Page 156 - Solutions Manual to accompany Electric Machinery Fundamentals

The phase current to the motor at rated conditions is
I 120 A
I   L   69.3 A
3 3

(c) The reactive power supplied by this motor to the power system at rated conditions is

Q rated  3V I A  sin   3 440 V 69.3 A sin36.87   54.9 kVAR

(d) The internal generated voltage at rated conditions is

E  V R I  jX I
A  A A S A
E A  440 0 V    0.3  69.3 36.87 A    j 4.0  69.3 36.87 A  

 E 634  21.7 V
A
(e) The stator copper losses at rated conditions are

P  CU 3I A 2 A  R   3 69.3 A 2   0.3   4.3 kW

(f) P conv at rated conditions is


P conv  P  IN P  CU 77.7 kW 4.3 kW 73.4 kW
(g) If E is decreased by 10%, the new value if E = (0.9)(634 V) = 571 V. To simplify this part of
A A
the problem, we will ignore R . Then the quantity E sin will be constant as E changes. Therefore,
A A A
 E  1 634 V 

 sin  1  A 1 sin  1   sin   sin    21.7    24.2
2
E A 2   571 V 
Therefore,
V  E 440 0 V 571  24.2




I   A   61.9 19 A
A
jX S j 4.0
and the reactive power supplied by the motor to the power system will be


Q  3V I A  sin   3 440 V 61.9 A sin 19  26.6 kVAR

5-20. Answer the following questions about the machine of Problem 5-19.
(a) If E = 43015 V and V  = 4400 V, is this machine consuming real power from or
A
supplying real power to the power system? Is it consuming reactive power from or supplying reactive
power to the power system?
(b) Calculate the real power P and reactive power Q supplied or consumed by the machine under the
conditions in part (a). Is the machine operating within its ratings under these circumstances?

(c) If E = 470-20 V and V  = 4400 V, is this machine consuming real power from or
A
supplying real power to the power system? Is it consuming reactive power from or supplying reactive
power to the power system?
(d) Calculate the real power P and reactive power Q supplied or consumed by the machine under the
conditions in part (c). Is the machine operating within its ratings under these circumstances?
SOLUTION

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