Page 139 - Solutions Manual to accompany Electric Machinery Fundamentals

5-6. If a 60-Hz synchronous motor is to be operated at 50 Hz, will its synchronous reactance be the same as at
60 Hz, or will it change? (Hint: Think about the derivation of X S .)

SOLUTION The synchronous reactance represents the effects of the armature reaction voltage E stat and the
armature self-inductance. The armature reaction voltage is caused by the armature magnetic field B S ,
and the amount of voltage is directly proportional to the speed with which the magnetic field sweeps over
the stator surface. The higher the frequency, the faster B S sweeps over the stator, and the higher the
armature reaction voltage E stat is. Therefore, the armature reaction voltage is directly proportional to
frequency. Similarly, the reactance of the armature self-inductance is directly proportional to frequency,
so the total synchronous reactance X S is directly proportional to frequency. If the frequency is changed
from 60 Hz to 50 Hz, the synchronous reactance will be decreased by a factor of 5/6.
5-7. A 208-V Y-connected synchronous motor is drawing 50 A at unity power factor from a 208-V power
system. The field current flowing under these conditions is 2.7 A. Its synchronous reactance is 1.6 .
Assume a linear open-circuit characteristic.

(a) Find V and E A for these conditions.

(b) Find the torque angle  .
(c) What is the static stability power limit under these conditions?
(d) How much field current would be required to make the motor operate at 0.80 PF leading?

(e) What is the new torque angle in part (d)?
SOLUTION


(a) The phase voltage of this motor is V = 120 V, and the armature current is I A  50 0 A .

Therefore, the internal generated voltage is
E  V R I  jX I
A  A A S A

 E 120 0 V   j 1.6  50 0 A  
A

 E 144   33.7 V
A
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