because it looks alike. Z kids, Where's the square? Is bought here? As you know that the squirrel keeps running inside the cage. So this cage looks alike. The squirrel cage. That's why it's called a squirrel cage. Okay, if you look at this in Z innovation, you will find here that this bars this part are short circuit pie. Arinc Okay, here and here supports are short circuit airports, Ender's boy aluminium or copper rings. Okay, Toe makes the short circuit between discover pours Okay. Similar to was a three phase winding in case off the one daughter are short circuit together. Now, before we end this this lecture, we need to understand the principle off operation off the induction motor. So we said that the induction motor is consistent or generator or whatever. Both of them are on the same principle. But the most important now is the induction. So we have the three fates input supply to these three phase off the state of and that we have here in case off the one brought on. We have a three phase in Z rotor itself, shifted by 120 degree, shifted by 120 degree. And that rotor is a short circuit with each other. OK, so how does the induction motor over it first? Win a three phase balance. It's a ploy. Three phase balance. It supply is applied toe the state whining. So we have here everyone veto and of course of history between see a three phase parents one or V A V V V C. Whatever we are talking about phase or lying, whatever we are talking about now, three face balance it's a ploy. So this one cause as three fears of balancing current city fair supply because the city face parents a current A I'll be I see that three currents are shifted by 120 degree. Why? Because it's a supply itself is shifted 1200.120 degree. Now, since Izzy three phase are shifted in his baseball 120 degree, what will happen as this city currents will produce a phenomena in Z induction motor, same as this in Chronos Generator. What is this phenomena that three face balance it currents produced a rotating a magnetic field at as bait off Cinco Maze's bead, which it depends on the frequency off supply. Okay, so this produces are rotating the magnetic field, having the same speed off thus in Christmas is be so the speed, as you remember and s for in his speed, is equal to secrecy F or 60. That's right. It f over being okay, So the speed off that or rotating field is dependent on the frequency off the supply. Okay, so it depends on the frequency of supply and rotates at us in Chronos is beat, so they are rotating the magnetic field here. Do toe the reasons off a three face parents. It's a ploy shifted by 120 degree. This rotating field will cut zero so that rotating magnetic field will cut zero, which will cause and use the meth inside it. So it produces as three phase and used in math. Okay. Sorry Fears, pal. Incident. Meth Okay, senses the rotor is short circuit. Therefore s 353 pal. Instant or three phase Palance, it currents will be produced. Okay, since its short circuit and we have vaulted here endures the voltage e another one here and another one here. So three phase balance in supply is produced. Okay, so that's three phase. Palin said currents here will do the same as the three face parents said currents here. The sneakers here produced a rotating magnetic field. This saree currents will also produce a rotating magnetic field. So what will happen is there the three phase here rotating magnetic field and another one here. The interaction between the two magnetic fields will produce a torque inside the machine. So the talk is produced due toa interaction between the store rotating fiends. So again. We bought a three phase supply here. Three fears parents It's employ causes a saree faced currents. The three face currents reduced their rotating the magnetic field. The rotating magnetic field cuts zero. So what will happen? It will produce as three phase India was the voltage Zack. Three veins induced. The voltage produces three phase currents. The three face currents will produce another rotating magnetic field. So we have here for examined as if this one was a magnet on this wasa magnet. But this magnet is rotating. Okay, The magnetic field is like a rotating magnetic field is like a magnet rotating. So this magnet is rotating. This one is rotating, so the interaction between them will cause the water to start toe, rotate all produce or produce a torque inside Z. No. Now we need to understand the frequency off the EMF induced inside this route. So first at starting this beat off the rotor in R is equal to zero. So the M s or the state or fields cut zero toe with this bit off. Unless we said that that state of field having a frequency equal toes, a supply frequency off ns. OK, So they're a mess. Got zero tour with as we defend ness so that in use them if inside the rotor will have the same frequency off supply, which is an s. Now the torque is produced. As we said before, and this, we'd end our starts to increase. So what happened in this case, This one? That rotating magnetic field like this, for example, will have a speed off a ness and zero tore itself route. It was an off. Okay. After torque is produced, So what will happen and mess? And in our So what is now? Is the frequency off cutting the frequency of cutting? What does it mean? It means that the rate at which is this field got zero. What is that? Relativists village off cutting that as his beat in our at in his bit. And are there m s or the fiend here? Got so with cut zero toe with a red relatives beat off an s minus in law. Okay. At the beginning, when in our 10 soc rotating, you feel cut zero toe with a write off an s, but now wins our auto start to store rotate. Then the relative is big between them is an s minus in north or the induced they make here will have a frequency the bending on the relatives beat. So in this case that a math off zero toe has a frequency effort toe After we said that the frequency is equal toe end be over 60. But there's been here will be the relative speed because it depends on the rate off cutting . So it will be an s minus in are. So if I'm out of light here by an s and the multiplied hereby in s So what will happen? We will have be and s over 60. So what is be over 16 s is Zach frequency F one or the supply frequency and we'll have an s minus in our over in s in s, minus in, all over in s. Now, this is known inside the induction machine as the slip. So the frequency off zero toe or the frequency off the voltage induced here is S F one. Where s is an s minus in all over Innis. So now is the relation between them Waas s F one between F two and F one now. What is the speed off em? Are off the rotating A feed off zero toe here M R. What is its relatives? Beat with respect to road. Okay, Z, remember something here which is really important that their field a mess and feel them are both of them have the same is bid which is a less or the same Chronos is beat so there's beat off m r, which is unless was a respected toes. This bead off rotor is what is an s minus in our Okay, so that is that speed off M r or the rotating a field here inside zero toe with respect to the road. Okay, since it has speed off an s and wrote or have in our So what is that? Relatives beat off M r. Who is respected toe the state. Oh, okay. It will be and s, which is he is bead off The M R minus is beat off the state state or is a stationary. So this bid off it is zero. So that speed relative speed off m r with respected toes, a state or assembly and s. So the question is, can zero to run at in s Kanzi rotor speed. Rich in s. The answer is no. Why? Because if the rotor rotates at N s, So look at the rotating, feared rotating field off the state or is rotating at a mess and zero toe is rotating at also in s. Okay, if we assume this this one would it that unless this wanted a tennis So what will happen in this case? You will find that zero toe, for example. This point will see is that was dating field as if it is a constant field. Why? Because both of them are rotating at same speed. So zero water will appear stationary toe AMs as if both of them are rotating and seems bead or most of them are stationary. Okay, they are stationary, not moving. So in this case, what would happen? No image would be indie used, so no image means that no currents will be produced. No rotating magnetic field off the total, and no torque is generator. So that in our maximum value is lower than in ness. Okay, So simply wins that Roto riches Z as bid off an s. The both of them off course. It will not reach an s. Both of them will appear stationary to each other's. They will appear as if they are on a state or for example, so no voltage will induced. Why? Because the voltage dependence on defy over DT. Okay, but the one off, most of them are rotating with the same speed. Both of them will appear or the photo will appear stationary for in this so that defy by oddity will be equal to zero. So no, a meth will be produced. So in this video, we discuss dizzy importance construction and Syria off machine Syria off operation off the induction. 148. Equivalent Circuit And Power Flow In Induction Motor: Now let's discuss the equivalent circuit off the induction. So simply the induction motor can be represented by a transformer. So, as you remember from Transformers, we have the resistance for this data. Is a circuit off the state or and is the circuit off the road? So it was a circuit off the stato consisting off number one V one is the voltage a pair face or C terminal voltage per face can be in case off induction motor. The boat is current. Okay, since we are drawing, here is the face circuit. So this can be considered as evil is the face terminal voltage are one. Is that a state of winding resistance? You know that it consists is off wires the state or so the wires have a resistance and have an inductive X one. Okay, so this is considered as the leakage in doctors in sizing machine. So we have our one and g x one, and we have our seen NJ exam. Similar dozy transformer. Whether we have the court itself, it can be risen by R c parent TJX M where RC representing the state or cool losses or the state of core resistance or equivalent resistance and exam are representing the state or magnetize ation reacted. This is very responsible for the magnet is a shin and signs that machine itself. So we have. After this we have e one and we have veto similar tools a transformer, the state or or the rotor having art or the resistance off the rotor and a J exito that induct ance or the rotor leakage in doctors. Okay. Or the rotor leakage reactions. So we have Here is the current I one, which is the state of current and the current I toe the rotor current Very simple. Now at starting. We know that in our equal to zero z as we eat off the road or is equal to zero and the slip in this case will be, well, toe one. Why senses he slipped symbol equal and s minus in our over. Unless so when in r zero at starting then in s over. And this will give us s equal one. So the frequency off zero toe will be similar. Tools a frequency off the supply. Now look at this. We have the one that induced the voltage, which, as if it was a transformer. The voltage off the primary and the voltage off secondary now is the secondary itself is obtained from the voltage. Here is a function in all of this. This is obtained from that sink Rama's machine similar to synchronous machine. As all remembers, that C field wanding causes DC flux And this D C flux rotates. And the cuts is the state or which produces as three phase current off and use the voltage having this value. So the induction machine or the inductions in a little similar to it or the induction motor , whatever both of them are similar now in a 4.44 is a frequent off the secondary. I am not a blood by the flux multiplied by the number off turns off the secondary multiplied by K. W. Or the winding factor which it depends on the winding itself. Okay, so what is important for us now? Is that the frequency we would like? Toa re bless e with some value. So we hav e ant beat Orza starting off in our equals zero. So we hav e r that in use the voltage in the rotor at zero speed. Okay, or at starting it will have this. So you are not will be equal toe senses of frequents off secondary equal toe F one. Okay, if the two is equal to F one so we can substitute with F one here. So we have 4.44 if one flux deface and decay winding. So this is equivalent to a value called e two or the voltage induced in the secondary and the starting. Now look at the inn doctors in Doctor's X. It'll is to buy F to a little toe pi multiplied by the frequency multiplied by the inductive simply from circuits. So we know that at starting effort to is equal to F one. So Exito is equal toe to buy f one a little which is exito at starting. So at starting we have Ito starting and exito starting and the resistance is independent on that sweet Now we would like toe see what will happen toe the circuit when we are at any others beat at any others we'd in are we know that the frequency off the secondary is equal toe s f one. So what does it mean? It means that e two is equal to 4.44. Effort to fry defaced O K. Wanting to. So if it'll will be replaced by Isis s if one So we have 4.44 as one flux deface que winding. So all of this is what this part and this part representing Z e at starting and s will be, goes here So e toe at in others being the voltage induced the year is equal toe s motto Blood by E at starting So it will be S E So the voltage induced in the secondary is variable wizards feet. Okay, now X, it'll exito here will be to buy f itto a little. And if it'll assembly s if one so X, it'll will be equal toe s Exeter at starting. Okay, If we take this one here, then it will be to buy as if one a little to by a foreigner. And little is simply exito at starting and we have us, which is a slip. So our X at any other speed is equal toe s Exeter at starting. So we have the current I one and I two and is the current or tent should be constant. Okay. What does it mean? It means that the current is equal toe s Ito at starting over. Our two blasts gs exito at starting. Okay, so this is our rotor current or the second, the current. Now we will find that the current is constant. So we can divide s hear and is here as an owner. Numerator and denominator. So dividing bias here and year it will be us A to our two over s J exit. Okay, so we can draw our equivalent circuit like this. We have our one Jakes one R C jakes em, and our toe over S and J exit. Okay, which is similar to that starting and eat, which is a tow at starting. So is a variable term. Here is our our two over s. Now we can make that referring off that wrote off circuit does the primary or the state, or as we did before. So how we can does this simply by using acetone is ratio. We said that acceptable dash, which means that the X or their actions off secondary with respect to tow the primary, it will be equal toe exito off the secondary multiplied by and one over any toe all square or that number off Dernis which I'm going toe. I'm going to tow the state all so it will be an s over in our in our is number off the onus off zero So which will give us any square? Over in our square is equal toe a square Which is that? Turness rescue square X two e To dish it toe Refer The two Z primary is simple equal toe e tow mater Blood boy and s over in our giving us a beetle Now are to dash are two days when our to refer the Tuesday primary It will be our toe multiplied by his attorneys issue square in s over in our all square which is a square now is the current I toe When it's referred to two z primary as we remember from transformers we said that I two is equal toe or I two dash is equal toe nr over N s. It is the inverse off Zito nutrition multiplied by C current inside the second So we have extra to dash e to dash r dash he told us now we can draw our equivalent circuit are one jakes one R c j X m And here's the current. I see. And I am. And I know I know is the current at Knollwood when there is no Lord, I told Ash will be equal to zero. So the current or will be I not only and we have here this circuit refer the Tuesday primary So it will give us JX to dash plus our today show over S J C dash R dash off s and of course, here plus minus e to dash. Okay, since it is referred now, this is school Dizzy exact equivalent circuit off the induction. Now we can dosomething toe simplify it. We can use the approximate equivalent sect What is the approximate here? We can move this branch here and some or this post off this resistance and in doctors. So it will be like this one entering and we have our see para Toshi exam and we took this part Here are 161 j exito There's are today's over s So we have I one i two dash and I know this is the approximate circuit and this is the exact equivalent circuit off the induction machine. Now we need to understand Is the power flow inside the machine Okay, at first we have here in the induction motor. We have the power here. So is the input power here. Since we are talking about, remember, we are talking in, um about three phase system. So the power is three. The phase voltage, Marta Blood Bisi current model Blood Boy. Go Zain Fry. Why? Since we are talking about with the import active power and the 4th 3 face system so the power can be equal to three multiplied by V phase Z phase voltage martyr Blood by Z face current must a blind by design five. Okay, designs angle. Since we are talking about the active power off the machine since the active part is the one which do useful power so we can do it like this. Or we can say that seapower is equal to Road City V lying I lying cosigned Go, Zion. Fine. Okay. This is from that basics off the circuits. So the power can be three v face I face goes on five or can be rotisserie V line. I line design five now is the power input. So the power input is root City we want as a line to line. I want designs the angle between the one and I want Okay, this is the inbuilt watt power or we can say city V one as a phase I want as affairs resigns, The angle between them now is the power flows here and finding dizzy state or couple losses the state or couple losses for a sniff. A system is as three I want to square our one Serie I wanna square are one. This is a state or a couple losses. Now, after this, we go like here and we have the core losses. So we have What is the value of physical losses? It will be Siri e one square over RC. Okay, City V Square over our or three e square over RC. All we can say three. I see square R c. All of them are similar to each other. This is representing the core losses, core active losses. Now, after this, something will happen After we removed from in both state orca Pelosis called losses, we will have a definition called Dizzy Bijie or that being get the air gap power now here is the B gap. Entering our sect now is a big gap is divided into two parts one from the losses on the resistance and the other is that developed the power we remember that are Do dash over s the equivalent circuit was here. J X two deaths are two days over s so we need to find from this turn or this perimeter we need to find that power developed in the rotor. Okay, since you are talking about induction motor so how we can do this, we can divide our to dash in tow are to dash, which representing that resistance inside the winding itself and other terms are to dash one minus is over. Is this representing? Is the voltage drop and losses off our today show off the equivalent resistance and this representing that developed power. So if we sums this two parameters are to dash plus our two days one minus x over s. This will give us our Today show Over s, which is obtained from the equivalent circuit so that big gap will be divided into a couple losses here and then finally being developed so the big gap Z power in the gap is simply equal to what? This symbol equal to three The current today square is the current flowing here which is I to dash square multiplied boy are today over its Why? Because that big gap is divided to our to dish and power to the develop and both off. Those are equivalent to our today show Over s Therefore the equivalent power is three I toe dash square multiplied. Boy, our today show over is this is a developed the power which is equivalent to two b m but minus estatal couple losses minus core losses. Now this big gap or the developed a Z gap, our burger power is divided into two parts. One is the couple says here three r tau square are today sh three I toe dash square are to dish If you look at sister which is that Kaparo? Two losses And to look at the big you'll find that the relation between them is that the cover rotor is equal. Toby Gap multiplied by us which is us. Begin. If we multiply this by s, we will have three I to dash square multiplied by Arto Dash three. You are it with a square, arto dash. Now this is the cover Roto losses. Finally, after removing this losses, we will have our developed power be developed. So that developed the power is simply equal to three. All right. Oh, dash square multiplied by R two dish one minus is over is our to dash one minus X ovaries, which is similar to what? Look at this and look at this. They are similar to each other, but it will be equal to be gap multiplied by one minus is if we take that you get and the multiply it in, boy. One miner says it will give us that developed the power. Now, after having the developed power on the rotor, we need to remove that frictional losses and the mechanical losses. So removing the mechanical losses we will have our finally is a pure Albert power. Okay, so this is our Albert Power, which we can get the album talk. So the relation between big get be developed and be I wrote a couple losses you'll find that be developed is one minus s big head and power losses on the resistance here is equal . Tow us be get and the submission off be developed. Blust couple losses one minus is plus s giving us one or that be Get now, looking at our circuit again we have that power in both or the import power is equal to Z state of couple losses s referred to state or cl copper losses plus Z losses in sick or plus is a power bi gap which is all of this power and be gap itself in sea power here is divided in tow wrote orca Pelosis rotor couple losses Plus is that developed a power here then finally that developed The power is divided in tow power Abbott on the shaft which is a pure our power plus Z mechanical losses inside the shaft such as friction losses, windage and so on And we said that that developed the power here is equal to a one minus SP Gap which we are going to lose in the problems and rotor couple losses is SB get now We need to find that dorky developed So the talking developed here on the soft We are talking about that developed not the out developed, developed, not zip you're up. So they developed a simple equal to be developed over the speed off the road to be developed over Omega Are you know that the power is equal toe torque but by omega or e monta blood my eye? Or I square much blood by the resistance here, so be developed. We say that it is one minus SP gap one minus sp game and omega are assembly equal toe or my guess. One minus is Where did we attend this assembly? Omega R is equal toe similar to toe by end over 60. Okay, so it is equivalent Does is beat. Now remember that just left is it well too? And s minus. And what over and s so N. S s and s equal to or minus and s Okay, equal negative and no. So in our or the roto the speed and are will be equal to an ness one minus s k by taking in ness as a common factor and s minus one and we have here and negative so it will be one minus is so their relation between the water current and in s or possessing Chronos is beat is an s not a blood by one man Assess. Similarly, if we multiply by, told by an over 60 So why in over 16 we can get that Omega r is equal toe May guess one minuses so we can take the store with sister and the finally torque developed is be developed for Omega are or big ab or Oh, me guess. OK, you can use this or use this. And the Alba torque from the machine itself is equal toe the power output. Since we are talking about our torque is a pure or the soft powers up your Albert, then we will have the speed off the up. Okay, but here we talk about began. So we take with it on my guess. And of course, this ratio give us Z developed torque and not the load torque. So we talked in this video about the equivalent assert off the induction machine and dizzy power floor inside the machine. In the next lecture, we are going to discuss Z torque is beat characteristics. Then we are going toe. Have examples on the induction 149. Torque-Speed Characteristics Of Induction Motor: now in this video we would like to get the talk is being characteristics off the induction . So as we remember that the torque developed is equal toe and be developed over Omega are okay be developed over arming our and we know that be developed is one minus is be gap as we discussed before And Omega are war minuses Oh, me Guess so. Torque developed is be developed off omega are or be gap over migas Now we would like toa drive more off this equation. So be gap is given as three i to dash square are toe that's over s okay, so and we need to know I to dash so from our equivalent circuit year assuming that the RC is neglected or you can give it it as you would like. But in order to go toe get I toe dash, we can go to assemble equations that 1st 1 is that first message is get the one Ok, we know that I want is equal toe be won over is the equivalent is it off the circuit? Okay, so I want is equal to be won over that equivalent. Then after obtaining Z I one. We can use current divider here. Talk, then I toe dash is a mess. Adios. The talk 10 z current I to dash another missile is by using Zy seven yn equivalent. So by taking or getting C seven an equivalent circuit off this part, then add it. Here we can get I two days. So first, let's get disease at seven and 77 as we remember that weeds called dizzy seven in equivalent circuit. If you don't know about it, you can go to my own course for electric circuits. So is that that the seven year assembly, by off course the activating all of the sources so everyone will be a short circuit are one GX, one g x m. So they said that seven in between A and B assembly are the one plus ZX one battery to J exam so that seven j x m baruch toe R one plus j exam. So then seven is equal toe J exam multiplied boy R one plus Jakes one over jx m plus R one plus j x one the barrel off to medians or to resistance. That said the seven and will give us finally by simplifying this. Give us resistance. All seven in equivalent and j X 17. Okay, you'll find something which is really interesting Is that when we look at it? Seven. In here you will find that J exam battery to our one projects. One J exam is a very large resistance. Okay. Or a very large impedance or a reactant. Very large reactors. Camembert, the Tuesday said, are one projects one. So we'll find that when we are taking a large impedance battery. Always a small impedance, the equivalent impedance is nearly the small impedance. So then this evidence is nearly equal. Toe are one block Jakes one. Why? Since Jackson is very, very large than our one logics one. So they equivalent that seven will be nearly are one projects one as if zey J X M is an open sect. Another thing is that V seven. Now we would like to get the voltage between a and two B were seven and so we have the one as a supply and we need the voltage across G X, m or A and B. So the voltage here assembly by using Walter's divider V seven is equal to everyone is the import supply. Everyone multiplied. Boy, J X m Okay, the impedance. We would like the voltage across it. Over the submission off to impedance are one projects want blood exam. Why? Because V one over R one logics one plus exam. All of this we want over all of the equivalent impedance, give us Z current flowing Zinzi current multiplied by G x m give us v seven you'll find Also that G exam is greater than our one projects one. So in this equation, J exam is very, very large number. The truth is so we can neglected this part and the finally will have 37 and equal V one j except over the exam, which means that V seven will be nearly equal toe V one. So when we are solving this equation, we does s and we does this, but we make sure off our calculations apply Knowing that did the seven and will be nearly equal to our one projects one and V seven would be nearly two V at one now drawing our equivalent circuit. We will have after we removed all of the state or part, we just both v seven and r seven j x 70. Okay, very some. So we bought every seven or seven plus J x seven and we have JAXA. Traditions are wrote off circuit are to dash over is so the current the following year is I toe dash required So the current I to dash what is equal to V seven over the equivalent impedance. So I toe dash equals V seven in over our seven m plus r two dash over s blast GX seven plus jakes to dish J X seven bluffs Xa two dash. So, by getting is the magnitude or the value I towed ashes I to dash as a magnitude is V seven and as a magnitude over the square road off this part plus the square root off this part or that square off this part of plus square off this part that rode off our seven plus our two dash over. It's all square plus x seven plus extra dash all square. So we said that the torque developed is equal to be gap over Omega s and the big gap is three I to dash square are to dash over us over Omega's. Now we have to dash from this equation. We can substitute it here So we have serene for roaming s stream over Omega s arto dash over s are today's over s and we have I to dash square So I toe dash square is v seven square over our seven m plus or to dash for s or square plus x 17 plus exito dash all square without the square root Of course, since we square the zika So this representing our equation for the torque developed. Now, if we draw the relation between Z torque and speed according toe, the previous equation, we will have that the torque developed at the beginning starts to increase from his bead off in r equals zero start is to increase until reaching maximum value at which the slip will be us M or the slip at maximum. Now we will find that this bead after this start is to decay going toe end ness or the same Chronos is big at synchro Nous is wheat. No torque is developed as we discussed before, and disease we'd will never reach Z n Sync wins. Now, in this reason, you'll find that at zero the slip is equal to one. As we discussed before at M s, the slip is equal. Toe zero. Okay, So slept increases from here going like here. So this is that a usual Where that machine work is as now. If we increase the slip beyond one, then we're using a phenomena all dizzy. Breaking off the d seem off for the induction machine. That breaking off induction machine. Okay, since you will find that the speed now is in the negative direction and the torque developed is postive saucy. Oppose each other. Now look at this. When we decrease, the slip slip becomes a negative. So what happened in this case, you will find that the motor will start producing a torque or torque. It becomes a negative. What does that all the negative mean? It means that the power is provided boys induction machine, not absorb it. So what does it mean? It means that it's starting toe work as a generate. But we said before that the speed cannot exceed the N s or cannot reach an s. But how we can make it work as a generator by supplying a mechanical power does the soft we can increase that speed beyond Z synchronous a speed so in that spirit will be greater than in s. So that machine or the induction machine starts to work as a generate. So in this reason, we provide power or you provide electrical power to the machine. So it works as a mountain and have us beat lesson lesson. Chromosomes beat. But if we provide electrical power, does Emma electrical mechanical power toe the shaft that we'd will increase Beyond discussing Chronis is bead. And in this case, zam machine will start providing power as a generate the equation off the maximum torque and starting torque, which will need in the next examples. First, the torque developed simply Quito three V seven and square over omega's or seven M plus r two dash over S or square plus x 17 plus extra dash or square. But the black by our to dash off rs. Now we need to find the maximum talk. So what does maximum value means in mathematics? It means that we can drive this torque developed with respect. It was a slip and equate It was here de torque developed over the s equal to zero. That derivative off. The torque it went up to is a respected toes, a slip equal to zero. So we can get at this from this condition. The slip at which is the maximum torque. OK, And after and derivative off this weekend. Get that s a maximum or the slip at maximum talk. Not meaning the maximum slip. It means that slip at which is the maximum torque. OK, it will be our to dash Overrode our seven in the square plus seven plus exito dash all square. So we'll finds that this representing Z s at which is the maximum torque. OK, now the torque maximum after substituting here, talk maximum assembly three v seven and square off to Omega as our seven plus road are seven square plus x seven plus extradition all square. Okay, so you will find that this equation obtained the pie substituting zehs in the equation here . Okay? Or instead, off course memorizing this. You can Mariah's general law. Then get and desire memorize e s maximum law, then by getting s a maximum movies off Stewart directly in the equation just like this. Okay. Now, to get the starting talk off the machine, somebody What does are starting to mean. It means that the n r is equal to zero and in or equal to zero means that this label will be equal to one. So here is a slip equal toe one It will be three V seven in the square are to dash omega S r seven plus arto dash all square plus x equivalent or x seven plus exito dash or the square. Now, if that the one or that impedance off the state or is neglected. Okay. We neglected our one and neglected the X one. What will happen in this case, we can drive our equations or is that we get a ratio between the talks and sickens. Now look at this. We have the right to dash is equal to V seven in overrode our seven plus our two dash over s square plus x seven plus extra dash or square. And this a maximum is arto dash are seven square plus six is seven plus exito dash or square. Okay, here square. Now, assuming that we neglected Sing Z that the one which is our seven r seven plus x seven xs seven g uh, servant So we neglected our seven plus Xs seven. So what happened? We make this 10 and women's this 10 and we make this one Z and this one Z So I told Ash will be this evidence over road arto dish over s square plus exito dash square like this and sm will be arto dash over exito dash. Okay, Now, if we get that issue between a slip number one and slip number two issue between currents or the square between two different strips. So we'll finds that in that first slip square, it will be v seven and square over road are to dash over s one or square or to a dash over s one all square plus exito Daschle square. And I told that square is similar to the 1st 1 but it's settled Okay. In this two currents, we only changed the slip and the voltage remained a constant. So v seven goes with V seven and we'll have this one will go here and this one will go here so that issue between the current square is our to dash over its two or a square plus exito dash all square over our two dash over s one All square plus exito dash or square Now we have here That s a maximum is our to dash over Exit to dash so we can do something here we can take extra dash all square as a common factor here and exito dash all the square as a one factory So what will happen? This was here and this goes here So divide this by this extradition or square are to dash square over Extradition square What does give a C maximum or today square over extradition square It's a maximum and we have a subtle So it will be a settle plus one Since we talked extradition as a common factor and the similarly here we have extradition as a common factor are today's square over extruded square is s a maximum over its one or square last one. So we obtained this Irish off currents with respect tothe es maximum and esto. So finally I to dash s one over I two dash at a slip number two all square is equal to a one. Plus it's a maximum over two square one Glass is the maximum over s one square This equation is used only when that is neglected that the one is neglect. Now to get that to work relation between each other, the torque developed is big AB overall me gas ash which is equal to three I to dash square are told us over s over. Omega is now if we get the relation between two torque is t one over. Tito. So take this at slip number one and exists at slip number two, you know, isn't we are working at a certain frequency. So the only change here is a slip I end Omegas. It's gonna me Guess will go with all my guests and our to dash goes was are two days three Gozo City. So we'll have s total goes here and s one goes down as to over s one and we have to dash square. It's one I don't ashes to square, which is this apart So that all could develop titty one of rt tools that issue between two different talks at the different slips off course, assist over s one about the blood by one. Plus it's a maximum one process maximum over a suit. Okay, so this relation is also use the wind that the one is neglected. So that's why here, when we drives the current, we make it. We made it square. Why? Because we needed the talk in the end. Okay, We needed their issue Between the talk and the talk. The Bendis on the current square now in the next video are going tohave some solvent examples on the induction motor and apply all off this equations which we learned. 150. Solved Example 1 On Induction Motor: Now let's have an example on the induction motors. So first off, in our first example, we have a three phase induction motor arounds at almost 895 rpm at no load. So somebody, what does this represent? It means that the speed at no load end off the rotor at no knows. Okay, And And it 170 city rpm adds a full load. So this is in our or the speed off the water at f N or the full load when supplied was power from a 60 Hurtis Siri face source so that supply frequency is equal to 60 Now the first requirement is how many balls does the moto have? So we know that we have a relation between that's in Cronos is wheat and s equal 60 f over the so we know the frequency as a 60 hurt us but with we need number off bulls. But we don't know that Seem promises beat. So how we can get this in chrome assist beat You know that in the induction motor, when it is running at no load, it is close to their That's encompasses beat very close to maxing chromosomes beat so we can assume that it 100 95 is easing promises. Okay, Just as an approximation. And we will get now the actual in s. So first we know that be, or the number of wars or in s equal, 60 f Overbey. So number of bulls is 60 f over in s. Now we know that this in Chronos is beat is nearly equal toe end are at no load, not for load nor loot. Okay at no loot. So that scene Chronis is bead will be nearly equal Toe 895 R B m So that's in promises Weed will be nearly 895. So take this here and frequency sexting hurt us, so we'll have the number of poles as 4.2 Okay, so number off boards cannot be four point your toe. We don't have a pool and two over 100 bulls. OK, It should be an on integral off course. So the number of bulls will have will be four. Okay, this is E approximation. Off course it be. You will be equal to four. So by knowing is that number of wars is four, we can get this actual synchronous is beat How? Just take the N s equal 60 f over B and B is four and the frequency is 60 hertz. You will find that the actual synchro Mrs Beat is 900 rpm So we get the N s orders in Chronos is we'd equalled 100 R b m you will find that again that at no load that no Lord is beat is nearly equal to was this thing promises beat 895 is close to 900 But it is not just in Chronos is sweet Is that second requirement is what is that? Percent slept at full load So we need to find the slip at full load We know that the innocents promise is 900 We know that the speed at full load is 873 so we can get the slip Isley so is the slip as you remember slept for load is an s minus in our over in s So we need at for lewd which is corresponding Qto in our at for lewd unless is 900 next 900 in our at full load is given as 873 from that given inside the problem. So that ratio here will give us all point or city or means that the slip is 3% or the variation off the is bead at full load from the synchro nous is beat with the respect Does a seed grants his weed is 3% that serve. The requirement is what is the cross burning frequency off their water current. So we need to find the frequency f two. So we know that every toe is symbolical toe s f one. Okay, so s is given as or point or three. And the frequency off the supply is 60 hertz. So the frequency off the rotor a symbol equal to 1.8 hertz. The frequency off course off the induced the Met or the frequency off the currents inside the boat. Now the force requirement What is that? Corresponding is beat off the road or feed. We needs a speed off m r with respect dozy motor and was respected toe the state motor here means was respected Toe Z roto. Okay. With respect to tow the root and with respect, it was a state. So what is the speed off m R. We said that MMR assembly having is a speed the same speed off N s or the speed off Z a mess which is ah, state off heat So that sweet off their water field, who is respected toe the roto. This is beat minus that sweet off rotor. So it will be an s minus in art. So because we are talking about the speed off the roto with respect toe zero And what is the speed off rotor field with respect rules the state N s, with respect to tow the state or the state or is a stationary. So this bead off it is here so that relatives speed between the roto feed and state, or is in s minus zero, which is an s So that rotor field speed with respect to tow the rotor assembly, quell an s minus in our okay or sns. It is the same. Why, since s s is equal toe in s minus in our over an s. So s and s assembly an s minus in on both of them are equal to each other. So it will be is a speed off wrote or field with respected toe wrote or 27 r p m And this is bid off. Wrote off field with respect to the state or is an s minus has read off a state which is zero So it will give us an s off my 100 RB 151. Solved Example 2 On Induction Motor: Now let's have another example on the induction machines. An example. Number two. Here we have 200 vault, then horsepower four Pool, 1710 rpm. Why Connected? Induction. So what does it mean? It means that the voltage given here inside the problem is the voltage v lying to line Not is that phase voltage So V line Thailand and RMS or the effective value and then her. So 10 horsepower is a power out and four pool. What does for poor meaning means that number off polls be here. We have a number of polls. B is equal toe four and the speed at for lewd is an R at for lewd or rated conditions is equal to 1710. Why connected off course is a connection off the boat is why so this values representing the rated condition off the machine. When you look at a machine and see then her stand horsepower at 4.1710. This representing Z conditions at full load. Okay for Lord Speed followed Power Albert and as the import voltage ad for loot. So it was the first requirement is What is that thing? Chronos is beat. We know that doesn Cronus is wheat and ness is equal to 1000 in heart 100 rpm where the do it gets us assembly. We know that in s is equal to or that's in promises with equal to 60 16 F over. Number off. Pull pairs. Okay, Number of poor purse. This is the total number of polls. But ballplayer is equal to two. Okay, so say Christine over to give us what text over to give us 30 f. Okay. So the frequency can be 50 artists or can be 60 hertz. So at 50 Hurtis at 50 hertz, for example, it will be 1500 at 60. Hurtis 16 Mortar blood by 30 Give us a 1800 R b m. So what do you think? Which off this toes bids are is easing. Chronos is beat off course that's in Chronos is beat Is close toes the inner at followed or at no load. So 1800 is close to 1710. So this representing our sink Ramos is beat. This one is refused This one at a frequency off 60 hurt us. This one at the frequency off 50 hertz. Now, the second Turkoman is what is the slip off this motor? Aggerated, Lewd simile we have in our at full load and we have the synchronous beat so we can get the sleep very easily. The slip at four load is in s minus in our over in s and necessary. In Crosby is 1800 and not is 1710 unless is 1800. So that ratio here give us or point all five Okay, is this is considered as the slip off seam? That sort of the requirement is what is the road or frequency? Somebody we said that effort or wrote or frequency assembly s motorbike, my F or the slip off the slip off the machine or the motor multiplied by the frequency off supply. So s So you find the year. As we said before that, the frequency 60 Hurtis by knowing that the speed is 1800 from that Since that beat, this one is close to 1700. Okay? Or as we before we go to the frequency we assumed 50 hertz and 60 orders. So we can get this. Now we have the frequency off supplies 60 Hurtis So as not a blood by 60 or or point or fight. What? The blood by 60 Giving us that. The frequency off the currents in the rotor is three hurts. That force requirement is what is this off the torque off this morning at the rated load condition. So simply how we can get this. Remember that the power out since you are talking about off to talk is equal to work, Albert, which is that? Softer torque required Multiplied Boy Omega are so power Albert is given here, then helps power talk about what is the required Omega is no point in our at for load over 60. So here that torque Albert is simply power are bought over roaming our power. Our is that 10 horsepower. We should convert it into what? So power toe? What? Or the horsepower toe? What is then horsepower multiplied by 746. What? Okay, this is the wattage off. One horsepower over Omega are Taub. I end over 60. The speed here is 1710. That speed at full load rotor speed at forward, so this would give us 41.7 Newton meters. This is that torque our off the induction moto add rated conditions. 152. Solved Example 3 On Induction Motor: Now let's have another example. Example Number three On the induction we have 480 volt 60 Hurtis, 50 horsepower city phase induction motor is drawing a 60 a bear at 4.85 Power factor legging. So we have this conditions off the rated Our power for underrated vault is a VM but as a line to line the line line And we have years of frequency six tortoise f and we have the power out power out and we have a stringy face. Induction motor is drawer wing 60 on bear at all 600.85 Power factor leg. So this is a current at full load conditions current I ad for loot and this one is the power fact was I in Zion Fry The state or couple losses are to kill what and zero toe couple losses are 700 watt. The friction and wiggle when Didja Llosa's are 600 What the cool losses are 1800 What? And a stray losses inside the machine is neglected Finds the following quantities Number one finds the air gap power So in this problem we have our input power which is 480 volt. Okay, Road three multiplied by 480. Vault multiplied by Z current to design for. So first we shall get that power in boat. A symbol equal toe rotisserie. Much obliged by relying tow line matter Blood by I won because I am fi one Road three villain tow line. I want resigned five. Or we can say three v phase I face cause I in five So routes three as it is. Very line to line is a given 480 volt. The current is 60 and bear power factor is 0.85 leg. So is the power in both? So the machine is symbol equal to 48.4 kilo. What? Now the question is the big gap here Z editor Power. What does it equal to? It is a quinto power in both from the powerful which we discussed power in boot minus a state of couple losses minus zeke or losses. So power in boot minus state or couple losses minus air corps losses. So that part of him what is 42.4 kill what ze state or couple losses are to kill what and the cool losses are 1.8 killed. What? 1.8? Get what? Tokyo What? So be gap or the bigger power which is entering a to Z rotor is 38.6 kilo. What now? The second requirement is the power converted? So what does power converted mean? The part converted a similar tools that developed the power on the soft. So we know that Z B gap is equal to be developed plus a rotor couple losses. So that developed the power will be quinto be gap minus rotor colossus. Now we got what is the value of bigger Big gap? Here is 38.6 and rotor couple losses. Water couple losses. Couple losses are 700 watt or Boeing seven kilo walked. So they developed the power on their soft 37.29 kill What? Now? Um, here we have that sort of the requirement is the output power. So what is the Albert Power? The out power assembly? We have the developed power and we can remove from it Z soft windage and so on. Or that additional losses. So let's get back to the problem. We have Z friction and windows losses are 600 watt. This is the losses inside the shaft itself. So we will take that. Developed the power here and sub director from it pointed or 0.6 7.9 minus or points 8.6 kill what? Which is our additional losses giving us 37 points. Three. Gail What? Which is the power out? And if we would like to express this power as horsepower, then we will convert. Does he kill what toe what? And divide it by 746. So then, at 50 horse power as an Abbott ball in this case now we will find something which is really interesting that z power I would hear. It's simply there 50 horsepower here, since we are operating at zero rated conditions. So the Power Albert, which is 50 hurt horsepower. It's the same as the power. After we removed all of this losses and reaching this step, the last requirement is the efficiency off Simone. We know that the efficiency is the power. Albert over. Supporter in boot, the Power Albert assembly sort seven points. Recall what power in both is simply the electrical power 42.4 kill what so multiplied by hundreds, giving us an efficiency off the induction motor off 88%. So this waas another example on the induction motor. 153. Solved Example 4 On Induction Motor: Now let's have another example on the induction motor. Example Number four. We have act well. We kill what? At 130. Vault three phase. Why? Connected machine 50 Hurt us for poor squirrel cage Induction develops are full load electromagnetic torque at a slip off open industry. So this is left is a slip as at for load when operated at rated voltage and frequency or at full load for that purpose is off. This problem rotational and colossus can be neglected. So what does it mean? It means that our see the core resistance will be neglected. The traditional losses a friction windage. All of this are neglected. Now we have seen impedance letter on the motor enorme zipper face. So we have the arms or the impedance off the motor equipment or the resistance Ian doctors and so on enorme as falling the resistance are one resistance off the state or is open 24 all Exxon equal extra dash z state or resistance inductions or is a reactant stato reactions equal Tosa extradition or the state or or the road or the actus was respected. Does the state all It was to open 25 Home and x m z magnetize ing reactors equal to 8.67 home. Determine zem maximum torque. So we need to find torque. Maximum at rated voltage and frequency and the slip at maximum torque and the internal starting torque at rated voltage and frequency. So we need here as three parts. All of them on in Newton meters. We need the maximum torque. We need the slip at maximum torque and we need the starting talk. So the first thing you are going to do in a problem like this is that we draws the equivalent circuit. We have our one x one x two dash XM's So the first thing we are going tohave are one J x one and Jake's Auto dash or toe. That's over us. And we have J X m. Okay, this is our circuit now. We need to in order to find easy torque. The slip we need to find is that v seven and our seven and excellent. So we need toe transform, is a circuit in tow and said O V one, it will be V seven anuses off our one jacks one and Jake them. It will be our seven J x seven Jakes to dash are today's over s and see Current flowing Here is I toe That's which is similar here. So how we can do this first, who are going to get his eyes at seven and V 17 so that seven by between this tool parties between this and zest, if we look at this, then that said the seven an equivalent is J X m battery toe r one plus ZX one. Okay, so j x m better toe are one logics one which means toe peral j exam Malta Bad boy R one plus shakes one over Jake's M j x m plus R one projects one R one plus g x one Now substituting was the value given exam is 8.67 are one is all point to four x one is open 25 . Okay, let's check Z or going 24 okay. Or 240.24. Now, after Gettings as it seven, you will find it will be quite to or going toe 20 to 6 plus Jay are going to 49 now what is the value off? Our seven r seven is open to six and x seven iso goingto 49 Now you will not something as we discussed before, is that extra seven is nearly equal to x one x one is open 25 x seven is open toe for nine , which is nearly open. Toe are one is 0.24 and our seven is all pointed to nearly 23 Okay, so it is very close toe are one. That's why you will find that that seven is nearly equal to R one plus jx one. Now let's get that V seven v seven is the voltage between this terminal and the study and we have supply voltage V one. So the voltage across J exam assembly V one multiplied by G x m Jackson m over our one logics on plus six in we have the one You know that the m word voltage here in the problem at sea is 230 volt and why connected? So since we are dealing with that phase a circuit, that single face circuit so it will be is that is voltage in why connection is 230 volt over road three, 230 vault over Road three. Why, in order to convert everyone from Lyon Tow line, Voltage toe phase, voltage again. You know that here we have the three phase like this, a store connection that given is the voltage here between this line and this line. 230 volt, 230 vault. And we need to find the voltage between the neutral and one face. This voltage is this voltage is simply equal toe 130 volt. Overrode three j x m 167 are one Jakes M plus X one as here. Then V seven horse will be 129.2 and an angle off 1.54 degree. This is the angle of the vault now. Is this value 129.2 is close toe V one, but a But what? But at phase voltage. 230 over roots 31 30 Over what city is 100 close to 120 lines now. If we drove the equivalent circuit, somebody will have e seven in 129 r seven or going toe to six x seven or went toe for mine . Exito Dash Given our two days given over s now Z in order to get the maximum talk to for us to comment is the maximum torque We need to find that slip at maximum talk. Okay, so first we know that our toe dash is known giving so let's get back to our problem here. Let's see, what is given are one x one extradition exam Buck or two dash is not given. So what we are going to do in this case we need our to dash in orderto get Essam Axman and toe get zing as the starting torque and the maximum talk. So I need to find our today's So what is icky? And this problem and this problem that well, we kill what? Here representing the power out. Okay, we said that the owns an impolite here gives us the maximum Albert power on the shaft. Okay, so that well, we kill what is rated power and you will find there some things that that traditional losses is neglected. So what does it mean? It means that to the power Albert is equal to develop the Power Institute in the soft. Why? Because our traditional losses is neglected. So the our power is equal to develop the power. So from this week and get the torque developed be developed here is 12. A killer. What? So let's get back. So we have the dorky developed is equal toe be developed over Omega are OK and that developed power is equal to power Albert plus the mechanical power or the mechanical losses inside the machines such as the additional losses so that develop the power is equal to with the Albert power. Okay, over Omega are since you are talking about developed about on the shaft so that speed will be that traditionally is beat So it will be be Albert over Omega are now that may guard is equal toe May guess one minuses now is the power Albert is given asked, Will we kill what? As we discussed the now z Omega s, we need Omega s. So how we can get on my guess? My guess. Assembly to buy and over 60 tool by and over 60. Okay. To buy and hold for 60 on you remember that n is equal to say Christie, if over being so What does it mean? It means that n over 60 n over 60 is equal to what equal to f over B and over. Secretary is equal toe f Overbey so we can replace an over 60 year by to buy f Overbey. So my guess is equal toe to buy f Overbey. And we have four poles. So it's a full bear. Pee will be equal to two. Here. That be means number of poor pairs. Not as in d. C machines. Aware p represented the daughter number off ports is that frequency is given as what is given as a 15 hurts. So the Omega s will be 157.8 Ready, Amber second. Now, Now, if we get back. So it finds that this slip at four. Load is four point or three so we can get there. Omega are forming. Gar is one minus. Eso my guess. My guess is 157.0. It s is all point or three, as we saw now. Or point all so here. So this will give us z speed required or that traditionally speed required now is the torque developed at full load will be equal towards the power Albert over Omega are 12 Eakle. What over omega are one on 52.3, which is 78.7 Newton meters. So we have here that torque developed at full loot and we have the low for that work he developed. Tourky developed is equal toe three v V seven square are to dash over s or may guess are seven plus or to dish over S X seven plus exito dance All square Now we seven is given slip at maximum torque or point or three given our seven Given s given. Oh, my guess given at 17 given extra dash given. So the only unknown here is our to dash as you see in this equation. So by simplifying this equation or by using calculator, you can simplify it toe an equation or a quadratic equation off second degree. So the art of this will have a two possible values. By solving the equation, we can have our to dash equals 4.105 on or can be our today s equal. 2.567 What? Blood by tempo. Negative three. So which off the solutions is correct. One in order to know which one off. This is the correct one we have the s at for lewd at the phone. Lewd equal All point or see on Don't know Now why do we need it now? The slip at maximum torque is equal toe Arto dash overrode our seven square plus x seven plus x two dash all square I don't know where why I didn't try Take seven home, but anyway are seven square plus x seven plus extra dash All square. So we talked to the art of this here and subsidise it in this equation and the way God is the s a maximum here. And we talked this value and so city here and we got the s maximum here. Now we will find that when we draw the curve between network and this beat. Okay? And we have years asleep at zero, which means that we are assessing promises weed and slip off one, which means that we are at a speed off here. Now we will find that at its maximum that torque at which is the speed at which maximum torque o care. We have a previous region where the talk increases reason increase in the speed and on after reason where that torque starts to decrease with his wheat, you will find something which is very interesting. This reason is honest, stable, Okay, on stable. Which means that that s a full load should not be here. And this region after s mix until here is in a region which is a staple region. So that s awful. Lord should be between s maximum and zero. What does it mean? It means that s at for load should be list then Z s a maximum. Okay, since it is 10 So we are increasing there s followed, then increasing after a c maximum then increasing until cycle one. So the maximum or the slip at which maximum torque Ok, there should be greater than s at four. So what does it mean? It means that this solution yes, Maxwell is greater than Z s at full load or 0.1 mine is greater than or point or three. So this solution is acceptable and the resistance are today is opened 105 But in this solution, you will find that s a maximum is listen or point or string. So this is I refuse the solution and this arto dish is not acceptable. So this art of rash is the one which you are going to use Now we have a slip at maximum torque. We need toe finds the torque maximum. So talk a maximum by taking its maximum and substitute in the general law off torque or by using the maximum torque equation which we drive before City V seven a square over to make us are seven plus wrote on seven square plus x seven plus extra dash all square. We have all of the unknowns here. All of them are given so we can get Z tour or the maximum torque now is the lost. The requirement is a torque or the starting torque off the machine. Starting talk one doesn't starting torque means starting talk means that the speed as is a well toe and s minus in our over an s. So at the starting in or is equal to zero. So the slip at starting is in s over and that's what she is. One. So we'll take that general law for that torque and subsumed by s equal one. So why they're doing this? We can get that starting work off the machine. So this waas another example on the induction motor and I hind advice you toe sold with this examines wire hand. If you solve it by your hand, you will understand. Is the induction motors well? 154. Solved Example 5 On Induction Motor: Now let's have one as our example on the induction. So we have at then kill What? 400 vote? Three phase for pool 50. Heart is star connected. Slipped. Bring induction. The rated our developed rated outward air iterated voltage and frequency with It's a slow break Short sect. Okay, there is no resistance inside, Singh wrote. The maximum torque is equal to twice Z for lord talk. Okay, so the maximum is equal toe to torque at full load, which occurs at a slip off 10%. This is slipped representing our maximum talk. Why? Because you'll find that the sentence is the maximum torque equal toe twic for low torque and occurs at a slip off. 10% is the state of resistance, and the traditional losses are neglected. So when we are saying state or resistance and neglected so what does it mean? It means that they're the one is neglected. Okay, that the one is neglected determines e slept and rotors beat at full load torque Z rotor army closest at full load torque, starting torque at rated voltage and frequency. So how we can solve and problem like this First, we need to find the slip and the rotary speed at four. Load torque. So how we can get this somebody at first we know that the relation between Z torque at for lewd and talk maximum is half. Why senses it or connection is twice zifa. Look for low torque. The maximum is equal to talk for load. So sense is that the one is neglected so we can use that issue equation we remembers. And that is that issue. We have one plus s a maximum over on this one. Okay, All square. Or here is subtle Kayla existences along the bracket and the multiplied boy as a tool s a number two exists. Okay, Over s one multiplied by one. Plus it's Max one, its maximum over s one. I should have concluded this instead off writing, but anyway okay, So esto multiplied by one plus s a maximum over s ato square over its one about the blood by one plus its maximum over s one all square. So, as we needs that issue between torque off a lord and torque maximum, so talking followed here is representing as number one and talk. The maximum is represent as number two so number two is s a maximum. OK, so price of a student as s two to s a maximum s maximum and this one is so maximum Okay, so what will happen? One plus as the maximum over s maximum This maximum over its maximum is one So one plus one is two So z upper side will give us to assess a maximum Do it's a maximum. The No one here is representing Z for lewd so it will be s a full load multiplied by one plus s a maximum over s a flute as offload one plus its maximum over its offload all square assembly substitute in the equation which will tend in the previous videos, that is the maximum is given. We said that it's 10% or 4.1, which is all 0.1. The only unknown here in this problem is s a full load so we can have an equation off. Second degree for it's a flute which will give us a sofa load off 4.37 street or it's a load off opening all 2679 Now we will notice something here that we said before that s awful. Lewd should be lower then. As so maximum lowers and open toe one. So all 10.373 is higher than or went one. So this one is refused. But as a full load, equal or point or 2679 is lower than or 26790.1. So this one is acceptable. So that slip at for Lord is open toe or toe 67 line. So the first thing is the slip at full load. Now police find zero toe speed. So somebody weekend get the rotors beat by multiplying one minus s multiplied by disease In Chronos is meat to let it lead a love this and to get back So where is he slept? Okay, we need that rotary speed. Okay. And s is equal to say Christie, what a blood boys! A frequency which is 50 artists 50 Hurtis 60 f over number off four pairs which is to this will give us 1000 500 r p m. Now we need that Rotors beat and not and nor would be 1500 multiplied boy one minus slip at full load which iwas or point or to mine as I remember. So this will give us Z rotary speed required this Waas solve it before. But I did not include it in the in solution. The second requirement is a roto army. Close is so what? Is that right or Miklos? Is that rotor on my closest assembly Z three I to dash square might have lied by are to dash This is representing Is that three phase or me closest off zero city Since we are having city phases I told that square are today cheesy losses off one face So we need to find this value. So how we can get this assembly We know that store cat for lewd is equal toe be developed off Rominger are okay be developed over omega Are that developed? The power is sorry. I told Ash Square are to dash over us and we have here This is that Gaby Gap power off course as that developed our is three I toe the square. Our tradition of rs multiplied by one minus is and omega is May guess one minus is or we can remove one minuses with one month s giving us be gap over. Oh, me. Guess we get history onto the square are traditional dress. Now we have the developed the power equal to how much then kill. What is the power is given as thinking. What so we developed is 10 kilowatts and omega are is equal toe May guess one minus X that for Lord. So my guess Woman's except for lewd. And this one is three. I told that square after that's over, a sofa load on my guests so we can remove my guests with on my guess. Okay, so we'll have to be developed over one minus x at forward. What matters is that for load is given as a flawed here. So that's three I toe dash square art with us over a sofa loot as a volunteer brought down here. So we'll find that I toe dash square. Also, Dash is at full load is equal to 9 to 1.7581 This is a solution. Okay? This solution, which I consider as a little complicated. OK, but the is your solution is that we know that is he I developed the power is thinking what ? Okay, then kill what? And we know that the developed The power is also one minus s multiplied. Boy, be gap. So big Gap is thinking what over one minus is then kill What? Over one minus s. This is what this is our being a gap. Now we need to find dizzy rotor couple losses. We know same believes that that be a roto cover losses is equal. Toe s much obliged by being gap, right? So it will be equal to as much obliged by began, which is 10/1 minus is multi blind. Then over one minus is very somebody is and doing all of this. You will find here that Syria I toe the square auto dash, which is a road to cover losses, is equal to then here, then over one minus is one minus ISS and the mater black bias and not the blood boy is from me, which will give us the road or couple losses. That's all of this. So this is the second requirement that certain requirement is believes. Get the starting torque at rated voltage and frequency. So how we can get the starting talk with somebody, we are going to use that ratio low. So by applying that ratio as we did here. The one over Tito is equal Toe s it over s 11 plus is maximum over a city wall. Square one glass is the maximum over its one all square. Now s it'll. We need torque, starting with respect to tow the maximum or that talks, starting with respected toe for low talk. Whatever both of them will give us is the same salute. So torque starting the maximum. That s total, which is the maximum s one, which is He s off the starting, which is 11 Glass is maximum over its maximum. Here s a maximum. It's one. Is the slip off the starting, which is one. Okay, so we will have talks starting over. The maximum is toe s a maximum over one plus is maximum square. And we got that s a maximum is 0.1 given inside our program in our problem, so is he talks starting with respected toe. Meaty maximum is 4.198 This is official between starting talk, anti maximum. So if we would like to get the actual value will multiply t maximum by opening toe one line it and we can get the maximum from here, the maximum is to talk off, load and talk awful load itself. It can be extended from be developed over omega so we can get finally talks starting as a function off in the unit off Newton meters. 155. Methods Of Speed Control Of Induction Motor: Now, in this video, we would like to discuss Z methods off as speed control in the induction mode so we can control that speed off the motor by several missiles number one weekend. It changes that slips bid where s is equal to and as minus in our over in s. So we can it change. That slip is beat Z a slept by several methods Number one we can change the state of altered to control. We can control the state or voltage which will affect Izzy slip at, which is the maximum or the slip at which is the full load of care. Second missile is the rotor Resistance Control weekend. By adding resistance in the rotor, we can control this meat. Another missile is a changing. That in s okay, so slipped but can be changed by an S or can be changed by in our by N s. We can control as the n s by using a we over F ratio control that frequency control and the changing number off balls. So we have 1123 for five methods off controlling the speed off. So let's discuss each off these methods that first message is state or voltage control controlling thievy seven or V one. So I start things. The starting current is equal Toe the voltage we won the input voltage or the state or voltage over that road are one plus r two dash or square plus examples exito dash all the square Where s equal one since we're talking now about the starting to talk as is starting current. So as the voltage increases azi starting current willing threes off course since they are proportional to each other. Second thing, when we increase the Walter, let's sees a starting torque from the torque equation and substituting by s equal one. Since you are at starting, you will find that the torque is directly proportional toe V seven and square or V one square. So as the voltage increases, the torque starting will increase, too. Number three, what will happen toes the maximum torque. Also, the maximum torque is directly proportional to that V seven in the square, so the maximum torque will increase as the voltage increase. Now, looking at the slip the slip, what would you slip a slip at, Which is the maximum work will. Okay, you will find that s maximum is our to dash over road or seven square plus x seven Ambrose exito dash old square So find eager that Z s maximum does not depend on Zini voltage. There is no voltage here in the equation, so the s a maximum Does no be affected or not affected by the voltage or the state or voltage. So if we draw the state or voltage variation with the speed characteristics Look at this. We have this in quantities. Beat and s is constant. Okay, All of them are at zero. They are at the same thing. Cornices, beat and ness. Now we have this girl. The first occurred and second curve answer the curve where we one is greater than Vito Graters M v three. We want veto. Obviously you will find that starting talk here is greater than this one greater than this one since we won greater Zen veto graters Envy three and the maximum torque the torque Maximum number one greater sent or two maximum number two greater than talk. Maximum number three from this equation is this one and this one now, But the s a maximum Zs at which is the maximum torque. OK, we will find that it is constant at the three, the front cases. So here and this innocent the maximum torque and the years in maximum torque and the maximum talk, so s a maximum is not affected. But how does the state or voltage control affected his beat off the motor Now, looking at characteristics off a lute tiene orza low torque off the air load or the mechanical load connected dozy induction motor, you'll find that zine load Have this characteristics where the torque is directive A personal with the sweet. Okay, this is one type off the torque characteristics so we'll find that the intersection between the low torque and a Z characteristics office scene and induction motor itself will give us the operating point. So it enter sectors here at, for example, cover number one intersected at here and this is be it. OK, Golic and Ness one. And then for the second, the curve intersects at here and as to okay and the year at unnecessary OK, so find at the front of Walter, Do we have the front is beats so we can by using the voltage we can have the frontispiece and you will find that as the voltage increases is this bead at which you are operating increase. But the problem here is that you will find that this part is very narrow, very small as feed control. So this leads to the advantages off the state or Walters control, which is number one. The starting current increases as the vaulted increases. So this is very bad because the starting current is already very high, so increasing the voltage at starting will cause the starting current toe be very high. Okay, which off course causes high losses. And of course, I can damage the winding And of course, a produce very on a large heat energy second thing is that not a speed control. Therefore, you will find that it can be used in low voltage range. We can control the speed in very or in low voltage We. Why? Because we cannot accede or exceed the rated voltage off the machine. Okay, That's why this time off message is used. The with low starting torque motors. Why? Because low starting torque means that we will provide low voltage. OK, but what is the problem off? Not exceeding zero rated. Walter, we cannot exceed the voltage greater than we rated. Why? Because if we increase the voltage beyond dizzy rated, value is in the insulation off the winding himself will not withstand this high voltage. Okay, so break down off insulation off the machine. Which off course not a good thing. Now this leads toe the second type off speed control, which is really important and very, very useful way that rotor resistance control are toe dash control. This missile is used for slip. Bring motors only. We cannot use it with a squirrel cage as the square of kids wrote or cannot be exist. But the slip ring. We remember that we use brushes and sleep brings so we can add external resistance. Dozy rotor resistance. We can add external resistance. Does he wrote or circuit? Now, looking at the different here is a different parameters here. And let's see the effect off the rotor resistance for I starting in this equation. As arto dash increases, we increased this part so I starting will decrease. So as we increase that, starting as the resistance or to dish Zinn's a store thinking current will be reduced now looking and distorting Talk as they are today increases here and here. What will happen? You will find that Z some mission off this increase here on this increase Here we lead in the end, an increase in the starting talk. So they're rotor resistance will help produce a lower starting current and the high starting talk. This is a very important message. Used the in starting off induction note. Now let's see that orca maximum is the maximum torque here does not depend on our to dish. So the maximum torque is constant C or a constant. But let's see a PSA maximum as our to dash increases the slip at which is the maximum talk cares well, increase. So why Starting as auto dash increases, I starting decreases torque starting the increases. The maximum torque is constant and s maximum increases. So looking at this girl, this is the 1st 1 which you are starting Good of a number one, then curve number two here where we increase our to dash Number two is greater than or two . That's number one then girl of the number three were also destry greater than auto dash number. So this is 12 and three. So assembly toe understands this. You will find that the torque is starting increases as the maximum here and here and here is constant but s is increasing as here Its maximum is different from its maximum Here different from this one. It's a maximum year is the largest increases as well Go from right to left. Another thing you will notice here. In order to fund our senses, you'll find this is the first occur when we increase the resistance As if we shifted disc er to was the left. Okay, look at this curve as if we shifted it Does he left So shifting is this curve to the left? Will it change the intersection? Point? Let's see in Ziska If we talk this curve and shifted like this as if we shifted it like this with the maximum torque and it will be like this. Okay, we shift. Is this curve like this? So the intersection here will be moved here. Okay, it will move like this. Okay. As if we took this girl and shifted it was he left as we increase the resistance so we can increase the resistance toe move this curve until the maximum torque becomes is the starting talk. Okay, this point and tar sectors here. How? By increasing czar to dish the advantage of off the rotor resistance control number one wide range off speed control. We can add as much resistance as we would like. She mess Aled. Their resistance is very sheep, so it does not require any variation in the voltage or any kind off voltage control or anything. It is just the addition off some resistance. It decreases are starting current, so it is used in starting off induction machines. It increases our starting talk so it does two important functions, increases starting torque and at the same time decreases the starting current off induction motor. We can increase the talk at starting by adding maximum roto resistance. Then decrease a grad a retail for so we can just increasing torque at starting, then remove the resistance. Gradually toe reduces it all as before. The reason for this why would reduce that rotor resistance? Why do we decrease it gradually, therefore lewd because that rotor resistance itself causes power losses. So we just use our roto resistance at the beginning to produce high starting torque and low starting current. Then, when reaching is a full load, we reduced the rotor resistance toe. Reduce Z couple losses in the machine. Now we deserve the missile is called V over F control. So what is the over f V over If it's called the constant flux message, What does it mean? It means that the by keeping is a racial V over f constant inside the machine, we will be able tow reserve a constant flux inside that machine. So you remember that E or the induced the meth inside that machine, which is nearly what does the voltage will be equal to 4.44 flux k winding day phase frequency. So we can say that the flux is equal toe V over all of the other factors flux equal toe be over the other factors. So all of this part is this part only is a constant. Que que winding Afghanistan is a factor off the one Afghanistan T phase number off donors is Afghanistan. So the only parameters which is variable is V over F. So if we keep the over f constant, then the flux will be constant. That's why we over if control is called Afghanistan Flux message now lets us see the effect off the over F control on that team maximum. But in this case, we will neglect our one. Then we will consider it in on other cases now neglecting or one we will have team maximum equals three V seven and square over to Omega s X seven blocks Exito dash like this after neglecting our one. So we removed our seven or are one and the make it zero. Now we need to find the over f. So remember that we re seven and square is a wall. De Gea is a B seven square now how we can get the frequency. You know that Omega s is to boy f over being so we can say that or my guess is directly with F like this So we can replace all my guess by toe by f Overbey or Afghanistan, not the blood by the frequency. And is the X is by f l. So we can say that the X is directly also with the frequency so we can just take this and substitute it here and take this unsolicited here so we'll find that we have f a square downward so the Torkham maximum will be directly proportional with V seven and square over F Square. So we over FX Constanta We said that we are using the over F control. What does the over f control means that if I increase the voltage, then I increase the frequency to keep their issue constant. If I decrease if voltage, I will decrease the frequency. Okay. Now we over efforts a constant. What does it mean? It means that the tour connects. Mom will be constant at any frequency when we neglect our one now effect off a T maximum or effect on the maximum considering are one. Now, look at this equation. We have 37 square over to make s r seven and plus roads are seven square plus x seven plus extradition. All the square now at low frequency when the frequency is low, What does it mean? X seven plus extra dash, which depends on the frequency, becomes very low. So this value is low. Camembert, the Tuesday resistance, so are seven square is Valya large, converted two x seven and square so we can remove the store neglect X seven square when we neglect it at low frequency only so that the maximum will be Stevie's. We seven square over to my guess to our 17. Why, since our seven plus route or seven square, which is two, are seven, So we find that we have 37 square above and don't ward. We have only one F, so the maximum would be directory V seven and over F multiplied by V seven. So what will happen? This party is a constant, so the maximum torque at low frequency is directly proportional with the voltage as the voltage in decreases as the voltage please, as we decrease the voltages that he maximum will also decrease. This is only happens in law frequency now at high frequency wins a frequency increases at high values. X seven plus extra dish becomes a very high number. The tools that to resistance So we can neglected the resistance or seven. And number two does this, so we will have in the end team maximum Serevi seven a square off our Tomei Guess x seven plus extradition. Same as we discussed in case off neglecting our one. So the maximum torque will be constant. So at no frequency the maximum will be director was we and High Frequency team Maximum will be honest is the effect on torque starting three V seven square off our omegas are seven plus arto dash or square plus exito dash plastic seven or square. So at high frequency, when's the frequency is very high? This term will be very high. So what will happen this term will be neglected. Extra dash will be greater, sends a resistance. So the equation will be three V seven a square over May. Guess extra dash plus x seven and all square. So we'll find here we have V seven square and we have F and F all the square, so we'll have f A Q. So talk starting is detectable. Washington with the square over F Q. So it will be the square off effort square, which is a constant multiplied by one over F. So the torque starting will be inversely proportional with the frequency at high frequency . So as the frequency increases, the starting torque will decrease. Now, what is the effect on s maximum? Its maximum is our to dash off. Our roads are seven square plus Xs seven members Extradition Old square now C s maximum with the frequency only. So as a frequency increases wins a frequency increases the X seven plus extra dash increases. So that s a maximum decrease. What is the effect on the N s assassin? Chronos Speed and s is equal to 60 f over B So as the frequency increases, possessing Chronos is being will increase Now we would like to draw all of the above cases or the previous cases in one diagram. So we have here V over f is decreasing. We are decreasing it from From here we are decreasing it from starting from here. So starting by h parameter, you'll find that assassin Chronos beat as a frequency decreases is asking Chronos is bid decreases. We are moving towards the left as we over a fresh witty crazes their frequency Or that Syncronys is being one decrees now at high frequency at high frequencies here at the beginning year, you will find that the Torkham maximum is constant. Then at a very low frequency, the torque maximum will decrease torque maximum at low frequency. So at high frequency here, here and here and here you will find that Z torque maximum is constant. But at a low, very low frequency, it becomes lower. Number three. You will find that as the frequency decreases, the starting torque here starts toe increase. Why? Because we said before that the starting torque is inversely proportional with the frequency. Okay, Now let's see another thing. The S a maximum s a maximum was here. Then it becomes here. Then it becomes here. And we said that the esta maximum is inversely with the frequency. So as if frequency decreases as to maximum shifted towards the left. Ok, all of this is obtained from the equation. You can get back to it if you don't understand, okay and applies him. Now, let's see. Is that frequency control or effort? Control Now effect on talk. Maximum need electing our one dorko maximise three via seven. Square over to Omega s extra dash plus xs seven in all square. So when we when we are talking about I was out square here When we are saying we are talking about the effect off f only we don't want a lot of the seven. So let's see. Where is the frequency frequency here and here. So is he talked to maximum is inversely proportional with F motto. Blood by F, which is Tourky maximum is an Fallujah inversely proportional with one of our effort square . So what does it mean? It means that as the frequency increases the maximum torque indicate, as if increases the maximum torque will victories. Now, what is the effect on the stork in starting torque? Here we have our equation for starting torque. As the frequency increases here, you will find the talk. Starting is also inversely with the frequency. So as the frequency increases is the starting torque will also decrease the effect on s maximum. Again, as the frequency increases, this part will increase, so it's a maximum will decrease. What is the effect on that sink? Wallace's beat Unless And that's equal 60 f over B. So as the frequency increases as a frequency increases, that's in promises beat well increased. Now, combining all of this in one diagram Looking at starting from here. This is our first occur. So as we increase the frequency, we increase the frequency, lie exist, frequency increases, so in S one will increase toe in there. So toe toe. Unnecessary senses are promises. Beat is dependent on zien frequency As frequency increases existing Chronos is weight increase. Now look at starting talk as the frequency increases the starting torque decreases from here and verse it was each other and torque maximum. Also, the creased orca maximum also decreases and its maximum What happened to it? It's maximum is anniversary with the frequency so as being so as the frequency increases S maxim indicates frequency increases So it's a maximum shift A to Z right where its maximum starts to decrease Here lower is in Lord here its maximum is Lord So the frequency control is used. The winds of frequency is greater than a freighted When we would like toa increases us be beyond desire eating to speed. So frequency told is yours the four high speed induction machine or induction? Because we can increase the frequency which will cause that as they beat toe increase beyond is R rated it's beat off the machine Now the last missile off controlling is a speed off the induction motor. We said that we can control the number of fools So as the number of bulls increases the speed decreasing. Same as what? Simmons, Sicilian on the lawn salient machine. Where's the silly into machine? Have larger number off bulls, so it have a lower speed. But the non salient have a low number of words, so it have high speed. So those are the message off controlling the speed and science e induction not. 156. Methods Of Starting Induction Motor: Now let's discuss in this video. Let's discuss Izzy starting off induction machine. So we have years the equivalent circuit for the induction motor and you'll find the one R one jx one j exam where we neglected here are seeing whatever if we added it, whatever it is, our today show over S and GX toe dash now would like to understand this at starting, so we'll find that that's starting. The current is very high. What is the reason for this? Can't So look at the starting. We have the slip. Okay, is a slip which effectively starting I've starting is this lip is maximum. The slip is maximum off number one. OK, it's equal one. So the R two dash r dash over s is our today show only, but in any other speed, for example, and treated his weed or to dash over efs at for lewd. It's a fool s sat for load maybe, for example, or point or three over. We can say that 100 over three. We can say that 100 over three are to dash, so Camembert toe this value at full load number. That was the starting where we have our today only and this one are to adapt, multiplied by 100 over three, which means that it is more than, like, 30 times or 32 times or whatever so find that are today is a lot higher at full load from at starting. So after starting with ER, today is very small, so we'll find that you will find that at the starting Z Arto Dash Blust J extra dish is a lot lower Zandi exam. So I had to starting this'll epic will one so the invidious would be minimum so the starting cannot would be high. Why? Because all of this this two elements are married to each other, so J x m is very large Camembert toe are today plus the extra that so we can cancels this bridge. Why, since in peril we can remove the very high resistance cumber or impedance convert toe the lower impedance at So I want a starting will be the one over road R one plus r two dash or square plus x one plus X. It'll dash all square, so find it now that the MBI Dent's here is the minimum value off impedance converted to any other condition as an example, z for load condition. Where are today is very high, so they're starting current, so the imminence minimum so starting current will be maximum. So when he toe reduces the starting current off the machine, and also if we can increase the starting torque off the machine, so we have a several message off a starting the induction motor or the induction machine. Number one, the direct online starter, which is used a four less and thinking what motors or low rating motors direct online means that we are connecting is this. Apply directly those a machine without any starting a missile. The second the missile is the star Delta starters. This method is used the for larger motors, and the state or winding is initially as a star configuration. Then it would be changed toe a Delta connection when that's bead or some water reaches that rated sweet the served. The message is the auto transformer missile where we changes. A number off turn is required, which changes the game board voltages so we can control the starting off induction machine . The last missile is a Rotary Resistance starter, or C, measured before the end one rotor resistance off as we discussed before by adding a rotor resistance, we can control the starting torque and starting Kurt. Another missile is called disease off to starter by using variables, be drive or by using as I restaurants, where we can control the embed voltage toe the machine. Now starting with the director line missiles we have here our three face mortal and we have here the three terminals off the motor and so return is also supply. By connecting the supply, we give the voltage toe z not we connect here is he wanted director. It was a supplying without any control or any starting message. The motors are connected or usually connected in Delta connection in orderto produces the maximum voltage since is the voltage faces that phase wattage here will be that relying tow lines the lyinto line voltage so that or comm produced is maximum. Okay, again, they are the motor re usually connected in Delta Not to start. Why? Because Z phase voltage will be easy maximum, which means that the torque produced will be maximum. I like ze star connection where the phase voltage would be relying over road three is that this adventure off this message is number one. It has, ah, high starting current senses as the weeds custom before the reason for starting current zero. I starting current because we don't have any message off starting on Lee suitable for small motors. So we will start to buy. Discussing is the store Delta message the store Delta method we have here our motor. Okay. And we have this representing zero overlord off Lord Wednesay as the loading exceeds, for example, 110% or 120% off the rated power of immortal A Z current exceeds 110 or 120. According to Z value, which is designed the four. The contractor cuts off the cirque. Okay, so that contact contact or Orza overload year is used as a protection, not the contractors. The overload here is used as a protection off the motor. From the overloading, we have conducted number one, protective number two and to contact on number three. This one is used. The four Delta connection. Why connection and this one is usedto supplies the power industry. When the two cases off course off Delta and star So you will find that at the beginning when I would like Toa make the store connection at the beginning. How can I does this? First we connected this contact. We operate it so this one would be closed. This one would be closed and this one will be closed. Then we close the contractor off. Why? Or Delta or Star? Why? Which is a star. We close its contacts like this. So what happens? The motor itself will be like this. The three tournaments are closed from as a site exists. Streets are closed and the other part is connected. Toe the three face supplying. So it will be like this. Okay. Like exist. Okay. The motor will be like this from the two sides. Okay, So in this case that wins, the three are closed with one point, which is a neutron off the star and the other is connected. Toe the three faced lie. Three face. Apply. Then what happens? This one is a star connection. Now, if I would like to have a delta connection, then we will turn off the Y Anderson on the delta contact. So when's the delta? Contact is closed. What will happen. You will find here that we have the three phase motor like this one and two and street. So what happens? He you'll find that we have no phase Number one phase number three 123 Whatever. This is an emergency Ryan's 12 and three as they are connected to the supply. So one and two and three are connected to visitor. And at the same time, you will find here that we have the first turn in 2nd 1 and served one. So you will find that this one this one is number three. OK? And this one is number one. This one is number one. Okay. And this one is number two cases. One is too. So we have here 12 and three from this side connected toes A supply. So we have Z 1st 0.1 and two and three connected. So the supply the other point here 312 connected toe the same supply. So what happens here? This is equivalent to what? As if we connected this one. I think this one here and take this one here and take this one and rotate it like this. Ok, so this point will be connected to the other point off the or the other terminal This one connected to this one and this one connected to the 1st 1 OK, number three connected to number one. Number three number city here connected to number one and number one connected to number two. Number one connected to number, toe one connected toe to. And the number two connected to three. Number two connected to three. Okay. And this is our supply CVS supply. So this is equivalent to delta connection. Now, in this mess out, we started the motor as a star connection. Zinzi Motor reaches as your top speed. Then it's connected as so why do we does this? First, you'll find that at starting when we're using Z Star Connection Star Connection is Then you will find that the voltage Jimbo toe the machine is very line over rotary. So is he starting current at star connection will be V phase over the road off the immediate. It's since V phase here is Villanova rotisserie OK, then see current off The star is less Zanzi current off delta. Why? Because in Delta connection, the voltage here will be a V line to line. But now, by connecting a star connection, the voltage will be relying over rotary, so this one will be equal toe delta divided by road three. So this is the advantage advantage by reducing distorting current about that. This advantage is that's a starting torque itself will be reduced. Why the starting torque is equal to three I faced Square Arto dash off our Omega's and the starting talk is directive proportional with my face. Starting square or directive was Nanto VI Square. So I faced square I face. Is this value okay? Which It depends on V face, which is very line line over roots three. So we'll find that the issue between torque starting at a star connection over director line, which is Delta, is this one is V line over rotisserie, and this one is relying as a total. So this is a square and this is square. Why senses a current is already square, so the ratio between starting torque at a star converted toe directo line or delta is reduced by one of our city. So this is a very bad this advantage. You reduce dizzy torque at starting, which means that if the torque off the load Greater Zanzi talk off star Zinzi Motor will not be ableto operate at start now another method used which is the auto transform Our message in all the transformer you will find that we have is the same But toe the three fairs in boat and we just take value off the on Z voltage. The voltage ambush is, for example, the Feres V one. So we take just a part off this voltage toe the machine. Okay, we take part off this voltage toe the machine So the voltage here entering his ex everyone where X representing the part off, determines which we are taking the part off V one. So the imode voltages x everyone. So we decrease the voltage at starting by. Using auto transformer to reduce is a starting current that this advantage is also that the starting torque will be reduced Because we said before that the starting told the bends on the voltage so that starting we reduces the voltage by no percentage x so z or one minus X so the vaulters will be reduced so the starting talk will be reduced. Now what is the equations here. This is an equivalent circuit off our or to transformer. Now we have ear resupply. Okay. Like this. This is our supply voltage. And we have current I line supply and we take part of this supply called a resupply, and brought it into our delta connection. Okay, so the Walt it here across the sea face is a V supply. Now, the current I face here in the Delta connection is a V supply over that. A V supply over that a be supplying for that. So this representing a resupply over that remembers that the supply over isn't representing dizzy current face current in direct online without, with the usage off the auto transform, resupplying will be the voltage across Zedillo. So the value off current I am or I motor as a face with respected toe director line is a I starting direct online. So they current here is reduced by a value off eight. Now, if I am lying, we are talking about the line voltage off Z Delta connection There line voltage here. Assembly roots three z phase current or what? Sitting a V supply over sandwiches. Rotisserie z I face Why? Because the relation between line current and the fist current in three phase Delta that issue between or the relation between line and defense is rotary. So I line is routes three the face current. What city? A supply over that. Or it means that this is similar to the eye line off direct on line or a direct online. Okay, AI starting but lying because in starting, let's make it clear for you like this. This is the delta and this is the first current. And this is in my eye line in LA direct online so that I line assembly Z phase. Life is current mata blood by Rote city So similar here is a face current multiplied by rote city But this current here is reduced by A from this one. So the line will be reduced by a from this one like this. Now the starting talk will be assembly three ifit square off to a dash over. Oh my guess since I face is reduced the bike A So that orca starting will be reduced by a square. Senses he can't hear is squared dork starting direct online. Why? Because he current here is reduced by a so here will be reduced by a square. Now we will find that. See, I line supplies. This current is equal to what equal toe s square are aligned Iron toe line which is equal to a square. I starting line. Direct line. Okay, it is a similar to each other. Z line supply here is equal toe the line but multiplied by a okay which is similar toe s square inside the ice starting line Director line. Why? Because island supply is equal toe A I am lying now. Another missile Dizzy Roto Resistance starter which we discussed before At the beginning, we said that when we increase the auto resistance, Z curve shifted to the left so they're starting to work is increasing. So this message is considered as the best starting measured as it increases. He talk at starting as you see here and reduces the starting current since the resistance is increasing. And of course, in this missile we start reducing zeros distance. When the motor started, why? To reduce Z copper losses? The last message school disease off the starter measured where we use here a group off Cyrus stores or bread director fires or a C. Shoppers are not Rectifier a C shoppers, this issue shoppers. He was the to reduce the voltage. How? By controlling the firing angle. Alpha, off this Cyrus stops. We can control the M word. Voltage toe. Zimmer. So I discussed the C A C shoppers off course in my own course for power electrics. But for now, if you don't, you know I will. Just to give you a small hint in this message, we controlled the input voltage. Does the induction motor by using the firing angle off this scientist and starting with yours high Alfa. Hi. All four or high firing angle means that's the voltage boxes here very long. Okay, so that's starting. The voltage will be no. Then we start after going after going from starting after going from starting, we started reducing Z alpha. Reducing the alpha will cause the voltage itto increase until we reach the rated value. Where's this I restaurant bosses. All of the So Those were the methods off controlling Z or starting off induction. Montel. Now, in the next video, we are going tohave an example on the starting off induction motor 157. Solved Example On Motor Starter: now let's have an example on the motorist. Are this example Will help you understand is a starting message off Simone when we're applies the most in equations. So we have ah, motor off frequency 60 Arturs 120 Walt Delta six balls by force A power that resistance R one is 4.45 arto dashes, or 0.5 for one. The Ex equivalent, which represents X 17 plus extra dash or X one plus X two dash and dizzy slipped at which is our full load occurs. The full torque is 5%. The line current at starting is this and that three I line at flu. This is a required you need line current at starting is lowers and three times the current at full load the torque load or the characteristics off Our Lord having 40.65 plus 24.781 minus x squared so that this is the characteristics off the North connected. No, no, current is neglected. Neglect RC and exam. This is representing as a Nollywood current or I note that the current which was absorbed by R C and exam so we neglect both officer now find is that the maximum I am and I line or the current off the motor and was a phase current and see line current and the torque starting the starting torque for each off this message. The largest online is the star Delta connection. Is he all to transform our and adding resistance toe zero? So the question is which off this message is is OK or can be used before starting off this motor and which is not acceptable or rejected. So how we can know this assembly? We have two conditions which we need. Those that's fine. The first condition, which is that I line at starting, should be lessons three times the island at full load. So we have here at Delta Connection and I am, which is the my face and we have eye line. So the eye line at starting should be less than three times. I line at full load. So we have our circuit here is equivalent circuit voltage off Holland, 20 vault off course is is our line to line voltage, which is the same as for his voltage in Delta Connection are one projects, one are two dash over S J Extra Dash. And this is the current face current at starting. So I want or the current equal 220 volt over our one block jakes one r one plus our tradition for s r. $1 our today show s or square plus x one plus x two dash or X seven plus extrajudicial square Everything is given This one is given This one is given our one given or two days given and we need I lying Starting Lamberto, I line for lewd So I lined for loot. That is what we would like to find. I line for Lord, we need to get I face for load So I faced for Lord means That s a flute which he has given inside the problem So we can get I face for loot And we know that the current line is the I face monitor blood by rotisserie route three my face give us certain city 30.168 number So this is the line current off the machine at full load condition So we need island and starting the well is then sorry I line for lewd so I line at starting should be three times . Listen, three times its value. So it will be mine tonight, 30.5 Ambien. So we have to make sure that three message orders are four methods. That island at starting is less than mine to 9.5 under. The second condition is that we need that work at starting, so that or cat starting should be greater sense. He talk off the load and starting. Okay. Salud itself having this characteristics which is dependent owns. I slip. We need to make sure that the torque at starting greater sands talk off the note, which means that it can start or not. So torque load at starting means at the snap equal one. So that all load at starting will be 40.65 This is the required torque off the off the load required tore off the road at starting. So we have to make sure that the starting but work is greater than 40.65 so that conditions off starting, which we need to satisfy, is that I starting line Lizin 9 July 9.5 Amber and starting torque vittles and 40.6 wife and their new team it So the first message is the direct line message. So in direct online, we will connect is in mortal by acting. So have Z. I face that starting I feel starting is relying toe line which is the same as V fears which is 220 volt overrode R one plus r two dash as equal one off course all the square plus x equivalent square. So this would give us 100 and 10 And what does this representing? Representing is the phase current. So now we need the lion can't the line current is route three multiplied by 110 are lying in director line is 100 and 10 wrote city which is 100 under 90 0.5. So this is our current Now we need to find the talk at starting door. Got starting a city I face I face OK, I face not lying. Of course, the face is the one which you produce the talk So three I face square are to dash over race which is s equal one over Omegas Omega s, which is to buy an over 60 or f over Be the frequency off a number off old bear. So I am as affairs is given as 110 from here. Ok, we already attend our today s given on the gasto by end of our sacristy or the YF over B has also getting so we can get that torque at starting to be 156.35 Newton. So these are starting to talk to here. Let's see if it satisfies the conditions are not so. First we need that the eye line director line which is this one, should be less than 99.5. But it is 190.5. So this missile is refused because 190 Greater Xan Zee, 99.5 The starting talks would be greater than 40.65 So starting talk here is 165 on 56. So this message is acceptable fourth or starting But the current is refused. So this method does not satisfy all our conditions. So it is refused the second The message is the store that starting So we have to connect is a star connection. Then we'll see the face current and the line here in the store connection The lying current is equal to face current. I line is equal toe. I am so I feels is equal toe we face We overrode serene since it is a star connection Overruled Are Ramblas arto Daschle square plus X one plus X two dash on square. So will find that this by substituting giving us 63.5 Mbare This is the lion and the face and gets off store connection This is the 1st 1 second one we need that work at starting which is three I face square or to dash over Rome A gas. This will give us a 52.1 Newton meat. So we have the current required and 52.1. Let's see the conditions I line here, which is our 63.5 seconds, is 3.5 Lizama interim 15 So it is correct. The starting to talk 52.1 is greater. Zan required 40.65 then Okay, so this is a measured which can be used in starting this motor and satisfying Z conditions . Aziz served. The message is the auto transformer message. So how we can does this somebody without going through the equations? We know that the Eid line in the auto transformer is equal Toe s square. The I line off direct online right which we attend inside the previous lecture. So I lined square Z I line off the and dialect online Anzi torque starting assembly equal toe s square. The talks starting in. Auto transformer is equal toe s square off the talks. Starting off the little line so we can obtain the eye line off Transformer and the torque starting off. What transformed? Ok, but in all the transformer here, we don't know the value off a year. And here, So we need to obtain a which cancels vices conditions. So the first thing is that I line off the auto transformer should be less than 99.5. So the island onto transformer is a square 180.5. So a should be lower than 4.76 point 7226 Okay, we divided a square. We divided 99.5 over 190.5. Giving us this and the starting torque should be greater than 40.65 So takes a starting toward like this and what it here 156.35 s square should be greater exam 40.65 So the A should be greater than 0.51 So we have here are condition A should be greater than 151 and at the same time this then or 1726 so that for proper starting and satisfying their condition, a should be greater xem 0.51 And it isn't 1726 now is the last message is the adding zero to resistance inside. See, So we have our delta connection and we need toe add a resistance. So we know that the I am as affairs is equal Toe de ville Anton, which is the same as phase voltage Over the square road off our one plus r two dash plus are added since is the added resistance which you don't alone plus x equivalent All square Now I vomited and 20 volts are will be are added here, or the total are whatever as a total r r one plus R two dash plus are added plus X one plus x It'll dash on square. Now we know that sea life is here. Should be equal to what? In order to satisfy their condition, you will find that we said that we need the eye line Maximum Toby 99.5 or listens that so in order to sort spices the face current here will be this value divided by three. Okay, this is the maximum theis current, so we can produce this maximum fits current boy adding a resistance. Okay, So what is the value of the resistance edit? We take this current and what it here in the equation. And we have 220 vault are square, which you don't know, plus x equivalent. Now. Why substituting? We can get our obesity 0.44 home and we can delete from it are one miles off to dash will give us z are added to reduces the current to do this value is 2.354 Okay, this is a minimum resistance required in orderto reduces the current toe 99.5. Now see, starting to talk in this case, what will happen? You'll find the people to three I face a square are to dash over s but are to dash plus are added. We added a resistance here so that torque starting this case will be 128.2 Newton meters which off course will be greater. We said that the added resistance or the added rotor resistance will cause the starting to talkto increase and reduces distorting car. So this message is off course acceptable. So this Waas as well, for example on the motor stopped. 158. Simulation of Induction Motor or Asynchronous Motor Using Simulink: Hi everyone. In this video we would like to simulate or both Z synchronous machine as synchronous machine or the induction motor inside z simulink or using Simscape. The first thing we are going to click on New, then we're going to choose a Simulink model in order to simulate our induction motor or the induction machine. So first we are going to use the blank model. Starting is Simulink. Now we have our Simulink, let's maximize it. So the first thing we are going to use the Simulink library. Since the first thing we are going to search for is the borrower GUI. Remember that z power GUI is the one which is necessary in every aspect of our GUI is an Enter. Then add block to the model on brightened. We added z continuous power Gui. Now again towards a Simulink library. Then we need to add, as in coronas machine synchronous Chronos, corners. Let's see Simulink, simulink, Simscape, Simscape. So let's see where a z induction machine as synchronous machine video and advantages, Okay? This is our synchronous machine. So this is inside z per unit values. If you are dealing with the power systems and we're going to see poverty on it or the per unit system. But since we need an actual values in order to measure the torque, these bead and set of currents and everything, we need actual values. We don't need that unit. Would use the SI units or the standard international units. Click on it and then right-click and add blocked OSI model untitled. Now we have here our asynchronous machine, like here. You will find here it is consisting of three terminals, a, b, and c. Is this Z state or currents, or the state or input currents. And ABC is that row torque cards. And we have here z, dm, or torque of the motor. We're here connect to our load and we have m, which is the measurement port. Now, what's the first thing we're going to do? We need to supply our model in order to Z motor to operate. We need a three-phase supply. We can simply, instead of using guys three-phase supply, let's do something different. So let's just say voltage source or voltage source. Let's see is that Simscape, of course. Okay, let's see what we have here. We have the AC voltage source, this one ad block to the model on tightened. Now taking this one here exists, maximize. Now connecting it to here. This is that first voltage which is a. So let's say here voltage source voltage, a voltage. Or let's say at Va. Va is a voltage of the terminal or z at first phase, which is a. Now we will select this one and control and drag in order to duplicate it. Is this. Let's move it like this. And this one here, this one here, now connected to this one here. And one here. We have VB b, v b here, v City of his input supply. And we need to add ZIM grounding. Why? Because we would like to connect disease motor as a star. We can use a star connection or the delta connection. So as an example, we are going to use the star connection. So we need the city terminals here connected to ground. So going into Simulink and typing ground, we have that Simscape. We need that Simscape ground. Ad block to the model on titled Kayla exists. This is our ground. And you will find that here connecting like this and this one here. This one here. I would like to give you a hint about something going into the Simulink. Look at this one. You will find here is that this one is in black. A black, black and the ground also here in blank. So this ground is suitable for z. Sources here finds that this ground is from the power library elements ground. Now let's take it back to the voltage source going down. This one is a power library, electrical sources, AC. So this one is from the library of z power library and dizzy ground. This one is also from the power library. That's why is this one can be connected to this one, okay, because this one is from Zippo library and this one is from z power library. Now if we look at this one, for example, FL library, which is not the same libraries. So if we add this one for example, and Ziploc, does the model untitled like this. And try connecting it here, it will not be connected. Why? Because this one is from a different library, Zan this one. So that is this one, and delete this one. Now, going back, if we look at our synchronous machine, asynchronous machine, look at here it is power library, okay? So we have our power library connected to an AC voltage source support library and the grounding our library. If we double-click on the asynchronous machine or the induction motor. You can find here is that weekend, uh, choose the rotor type. If it is a want or a squirrel cage or wl squared cage or whatever you would like to simulate. Now as an example, if I would like to change, is this rotor type into another type such as the square root gauge. For example. Now in the square root gauge, you can add a preset parameters squared cage, Breathe set model. So if I click on it, you will find here is that we have a different types of squirrel cage. You will find here, for example, five-fourths power 460 volt. Remember that's a 460 volt is automatic and line-to-line ends a frequency of 60 hertz and the RBM is 1750s. This is bid is rated as meat. We would like to test this motor or this induction motor at a different loading. And we would like to see is our state or currents 0, torque, currents, Ziad, dork or beat and everything. What will happen inside this induction machine? As an example, a weekend, it choose this one, for example, 5.4 horsepower for kilowatt, 400 voltage, 50 hertz is n 1300s thirsty RBM. Try to remember this. So we have 400 volt, which is a automatic value line to line Apply and 50 hertz. Now we will find that here, Z sense it is a squirrel cage, will find that there are three phase. Here is a three-phase and currents Albert disappeared and z all combined in one measurement bought. Let's see what will happen here. If we double-click here, we have a 5.4 and horsepower, or four kilowatt, 400 volt, and 50 hertz. Going through the phase a. What is the big value? As you remember that from the electric circuits that in order to change as the line-to-line voltage to voltage, remember is that we divide for that line-to-line voltage by your root three, root, three, root three as 1.73 to 1.732. We have a 400 volt divided by 1.7321. This is the phase voltage, but as an RMS, in order to change this value to the big value, we multiply it by root 2230. Let's delete all of this. I hit this calculator really, really I hit it. Route into root is 1.414 multiplied by 200 uncertain. Mine for equal a 126.593126. Okay, Let's take this one here. Copy 26.59. As I remember, Control C. Now this is a, have a 0 phase shift ends at frequency 50 hertz. Big value. We remembered as a 400 voltage is line to line. The RMS in order to change as the line-to-line two-phase divide by root city. And therefore would like to change this phase voltage from RMS to a big value. We multiply by root two. This is our first supply. Second one which is B. Same value of the voltage. Phase shift minus 120 degrees shifted by 120 degree frequency 50 hertz. Phase number C, 120 degree plus 120 degree 50 hertz. Okay? Now we have our three-phase supply. Phase a, phase B, phase C, phase voltage, sir 126. And we have Z connected to our induction motor. Now we need to connect his erode. And do we need some measurement? First, let's see some measurement. In order to get z measurement ear, it includes a lot of values that machine, such as the state or currents wrote or grants and so on. How can I do this? First, you are going to select in Simulink library bus Korea it. So we have here xy Simulink, boss, a selector and z boss create. So we are going to select this one. Boss created adds the model tool is the modal untitled and the boss selected. Let's move them away from each other. Kayla exists, delete this one, make this one kid larger. Exist, and maximize this one. And move this one here. What does this do? Z pass, select or simply connect the z measurement espouse in order to produce an output measurement signals. So if we double-click on here, we will understand how it is. Selected signals, select all of these, Delete, Delete. Now, you will find that here. While it does EPA selector do Ziebarth selector simply takes as a measurement, which is here signals in zeros. In this measurement, we have zeros on measurement, estate or measurement and the mechanical measurement. Then we can dig these signals and reduce our wood signals. What does it mean? It means that mechanical select is our router is bid in and omega m or in z radian per second, and click on select. We select it first as a mechanical rotor speed. This is one which I would like to measure. And that electrode, electromagnetic torque produced select, we selected ZAP and Omega, or the rotor speed and the torque produced. Now also I would like to select his estate or currents. Abc select. Instead of current, a select set are currently being a select set of currency. The four z rotor I would like to select rotor current, the current TB rotor current scene, and so on. So we have 123456788 out signals. Will see is that here, what will happen if I click on Apply? You will find here 12345678. This one, the first one is representing the first one, which is a mechanical rotor speed. Second one representing the mechanical electromagnetic torque. So the one representing the state or measurement, measurement to measure and so on. So now I would like to measure Z. Z to C is the output Doric and would like to see at the same time what is VT going through the Simulink and typing the scope. Scope, right-click Add block Tuesday model Untitled, that display, display. Display. We have the display ad Ziploc to model untitled. Moves this one here. This one here. Now look. This one. Mechanical rotors bids and mechanical torque is in set or IA IB IC and the rotor IA IB IC. So we can select the first one, which is that mechanical, his VDD, and see it here. Remember that this speed is Omega M. Mechanical is bid in radian per second. And you'll see here that this read here in 1 thousand for onset to RBM. I would like to change his radian per second to RBM. How can I do this? Remember that z beat itself. Z omega is equal to two pi n over 16, okay? We exhibit lenses before two pi n over 60. In order to change from omega to n, We will multiply the Omega by 16 over two by going into the constant K or Z naught z constant about ZEN. Then right-click Add blocked OSI model on titled. This one here. They exist here. And then moves this one, delete this one. They exist one here. And then here. Then double-click this one to convert dizzy at Omega M into Zn or rpm multiplied by 60 over volume. This will convert rotary speed, z, z RPM or Zara revolution per minute. So this one is speed. Speed. They exists relay here to see what will happen to the speed. Now what does an extra step? The next step is that we need to add the electromagnetic torque seminar as before, we need a scope and we need SBE scope and we need that display, control and drag. Then we're going to take this one here. And this one here. Here. We have display torque is this is a three-phase stator current, three-phase rotor current. So what will happen here, here? Z? Let's select this one and make it like this. What does Z pass creator do? The Abbasid period or assembly combined signals together. Combines the signal to noise. So double-click on this one. The mixer number framework. We will understand and our y exists and the control and drag. We have three-phase rotor current, I would like to disability them together. And the three-phase stator current, I would like to display them together. So the eggs are s1 stator current, IA, IB, IC, and Ruto current. Rotor current or EB rotor current. We have one tool, okay, ever saying now the stator currents and 0 tokens, now, I would like to display all of them in one score. I will take two scopes here, Control and drag. Now we will take for each of these scopes, okay, current one or a state or current, rotor, current, current. Then takes this one here and this one here. Now we have a display for the electromagnetic torque, rotor speed. We have Z score for each of the currents. Now we would like to add our torque. So our torque assembly, Let's see z machine itself where we have a four kilowatt. This is the maximum output power. So let's go to the calculator again. Then. First we would like to see what is the maximum output torque. So z power, which is four kilowatt, four multiplied by 100, which is 4 thousand of course. Z power over Z speed, which is two by n over 60. Let's see, two multiplied by Pi, which is 3.14. Okay? Three multiplied by 3.14 multiplied by two pi n, n, which is 1313 over 60. This is the rated omega TBI and over 60 and takes a swan multiplied by four thousand and forty thousand divided by 1.6733349. It will give us the maximum torque to be 26.72. In 6.72, okay, I remember this value which is the maximum torque. What do are going to do this step? So first, we are going to use a step, step in this step block to the model untitled. It takes is one here. We need to reduce a variable torque. What are going to both at the front, the torque is at a different times. What I mean by this, Let's see. We will take four conditions. So we need four steps like this. Okay? So this one step at five seconds, five seconds, step at ten seconds. Ten seconds. This one at 15 seconds. This one at a 20 seconds. The first one which is at five seconds, initial value, value 0, and the final value is 26.7260.72. So this one is the initial load, which is the maximum torque. Now what I'm going to add some ink note, okay? For the summing node, we will type sum and then add block to the model entitled they exist one here. What I'm doing, I don't know, Delete, then maximize, come here, maximize, double-click, plus, minus, minus, minus. So we have four conditions. The first one is Z, maximum torque applied. So it is a positive value. So add this one to this sternum. So add five seconds, adds the time of five seconds. We are applying the maximum torque of 26.7. Step time is a step. Time is five seconds. The initial value is 0 and the final value is 26.72. Adds this instant is the maximum torque will be applied at a 10 second. I would like to reduce this torque to half its value. So in order to both the hav divided by 13.36, okay, him 13.363636. At a time off, ten seconds. At a time of 10 second, we will apply a certain 0.36, but with a negative value. So we have originally 26. The water blind at sardine was a negative value, so it's a total of them will be certain. We are reducing the torque. Now at 15, I would like to reduce it to z quarter. Going through the calculator, divide by two again, 668. What will happen at the time of 15 Zach total torque will be the quarter. This one will be also 6.68 in order to make the torque becomes 0.686. What happens here? This one here exists at a time of 5 second. We apply the full load torque at a time of ten seconds. We will reduce this torque by quarter. It's a value. At the time of 15 seconds, we will reduce another quarter. We reduce here half of the torque, and here we'll use ZAP dorky auto, it's a quarter, it's a value. And here we reduce the torque T2 0 for load torque and the torque quarter of Zika torque 0 torque. We would like to see is a change in size, the torque itself. So we need a scope. Scope, scope, scope. Lags, S, and G, L. Load torque. We would like to simulate this for 20 seconds or five seconds more than the time. Now we revert everything here. We added z measurement for the torque. These VDD. The currents and every single. Now we would like to start simulating this and see what will happen when we start simulating this torque. Now after simulating Z program, you will find that here for the rotor speed, finally, we have a 0 torque. As you remember from the synchronous machine off 1300s and safety RBM. This is bead. Is that rated is bead bid at full load. At no load is as beat is nearly equal to assessing chromosomes VT. Okay, As you remember from our explanation for the induction motor, we said that the speed at no load nearly equal to is the synchronous speed. Synchronous speed is one thousand five hundred one thousand four hundred ninety nine is acceptable. Final torque value is 0.4686, which is a very negligible value of torque, very small value for torque. Now let's see what happened to 0 towards VDD or warnings or skill. It says wheat adds up beginning at no load. It says bid was nearly equal to the synchronous speed, which is 1500 rpm. Five seconds. What happened this instant, we apply the full load torque. So this is beat goes down to 1400 and certainty is that exhibit or rated speed or motor itself. Then at a time of ten seconds, we reduce the load by half of it. Finds as speed increases, again, Zen at 15, we reduce this bead as a load to the quarter as increases again. Then at 20 we remove these are total load so it increases to the final value. And you will see is that here, there are some transient due to change of fluid. Now for the torque itself, at 00, our torque nearly 0 or torque. Then we apply the load which is 26, so it increased to 26. Then we attend, we reduce a to have width 13. Then add 15 will reduce the Tuesday quarter, which is 66 to 20. Waiter moves the total load going back to 0. Now is the current state or currents. You will find here is that it's a state or currents adds a beginning was little. Then add five seconds when we increase desired torque to the full-load torque or friends as a stator, current increased because we absorb more current in order to produce a torque. Then at then we reduced it to half. So the current is reduced to half, the three-phase current reduced to half, then add 15, reduced to quarter of Z load. Then at 20, we remove this total is the total load will find the years that this is at minimum current, maximum current ads for load. Then it starts to decrease as the loading decreases because we absorbed but more current, the Windsor load increase. Now seeing here is that rotor current at no load, 0 current row does not have any current that because we don't have any load right now. At full load is a three-phase current is produced. Three-phase current reduced due to reasons or float. When we reduces the load, the torque Z current is reduced to form the for-loop torque. Then introduced again adds the quarter, then it is 0 at no load. Now watching Zach load torque 0 at five, it changes to 26.7 zen and then reduce it to half. Then add 15, reduces to quarter, then add 20, reduce it to 0. Now we'll find the resist is a disability for that rated speed is a final rotor is EBIT, and this one is the final torque at no load. Now, I felt would like to see that change in these values during the simulation. What can I do? Similar, we'll go to this one which is step back. Stepping back option enabled is saving in the back, then we can maximum number of safety back steps, ten steps, okay, interval between stored simpler, we can use five or let's make it three, for example. Watches values here. Why during the simulation, you will find these values. Is it changing during the simulation of the time you change, you will see is a variation in values during the simulation. This is how to simulate Z induction motor or asynchronous motor or asynchronous machine inside Z MATLAB Simulink. 159. Principle Of Operation Of Doubly Fed Induction Generator: So now let's discuss Is the principal off operation off an induction generator? So we have here an image off induction motor or it can be an induction generator. So how does an induction generator works? Okay, as we remember that we had two parts here we had state or and we had that a roto Okay, The state or is connected to a three face a ploy giving us a surface current giving us are rotating the magnetic field causing current year, or a three faced current here which reduces another rotating magnetic field. So we bought here are supply in order to get an Abbott rotating magnetic field in order to produce at all. Now, in the inductions in Ritter, we are goingto does the reverse. We are going toe supplies Arlotto with the three phase current, okay? And rotate the rotor at the same time. So we have Here's a torque or say rotation off the rotor and we have your also the three phase magnetic field, okay, or the three phase current producing a rotating magnetic field. Then, by doing this, we will cut the state Oh, and the produce, as three phase are, would walked it. So in that motor we have here our in boat reducing a rotating the magnetic field then would reduce the Urus Refits current, which produced rotating magnetic field. Then we produced art or do toes interaction between the magnetic feeds. In that generator, we are goingto supplies are over with as three face current, which produces a rotating magnetic field. Then, by rotating busy router, we will be able to produce, and I would current here inside the state. So now let's see their induction generator torque is beat characteristics in order to understand, how does an induction machine works? You will find years that we have here a relation between Z torque reduced, the boy am motor or an induction generator, and we have yearsas beat off the road. So we'll see that we have a different reason. From here we have a region called is a baking Reason where we wanted to stop our motor by providing 02 with a negative is speed from here from zero. Until that synchro Maciste speed, you will see that we are working in the motoring Greason, this reason where our induction machine is working as an mood. If we increase is a speed off zero toe Greater Zen that's in crosses beat. We will be able to generate electricity. So again, in the induction motor, we work it from zero until za synchro Mrs B. During this reason, we have motoring reason The reason where our induction machine is working as a motive. If we increased that's beat off, zero toward greater sends us in Caracas is beat. We will have a generation. Okay, we will generate electricity So we understand the now that we need toe have as bead off our order. Greater sentencing crosses weed in order to generate electricity. Now let's see their double fit induction generator, which is used in when the energy you'll see here that here we have our window meals which which rotates, do toe wind. Okay, we have Here are gearbox this gear books changes as with it is just excellent or increases beat by changing Izzy gears off gearbox. We ons Inzaghi Books is connected toe a double fit induction generator. So let's to take it easy. We have for us. There went, which produces mechanical energy. Then we have the gearbox. The Gill books is usually used or its purpose is to take This is beat off. He went and increase it beyond discussing promises Be okay in order for the generator to work. So the went rotating the rotor with us bead Greater sentencing promises be the went hever usually have laws beat So we use that give books in Orderto agrees this beat greater sentencing Coronas his weed. Okay, so why do we does this in orderto operate in then? Reason off generation inside that induction machine. Okay, now this was the first thing. Second thing is that we have two parties in the induction generator. We have that three phase or the state or and the three face off zero to Okay, We said before that, in order to generate electricity, we need to connect Z rotor do and easy supply. Okay, we said that we will supply. Here's a photo is a three face current and rotating. It was as be greater sensing promises beat. We were able to generate electricity in that state or winding So that waas Exactly what you are doing here we first to connect our state or toes egret the great is the power system or where we are generated interested goes to So we take at the beginning. We take three faced current here from the great okay, and then convert disease. This three phase a c or is he current in tow? D c. Okay. By using a part of running devices, then we changes a D. C again toe a c. Why do we do this in order to control our voltage of from cigarette voltage and frequency? Okay, so first we take a three phase here. Voltage, we convert it into D C. Voltage. Then we take the D. C. And converted again to a C. This method is used to control the frequency off the the M word. Voltage, Atos the rotor and the value off the vaulted itself inside the road. Okay, so this part used the toe control the M boot voltage and the frequency and dozy wrote Okay , remember that the frequency off cigarette is constant. Okay? It does not affected by anything. So we take Here's the frequency and voltage and control it inside the road. Okay, Now we have here again. We have as big, greater sensing promises beat by using the gearbox. And we have here the MBA tree phase voltage A to Z rotor. Therefore, we can produce electricity inside that. So again we have Here is a bubble if it induction generator consistent off a Steve phase inside the rotor and see phase inside the state that router is fed with three face signal. Okay, by taking it from the great and controlling it, then we provide it to our route. Okay. Providing a stiffest current torture produces a three phase rotating defeat. All are rotating a magnetic field as the window or pine rotates, it produced the mechanical force or mechanical movement on zero as rotor rotates, the magnetic field that produced the due to the A C current also rotates at as we'd proportional to the frequency. What does it mean? It means that we have here the boat, voltage and frequency which we controlled, which causes a three phase current. The three face current inside Z rotor is controlled the Boise frequency off. See Abbott from Z power Electronic device. Ok, so the frequency from the power electronic devices control There's a frequency off the magnetic field. They're rotating magnetic field the bosses to Rosa state or and causing a three phase current. Okay, So it is the same ends the induction motor, but they reverse off the operation and instead off providing here a Strief s current we provide inside the row. Torres refits current toe produce as three phase inside the state of sauces as read off the rotation off the state or magnetic field, the benders on zero to re speed as well as a frequency off a C. Ok, so here is an important thing you will find here. Is that the frequency year and the rotation of the rotor control, There's a frequency off the output. Okay, so we have two factors here. The frequency off the import voltage and the frequency or the rotation off the mechanical board. Or is that rotation off zero toe? All of this effect is's the Albert frequency and voltage. So in order to control or produce a constant frequency, we will use Z power electronics converters to change the frequency. Okay, So, as you know that that that when this beat is not constant, okay, so there's beat off. The rotor is not constant. So we need to change is a freak one scene, Toby able to produce the same Constanta frequency here. Okay, we have here. A variable is beat, so we'll use Zipporah electronics. Converter toe changes a frequency off the boat A c current. OK, By changing this one and the change inside the rotation, we will finally get a constant value here. So that is a benefit off. Using an induction generator is their induction generator can be working with a variable is beat but us in chromosome machine If's we connected to year toe when the turbine, we will have a variable Abbott frequency. Okay, so that was the benefit off. Double fit induction generator and it is only used in sides Owen demands, okay? 160. Self Excited Induction Generator: Now let's discuss another type off induction generator, which is the self excited. Okay, so in the previous one, we discuss a double fit induction generator. We connected the this generator in tow. Sigret, and we absorb it is the excitation, which is, as a current required foresee rotor. As you remember that we took from the grid, we connected there three phase in tow, the power electronics devices. And then we injected current inside the road, which is necessary for excitation. Now, how we can excite our induction generator without connecting does a great Okay, so and the beginning, if we operate as previous inductions and marital before or as as generator or as a motor? Okay, that's three. For his induction, genital will have something which is called the residual Flux. Some flocks or some magnetic field remained inside their rotor itself or inside the machine itself. Okay, so the theme, the amount of the flux which representing inside the rotor and then we rotate the rotor by Z wend, for example, or any mechanical movement this world causes some initial voltage or some initial current inside the state. Now, for a self excited, we added at a bus for banks. This cover story banks is user toe provides excitation. Okay, as you remember that the investors in Z bar system used to improve the power factor, or Dickie decreases the reactive bar required by injecting reactive bar. Okay, senses the inductive loads absorb sq at a certain moment Z caressed or banks supply Q or supplier active. Okay, So what happens here in this machine is that at the beginning, we have some reasonable flocks presenting inside the machine Is this also provides the initial excitation. We have a small excited on or a small magnetic field inside the road. And when we are rotating our motor boy as speed, greater sensing promises beat, for example, in wind energy, then we are going toe have some induced e meth inside the state. Okay, we'll produce some induce the image. I very small value this more value will produce. I current. Okay. Is this current will boss Rosie cholesterol which causes he covers, talked to supply or give us a cube OK, but produces the excitation required for the machine. So the total flux or the current year inside the campus to bank increases the total flux or the total excitation this will cause is against the voltage ear to increase again. So this process will continue until we have a steady state value. Or until we have our final value. Where's the characteristics off the machine or the rated value off the machine and dizzy Capstar bank of all trajectory into characterised intersect? What I mean by is it is that we have here the relation between the voltage and current off the covers to bank. Okay, you will find here is that we have here is a magnet ization girl or their value off excitation required at every current off the camera store. Zima magnetize, Asian Careful representing Zomig notarization off the machine. And we have here is a reactor Salama to represent is their relation off the over I or Ecstasy. Ecstasy is very actimates off the custom. Okay, so if we draw this line and we draw this line, we have an intersection. At this point at this point is called the City State Point, where the both of them intersect. Okay, so I want finding value. Will have the one and I see one V one is considered as here as a rated value off the machine. Okay, so at the beginning, we have a small amount of flux. Is this small amount of flux will produce a small current. So the current, as the current increases the current itself causes increase in sands excitation off the machine or increases their total flux inside the machine, causing the voltage it'll increase. Then, after the voltage increases the current eyes, he increase and so on until the city state value. So let's again revise Z a self excited induction generator at the beginning. OK, if it is a new machines, then we will start it as a motor in orderto have some residue, all flocks okay before operating it as a generator. So I had the beginning. When we are using it as an induction generator, we have some residual flux, some remaining the flocks inside the machine, this remaining the flux inside the rotor and which means some very small value off a rotating a magnetic field, very small value. And we rotate the rotor boys at your books at as we'd greater sensing promises bead. We will have the year some inducing myth or some Albert Walter. Very small value. Okay, a very small value. Is this a small value off induced a metal produce current inside the state or Zika? Is this currents and signs a state or will boss or Ruzicka buster banks causing the total voltage ito increase? Or it means that they are providing a flux in face or increasing the total flux off the machine. Okay, The Windsor Capacitor Banks Wednesay current was throws a crystal Banks. The cluster banks is used to provide AK. You are every active boat, and at the same time, it said toe increases the total voltage so the capacitor banks provide a current which produces a flux. This flocks is infants with the road or flux so that daughter magnetic field off Z rotor increases. So when's that autumn magnetic field increases? Z out here will start to increase, and at the same time, Z current here will increase until this operation continues until the city state where we have the rated output voltage. So Sam billy the road or have some flux. This flux produces a small voltage this voltage. It produces a small current. This current produces another flocks in face or increasing is a total flux Z total flux reduces again higher value off E M. F. This team effort produces another current which increase the total current and so on until a steady state. So at the beginning, we should have some reasonable flux. If there is a whole flocks does not exist. Then we should connect our machine or induction machine as a motor in orderto have some flux at the beginning. Okay, so that is a benefit off ourself excited Induction genital which is not connected to a cigarette. You will see that here it's connected toe the road. We don't have immigrate, so it cannot absorb is excitation okay? We absorbs excitation in case off a double fit induction generate.