Page 143 - Solutions Manual to accompany Electric Machinery Fundamentals

It is also consuming reactive power, because E A cos  V .

(b) The per-unit current flowing in this machine (assuming that it is a generator) is
E  V R I  jX I
A  A A S A
  
E  V 112 pu 1 0 pu



I  A    0.208 11.7 A
R  A A jX S 0.1 j 1.0
The current angle in this generator is 11.7, so the impedance angle  is -11.7. Therefore the real power
supplied to the power system by this machine is
P  3V I A cos  3 1.0   11.7   0.611 pu
 0.208 cos

Converting from per-unit to real power in watts, we get

P  base pu S 500 kVA 0.611 pu   305.5 kW
P 
(c) The reactive power consumed by this motor is
Q  3V I A sin  3 1.0   11.7     0.127 pu
 0.208 sin

Converting from per-unit to reactive power in var, we get

Q  Q  S 500 kVA    0.127 pu   63.5 kvar
base pu
(d) The total apparent power of this machine is

S  2 Q  2  P  305.5 kW 2    63.5 kvar 2  312 kVA

The machine is operating within limits.

5-12. Figure P5-3 shows a small industrial plant supplied by an external 480 V three-phase power supply. The
plant includes three main loads as shown in the figure. Answer the following questions about the plant.
The synchronous motor is rated at 100 hp, 460 V, and 0.8-PF-leading. The synchronous reactance is 1.1
pu and armature resistance is 0.01 pu. The OCC for this motor is shown in Figure P5-4.
(a) If the switch on the synchronous motor is open, how much real, reactive, and apparent power is
being supplied to the plant? What is the current I in the transmission line?
L
The switch is now closed and the synchronous motor is supplying rated power at rated power
factor.
(b) What is the field current in the motor?
(c) What is the torque angle of the motor?

(c) What is the power factor of the motor?
(d) How much real, reactive, and apparent power is being supplied to the plant now? What is the
current I in the transmission line?
L
Now suppose that the field current is increased to 3.0 A.
(e) What is the real and reactive power supplied to the motor?
(f) What is the torque angle of the motor?

(g) What is the power factor of the motor?

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