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

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 3phase 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

THREE PHASE TRANSFORMER WINDING DIAGRAM

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 BB1B2B and induced voltage in c1c2 will be in phase with applied voltage across C1C2. 

Now let us join the terminals A2, BB2 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, B1B 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 =200*1.73 VLL, the magnitude of the voltage impressed across each of the primary coils will be 3 times less i.e., 200 V. However, the phasors 12AAV  12BBVand 12CCVwill 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 are shown in figure 26.2. 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 200   3V. Thus,             Va b11           ,           b c12V and    2c a1V are of same magnitude and displaced mutually by 120º to form a balanced 3-phase voltage system. Primary 3-phase line to line voltage of 200  3V is therefore stepped down to 3-phase, 100      3V line to line voltage at the secondary. The junction of A2, BB2 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.

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 windings are connected by shorting A2, BB2 and C2 together

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

. If a voltmeter is connected across S (i.e., between a2 and c2), it is going to read the length of the phasorV. By referring to phasor 2diagram of figure 26.9, it can be easily shown that the voltage across the switch S, under this condition isV= a c o 100+ 2cos60 100 = 200V . So this connection is not proper and the switch S should not be closed.