CHAPTER FOUR see a continuation of the three phase per unit analysis and transformer configurations. We are now going to look at a Delta Wye connected transformer. And that is, it's going to be delta on the primary and why connected on the secondary. And I'm not going to go through the connection slowly because we've already gone through the connections. The only thing is that those connections were either on a y wire or a delta delta transformer or it was the Y delta transformer only in this case, the connections are Delta on the primary and y on the secondary and we've already gone through those connections and they look like the diagram there. And we're going to designate the same as we've done before that the connections on the high side of the transformer are going to be h1 and h2 on the coils have the primary of the transformer and the terminals on the coil to the secondary of the transformer are going to be labeled x one and x two.

And they are going to be connected like shown in the diagram on the right hand side of the, of the slide there. The takeaway really from this is the fact that you can see that the coil on the secondary labeled x one two x two, and I've labeled with a lowercase r is going to be in phase with a coil that's connected h1 to h2. On the primary side of the transformer labeled capital R capital W, which is a phase two phase voltage. The phase two phase voltages on the primary coils are infinite phase with the phase two neutral coils of the secondary. That is the important takeaway from this introduction. I'm going to compare the phase two phase voltages on the secondary with the phase two phase voltage on the primary.

And I'm only going to look at one phase, but they're all relatively the same. Now looking at the secondary voltages, the phase two phase voltage on the secondary by virtue of the phase relationship of a balanced system and this is a balanced system. The phase two phase voltage leads the phase two neutral voltage by 30 degrees. And that is by virtue of the fact that there's a phase relationship in a balanced system. Now I've already said that the rest Phase red to neutral voltage on the secondary is in phase with red to white voltage on the primary. So if the red to white is leading the red to neutral on the secondary by 30 degrees, the phase two phase voltage on the secondary is going to lead the phase two phase voltage on the primary.

And I've only shown the red phase voltages and the red to white voltages on the primary. But all of the all of the phase two phase relationships are the same. The phase two phase voltages on the secondary lead the phase two phase voltages on the primary, or I might say that the secondary leads the primary by 30 degrees now I'm going to have a look at the magnitude of the phase two phase voltages now and compare the primary to the secondary. And when I'm looking at the magnitude, I'm looking at the length of the phasor arrow if you would. And I'm going to designate the magnitude by putting the absolute signs on the letters of the phasor. And in the case of the red to white voltage on the secondary, the red to white magnitude is equal to root three times the red to neutral secondary voltage.

And that is because of the fact that we have a balanced system here. And that's the phase relationship of a balanced system. The turns ratio of each of the transformers and I'm going to just look at the red one for now, but they're all have the same ratio turns ratio and the is designated by the magnitude of the primary red to white voltage over the magnitude of the red to neutral secondary voltage. And that is the voltage line to line on the primary and the voltage line to neutral on the secondary. Now, I'm going to rewrite that equation because I want the line to neutral voltage on the left hand side of the equation. And so that's the magnitude of the secondary read to neutral voltage is equal to the magnitude of the primary read the white voltage all over the turns ratio.

Now I want to in the first equation that we had there for the secondary red to white or secondary phase to phase voltage. I'm going to replace the magnitude of the red to neutral voltage with what I have on the right hand side of the turns ratio equation. And now I can say that the red to white voltage magnitude on the secondary is equal to root three times the red to white voltage on the primary divided by the turns ratio. We've now compared the voltages in a Delta two y connected transformer. And we found the how the magnitude and the phase angles compared to each other. Now I want to have a look at the currents in a delta to Hawaii connected transformer.

And in order to have a look at the currents, we have to apply some type of a load and I'm going to use a purely resistive load. So I won't have to contend with any kind of angle deflection due to the load. The load is purely resistance and in this case, I'm going To connect the load balanced, but I'm going to connect it in a Wye configuration on the secondary of the transformer Of course. And I'm going to say that the current flowing in the read phase line that's a distribution line to the load is going to be delivered by the read phase transformer secondary, and the current is going to flow out of the spot of the secondary of the transformer coil. And I'm going to show the phaser just above our diagram there and I'm going to label it r for red to neutral and it is equal to the line red secondary current.

Now, that current in that coil to the red transformer is induced by the coil on the primary side of the transformer and that's induced by current flowing into the spot side of the terminal h1, and that coil is connected red to white, but I'm going to label the current flowing in the coil of that transformer with a capital R. Now there is going to be a white phase current flowing to the load and that white phase current is coming from the green transformer and the current is flowing out of the spot side of the green side of the secondary of the transformer to our load and the current flowing in the coil of the secondary white phase is induced by current flowing into this spot on the primary side of the transformer. And I've indicated the phasor in the diagram there and it is a phase two phase current similarily, there's going to be current flowing in the blue phase coil, and the blue phase current is coming from current flowing through the blue phase coil coming out of the spot side of the blue phase coil.

And that current is induced by a current flowing into it the spot on the primary side of the transformer and I've labeled that with a capital B. It goes without saying that the currents in the coils on the secondary side are induced by currents on the primary side and those primary currents are in phase with the induced currents on the secondary of the transformer. And the reason for that is quite obvious, obvious, they're magnetically linked. So, they are in phase and you can see that from our phasor diagram, that the read phases on the second or the read phase on the secondary of the transformer, labeled with the letter, the lowercase letter R is in phase with the current labeled with a capital R, and that the lowercase w phaser is in phase with the capital letter W. White phase on the primary and the blue phase.

Secondary induced current is in phase with the blue phase current on the primary. And the secondary currents again, are equal to the line currents that are taking the current away. In other words, the red phases equal to eyeline current. The white phases equals two It's equivalent line current and the blue phase is equal to its equivalent line current. The current that is causing the current the flow in the primary of the coils and I'm only going to look at one phase right now but all three phases are similar. I'm going to look at the line current coming in on the red face.

And that eye line red primary current is made up of current that is flowing into the read phase coil, which is shown here again, I've repeated the phaser but there's current flowing back from the blue phase that's returning through the line in that direction, so we have to subtract the blue face current from the red face current in order To get the line current, and those two vectors added together to give us the read phase primary line current. Now I've gone through this equation several times before. And we know that the contained angle formed by the phaser have the red face and the minus blue phase is 120 degrees. And because the magnitude of the B phase or the minus b phases, same magnitude as the red phase, the angles on either side of that triangle are equal and they are 30 degrees each. So the line current on the primary red side is lagging the red phase coil current by 30 degrees.

And I've said that the read to neutral secondary phase is in phase with the red phase current on the primary side. So if I move the line the red phase line current on the primary down, you can see that it's going to lead the red to neutral voltage current on the secondary side and the read phase coil is equal to the line current on the secondary side. So the line current, the read phase line current on the secondary leads the read phase, line current on the primary side, you might say then that the secondary leads the primary by 30 degrees. We've seen what happens in regard to the phase shift of the current in this transformer when we go from the price To the secondary, I want to now look at the magnitudes of this current. And in order to do that, I'm going to have to shift and resize some of my diagrams to make room for my equations that I'm going to write.

Now we've seen that the read phase minus the blue phase forms, and I saw Sully's triangle, which results in the phasor of the line current in the red phase on the primary. And we've already seen what the angles are in this type of isosceles triangle in the previous example, so I'm not going to go through that again. We're going to accept the fact that part of the angles in this isosceles triangle form a 30 6090 degree triangle that has the sides in the ratio of one, two and the root of three I'm going to write the equation now for the line current in the red phase of the primary in terms of the resized phasers that are in the ratio of the red face times root of three over two plus the minus blue face times root three, all over two, which are the phasers that are lined up along the line side of the primary current.

And I've drawn them in there just to show you what I'm looking at. And I'm going to move them up here so that you can see, each one of those terms represents the partial sum of a phaser. That when added together gives us the line current in the red phase on the primary side. Now, I said I'm looking at magnitudes and I want to deal with the magnitudes only. And that is I want to deal with the length of the phasers, I'm not really that interested in the angles. So I'm going to put absolute value signs on my equation, such that the absolute value or the length of the phaser in the line is equal to the absolute value of the read phase, or the length of the read phase, times root three over two, plus the magnitude of the minus b, or the absolute value of minus b times root three, all over two.

Now when we're looking at the absolute values, the absolute value of the read phase is equal to the absolute value of the blue phase. In other words, the length of the red phase is equal to the length of the minus blue phase. The sign doesn't really come into play when we're done. Dealing with absolute values. So I can rewrite my equation now. And I can replace the minus b quantity absolute quantity with the absolute value of red because they're equal.

So this is the new equation, which is the line current on the primary side is equal to root three times the quantity absolute value of red phase plus the absolute value of the red phase all over two. And I can collect like terms, and that equation now becomes the line current, the absolute value of the line current is equal to root three, two times the absolute value of the read phase all over two. Well, common terms in the numerator and the denominator of two will cancel out. And that will leave us with this final term, which is the line current in the red phase on the primary is equal to root three times the absolute value of the red face. Now I've been dealing with just the red phase, but we can we could do this with each one of the phases, and then come up with a similar answer.

But I'm going to rewrite the general equation now. That says, the absolute value of the line current on the primary is equal to root three times the absolute value of the line to line current. On the secondary. The term in the equation I subscript line to line all written in uppercase letters, is referring to the current that's flowing in each one of the primary coils of the transformer. The current flowing in the primary red phase coils the current flowing in the primary of the white phase coils, and the current flowing in the primary of the blue phase coil. I want to start looking at the turns ratio of the individual Transformers here.

And I'm going to be talking about magnitudes only for the next couple of equations, I'm going to leave the absolute signs off for brevity and clarity for now. But the turns ratio of the individual Transformers A can be described by taking the line the line voltage of the primary and putting it over the line to neutral voltage of the secondary. And if there is a load on this transformer, there's going to be current flowing in the primary in the secondary as well. So it can also describe the turns ratio using the current but it is the inverse of what the voltages are so that the Actual currents themselves will be the line secondary current over the line to line current of the primary. So that that is the actual currents flowing in the coils of the transformer. Now I can rewrite this equation, because I would like to have the line secondary current on the left and all the rest of the terms on the right, I'm going to rewrite it one more time, so that I have the line to line current on the left side.

And that's going to equal the line secondary current all over the turns ratio. So that will allow me to replace the current line to line that I have already established my equation with this one that involves the turns ratio. So that tells me that the line primary current is equal to root three times the line secondary current all over the turns ratio. I want to simplify this equation by replacing the root three over a with one over a primed. So my equation will now look like this, the primary current is equal to one over a prime, the secondary line current. Now we've already established the fact that the secondary leaves the primary by 30 degrees, so I can change this absolute value equation to a phasor equation by putting in the fact that the secondary leaves the primary by 30 degrees.

So now my equation will look like this at the primary line current will equal one over a prime times the secondary light and current minus 30 degrees. Now that we have developed a relationship between the voltages and currents in a Delta Wye transformer, I want to develop a per phase equivalent circuit and a per unit equivalent circuit for this transformer. And in order to do that, I'm going to return to my voltage diagrams and phasers here. And I'm going to again resize them and shift them so that I have room for my equations. We already seen on the secondary side of the transformer, that the line to line voltage is equal to root three times the line to neutral voltage times 30 degrees. I'm going to rewrite that equation because I want to use it in this form later on.

Such that the line to neutral voltage on the secondary is equal to the lines to line voltage on the secondary all over root three all over 30 degrees. We've also seen that the turns ratio, the transformer can be described by the line to line voltage on the primary over the line to neutral voltage in the secondary. And I'm going to rewrite that equation as well, because I want to keep the light neutral voltage on the left hand side of the equation. So the voltage line to neutral on the secondary is equal to the line the line voltage on the primary all over the turns ratio. Now I'd like to start to develop the per phase equivalent circuit and doing that I'm going to start with a procedure for per phase analysis. And the first step in the per phase analysis is to convert all Delta loads and sources to their equivalent wire connections.

Now there is no neutral in the primary sides. I'm going to develop a hypothetical line to neutral voltage based on the phase relationship of a balanced system. And that will tell me that the line to line voltage of the primary is going to be equal to root three times a hypothetical line to neutral voltage times 30 degrees. I'm going to rewrite that equation because I want to use it in this form later on. So I want the line to neutral voltage on the left side of the equation, which will equal the phase two phase or line two line voltage of the primary all over root three all over 30 degrees. Now I want to have that 30 degrees in the numerator and if I'm going to To move the 30 degrees from the denominator into the numerator, it's going to go from plus 30 degrees to minus 30 degrees.

Okay, for the next few slides, I'm going to go through some mathematical manipulations and don't be put off by it. It's nothing magical or complex. It's just pure algebra. But I want to be left with the equations that will describe a per phase equivalent circuit in a per unit equivalent circuit. And I'm going to start with taking this equation and dividing it by this equation. And I'll have to do it starting with the terms on the left hand side of the equations, which means I'm going to take the line to neutral voltage from the primary and divided by the line to neutral voltage on the secondary and if it Do that with the left hand terms of the equations, I have to do it with the right hand terms of the equation as well.

And I'm left with this complex looking equation. So I want to really reduce this to something that's a little bit easier to manipulate and to work with. And I have on the right hand side of the equation, I've got three dividing lines or two sets of fractions, one dividing into the other and I'd like to get rid of some of the fraction signs. So I'll do that. I can move the root three term from the numerator in the denominator. And then I'll move the turns ratio a from the denominator of the bottom fraction into the numerator.

And that leaves me with just one fraction line to worry about and this is much easier To look at and to work with, I'm going to make this equation even easier to work with because as you can see, we've got a common term in the numerator and denominator, that's the line the line voltage of the primary, so I can cancel that out. And I also would like to take the A, which is the turns ratio of the transformer, and it is over root three, so I'm going to replace a over root three with a primed. Now the equation will look like this, the voltage line to neutral in the primary over the voltage line to neutral in the secondary is equal to A prime at minus 30 degrees. Now we're dealing or we have line to neutral voltages in this equation and Because we have a Delta Connection, there is no neutral in the primary side, there isn't a secondary.

But I'd like to change the line to neutral values to line to line values. And I can do that with my phase relationships, which I've already developed. And I promised that I would be using these equations later on. And this is where I'm going to use them. I'm going to take these two equations that relate the line to neutral voltages to their line to line equivalents. And I'm going to make them line to line voltages on both the numerator and the denominator.

And again, I can reduce that complex fraction into one fraction. And again, we have like terms in the numerator and the denominator so I can cancel those out. And I'm left with the fact that the line to lie voltage of the primary over the line to line voltage of the secondary is equal to A prime at minus 30 degrees, which also happens to be equal to the line to neutral voltage in the primary over the line to neutral voltage in the secondary. This last equation describes the relationship between the primary and secondary voltages on a Delta Wye transformer. And it helps to break it up into actually two equations because there are two equations in this one that we just developed. And that is one describes the line to neutral voltage relationship and the other describes the line to line voltage relationship.

Now, the first one, the line to neutral voltage on the primary side is equal to A primed times aligned to neutral On the secondary side minus 30 degrees, we will use that equation to give us our per phase equivalent circuit which looks like or it is a single phase transformer, the primary voltage is lying to neutral voltage and the secondary voltage is aligned to neutral voltage. Now, that equivalent circuit has two operators that will relate the two voltages. In other words, if we have the secondary voltage and we want to calculate or figure out what the primary voltage is, we are going to have to multiply by a prime and if we're going to find out what the phase relationship of the primary is, we're going to have to subtract 30 degrees from the secondary because the secondary voltage leaves the primary voltage range arlis of your talking line to neutral or line to line voltages.

In this case, though, we're talking per phase equivalence over dealing with the line to neutral voltages. Now if you remember, a couple of slides back, we developed a formula for the relationship between the line current ad on the primary side and the line current on the secondary side, and the primary line current is equal to the line on the secondary side current divided by A prime and at minus 30 degrees. So the operator when we're looking at currents on this per phase equivalent circuit, if we are moving from the primary side to the secondary side, we are going to have to multiply by a prime because the secondary side We'll be a prime times the primary side. Also, if we are moving from the secondary side to the primary side, phase wise, the secondary leads the primary as far as the current is concerned, so we're still going to have to subtract 30 degrees.

Now remember what a prime is a prime is equal to the turns ratio all over root three, or one over a prime is equal to root three, all over the turns ratio. So if we are going from the secondary to the primary current wise, we're going to have to divide by the turns ratio. However, if we're going from the secondary side to the primary side, magnitude wise, we're going to have to multiply by the root of three, because the phase, the resultant line current on the primary is root three bigger than the line current on the secondary by virtue of the Delta two y connector connection. I would like to develop the per unit equivalent circuit now for this transformer connection, and I'm going to start with our per phase equivalent circuit. And in order to find the per unit values for our, our per unit equivalent circuit, I'm going to have to establish my base voltages.

And there's two voltages because there are two voltage levels in this transformer. I'm going to say the coils or everything connected on the primary side is my database one and I've outlined the the zone in green, as you can see in the diagram, now if we go over to the other side, the secondary side of the transformer, that will give us our second base voltage, and I'm going to call that the base two, and everything on that side will have to be calculated using the voltage base the base two. So now I'm going to move after I've calculated all my per unit values, I will now move that per phase equivalent circuit into what I call a per unit equivalent circuit and that transformer will will virtually disappear and I'll be left with two wires that is my per unit equivalent circuit. However, in this particular transformer, there is one operator that we have to work or deal with when we are developing our per unit equivalent circuit and that is when I move From zone to zone one, I'm going to have to subtract 30 degrees, whether I'm talking about line to line voltages line to neutral voltages or line currents, there is a phase shift from the zone one to the zone two.

And we have to keep track of that. In this case, that is the only complexity that in that we're involved with in a Delta two Wye transformer, and it has to be shown on our per unit equivalent circuit. The zones are still here, and right now I'm describing my green zone using my line to line voltages which will give me my v base one. I could have used the line to neutral voltages, but that would mean when I come From a per unit into the actual values, I would end up with a line to neutral values. And if I'm on the primary side there is no neutral. So I'd have to do a conversion to get it into line to line.

So rather than do the double step conversion, I'm going to use the line to line voltages for my zone my base zones and I can do that. So anything connected or associated with the per unit equivalent circuit in the green zone is going to be using v base one and V base two is looking like this. And it will be also the line to line voltages. Now whatever base voltage you use, whether it's lying to neutral or lying to lie, you have to be consistent. If you use one or the other. You have to stick with it.

However, you can use both if you want. As I said the only difference is when You're taking your per unit values and calculating the actual values, you're going to end up with anything in the way of a voltage is going to be the line to neutral voltage. So, when you have this per unit equivalent circuit, the voltages on both sides, or I should say in both zones are equal because their per unit values once you come out of the per unit value into actual values, the voltages will be different, but as long as you're working in per unit, doesn't matter what zone you're in, the per unit voltages are the same. Now if you go from the voltage on the zone to to zone one, whether it's or if it's per unit voltages, you're still going to have to subtract 30 degrees when going from zone to zone one and you're going to have To add 30 degrees, if you go from zone one to zone two, that's because you have to take care of the Delta Wye connection, which adds or subtracts 30 degrees depending on which way you're going in your circuit.

Also, the current in a per unit equivalent circuit, that currents, the per unit currents are the same, because their per unit currents at least the magnitudes are the same. However, if you're going to go from the second zone to the first zone, For Currents, you are going to have to subtract 30 degrees, you have to keep track of that 30 degree phase shift in a Delta Wye transformer and that, again, I'm repeating myself but it's worth repeating that the voltage and the currents are shifted the same 30 degrees and it doesn't matter whether you Talking about lying to neutral voltage or line to line voltage, you're still going to have that 30 degree phase shift. Now, if you have impedances described for the transformer, if you are on a per phase equivalent circuit, you have to be careful of what side of the coils are what whether you're in zone one or zone two are on the primary or secondary side, because the impedance of the transformer will change when you go from one zone to the other, and then they're related by a square of the turns ratio.

However, if you're working in per unit values, it does not matter whether you're in zone one or zone two, the impedance is the same, because it's per unit values. So remember that if you have a transformer per unit impedance Doesn't matter which zone you're you're in as long as you're still in the per unit equivalent circuit. I would like to review the phase shift through a wide delta and a delta y connected transformer starting with the star delta over wide Delta connected transformer. I would like to look at the voltages first and these are the phasers or the voltage vectors of this transformer. And the thing to note here is that the secondary phase two phase voltage is in phase with a primary phase to neutral voltage. So in comparing the phase two phase values, then I'm going to look at the read phase for now.

The red to white primary voltage lead Read the primary read to neutral voltage by virtue of the fact that it's a balanced system and these are the phase relationships, the red to white voltage leads the red to neutral voltage by 30 degrees. And since the secondary red to white voltage is in phase with the primary red to neutral voltage, then it stands to reason that the primary red to white voltage leads the secondary red to white voltage by 30 degrees. Now, I'm going to shift gears a little bit here and I'm going to look at the current in this star Delta transformer. And what you see in the colored arrows are the phasers for the actual currents. And in the primary side, the line currents are the same currents that are flowing through the phase currents in other words, the line currents are the same currents that are flowing through each of the primary coils and those feed phasers are shown in the diagram.

In the secondary, the line currents are made up of the sum of two of the coils. And in the case of the line current for the read phase, it's made up of the red to white coil current minus the blue to red coil current. And I'm showing the vectors here and you can see how they are summing up to form the secondary red line current. Now, the phase current of the secondary red phase is in phase with the line current of the primary. So if we can compare the Primary red phase line current to the secondary red phase line current, you can see that the line current of the secondary lags the line current of the primary by 30 degrees. Before leaving this connection, I'm going to return all the voltage Phasers to the diagram so that the diagram will have both the voltage and the current phasers.

And I'll return to do some comparisons in a couple of slides. But for now, I'm going to move on to the delta star or the Delta Wye connected transformer. And these are the voltage phasers that are associated with this type of connection. And the thing to note here is that the primary phase two phase voltages are in phase with interest associated phase two neutral voltages on the secondary side. So if I want to compare phase two phase voltages primary to secondary, I'm going to look at a sample which is the red to white voltage phasor all of the rest can be compared similarly, but on the secondary side, the phase relationship between the phase two phase and the phase two neutral voltages. The red to white phase two phase voltage leads the red phase voltage to neutral by 30 degrees.

So, if I move that phasor up to compare it to the primary side you can see that the secondary red to white voltage leads the primary red to white voltage by 30 degrees. I'm now going to move on to compare currents In the currents associated with this type of a connection, you can see that the line currents that feed the secondary or the line currents that feed the load and come from the secondary are the same currents that are flowing in each of the coils of the transformer. On the primary side though, the line current that's connected to the Delta Connection is made up of the red to white and blue to red phasers such that the red to white minus the blue to red voltage make up the line current or the red phase line current. So I'm going to compare the line current from the secondary to the line current From the primary, the line current primary lags the line current secondary by 30 degrees.

Or you might say the line current secondary leaves the line current primary by 30 degrees. Now returning all of the voltages and currents and I'm going to do some comparisons here. And starting with the start Delta Connection, you can say that the secondary lags the primary by 30 degrees regardless if you're talking about current flows or voltages, the phase two phase voltages of the secondary lags the phase two phase voltage of the primary by 30 degrees and the line currents of the secondary legs Line currents of the primary by 30 degrees. For a delta star connection, the secondary leads the primary by 30 degrees. Regardless if you're talking about voltages or currents, the phase two phase voltage of the secondary leads the phase two phase voltage of the primary by 30 degrees and the secondary line current leads the primary line current by 30 degrees. I would now like to look at the associated per unit equivalent circuits for these two types of connections.

And in the case of the wide Delta Connection transformer, this is what the per unit equivalent circuit would look like. Now normally a non equivalent circuit Per Unit, an equivalent circuit for a transformer is just a straight connection of wires and there's nothing else associated. But with this type of connection, you have to keep track of the phase shift of the currents and voltages associated with the connection. So the double wire connection that's normal with a per unit equivalent circuit, we have to have a 30 degree phase operator in there and I'll explain that in a few minutes. In the case of the delta star connection transformer the per unit equivalent circuit is very much the same except the 30 degree phase shift is different. Now, what this operator means in the case of these Transformers is that in the case of the Y delta transformer, when you go from the secondary side to the primary side Because of the 30 degree phase shift, in other words, the secondary lags the primary by 30 degrees.

If you go from secondary to primary, you will have to add 30 degrees to the currents and the voltages. In the case of the delta star connection. In going from the secondary to the primary, you have to subtract 30 degrees because the secondary leaves the primary by 30 degrees. And what it essentially means if you're moving from one zone to the other, in other words to the orange from the orange zone to the green zone, that's what you have to do for your per unit values. Now, in the case of the magnitudes of the currents and the voltages, the magnitudes are the same regardless of which zone you're in. So that doesn't change when you move from one zone to the other.

However, where it does change is when you want to calculate the actual value from the per unit value, you have to use the proper base value in order to make that conversion but if you're working in per unit, the magnitudes are the same. However, in the case of the wide Delta connected transformer, you have to know and remember that the secondary lags the primary by 30 degrees. So you have to convert the secondary primary and voltages to the primary voltages by adding third degrees 30 degrees. In the case of the Delta Wye transformer, the secondary leaves the primary by 30 degrees. This ends chapter four c