Page 62 - Solutions Manual to accompany Electric Machinery Fundamentals

2-16. Prove the following statement: If a transformer having a series impedance Z eq is connected as an
autotransformer, its per-unit series impedance  Z as an autotransformer will be
eq
N
Z   SE Z
eq
N SE  N C eq
Note that this expression is the reciprocal of the autotransformer power advantage.

SOLUTION The impedance of a transformer can be found by shorting the secondary winding and
determining the ratio of the voltage to the current of its primary winding. For the transformer connected
as an ordinary transformer, the impedance referred to the primary ( N ) is:
C
Z 1 Z 2
+ +

V N N V
1 C SE 2
- -

 N  2
Z  Z  1  C Z
eq
 N  SE  2
The corresponding equivalent circuit is:

Z eq
+ +

V 1 N C N SE V 2

- -

When this transformer is connected as an autotransformer, the circuit is as shown below. If the output
windings of the autotransformer are shorted out, the voltages V H will be zero, and the voltage V L will
be

+ +
I
SE
.
V SE
N
I SE
L
- V H
+ + I C
Z
eq
.
V L V
C
N C
- - -

V  I C Z eq
L
where Z eq is the impedance of the ordinary transformer. However,

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