Page 54 - Solutions Manual to accompany Electric Machinery Fundamentals

V  510 V I SC  12 A 6 . P  3000 W
SC
SC
(a) If this bank delivers a rated load at 0.8 PF lagging and rated voltage, what is the line-to-line voltage
on the primary of the transformer bank?
(b) What is the voltage regulation under these conditions?

(c) Assume that the primary phase voltage of this transformer is a constant 8314 V, and plot the
secondary voltage as a function of load current for currents from no-load to full-load. Repeat this
process for power factors of 0.8 lagging, 1.0, and 0.8 leading.
(d) Plot the voltage regulation of this transformer as a function of load current for currents from no-load
to full-load. Repeat this process for power factors of 0.8 lagging, 1.0, and 0.8 leading.
(e) Sketch the per-unit equivalent circuit of this transformer.

SOLUTION From the short-circuit information, it is possible to determine the per-phase impedance of the
transformer bank referred to the high-voltage (primary) side. Note that the short-circuit information is
given for one transformer of the three in the bank. The voltage across this transformer is

V  ,SC  510 V

the short-circuit phase current is
I  ,SC  12.6 A

and the power per phase is
P  ,SC  3000 W

Thus the per-phase impedance is

510 V

Z  R  jX   40.48
EQ
EQ
EQ
12.6 A
P 3000 W
  cos  1 SC  cos  1  62.1

VI  510 V 12.6 A 
SC SC

Z EQ  R EQ  jX EQ  40.48 62.1    18.94  j  35.77
R EQ  18.94 
X EQ  j 35.77 
(a) If this Y- transformer bank delivers rated kVA (300 kVA) at 0.8 power factor lagging while the
secondary voltage is at rated value, then each transformer delivers 100 kVA at a voltage of 480 V and 0.8
PF lagging. Referred to the primary side of one of the transformers, the load on each transformer is
equivalent to 100 kVA at 8314 V and 0.8 PF lagging. The equivalent current flowing in the secondary of
one transformer referred to the primary side is
 100 kVA
I   12.03 A

,S
8314 V


 ,S  I 12.03  36.87 A
The voltage on the primary side of a single transformer is thus
 
V P ,   V S ,   I S ,  Z EQ, P

 8413 0 V    V  36.87 A 12.03 18.94  j 35.77   8856 1.34 V  


 ,P
The line-to-line voltage on the primary of the transformer is
48