Three Phase Transformer Phase Groups | Electrical Machines - Electrical Engineering (EE) PDF Download

Three Phase Transformer Phase Groups Part - I 
So far, we have seen some constructional features of a 3 phase transformer, and we have indicated that even for the simplest of the 3 phase transformer, there are six windings and twelve terminals.

(Refer Slide Time: 01:12)

So, there are three high voltage windings and three low voltage windings. This is the minimum. In many cases, either the high voltage winding or low voltage winding can be split into two parts giving nine sets of windings. Even in the simplest case, there will be at least six windings. Now, each of this high voltage or low voltage winding can be either star connected or delta connected. And if one set is split into two, it is also possible to have a zigzag connection. So, theoretically, either set of winding – high voltage or low voltage can be star delta or zigzag connected. So, in order to completely specify the transformer winding connection, we have to mention the high voltage connection whether it is star-HV connection, whether it is star-delta or zigzag. Similarly, the LV connection; whether it is star-delta or zigzag. However, that is not sufficient.

In our last lecture, we have seen how to find out the line voltage and current as well as phase voltage and current conversion ratios of a 3 phase transformer, even the winding turns ratio. So, we have seen that, the voltage magnitudes on either sides are different. That is the purpose of the transformer. However, a closest scrutiny will reveal that, not only the magnitudes of the high voltage and low voltage sides are different; in many cases, they are also not in phase.

So, when we specify the winding connection on the high voltage and low voltage sides in addition to specifying whether they are star-delta or zigzag connected, we will have to also specify what is the phase angle between the high voltage line to neutral phasor – line to neutral phasor of high voltage; the angle between line to neutral phasor of high voltage and low voltage winding. So, a complex specification of 3 phase transformer winding connection will involve specifying the high voltage side connection – star-delta or zigzag, low voltage side connection – again star-delta or zigzag, and the phase angle of the low voltage line to neutral voltage phasor with respect to the high voltage line to neutral voltage phasor.

For example, we may specify the connection to be Y, d, plus 30 degree. This means the high voltage is star connected, the high voltage line to neutral phasor – high voltage is star connected; the low voltage is delta connected; and the line to neutral phasor of low voltage winding leads the… This is high voltage line to neutral phasor. This is low voltage line to neutral phasor. This leads the high voltage line to neutral phasor by 30 degree. So, this kind of specification is called the phase group specification of a 3 phase transformer. The phase group specification involves three specifications: one is the connection of the high voltage winding, connection of the low voltage winding and the phase angle between line to neutral voltages of low voltage winding with respect to the high voltage winding.

(Refer Slide Time: 06:29)

Now, this phase angle – there are two conventions of specifying the phase angle. Before we talk about the convention, let us assume what kind of phase angles are possible. There are four types of phase angle that are normally possible. The phase angles can be either 0 degree, that is, the line to neutral voltage phasor of both sides may be cophasor; or, 180 degree, that is, they may be opposite in phase. The one can… The low voltage winding voltage phasor may lag the high voltage winding by 30 degree or it may lead by 30 degree. So, correspondingly, there are four groups. This is called group number 1; this is group number 2; this is group number 3; this is group number 4.

In many cases, particularly, in older installation, this phase angle is indicated by a clock number. For example, if we take the analogy of a clock and say that, the minute hand represents the line to neutral phasor of the high voltage side; and the hour hand, which is smaller represent the line to neutral phasor of the low voltage side; then 0 degree phase angle. This is high voltage line to neutral phasor and this is the low voltage neutral phasor.

On a clock, if we assume this to be a clock, then this is 0 hour. So, this is called 0 – clock number 0. Similarly, for 180 degree, this is the high voltage-voltage phasor; this is the low voltage-voltage phasor; their angle being 180 degree. So, on a clock, this represents 6 o’ clock. So, this is clock number, is 6 for this. For minus 30 degree, this is the minute hand representing the high voltage side line to neutral phasor and this is the low voltage side neutral phasor – line to neutral phasor. This is HV; this is LV. Here the line to neutral phasor of the LV side leads the line to neutral phasor of the HV side by 30 degree. So, this is group number 4. This is called… This copy… This represents 11 o’clock. Therefore, this clock number for plus 30 degree is 11. Similarly, for minus 30 degree, this is HV line to neutral phasor; this is LV line to neutral phasor. This represents 1 o’clock. Therefore, this clock number is 1. Hence, actually, the phase groups can be specified either in terms of phase angle or in terms of clock number.

(Refer Slide Time: 10:39)

Therefore, for example, this Y, y, 0 degree can also be written as Y, y, 0. This is the phase angle. This is clock number. Similarly, D, d, 180 degree can also be written as D, d, 6, because this is the clock number representing 180 degree phase side. Let us say Y, D, plus 30 degree. This will be… Corresponding clock number representation will be Y, d, 11. Let us say Y, z, minus 30 degree. This will be… Corresponding clock number representation will be Y, z, 1. So, this is the correspondence between phase angle representation and clock number representation. They are interchangeable. And in many cases, the phase groups will be specified like this; in many cases, it will be specified like this. But, they represent the same thing.

Let us see what are the different combinations possible. For example, it is easy to understand that, we can always have a Y, y, 0; D, d, 0; or, D, z, 0. In all cases, of course, the high voltage and low voltage side connections may be interchanged. This is one of the possible phase groups – set of phase groups with 0 degree phase angle. We can also have Y, y, 6; D, d, 6 or D, z, 6. However, it is interesting to note that, Y y, Y z 6 or 0 is not possible; why? We will see shortly. These are 0 degree and 180 degree phase shifted phase groups.

(Refer Slide Time: 14:52)

For plus minus 30 degrees, you have D, y, 1. This is minus 30 degree. Then… Or, you can have Y, D, 1; or, you can have Y, z, 1. Again, the high voltage and low voltage sides connections can be interchanged. However, D z 1 is not possible. So, this was 0 degree phase shift; this is 180 degree phase shift; this is minus 30 degree phase shift. And then you can have D, y, 11; Y, D, 11; and Y, z, 11.

These are plus 30 degree phase shifted configuration. The configuration that are not possible are Y, y, plus or minus 30 degree – this is not possible; D, d, plus minus 30 degree – this is also not possible; Y, z, 0 degree – not possible; Y, z, 180 degree – not possible; D, z, plus minus 30 degree – this is also not possible; or, z, D, plus minus 30 degree – this is also not possible. So, we have seen that, possibly, there will be twelve different connections of 3 phase transformer. Let us see how these connections are made.

(Refer Slide Time: 17:31)

Let us start with the simplest one, that is, Y, y, 0 degree. So, how the Y, y, 0 degree line to neutral phase voltages will look like – the phasor diagram? Let us say this is phase A of the high voltage side and this is phase B of the high voltage side; this is phase C of the high voltage side. The phase groups says that, the line to neutral voltage of the low voltage side will be cophasor to the line to neutral voltage of the high voltage side. Therefore, if this is the neutral, then on the low voltage side, this will be phase a; this will be phase b; this will be phase c; this will be the neutral. Now, let us say this A is actually the voltage phasor A 2 A 1. And on the low voltage side, this voltage phasor is between small a 2 and small a 1; this is between B 2 and B 1 and B 2; and this phasor is between C 1 and C 2. This is again between b 1 and b 2; this is between c 1 and c 2.

(Refer Slide Time: 19:47)

Now, from this voltage phasor, it is easy to see how the connections will look like. For example, if these are the windings – high voltage windings; this is A 2 A 1, B 2 B 1, C 2 C 1. And these are the low voltage windings a 2 a 1, b 2 b 1 and c 2 c 1. Then from this phasor diagram, we can see that, the high voltage neutral is formed by joining capital A 1, capital B 1 and capital C 1. So, this will be the neutral point N; this will be the line A; this will be line B; this will be line connected to line C. Similarly, on the low voltage side, the neutral is formed by connecting terminals small a 1, small b 1 and small c 1; and the lines are obtained from the other side. So, this is a, this is b, this is c. So, this is what the connection Y, y, 0 will look like.

Next… So, let us try to do the same thing with a 6 connection; let us say D, d, 6; what does D, d, 6 means? That is the line to neutral phasor of high voltage side and low voltage side should be in phase opposition. So, let us again see. So, this is the line to neutral phasor of the high voltage side A, B, C. Then the low voltage side, we want it to be like this. This we want to be a; this b; and this c. Again let us say; however, please understand that, the connections on the winding are now delta. Therefore, the line to neutral voltage is not same as the voltage across a winding.
 

(Refer Slide Time: 23:19)

However, we still assume that, the lines are connected to A 2; this is terminal A 2; this is terminal B 2; this is terminal C 2. Similarly, on the low voltage side, this is terminal small a 2; this is terminal small b 2; and this is terminal small c 2. Then how do we make the connections? Please remember that, the connections have to be such that, the winding voltages are either in phase or they are in opposite phase. So, what will be the voltages across the windings? It will be the line voltages. So, where will be terminal A 1? So, let us say this is terminal A 1.

So, this is terminal A 1; this is terminal B 1; and this is terminal C 1; that is, the winding voltages are A 1 A 2, B 1 B 2, and C 1 C 2. On the low voltage side, corresponding a 1 a 2 should be in phase with the voltage at… The voltage will be parallel to voltage a 1 a 2; therefore, in phase opposition. So, if we say this terminal is a 1, the phasor a 1 a 2 will be in this direction; if this terminal is c 1, then this is the voltage c 1; and if this terminal is b 1, then this is the voltage b 1. So, we see that, the winding voltages B 1 B 2 and b 1 b 2 are in opposite phase.

Therefore, if we see the winding connections like this with this A 2 A 1, B 2 B 1, C 2 C 1, the delta on the high voltage side is formed by connecting A 1 to B 2, then B 1 to C 2, and C 1 to A 2. And the lines are connected to A 2, B 2 and C 2. These are the lines A, B, C. On the low voltage side also, this is a 1 a 2, b 1 b 2, c 1 c 2. However, the dots are now this way; that is, instead of a 2 and capital A 2 having the same instantaneous voltage, now a 1 and a 2 should have same instantaneous voltage, because we are seeing that, the voltage V A 2 A 1 and the voltage V a 2 a 1 should be in phase opposition. The connections are made again by connecting a 1 to b 2, b 1 to c 2 and c 1 to a 2; and the lines are connected to a 2, b 2, c 2. This is the connection D, d, 6. Similarly, we can see how the connection D, d, 0 or Y, y, 6 will look like.

(Refer Slide Time: 29:49)

So, let us turn our attention to a slightly more complicated connection let us say, D z 0. So, again here we have the line to neutral voltage phasors A, B, C. These are the line to neutral voltage phasors. If we assume the terminals are connected from A 2, B 2 and C 2; then let us say this is A 1. So, the winding voltages A 1 A 2, B 1 B 2 and C 1 C 2. These are the winding voltages. Now, this is the delta side connection A 2, B 2, C 2. Now, it is to be understood that, in a zigzag transformer, each of the secondary winding has two parts.

So, the voltage phasors a 1 a 2… There will be two voltage phasors. This is a 1 a 2 and a 3 a 4, which are parallel to the capital A 1 A 2. Similarly, there will be two voltage phasors: b 1 b 2 and b 3 b 4 and two voltage phasors: c 1 c 2 and c 3 c 4. It is necessary to make the connection as D z 0; which means that, the zigzag side line to neutral voltage should be in phase with the line to neutral voltage of the delta side. Therefore, the zigzag side line to neutral voltage should be… This should be a; this should be b; and this should be c.

Now, in a zigzag transformer, each phase is formed by connecting two different… Each phase is formed by connecting two different winding sections. So, how the… And these two different winding sections belonging to two different phases. So, how can I construct this line to neutral voltage phasor of a zigzag winding using two different phase voltages? One of them will belong to the a phase; the other should be either b phase or c phase. So, it is usually… The last one will be the a phase.

So, let us say this is connected by connecting a 4 a 3. Then the other phase must be – phase voltage must be this. Now, this phase voltage by comparing with this can be either c 2 c 1 or c 3 c 4. Generally, it is the first part that is taking. So, this will be c 1 c 2. Similarly, the b phase will be connected using b 3 b 4 as the last leg; this can be a 1 a 2. c phase will be formed with c 4 c 3 as the last leg; and this will be b 2 b 1.

(Refer Slide Time: 37:20)

So, if we look at the winding connection diagram, this is the high voltage side windings. This is A 2 A 1, B 2 B 1, C 2 C 1. The delta is formed by connecting A 1 to B 2, B 1 to C 2, and C 1 to A 2. These are the lines A, B, C. Now, on the low voltage side, you have two sets of windings here: one set, second set. This is a 1 a 2, a 3 a 4, b 1 b 2, b 3 b 4, c 1 c 2, c 3 c 4. Now, let us look at the phasor diagram. The star is formed by connecting a 2, b 2, c 2. This is the neutral point on the zigzag side. The lines are taken from a 4, b 4, c 4. So, this is terminal a, terminal b and terminal c. Inside we find that, c 1 is connected to a 3. c 1 should be connected to a 3. Similarly, a 1 should be connected to b 3 and b 1 should be connected to c 3. That completes the connection of a D z 0 transformer.

(Refer Slide Time: 41:19)

How do we get a D – z – 6 degree transformer? D – z – 6 – again the line to neutral voltages are these on the delta side. So, this is the voltage phasor A 1 A 2; this is the voltage phasor C 1 C 2; and this is the voltage phasor B 1 B 2. This is terminal A; this is terminal C; this is terminal B. So, these are the voltage phasors. So, you will have two voltages: a 1 a 2, a 3 a 4; then b 1 b 2, b 3 b 4. These are the different winding voltage phasors that we will obtain on the LV side c 1 c 2, c 3 c 4. Now, the connection is D – z – 6 degree.
 

So, the line to neutral voltage phasor on the low voltage side will be… This will be a; this will be b; and this will be c. So, the last leg should be formed with a voltage phasor of a and it should point towards this. So, this is found by taking a 3 a 4. So, this is a 3 a 4. Then the next voltage phasor should be this. Obviously, this should be c 2 c 1. Similarly, the b voltage phasor should be formed with b 3 b 4; and this should be a 1 a 2; this should be formed with c 3 c 4; and this should be formed with b 1 b 2.

(Refer Slide Time: 46:10)

Hence, the winding connection wise, this is A 1 A 2, B 1 B 2, C 1 C 2. The connection is A 1 connected to B 2, B 1 connected to C 2, and C 1 connected to A 2. And the supply is given to A 2, B 2, C 2. On the zigzag side, you have two sets of windings: a 1 a 2, a 3 a 4; b 1 b 2, b 3 b 4; c 1 c 2, c 3 c 4. According to the phasor diagram, in this case, the star point is formed by connecting a 1, b 1, c 1. So, this is the star point. And terminals are taken out from a 3, b 3, c 3. So, these are the terminals taken out: a, b and c. Connection wise, a 2 is connected to b 4, b 2 is connected to c 4, and c 2 is connected to a 4. So, this completes the connection of D – z – 6. In the similar manner, remaining connections can be easily drawn.

(Refer Slide Time: 49:40)

Let us say what will be D – d – 0; D d 0 – A, B, C; A 2, B 2, C 2. This is C 1 also; this is A 1; and this is B 1. So, this is the winding voltage phasor A 1, A 2; this is B 1 B 2; and this is C 1 C 2. D – d – 0 means line to neutral phasors are cophasors; so will be the line to line phasors. So, on the secondary side, this will be the phasor; this will be another phasor; and this will be another phasor. This will be a 1 a 2; this will be c 1 c 2; this will be b 1 b 2. Connection wise the simple; this is A 1 A 2, B 1 B 2, C 1 C 2. Connections are made by connecting A 1 to B 2, B 1 to C 2 and C 1 to A 2. And the supply is given to A 2, B 2, C 2.
 

On the low voltage side, a 1 a 2, b 1 b 2, c 1 c 2. The connection is made by connecting a 1 to b 2, b 1 to c 2, and c 1 to a 2. This case gives the connection of D – d – 0. Please compare this with the connection of D – d – 6. Let us compare it with the connection of D – d – 6. Here also the connection was similar, but here the polarity of the terminals – instantaneous polarity were differs. So, if this has to be reconnected into D – d – 6, these connections are to be reversed. In other words, a 2 has to be connected to b 1, b 2 has to be connected to c 1, and c 2 has to be connected to a 1; and the supply is given to a 1, b 1, c 1. That will give a connection of D – d – 6. Similarly, we can obtain the connection of Y – y – 6; which is left as an exercise.

Three Phase Transformer Phase Groups Part - II 
In the last lecture, we have seen how to make transformer connections when the phase group such that the high voltage and the low voltage side line to phase voltages are either in phase or out of phase; that is, either they have clock number 0 or 6. Now, let us look into some transformer connection, where the clock numbers are either 1 or 11; that is the line to neutral phase voltage of the LV side leads or lags the line to neutral voltage of the HV side by plus minus 30 degree. What are the transformer connections in these two groups?

(Refer Slide Time: 01:45)

For example, they can be D, y, 1 or Y, d 1 or Y, z, 1. This can also be interchanged. However, D, z, 1 is not possible. We have seen that, D, z, 1 is not possible; it can be either D, z, 0 or D, z, 6; D, z, 1 is not possible or 11 similarly, is not possible. This is minus 30 degree connection. For plus 30 degree connection, you can have D, y, 11 or Y, D, 11 or Y, z, 11. Similarly, D, z, 11 is not possible. So, let us look at… This is plus 30 degree connection. So, let us look at how we make these connections.
 

(Refer Slide Time: 03:29)

Just start with D – y – 1; D – y – 1. So, the line to neutral of the high voltage side – let us say this is the line to neutral of the high voltage side. This is A; this is B; this is C. Again let us say this is the terminal A 2; this is B 2; this is C 2. Similarly, on the load voltage side, the low voltage side line to neutral voltage should… Since this is 1, it should lag the high voltage side line to neutral voltage by 30 degree. So, this should be a; this is should be b; and this should be c. Similarly, let us say these are a 2, b 2 and c 2. And obviously, these are a 1, b 1 and c 1. Hence, it is imperative that, the high voltage side line voltage a 1 a 2 be parallel to the low voltage side line to neutral voltage a 1 a 2.

So, in this case, this terminal will be A 1, so that the phasor A 1 to A 2; this is the voltage phasor A 1 to A 2 is parallel to the low voltage side voltage phasor A 1 to A 2. Similarly, B 1 B 2 should be parallel to this voltage; hence, this terminal should be B 1, so that this voltage phasor is parallel to this. And thenthis should be C 1, so that this voltage phasor is parallel to this. Hence, connection wise it will be… This is c 1 c 2. These are the terminals A, B, C; these are the terminals small a, small b, small c. A neutral point is formed by connecting a 1 b 1 c1; this is n. On the delta side, now, we see that, the connections are slightly different. Here B 1 is connected to A 2, C 1 is connected to B 2, and A 1 is connected to C 2. This is the voltage phasor diagram and the connection diagram of the phase group D – y – 1.

(Refer Slide Time: 08:25)

Let us similarly, look at Y – d – 1; Y – d – 1 – the high voltage side. This is let us say A 1 A 2; this is B 1 B 2; this is C 1 C 2. Hence, this is the neutral point N. On the low voltage side, we have the voltages a 1 a 2, which is parallel to a 1 a 2 here. We also have the voltage b 1 b 2, which is parallel to the high voltage side voltage B 1 B 2. And the voltage c 1 c 2, which is parallel to high voltage side C 1 C 2. Hence, the line to neutral voltage of the low voltage side calling this to be terminal a; this is to be terminal b; this is to be terminal c. We see that, the line to neutral voltage on the low voltage side lags the line to neutral voltage of the high voltage side by an angle 30 degree. So, this connection gives me Y – d – 1.
 

Generally, for high voltage side, the representing letter is written in capital; for low voltage side, the representing letter is written in small. So, from connection wise, it will be… Neutral point is formed by connecting A 1 B 1 C 1; suppliers are given to the terminals A 2 B 2 C 2. On the low voltage side, you have again three windings: a 1 a 2, b 1 b 2, c 1 c 2. In this case, the terminal a is formed by connecting a 2 to c 1; this is terminal a.

And, terminal b is formed by connecting a 1 to b 2; this is terminal b. Terminal c is formed by connecting b 1 to c 2; this is terminal c. So, this is the connection of Y – d – 1. So, this is D – y – 1 connection; this is Y – d – 1 connection. Let us look at… These were… Both were minus 30 degree connection. Here also the line to neutral voltage phasor of the low voltage side lags the line to neutral voltage phasor of the high voltage side by an angle of 30 degree.

(Refer Slide Time: 13:07)

Let us see some plus 30 degree connection; that is, D – y – 11 connection. Again input side, this is terminal A; this is B; this is C; it means this is A 2, B 2 and C 2. Where is the terminals A 1 B 1 C 1? That is what we will have to see. Now, here we are specifying that, this is D – y – 11. Hence, the low voltage side line to neutral voltage must lead the high voltage side line to neutral voltage by 30 degree. So, this should be the line to neutral voltage of phase b; this should be the line to neutral voltage of phase a; and this should be the line to neutral voltage of phase c. This terminal is a 2; this terminal is b 2; this terminal is c 2.

And, this terminal is a 1; this is b 1; this is c 1. Hence, the winding voltage phasor a 1 a 2 is in this direction. This should be parallel to the winding voltage phasor on the high voltage side. Hence, this terminal should be A 1, so that the line to the winding voltage phasor capital A 1 A 2 is parallel to the low voltage side line to the winding voltage phasor a 1 a 2. Similarly, this should be terminal B 1, so that capital B 1 B 2 is parallel to small b 1 b 2. This should be the terminal C 1, so that capital C 1 C 2 voltage phasor is parallel to small c 1 c 2 voltages.

The connection wise… a 1 a 2, b 1 b 2, c 1 c 2. The Y point is formed by connecting a 1 b 1 c 1; supplies are given to a 2 b 2 c 2. This is terminal a, terminal b, terminal c. On the delta side, we find that, A 2 is connected to C 1; then A 1 is connected to B 2; and B 1 is connected to C 2. This gives me… And the supplies are given to these points A, B, C. Let us compare this connection with D – y – 1. We see that, the star side connection of both of them are identical. On D – y – 1, we had connected A 2 to B 1; here we have connected A 1 to B 2; B 2 to C 1; B 1 to C 2; C 2 to A 1; C 1 to A 2. Therefore, just by interchanging these connections, a D – y – 1 transformer can be converted to a D – y – 11 transformer. Similar conclusion can be drawn for Y – d – 1. Let us look at that.

(Refer Slide Time: 19:14)

Let us see the transformer connection Y – d – 11. The high voltage side is Y connected. Therefore, the line to neutral phasors are also the winding voltage phasors. Hence, this is line A or winding terminal A 2; this is line B – winding terminal B 2; this is line C – winding terminal C 2. And these are the winding terminals A 1, B 1 and C 1, which forms the star point N. On the low voltage side, the winding voltages will be in phase with the high voltage side winding voltages.

So, this will be a 1, a 2; this is will be… This will be a 1 a 2; and then this will be c 1 c 2; and this will be b 1 b 2. If we want the line to neutral voltage of the low voltage side to lead this; then this connection if we make; if this is the connection; however, this does not give Y – d – 11; it gives Y – d – 1. Hence, this connection cannot be accepted for this case. Hence, the connection will be like this – a 1 a 2, b 1 b 2 and c 1 c 2. In this case, if we make this connection; then the line to neutral voltage of the low voltage side will lead the line to neutral voltage of high voltage side and this will be a Y – d – 11 connection.

So, what will be the winding connections here? This is the high voltage winding; this is not acceptable. On the high voltage side, the star point is formed by connecting A 1 B 1 C 1. This is the neutral N. These are the line terminals A, B and C. On the low voltage side, now, we connect a 2 to b 1, b 2 to c 1 and a 1 to c 2. The lines are connected to a 2 b 2 c 2 – a, b, c.

Now, let us compare it with the connection Y – d – 1. When we compare, we see that, in this case, the high voltage side connection of both the transformers are identical. On the low voltage side, while in this case, a 1 was connected to b 2, b 1 was connected to c 2, and c 1 was connected to a 2. Here it has been reversed. Here a 2 is connected to b 1, b 2 is connected c 1, and c 2 is connected a 1. But, in both cases, the lines are obtained from the terminal a 2 b 2 c 2. So, this is the difference between Y – d – 1 and Y – d – 11 connections.

(Refer Slide Time: 26:01)

Now, let us look at an interesting aspect of these connections. Let us take two connections Y – d… a connection of D – y – 11. The D – y – 11 connection was like this – A 1 was connected to B 2; B 1 was connected C 2; and C 1 was connected to A 2. And the terminals were obtained from A 2, B 2, C 2. On the low voltage side, we had… This is a 1 a 2, b 1 b 2, c 1 c 2. This was originally D – y – 11 connection. Now, let us see the supply is given to high voltage side with A phase connected here, B phase connected here, C phase connected here. Now, let us exchange two terminals: b and c of the supply; that is, instead of connecting phase B to this, if we connect phase C here; and instead of connecting phase C to this, if we connect phase B here; then let us see what happens.

So, what is the winding voltage now? This supply phase sequence is A B C; this is A; this is B; this is C. If we interchange, then what happens? The winding voltage phasor V A 1 A 2 is now the line voltage V A C. The voltage of terminal A 2 with respect to A 1 is now the line voltage V A with respect to C. So, this is the line voltage. This is A 2; this is A 1 as well as B 2; this is A 2 as well as C 1. Similarly, the winding voltage B 1 B 2; that is, B 2 with respect to B 1 is now voltage V C B – V C B. This is terminal B 1. And the winding voltage V of C 2 with respect to C 1; this is also C 2. So, this is the voltage phasor C 2 C 1. So, let us see.

Now, we have the high voltage side line voltage phasors of this. So, on the low voltage side, the voltage phasor b 1 b 2 will be… This will be b 2; this will be b 1. a 1 a 2 similarly will be… This will be a 1; this will be a 2; this will be c 1; this will be c 2. Now, let us also exchange the terminal on the low voltage side. Let us call this in the c phase and let us call this the b phase. Hence, this will be line a; this will be line b; this will be line c. On the high voltage side, this we are… this is line A; this is line B; this is line C. So, we see in this case, line to neutral voltage phasor on the high voltage side is this. This is the a phase line to neutral voltage phasor.

On the low voltage side, on the other hand, the line to neutral voltage phasor is this. Hence, the low voltage side line to neutral voltage phasor now lags the line to neutral voltage phasor of the high voltage side. Hence, this becomes effectively a D – y – 1 connection. So, we see that, we can very easily convert a D – y – 11 to D – y – 1 by simply exchanging two terminals – external terminals. There is no need to change the connection – internal connection of the transformer windings. This is sometimes useful; particularly, while connecting transformers in parallel. As we will see for parallel operations of 3 phase transformers, it is essential that, the line to neutral voltage phasor of both the transformers should be in phase.

(Refer Slide Time: 33:46)

Now, let us see how a zigzag connection can be handled. So, let us first take up the case of Y – z – 1. As we have seen, the D – z – 1 is not possible. So, input side is Y connected. Hence, the line to neutral voltage phasor is same as the winding voltage phasor. So, let us say this is the A phase; this is B phase; and this is C phase. This is terminal A, B, C lines. Hence, this is also A 2; this is B 2; and this is C 2. This is A 1, B 1, C 1. On the low voltage side, we will have six such phasors a 1 a 2, a 3 a 4, b 1 b 2, b 3 b 4, c 1 c 2, c 3 c 4. Since this is D z 1, the low voltage side line to neutral voltage phasor must lag the high voltage side line to neutral voltage phasor. Therefore, the line to neutral voltage phasor of the low voltage side should look… This should be c; this should be a; and this should be b.

How do we obtain this from using this set of winding voltage phasors, and with the constants that, the last leg of the winding should be made of the same phase; that is, a phase should be either a 1 a 2 or a 3 a 4. Usually, it will be a 3 a 4. So, we want to make this phase let us say using a 3 a 4; this is the phasor a 3 a 4, which is in phase with capital A 1 A 2. Hence, what should be this one? This can be… This phasor should be like this. From here we see that, it should be c 1 c 2; that is, this is c 2; this is c 1, because this is in phase opposition to this. Similarly, for b phase, we will have b 3 b 4… Hence, this phasor can be only a 1 a 2. For the c phase, this is c 4. Hence, this phasor can be b 1 b 2.

(Refer Slide Time: 38:47)

As far as the connection is concerned, we have three windings on the high voltage side – A 1 A 2, B 1 B 2, C 1 C 2. The star is formed by connecting A 1 B 1 C 1. The lines are given to A 2 B 2 C 2. This is line A; this is line B; this is line C. On the zigzag side, we have six windings: a 1 a 2, a 3 a 4, b 1 b 2, b 3 b 4, c 1 c 2, c 3 c 4. The star point as we see is formed by connecting a 2 b 2 c 2. This is the star point. And lines are taken from a 4 b 4 c 4. This is line a; this is line b; this is line c. Internal connection wise, we find that, a 1 is connected to b 3, b 1 is connected to c 3, and c 1 is connected to a 3. That completes the connection of Y – z – 1. This is the Y – z – 1 transformer connection.

(Refer Slide Time: 41:36)

So, the last connection that we will see will be the Y – z – 11 connection since Y – z – 0 or 6 is not possible. So, here again, the high voltage side is star connected; hence, the line to neutral voltage phasor is same as the winding voltage phasors. So, this is line A; this is line B; this is line C; this is the neutral point N. This is also terminal A 2; this is terminal B 2; this is terminal C 2. Hence, this is terminal A 1; this is terminal B 1; and C 1. On the low voltage side, again we have six phasors: a 1 a 2, a 3 a 4, b 1 b 2, b 3 b 4, c 1 c 2, c 3 c 4.

In order to have a Y – z – 11 connection, the low voltage side line to neutral voltage should lead the high voltage side line to neutral voltage by 30 degree. Hence, for the Y – z – 11 connection, the line to neutral voltage on the low voltage side should be like this – this should be the line b; this should be the line a; and this should be the line c. Let us see how we can obtain this kind of line to neutral voltage using this winding voltage phasor with the constant that, the last leg should be formed with the same phase voltage preferably the second set. So, this should be a 3 a 4. Hence, this phasor can only be b 2 b 1; this is b 1; this is b 2. Similarly, for b phase, this should be b 3 b 4; this should be c 2 c 1; this should be c 4 c 3; and this should be a 1 a 2.

(Refer Slide Time: 46:29)

Connection wise, this is the high voltage side windings. There are six windings on the low voltage side: a 1 a 2, a 3 a 4, b 1 b 2, b 3 b 4, c 1 c 2, c 3 c 4. Again, we find here that, the star point is formed by connecting a 2 b 2 c 2. From this phasor diagram, we find that, the star point is formed by connecting a 2 b 2 c 2. This is the neutral. The lines are still obtained from the terminals a 4, b 4 and c 4. This is line a; this is line b; this is line c. Now, internal connection wise, we find that, a 1 now is connected to c 3; a 1 is connected to c 3; b 1 is connected to a 3; and c 1 is connected to b 3. This completes the connection on the low voltage side. On the high voltage side, as usual, the neutral point is formed by connecting A 1 B 1 C 1; and the lines are supplied to A 2 gets A, B 2 gets B, and C 2 gets C. This is the connection diagram for Y – z – 11; where, we find that, the line to neutral voltage on the low voltage side leads the line to neutral voltage on the high voltage side by an angle of 30 degree.

It will be interesting to compare the connection of Y – z – 1 and Y – z – 11. This was the connection of Y – z – 1. We find that, the high voltage side connection on both sides, are identical. That is expected on the low voltage side in both cases; in both cases, the star point is formed by connecting a 2 b 2 c 2. However, for… As far as… Then the lines are obtained in both cases from a 4, b 4 and c 4. However, as far as the internal connections are concerned, here we see that, a 1 is connected to b 3; in this case, a 1 is connected to c 3; b 1 is connected to c 3; here b 1 is connected a 3; c 1 is connected a 3; here c 1 is connected to b 3. This is the only difference between the two connections.

The implication of this will be clear if we look at the two corresponding phasor diagrams. We see that, on the low voltage side, in both cases, the last leg of the phase is formed using a 3 a 4, b 3 b 4, c 3 c 4 in both cases. However, the initial part on the Y – z – 1 connection required c 2 c 1; whereas, Y – z – 11 connection required b 2 b 1. Hence, in Y – z – 1, the a phase is formed using a phase and c phase; while in Y – z – 11, a phase is formed using a phase and b phase; that is the difference. The rest of the connections for these two are same.

Thank you.