Page 154 - Solutions Manual to accompany Electric Machinery Fundamentals

Note: The reactive power in the motor is now

Q motor  3V I A  sin   3 280 V 95.3 A sin  10.8     15 kVAR

The motor is now supplying 15 kVAR to the system. Note that an increase in machine flux has
increased the reactive power supplied by the motor and also raised the terminal voltage of the
system. This is consistent with what we learned about reactive power sharing in Chapter 4.

5-17. A 440-V, 60 Hz, three-phase Y-connected synchronous motor has a synchronous reactance of 1.5  per
phase. The field current has been adjusted so that the torque angle  is 25 when the power supplied by
the generator is 80 kW.
(a) What is the magnitude of the internal generated voltage E A in this machine?

(b) What are the magnitude and angle of the armature current in the machine? What is the motor’s
power factor?
(c) If the field current remains constant, what is the absolute maximum power this motor could
supply?

SOLUTION
(a) The power supplied to the motor is 80 kW. This power is given by the equation
3VE
P   A sin
X S

The phase voltage of the generator is 440 / 3  254 V , so the magnitude of E A is
XP 1.5   80 kW 

E  S   373 V
A
3V   sin  3 254 V sin 25
(b) The armature current in this machine is given by
V  E 254 0 V 373  25




I   A   119 28 A
A
jX S j 1.5
The power factor of the motor is PF = cos 28º = 0.883 leading.
(c) The maximum power that the motor could supply at this field current is
3VE  3 254 V 373 V 
P   A   189.4 kW
max
X S 1.5 
5-18. A 460-V 200-kVA 0.85-PF-leading 400-Hz four-pole Y-connected synchronous motor has negligible
armature resistance and a synchronous reactance of 0.90 per unit. Ignore all losses.
(a) What is the speed of rotation of this motor?
(b) What is the output torque of this motor at the rated conditions?

(c) What is the internal generated voltage of this motor at the rated conditions?
(d) With the field current remaining at the value present in the motor in part (c), what is the
maximum possible output power from the machine?

SOLUTION
(a) The speed of rotation of this motor is
120 f 120 400 Hz 
n  se   12000 r/min
sync
P 4
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