Page 85 - Solutions Manual to accompany Electric Machinery Fundamentals

The resulting table is
Number of Poles f = 25 Hz
e
2 1500 r/min
4 750 r/min
6 500 r/min
8 375 r/min
10 300 r/min
12 250 r/min
14 214.3 r/min
The highest possible rotational speed was 1500 r/min.
th
(b) Core losses scale according to the 1.5 power of the speed of rotation, so the ratio of the core losses
at 25 Hz to the core losses at 60 Hz (for a given machine) would be:

 1500 1.5
ratio    3600   0.269 or 26.9%

(c) At 25 Hz, the light from incandescent lamps would visibly flicker in a very annoying way.
3-11. In later years, motors improved and could be run directly from a 60 Hz power supply. As a result, 25 Hz
power systems shrank and disappeared. However, there were many perfectly-good working 25 Hz motors
in factories around the country that owners were not ready to discard. To keep them running, some users
created their own 25 Hz power in the plant using motor-generator sets. A motor generator set consists of
two machines connected on a common shaft, one acting as a motor and the other acting as a generator. If
the two machines have different numbers of poles but exactly the same shaft speed, then the electrical
frequency of the two machines will be different due to Equation (3-34). What combination of poles on
the two machines could convert 60 Hz power to 25 Hz power?
nP
f  sm (3-34)
se
120
SOLUTION

From Equation (3-34), the speed of rotation of the 60 Hz machines would be
120 f 120 60 Hz  7200
n sm 1  se 1  
P 1 P 1 P 1
and the speed of rotation of the 25 Hz machines would be

120 f 120 25 Hz  3000
n  se 2  
2
sm
P P P
2 2 2
If the machines are tied together in a motor-generator set, the shaft speed must be the same for both
machines, so
7200  3000
P 1 P 2

P 1  7200  72
P 2 3000 30

This result says that a 72-pole machine at 60 Hz would rotate at the same speed as a 30-pole machine at
25 Hz. Each machine would rotate at 100 r/min.
120 f 120 60 Hz 
n  se 1   100 r/min
1
sm
P 1 72
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