# Three Phase Transformer

It is the three phase system which has been adopted world over to generate, transmit and distribute electrical power. Therefore to change the level of voltages in the system three phase transformers should be used.

Three number of identical single phase transformers can be suitably connected for use in a three phase system and such a three phase transformer is called a bank of three phase transformer. Alternatively, a three phase transformer can be constructed as a single unit.

__Introducing Basic Ideas:- __

In a single phase transformer, we have only two coils namely primary and secondary. Primary is energized with single phase supply and load is connected across the secondary. However, in a 3-phase transformer there will be 3 numbers of primary coils and 3 numbers of secondary coils. So these 3 primary coils and the three secondary coils are to be properly connected so that the voltage level of a balanced 3-phase supply may be changed to another 3-phase balanced system of different voltage level.

Suppose you take three identical transformers each of rating 10 kVA, 200 V / 100 V, 50 Hz and to distinguish them call them as A, B and C. For transformer-A, primary terminals are marked as A1A2 and the secondary terminals are marked as a1a2. The markings are done in such a way that A1 and a1 represent the dot (•) terminals. Similarly terminals for B and C transformers are marked

It may be noted that individually each transformer will work following the rules of single phase transformer i.e, induced voltage in a1a2 will be in phase with applied voltage across A1A2 and the ratio of magnitude of voltages and currents will be as usual decided by a where a = N1/N2 = 2/1, the turns ratio. This will be true for transformer-B and transformer-C as well i.e., induced voltage in b1b2 will be in phase with applied voltage across B1B2 and induced voltage in c1c2 will be in phase with applied voltage across C1C2.

Now let us join the terminals A2, B2 and C2 of the 3 primary coils of the transformers and no inter connections are made between the secondary coils of the transformers. Now to the free terminals A1, B1 and C1 a balanced 3-phase supply with phase sequence A-B-C is connected. Primary is said to be connected in star.

If the line voltage of the supply is *V**LL *= 200 3 V , the magnitude of the voltage impressed across each of the primary coils will be times less i.e., 200 V. However, the phasors *V*,

*VB B *and *VC C *will be have a mutual phase difference of 120º. Then from the fundamental principle of single phase transformer we know, secondary coil voltage 12aaVwill be parallel to 12AAV; 12bbVwill be parallel to 12BBVand 12ccVwill be parallel to 12CCV. Thus the secondary induced voltage phasors will have same magnitude i.e., 100 V but are displaced by 120º mutually. The secondary coil voltage phasors 12aaV, 12bbVand 12ccV. Since the secondary coils are not interconnected, the secondary voltage phasors too have been shown independent without any interconnections between them. In contrast, the terminals A2, B2 and C2 are physically joined forcing them to be equipotential which has been reflected in the primary coil voltage phasors as well where phasor points A2, B2 and C2 are also shown joined. Coming back to secondary, if a voltmeter is connected across any coil i.e., between a1 and a2 or between b1 and b2 or between c1 and c2 it will read 100 V. However, voltmeter will not read anything if connected between a1 and b1 or between b1 and c1 or between c1 and a1 as open circuit exist in the paths due to no physical connections between the coils.

Imagine now the secondary coil terminals a2, b2 and c2 are joined together physically. So the secondary coil phasors should not be shown isolated as a2, b2 and c2 become equipotential due to shorting of these terminals. Thus, the secondary coil voltage phasors should not only be parallel to the respective primary coil voltages but also a2, b2 and c2 should be equipotential. Therefore, shift and place the phasors 12aaV, 12bbVand 12ccVin such a way that they remain parallel to the respective primary coil voltages and the points a2, b2 and c2 are superposed.

Here obviously, if a voltmeter is connected between a1 and b1 or between b1 and c1 or between c1 and a1 it will read corresponding phasor lengths a1b1 or b1 c1 or c1a1 which are all equal to 2003V. The junction of A2, B2 and C2 can be used as primary neutral and may be denoted by N. Similarly the junction of a2, b2 and c2 may be denoted by n for secondary neutral.

__A Wrong Star-Star Connection :- __

In continuation with the discussion of the last section, we show here a deliberate wrong connection to highlight the importance of proper terminal markings of the coils with dots (•). where the secondary coils are yet to be connected. To implement star connection on the secondary side, let us assume that someone joins the terminals a2, b1 and c2 together.

The question is: is it a valid star connection? If not why? To answer this we have to interconnect the secondary voltage phasors in accordance with the physical connections of the coils. In other words, shift and place the secondary voltage phasors so that a2, b1 and c2 overlap each other to make them equipotential. The lengths of phasors 12aaV, 12bbVand 12ccV are no doubt, same and equal to 100 V but they do not maintain 120º mutual phase displacement between them as clear. The magnitude of the line to line voltages too will not be equal. From simple geometry, it can easily be shown that

Thus both the phase as well as line voltages are not balanced 3-phase voltage. Hence the above connection is useless so far as transforming a balanced 3-phase voltage into another level of balanced 3-phase voltage is concerned.

Appropriate polarity markings with letters along with dots (•) are essential in order to make various successful 3-phase transformer connections in practice or laboratory.

__Bank of Three Phase Transformer:-__

In the background of the points discussed in previous section, we are now in a position to study different connections of 3-phase transformer. Let the discussion be continued with the same three single phase identical transformers, each of rating 10kVA, 200V / 100V, 50Hz,.

These transformers now should be connected in such a way, that it will change the level of a balanced three phase voltage to another balanced three phase voltage level. The three primary and the three secondary winding’s can be connected in various standard ways such as

**Star / Star****Star / Delta****Delta / Delta****Delta / Star**

__Star-Star Connection:-__

We have discussed in length in the last section, the implementation of star-star connection of a 3-phase transformer. The connection diagram along with the phasor diagram.

As discussed earlier, we need to apply to the primary terminals (A1B1C1) a line to line voltage of 2003 V so that rated voltage (200 V) is impressed across each of the primary coils of the individual transformer. This ensures 100 V to be induced across each of the secondary coil and the line to line voltage in the secondary will be 1003 V. Thus a 3-phase line to line voltage of 2003 V is stepped down to a 3-phase line to line voltage of 1003 V. Now we have to calculate how much load current or kVA can be supplied by this bank of three phase transformers without over loading any of the single phase transformers.

From the individual rating of each transformer, we know maximum allowable currents of HV and LV windings are respectively IHV = 10000/200 = 50A and ILV = 10000/100 = 100A. Since secondary side is connected in star, line current and the winding currents are same. Therefore total kVA that can be supplied to a balanced 3-phase load is ()33310010030LLLVI==kVA. While solving problems, it is not necessary to show all the terminal markings in detail and a simple and popular way of showing the same star-star connection.

__Star-Delta Connection:-__

To connect windings in delta, one should be careful enough to avoid dead short circuit. Suppose we want to carry out star / delta connection with the help of the above single phase transformers. HV winding’s are connected by shorting A2, B2 and C2 together as shown in the figure 26.8. As we know, in delta connection, coils are basically connected in series and from the junction points, connection is made to supply load. Suppose we connect quite arbitrarily (without paying much attention to terminal markings and polarity), a1 with b2 and b1 with c1. Should we now join a2 with c2 by closing the switch S, to complete the delta connection? As a rule, we should not join (i.e., put short circuit) between any two terminals if potential difference exists between the two. It is equivalent to put a short circuit across a voltage source resulting into very large circulating current. Therefore before closing S, we must calculate the voltage difference between a2 with c2. To do this, move the secondary voltage phasors such that a1 and b2 superpose as well as b1 with c1 superpose – this is because a1 and b2 are physically joined to make them equipotential; similarly b1 and c1 are physically joined so as to make them equipotential. The phasor diagram is shown in figure 26.9. If a voltmeter is connected across S (i.e., between a2 and c2), it is going to read the length of the phasor 22acV. By referring to phasor diagram of figure 26.9, it can be easily shown that the voltage across the switch S, under this condition iso100+2cos60100200V22acV==. So this connection is not proper and the switch S should not be closed.

Another alternative way to attempt delta connection in the secondary could be: join a1 with b2 and b1 with c2. Before joining a2 with c1 to complete delta connection, examine the open circuit voltage 21acV. Following the methods described before it can easily be shown that 21acV= 0, which allows to join a2 with c1 without any circulating current. So this, indeed is a correct delta connection and is shown in figure 26.10 where a1 is joined with b2, b1 is joined with c2 and c1 is joined with a2. The net voltage acting in the closed delta in this case is zero. Although voltage exists in each winding, the resultant sum becomes zero as they are 120° mutually apart. The output terminals are taken from the junctions as a, b and c for supplying 3-phase load. The corresponding phasor diagram.

Here also we can calculate the maximum kVA this star / delta transformer can handle without over loading any of the constituents transformers. In this case the secondary line to line voltage is same as the winding voltage i.e., 100V, but the line current which can be supplied to the load is1003. Because it is at this line current, winding current becomes the rated 100A. Therefore total load that can be supplied is()33 1003 100 VA=30 kVA LLLVI=. Here also total kVA is 3 times the kVA of each transformer. The star-delta connection is usually drawn in a simplified manner for problem solving and easy understanding.

Another valid delta connection on the LV side is also possible by joining a2 with b1, b2 with c1 and c2 with a1. It is suggested that the reader tries other 3-phase connections and verify that the total KVA is 3-times the individual KVA of each transformer. However, we shall discuss about delta / delta and open delta connection.

__Delta / Delta and open Delta Connection:-__

Here we mention about the delta/delta connection because, another important and useful connection namely open delta connection can be understood well. Valid delta connection can be implemented in the usual way as shown in the figure 26.13. The output line to line voltage will be 100V for an input line voltage of 200V. From the secondary one can draw a line current of 1003A which means a total of 30 kVA can be supplied without overloading any of the individual transformers. A simplified representation of the delta-delta connection along with the magnitude of the currents in the lines and in the coils of HV and LV side.

Let us now imagine that the third transformer C be removed from the circuit as shown in the second part of the. In effect now two transformers are present. If the HV sides is energized with three phase 200V supply, in the secondary we get 3-phase balanced 100V supply which is clear from the phasor diagram. Although no transformer winding exist now between A2 & B1 on the primary side and between a2 & b1 on the secondary side, the voltage between A2 & B1 on the primary side and between a2 & b1 on the secondary side exist. Their phasor representation are shown by the dotted line confirming balanced 3-phase supply. But what happens to kVA handling capacity of the open delta connection? Is it 20 kVA, because two transformers are involved? Let us see.

The line current that we can allow to flow in the secondary is 100A (and not 1003 as in delta / delta connection). Therefore total maximum kVA handled is given by()33 100 100 VA=17.32 kVA LLLVI=, which is about 57.7% of the delta connected system. This is one of the usefulness of using bank of 3-phase transformers and connecting them in delta-delta. In case one of them develops a fault, it can be removed from the circuit and power can be partially restored.

__3 – Phase Transformer – a Single Unit:-__

Instead of using three number of single phase transformers, a three phase transformer can be constructed as a single unit. The advantage of a single unit of 3-phase transformer is that the cost is much less compared to a bank of single phase transformers. In fact all large capacity transformers are a single unit of three phase transformer,

To understand, how it is constructed let us refer to. Here three, single phase transformers are so placed that they share a common central limb. The primary and the secondary winding’s of each phase are placed on the three outer limbs and appropriately marked. If the primary winding’s are connected to a balanced 3-phase supply (after connecting the winding’s in say star), the fluxes φA(t), φB(t) and φC(t) will be produced in the cores differing in time phase mutually by 120°.

The return path of these fluxes are through the central limb of the core structure. In other words the central limb carries sum of these three fluxes. Since instantaneous sum of the fluxes, φA(t)+ φB(t)+ φC(t) = 0, no flux lines will exist in the central limb at any time. As such the central common core material can be totally removed without affecting the working of the transformer. Immediately we see that considerable saving of the core material takes place if a 3-phase transformer is constructed as a single unit. The structure however requires more floor area as the three outer limbs protrudes outwardly in three different directions.

A further simplification of the structure can be obtained by bringing the limbs in the same plane. But what do we sacrifice when we go for this simplified structure? we note that the reluctance seen by the three fluxes are same, Hence magnetizing current will be equal in all the three phases. In the simplified core structure, reluctance encountered by the flux φB is different from the reluctance encountered by fluxes φA and φC, Hence the magnetizing currents or the no load currents drawn will remain slightly unbalanced. This degree of unbalanced for no load current has practically no influence on the performance of the loaded transformer. Transformer having this type of core structure is called the core type transformer.

__Vector Group of 3-phase Transformer:-__

The secondary voltages of a 3-phase transformer may undergo a phase shift of either +30° leading or -30° lagging or 0° i.e, no phase shift or 180° reversal with respective line or phase to neutral voltages. On the name plate of a three phase transformer, the vector group is mentioned. Typical representation of the vector group could be Yd1 or Dy11 etc. The first capital latter Y indicates that the primary is connected in star and the second lower case latter d indicates delta connection of the secondary side.

The third numerical figure conveys the angle of phase shift based on clock convention. The minute hand is used to represent the primary phase to neutral voltage and always shown to occupy the position 12. The hour hand represents the secondary phase to neutral voltage and may, depending upon phase shift, occupy position other than 12.

The angle between two consecutive numbers on the clock is 30°. The star-delta connection and the phasor correspond to Yd1. It can be easily seen that the secondary a phase voltage to neutral n (artificial in case of delta connection) leads the A phase voltage to neutral N by 30°. However the star delta connection correspond to Yd11.