Page 64 - Solutions Manual to accompany Electric Machinery Fundamentals

(a) Sketch the transformer connection that will do the required job.
(b) Find the kilovoltampere rating of the transformer in the configuration.

(c) Find the maximum primary and secondary currents under these conditions.
(d) The transformer in Problem 2-18 is identical to the transformer in Problem 2-17, but there is a
significant difference in the apparent power capability of the transformer in the two situations.
Why? What does that say about the best circumstances in which to use an autotransformer?

SOLUTION (a) For this configuration, the common winding must be the larger of the two windings, and
N  4N . The transformer connection is shown below:
C SE
+

N
SE

+
600 V
N
C
480 V

- -
(b) The kVA rating of the autotransformer can be found from the equation

N  N N  4N
S  SE C S  SE SE  10 kVA  50 kVA
IO
N SE W N SE
(c) The maximum primary current for this configuration will be

S 50,000 VA
I  P   83.3 A
V P 600 V
and the maximum secondary current is

S 50,000 VA
I    104 A
S
V S 480 V
(d) Note that the apparent power handling capability of the autotransformer is much higher when there
is only a small difference between primary and secondary voltages. Autotransformers are normally only
used when there is a small difference between the two voltage levels.
2-19. Two phases of a 14.4-kV three-phase distribution line serve a remote rural road (the neutral is also
available). A farmer along the road has a 480 V feeder supplying 200 kW at 0.85 PF lagging of three-
phase loads, plus 60 kW at 0.9 PF lagging of single-phase loads. The single-phase loads are distributed
evenly among the three phases. Assuming that the open-Y-open- connection is used to supply power to
his farm, find the voltages and currents in each of the two transformers. Also find the real and reactive
powers supplied by each transformer. Assume that the transformers are ideal. What is the minimum
required kVA rating of each transformer?
SOLUTION The farmer’s power system is illustrated below:

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