Page 97 - Electric Machinery Fundamentals

TRANSFORMERS 73

The apparent impedance of the primary circuit of the transfonner is
Z' _ Vp
L - Ip (2-14)

Since the primary voltage can be expressed as
Vp = aVs
and the primary cunent can be expressed as
Is
Ip =-
a
the apparent impedance of the primary is
Z' _.Ye - aVs - a2~
L - Ip - Isla - Is

(
(2-15)

With a transformer, it is possible to match the magnitude of a load imped-
ance to a source impedance simply by picking the proper turns ratio.

Analysis of Circuits Containing Ideal Transformers
If a circuit contains an ideal transformer, then the easiest way to analyze the circuit
for its voltages and currents is to replace the portion of the circuit on one side of the
transformer by an equivalent circuit with the same terminal characteristics. After the
equivalent circuit has been substituted for one side, then the new circuit (without a
transformer present) can be solved for its voltages and currents. In the poltion of the
circuit that was not replaced, the solutions obtained will be the correct values of volt-
age and current for the original circuit. Then the turns ratio of the transfonner can be
used to determine the voltages and currents on the other side of the transformer. The
process of replacing one side of a transformer with its equivalent at the other side's
voltage level is known as referring the first side of the transformer to the second side.
How is the equivalent circuit formed? Its shape is exactly the same as the shape
of the original circuit. The values of voltages on the side being replaced are scaled by
Equation (2-4), and the values of the impedances are scaled by Equation (2-l5). The
polarities of voltage sources in the equivalent circuit will be reversed from their di-
rection in the oliginal circuit if the dots on one side of the transformer windings are
reversed compared to the dots on the other side of the transformer windings.
The solution for circuits containing ideal transformers is illustrated in the
following example.
Example 2-1. A single-phase power system consists of a 480-V 60-Hz gen-
erator supplying a load Z\oad = 4 + j3 .n through a transmission line of impedance
Zline = 0.18 + )0.24!1. Answer the following questions about this system.
(a) If the power system is exactly as described above (and shown in Figure 2- 6a),
what will the voltage at tlle load be? What will the transmission line losses be?

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