Transformer:Transformer with Resistance and Leakage Reactance

Transformer with Resistance and Leakage Reactance

In Fig. 32.28 the primary and secondary windings of a transformer with reactances taken out of the windings are shown. The primary impedance is given by

The vector diagram for such a transformer for different kinds of loads is shown in Fig. 32.29. In these diagrams, vectors for resistive drops are drawn parallel to current vectors whereas reactive drops are perpendicular to the current vectors. The angle f1 between V 1 and I1 gives the power factor angle of the transformer.

It may be noted that leakage reactances can also be transferred from one winding to the other in the same way as resistance.

Example 32.15. A 30 kVA , 2400/120-V, 50-Hz transformer has a high voltage winding resistance of 0.1 W and a leakage reactance of 0.22W. The low voltage winding resistance is 0.035 W and the leakage reactance is 0.012 W. Find the equivalent winding resistance, reactance and impedance referred to the (i) high voltage side and (ii) the low-voltage side.

(Electrical Machines-I, Bangalore Univ. 1987)

Example 32.16. A 50-kVA, 4,400/220-V transformer has R1 = 3.45 W, R2 = 0.009 W. The values of reactances are X1 = 5.2 W and X2 = 0.015 W. Calculate for the transformer (i) equivalent resistance as referred to primary (ii) equivalent resistance as referred to secondary (iii) equivalent reactance as referred to both primary and secondary (iv) equivalent impedance as referred to both primary and secondary (v) total Cu loss, first using individual resistances of the two windings and secondly, using equivalent resistances as referred to each side.

(Elect. Engg.-I, Nagpur Univ. 1993)

Example 32.20. A 100 kVA, 1100/220 V, 50 Hz, single-phase transformer has a leakage impedance of (0.1 + 0/40) ohm for the H.V. winding and (0.006 + 0.015) ohm for the L.V. winding. Find the equivalent winding resistance, reactance and impedance referred to the H.V. and L.V. sides.