Electrical Power Transformers (Single Phase & Three Phase) | Graham Van Brunt | Skillshare

Electrical Power Transformers (Single Phase & Three Phase)

Graham Van Brunt, Professional Electrical Engineer

Electrical Power Transformers (Single Phase & Three Phase)

Graham Van Brunt, Professional Electrical Engineer

Play Speed
  • 0.5x
  • 1x (Normal)
  • 1.25x
  • 1.5x
  • 2x
9 Lessons (5h 37m)
    • 1. Ch 00 Introduction to Transformers, Connections and Protection

      9:30
    • 2. Ch 01R1 The Ideal Transformer

      54:31
    • 3. Ch 02R1 The Real Transformer

      9:09
    • 4. Ch 03R1 Instrument Transformers

      18:42
    • 5. Ch 04a Three Phase Power Transformers

      109:42
    • 6. Ch 04b Three Phase Power Transformers

      16:51
    • 7. Ch 05R1 Transformer Construction and Cooling

      25:59
    • 8. Ch 06 Transformer Protection

      53:43
    • 9. Ch 07 Transformer Relays

      38:29
  • --
  • Beginner level
  • Intermediate level
  • Advanced level
  • All levels
  • Beg/Int level
  • Int/Adv level

Community Generated

The level is determined by a majority opinion of students who have reviewed this class. The teacher's recommendation is shown until at least 5 student responses are collected.

99

Students

--

Projects

About This Class

This course starts out at the sub-atomic level with a description of current flow and then moves on to electrical magnetism. Mutual inductance leads to the "ideal Transformer" model and its ratio calculations. The characteristics of a "Real Transformer" are discussed and modeled as well. Three-phase transformer connections (Y - Y; Delta - Delta; Y - Delta; Delta - Y & Y - Zig-Zag) are looked at along with their inherent phase shifts. Power transfer is among the topics discussed.

Protection of power transformers is presented in this course.

Meet Your Teacher

Teacher Profile Image

Graham Van Brunt

Professional Electrical Engineer

Teacher

Hello, I'm Graham Van Brunt B.Sc; P.Eng.I have spent an entire career in the power sector of electrical engineering, I graduated from Queen's University in Kingston Ontario, Canada. Coupled with subsequent studies with Wilfrid Laurier University I have traveled the globe and applied my skills to garner my protection and control experience internationally.

I have a passion for staying in touch with my profession as an electrical engineer and have a kinship for mentoring that has kept me in front of an audience of learners.

See full profile

Class Ratings

Expectations Met?
  • Exceeded!
    0%
  • Yes
    0%
  • Somewhat
    0%
  • Not really
    0%
Reviews Archive

In October 2018, we updated our review system to improve the way we collect feedback. Below are the reviews written before that update.

Your creative journey starts here.

  • Unlimited access to every class
  • Supportive online creative community
  • Learn offline with Skillshare’s app

Why Join Skillshare?

Take award-winning Skillshare Original Classes

Each class has short lessons, hands-on projects

Your membership supports Skillshare teachers

Learn From Anywhere

Take classes on the go with the Skillshare app. Stream or download to watch on the plane, the subway, or wherever you learn best.

phone

Transcripts

1. Ch 00 Introduction to Transformers, Connections and Protection: this training session is on the fundamentals of Transformers. More specifically, we're gonna look at the connections and protection of transformers. Now, this course is a boat four hours in length and you can take it in stages if you want or all at once. It's up to you. If you, uh, wanna do it a chapter at a time, or even a partial chapter at a time, it will be available at all times to you, Thio Thio. Review the various chapters and then go away and come back if you want, Of course there. So with a review of electromagnetism on the quantities and formalism, the furies and laws associated with electoral magnetism and how they relate to transformers because electromagnetism let's face it is a very fundamental part of transformers that will lead us to having a look at the ideal transformer. And then we will move on to what is known as where we will call the rial transformer, which will include losses and leakages and how we represented in electoral diagrams. We. Then we'll have a look at instrument transformers, potential transformers and current transformers. We will then move on to a three phase transformer starting out with the core construction and how the three face transformers are put together. We will look at configuration such as, Why toe Why and Delta Tau Why? And we will also look at the complex wide as exact transformer and the reason behind using it. We're then gonna look at the protection off transformers, everything from fuses to differential protection. We will then look at cooling, and we will look at the mechanical protection device called the Buckles Relay, which is made to monitor the gas accumulation in a transformer. And finally, we will look at oil analysis in a transformer which is fundamentally important to maintaining power transformers. As I said, we are going to start off with a quick review of electromagnetism. Included in that review will be reviewing the designation of how we describe various quantities when examining electromagnetism, including magnetic lines of flux and flux density and the various units of ever used to describe these magnetic quantities. We will also be reviewing the laws associated with the electromagnetism, such as Faraday's long lenses law and how changing magnetic flux lines around and Coyle will induce voltages and currents in a coil that will lead us to the development of the ideal transformer, which will be used to study transformation of two winding and three winding transformers, and having a look at such things as turns ratio on how to predict the secondary voltages with respect to the primary voltages and the currents involved in the primary and secondary as well. From there we will move on to the rial transformers and how they are constructed and the various things that we have to take into account when we're dealing with riel transformers as opposed to ideal transformers. And there are things that have to be taken in consideration in the real world, such as the losses associated with a real transformer, including copper losses, leakage, flux losses, eddy current losses, histories of losses, etcetera. As part of the development of the rial transformer, we're going to be looking at some special transformers that are called instrument transformers, and in this case it will be the two types of instrument transformers that are primary used out their current transformers and potential transformers. We'll be having a very close look at how we describe the polarity of these transformers, starting with the current transformer. We will look at how they are marked so that we can predict how this secondary currents will react with respect to the primary currents. We will also be looking at a potential transformer polarity as well. And we will see again how they are, mark and how we can predict the polarity of the secondary of potential transformers with respect to their primaries. We're also gonna before leaving instrument transformers. We're gonna look at coupling capacitor voltage transformers because they are a little bit different than others. But they're very prevalent out there, so we will have a look at them as well. We're gonna look at transformer Connections. We're gonna look at the basic wide a Delta Delta Tau. Why, we're gonna have a look at how the various phases are affected by their various connections . We're going to establish the fact that there is a 30 degrees phase shift when dealing with the Y Delta or Delta Y connections on a transformer. We're gonna move on to having a look at the why zigzag transformer and the the need for using a zigs. Ike Transformers in the modern day distribution system where they gonna look at transformer construction of in its basic form, looking at everything from the tank containment in the oil and the how the low voltage wind ings and high voltage winding zehr wrapped on the laminated steel core and then the terminals air, then brought out in the form of bushings on a power bank. We're gonna look at cooling of transformers. Certainly, in the case of transformers of losses, there's a great deal of cooling required to keep the transformer operational. And we're gonna look at the various methods of how that is done. As we get into transformer connection, we're gonna be looking at fuses and how fuses are used in the distribution transformers. And we're gonna have a quick look at the time current curve and how fuses are used to coordinate tripping and protection of the transformers. We're then gonna move on to relaying, and we're gonna look at differential protection. And it's more specifically we will move into how a three phase transformer differential protection is connected and how it works. We're then gonna look at some of practical applications and we're gonna look at some old school reeling because there's still a lot of them out there and we're going to see how they are connected into the system. Holly Really, to the theory that we will be developing. And then we'll move on to the more modern type relays, which R. B I. E. Ds or the intelligent electrical devices. And we're gonna have a look at three examples of the many of them that are out there in in the world today. As we get closer to the end of the of the lessons, we will have a look at a mechanical protection device called the Buckles Relay, which does react to gases in a transformer, and we'll see how they're connected and how they work to protect the transformer. And lastly, we're gonna look at dissolved gout, gas analysis or oil analysis in a transformer because that is a big part of transformer maintenance. We will leave that to the end, but we will review the various items under that heading, and this brings us to the end of the introduction in regard to transformer fundamentals. 2. Ch 01R1 The Ideal Transformer: Chapter one. The ideal transformer transformers are commonly used in applications which require conversion of a C voltage from one voltage level to another. There are two broad categories of transformers. Electronics transformers, which operate at a very low power and are used for, UH, consumer electronic equipment such as television sets, VCR's CDs, personal computers and many other devices. To reduce the level of the voltage from 110 to 20 which is available at the A C. Maine's to the desired level at which the device operates. The other category A transformer is power transformers, which process thousands of watts of power. Power transformers are used in power stations, transmission and distribution systems to raise and lower the level of the voltage to the desired levels. The basic principles of operation of both of these transport types of transformers are the same. The transformer fundamentals we're going to talk about in the next few slides applied of both the electronic transformer and the power transformer. It was discovered quite some time ago that all objects are composed of extremely small building blocks known as Adams, and that these atoms are in term composed of smaller components known as particle protons, neutrons and the electrons. Whilst the majority of Adams have a combination of protons, neutrons and electrons, not all Adams have neutrons. Collectively, the protons and neutrons oven adam make up the nucleus or the center core of the atom. Each electron has a negative charge of minus 1.602 times 10 to the negative. 19 cool OEMs, and each proton in the nucleus has a positive charge of plus 1.6 year old two times 10 to the minus 19. Kulov's neutrons have no charge, just the mass that's associated with it. Because of the opposite charge. There is some attraction force between the nucleus and the orbiting electrons. Electrons have relatively negligible mass compared to the mass of a nucleus. The mass of each proton and neutrons is 1840 times that the mass oven electron and Adam becomes a positively charged I in when it loses an electron and similarly on Adam becomes negatively charged when it gains an electron. I would now like to crudely demonstrate the magnitude and general situation of what's going on at the subatomic level and try to bring into reality. What's going on in electric circuit, starting with one Adam that has a proton and one electron? As you can see, most of the atom is made up of free space. I'm going to assume that one electron is a free electron. That is, it's free to move from one atom to another, concentrate on the electrons on Lee and start to zoom out note and out and out and out to the point where you cannot collectively see all of the electrons and the circuit off at one time. So we just have to imagine what it ISS and know that the electric charge of one cool is made up of six million, 250,000 with 15 0 electrons. That is 6.25 million 1,000,000 1,000,000 1,000,000 electrons. That's a very, very, very, very, very large amount. Imagine if you would a $1,000,000 in large denominational notes. One person would have difficulty lifting that amount of money. Now multiply that by a 1,000,000 that will require one million people to pick it up. Now multiply that by one million. That would require one billion people to pick it up. Now multiply that by one million that were required more people, then our living on this planet. Now to pick it up, that is the equivalent to in the order of magnitude of the number of electrons that air flowing in one amp. Keeping this concept in mind, I would like to explore and compare the speed of electricity and the speed of electron flow . Looking at this example of an electric circuit made up of a battery and a resistor and a switch if we close the switch, there seems to be an instantaneous movement of electrons at every point in the circuit. However, this is not quite instantaneous, but it is very close. It depends on a lot of parameters, such as the wire size and the length of the wire and the battery voltage and the temperature. And ah, lot of things depend on exactly how fast the speed of electricity is. However, it is always very close to the speed of light, which is 186,000 miles per second. Now, if we open this which the reaction speed is the same, the electricity will stop flowing almost instantaneously or close to the speed of light However, this is not the speed of electron flow, which is often referred to as drift velocity. And, as I said, this is not the speed of an electron flow. It is not. Electron is not flowing at the speed of light. In fact, if we were to compare the speed of an electron flowing in a wire to that of a common garden snail, the garden snail would hands down beat the electron in a race because the garden snail moves at a vote khalfan inch per second, whereas an electron moves in the wire at about 0.28 inches per second. So what's going on here? How can electricity seem to move at the speed of light? Yet electron flow is slower than a garden snail. In order to answer that question, I'm going again. Zoom in to the subatomic level and consider what's going on in a wire, in this case, in a two dimensional fashion. Three Atoms by 10 Adams. As you can see, there's a positive charge on the left hand side and a negative charge on the right hand side, which would be indicative of connecting a battery with the positive end on the left and the negative in on the right. As you can see, electron seem to be moving freely about, but if you watch for a while or seems to be a flow or adrift from right to left. Some electrons, however, seem to be moving left to right. But that is because they are bumping into each other, and actually, they're not actually bumping into each other. They're coming close and being repelled into the opposite direction, which looks like they might be bumping into each other. But there is a general net flow from right toe left. Now, if we multiply that net effect by 6.2 1,000,006,000,000 you would see that there is definitely one AMP flowing in the circuit. But that still doesn't necessarily explain the instantaneous reaction for that. Let's move on. Consider what is often referred to as Newton's cradle, and I'm sure you've all seen this of one time or another. A lot of people have him decorating their desk. You can see that you have a metal ball at one side, and as that ball swings in, it connects to the next one, which connects to the next one, which connects to the next one and pushes off the one on the end. And that reaction or that flow of action, if you would, seems to be taking place very quickly. In fact, almost instantaneously, however, the ball is not quite moving from left all away to write, but the action itself is moving from right to left. Now that's a take a look at, and this again. I apologize for the crude animation, but let's assume we're looking at a bunch of electrons in that wire. What is happening when you close the switch, Your actually pushing one electron into the bunch and almost instantaneously, I dispute light on electron at the other end flows out, and what's happening is they aren't colliding, as I said, but they are electrically charged. So you're actually getting a electrostatic wave going from right to left. And that is happening at the speed of lengthy electron itself is not flowing down the line . It is moving, but it's the actual action or the wave of electrostatic. So that's moving down the wear, and that is what electric electricity is. So I hope this crude analysis helps you visualize what is actually going on in an electric circuit before diving into the inner workings of the transformer. Let's back up a couple of paces and review electromagnetism first, fundamentally transformers Air governed by the modeling rules and observations involving electromagnetism, which involves the electromagnetic forces of physical interaction that occurs between electrically charged particles. These electromagnetic magnetic forces are modeled by making use of the existence of electromagnetic fields. A moving charged particle Q one moving at a velocity V one will create a magnetic field, which we will call B one and sometimes refer to as the beta rather than be. But let's call it be one for now, the magnetic field be one forms that closed loop or a ring around the moving particle. This magnetic field and ring actually has some direction, and we have arrows indicating that direction. But before going too much further in establishing that direction, I want, oh, bring emphasis to a very subtle difference of reality and what is modelled here. In actual fact, there isn't a magnetic field as such. You can't see it. You can't feel it, but what we're doing here is creating a model off what we call a magnetic field and we will just refer to it as a magnetic field from here on. But it is a model and what it is, it affects electrical charges or electricity because of the way we've modeled it. Now we're gonna continue to build this model, and this model will govern how things react inside a transformer later. But keep in mind, it is a model that we have created, but we're going to refer to it now as a magnetic field that forms a closed route loop with some direction. In this model of a magnetic field, as I said has some direction and under to find out the direction of that magic field magnetic field, we use what they call the right hand rule. The field direction is identified by having using our right hand and having our thumb point in the direction of the charged velocity. The fingers of the right hand will point in the direction of the magnetic loop that is formed by the movement of the electric charge. So just repeating that if you put your right hand and wrap your fingers around the velocity direction of the of the charged particle and point your thumb in the direction of that velocity. Your fingers will point in the direction of the magnetic field. The field direction and strength depends on the type and the amount of charge. We've been looking at positive charges, and if there are more than one charge or even many charges, the field strength will increase and is directly proportional to the amount of charges. Also, if the charges are negative, the field will be in the opposite direction. Toe the motion of the negative charges, and we're gonna look at that when we start to talk about current. However, for now, the field will be in the opposite direction if negative charges are moving and just isn't a case of positive charges. The MAWR charges that air flowing, the stronger the field strength. This movement of electric charges can be extrapolated to the magnetic field that's produced by an electric current. Now, an electric current is movement of electrons. It has always oriented. That is, the magnetic field produced by the charged particles. The magnetic field is always oriented perpendicular to the direction of the flow. A simple method of showing this relationship again can be determined by the right hand rule . Simply, we can put the right hand around the wire with your thumb, pointing in the direction of the current flowing, and your fingers will point in the direction that is the magnetic field that is caused by the current flowing in the wire, the magnetic field in circles, this street piece of wire carrying the current. And it should be noted that the magnetic flux here has no defined north or South Pole. At this particular time, however, it does have the lines of flux. Have a direction in that direction is indicated by the right hand rule. I've been using the terms flux and Flux Field rather loosely, so let's define what we're actually talking about here When analyzing magnetic fields. We need to define them as being made up off flux lines, as you see here, and they have a direction, and we assume the direction in this case is going from bottom left to top right, and if we group them together, they form what is known as magnetic flux field, symbolized by the Greek letter Phi. And it's a measure of the quantity of magnetism, and it's measured in terms of Weber's short form W B. It takes into account the strength and the extent of the magnetic field. If we consider a flat surface area such as indicated here, will call it a, uh, the area that the magnetic field passes through. Then we can define the magnetic flux density as the amount of magnetic flux in an area that is perpendicular to the direction of the magnetic flux. Or, in other words, the magnetic flux density is the amount of magnetic flux perpendicular to a flat surface area divided by that area in the S I system. This flux density is measured in Tesla, but mostly we just talk about Webber's per square meter. And in summary we have. This chart, which is magnetic flocks, is indicated by the Greek Letter five, and the units are Weber's, and the magnetic flux density is be or beta uh, which is measured in terms of Tesla or, more simply, Weber's per square meter. To create a stronger magnetic field force and consequently more field flocks with the same amount of electric current, we can wrap the wire into a coil shape where the circling magnetic fields around the wire will join to create a larger field with a defined magnetic north and south polarity. The amount of magnetic field force generated by a coil wire is proportional to the current through the wire, multiplied by the number of turns or raps of the wire in the coil. This field force is called Magnum Motive Force, or MM math, and it's measured in an pair turns. Now this formula will be returning to quite often, and it's a very important formula and that ISS the magnetic flux is proportional to the current. The right hand rule comes to play here again. The poll of a magnetic field, other solid way can be determined again by the right hand rule. Imagine your right hand gripping the coil of the soul. Annoyed such, the fingers are pointing in the same way as the current is flowing in the coil. Your thumb then points in the direction of the field. That is, it's pointing towards the north the way the arrows air coming out of the field. Since the magnetic field line is always coming out of the North Pole, therefore, the thumb points towards the North Pole. Here we have wrapped our coil of wire around a block of iron, which I'll refer to as core material. The nature of this material is such that the magnetic lines of flux will want to travel through it rather than the air. In fact, it will boost the amount of flux that is produced by the current in the coil. In this example, the magnetic flux will still vary as the current in the coil, but at a greater extent due to the core material. The magnitude of the magnetic flux will also depend on the number of turns of the coil. As I said, the magnitude of the magnetic flux will also depend on the material through which the flux will travel. If an iron core is substituted for an air corps in that given coil, the magnitude of the magnetic field is greater and it's greatly increased. All materials have a property defined as permeability, which is the measure of the ability of a material to support the formation of a magnetic field within itself. Hence, it is the degree of magnetism ation that material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the Greek letter from you. Permeability, also called magnetic permeability, is constant, and it's a constant, constant proportionality that exists between magnetic induction. Do the current flow and my name magnetic field intensity. The amount of flux produced this constant is equal to approximately 1.257 times 10 to the minus six Henry's per meter in free space or a vacuum. In other materials, it can be much different, often substantially greater than the free space value, which is symbolized by the Greek letter mu with a sub script. Zero materials that cause the lines of flux to move further apart, resulting in a decrease in magnetic flux density compared to a vacuum are called dia magnetic materials. Materials that concentrate magnetic flux by a factor more than one but less than or equal to 10 are called pera. Magnetic and magnetic materials that concentrate the flux by a factor of more than 10 are called ferro magnetic. The permeability factors of some substances change with rising or falling temperatures or with the intensity of the applied magnetic field. In engineering applications, permeability is off, often expressed in relative rather than absolute terms. If immune not represents the permeability of free space and Mu represents the permeability of a substance in question. Also specified in Henry's per meter than the relative permeability is mu subscript. R is given by mu times 7.958 times 10 to the fifth power. Although there is an ability to increase magnetic flux due to make the magnetic material, the material is also said to have a reluctance or a resistance to the ability to support a magnetic field. The reluctance of magnetic materials proportional to the mean length and the and it's inversely proportional to the product of the cross sectional area and the permeability of the magnetic material where are is the reluctance magnetic resistance of the material and mu is the magnetic permeability coefficient. L, which is measured in meters, is the length of the material and A is the cross sectional area of the material in meter squared. Therefore, ferro magnetic materialise, said toe, have a reluctance are to the flux. The flux, current and reluctance are related by the equation and I is equal to five times are and I of course, is known as the Mag Motive Force or in the MF Magna Motive Force or Mmf, of course, is measured in terms of an pair turns. It is sometimes helpful to draw an analogy between the electric circuit and the magnetic circuit, where MMF is related to E. M. F. Current is related to flocks, and resistance is related to reluctance. Looking back and a quail of wire in air or a vacuum with current flowing in at the current produces an MMF or a field intensity that is directly proportional to the current, which produces a magnetic field, which, measured over an area, is known as magnetic flux density. If we were to plot this flux density, as the current or field intensity increases, it would be linear or a straight line. This is known as a magnetism ation curve or a B H curve, even though it's not much of a curve. But the reason we call it a curve will be evident when we see the next few slides. Now, if that coil of wire is wrapped around a ring of magnetic material, the current flowing in that coil also produces an MMF, or field intensity that is greatly enhanced due to the properties of the material and will also increase with the current again just is in a coil of wire in air that current produces a magnetic field, which, measured over an area, is known as flux density. However, this time, if we're to plot this flux density as the current or field intensity increases, it would not entirely be linear but would curve and start to flatten at some point, depending on the type of material that it is inside the coil. This flattening of the curve is known as saturation and his characteristic of what happens in transformers that are wound on a magnetic material. Most transformers are designed to operate in the linear region of the BH curve, but a times they're pushed into the nonlinear regions of the curve, which could produce and problems that we'd have to deal with. And we'll see those a little bit later. Another court to calm, found. Our analysis of magnetic flux versus force is the phenomenon of magnetic histories is as a general term history, sis means a lag between the input and the output. In a system upon the change of direction is much the same as what you might have experienced in an old car who, steering is very, very sloppy, and as you steer, you have to oversteer in order to bring it back in the other direction and want to Going in one direction in a magnetic system, history says, is seen in effect in a ferro magnetic material that tends to stay magnetized after an applied field force has being removed if the force is end. If the forces were in reverse direction. So let's see how the head works. Let's use the same graph again. Onley Extending the axis in the negative direction First will apply an increasing field force current through the coils of our electromagnets. We should see the flux density increase go up into the right according to the normal magnetism ation curve. Next, we'll stop the current going through the coil of the electro magnet and see what happens to the flux, leaving the first curve still on the graph. Due to the relativity of the material, we still have a magnetic flux with no applied force, no current through the coil. Our electro magnet magnetic core is actual actually become a permanent magnet at this point . Now we will slowly apply the same amount of magnetic field force in the opposite direction . The flux diversity has now reached a point equivalent to what it waas in the full positive value of field intensity. Except it's in the negative direction or in the opposite direction. Let's stop the current going through the coil again and see how much flux remains once again due to the nature of the relativity of the material. It will hold a magnetic flux with no power applied to the coil. Except this time it's in a direction opposite to that of the last time when we stop the current. If we re apply power in the positive direction again, we should see the flux density reach its prior peak in the upper right hand corner of the graft. Again, this s shaped curve trace by these steps form what is called the history says curve of a pharaoh magnetic material for a given set of field and intensity extremes. When a ferro magnetic material approaches magnetic flux saturation, disproportionate levels of magnetic field force mmf are required to deliver equal increases in the magnetic field flocks fi. As you can see from the graph, a large increase of mmf is required to supply the needed increases influx, which result in a large increase in coil current. Thus coil current increases dramatically at the peaks in order to maintain the flux way form that isn't distorted. This is why Transformers Air designed to operate in the linear read region of the magnetic material. And that's why problems can occur when transformers air driven into saturation, especially in the cases of instrument transformers that rely on linearity to accurately measure current and voltage is our modern world would be impossible without electromagnetic induction, the phenomenon that underlies the operation of many devices, including Transformers. Qualitatively here is how electromagnetic induction works as the lines of flux cut across a coil or coils of wire, the number of magnetic lines of flux cutting the coil will be increasing or decreasing as it increases and decreases. Ah, voltage will be induced in the coils quantitatively fair days. Law of Electromagnetic induction relates the magnitude of an induced voltage to the rate of change of the magnetic flux linking a circuit. Fair Day's law states that the magnitude of the inducts are induced. Voltage in a circuit is equal to the magnitude of the rate of change of the magnetic flux linking the circuit and can be described by this formula or in terms of calculus, the magnitude of the Indosat voltage in a circuit is equal to end defy by DT. The terms defy by D t means the same thing as dealt If I buy Delta T Onley in terms of calculus, the D five i d. T. And indicates on infanticide really small change in flux and the time the of course is instantaneous induced Voltage five's. The magnetic flux in Weber's defy is the change of magnetic flux. Also in Weber's and D T is a change of time in seconds, notice the minus sign. This becomes significant if the circuit is complete and current flows. But for now, we're considering it on open circuit. Let's close the loop now, and we'll do that using a resist ER in order to limit the amount of current that will be flowing because of Fair Days law, a voltage will be induced in the coil, and since we have closed the loop of the circuit, the coil current will flow through that resistor. This brings us to another significant law of electromagnetic induction called lenses. Law lenses law goes along with Faraday's law, in that it states when an E. M F is generated by a change of magnetic flux. According to Faraday's law, the polarity of the induced E. M F is such that it produces a current who's magnetic field opposes a change which produces it. Let's read that again and follow it. Step by step on E. M F is generated by a change of magnetic flux that would be induced in the voltage drop across the resist er are and according to lenses law, the induced current will produce a magnetic field. Remember, now that any time current flows, there's a proportional amount of magnetic field induced and that it opposes the change, which produces it, as indicated by the green dashed line. In other words, the induced magnetic field is always opposite to the magnetic flux which produced it. This is the reason for the negative sign in the Fair Days law equation, So in order to check this out, we will apply the right hand rule. The fingers must point in the direction of the magnetic field right to left. The thumb will point in the direction of the current, which is up and over, which flows through the resistor, indicating the polarity of the voltage drop as it flows through the resisters or the resistor. This is all happening for one direction of the permanent magnet movement, which is a net increasing of magnetic flux. When the permanent magnet stops, the voltage will go to zero, and when it moves in the other direction, the magnetic lines of flux linking the coil is decreasing, causing a reversal of the flow of current as well as the polarity of the voltage drop across the resistor. Faraday's Law and Lenses law are very important when analyzing a transformer, as you will see in the next series of slides. If two coils of wire brought into close proximity to each other so that the magnetic field from one links the other, a voltage will be generated in the second coil as long as there is a changing magnetic field. This is called mutual in doctrines. When changing voltage impressed upon one coil induces a voltage in the other. The key here is Fair Days law. The induced coil experienced the change influx over a period of time. In other words, a circuit of wire. A coil must experience a change in the flux. Delta Phi over time. Delta T Fair Day's law states that if a coil of wire experiences a change in magnetic flux , a voltage will be induced in that coil, such that a voltage will be induced when the flux is increasing, then returns to zero when the flux ceases to change current to steady, then a voltage will be induced in the other direction when the flux is decreasing to zero, then returns to zero when flux is at a zero and ceases to change. Lenz's law does not play a role in this situation, as there is no current flowing in. The second coil at this time because of old meter has a very high impedance and his measuring only the open circuit voltage. So let's repeat that a voltage will be induced when the flux is increasing, then returns to zero. When the flux ceases to change, that is, the current is steady. Then a voltage will be induced in the other direction when the flux is decreasing to zero, then returns to zero. When that flux is at zero and his ceasing to change before proceeding I want to emphasize an important concept to remember, and that is flux and flux. Density are related to the current, such that the current is always proportional to the flux and the flux density that IHS, regardless of whether that current is a C or D. C, which means that when flocks and flux density are zero, the related current must be zero. When the flux and flux density are at a maximum or positive maximum, the related current is at a positive maximum. And when the flux and flux density are at a minimum or at a minus maximum, that related current is at a minimum, aura minus maximum. In other words, flux and flux density are always proportional to the current that's flowing. That causes the flux or flux density. And you can also look at the inverse. And that is, if the flux are flux. Density is the thing that is driving the current. Then the current is always proportional to that flux and flux density, regardless of whether it's positive, negative or zero. If we wind two coils on a steel core, we can cause almost all of the flux to link both coils and weaken further hypothesize the case in which 100% of the flux is linked by both coils. In this ideal case, it is called an ideal transformer. Now let's input a Sinus idol, a C voltage on the red coil on the left. This is known as the primary winding. This a C voltage will cause a small current to flow in the primary coil. The amount of current flowing is limited by the reactant of the primary coil. In an ideal transformer, this reactant is 100% induct its so the current will lag the voltage by 90 degrees. This current is no one as the magnetism ation current. Remember that any time a current flows it will produce a magnetic flux proportional to it. Which means it too, is Sinus idol and in phase with the current. And since we are dealing with an ideal transformer, all of that flux flows in the iron and links both coils. Considering the primary coil, we will measure a voltage drop. This voltage drop will call the one across its terminals and it will be equal to the applied voltage V A C because it's directly connected to the applied voltage in coil one. The flux produced by the generator is related to the voltage V one. By Fair Days law, which involves the changing flux times a number of turns in the primary coil in the coil to the secondary coil. The voltage produced by that same flux by mutual induct INTs is also given by Fair Days law , which involves the same changing flux but times the turns in the secondary coil. That voltage is either larger or smaller than the one, depending on in one and end to the turns of the primary and secondary coils. But it is in phase with the applied voltage, the A C. Mathematically, we can rewrite. The two fared. A law equations for both the primary and secondary coils, keeping only the associated voltages and coil turns numbers on the right hand side of the equations. As you can see, both the right hand sides are equal to the same changing flux, minus defy by DT. Therefore, we can write minus defy by DT is equal to the one divided by N. One is equal to V two, divided by end two, which means V one all over N one is equal to V two all over and to or rewriting it, we can see that it's the one all over. V two is equal to N. One all over and to these two ratios V one to V two and N one to N. Two are known as the turns ratio of the transformer, and sometimes it is designated with the letter A. Now, let's add some impedance to the secondary coil of the transformer. We know that the voltage drop across the impedance will be be, too, and that it is in phase with the applied voltage V A C. By virtue of homes law, a current will flow in, said to whose magnitude is given by V to Oliver said to and depending on the impedance, zed to the current will either lead or lag or be in phase with the voltage V to end the A C . The current in said to will produce a Magna Motive Force MMF to which is equal to N two times I two and cause of flux in the core limited on Lee by the reluctance of the core material are depending on the direction that the coil is wrapped in and it may be in this direction. We'll assume that for now. This Magna Motive Force mmf two links the primary coil resulting in an induced current I to which must equate to mmf to. But because there are in one turns in the primary coil, mmf too must equal in one times I won since the Magna Motive Force is the same in both coils. Then in one times I one must equal in two times I to now remember lenses law, which states the induced currents magnetic fields opposed the change which produces it or the induced magnetic field acts to keep the magnetic flux in the loop constant. So if the increase in current, I too will try to increase the magnetic flux, or mmf, which I've indicated by the mmf i Tuero, then I one will counter act the attempt to increase the flux or mmf by producing a counter flux or mmf in the opposite direction. This is lenses law. The net effect will be that the magnetic flux in the core will not change due to the current flowing in the secondary coil, but will remain the same, that being the magnetism ation flux on Lee. We can now express the turns, ratio and want, and to in terms off the primary and secondary currents. That is the turns ratio is equal to I to all over I won. That is, of course, if we are loading the transformer in, there is current flowing in the secondary side. In comparison, this is the inverse of the voltage ratio, which is equal to be won over V two. Now let's look at the power flow through the transformer. If the transformer is loaded, as is the case, by adding Zed to to the secondary, we can measure the power flow into the primary. By measuring the voltage V one and the current I want and multiplying them together to give us this equation, we can measure the power flow out of the secondary similarly, by measuring V two and I, too, and that will give us the power flow out of the secondary. Now we can take the power flow into the transformer equation and converting I won and the 12 i two and V two using the turns ratio. We get this equation and clearly we can cancel out the turns numbers In other words, the end one in the numerator cancels out with and then one in the denominator, and similarly, the to end twos could be canceled. Notice well, leaving us with the Wafi two times I to which is equal to the power out. This means that the power out is equal to the power in, which should be no big surprise because a transformer can't add power to the system. It's neither created nor destroyed. It just flows through the transformer. Let's take another look at this transformer set up with a load in the secondary of the transformer, and there's going to be current flowing in the primary, as we have calculated, and there is a voltage drop across the primary coil, so the power supply sees an impedance because it's reflected due to the impedance on the secondary. And we can calculate with that. Reflected impedance is by measuring the voltage drop across the primary coil and the current into that coil, and that would give us the reflected impedance. In other words, V one. All over I won is going to give us the reflected impedance. We can substitute for the one by using the turns ratio and the to, and we can substitute for I one using I two and the turns ratio off the transformer to give us this equation, which is in one all over and two times V two all over and two over in one times I to while the two all over I to is just zed to and n one all over in two, all over into over, and one is n one over in two squared. So said one is equal to Zed to multiplied by the square of the turns ratio, which is the same as a squared times. Zed to this ends Chapter one. 3. Ch 02R1 The Real Transformer: Chapter two, the rial transformer. The ability of iron or steel to carry magnetic flux is much greater than it is an air, and this ability to allow magnetic flux to flow is called permeability. Most transformer cores are constructed from low carbon steels, which can have permeability ease in the order of 1500 compared to just one for air. This means that steel cores can carry a magnetic flux 1500 times better than that of air. However, when magnetic flux flows in a transformer steel core, two types of losses occur in that steel. One is termed eddy current losses and the other is termed history says losses. In fact, riel transformers have other losses that occur us well, for instance, copper losses or I square to our losses, leakage, flux, losses, core excitation and core losses, which we've already mentioned, including Eddy. Current losses in history says losses. Now we're going to go on to look at just how these occur. Transformer eddy Current losses are caused by the flu off circulating currents induced into the steel caused by the changing magnetic flux around the core. The's circulating currents are generated because the changing magnetic flux sees the core as a single loop of wire. Since the iron core is a good conductor, the eddy currents induced by a solid iron core will be large. Eddy currents do not contribute anything towards the usefulness of a transformer, but instead they oppose the flow of the induced currents by acting like I'll, a negative force generating resistive heating and power losses within the core eddy. Current losses within a transformer core cannot be eliminated completely, but they can be greatly reduced and controlled by reducing the thickness is of the steel core. Instead of having one big, solid iron core as the magnetic core material of the transformer or coil, the magnetic path is split up into many thin pressed steel shapes called lamination. These lamination Z are insulated from each other by a coat of varnish to increase the effective resistive ity of the core, thereby increasing the overall resistance to limit the flow of eddy currents. The result of all this insulation is that the unwanted induced any current power loss in a core is greatly reduced, and it is for this reason why magnetic iron circuits of every transformer and other electro magnetic machines are all laminated using lamination. Zin transformer construction reduces eddy current losses. Transformer history says losses air caused because of the friction of molecules against the flow of magnetic lines of force required to magnetize the core, which are constantly changing in value and direction first in one direction, then the other do the influence of the Sinus idol supplied voltage or current. This molecular friction causes heat to be developed, which represents on energy loss in the transformer. Excessive heat loss can, over time shorten the life of the insulating material used in the manufacture of the wind. Ings of the structure also transformers air designed to operate at a particular supply frequency. Lowering the frequency of the supply will result in increased history since or higher temperature in the iron core, so reducing the supply frequency safe from 60 hertz to 50 hertz will raise. The amount of history's is present, decreasing the V a capacity of the transformer. But there is also another type of energy loss associated with transformers called copper losses. Transformer Copper losses are mainly due to the electrical resistance of the primary and secondary wind. Ing's most transformer coils are made from copper wire, which has resistance. This resistance opposes the magnetize ing currents flowing through them. Not only that, when a load is connected to the transformer secondary winding, large electrical currents flow in both the primary and the secondary wind ings, electrical energy and power, or I squared. Our losses occurs at in the form of heat. Generally, copper losses very, with the load current being almost zero at no load and at a maximum at full load. When current flows at a maximum. A transformers rating can be increased by better design and transformer construction. To reduce these copper losses. Transformers with high voltage and current ratings require conductors of large cross sectional area to help minimize their copper losses. Increasing the rate of heat dissipation through better cooling by forcing air or oil and or by improving the transformers insulation so little withstand higher temperatures can also increase the transformers rating. The losses that occur in a transformer have to be accounted for in an accurate model of transformer behavior. This model would have to include copper or I squared our losses. Copper losses are the resisted heating losses in the primary and secondary wind ings of the transformer they're proportional to the square of the current in the linings. Eddy Current losses Eddy Current losses are resistive heating losses in the core of the transformer. They're proportional to the square, the voltage applied to the transformer. History says Losses. History says losses are associated with the arrangement rearrangement of the magnetic domains in the core during each house cycle. They are a complex, nonlinear function of the voltage applied to the transformer leakage flux. These air flux is which escaped the core and pass through only one of the transformer linings. These escape flux is produce a self inducted in both the primary and secondary coils. In order to make the calculations required of a real transformer, we simply use an ideal transformer with add ons that, when added to the circuit, produced the equivalent results. This is known as the equivalent circuit of a transformer modelling. The copper losses, or resistive. Losses in the primary and secondary winding of the core are represented in the equivalent circuit by R one and R two modelling. The primary and secondary leakage flux are represented in the equivalent circuit by L one and L two. The core excitation is modeled by Tell em and the court any current and history says losses are modeled by R. C. The bear symbol for Ah Transformer gives no indication of the phase of the voltage across the secondary. The phase of that voltage depends on the direction of the linings around the core. In order to solve this problem, polarity dots are used to show the phase of the primary and secondary signals. The voltages are either in phase or 180 degrees out of phase. With respect to the primary voltage docks are used to indicate the points in the transformer schematic symbol that have the same instantaneous polarity points that are in phase. This ends Chapter two. 4. Ch 03R1 Instrument Transformers: Chapter three instrument transformers Instrument transformers. Instrument transformers are a special type of transformer used for the measurement of voltage and current, as the name suggests these transformers air used in conjunction with the relative instruments such as a meters bolt meters, what meters and energy meters as well as protective relays. Such transformers are of two types. Current transformers. Current transformers are used when the magnitude of a sea current exceeds the safe value of the current required for the measuring instruments. Potential transformers or voltage transformers are used where the voltage of the A C circuit exceeds 750 volts, and it is not possible to provide adequate adequate insulation on measuring instruments for voltage. More than this, these are examples of current transformers that may be found on the bushings of a circuit breaker or a transformer. They're known as donut. See keys for their similar, similar look to a donut. The picture on the right is not a CT, but a typical transformer breaker bushing, which would be mounted through the center of a doughnut CT. The secondary winding is wrapped concentric plea around a tor oId, which is usually made up of laminated iron or steel. The primary is a single conductor, usually a bushing mounted through the center of the tour, right? The donut fits over a conductor pushing or bus bar, which constitutes the primary having one primary turn. The secondary is wound around a torrid core, which is usually made up of laminated iron that concentrates the magnetic flux and forces it through. All of the secondary turns some donuts. Seti's come with the primary conductor incorporated in the C T itself, and connections are made by bolting to the primary lead. If the tour oId is wild, with 240 secondary turns than the ratio of the C T is 240 to 1 or 1200 to 5. The five AM's designates that continuous rating of the secondary winding and is normally five amps in North America. And sometimes it's one AM per poi 10.5 amps and other parts of the world. This type of C, T or Dole it SETI is mostly found in circuit circuit breakers and transformer bushings. The SETI fits into the bushing turret, and the bushing fits through the center of the donor. It's not uncommon to find up to four si tes of this type installed around each bushing in a breaker or a transformer. Let's take a closer look at current transformer ratios in an ideal transformer with a simple load on the secondary and an A C voltage on the primary The secondary voltage. The sub script s is determined by the turns ratio such that DS over V P is equal to N s all over and p, the secondary current is determined by the turns ratio such that i p n p is equal to i s and S We're this I s is equal to i p times ratio np over and s. If N P is equal to one, then the secondary current is equal to the primary current divided by the secondary turns in a current transformer. The secondary current is determined entirely by the current flowing in the primary system and not by its own secondary load, which is usually referred to as the burden. However, the voltage across the secondary loader burden is very much dependent on the secondary load , since the current in the secondary is constant. If the primary current is constant then, according to Owens law. The higher the impedance of the secondary load, the higher the voltage across the load will be. If the secondary load is very high, say open circuited, then the voltage will rise accordingly and could result in a very dangerous condition. This is why the secondaries of a CT should be shorted rather than opened when not in use and should never be opened during testing procedures. Both the primary and the secondaries of Seti's have relatively few turns of heavy wire and us low impedance. Subsequently, a current is readily induced into the secondary, proportional to the primary current, as we have seen, see keys behave according to this mathematical relationship, where the secondary current is given by the primary current times the turns ratio of the C T. If the primary is one or it's ah bushing or a bus bar going through the donut CT, then the secondary current is equal to the primary current divided by the number of turns of the secondary. There is a unique problem encountered with CT's in order to magnetize the core of a current transformer. A certain amount of excitation current is required, part of the current induced from the primary is used to accomplish this. Since the induced current represents the current flowing in the load circuit, the meter's current coil will be influenced proportionally by the load current minus this excitation current. This represents a small loss of load current and L B A. Small does affect the accuracy of the reading of the secondary. Current transformer losses, called Ares very for different types of transformers in the burden or the load on the secondary standards have been have been established with acceptable error limits that transformers must fall within. Engineers must take this into consideration when designing, relaying and metering setups. The transformer ratio of a CT is usually designated by stating the primary current versus the secondary current and the stated secondary current is usually the rated secondary current of the C T. For a given C T, where the primary current is 100 amps and the secondary current, it's five amps. The transformer ratio is 100 over five or 100 to 5. Yeah, 20 to 1 for the same C t. What would happen if the primary was back and then fed through the c t one more time? The C T would see 100 times to which is equal to 200 amps. If 100 amps was flowing in the primary, the secondary would then read 10 amps. The transformer ratio would equal 100 to 10 or 10 to 1. This, of course, exceeds the reading of the secondary. However, this is Onley used if the primary current is too low for the meter reading. In other words, the primary is usually while below 100 amps, making a secondary current while within limits. Designating the polarity is very important, and it's done by marking the CT's primary and secondary terminals. This is especially important for the measuring of power flow direction and when sea keys air used for directional relay. There are standards, but they all pretty much mean the same thing. One primary terminal is designated with a marking relative to a secondary terminal marking the primary, and secondaries are marked to indicate which direction current will flow. During each half cycle of current, a primary terminal is marked to associate it with a secondary terminal. We say that the primary terminal ISS spot, with respect to the associated secondary terminal mark spot in the case of a donut CT where the primary is the conductor running through it. One side of the SETI is marked with a spot. In this case, the front is spot. The back is not. The spot. Marks can be a dot or any similar symbol. The I Tripoli, the Institute of Electrical and Electronics Engineers use H one and X one in place of the spots. The I. E. C. Or the International Electro Technical Commission used P one and S one. What this indicates is that when the primary current is positive during the Sinus idol half cycle current into the spot, the secondary current will be out of the spot. And what this also indicates is that when the primary current is negative during the Sinus idol half cycle, that is the current out of the polarity spot. The secondary current will be out of the non polarity spot for potential transformers. In general, the ratio of the secondary voltage to the primary voltage is governed by the turns ratio of the wind ings of the transformer. This relationship is not completely exact for the following reasons the excitation current that is necessary to magnetize the iron core causes a small impedance drop and a phase shift in the primary wind ing's. The load current that is drawn by the burden also costs another small impeding strong. Both of these produce an overall voltage drop in the transformers and introduce heirs into the ratio and phase ankle. The net result is that the secondary fall to just slightly different than the ratio of the turns for the transformer, and there is also a slight shift in the phase relationship. These two errors, all car called ratio airs and phase angle airs and maybe represented and taken into consideration by using the equivalent circuit of a riel transformer, which is showing here. The reason for these ratio and phase angle airs in a potential transformer have already been discussed in previous chapters under riel transformer losses, and the reason for and the theory behind the equivalent circuit of a transformer, which also applies to a potential transformer, has also been explained. Designating the polarity of a PT is very important and done much the same as in the case of a CT, by marking the PT primary and secondary terminals and or indicating it on the nameplate again. This is especially important when peak ease air used for relays and revenue meters, as in the case of the C T polarity. The primary and secondary terminals are marked in such a way that when the primary current is positive during the science first sight Sinus idol half cycle that's current into a polarity spot. The secondary current will be out of the polarity spot on the secondary or in terms of voltage. Since we're dealing with a voltage transformers, a voltage rise on the H one terminal gives gives a voltage rise on the X one terminal. Another type of potential transformer that's in common use today is the capacitor voltage transformer. You're capacitor coupled transformer and sometimes designated as a CVT or a C C. D. T. The capacitor voltage transformer is a transformer used in power systems to step down extra high voltage signals and provide a low voltage signal for metering or relaying operations. In its most basic form, the device consists of three parts to capacitors across which the transmission line signal is split, an inductive element to tune the device to the line frequency and a voltage transformer to isolate and further step down the voltage for the meeting or protective relaying device. The tuning of the divider to the line frequency makes the overall division ratio less sensitive to changes in the burden of the connected metering or protective relay devices. The device has at least four terminals, as shown here, a terminal for connection to the high voltage uh, signal a ground terminal and to secondary terminals, which connect to the instrumentation or the protective relates in practice. Capacitor C one is often constructed as a stack of smaller capacitors connected in Siris. This provides a large voltage drop across. See one and a relatively small voltage drop across see, too, as the majority of the voltage drop is in C one. This reduces the required insulation level of the voltage transformer. This makes CV teas more economical than wild voltage transformers under high voltage conditions such as anything over 100 K V. As the latter one requires more winding and more material on schematic drawing Seti's with their polarity markings. Look something like this, representing the concept of an actual C t on schematic drawings. PT's with their polarity markings. Look something like this, representing the concept of an actual PT. This is an actual standard drawing using Pts and Seti's with their polarity marks and connected to give the right measurement. For a kilowatt hour meter, you can see the CT's are connected on the lines. They are in the bold type line, drawing there, and they have spot markings like a little square on the, uh on the primary as well. If the secondary, the potential transformer is in thinner lines there just to the left and the spot markings are actually axes on the various terminals of the potential transformer. This is another example where a differential relay protection is on a delta Y transformer on the spot markings of the instrument transformers. The SI tes in this case are very, very clearly visible and the including the spot markings of the power transformer for which is being for which it is protecting. And this ends Chapter three 5. Ch 04a Three Phase Power Transformers: Chapter four three Phase Power transformers three phase power has become the standard of for power transmission and distribution. Today, three phase power generation transmission and distribution is advantageous over single phase power for the following reasons. Three phase power distribution requires lesser amounts of copper or aluminum before transferring the same amount of power as compared to single phase. The size of three phase motor generator sets is smaller than the single phase motor generator of the same rating. Three phase motors are self starting as they can produce a rotating magnetic field. The single phase motor requires special starting wind ings as it produces only a pulsing magnetic field in single phase motors. The power transferred in motors is a function of instantaneous current, which is constantly varying. Hence, single phase motors are more prone toe vibrations, whereas in three phase motors, the power transfer is much smoother and much more uniform throughout the cycle. Hence, sirs, fewer vibrations to be concerned about mainly for these reasons, it's found at the generation. Transmission and distribution of electric power is more economical in three face systems than in a single phase system. It is interesting to note that the development of three phase systems evolved, starting with the war of the Currents era, or the Battle of the currents. In the late 18 hundreds, George Washington and Thomas Edison became adversaries due to Edison's promotion of direct current or D C, for electrical power distribution against alternating current A C advocated by several European Cup companies and Westinghouse Electric, based in pits, Pittsburgh, Pennsylvania, which had acquired many of the patents. By Nikolai Tesla. Nikola Tesla went on to develop three phase power systems in order to understand and work with three face systems. We work with voltages and current vectors that are derived from single phase values. That or Sinus eitel and all sign you slide away. Forms, of course, are repetitive. In an A C power system, the power source will supply voltage that is Sinus. Eitel is a Sinus little wave of one particular frequency, usually 60 cycles per second. The voltage starts at zero, holds peaks at plus a volts, travels through zero and peaks negatively at negative. A volts then returns to zero. It repeats itself 60 times a second when mathematically modeling, a sine wave such as V is equal to a sine Omega T. It can be considered to be directly related to a vector of length, a revolving in a circle with an angular velocity of omega. The can be represented by a revolving vector where its magnitude is a It's angular velocity is Amiga, and the angle of the vector at a particular time is given by Omega T. When considering to sine waves that are not in phase, one wave is often said to be leading or lagging the other. This terminology makes sense in the revolving vectors picture here, the blue vector is said to be leaving the red vector, or, conversely, the red vector is lagging the blue vector. These vectors could be current or voltage or one of each. If the blue vector is voltage and the red vector is current than the current is said to be leading the voltage. Or conversely, the voltage is lagging. The current in a utility power grid, omega is 60 cycles per second, or CPS. In some countries, as such as Europe, this is usually 50 cycles per second for the power grid there. But here in North America, it's 60 cycles per second. All voltages and currents are vectors. All are rotating at the same angular velocity, omega and all. Maybe Mac mathematically dealt with but must follow the rules for vector analysis. Because thes vectors have this added property of angular velocity of rotation, they are renamed and no. One as phasers. When considering three phase power generation, you can assume that's made up of three single phase generator connected together on one terminal. The generated voltage vectors, or phasers, are 120 degrees apart and rotating counter clockwise at 60 cycles a second. The loads can be connected in various configurations. Shown here is a why connected, configured load. However, the load can be any configuration. Three phase transformers can be thought off as three single phase transformers, each consisting of a primary winding linked magnetically to a secondary winding. They become a three phase unit by virtue of their excitation voltage and how they are connected to one another. They may also share the same core, but they may be considered individually. Here they are energized by three voltage phasers there, out of fees by 120 degrees, but are joined at one point or neutral, and the phasers are considered rotating in a counterclockwise direction. Transformer and distribution stations, with very few exceptions, handled three phase power and the transformers are either three phase units or three single phase units in a bank. The exception to this is where two transformers air operated in open Delta to supply three phase power. This is not a common situation is usually used in emergency situations. However it does exist. The connections of a three phase circuit may be divided into two basic classes. A star connection or a Delta connection. The Star connection has a neutral point at the junction of the three of individual phases, and single phase loads may be fed from any one of the phases to neutral. Such a connection is used at some transformer station to supply three phase power to motors and a single phase power to, say the lighting system. Delta circuits are mostly used for straight transformation of three phase power of medium voltage range, where single phase loads do not have to be provided for when three single phase transformers of equal capacity are connected, star to star or Delta Tau Delta. The capacity of the bank is equal to three times the capacity of each of the individual transformers. Note that when the wind ings of a transformer are referred to as being primary or secondary wind ings the winding regardless of the voltage level, the one connected to the source of the power is always considered the primary winding three phase Electric power is a common method used for the generation transmission and distribution of alternating current electric power. This poly face system is the most common method used by electrical grids worldwide for the transfer of power. The three phase system was invented and developed in North America by Nikolai Tesla in the late 18 hundreds, and I encourage you to go into YouTube and find some of the history of this fellow. He's very interesting. A lot of what he developed is still in use today, and he's highly underrated inventor, and I think you'd find his life fairly interesting. So I encourage you to go there and have a look at it. As a result of this development, transformation of power between voltage level has given rise to various transformer connections or configurations, the most common of which we're about to look at in the next series of slides, Star star sometimes called Why? Why Connected transformers condole ever to voltage levels face to face or face to neutral on both the primary and secondary. Also, the terminal bushings can be Grady in insulated and hence less expensive to manufacture. With this type of connection, one terminal of the primary terminals is connected to the system lines, buses, etcetera. The other terminals are connected to together to form a primary neutral. Similarly, on the secondary side, one of the terminals on the low voltage system is connected to the lines and buses. The other terminals are connected together to form a secondary neutral. These neutrals, primary and secondary, are not necessarily connected together, and sometimes they're grounded or not grounded. And sometimes one is and the other isn't and sometimes they both are. But if they both are, then of course they're connected. Considered connected together, the high voltage H one terminals are connected to the individual face conductors and the high voltage H two terminals are connected together to form a neutral. The low voltage X one terminals are connected to the individual conductors, and the low voltage X two terminals are connected together to form the neutral. The transformer having it's H one terminal connected to the red fees is referred to as the red phase transformer. Likewise, the transformer, the H one terminal connected, the white phase is considered the weight face transformer, and the transform, with its H one terminal connected to the blue phase, is referred to as the blue phase transformer. The vectors or phasers, look like this. The red phase, both primary and secondary disregarding the magnitudes, are in face. The weight phase on both primary and secondary are also in phase, and the blue phase, both primary and secondary, are in phase. The H two and X two terminals form a neutral for both the primary and secondary, respectively. They are not necessarily connected together. The phasers are 120 degrees apart and rotating counter clockwise transformers, four star connection and solidly grounded neutrals maybe made with only one terminal brought out in a bushing and the winding insulation graded so that less insulation is required toe to use towards the grounding. This result in considerable savings in costs and when constructing a transformer. As I have said, the Star Star connected transformer can deliver to voltage levels at both the primary and secondary that is face to neutral or phase to face. Let's look at the primary side only, for example, the secondary site is exactly the same, only at different voltage levels. We can use the phase two neutral voltages as seen here, or we can use the phase two phase voltage. The red toe White voltage, for example, is a difference between the red phase voltage and the white phase voltage or read minus wait, which is the red phase vector, plus the negative white face vector, which gives us the red to white fazer. Similarly, we confined the white toe blue phase two phase voltage and the blue to red phase voltage. As we know in a balanced star star system, the phase two neutral voltages are 100 and 20 degrees apart. The face to face voltages, then, as can be seen, form an equal lateral triangle, the interior angles of which are equal and equal to 60 degrees. As could be seen, the to phase two neutral voltages and the phase two phase voltage form to a Jason Jason 60 30 90 degree triangles, each of which have the sides in the ratio of 12 and the square root of three. Therefore, it can be seen that the magnitude of the face to neutral voltage and the magnitude of the face to phase voltage are in the ratio of 2/2 times the root of three or the phase two phase. Voltage is equal route three times the face to neutral voltages, and this is magnitude only, of course, as can be seen, the phaser of the red toe white voltage leads the phaser of the red to neutral voltage by 30 degrees. Or generally speaking, the phase two phase values are factors lead the face to neutral vectors or phasers by 30 degrees. Although I've been demonstrating this using the primary voltages of the three phase transformer. Generally speaking, this is usually referred to as the phase relationship in a three phase system, I now want to take a closer look at this phase relationship. In regard to the primary and secondary of this transformer. The primary and secondary phase two phase voltage relationship are both the same with respect to their respective face to neutral voltages. The primary phase two phase voltage leads the primary face to neutral voltage by 30 degrees and the magnitude is Route three Bigger. Similarly, the secondary phase two phase leaves the secondary phase in neutral by 30 degrees and the magnitude is Route three bigger. The turns ratio of this transformer is given by the face to neutral primary over the phase two neutral secondary voltages. Because the phase relationship the lying to neutral voltages can be written in terms of the line toe lying voltage which, as you can see, can also describe the turns ratio when analyzing these transformer connections. For the most part, if if not all of the time, we are considering this system to be balanced, that is, we have balanced voltages that air equal in magnitude in 120 degrees apart. So if we wanted to develop the per phase analysis of a transformer, that was why why connected the per phase equivalent of this transformer would look like this. We would be using the line to neutral voltages both for the primary and secondary. And if we were to convert the secondary allying to neutral voltage to the primary lying to neutral voltage, we would have to multiply by the turns ratio, which is designated as a here. And if there was current flowing in this single phase equivalent, then the ratios of the line currents would be the inverse of the turns, Rachel. In other words, if we wanted to calculate the secondary line current, we'd have to multiply by the turns ratio. And it goes without saying that there are two voltage levels to be looking at a primary and a secondary voltage levels and weaken describe them in terms off the lying to neutral voltages. And if we adopted these two voltages as the base values went considering a per unit equivalent circuit, then our per unit equivalent circuit would look like this, which is says that which essentially is just two layers neglecting, of course, the turns ratio of the transformer because we're dealing in per unit values here. Now we have used the base voltages and we can either use lying to neutral base voltages or lying toe line based voltages. However, the per unit magnitudes of the voltages are the same because we're dealing in per unit values now, as are the per unit values for the current. In this slide, I made a quick reference to the per unit equivalent circuit and in each one of the configurations. As we go through them, I will be referring to a per unit equivalent circuit. If this seems very mysterious to you, I would encourage you to have a look at the course that we offer on per unit analysis, because per unit analysis is a whole whole other course in itself. However, I will make this reference if you don't have an interest in per unit values and you can disregard the the last little portion referred to. However, a ZAY said, I would encourage you to have a look at the course on per unit analysis and that will remove the mystery of the per unit equivalent circuit. Harmonic voltages and currents in an electrical power system are the result of non linear electric loads. Harmonic frequencies in the power grid are a frequent cause of power quality problems. These in turn, could result in an increased heating of the equipment and conductors, or the misfiring in variable speed drives and torque pulsation motors. When a nonlinear loads such as a rectifier is connected to the system, it draws a current that is not necessarily Sinus. Seidel, the current way form can become quite complex, depending on the type of load, and it's intersection or interaction that is with other components in the system. Alway forms, no matter how complex, as long as they're repetitive, can be broken down into the some of the fundamental Sinus idol wave, plus multiples or harmonics of the fundamental frequency. In order to analyze this, we have a system of doing that called for e analysis. However, Justin understanding that complex way forms, if repetitive, are made up off the fundamental frequency, plus integral harmonics or multiples of the fundamental component harmonics. One of the major effects of power system harmonics is the unwanted increase in system. Third, harmonic currents. Third, harmonic currents are often the result of nonlinear transformation caused by the history, says effect of the iron core. This can cause a sharp increase in the zero sequence current and therefore increase the current in the neutral conductor. This effect can require special consideration in the design of the electric system. We are about to look at one of those solutions, but first, let's take a closer look at the third harmonic generated by the nonlinear transformation. If the fundamental frequency is sine omega T. Then the third harmonic is a frequency that is three times that of the fundamental frequency and can be written sign three times omega t. So, in a three phase system, if we place the red phase fundamental frequency as our reference phaser at zero degrees than a Sinus idol wave formula is given by a is equal to a sine omega T plus zero degrees. And I plotted it on the bottom of the slide. The blue phase fundamental frequency is leading the red phase by 120 degrees than the blue face Sinus idol Wave formula is given by B is equal to b sine omega T plus 100 and 20 degrees and the white phase formula frequency is lagging the red phase by 120 degrees, making the Sinus idol wave form formula W is equal to w sine omega T minus 120 degrees. Now, keep in mind, we're talking about a balanced system here, so the magnitudes of the A B and W phasers are equal, but I'm gonna leave them as a BMW for now and the following third. Harmonic magnitudes, uh, 1/3 harmonic Be third. Harmonic and W third harmonic are also equal in magnitude. Now the red phase third harmonic frequency is given by a magnitude a three H times sign three times omega T plus zero degrees. And if we take the three times inside the frequency of brackets, it's going to read a three h Sign three Omega T plus three times zero degrees, which is equal to a three h sign. Three Omega T Looking at the blue phase. Third harmonic. It can be written B three h signed three times Omega T plus 120 degrees. Taking the three inside the bracket, we get be three h sign three Omega T Plus 3 63 60 degrees is the same A zero degrees, so the result will be be three h Sign three Omega T. The white phase is given by W three h. Sign three times Omega T minus 120 degrees, bringing the three times inside. The frequency bracket gives us W three h sign three Omega T minus 3 60 Wow, 3 60 is still zero degrees, so if you subtract zero degrees, you're left with W three h signed three Omega T and all three of the A B and C third harmonics you can see are equal and in face. No, remember what I said, that the magnitudes of the third harmonics are all equal to so that the third harmonic. The frequencies are all in phase and you can see them plotted one on top of the other in the time domain graph at the bottom of the page. A solution to this problem is to provide a path for these third harmonics. This is accomplished with a tertiary winding connected in a way that allows the circulating currents to flow. The provisions of this extra winding increases the cost of the transformer considerably, but it may be used to supply power to an extra load, such as station service. This consists of 1/3 winding on each of the transformer legs. They are connected to form a Delta connection. The fundamental voltage vectors look like this, and thus the main transformation, maybe to 32 1 10 with a with a circuit of 13 K V being fed from the tertiary, winding for local use to tie in the synchronous condensers or supply local power the third . Harmonic currents, however, are rotating at three times 60 cycles a second, are in phase with each other and will circulate in the delta as shown here. Now let's look at a Delta Delta configuration. In this configuration, one terminal of the primary terminals are connected to the system lines or buses. The other terminals are connected to the adjacent primary terminal. Similarly, one terminal of the secondary terminals are connected to the system lines or buses, and the other terminals are connected to the adjacent secondary terminal. That is to say, the H one terminals are connected to individual face conductors, and the high voltage H two terminals are connected to the adjacent primary H one terminal. Similarly, the X one terminal of the secondaries air connected to the individual phase conductor's, while the low voltage X two terminals are connected to the adjacent secondary Terminal X one, the transformer having it's H one terminal connected to the our fees or the red fees is referred to as the red face transformer and likewise, a transformer with the H one terminal connected to the white fees liner bus is on his green . In our diagram, Of course, is referred to as the white Face transformer, and the transformer, with its H one terminal connected to the blue phase, is referred to as the blue phase transformer. The vectors or phasers look like this both primary and secondary away put him both up at the same time because it connected the same way or similar way. The red to white phasers, face to phase, are showing here. The white to blue phaser is showing like this and the blue to Rand phaser. Both the primary and secondary are showing like this. All of these phasers, of course, are rotating counterclockwise. You'll notice that there is no neutral connection in a Delta Delta connection. No difficulty due to third, harmonic circulating currents is encountered, since the Delta connected winding is provide a path for them. The third harmonic current vectors of each phase are in phase and will circulate in the delta, as shown, the Delta connection is used for transformation in a medium voltage ranges where a neutral point is not necessary for load purposes. Transformers with a delta to Delta operation must have the entire winding and all the bushings insulated for the full line tow line. voltage of the circuit to which they are connected. Therefore, construction is more expensive. Starches are or Delta Delta connections do not introduce any phase shift into the circuit from primary to secondary. Thus, all related primary voltages will be in phase with the related secondary voltages. I'm gonna move everything slightly here and shrink it down so that I can fit some equations on the slide while looking at the diagram at the same time. And I've rotated the phasers slightly, which I'm allowed to do as long as I maintain their relativity for a Delta Delta connected transformer, The turns ratio is given by the primary phase two phase voltage over the secondary face to phase voltage. That is because the face to phase voltages bridge the entire coil of each of the transformer legs in coming up with a per phase equivalent circuit for this type of transformer. The first step in the procedure for a per face analysis is to convert all Delta loads and sources, and the transformer is a source in this case to their equivalent. Why connections? The neutral, of course, is hypothetical because there is no neutral in this connection. However, it can be calculated by referring to the three phase phase relationships because we're talking about a balanced condition here. So again we can use the phase relationships to come up with a turns ratio using the hypothetical phase two neutral voltages, then right that Phase two phase turns ratio in terms of ah, lying to neutral voltage, we can now construct the per phase equivalent circuit using the hypothetical phase two neutral voltages. The face to neutral primary voltage can be calculated from the face to neutral secondary voltage by multiplying by the turns ratio or if current is flowing in this single face transformer, the secondary line current can be found by multiplying the primary lying current by the turns ratio. There are two voltage levels that be used for per unit analysis and the voltage bases that are required for that per unit analysis. And this is what the per unit equivalent circuit would look like. Four. A Delta Delta connected transformer. And of course, there are two zones vaulting zones for that per unit equivalent circuit, and we'd have to use whichever V base we used either the lying to neutral or lying toe line . However, the per unit. Voltages on in either zone are equal in magnitude, as are the currents in each of the V base souls for a star Delta connected transformer. We have already gone through the exercise of seeing how the high side of a star connected transformer is as well as we've gone through the exercise of connecting the low side in a delta connection. However, I'm going to go through the process now because this is the first time we're looking at connecting. Why across to a delta, one terminal of the primary terminals are connected to the system lines or buses and the other terminals are connected together to form a primary neutral. The in the secondary of the transformer, one terminal of the secondary terminals are connected to the system lines, buses, etcetera. The other terminals are connected to the adjacent secondary terminals. The high voltage H two terminals are connected together to form a neutral, and the H one terminals are connected to the individual phase conductor's. The transformer, having the H one terminal connected to the red phase bus, is referred to as the red face transformer. Likewise, the transformer with the H one terminal connected to be white phase. It is referred to as the white face transformer and the transformer. With this H one terminal connected to the blue phase bus or line is referred to as the blue phase transformer. The X one terminal of the transformer are connected to the individual conductors, and the low voltage X two terminals are connected to the adjacent secondary X one terminal . Before going any further, I want toe explain the gnomic later that I'm gonna be using In describing the voltages of the transformer, primary and secondary as we go forward, you have already seen that I'm separating out things in color to make things a little bit easier to understand. When I'm talking about the primary side voltages, I'm going to use upper case, uh, letters or capital letters R, w and B for red, white and blue and in for if I'm describing the voltages in the secondary side of the transformer, I'm going to use the lower case letters R, W and B. If we're talking about phase two phase values, I will use both letters. In other words, if the voltage is red white, I will say R W and if it's white to blue, I'll say WB and cetera. I will use color and they should make sense, but don't necessarily. The thing that's most important is the letters themselves. They are in the w, not necessarily the color, although I will try to maintain some sense in regard to the color. But as you can see, it gets a little bit confusing when we're talking face to face values because we're talking about two cultures. However, I think it'll be pretty obvious as we go along. And if I'm talking about phase two phase values in the secondary, I'm going to be adopting the scene standard, except that it's going to be lower case letters. Now when I talk about the phase two neutral voltages, they are, and they should always be two designation or two points because that would describes the potential difference. So in the case of the primary side, I'm going to be using capital letters again. Read to neutral White to neutral blue to neutral, in other words, are in WN beat end and in the in the secondary, I will be using lower case letters are in WN and be in now I'm going to make one exception , and that is because we are going to be trying to get everything condensed onto one slide in cases, I will be taking the liberty of dropping the end or the neutral. So a lot of times I will be referring to the phase two neutral value with just the upper or lower case letter now in a wide Delta transformer. Of course, there is no neutral, but we will be talking at times about a hypothetical neutral, in which case of I will just be referring phase to neutral value with just the one letter. This could lead to some confusion as you go forward, but I'm going to make sure that things are pretty clear as we go along. And even though I should be having the end in there, you'll see it's clear and easier to understand if I do leave it out during the analysis. So the connections are fairly straightforward because this is the second time we've gone through them. The thing that is different, though, is the phaser relationships between the primary and the secondary. Comparing the phase two phase, voltage is starting with the red toe white faces both the primary and secondary looking at the primary side. The phase relationship tells us that the phase two phase voltages route three times the face to neutral voltage, and the phase two phase voltage leads the phase two neutral voltage by 30 degrees. And because the fees to neutral primary is magnetically linked to the phase two phase secondary, let me repeat that because the Phase two neutral primary is magnetically linked on each transformer to the Phase two phase secondary. As you can see from the phaser diagrams, the Phase two face primary leads the phase two phase secondary by 30 degrees, and the turns ratio is given by the magnitude of the primary face to neutral voltage over the magnitude of the secondary. Phase two phase voltage, which means the secondary read toe white voltage is equal to the primary red to neutral voltage, divided by the turns ratio or mathematically. You can also say that the primary red to neutral voltage is equal to the turns ratio times the secondary read toe White fault Egx. We're talking about magnitudes here, of course, and it relates the primary and secondary phase two phase voltage magnitudes. Since we already know that thesis Kandarian is lags the primary by 30 degrees. Then we can calculate the primary and secondary phaser relationships for a why to Delta Transformer. Let's look at the currents now in this transformer and in order to look at the currents. Of course, we have toe Adul load and I've chosen a Delta low. What I could have just as easily chosen a Y load. It's not going to make that much difference to the flow of the secondary or the primary currents, for that matter. And I've chosen a resist of load because I don't want any phase shifting going on due to the load itself. Certainly it will add to the shifting if there is any. But that isn't what we're looking at right now. So that's just assume that the load is purely resistive. I've also drawn in the voltage phasers in miniature up here, the title there just so we can keep track of them. Now I have adopted the same standard pretty much that I did with the voltages. But keep in mind now we're looking at currents, so all the currents that are associated with what we're gonna look at on the primary side. I'm gonna use capital letters or upper upper case letters. And on the secondary side, I will be using the lower case letters, the line currents. I'm going to title them as I lying our primary I line White Primary and I line Blue Primary . You'll notice that I've capitalized the our prime in the W prime and the B prime to indicate that that is the primary side that we're talking about. And I'm going to do a similar thing on the secondary. The lines coming off of the transformer I'm going to call I lying with lower case are secondary in a lower case W secondary and a lower case Blue Secondary, the Transformer Primary Winding current I'm going to refer to with a Capital R and the current coming in the line is going to flow down and into the spot of that red transformer , and all of the current flowing through the red face coil or winding of the transformer is going to be equal to I line are primed in a wide delta connected transformer. Similarly, the current flowing in the winding off the primary white transformer is going to flow into the spot on that transformer from the eye line w prime. And the same thing is it's going to be equal to the line current. And similarly, the blue phase is going to be the uh is going to be, ah, designated B, and it's going to be equal to the lying current on the blue face line coming in. That is because we have a why connected primary. Now on the secondary winding of the transformer, I'm going to call the current flowing in that winding as lower case R. And in the case of a lower case, R on the current flowing in this transformer. Because it's float, the current is flowing into a spot on the primary. It's going to flow out of the spot on the secondary, and similarly, the white phase secondary current coil is going to flow out of the spot, and the blue phase current coil is gonna flow out of a spot. Now we would like to find out what the current is that's flowing in the eye line are secondary or our sec, W sec and be second. We're gonna have a look at that right now. This transformers connected toe a balanced system and let's assume that it's connected to a bus and it's gonna have the red, white and blue phase currents coming in from the primary side. And it's a bound system, so those currents coming in will be the equal in magnitude in 120 degrees apart, and the current that's flowing in the red face transformer is going to flow into the spot primary, and it's going to be I'm going to assume that it's straight up and down, or it's pointing straight up. It is magnetically linked with the secondary, so the current flowing out of the spot on the secondary is going to be in phase with the current flowing into the spot on the primary, And I've indicated the phasers for both currents in the primary and the secondary winding of the transformer. Similarly, the white face current is 120 degrees lagging the red phase, and that's going to be flowing into the spot on the white phase transformer primary. And because it is also magnetically linked with the secondary, the current will be flowing out of the spot on the secondary, so it will be in phase with the current flowing in the primary side, however, the X one terminal of the White Phases connected the X two terminal of the red fees, so the head of the arrow of the white phase will be connected to the tail of the arrow off the red face. Similarly, the blue phase current is going to be 100 and 20 degrees, lagging the white phase current because the system again is balanced. So the current flowing into the spot on the second on the primary side of the transformer is going to be 120 degrees from the white phase, and I've indicated it there on the slide. Now the secondary winding of the transformers magnetically linked to the primary. So the current flowing in the secondary has to be flowing out of the spot, but it has to be in phase with the current flowing in the primary. But its X one terminal is connected to the white fees X two terminal, and it's X two terminal. Ah, that is of the blue phases connected to the X one terminal of the red face, so the tail of the blue phase era will be on the head of the red fees and the head of the blue phase will be on the tail of the white face, as indicated on the slide. I would now like toe figure out what the currents are that air flowing in a lying to the load, and I'm going to start with the red phase lying secondary current. And if you go back to the transformer, you'll see it's connected in two places. It's connected to the X one terminal of the Red Transformer and is connected to the X two terminal of the Blue Fees transformer. What that means is, the current that's flowing in the line is going to be made up of the read phase current, but the current we have to subtract. The current is flowing into the blue phase because it's flowing out of the line. So we have to subtract the blue phase current, and we know what the plus blue phase current is. The minus blue face current is just 100 needy degrees from that, So these air the two phasers that make up the line current. So all we need to do is connect them, and that will be the current that's flowing in the secondary of the line of the red face. The delta connected secondary currents form a triangle of three equal sides, which is unequal. Lateral triangle on the contained angles are 60 degrees. So in trying to come up with the angle between the red phase and the minus blue phase, if we move the minus blue phase over, it forms a straight lying with the plus blue phase. And if we subtract 60 degrees from 180 degrees, which the straight line forms, then we're left with 120 degrees. And that is that contained angle between the red phase and the minus blue phase current. Now the triangle formed by the red and minus blue phase currents and the eye line are secondary current. It is in a sauce Elise trey ankle. So the two sides that are equal will share the 60 degrees that are left over when you subtract 100 and 20 from 100 nadie and were left with 30 degrees. So that's just it quick breeze of trigonometry there just to prove that we have a triangle with two contained angles of 30 degrees and one of 120 degrees. If we move I line are secondary up to compare it to the primary side of the transformer. We know that the red phase primary current flowing in the primary side of the transformer is equal to the wine current coming in so we can see that the I line are secondary will lag the eye line. Our primary by 30 degrees or in generally speaking, will say that the secondary lags the primary by 30 degrees because we've just done the investigation for just one line. E I line are secondary. However, we can go through the same exercise for the white phase in the blue phase, and we'll come up with the same thing that the line currents of the secondary lagged the line currents of the primary by 30 degrees. And that is not necessarily too difficult to think about because we already saw that the line to line voltages lagged the primary lying toe line voltages air phase two phase bolt just by 30 degrees, and we just added a resistance load so the current should be lagging by 30 degrees as well . However, what we haven't discovered yet we're going to go on. To see that in the next few slides is the magnitude of these currents that air flowing in the primary and the secondary looking closer at this triangle, which is made up of the read phase current in the minus blue phase current in the eye line of the red Face secondary, we'll call him ar minus B, and I line it is an a sausage, these triangle, and we've seen this exercise before. The triangle is made up of two 60 30 90 triangles, which means the length of the arrow I line are secondary or the magnitude I lying are secondary is made up of the ratios of the red Magnitude Route 3/2 plus the minus B magnitude Route three All over, too. And because we're dealing with just magnitudes, we can say that the red magnitude is equal to the minus blue magnitude so we can replace the minus B magnitude in our equation with the our magnitude rewriting the equation. We get route three times, two times the are magnitude all over, too, and the twos in the numerator and denominator cancel out. Leaving us with eye line are secondary is equal to root. Three times are magnitude. Now, I'm just gonna switch back a little bit for before progressing on a good recall, The voltages of this transformer. We did this in a couple of slides before the turns. Ratio of the vault of the transformer is given by the voltages of the red face magnitude the voltage across the coil or the wind ings of the red face over the voltage drop across the wind ings of the read toe white, uh, secondary terminals cause red to white is connected Delta. So the turns ratio when we discovered this before is given by the magnitude are all over the magnitude are w and the currents. Then if you look at our diagram, the currents in the secondary, uh, findings over the currents in the primary wind ings the magnitudes also for the turns Racial of the transformer. And just to recall the theory, I'm gonna look back at the slide that that discovered this, that the turns ratio can be described in either the voltages or the currents, but they are the inverse of each other. So going back to our equations and looking at the current uh, formula that we just developed. Do we can rewrite the You are sorry we can replace the upper case are in the primary because all of the current flowing in the eye line primary flows through the wind ings of the red face transformer. 6. Ch 04b Three Phase Power Transformers: Chapter four b transformer clock system vector nomine clay jer. The main purpose of power transformers and the system is to change voltage levels that is, to convert the magnitude of the voltage either up or down, depending on the requirements. For example, distribution utilities may want to take the high voltage transmission levels of 500 to 30 115 K V two voltage levels. Say 25 k V for ease of retail sales to customers or an independent power producer may want to step the generation voltage up to the level for the that could be connected to the transmission utility. If we were dealing with a single face quantity, the choice of connections would be simple would be a simple matter of using the correct turns ratio. However, when dealing with three phase quantities which aren't the ideal for economical transmission and distribution, not only the turns ratio has to be taken into consideration, but also the variety and permeability off connections. That is why transformer clock system vector nomine clincher was developed With every power transformer installation. We will have a primary system connected to the primary side of the transformer and a secondary system connected to the secondary side of the transformer. For simplicity sake, we can assume that the primary side is energized by a three face balanced set of voltages, rotating counter clockwise and having a phaser separation of 120 degrees. Depending on the transformer connections, the secondary voltages can either be rotating in a clockwise or counterclockwise direction . Assuming, however, that we're still dealing with a balanced system. The secondary voltages are equal in magnitude and 120 degrees apart, but May leader leg the associated primary voltages. But in all systems, it is desire to have both primary and secondary systems rotating in the same direction, and that, as a standard, is usually counterclockwise. This, of course, goes for the phase two phase voltage isas. Well, specifically, when we're dealing with a Delta Delta connection, take, for example, a star star or a y y connected transformer. We have already looked at this connection, and it is fairly straightforward. However, if we reverse the connections of each of the secondary wind ings, it would still be why why connected? But certainly the secondary phasers would have to be different, as is the case for a Delta Delta connected transformer, a gain we have already looked at. This connection at it, too, seems fairly straightforward. However, once again, if we reverse the connections of each secondary winding, it would still be Delta Delta connected. But certainly the secondary phasers would have, ah, have to be different. Another example would be this star Delta connected transformer, which we also have studied, and we used these secondary connections. As you see in the diagram, we could have just as easily used the secondary. Winding is connections that you see here now, and it would still be a star Delta transformer. So how do we simply convey the configuration along with the connections? The answer is transformer clock system Vector Norman Clay Chur, As its name suggests, we used a clock face as a reference for relating the secondary voltage to the primary voltage. The digits 01234 etcetera relate to the phase displacement between the high voltage and the low voltage wind ings using the clock face notation. The phaser representing the high voltage winding is taken as a reference and set at 12 o'clock. It is assumed that the phasers are rotating in a counterclockwise rotation. We use the our indicator as the indicating phase displacement angle. Low voltage lags the high voltage by 30 degrees in this instance because there are 12 hours on the clock and a circle consists of 360 degrees. Each hour represents 30 degrees. For example. Two o'clock is 60 degrees. Three is 90 degrees. Four o'clock is 120 five is 150 six o'clock is 180 seven is to 10 8 o'clock is to 49. Oclock is to 70. 10 is 311 is 3 33 160 puts us back at the 12 oclock position. This can also be referenced as zero degrees, so it could be zero. We're now going to look at some examples of the workings of ah, clock face nomine creature. And I'm gonna start with the why y connected transformer. And we've seen this connection before. And believe it or not, there are six different ways to connect up the secondary wind ings of this transformer number one. Starting with our previously studied connection, the secondary phasers would look like this showing that the secondary voltages are in phase with the respective primary voltages using just one set of phasers. The red one. In this case, the clock system of vector nomenclature would tell us that there is zero degree do placement displacement from the secondary to the primary wind ing's the clock system gnomic later would be. Then why? Why zero? We could have also said, Why? Why three? 60? But normally we just choose zero instead of 3 60 It's much easier to write on a piece of paper, I guess. Notice also that the primary side is designated with a capital. Why, where the secondary is designated with a lower case. Why followed by the displacement, which is zero the second? Why white connection would look like this. The red winding X one terminal is connected to the secondary blue phase bus. The white winding X one terminal is connected to the secondary read phase bus. The blue winding X one terminal is connected to the secondary white phase bus, and all of the X two winding terminals are connected together to form a secondary neutral. The secondary phasers looked like this showing the secondary voltages are 120 degrees lagging their respective primary voltages. Ah, gain just using the red face factors. The clock system of vector nomenclature would tell us that there is 120 degree displacement of the secondary voltage. The clock system nomine clay chur would be Why, why four? For the third connection, the Y Y connections would look like this. The red winding X one terminal is connected to the secondary white phase bus. The white winding X one terminal is connected to the secondary blue face bus and the blue winding X one terminal is connected to the secondary read phase bus and all of the X two terminals are connected together to form a secondary neutral. The secondary phasers look like this, showing that the secondary voltages are 120 degrees leading their respective primary voltages, a gang just using red phase vectors. The clock system of vector nomine creature would tell us that there is 100 and 20 degree displacement leading of the secondary voltage. The clock system, not nomine creature, would be why why eight? The fourth connection of the Y y configuration would look like this. The X one terminals are connected together this time to form the secondary neutral and the X two winding terminals are connected to their respective red, white and blue phases. On the secondary bus, the secondary phasers would look like this, showing that in the secondary voltages air 180 degrees out of phase with the respective primary voltages. The clock system of Vector gnomic later would tell us that there is 100 and 80 degree displacement of the secondary voltage. The clock system would say Why? Why six For the fifth connection of the Y Y configuration, the X one terminals again would be connected together to form a secondary neutral. The red winding X two terminal is connected to the secondary blue phase bus. The white winding X two terminal is connected to the secondary read phase bus, and the blue winding X two terminal is connected to the secondary white phase bus. The secondary phasers would look like this, showing that in the secondary, voltages are 60 degrees leading their respective primary voltages the clock system. Who would tell us that there is a 60 degree leading displacement of the secondary voltage, meaning the clock system, gnomic later would be why, why 10 the sixth and final connection of a Y Y configuration would look like this. The X one terminals again would be connected together to form a secondary neutral, while the red winding X two terminals connected of the white face bus. The White X two terminal is connected to the blue phase bus. The blue X two terminal is connected to the red face bus. The secondary phasers would look like this, showing that the secondary voltages are 60 degrees lagging the respective primary voltages . The clock system of Vector gnomic later would tell us that there is a 60 degree to plate displacement in the secondary voltages and the clock system would then read Why, Why, too? Now, let's look at a Delta Delta configuration. We have already studied this configuration with the primary winding is connected like this . It would it would produce these face to face voltages on the primary side with the secondary, winding is connected in a similar fashion. It would produce voltages that would look like this. The red toe white primary voltages in phase with the secondary read toe white voltage. The white to blue is in phase with the white to blue and the blue to red is in phase with the blue to red primary secondary. Of course, in general terms, we might say that the primary is in phase with the secondary. So the clock face nomine creature would tell us that these the primary isn't phase with the secondary such that this Delta Delta connection would be D D zero. Now, this Delta Delta connection could have a variation of six different secondary connections if you wanted to go through them all. I'm not going to do this at this point because we've already done that exercise with a star star connection. However, I will look at one, which is fairly simple. What would happen if we reversed the secondary terminals of this Delta Delta connection? The phasers of the second area would be reversed, giving us this fazer configuration, meaning that the read toe white primary voltages 180 degrees out of phase with the read toe white secondary. The white to blue is 180 degrees out of phase, with the white to blue primary to secondary, as is the blue to red primary, 100 degrees out of phase with the blue to red Secondary, and in general terms, we was say that the primary is 180 degrees out of phase with a secondary. The cock clock face nomine clay chur would then be D D six, indicating this 180 degree phase shift for the Why Delta connection. We have being through this exercise before, and we saw that the red toe white secondary is in phase with the red to neutral primary and that the red toe white primary voltage is leading the red to neutral primary voltage by 30 degrees, meaning that the red, the white primary voltage is leading the secondary red white voltage by 30 degrees. And again, in general terms, we can say that the secondary is lagging the primary by 30 degrees. The clock face gnomic lecture would then be why d one indicating this 30 degree lagging phase shift. This ends the chapter on transformer clock system vector gnomic leader 7. Ch 05R1 Transformer Construction and Cooling: Chapter five transformer construction and cooling transformers are a critical and expensive component of the power system due to long lead times for repair and replacement of transformers. A major goal of transforming protection is limiting the damage to defaulted transformer. Some protection functions, such as over excitation protection and temperature based protection, may aid this goal by identifying operating conditions that may cause transformer failure. The comprehensive transformer protection provided by multiple function protection relays is appropriate for critical transformers in all applications. The type of protection for the transformer varies depending on the application and importance of the transformers. Transformers are protected primarily against faults and overloads. The type of protection used should minimize the time of disconnection for faults within the transformer and to reduce the risk of catastrophic failure to simplify eventual repairs. Any extended operation of the transformer under abnormal conditions such as false or overloads compromise is the life of a transformer, which means adequate protection should be provided for quicker isolation of the transformer . Under such conditions, most transformer failures fall into these categories. Winding failures due to short circuits turn to turn false face to face faults, face to ground faults and open wind ing's core faults, core insulation failures and shorted lamination. Terminal failures, open leads, loose connections, short circuits on load tap team changer failures. Mechanical, electrical or short circuit overheating. Abnormal operating conditions over flexing, overloading over voltage and external faults, which could lead to overloading. If not detected and isolated from the system. Catastrophic results could occur, ending in losses to the utility fleet equipment, not to mention the secondary losses that the client may occur and for the utility in terms of revenue. The construction of a transformer in its basic form consists of two coils. At least one high voltage and one low voltage linked by mutual induct IMS and a laminated steel core In all transformers that are used commercially, the core is made out of transformer sheet steel. Lamination is assembled to provide a continuous magnetic path with minimum of air gaps. The steel should have high permeability and low histories is loss by effectively laminating the core. The eddy. Current losses can be reduced. The two coils air insulated from each other and from the steel core. The device will also need some suitable container or tank for the assembled core and wind ings and to hold a medium such as oil, which the core and its wind ings can be insulated and cooled in order to insulate and bring out the termini of the terminals of the wind ings from the bank appropriate bushings that are made out of either porcelain Ceramics must be used generally the name associated with the construction of a transformers dependent upon how the primary and secondary wind ings are wound around the central laminated steel core. The two most common and basic designs of a transformer construction are the core transformer and the shell transformer in the core tight transformer, the primary and secondary winding czar wild outside and surround the core ring in the shell type transformer, the primary and secondary winding ZPass inside the steel magnetic circuit. The core, which forms a shell around the findings as shola in both types of transformer core designs , the magnetic flux linking the primary and secondary wind ings travel entirely within the core, with little or no loss of magnetic flux through the air. In court type transformer construction, 1/2 of each winding is wrapped around each leg or limb of the transformer magnetic circuit as shoulder. The coils are not arranged, with the primary winding on one leg in the secondary on the other. But instead, half the primary winding and half the secondary winding are placed one over the other concentric Lee on each league in order to increase the magnetic coupling and allowing practically all of the magnetic lines of force to go through both the primary and secondary wind ings. At the same time, however, with this type of transformer construction, a small percentage of magnetic lines of flux flow outside the core and this is called leakage flux. Shall tight transformers cores overcome this leakage flux as both the primary and secondary winding czar wound on the same central leg or limb, which has twice the cross sectional area of the two outer limbs? The advantage here is that the magnetic flux has to closed magnetic passed to flow around, uh, external to the coils on both left and right sides before returning back through the central coils. This means that the magnetic flux circulating around the outer limbs of the core of the transformer construction are equal and 1/2 the total, as the magnetic flux has a closed path around the coils. This has the advantage of decreasing core losses and increasing overall efficiency. Next is a short video on how a simple three face transformer bank is constructed, and this video is available on YouTube and was produced by Siemens, starting with the laminated iron core, which is open at this present time to receive the low voltage wind ings first. Then the concentric high voltage wind ings with the leads bringing out the connection that top part of the laminated cores then put on the leads for the low voltage are connected. Then the top of the transformer is put in place to receive the high voltage bushings and the low voltage bushings, all of which is immersed in the container or tank, which would be ultimately filled with oil. This videos, produced by Siemens as a sadness available on YouTube at this Web address, as you see here, transformers air, usually classified by voltage, starting with low voltage, then going to medium voltage, high voltage, extra high voltage and ultra high voltage. This table shows the voltage ranges for each classification. Three wire means a delta connection, and four wear means a star or a white connection. And here is what the levels might look like connected in to the system, starting at the highest voltage of 380 K V and dropping down to 400 bowls. The main source of heat generated in a transformer is its copper losses or its ice square our losses, although there are other factors contributing to the heat in a transformers such as history since an eddy current losses, the contribution of the ice where are our loss dominates all of them. If this heat is not dissipated properly, the temperature of the transformer will rise continually, which may cause damage in the insulation and liquid insulation medium inside the transformer. So it is essential to control the temperature within permissible limits. To ensure that the long transformers last a long life by reducing the thermal degradation of its insulating system In electrical power transformers, we use external transformer cooling systems to accelerate the dissipation rate of heat of the transformer. There are different transformer cooling methods available for transformer, so let's look at some of them. The most basic form of heat dissipation in a transformer is the natural air convict conviction, which means the transformers just standing an air and relies on the dissipation of heat into the air through natural natural conviction means you'll often see the term a n stamped on the transformer, which means air, natural or naturally cooled. These transformers can be naturally cooled with air. The natural conviction of the air removes the heat generated by the transformer. As I said, the symbol for this type of transformer is capital, a capital in who n a n cooling of transformers. This is one of the simplest transformer cooling systems. Well, in an is oil natural hair natural here, natural conventional flow of hot oil is utilized for cooling. Oil will absorb the heat from the transformer, wind, ings and core, then migrate to the top of the transformer. It will then flow naturally into the radiators, which will dissipate the heat into the atmosphere by natural conduction and radiation, thereby cooling and moving to the bottom of the rats and tank to start the process over again. In this way, the oil in the transformer tank continually circulates when the transformer is under load, as the rate of dissipation of heat in to the air depends upon just the dissipating surface of the oil tank. It is essential to increase the effect of surface area of the tank, so additional dissipating surfaces in the form of tubes or radiators connected to the transformer take tank will do this well in a F cooling of transformers which stands for oil natural air. Forced heat dissipation can obviously be increased if discipline the dissipating surfaces increased, but it can be made further and faster by applying forced air to flow over the dissipating surfaces. Fans blowing air on the cooling surfaces is employed. Forced air takes away the heat from the surface of the radiators and provides better cooling than just natural air conviction. As the heat dissipation rate is faster, electrical power transformers can be loaded mawr without crossing the permissible temperature limits the air, forcing fans air sometimes switched on and off in stages, providing stage ratings for the transformer. The heat dissipation rate can still be increased further if this oil circulation is accelerated by applying some force in O. F A. F cooling systems, the oil is forced to circulate within the closed loop of the transformer tank by means of oil pumps. Oh f A F means oil forced air force cooling methods of transformers. The main advantage of this system is that it is compact and for the same cooling capacities , O F. A. F occupies much less space. We know that ambient temperature of water is much less than atmospheric air in the same weather conditions. So water may be used as a better heat exchanger medium than air. And that is especially true if the uh, there is plenty of water available, which is the case for hydraulic generating stations. So quite often in some of the larger hydraulic generating stations, transformers as well as some of the generators have water cool rad eaters that keep dissipate the temperature away from the equipment. In o f wf cooling systems of transformers that hot hot oil is sent to oil to water heat exchanger by means of oil pumps. And there the oil is cooled by circulating cold water on the heat exchanger oil pipes. Oh f W f means oil forced water, forced cooling in transformers. This is the case for the main step up transformers at the Churchill Falls Generating Station that takes the voltage from the 11 generating units at the station and steps the voltage up to 230,000 volts. The fact that these transformers air located underground, it means that they want to keep the dimensions at a minimum so they employ water cooling for the transformers. And, of course, there's plenty of water available because it is a a hydraulic generating station. This is a cut away or a side view of the generating station, and you can see the transformers located. Add about 1000 feet underground, and the water from the intake is circulated to radiators in the transformers themselves. In order Teoh carry the heat. These are the transformers that are located in the underground facility. Here we see one of them, and indeed not only the water is used to cool the transformer itself because there's about 33,000 amps flowing in the primary of the transformers that takes the the power from the generating units. Even the duct work is enclosed. Um, sorry. Even the bus low voltage bus is in ductwork that is cooled by water as well liquid cooled transformers. These transformers have coils immersed in insulating medium, usually oil, which serves multiple purposes first to act as an insulator and second to provide a good medium through which to remove the heat. Liquid cooled transformers cooling classes went through a major change when the I Tripoli adopted the standard of a four letter designation found on most modern power transformers. The first of these four letters designates the internal cooling medium in contact with the wind. Ing's oh stands for mineral oil or synthetic insulating liquid with the fire point of less than 300 degrees C. Okay stands for insulating liquid with a fire point of greater than 300 degrees C and L is insulating liquid with no measurable fire point. The second letter designates the circulation mechanism for internal cooling mediums n stands for natural conviction flow through cooling equipment and wind. Ing's F is forced circulating through cooling equipment such as cooling pumps and uses also natural flow of conviction of the winding themselves and isn't necessarily directed. The DEA's is the directed element. It actually stands for forced circulating through cooling equipment that is directed from the cooling equipment into the at least the main wind ing's. The third letter stands for the or describes the external cooling medium A for air W for water. The fourth letter stands for the circulation mechanism for external cooling media and for natural conviction F for forced circulation such as fans and pumps. Here's an example of what you might find Stamp on transformer only in a F, which stands for oil. Natural air forced pull in a N stands for oil, natural air natural and O F. A F cooling of transformer stands for oil, forced air forced and a left wf. It stands for oil forced water forced. Unfortunately, a lot of transformers that were built in are still in service today. Prior to the eye Tripoli adopting at standard of a form letter designation, the ratings may not be found in their full four letter designation. In these cases, you will have to use your ingenuity and a little imagination to interpret the cooling ratings as you will see in the following examples. Here is an example of an older transformer that doesn't use the standard four letter designation before the cooling method. In this case, it's multi rated and it uses either a two letter or a three letter designation, which is similar to the four letter designation. The first level of rating on the transformer is 50 50,000 k V A or 50 M V A of which allows for a 55 degrees rise in temperature. But it's the old a designee. Each designation means that it's the oil and the air is just natural conviction used for cooling the transformer, and it's rated at 50,000 K V A. If at the next stage of the transformer is to turn on some fans and you would have forced air cooling, which would increase the rating of the transformer to 66.667 m v a. And that would allow the transformer to provide that load with rising about 55 degrees C. Next is forcing the oil as well as the air. So that means they've got oil pumps as well as fans cooling this transformer, which would increase the rating of the transformer to 83.333 m v a. And it would allow that type of a load without exceeding the 55 degrees C. You can also raise the output of the transformer temperature to 65 which would allow you to go to 93.333 m v A and the. This will be, of course, running the force air as well as the oil pumps to cool this type of transformer. The mechanical assisted equipment is usually automatically switched on as the operating temperature rises, but it could be operated initiated in either click. In either case, close observation is required as this expensive equipment is operated close to its reading limits. In any event, protective reeling should take it out if the limits are exceeded for too long. Here is another example of a transformative, this multi rated, depending on the cooling type that's implemented. And again, it's an older type transformer, so it doesn't have the four letter designation. But it does have two letter designations here. The natural conviction method or without fans or pumps. The Thedc transformer has two ratings for at different temperatures. 24 m. V. A rating at 55 degrees C and a 26 m V a rating at 65 degrees C. The there appears to be two stages of fans for this transformer, so the first stage of fans being turned on would allow a 32 m v A rating not to exceed 55 degrees C and US 35 and the A rating not to exceed 60 five degrees C. If the last bank of fans has turned on. This will allow a rating of 40 M V A at 55 degrees C and A 44.8 MBA at 65 degrees C. Again, these fans should be turned on automatically. However, if they are watched by an operator, these temperatures will have to be adhere to and again. Ultimately, there are. There is relaying the transformer that will take it out if the temperatures are exceeded for a longer period of time. Here is 1/3 and our last example. It is a smaller transformer, and it is, I guess, fairly newer because it does have the four letter I Tripoli standard designation for cooling method, but it does have a multiple rating as well. It is an old in a N cooling, which is air oil, natural air natural, and it has a dual rating, depending on the temperature you want operate. The transformer at it has a 7.5 n v a and should not exceed 55 degrees c. Ah and it should be able to put out 8.5 MBA and should not exceed 65 degrees C and this ends Chapter five. 8. Ch 06 Transformer Protection: Chapter six Transformer protection transformers are a critical and expensive component of power systems due to the long lead time for repair and replacement of transformers. A major goal of transformer protection is limiting the damage to faulted transformers. The comprehensive transformer protection provided by multiple function protective relays is appropriate for critical transformers off all applications. The type of protection for the transformers varies depending on the application and the importance of the transformer. Any extended operation of the transformer under abnormal conditions such as falter overloads, compromises the life of a transformer, which means adequate protection should be provided for quicker isolation of the transformer . Under such conditions. Looking at the after mentioned in a little bit more detail, the reasons to provide transformer protection are first of all to detect and isolate the fault the faulty equipment. Secondly, it's to maintain system stability then. Thirdly, we want to limit the damage, and that involves minimizing the risk of fire and of course, minimizing the risk risk to personnel, including workers and the general public factors that are affecting the transformer protection. First of all, thecornerscores repair of the equipment. As I said, the transformers are a extremely expensive inventory item. And we, uh, in order to repair or replace him costs a ah lot of money. So we wanna minimize the cost of repair. Also, we don't want the damage to be too extensive. So we want to minimize the cost of downtime because we ultimately could be losing revenue as a utility because of equipment outage, not to mention the public relations. If we have people in, uh, out of power for any length of time, and then it also affects the rest of the system and how the system would be operating without that equipment. And, of course, if there is a catastrophic failure, like in the case of a transformer, if it explodes, there's a potential for damaging adjacent equipment. And, of course, Ah, it's I've also mentioned the length of time of repair or in order to replace the equipment . At times, some of the generating stations air in a very remote location and in order to get a heavy piece of transformer equipment up to that location, would require a lot of time and a lot of logistical movement of inventory. In person. Out protection requirements fall under four categories. Selectivity, selectivity, means that the protective scheme should accurately identify the system element which is at fault, and initiate the tripping off on Lee. The minimal possible number of circuit breakers required toe isolate the defective element or elements. Proper selectivity ensures that the minimum number of customers air interrupted and the minimum number of system elements air taken out of service. Unnecessary interruptions cut into revenue and reduce customer satisfaction. Unnecessary removal system elements contributes to overloading of equipment remaining in service and could contribute to the instability of the entire system. There must be a correct coordination provided in various power system protection relays in such a way that a fault at one portion of the system should not disturb another healthy portion. Fault current may flow through the part of the healthy portion, since they are electrically connected, but relays associated with the healthy portion should not operate faster than the relays of the faulty portion. Otherwise, undesired interruption of healthy equipment will occur again if relays associated with the faulty portion is not operated in proper time. Do do any defect in it or other reasons than on Lee, the next really associated with the healthy portion of the system must be operated to isolate the fault. Hence it should neither be too slow, which may result in damage to the equipment. Nor should it be too fast, which may result in undesired operation next there. A speed speed means the protective relays must operate after required speed. Speed of a fault clearance is essential, since the likelihood of a widespread system disturbance or complete system collapsed increases with the duration of the fault. Rapid clearance of fault minimizes the damage to faulted equipment and also minimizes the hazard to personnel who may be in the vicinity. Reliability is the most important requisite of a protective. Really. Relays remain inoperative for long periods of time before a fault occurs. But if a fault occurs, the really must respond instantly and correctly. Reliability that is dependability and security is essential for any real a scheme. Dependability is defined as the assurance that the relay will operate when required to security is the assurance that they will not operate when not required to. Traditionally, utility facilities have favored dependability rather than security that IHS false trips outnumber failures to trip. When our while false trips are obviously not desirable, the emphasis on dependability is preferred, since the consequences of a failure to trip are generally much more severe than the consequences of a false trip. And lastly, there is sensitivity. Sensitivity of the reeling equipment must be sufficiently sensitive so that it can operate reliably when the level of a fault condition just crosses a pre defined limit. Having said all that transformer, false could fall into one of three categories. First of all, there's overloads. These tend to not be extremely fast. In fact, they kind of slowly grow as the load is added to the system. But there is a pre defined limit. Ah, that transformers should not exceed both noi of temperature and current flow and some other factors. But overloads could cause damage. And when they cross the pre defined limit, that's when reeling action must be taken in consideration and either tripped the transformer off or adjust feeders coming off the transformer so that the overload condition will not exist. Then there's internal false these air. The major reasons why we have relaying protection on a transformer. These can be very catastrophic if they've left in the system too long, and depending on the type of fault could actually destroy the whole transformer. So we definitely want to have good reeling in place for the detection and the isolation of internal faults within a transformer. Then there are through false and we talked about false external to the transformer, but through false could cause the transformers to become overloaded in themselves. And they certainly have to have protective equipment there in case the outside elements, uh, fail to isolate the fault and a through fault condition could still damage the transformer . And you want to make sure that that does not happen. Transformer over current protection falls into two main categories. Relays and fuses, the choice of which is largely dependent on the transformer size, voltage levels and downstream loads. Small distribution transformers are commonly protected only by fuses. In many cases, no circuit breakers provided making fuse protection the only available means of automatic isolation. Fuses are over current devices and must have ratings well above the maximum transformer mode current in order to carry without blowing the short duration overloads that may occur when starting large motors, and also to withstand the magnetize ing in Russia. Currents drawn when a power transformer is first energized. It should be noted here that HRC or high rupturing capacity fuses, although very fast in operation with large fault currents, are extremely slow, with currents of less than three times their rated value. It follows that such fuses will do little to protect the transformer when load limit thresholds air just slowly approached and then exceeded serving only to protect a system by disconnecting a faulty transformer after the fault has reached advanced stages. Larger Transformers 100 TV A and over may be controlled by circuit breakers, in which case protection can be provided by over current relays. Improvement in protection is obtained in two ways. One, the excessive delays of the HRC fuses for lower fault currents is avoided and an earth fault tripping element can be provided. In addition to the over current features, time delay characteristics are chosen to discriminate with circuit protection downstream on the secondary side, instantaneous trips may be added, the current setting being chosen to avoid operation with short circuits on the secondary side. Also, HRC fuses may be used to back up the circuit breaker. Although full discrimination with secondary circuit protection is necessary, the fuse rating need not be a highs through fault. Current depending on the transformer, reactant the source fault power and whether the secondary system is a single circuit or subdivided into several branches, with each having its own protection. The main function of such instantaneous protection is to give high speed clearance to close in an internal false. The settings, therefore, may be relatively high when determining the parameters or limits of the protection for the various types and sizes of transformers. The following I Tripoli standards are used as guidelines for the choice and settings of transformer protection. C 37.91 The I Tripoli Guide for Protecting Power Transformers C 57.12 point 00 the I Tripoli standard for general requirements for liquid immersed distribution power and regulating transformers and C 57.109 which is the I Tripoli Guide for Liquid Immerse transformers through fault current duration for the choosing and setting of over current protections, the following must be known and if my supply by the manufacturers transformer documentation can be estimated using the I Tripoli standards rated current, which is in Va or K V a, the in rush current short circuit currents and the transformer damage curves. These parameters air plodded either on graph paper, which is the old method or on a computer. The characteristics of the really and and or fuse protection is that then fitted inside the envelope created by these four variables, let's walk through a simple example, given a 3750 K V a transformer 13.8 K V 2 41 60 volts Delta y transformer. We are to select the proper fusing on the primary site. The rated primary current can be calculated by the K V, a reading of the transformer or the rating of the transformer, which is the V A, divided by the lying to neutral voltage. And we don't have the lying to neutral voltage, so it must be calculated. So it's V a all over route three times the lying toe lying voltage, which is 3750 k v a all over route three times 13 pointing K V, which is equal to 157 amps, the rated secondary current. It may be calculated in the same way it's the Via over Route three times a line. The Line Voltage, which gives 520 amps. The in rush current is either supplied by the manufacturer or is given by the I Tripoli standard as 12 times the rated current, so that would be 157 times 12 or 1800 and 84 amps. The transformer damage curves can be obtained from the I Tripoli standard of 57.109 which is the guide for liquid immersed transformers through fault duration. These values air plotted on a time current curve or a TCC using log log graph paper or on a computer today with coordination software. A lot of the transformer information is inaccessible databases, including manufacturers, transformer information and how it's related to the eye Tripoli standards as well as most popular fuse and relay curves. From this information that transformer damage curves can be plotted along with the in rush current of 1884 amps. The transformer primary full load amps of 157 can also be added to the graph, so the fuse curve should lie between the transformer full load amps in the in rush current curves and its damage curves. And it does this shape to miss the full load amps and it of the transformer and not be affected by the in rush current, but will melt below are before the onset of the damage hers. As transformers get larger, it gets more difficult to fit the fuse curves. Also, the need for speed increases in relays and breakers will give the speed and characteristics that are required. We now replace the fuses with instantaneous and time over current relates and breakers, allowing us to fit the tripping characteristics of the relate to our transformer parameters perfectly. The instantaneous over current is set to pick up just above the in rush current level with some margin of error, of course, and the time over current characteristic ISS set to line up just below the damage curves. A relay is usually chosen with a family of curves that will fit the situation, and the one curve that perfectly matches the require parameters is then chosen. Transformer differential protection schemes are ubiquitous to almost any power system, while the basic premise of transformer differential protection is straightforward. Numerous features air employed to compensate for challenges presented by transformer applications. Although this type of protection provides the best selectivity and speed for the detection and clearing of system false, it's not without its challenges. Primarily current mismatches. Air often caused by different CT ratios or even using different manufacturer CT's and mixing them in the system may cause a mismatch, and they have to be carefully looked at transformer configuration Delta. Why? Why Delta y zigs I type Transformers introduced current shifts that have to be accounted for when applying differential protection. And if the transformer has on load. Tap changers assumes the tap changer starts to move. You automatically introduce midst mismatches between the current ratios on the primary and the secondary, and you also run into current saturation XYZ and the occur. And the history says remnants of current transformers, which have to be ah, allotted for and with the transfer power transformers. There's the in rush phenomenon that also introduces ah, large amount of harmonic content that has to be accounted for. Current differential reeling is applied to protect many elements of the power system. The simplest example of current differential relaying scheme is shown in this slide. The protected element might be a length of circuit conductor, a generator winding a bus section or, more to the point in our case, a transformer. It could be seen that the current differential relaying is a basic balancing of current. Using the application of Kirchoff is current law. The relay operates on the some of currents flowing in the SETI secondaries, that is, I one plus I to under normal conditions or false. Outside the protected element. I one equals I to. If the turns ratios of the C T are the same for both currents in the C. T secondaries will be the same. Therefore, by virtue of the SETI connections I won and I to add to zero through the relay, that is, I subscript D I f f or I. Def is equal toe I one plus I to is equal to zero. The secondary currents thus appear to circulate in the SETI secondaries on Lee and not through the relay. When a fault occurs inside the protected zone, let's see what happens under fault conditions in the zone of protective equipment. I one does not equal I to the currents in the SETI secondaries may be quite different and will flow out of the spot secondaries. Therefore, by virtue of the C T connections I won and I to ad to a value greater than zero through the relay, that is, I def is equal, though I one plus I to is not equal to zero. The secondary currents thus no longer appear to circulate in the Seiki secondaries only, but will add to a substantial amount flowing through the differential relay coil. In power transformers. The input power is equal to the output power. However, the voltage and the current in both the primary and secondary sides are different, depending on whether the transformer is step up or step down. For instance, if the transformer is a step up transformer, that means the input voltages higher than the output voltage. And conversely, while the input current is higher in the old put current. For this reason and in order to balance the currents for differential protection, the CT's in the primary and the secondary sides of the power transformer will not have the same turns ratio. However, there carefully selected in terms of turns ratio so that they both have the same output current under normal conditions of operation. Even if of different turned ratios, the same make and model of SETI's should be used. If this is not possible, other ones with characteristics as close as possible should be chosen. However, dismiss match can and will lead to erroneous differential current flowing in the operating coil. The higher the current, the larger the mismatch will be generated for the differential current. However, if the CT's are matched with the proper ratios and we consider per unit values for the current under normal conditions or for false outside the protective equipment I won per unit is equal toe I two per unit. If the turns ratio of the CT's air matched to the turns ratio of the transformer, both currents in the sea, T secondaries will be the same. Therefore, by virtue of the SETI connections I want and I to add to zero through the relay. The secondary currents thus appeared to circulate Onley in the SETI secondaries and not through do you oil of the differential relay. This brings us to one of the challenges with transformer differential protections as mentioned previously, and that is Seiki saturation and reminisce as was stated, A few slides back in power transformers. The input power is equal to the output power and the voltage and the currents in both primary and secondary sides could be quite different for a step down transformer. The input current is lower than the output current. However, under ideal conditions. If the C T ratios were selected correctly, the L put current from both see keys balance. However, even though the C T ratios were selected to balance the secondary, SETI could go into saturation before the primary CT, causing an imbalance in the secondary currents. This, of course, who could result in often would result in the erroneous operation of the differential relay . Four. False outside the protected zone transient magnetize ing in rush or exciting current occurs in the primary side of the transformer whenever the transformer is switched on or energized . This is the current that is required to set up the magnetic flux that links the primary to the secondary of the transformer. At this time, the first peak of the flux wave is higher than the peak of the flux at the steady state conditions. This current appears as an internal fault, and it is sensed as a differential current by the differential relay, the value of the first peak of the magnetize ing current, maybe as high as several times the peak at full load. The magnitude and duration of the magnetize ing in rush current is influenced by many factors. Some of these factors are the instantaneous value of the voltage way form at the moment. Then a circuit breaker is closed. The value of the residual or remnant magnetic flux, the polarity of that residual magnetize ing flux. The type of iron lamination is used in the transformer core, the saturation flux density of the transformer core, the total impedance of the supply circuit, the physical size of the transformer, the maximum flux carrying capability of iron core lamination ins and the input supply voltage level. The effect of the in rush current on the differential relay could result in false tripping of the transformer without any existing type of fault from the principle of operation of a differential relay, the relay compares the currents coming from both sides of the power transformer. However, the in rush current is flowing Onley in the primary side of the power transformer so that the differential current will have a significant value due to the existence of current in only one side. Therefore, the relay has to be able to, uh, distinguish or recognize that this current is a normal phenomenon and not to trip as a result of it. This current is usually taken as 12 times the rated K V A current for 0.1 2nd An on load tap changer is installed on a power transformer to control automatically the transformers output voltage. This device is required whenever there are heavy fluctuations in the power system. Voltage. The transformation ratio of the CT's can be matched with Onley, one point of the top change of range. Therefore, if Thea on load tap changer has changed unbalanced current flows in the differential relay operating coil, this action causes a SETI's to be mismatched. This current will be considered as a fault current, which could make the relay operate and send out a trip signal. Here again, the really has to be designed to recognize this type of current as a normal phenomenon and not to trip due to this current. So to summarize there exist. Three main difficulties attend a handicap. The conventional transformer differential protection. They induce the differential relate to release a false trip signal without the existence of any fault. They are the magnetize ing in rush current during the initial indigenisation of the transformer C T mismatch and saturation and transformer ratio changes do do tap changer operation. A solution to these difficulties is the percentage differential type relay. This really has three coils one operating coil, which operates the same as a simple differential relay coil, except that it is restrained from operating by two restraining coils. These coils restraining strength depends on the amount of flow through current, the differential current required to operate This relay is a variable quantity only going to the effect of the restraining coils in the percentage restraint Current differential relay. The operating current is the vector sum of the C T currents. I is equal to I one plus I to the operating current must be large enough to overcome the restraint provided by some percentage K of the flow through current, which is derived from the some of the magnitude of the individual C T currents. That current is equal to K times a magnitude of I one, plus the magnitude of I to the operating characteristic of such a relay is shown here, except for a slight effect of the control spring at low currents over the minimum pickup value. The ratio of differential operating current to the average restraining current is a fixed percentage, which explains the name of the really. The advantage of this really is that is less likely to operate incorrectly for false that occur external to the protected soul, the operating characteristic of the percentage restraint differential really with a slope K one you're showing here, the operating soul is indicated in green and the restraining zone is indicated in red restraint Differential relays can have different restraint slopes depending on the really it shoes and some relates, actually have dialling features that you can control the percentage or the slope of the does operating characteristic of the relay. Some percentage differential relays may have a dual slope characteristics that showing in this slide the dual slope percentage restraint characteristic improve the security of the current differential really for false external to the protected zone. This is a particular advantage because current transformers may not accurately reproduce the primary fault currents under transient fault conditions. The dual slope restraint. Characteristic is a form of adaptive restraint in which the magnitudes of the restraint quantity is increased for high current conditions, where Seiki accuracy is worse and Seiki saturation becomes more probable. The minimum pickup region is used between zero and approximately 00.5 per unit restraint current. It provides security against CT remnants and accuracy errors and is usually set between 0.3 and 0.5 per unit. The slope one region is used between the minimum pickup region and the next slope Break Point Slope one provide provides security against false tripping due to see key accuracy. Class C C teas Accuracy is about plus or minus 10%. Therefore, 20% should be the absolute minimum setting, with a greater than 30% preferred for on load tap changer applications. Another plus or minus 10 percents at it slope to provide security against false tripping during through fault events where CT saturation is likely in this area, the signet, a significant D C current component, will be present and therefore saturation is likely. Slope to is normally set at 60 to 80%. The differential protection method implies that for normal loads or through faults, the vector summation of all currents entering and linking the protected zone must be equal . Therefore, there will be no current flow in the operating coil of the protection, really for loads or external full faults. But there will be relayed current proportional to fault current for internal faults. As I've already mentioned, a common problem that exists for differential bus or end or transformer protection is C T saturation during external fault conditions. As we have already seen, one or more SETI's in the differential scheme can become saturated. In this case, the saturated C T then acts as a low impedance short circuit. The saturated C T will not perform correctly in order to transform the effect of fault current. The other SETI's that do not saturate will output secondary fault current accurately. As a result, the differential really receives some current that could trip incorrectly. In the case of high voltage buses and transformers, the system cannot tolerate the protection time required to operate the low voltage bus protection. High voltage internal buses and transformers must be cleared Ah, false instantaneously with no time delay if we could increase the impedance of the relay path substantially above that of the saturated C T two. We could then prevent the relay from operating with an external resistance added in Siris with the coil. The current output of Seiki one will now be forced through the low impedance of Seiki, too. Therefore, no or very little current will pass through the relay coil and the really a lot operate. If we now consider an internal fault, both Seiki one and CT to transform a fault current correctly as the protection will operate fast enough to prevent any Seiki saturation. Both I won and I too will add and flow through the resistor and relay combination to correctly produce an instantaneous trip. This modification two simple differential protection is No. One as high impedance differential protection with high voltage buses and transformers. The fault currents are normally very large with the addition of external resistance in the relay path, the voltage developed across are relaying and the C T secondaries will therefore be very high. This high voltage could in turn damage the secondary winding of the C T circuit and the over current relay. If we installed a nonlinear resist er in parallel with the external resistor relay, combination, we can limit the voltage to a very safe level. This type of nonlinear resistor used is called a metros ill. It will limit the voltage to approximately 300 volts for internal false at low voltage. The mattress ill will behave like an open circuit, and for voltage is greater than 300 volts. It will begin to conduct and shunk some of the relay current. As a result, the differential junction voltage is limited to a safe value and still allows the relay to operate correctly. This is what an installed metros ill looks like. It will limit the voltage to approximately 300 volts for internal faults. Let's consider a three phase transformer protected by differential relay. This is a typical step down power transformer carrying normal load power flow is from the 115 K V system to the 12 K V system. This 30 M V, a power transformer has a why connected primary winding with a delta connected secondary winding. As a result, we will obtain a 30 degree phase shift across the transformer that is the secondary currents and voltage will lag to primary by 30 degrees to account for the phase shift. The protection Seti's on 115 K B. Y site of the power transformer are connected in Delta, while the sea keys on the 12 K V Delta side are connected and why, therefore, the current entering the really restraint coils from 115 K V side will be equal and in fees , with the current leaving the relay on a 12 K V side, disregarding the transform orations for the moment. Unless have a look at that and see how that works. Let's follow the currents for convenience. And let's assume that the CT's matched the transformer ratios. The red face current enters the H one bushing of the transformer and we'll call that the read phase leg of the transformer. The white phase current enters the age to bushing off the transformer Wait Things leg and the blue phase Current inter ch three bushing of the transformer. These three currents set up in phase currents in the secondaries of the transformer like so So the in phase currents in the secondary winding czar in phase with the primary turns of the transformer, the secondary Our phase is made up of the some of the red phase or the current flowing out of the red phase leg of the transformer minus the blue phase. We will call that I subscript r minus B, and we will call the current flowing in the secondary of the C T. I subscript R minus be lower case in, as is the secondary side of the sea teas. Similarly, the secondary white phase is made up of this sum of the white face current minus the red phase current, and it sets up a similar current in its secondary. I w minus are the secondary blue phase is made up of the some of the blue face. Current minus await face current on the secondary, and that sets up a secondary current flowing in that C T I B minus w Moving back to the high side, we see that the our NBC T secondaries are some, and that means the current flowing in to the red phase restraint coils will be made up of i R minus B. The current flowing into the white phase differential relay restraint coils will be made up of the I W. Minus our faces and similarly, the current flowing into the blue face differential really will be made up of I B minus w. These three currents flow through the restraint coils of the really and match the like faces in the secondaries off the low voltage SETI's. As a result, we should have zero colon current flowing through the relay operating coils. Let's consider the phaser diagrams for this. The secondary read. The white voltage will be in phase with the primary red to neutral voltage as well. A secondary wait to Blue Voltage is in phase with the primary white to new Travolta. Jenna Secondary Blue to Red Voltage will be in phase with the primary blue to neutral voltage. For simplicity, let's assume a unity power factor load. Corresponding currents are in phase with the voltages. Therefore, the red face current is drawn in phase, with the primary red to neutral voltage and the white to blue currents are showing in phase with a way to neutral and the blue to neutral voltage. Respectfully. So what we're looking at here are the current phasers of the transformer, moving the drawing out of the way for now. But let's keep it visible, at least, and let's move the phasers to give us more room for plotting the results. The secondary currents of the sea tease on the high voltage side of the transformer are flowing through the red phase differential Railly, and they are made up of the some of the red, minus the blue phase currents from the sea teas. This is my matched up, with the red minus the blue phase and the low fate low voltage currents flowing through the CD secondaries. There, the secondary currents flowing through the white phase differential relay is made up of the some of the primary white, minus a red face secondary CT currents. And this is matched up with the white Linus red face of the little voltage currents. The secondary currents flowing through the blue phase differential relay is made up of the some of the blue, minus the white face, uh, currents from the SETI's. And this is matched up with blue minus white in the low voltage currents, uh, that are flowing in the secondaries of the sea keys. There. Now for clarity, we have removed all of the phasers, accept the results by rearranging the phasers. It can clearly be seen that the currents on both sides of the relay match for normal operating conditions or for false outside the protected zone. So far, we have disregarded transformer ratios. Therefore, let's look at ratio matching in order to calculate to C T ratios that are required. We know the transformer rating is 30,000 k b A, which is given by this formula, where the TV A or the the rating is equal to three times the lying to neutral voltage times aligned current. We don't know the line to neutral voltage, but we do know the line tow line. Voltage. So we will make the conversion in our formula because we know the relationship between the line to neutral voltage and the line tow line current and that gives us the V A is equal to root three times be lying the lying times, the line current rearranging the formula in order to solve four. What the line current would be at the rated TV A gives us a k v A all over route three times the line the line voltage. Now we have to be careful here of the cavey multiplier. But since we're using K B A in the numerator we can use kv in the denominator and the 1000 multiplayer takes care of itself. So on the 115 k V side the line current would be 30,000 k v a all of a route three times 115 K V, which means the primary amps flowing in the transformers 151 amps. If we choose primary si tes that is place 3 300 to 5 AM si tes one on each phase of the primary. And in fact, the these ratios have already been chosen for us so that we know that the primary CT ratios are 300 to 5. So then the current flowing in the secondaries of each one of those Seti's is the primary EMS 151 divided by 300 divided by five, which gives us 2.52 amps flowing in the secondaries of each one of the SETI's. We now know the current that would be flowing in each of the primary CT secondaries, but the currents flowing into the relay is the sum of two C T secondary currents. So let's start with looking at the blue phase differential relay. The relay sees from 100 cave 115 k V side si tes the blue face current minus the white face current, which is the blue phase current added to minus the white face current. And each of these currents we know is 2.52 amps. This would give us the are the resultant will label as I subscript B minus W, which stands for the blue phase minus the white face current looking at the triangle. We've seen this ratio before, so we know the resultant I subscript B minus w is going to be equal to root three times the white phase current. Therefore, the relay. We'll see route three times 2.52 amps, which is equal to 4.36 amps. We already know that the secondaries of the primary and secondary matching phase So now we have to make sure that the current magnitudes are equal in order to net zero flowing through. You relays operating coil on the 12 K V side using the same formulas. But this kind the landline voltage is 12 ky V. Therefore, the secondary current would be given by 30,000 TV a over three times 12 K V, which is equal to 1443 amps that are flowing in the secondaries of the power transformer lines under normal or rated load conditions we have on the secondary side of the power transformer bushing CT's and there's one for each face. So there's three of them with the multiple tap ratios of 2000 1600 1200 to 5. So if we wanted to calculate what the exact Seiki ratio should be in order to match up with the primary current flowing in the ah into the rial A. It would be the, um, the's secondary amps that are flowing in the secondaries, the power transformer divided by those really amps, which happens to be 4.36 And if we divided 1443 amps by 4.36 amps, who that would tell us we would like to have ah CT ratio of 330.9 six toe one or 1655 to 5 . However, we don't have that luxury of exact ratios of the current transformer. We've been dealt with ah ratio. That's the closest one is 1600 to 5. So that's the one that we would pick. And that would give us our best fit, the relay settings that would then be calculated and calibrated in order to give us enough leeway that the 1600 to 5 tap ratio would work. So this ends Chapter six. 9. Ch 07 Transformer Relays: Chapter seven transformer relays. In this chapter, we're gonna look at various assortment of relays, both old and new. Uh, we're not going to spend a lot of time on the older installations, although you will find out there that they're still existing. Ah, lot of the older type relays because they're still functioning and still working fine. And they still protect the transformer. However, we are also gonna show you some relatively new transformer relay center called I E. D's or the intelligent electrical devices that are basically computers that work extremely fast and provide a multiple of functions for protecting the transformers. We're also gonna look at the oil flow, protection the buckles, really towards the end of this chapter, which is used in most of the oil immerse transformers that are protected and in today's protection schemes, this is an example of a three phase or a three element restraint differential relay. It's the CIA or Brown Bovary. What if she waas when in her first key mode? Ah d 21 s e used to protect a to winding transformer. It's definitely old school, but there's still a lot of them in existence today, so we will have a quick look at one of them. Right now, I've highlighted here what is considered the would be considered the red phase operating and re strained coils for this relay being fed with SETI secondaries from the high side and the low side of the transformer. This shows the white phase operating and restraint coils being being fed from the hi side and the low site of the transformer. And this is the operating and restraint coils for E high voltage blue phase side of the transformer. Andy Blue Phase Louisville each side of the transformer. Each of these operating coils will pick up a high speed contact that is designed to bring in the 110 or two full to up to 2 40 volts. DC. Control. Tripping the mechanism for any breakers that would be required to isolate the transformer, and this will pick up in eggs Ilary relay with multiple contact outputs. It's simple and effective and carries out the function of a restraint differential. Relate an intelligent electronic device, and I E. D is a term used in the electrical power industry to describe microprocessor based controllers for power system equipment. IED's received data from sensors and power equipment and can issue control commands. Such a stripping circuit breakers if they sense portage currents or frequency anomalies or raise and lower voltage levels in order to maintain the desired level. Including included in the realms of I e DS are the modern protective reeling devices. Some recent I E DS are designed to support the I. E. C 61 8 50 standard for substation automation, which provides interoperability and advanced communications capabilities in utilities and industrial, electrical power transmission and distribution systems. A digital protective relay is a computer based system with software based protection algorithms for the detection of electrical faults. Such relays are also termed as microprocessor type protective relays. They are functional replacements for the Electromechanical protective type release and may include many protection functions in one unit, as well as providing metering, communications and south testing functions. The digital numeric relay was invented by Edmund O. Schweitzer in the early 19 eighties. SCL, Areva and a BB groups were early forerunners, making some of the early market advances in the arena. But the arena has become crowded today, with many manufacturers in transmission line and generator protection by the mid 19 nineties, a digital relay had nearly replaced a solid state and electromechanical relays in new construction in distribution applications. The replacement by the digital relay preceded a bit more slowly. While a great majority of the feeder relays in new applications today are digital assaulted , State Relates still sees some use where simplicity of application allows for simpler relays , which allows one to avoid the complexity of digital relays. The progress and enhancement of these relate changes happens continually, and as such, the following examples have already been improved and additions made. However, the basics air still there and even know newer versions are available. These examples will give a good idea of what is out there and what happens. It has happened in the way of I e DS for transformer protection today. Transformer differential protection relays in used today are more advanced and usually part of a multi functional really, so they are often referred to as transformer management relays. The relays air microprocessor based and commonly referred to as intelligent electronic devices or I E. DS. Examples of these transformer management release that we'll look at are the G Multi Lin, s. R. 7 45 the seaman's seven U T 51 and the mike on P 6 32 Now these air only three of a multitude of relays that are out there on the market and certainly internationally you'll find even Mawr. However, these ones are good representation of what is out there today. And with technology changing as it does, these devices are changing very rapidly in themselves. However, if we look at these three samples, they'll give us a good idea of what the I E. D type real ace function as and what they're capable of doing out there in the way of transformer protection. Compensation for the transformer primary tap changers also accounted for when applying relay set points. Harmonic restraints is provided and addresses the problem of false stripping for magnetize ing in rush current. During transformer energy ization, the relay settings are entered using applications. Software run from a computer, usually a laptop. Um, that's ah, brought into the field. In general, you can create a new relay setting files from scratch, or you can modify existing settings and send them to another. Really, let's take a closer look at one of these relates and we're going to start out with the G. Multi Lynn S. R. 745 The 7 45 transformer protection system is a full featured transformer protection really suitable for applications on small, medium and large power transformers. The 7 45 can be applied to two winding and three winding transformers. Multiple current and voltage inputs are used to provide primary protection, control and backup protection of transformers, including current differential restricted ground fault neutral ground over current over flexing and on load tap changer compensation. The 7 45 also includes analog inputs and outputs, while incorporating advanced features such as transformer, loss of life monitoring for protection and control. The 7 45 has variable dual slow percentage differential protection magnetize ing in Russian over excitation blocking phase and ground over current elements. Adaptive time over current using flex curve elements under frequency and over frequency protection, frequency, rate of change, detection over excitation protection, restricted ground fault protection and transformer overload protection. This really as well as most modern IED's come with communication capabilities that include the network interfacing Rs 2 32 in Rs 45 RS for 22 ports. It has an Ethernet port, Uh, for sample rates of the 10 megabits per second and uses multiple protocols. Mod Bus, Archy, you mob us, our Q, t, c, p, I, P, D, N, P and, uh, several others remove communications to a DAX or a skater or a PLC type system and its design or designed to allow simultaneous communication via all ports along with the protection and control features. This package also includes smearing of current voltage sequence components per winding power and energy. It also tracks third harmonic Distortion and the other harmonics up to the 21st. It is also in events recorder. It will also attract the top positions of a on top changer transformer up to 50 top positions. It will also record the ambient tent temperature using an analog input, and it also has a analog transducer inputs for other functions. It also has a built in a Silla graph and data logger to track any events that need to be looked at after the fact. This really has its own software, its trademark registered called Inter Vista software that includes sophisticated software for configuration and commissioning. It's got a graphical lot logic designer with the logic monitor that simplifies designing and testing procedures. Ah, it has documenting software for tracking and archiving information, and it's easily integrated data of the 7 45 into new and existing monitor and control systems that are being developed out there. This is the functional diagram for the relay. Ah, it may appear a little bit confusing because each one of the function numbers associated with the end one of the individual three wind ings of the power transformer, are prefixed with that with a 12 or three, depending on the winding that's associated with. For example, winding one. The prefects on the functional numbers is one for winding to the prefects. Number is to and for winding through the prefects numbers. Three. So if you just remove those winding numbers, it becomes a little bit more obvious. Uh, the standard, uh, functional numbers are as listed here on the diagram. As you can see, it pretty well covers the entire spectrum of protection that's required for the transformer and then some. The 7 45 offers percent differential protection and features the equivalent of three single phase differential current relays. Each has dual slow percent differential with second and or fifth harmonic restraint to protect against Mel operation due to magnetize ing in rush current during transformer energy ization and over excitation. Each differential element has a programmable dual slow percentage restraint with adjustable slope break points. The 7 45 can be used to provide backup protection for transformer and adjacent power system . Equipment instantaneous over current elements can be used to fast clear a severe internal fault or external through faults timed over current protection elements per winding allowed to coordinate with the Jason protected zones and actors of backup protection. Time over current protection functions are provided for phase and gravel currents, a variety of standard time current curs and defined times are provided flex curves to coordinate with the adjacent protections, including fuses while it's transformer damage occurs and thermal damage curves for downstream equipment. Additional features for the 7 45 include negative sequence over current. For Delta y impedance, grounded transformers over current protection is particularly difficult to set. A negative sequence based over current element provides the required sensitivity dynamic CT ratio, Miss Mismatch correction accounts for various variations in on load tap changer positions. Top positions are monitored in SETI ratios are corrected accordingly automatically for over current and under frequency protection. A 7 45 calculates and maintains a running average of the system frequency and the frequency rate of change two under frequency and four rate of change elements are provided to implement traditional and advance loadshedding schemes. Additionally, an over frequency element can be used to trigger a generator. Ramped out analog inputs, which are optional, include seven transducer output channels, allowing individually programmed outputs for ranges of 0 to 1 million. AP 0 to 5 million amps, 1 to 10 million amps, 0 to 20 millions and 4 to 20 million channels are assigned to any measured parameter. All feed in Seiki Zehr connected in a Y configuration for simplicity, then all phases and magnitude corrections as well. A zero sequence current compensations are performed automatically based on a choice of over 100 transformer types. The loss of life feature provides an estimate of how much the transformers total insulation life has elapsed based on I Tripoli Standards Guide for Loading Mineral Oil, immersed Transformers and guide for loading, dry type distribution and power transformers. Now let's look at the Seaman's seven U t 513 Some of the features of the seaman's seven U T 513 include short circuit protection for two and three minding transformers, restraint gearing in rush over excitation and Seiki saturation, short circuit protection for generators and motors overload protection with thermal characteristics to stage definite timed inverse and time over current protection, a restricted earth fault protection and definite time over current protection and direct injection of two external open commands. It also features a real time clock and permanently stored operational and fault indicators in the event of auxiliary voltage failure. Substation Control Interface has also a commissioning age aid for setting up new installations, and it is self monitoring for internal false. The seven U T 51 could be accessed using the Digs E operating program on a compatible PC front connected to the relay or the substation control interface can be a fiber optic interface or AH standards substation control system interface. Alternatively, this can also be an isolated interface using Rs 2 32 C with the seaman's seven U T. 513 relay. All CT inputs to the relay are connected in why, regardless of the power transformer, winding configurations and secondary phase shifts. This is because the vector group compensation is accomplished mathematically within the relay itself. Matching of the C T ratios between the primary and secondary power transformer wind ings is accomplished within the relay settings. The actual C T taps should be selected to produce approximately the same secondary relay current. The relay has three main sets of three phase C T inputs and a capability of having two additional single phase neutral CT inputs. The user defines which winding czar reference to the primary and secondary winding of the transformer. The single phase inputs are used for restricted gala fault and ground over current protections. The relay contains two independent thermal over current elements that can be associate ID to any of the three face ET inputs. These elements model the actual thorough behavior of the protected wind ing's. In addition to the transformer protection, the seven Youth P 513 is designed for application on bus differential protected zones. The relay has various techniques to recognize CT saturation. This really also has five discrete binary inputs that are used to bring the status of external physical contacts into the relay the relate contains an internal lithium battery that is used to maintain the state of alarm indications and a real time clock and calendar through a D. C. Supply interruption. If indeed it happens, this really has fast clearance for heavy internal transformer false. It also has a restraint of in Rush current, uh, recognizing second harmonics. It's restraint against over flexing with the choice of third or fifth harmonic recognition . Additional restraint for external faults with current transformers that saturation and the differential protection function can be externally blocked if required and just out of interest. This is how the seaman's seven U T 513 is connected to the system. The my calm relays, the last one would we'll look at very quickly. The p 63 Siri's provides high speed tripping three system deferential protections using a triple slope characteristic and too high set differential elements in combination with transformer in rush restraint over flexing restraint and through stabilization, amplitude and vector group matching is done just by entering the nominal values of the transformer linings and the associated Seti's. It has numerous integrated communication protocols to allow easily interfacing to almost any kind of substation control or skate a system. The integrated protection interface of the Inter My com provides direct and and communications between two protection devices. The following functions are generally available on all P 63 Siri's relays parameter subset selection for alternative setting groups meeting operating data recording overload, recording and overload, data acquisition and fault recording of all C T and VT inputs and binary events. And these are the My columns P 6 32 functions. Uh, protection wise, it has differential protection, Restricted Earth fault protection. It has definite time over current protection as well as in verse time over current protection. It has thermal overload protection over and under old, each protection over in under frequency protection over excitation protection. And it's also capability of using or, uh, having a circuit breaker failure protection built into it as well as well. We have, ah current transformer supervision me measuring circuit monitoring limited value monitoring program, biologic functions. They have measuring units for phase currents and residual currents and voltages, and several other options, including the communication interfaces that are standard that are out there. And it is also capable of, uh, interlocking with the i e. Sees 61 8 50 interface, not necessarily going into it in detail. But this is the functional diagram showing the functionality for all of the P 63 Siri's monitoring relays. This is the tripping characteristic of the differential protection, which has two knees. The first knee is dependent on the setting of the basic threshold value, which is, uh, indicated as I d. In the diagram the My Calms p 63. Siri's differential protection devices are provided with a saturation discriminative discriminator that allow for such things as the startup of directly switched a synchronous motors that could cause transient transformer. Separate saturation restraint under in rush conditions is based on the presence of second harmonic components in the differential currents for restraint under over flexing conditions. The ratio of the fifth harmonic to the fundamental wave for the differential current of the measuring system serves as the criterion zero sequence set filtering may be deactivated separately for each winding in case of an operational grounding within the protected zone. Information exchange is done via the local control panel, the PC interface and to optional communication interfaces. The first communication interface has a setubal protocols conforming to the standard mob boss and courier connections and is intended for integration with substation control systems. The second communication interfaces intended for central settings or remote access clock synchronization can be achieved. Achieved using one of these protocols or using a standard external input signal. So this has been a very brief look at three examples of the modern type I E. D relays that are out there. Um, it was certainly not intended to fully cover all of the aspects of the relays. I would take a lot longer to do, and it certainly wasn't intended to be a sales pitch for any of one of the three manufacturers. It was intended solely for a quick glance at what is out there. And what is the capability of these relays in today's day and age. The last protection device to be discussed in this chapter is more mechanical than electrical. At least the initiating variables, pressure and flow are measured mechanically. This really measures the rate at volume of gas accumulation in an oil immerse transformer. It was developed by Max buckles in 1921 and since has been known as the Buck holds relay, which has been applied to large power transformers. Since UH, about 1940 it has, uh, being slightly modified over the years. But essentially, the basic principle of operation has remained unaltered. The buckle to really is located in the oil line that connects the conservative tank in the main transformer body. This position of the relay above the main tank will accumulate any and all gases that are formed and rise in the transformer. Also, any pressure surges that occur will pass through the oil connection line on the way to the conservative tank. The buckles really usually has two elements that monitor number one gas accumulation, which is made up of afloat, and some kind of position activated switch. In this case, it shows a mercury switch, which in the more equal friendly designs of today, can be a possibly a reed relay acted upon by a moving magnet. The second element measures gas pressure change, which is made up of a moving diaphragm and again, some kind of position activated switch, a mercury switch or the more equal friendly reed relay. For the time being and for simplicity, let's assume that the mercury switches being used in both cases under normal conditions. There is little or no gas in the buckles relay, and the float keeps the mercury switch open on a slow accumulation of gas. Due, perhaps to slight overload. Gas is produced by decomposition of the insulating material as well as the oil. These gases will slowly rise in the transformer and accumulate in the top of the relay. As more and more of these gas bubbles collect, they will force the oil level down in the relay. The float switch in the relay will close an initiate an alarm signal. Depending on the design of the buckles relays, there could be a second float, and it will detect or is designed to detect slow oil leaks in the oil in the oil of the transformer. And if the oil level drops too low, and in this case it would initiate a trip of the transformer. If an arc forms, Gas accumulation is rapid and oil flows rapidly into the conservative tank. This flu of oil operates a switch attached to a vein located in the path of the moving oil . This which normally will operate a circuit breaker toe, isolate the apurate apparatus before default causes additional damage buckles. Relays have a test port to allow the accumulated gases to be withdrawn for testing. Flammable gases found in the relay indicate some internal faults, such as overheating or our king, whereas air found in the relay may only indicate low oil level or a leak. Dissolved gas analysis or D G. A. Is the study of dissolved gases in transformer oil, insulating materials within transformers and electrical equipment breakdown to liberate gases within the unit. The distribution of these gases can be related to the type of electrical fault, and the rate of gas generation can indicate the severity of the fault. The identity of the gas is being generated by particular units can be very useful and this information is useful in the preventive maintenance program for the transformer. The collection and analysis of gases in an oil insulated transformer has been done as early as 1928. Many years of empirical and theoretical study have gone into the analysis of transformer fault gases. DJ A usually consists of sampling the oil and sending a sample to a laboratory for analysis . Mobile DJ A units can be transported and used on site as well. Some units can be directly connected to the transformer. Online monitoring of electrical equipment is an integral part of some of the transformers. Transformer oil is used to cool and insulate the internal components of a transformer because it be's every internal component. The oil contains a great deal of diagnostic information. Justice Blood tests provide the doctor with a wealth of information about the health of a patient. A sample of transformer oil can tell a great deal about the condition of the transformer. The oil analysis is broken into two parts. Physical, electrical and chemical tests can be a value. Can evaluate oil for indicators of die electric insulation breakdown, power factor, inter facial test attention and, as city in color, dissolved gas analysis or D G. A looks for certain gas quantities and combinations that can determine the likely failure mode. Here are some of the gases that could be found dissolved in the transformer oil and their possible causes to be prevented. Hydrogen indicates partial discharge or corona. Inside the transformer methane presence indicates overheating and a settling would indicate our king presence. Inside the transformer after leading would indicate the most likely failure to be in localized overheating, where ethane would indicate a general overheating of the unit. Carbon monoxide indicates cellulose overheating, which would be the wrapping. Insulation on the findings itself could be breaking down, and carbon dioxide would indicate that the oil and or cellulose would be overheating. The ability of insulating oil analysis provides an early warning sign of a problem condition and is dependent on the quality of the oil samples that is sent to the lab. A sampling point on any equipment should be identified and clearly labeled. The same location should be used each time a sample is collected to ensure representative conditions are tested. This point should be located in a place where they live. Oil sample is active rather than in an area where the oil is static. Fluids with specific gravity greater than one should be sampled from the top because free water will float for fluids with specific gravity less than one, such as mineral based transformer oil, synthetic fluids or silicon oils, the sample should be taken at the bottom. Since water will tend to drop to the bottom of these fluids, there are a number of environmental variables, such as temperature participant, precipitation, etcetera, to consider before collecting a sample. The ideal situation for collecting a sample from an electrical apparatus is 90 F or 35 degrees Celsius or higher 0% humidity and no wind would be very helpful. A swell cold conditions or conditions where relative humidity is an excess of 70% should be avoided as this will increase the moisture in the sample. Collecting a sample during windy condition is also not recommended because of dust and debris that could enter the sample easily and destroy and disrupt accurate particulate counts. If sampling the oil is unavoidable when the outside temperatures are at or below 30 due to 32 degrees fair nights or zero degrees Celsius, it should not be tested for water content or any properties that are affected by water, such as die electric breakdown. Voltage for dissolved gas analysis and elaborate procedure must be followed, including the use of glass syringes with strict adherence to sampling protocol to ensure that the concentration of dissolved gases is not influenced in any way by the sampling procedure and this ends Chapter seven