What Is The Equivalent Circuit Of A Three Winding Transformer?

Various forms of a three-winding transformer equivalent circuit have been proposed, but the simplest and most useful is the so-called T equivalent circuit, shown in Figure 4.9.

The magnetizing branch is omitted in the T equivalent since the magnetizing impedance is normally much greater than the series impedances. If voltages and impedances are expressed in per unit values, then the ideal transformers can sometimes be omitted also; however, in some cases 1:1 ideal transformers are retained so that the connections to the primary, secondary and tertiary circuits can be properly represented by the equivalent circuit.

In a three-winding transformer, eddy-current losses occur in each winding from stray flux produced by the other two windings, even if the third winding is not carrying any load. Therefore, each series resistance element in the T equivalent circuit of a three-winding transformer represent eddy-current losses produced by currents in other windings.

Hence, a series resistance does not belong to any particular winding but is distributed among all three widings. To derive the series impedance values in the T equivalent circuit, impedance measurements are made of each pair of windings taken two at a time.

One winding is short-circuited with voltage applied to the other winding while the third winding is open-circuited. The current is measured through the winding with the applied voltage. The impedance is equal to the applied voltage divided by that current.

The test setup to measure the impedance between the H and X windings of a single-phase three-winding transformer is shown in Figure 4.10.

The test for a three-phase, three-winding transformer is similar except that three-phase voltages are used. There are three sets of measurements taken. 

The first set of measurements applies a three-phase voltage to the H1, H2, and H3 terminals with the X1, X2, and X3 terminals shorted together and the Y1, Y2, and Y3 terminals open. 

The second set of measurements applies a three-phase voltage to the H1, H2, and H3 terminals with the Y1, Y2, and Y3 terminals shorted together and the X1, X2, and X3 terminals open. 

Finally, a three-phase voltage is applied to the X1, X2 and X3 terminals with the Y1, Y2, and Y3 terminals shorted together with the H1, H2, and H3 terminals open. The ZHX, ZHY, and ZXY impedance values are determined by dividing the voltages by the currents in each test. 

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