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# Determination of Equivalent R, X, and Z of a Transformer by Test

Author: E.E. Kimberly

If the secondary coil of a transformer is short-circuited and just enough voltage is applied to the primary to cause rated full-load currents to flow in the primary and secondary coils, the mutual flux required is so small that the exciting current may be neglected. Also, because of the low flux density in the iron, the iron losses may be neglected. However, the effective resistance and reactance are unchanged and may be determined by measurements. With reduced voltage applied to the transformer, readings of P, V, and I1 are the only ones necessary for calculating the constants. Thus,

Inasmuch as the test is made with low voltage, it is advantageous to short-circuit the low side of the transformer because the voltage then needed on the high side will be generally better suited to the available instruments. If the test were made with the high side short-circuited, the reflection constant would be

Example 17-2. - A 5-kv-a, 440/110-volt transformer is short-circuited on its low side, and reduced voltage is applied to the high side. The meter readings are as follows: P = 110 watts, V = 13 volts, and I1 = 11.38 amp. Calculate the equivalent resistance R and inductance X of the transformer.

Solution. - By equations (17-4), (17-5), and (17-6),

Unless the transformer is of unusual design, X1 may be taken as equal to and R1 may be taken

as equal to

Then,

Last Update: 2010-10-06