Page 142 - Solutions Manual to accompany Electric Machinery Fundamentals

I
A
X I sin 
V S A
  }
jX I } X I cos 


S A  S A

R I
 A A
E }
A
R I cos 
A A
Therefore,

XI cos  R I sin
tan  SA A A
V   X I sin  R I cos
A A
SA
 XI cos  R I sin  

  tan  1  SA A A 
 V   X I sin  R I cos 
SA
A A
5-10. A synchronous machine has a synchronous reactance of 1.0  per phase and an armature resistance of 0.1
 per phase. If E = 460-10 V and V  = 4800 V, is this machine a motor or a generator? How
A
much power P is this machine consuming from or supplying to the electrical system? How much reactive
power Q is this machine consuming from or supplying to the electrical system?
SOLUTION This machine is a motor, consuming power from the power system, because E A is lagging V .

It is also consuming reactive power, because E A cos  V . The current flowing in this machine is




V  E 480 0 V 460  10 V

I A  R  A  jX A S  0.1 j 1.0   83.9  13 A
Therefore the real power consumed by this motor is

P  3V I A cos   3 480 V 89.3 A cos 13  125.3 kW

and the reactive power consumed by this motor is


Q  3V I A  sin   3 480 V 89.3 A sin 13  28.9 kVAR

5-11. A 500 kVA, 600 V, 0.8-PF-leading, Y-connected synchronous motor has a synchronous reactance of 1.0
per unit and an armature resistance of 0.1 per unit. At the current time, E = 1.0012 pu and V  =
A
10 pu.
(a) Is this machine currently acting as a motor or a generator?
(b) How much power P is this machine consuming from or supplying to the electrical system?

(c) How much reactive power Q is this machine consuming from or supplying to the electrical
system?

(d) Is this machine operating within its rated limits?
SOLUTION

(a) This machine is a generator, supplying power to the power system, because E A is leading V .


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