Open-Circuit and Short-Circuit Tests, Exciting Admittance, and Equivalent Impedance

The constants of the transformer for the approximate equivalent circuit can be determined from the open-circuit and short-circuit tests.

The open-circuit test is made to obtain the values of the exciting-admittance, conductance, and susceptance. In the case of power transformers or constant-voltage transformers operating at one specified frequency, the open-circuit test consists in the application of rated voltage at rated frequency usually to the low-voltage winding with the high-voltage winding open circuited. Measurements are made by means of indicating instruments (voltmeter, ammeter, and wattmeter) of voltage, current, and power. Actually, the open-circuit test can be made by applying rated voltage at rated frequency to the high-voltage winding with the low-voltage winding open circuited. However, it is usually more convenient to work on the low-voltage side because the lower voltage is easier to handle.

Figure 6-16. Open-circuit test with indicating instruments

The quantities involved in most communication transformers are generally too small for wattmeter and ammeter measurements. Methods involving the use of a-c bridges or other suitable devices are employed. In Fig. 6-16 let

I_exc = the exciting current as read by the ammeter, A⁽¹⁾
V = the applied voltage as read by the voltmeter, V
P_oc = power as measured with the wattmeter, W

Then the exciting admittance is

[6-46]

and the exciting conductance is

[6-47]

from which the exciting susceptance is found to be

[6-48]

The short-circuit test yields results from which the equivalent impedance, equivalent resistance, and equivalent leakage reactance of the transformer can be evaluated. In Fig. 6-14(b) the equivalent impedance of the transformer referred to the primary is

[6-49]

in which the equivalent resistance referred to the primary of the transformer is

[6-50]

and the equivalent leakage reactance referred to the primary is

[6-51]

The equivalent impedance referred to the secondary is

[6-52]

from which

[6-53]

and

[6-54]

It is the general practice, in the short-circuit test, to short circuit the low-voltage winding and to apply voltage, at rated frequency, such that rated current flows in the transformer. Measurements are made of input current, power, and voltage, using indicating instruments, i.e., ammeter, wattmeter, and voltmeter as shown in Fig. 6-17. Again, in the case of communication transformers, an a-c bridge method or an arrangement adapted for measuring the smaller quantities associated with such transformers is used.

Figure 6-17. Short-circuit test with indicating instruments

The short-circuit test could also be made by short circuiting the high-voltage side and making the measurements on the low-voltage side. This, however, is more inconvenient since the applied voltage is low and the measured current high. These quantities are handled and measured more readily on the high-voltage side.

For the short-circuit test let

V_sc = applied voltage as read by the voltmeter, V (in Fig. 6-17)
I_sc = input short-circuit current as read by the ammeter, A (in Fig. 6-17)
P_sc = input power as read by the wattmeter, W (m Fig. 6-17)

The voltage V_sc is low in comparison with the rated voltage. It can be shown that, in the case of the transformer of Example 6-2, the short-circuit voltage is less than 3 percent of rated value, On that basis, the exciting current can be neglected and the short-circuit impedance Z_sc assumed to equal the equivalent series impedance of the transformer. Hence, the equivalent series impedance is

[6-55]

and the equivalent series resistance is practically equal to the short-circuit resistance

[6-56]

Also, the equivalent leakage reactance of the transformer is

[6-57]

1	When the exciting current is so small that the current in the voltmeter and the current in the potential coil of the wattmeter are appreciable, the voltmeter and the wattmeter potential coil should be disconnected from the circuit when the exciting current is measured.