Chapter Four, a three phase per unit analysis and transformer configurations. We are now going to look at per unit analysis as it applies to three phase circuits. And there's nothing different about three phase circuits compared to single phase circuits other than the fact you have two other phases to worry about. What you have to keep in mind though is that these three phases are phase related and we'll talk about that in in a few minutes. In three phase systems, usually the voltage is given in line to line voltages and you can switch back and forth from line to neutral in line to line voltages but usually they are given in line to line voltages. transformer ratios are always given in terms of line to line voltages.

Regret arlis of the connections of those transformers and you have to keep that in mind because that's one of the powers of using per unit analysis and we'll talk more about that a little bit later. And the line currents are simply the current that's flowing in each of the lines. apparent power when it's mentioned or given in a three phase system is usually always three phase power as opposed to single phase power. In single phase, apparent power, the magnitude of a single phase, apparent power is given by the line to neutral voltage times the line current or talking about magnitude here. In a three phase system. It is three times the single face value And because of our phase relationship in a balanced system and where we are talking about balance systems here, we can replace the voltage line to neutral with line to line voltages.

So that this equation would look like this. three phase power is three times a single phase power. And in replacing the line to neutral voltage with line two line, we have to divide by root three. So the equation for three phase power is three times the line two line voltage times over root three times a line current. And of course, root three divides into three once so your equation now will be root three times a line two line voltage times the line current. Let's look at this in a slightly different way with a different graphic that we'll look at Explain the equations just a little bit better in a three phase system that has a load and we'll look at the load is connected in a Wye configuration as well as the generation.

So we have three single phase generators feeding, why connected load, we can do a per phase analysis of this three phase system quite easily. And we can find the single phase apparent power that's delivered to the load by looking at the line to neutral voltage and the line current, which essentially is a single phase circuit. And the line to neutral voltage is indicated there. It's just the voltage of the red phase generator to neutral. And it's the red phase current that's flowing through the red phase load. That will, if you're going to calculate the apparent power is just simply the line to neutral voltage times the line current and we're talking about magnitudes here.

We're not going to worry about The the phasor, really the phasor representation at this point in time, we're only talking about magnitudes. So now we can add the other two phases. And that doesn't change the line current or the line to neutral voltage, it's still flowing, what is changed is the fact that the return current isn't going through neutral because it's a balanced load, it's returning on the other two phases. But since we've added two more phases, we've added two more per phase systems which again, will dissipate each one of them single phase apparent power, and it's a blue phase and we will call it a white phase, but it's indicated in green because, again, White can can be demonstrated to well on a white background. So the actual total apparent power that's dissipated in a three phase load is three times single phase apparent power of each face.

Now, we know that the system is a balanced system. So there's a phase relationship between line to line voltage and line to neutral voltage. And that is aligned in line voltages is equal to when divided by root three is equal to the line to neutral voltage. So we can replace the line to neutral voltage in our equation with a term, line two line voltage over root three, but we're multiplying it by three because there's three separate phases there. And if we divide both sides of or the numerator and denominator, or I should say we should multiply both the numerator and denominator by three or sorry, root three, then the the three in the numerator and denominator will cancel out and you're going To be left with the fact that the three phase apparent power is going to be given by root three times the line the line voltage times the line current.

With these equations and relationships in mind, let's now take a look at the normalization process once again. And this time, let's keep in mind that it's a three phase system that we're doing the normalization process. And the the steps are exactly the same as it as a single phase system. The only thing is you have to keep in mind that we're working in a three phase system. So the first thing you're going to do is specify a VA base and again, that's arbitrary. You can pick whatever number you want and whatever number you pick, it is a magnitude only or a scalar quantity.

It has no direction. Normally VA is given with a magnitude in a direction or a quantity at an angle, and the the base value is simply a quantity. And that's the same as what happens in a single phase system. And the same thing happens in three phase system. Now, the three phase bass that you pick, once you've picked a bass quantity, you have to designate whether it's a three phase bass, or a single phase bass because in our previous couple of slides, we determined that the apparent power, three phase apparent power is three times the single phase apparent power. So once you've picked a VA base, you have to specify is that VA bass, a single phase bass or is it a three phase bass.

Once you said one, you've already said what the other is. And base values of real power reactive power and complex power in this system, as it does in a single phase system have the same base values. So what we're seeing is the base value for three phase power is the same as a three phase base for a parent power. And for reactive power, the base is also the same. And these are also equivalent or have to be mentioned, and in regard to whether it's a three phase bass or a single phase bass, the same relationships hold true. So the next step that we're going to do is we're going to determine or pick a voltage base and like a single phase system.

Voltages that are based values do not have any direction. They are magnitude only. So they are only the quantity and they have volts but they they're a mat. They're a scalar quantity, you don't have any direction. And the other thing that's very important is once you've picked the voltage base, that voltage base can either be line to line voltage, or single line to neutral voltage, single phase or three phase reference if you would, if you would. However, once you've picked your base voltage and you have to designate whether it's line to neutral or line to line voltage, then your line to neutral base is equal to the line two line base divided by root three So, if you pick 230 kV as your line two line base, then your line to neutral base is going to be root three times that.

So, bottom line is you're allowed to pick one voltage base and then your three phase and single phase or line to neutral line two line voltage bases are related in this fashion, a very important concept. Now, the other thing that was mentioned or stated and as important in single phase voltage based selection is the fact that there is a voltage base for each and every voltage level in the system. So here you have a three phase transformer, that y to delta and the transformer is rated and listed as a two 30 kV to 115 kV transformer. The other thing that is extremely important to remember that transformer ratios are given and stated as a standard as line to line voltages doesn't matter whether it's a Wye connected transformer or a Delta connected transformer, the ratio of that transformer is stated as line to line voltages, a very important fact.

Once you start to work with per unit systems and you'll see that the configuration is taken into consideration automatically, and we're going to talk about more of that later. But for this particular point, you have to remember very important that the lines to neutral voltage is base voltage is equal to the line to line base voltage divided by root three and there is a voltage base for every voltage level in the system and transformer voltage ratios are given as line to line voltages. Okay, we're gonna look at step three of the normalization process and it might look pretty familiar to you because it's identical to the single phase process and that is we're going to determine the impedance bases and the current basis, but we've already selected the VA and the voltage basis so that we've automatically set what the impedance base and current bases are because they are calculated from the VA and the voltage basis.

Looking at the current base, first it I base is equal to in a single phase system Base all over V base and that voltage has to be line to neutral if we're talking about a single phase quantity. Now, we know from our phase relationships as we just looked at that we can replace the single phase s base and the line to neutral base with a three phase quantity and a line to line voltage quantity. Because the single phase s base is one third of a three phase base, so we can substitute the S base in the numerator with three phase s base divided by three. And in the denominator, we can replace the line to neutral voltage with the line to line voltage but we have to divide by root of three. Now we can mathematically shift this equation slightly to get rid of the multiple division signs and we are left with root three times the three phase space all over three times the voltage line to line base.

Now we'd like to get rid of Have some of the complexity of this of this equation. And we do that by splitting the three in the denominator and replacing it with root three times root three, which is the same thing. But in doing that, we're able to eliminate the root three in the numerator, and we're left with only root three in the denominator, which means the I base can be described in terms of three phase base quantities and the line to line voltage base quantity. So it's the eye base is equal to three phase s base, all over root three times the line to line voltage base. Let's look at the impedance basis now. And again, we'll start with the single phase equation and the Zed base.

Or impedance spaces given by the line to neutral voltage all over the line current, we can replace the line current with the term, s base all over V bass line to neutral, but I've done two steps here and converted that over and the the S base all over the line to neutral voltage base flips a another line to neutral voltage base into the numerator. And if you take those two together, you're going to be squaring them. So, the Zed base or impedance base is equal to voltage squared all over s base and we discovered that equation in our single phase study of the base quantities. Now we can as I said before, we are working in a three phase system and usually in a three phase system. quantities are given to you as a line two line voltages and three phase apparent power. So we're going to replace the single phase or the line to neutral voltage components of this equation with their line to line voltage and the the three phase, Espace quantities and we just make the substitution, but we have to divide the line two line voltage by root three, and we have to divide, divide the three phase s base quantity by three and that equation, then we'll simplify to one third times the voltage line to line base squared, all over one third, the S base which is three phase three phase quantity in the denominator, and of course the two one thirds will cancel out.

And that will leave us with the impedance space is going to be equal to The line two line voltage squared all over the three phase, Espace quantity. I'm going to leave this slide up just for a couple more seconds because it is a very important slide when you're working in the per unit system, especially when you're doing the normalization process. These equations whether you're working in a single phase system or a three phase system, these are the equations that you will have to know and if you don't memorize them, and I don't suggest that you run around memorizing them, but at least make sure you keep them handy, because you are going to want to refer to them when you are trying to calculate your current basis and your impedance bases and indeed, the switching back and forth from three phase quantities to single phase quantities.

So keep these in equations handy, especially when you're working in a per unit system. The next two and final steps in the normalization process are the same as in a single phase system. The next step, then step number four, is we're going to calculate the per unit quantities in the system. And you can calculate a per unit quantity by taking the actual value and dividing by its equivalent base value. What you have to be careful of here though, is whether you're talking about single phase or three phase, whether you're talking about line to neutral voltage, or line to line voltage, you have to pick the right value to divide by, and all you have to remember is whatever that actual value is, you're going to choose an equivalent base value. So if it's at line to neutral voltage, you're going to find a line to neutral base.

Voltage to divide by, if it's a line to line voltage, you're going to use a line to line base value. Bottom line, the per unit value is calculated by taking the actual value and dividing by its equivalent base value. For each component, its actual value may be found by multiplying its per unit quantity by the base value for that quantity at its connection location. And that is given by the actual value of the quantity is equal to the per unit times the equivalent base value of that quantity. And again, you have to make sure that you're multiplying by the correct base value, which depends on whether you're talking about line to neutral or line to line quantities or your Talking about three phase or single phase quantities. And you also have to be aware of which zone you're talking about, depending on the number of Transformers that are in the system that you're analyzing.

There may be more than one voltage base that you have to worry about. And consequently, there may be more than one impedance base and there may be more than one current base. So you have to know where you are in the system. And you want to know exactly which value that you're dealing with line to neutral line two line or single or three phase quantities. Transformers, especially three phase Transformers can be very mysterious and difficult to deal with, unless they're broken down into a very simplistic approach, which I'm going to try to do in the next few slides. Three, phase two Transformers whether they're three individual Transformers or a bank, that is a three phase transformer bank, electrically, they can be considered as three individual transformers.

And they are characterized by two things one, the the type of voltage that excites them and their connections one to the other. For example, you could have phasers, red, white and blue phasers. And again, I'm going to call the one that's shaded in green as a white phaser. Because if I drew it in white, you wouldn't see it. So, these if you look at these individual transformers, they are excited in this diagram by voltages that are out of phase with each other, but it doesn't really matter because the transformers are not connected to each other. However, once we do connect these Transformers to in some fashion, then the vectors take on a whole other nature.

For example, the primary of this these three transformers are connected in what we call a Wye connection, which essentially pins the tails of the phasers together. So that now we have to consider these vectors in this manner. Now these vectors are in a three phase system 120 degrees apart. And in a balanced system they're they are equal in magnitude and rotating counterclockwise. So let's continue with this connection. And in this case, we're going to look at what we call a star star or a why why connected transformer bank we've already had a look at the Primary side of the transformer and the three horizontal lines red, white and blue are essentially could be considered a red white and blue bus in a say a transformer station.

However we connected the primary is up in this fashion and if we designate the primary connections on the Transformers as h1 and h2, this is the phaser that would designate the voltage between h1 and h2. carrying on with the white phase connection, you will see that h1 and h2 are connected like this and carrying on with the blue phase h1 and h2 are connected like this. So we have a star connected transformer. Hence, this is why the The system is called Star connection or a Wye connection because it it the phasers when connected on their h two terminals form a star or a Wye connection. So these phasers are equal in magnitude and 120 degrees apart and rotating counterclockwise. So if we were to look at the secondary of this transformer, the secondary of the transformer is also connected in star or y.

And it's connected to a secondary bus if you would, and the terminals of the transformer are connected to the secondary bus in this manner and I've written the red white and blue in in non capital letters so we can differentiate it from the primary. You'll also notice in the Transformers that I've put a.on, the transformers and that designates the polarity of the transformer. Now, the x one and x two terminals of the transformer are connected like this the phasor is shown in our diagram for x one and x two and the read phase and because the read phase in the primary that capital our phaser is magnetically linked to the secondary salt small our side of the transformer it is magnetically linked So, that the phaser the voltage induced from the primary to the secondary has to be in phase or the primary voltage has to be in phase with a secondary voltage because they are magnetically linked.

Similarly, if we look at the white phase on the secondary side the actual x one and x two terminal because the secondary of the white phases magnetically linked to the primary red h1 h2 terminal, then the x one x two terminal has to be in phase because they are magnetically link. Similarly, with the blue phase you have an x one x two terminal and because it's magnetically linked to the primary side of that transformer, then it two is going to be in phase. So the three primary voltage phasers and the three secondary voltage phasers are in phase with each other in a star star connected transformer. You'll notice that the common connection on the primary side the black line is called is connecting the h2 terminals of all the coils and that is called The neutral of the connection on the primary side. Similarly, on the secondary side all of the x two terminals are connected together and they form a secondary neutral connection.

Now, these connections may or may not be grounded, they very seldom are connected one to the other from the primary to the secondary side. But suffice it to say for now, these are just the neutrals associated with the primary coils and a neutral associated with a secondary coils. I want to look further at this star star or why why connected transformer and I want to be able to find out what the per phase equivalent circuit would look like. And ultimately I want to find out what the per unit equivalent circuit would look like because I going to want to work in per unit values when I'm solving the equations in our circuit. If we look at the phase two phase values, looking at the phase two phase voltages on the primary side, the phasor is shown here in the diagram, and it's labeled red to white on the primary site.

Looking at the secondary side, the phase two phase voltage is designated as red to white in lowercase letters. And it looks like this, as I've indicated on the diagram. We've already had a look at the primary voltage relationships and we know that the red to white or voltage on the primary side will be leading the face to neutral voltage by 30 degrees. So that the equation would be for the phase relationship on the primary side is the rental white voltage is equal to root three times the rent to neutral voltage. And it's leading by 30 degrees. And actual fact, all three phases have the same relationship.

So rather than just designating the equation in terms of the red and red to white voltages, we're going to say the voltages line to line are equal to root three times a voltage line to neutral times 30 degrees. The secondary voltage relationship is the same. You can see that the red the white voltage leads the red to neutral voltage by 30 degrees, and it is its magnitude is root three larger than the red Neutral voltage. So the red white voltage is equal to root three times the red to neutral voltage times 30 degrees. And again, the phase relationship for all three phases are the same. So we can say that the line the line voltage is equal to root three times aligned to neutral voltage times 30 degrees.

Now if we look at the turns ratio of the transformer, the turns ratio is given by the primary line to neutral voltage all over the secondary line to neutral voltage in this particular connection, I'm going to designate the turns ratio with the lowercase letter A. And that is equal to if you look at our connection diagram, the red transformer the red primary voltage over Read secondary voltage is also equal to the turns ratio of the transformer, as is the white primary over the white secondary, and the blue primary over the blue secondary. Now, the primary voltage line to neutral over the secondary line to neutral voltage can be expressed in in terms of the line to line voltages, but we have to divide by the root of three. And I've indicated that in our in the equation here, and we'd like to simplify that equation. And we can do it by getting rid of some of the division lines and remaining with one doing a trick called cross multiplication as they do in mathematics.

You can see that the root threes actually cancel Load in the end, so, that the turns ratio of the transformer can be expressed in terms of the line to neutral voltage over the line to neutral voltage or the line to line voltage over the line to line voltage whether you're talking primary or secondary. So, it is the line to neutral voltage over primary over the line to neutral voltage secondary the primary line to line voltage over the secondary line to line voltage. If I wanted to do a per phase analysis of a system involving this transformer bank, I would be looking at one phase and one phase only. So, the per phase equivalent circuit would look like this where we have one transformer or a single phase transformer and the primary voltages of voltage on that track. from A to B, the line to neutral voltage and the voltage on the secondary be going to neutral voltage.

And those voltages are related by the turns ratio such that if I want to calculate what the line to neutral voltage was reflected onto the primary side, I would have to multiply by the turns ratio. Now, the turns ratio is also related to the current that's flowing in a transformer. However, it's the inverse of the voltage so that the turns ratio would be given by the secondary line current over the primary line current. Which means, if I had the primary line current, I wanted to calculate what the secondary line current was, I would have to multiply by the turns ratio. Now, as we want to move or we do want to move from per phase equivalent to a per unit equivalent circuit, we have to start to convert All of our values two per unit values and in doing that, we would have to establish voltage basis.

And in this single phase transformer we have two voltage basis because we have two voltage levels. We have a voltage level, we'll call it a green zone or V base one on the primary side of the transformer. And we have another voltage zone we'll call it v base two on the secondary side of the transformer and we have two voltage basis. Now, if we do convert all of our system quantities to per unit values, then we essentially remove the transformer and transformer ratios from the circuit. So our equivalent per unit circuit would look like this, which is just two wires straight through. We don't have to worry about the turns ratio of the transformer at all and the zones would still be established on our diagram there would still be voltage base one and that could be line two line voltages and voltage base two which could be a line to line voltage base as well because the line to line voltages are the same ratio as a line to neutral voltages.

So you could use either one of them for your voltage zones. However you have to be aware of when you're coming out of per unit calculations that you use the proper base voltage if you're going to want to use the line to line voltage basis and come out of per unit values. You will have line to line voltages when you come out. If you're using line to neutral values, when you come out of it. He will have like two neutral voltages and In the per unit circuit itself, the voltages regardless of which zone you're in, are going to be equal because the per unit values are equal. It will make a difference when you're converting your per unit voltages to actual voltages.

But when you're working in per unit, they're the same. And similarly, currents are also the same because their per unit values. If we had impedances for this transformer, and we were working in the per phase equivalent circuit, we'd have to be aware of what side of the transformer you're on, because it would make a square of the turns ratio difference to the impedance depending on what side of the transformer you're talking about. But in the case of per unit impedances, because impedances are equal on on both sides of the transformer It doesn't matter which zone you're in the per unit impedance of the transformer will be the same. In the delta delta transformer, the primary terminals are connected to a bus that is carrying red, white and blue voltages. The red white and blue voltages are equal in magnitude and 120 degrees apart and their phasers are shown in the upper right hand corner.

The transformers are going to be named as we go through them, but I'm going to refer to them as we go through as red colored, green colored and blue colored being Red, Green for white and blue for blue Of course. Now the red colored transformer is connected to the red and white bus voltages. So it's called the red to white transformer and its terminals h one and h two are connected to the red phase bus and the white phase bus forming a vector or a phaser. As you see in the upper right hand corner, the green transformer is connected to the white bus terminal or the bus phase and the h2 is connected to the blue bus phase. Hence, the vector or phaser for that coil is shown in the upper right hand corner and its h1 terminal is connected also to the h2 terminal. The blue face or the blue color transformer is called the blue to red transformer and it's h1 terminal is connected to the blue bus voltage and its h2 terminal is connected to the red bus voltage.

So it forms a triangle or a Greek letter Delta type formation with its phasor diagram, hence the name Delta transformer and this is how the primary is connected to the red white and blue bus voltages. Looking at the secondary of the transformer, the secondary coils have to be in phase with the primary coils. That is to say if we're looking at the red colored transformer, the secondary coil of the red color channel transformer has to be in phase with the red to white voltages. The white or the green colored transformer has to be in phase with the white to the blue primary coil and the blue colored secondary coil has to be in phase with the blue to red on the primary side as well. The reason for that is they are magnetically linked so the secondary coils will be energized with a voltage that's in phase with the primary.

Hence we're going to call those coils red to white, white to blue and blue to red. Now, they are connected in a similar fashion as the primary which we will call a Delta Connection. And we'll go through those connections right now. The red to white coins The x one terminal is connected to the red phase boss, the x two terminal is connected to the white phase bus. Now as I said it's its voltage phasor has to be in phase with the primary red to white voltage because they are magnetically linked. So you can see on the phasor diagram to the right, I've drawn the red to white secondary in phase with the red to white primary.

Now, the green colored Transformers secondary is connected such that x one is connected to the white phase boss x two is connected to the blue phase bus, making the fact that red to white x two terminal is connected to white to blue x y terminal. And finally, the blue to red secondary coil is connected x one to the blue blouse and x two to the red bus making the connections x one blue to red, two X to white to blue, and x to blue to red to x one red to white. That will form the secondary bus which will provide red, white and blue voltages which have phaser vectors such as I've drawn on the right hand side. I want to further analyze this Delta Delta Connection similar to what I've done with the previous connection. In that I want to come up with a per phase equivalent circuit for This transformer.

And I ultimately would like to come up with a per unit equivalent circuit as well. I'm going to look at the turns ratio of this transformer now. And the turns ratio because of the way it's connected can be described as the primary line the line voltage over the secondary line kaline voltage. And that is equal to we'll say a and that is the turns ratio of the transformer which also can be described by putting the red to white primary voltage over the red to white secondary voltage, as well as the white to blue primary voltage over the white to blue secondary voltage and the blue to read primary voltage over the blue to read secondary voltage. Now proceeding to do a per phase analysis, I'm going to follow the steps of our procedure for per face analysis. And the first step is to convert all the loads and sources to equivalent y or their equivalent wide type connection.

Well, in a Delta Delta Connection, if we want to come up with a Wye connection, there is no neutral that we can actually do the measurement too. But we can do a hypothesis based on the phase relationship of these two primary and secondary voltages. And it would look like this in our diagram and lying to neutral voltage would be given by if there was a neutral would be given by the line to line voltage over root three, but it's also lagging by 30 degrees. We can do the same thing with a secondary voltage, the secondary aligned to line voltage is equal to the voltage line the line over root three lines at 30 degrees. So if we wanted to find the, this is now describing a single phase quantity, if we wanted to define the ratio of this single phase transformer, we'd take that first equation and put it over the second equation, which is the line to neutral primary voltage over the line to neutral secondary voltage.

And I'm only going to deal with the magnitudes for now. So I've got the left hand side of those equations one or the other, I have to do the same thing with the right hand side of the equation. And that gives us a big, ugly looking fraction here, which we would like to simplify. And we can do that mathematically simply by manipulating the numbers in the equation and I'm doing that right now. nothing magical about it was just pure mathematics and the two root threes would then cancel out, leaving us with just the voltage line to line primary over the voltage line to line secondary. And what that tells us is that the line to neutral voltage primary over the line to neutral voltage secondary is equal to the same ratio as the primary line the line voltage over the secondary line to line voltage.

So, we can draw a single phase equivalent circuit to do our per phase analysis. And that would be a single phase transformer whose primary and secondary voltages are described by the equations that we just manipulated here so we have a voltage line to neutral on the primary side that's related to the voltage on the secondary side. By the turns ratio, that means that if we were to move the transformer voltage line to neutral from the secondary to the primary, we would have to multiply by the turns ratio. And the turns ratio is also described by the current flowing in that per phase circuit. Only it's the inverse of the voltage meaning that the secondary line voltage over the primary line voltage would give us the turns ratio. That would mean that if we were to describe or move the line voltage from the primary over to the line voltage on the secondary or what is the line voltage on the secondary with the line voltage of the current being a particular value, we would have to multiply the primary current By the turns ratio in order to get the secondary line current.

Now, as we develop the per unit equivalent circuit, or we're going to move to a per unit analysis we have to establish base values for this circuit and because it is a transformer, there are two voltage levels for that transformer. And the two voltage levels describes zones that are called we'll call the base one and V base two which are made up of the voltage levels of the left hand side of the transformer and voltage levels on the right hand side of that transformer. Now, if we were to draw the equivalent circuit after converting all of the quantities in our product These equivalent circuit to per unit equivalent circuits, the transformer disappears. And we're left with basically two wires. And that is our equivalent per unit circuit for this transformer. And we still have our two zones.

And those two zones can be given by voltage basis and the voltage basis that we're using here. It doesn't matter whether we use line to neutral voltages for our voltage basis or line to line voltages because of their they're in the same ratio. But because it's a Delta connected transformer, there is no voltage lying to neutral it was hypothetical. So we might as well stay with voltage line to lying because once we convert our per unit voltage is too accurate. values, we want to come up with line to line values. So the voltages in our per unit equivalent circuit are going to be the same because they're in per unit.

So it doesn't matter which zone you're in, in the per unit equivalent circuit, because the voltages are the same. It will matter once you start to calculate the actual values because you have to use the equivalent base value to convert them to the actual values. Also, the per unit values are the same. And because we're in per unit, and again, it would only make a difference when you come and you calculate the actual values because that's when you multiply by your base values. Also, if we were to describe the impedance of That transformer the transformer had some internal impedance, it would look like this in our diagrams, and in the per phase equivalent diagram, it wouldn't matter which side of the transformer you're on. Because you'd have to change it by multiplying by the square of the turns ratio.

But in the case of the per unit equivalent, it does not matter which zone you're in, because the impedances are the same regardless of what zone you're in. So you could actually move the per unit transformer impedance to either zone it would not matter, it will only matter like all the rest of the per unit values. When you calculate the actual values. This ends chapter for a