 # Transformers

The equivalent circuit of one phase of a transformer referred to the primary winding is shown in Figure 3.31. The resistances and reactances can be found from the well- known open- and short-circuit tests. In the absence of complete information for each winding, the two arms of the T network can each be assumed to be half the total transformer impedance. Also, little accuracy is lost in transferring the shunt branch to the input terminals.

In power transformers the current taken by the shunt branch is usually a very small percentage of the load current and is neglected for most power system calculations.

## Phase Shifts in Three-Phase Transformers

Consider the transformer shown in Figure 3.32(a). The red phases on both circuits are taken as reference and the transformation ratio is 1: N. The corresponding phasor diagrams are shown in Figure 3.32(b). Although no neutral point is available in the delta side, the effective voltages from line to earth are denoted by Ern, Eyn, and EB'n. Comparing the two phasor diagrams, the following relationships are seen: that is, the positive sequence or normal balanced voltage of each phase is advanced through 30°. Similarly, it can be shown that the positive sequence currents are advanced through 30°.

By consideration of the negative phase-sequence phasor diagrams (these are pha- sors with reversed rotation, that is R-B-Y) it will readily be seen that the phase currents and voltages are shifted through —30°. When using the per unit system the transformer ratio does not directly appear in calculations and the phase shifts are often neglected. Figure 3.32 (a) Star-delta transformer with turns ratio 1: N. (b) Corresponding phasor diagrams (N taken as 1 in diagrams)

In star-star and delta-delta connected transformers there are no phase shifts. Hence transformers having these connections and those with star-delta connections should not be connected in parallel. To do so introduces a resultant voltage acting in the local circuit formed by the usually low transformer impedances. Figure 3.33 shows the general practice on the British network with regard to transformers with phase shifts. It is seen that the reference phasor direction is different at different voltage levels. The larger than 30° phase shifts are obtained by suitable rearrangement of the winding connections.