Problem 92-7   Source:   Example 2-2 - page 64 -    FITZGERALD, A. E. , KINGSLEY, Charles Jr. , UMANS, Stephen D. -    Book: Electric Machinery - 5th ed. - McGraw-Hill - 1990.

A 50 kVA, 2 400:240 V , 60 Hz distribuition transformer has a leakage impedance of 0.72 + j 0.92  Ω in the high-voltage winding and 0.0070 + j 0.0090  Ω in the low-voltage winding. At rated voltage and frequency, the admittance Y_ex of the shunt branch accounting for the exciting currents (0.324 - j 2.24) x 10^-2 mhos when viewed from the low-voltage side. Draw the equivalent circuit referred to:

a) the high-voltage side.

b) the low-voltage side.

Solution of the Problem 92-7

The transformation relation of the transformer is:

Item a

Knowing the transformation relation we can reflect the impedance of low voltage to high voltage, that is:

Note that we are using Z'₂ to represent the reflected secondary impedance for the primary. So, with this data we can design the electrical schematic of the reflected transformer for high voltage, as can be seen in the Figure 92-7.1:

Note that when we refer to the impedance from the secondary to the primary, we multiply the value by a². However, in the case of the transformer's excitation winding, its value was divided by a², this because it was represented as admittance (Y_ex ) and not as impedance. As admittance is the inverse of impedance, we must divide it by a².

Item b

To achieve the equivalent circuit of the transformer referenced to the low voltage circuit, we must reflect the impedance from the primary to the secondary. In this way, we will represent this impedance by Z''₁, or:

Thus, in the Figure 92-7.2 we present the electrical schematic of the transformer referenced to the low voltage winding.