11.3 TRANSFORMER EQUIVALENT CIRCUITS 485The equivalent circuits shown in Figure 11.3.4 are often known as transformerT-circuits
in which winding capacitances have been neglected. Other modifications and simplifications
of this basic T-circuit are used in practice. Approximate circuits (referred to the primary)
commonly used for the constant-frequency power-system transformer analysis are shown in
Figure 11.3.5. By moving the parallel combination ofRCandjXmfrom the middle to the left,
as shown in Figure 11.3.5(a), computational labor can be reduced greatly with minimal error.
The series impedanceR 1 +jX 1 can be combined witha^2 R 2 +ja^2 X 2 to form an equivalent
series impedance,Z ̄eq=Req+jXeq. Further simplification is gained by neglecting the exciting
current altogether, as shown in Figure 11.3.5(b), which represents the transformer by its equivalent
series impedance. WhenReqis small compared toXeq, as in the case of large power-system
transformers,Reqmay frequently be neglected for certain system studies. The transformer is
then modeled by its equivalent series reactanceXeqonly, as shown in Figure 11.3.5(c). The
student should have no difficulty in drawing these approximate equivalent circuits referred to the
secondary.
The modeling of a circuit or system consisting of a transformer depends on the frequency
range of operation. For variable-frequency transformers, the high-frequency-range equivalent
circuit with capacitances is usually considered, even though it is not further pursued here.
a^2 ZL+−V 1 RC jXmIC ImReq = R 1 + a^2 R 2 jXeq = j(X 1 + a^2 X 2 )−IoaV 2+−I 1 I 2 /a(a)
Figure 11.3.5Approximate trans-
former equivalent circuits referred to
primary.a^2 ZL+−V 1jXeq = j(X 1 + a^2 X 2 )
−
aV 2+−I 1 = I 2 /a(b)
Req = R 1 + a^2 R 2I 2 /aa^2 ZL+−V 1jXeq = j(X 1 + a^2 X 2 )
−
aV 2+−I 1 = I 2 /a(c)