Page 87 - Solutions Manual to accompany Electric Machinery Fundamentals

Chapter 4: Synchronous Generators

4-1. At a location in Europe, it is necessary to supply 1000 kW of 60-Hz power. The only power sources
available operate at 50 Hz. It is decided to generate the power by means of a motor-generator set
consisting of a synchronous motor driving a synchronous generator. How many poles should each of the
two machines have in order to convert 50-Hz power to 60-Hz power?
SOLUTION The speed of a synchronous machine is related to its frequency by the equation
nP
f  sm (3-34)
se
120
To make a 50 Hz and a 60 Hz machine have the same mechanical speed so that they can be coupled
together, we see that
120  50 Hz 120  60 Hz
n  
sync
P 1 P 2
P 2  6  12
P 1 5 10

Therefore, a 10-pole synchronous motor must be coupled to a 12-pole synchronous generator to
accomplish this frequency conversion.

4-2. A 13.8-kV, 50-MVA, 0.9-power-factor-lagging, 60-Hz, four-pole Y-connected synchronous generator has
a synchronous reactance of 2.5  and an armature resistance of 0.2 . At 60 Hz, its friction and windage
losses are 1 MW, and its core losses are 1.5 MW. The field circuit has a dc voltage of 120 V, and the
maximum I F is 10 A. The current of the field circuit is adjustable over the range from 0 to 10 A. The
OCC of this generator is shown in Figure P4-1.

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