Page 68 - Solutions Manual to accompany Electric Machinery Fundamentals

(b) The per-unit primary voltage at rated conditions and unity power factor is
V  V I Z
P S S EQ
1 0 V 
V P   1 0  0.041 j 0.101   1.046 5.54 pu  
The per-unit power consumed by R is
EQ
P  EQ 2  I R  1 pu 2  0.041 pu   0.041 pu

The per-unit power consumed by R is
C
2  V 1.046 2
P  P   0.0136 pu
C
R C 80.3
Therefore the efficiency of this transformer at rated load and unity power factor is
P P 1.00
  out  100%  out  100%   100% 94.8%



P in P  out P  EQ P C 1.00 0.041 0.0136
and the voltage regulation is

1.046 1.00

VR   100% 4.6%
1.00
(c) The voltage and apparent power ratings of this transformer must be reduced in direct proportion to
the decrease in frequency in order to avoid flux saturation effects in the core. At 50 Hz, the ratings are
50 Hz
S   50 kVA  41.7 kVA
rated
60 Hz
50 Hz
V   20,000 V  16,667 kV
,rated
P
60 Hz
50 Hz
V   480 V  400 V
,rated
S
60 Hz
(d) The transformer parameters referred to the primary side at 60 Hz are:
R  C Z base R C ,pu  8 k 80.3  642 k 

X M  Z base X M   ,pu 8 k  214 k   26.7 
R EQ  Z base R EQ   ,pu 8 k 0.041  328  
X EQ  Z base X EQ   ,pu 8 k 0.101  808  

At 50 Hz, the resistance will be unaffected but the reactances are reduced in direct proportion to the
decrease in frequency. At 50 Hz, the reactances are

 50 Hz 
X M     214 k  178 k
 60 Hz 
 50 Hz 
X   808   673 
EQ  
 60 Hz 

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