Page 155 - Solutions Manual to accompany Electric Machinery Fundamentals

(b) Since all losses are ignored, P  P  S  PF  200 kVA 0.85  170 kW . The
IN ,rated OUT ,rated rated
output torque of this motor is
P 170 kW
  OUT   135 N m

load
 m  12000 r/min  1 min   2 rad  
  60 s     1 r  
(c) The phase voltage of this motor is 460 V / 3 = 266 V. The rated armature current of this motor is
P 170 kW
I  A I  L   251 A

3 V T PF   3 460 V 0.85 


Therefore, I A  251 31.8 A . The base impedance of this motor is
3V 2   3266 V 2
Z   ,base   1.06 
base
S base 200,000 VA
 0.954  . The internal generated
so the actual synchronous reactance is X  0.90 pu 1.06 
S
voltage of this machine at rated conditions is given by
E  V jX I
A  S A

 E 266   j 0 V  0.954  251 31.8 A   441   27.4 V
A
(d) The maximum power that the motor could supply at these conditions is

3VE  3 266 V 441 V 
P MAX   A   369 kW
X S 0.954 
5-19. A 100-hp 440-V 0.8-PF-leading -connected synchronous motor has an armature resistance of 0.3  and
a synchronous reactance of 4.0 . Its efficiency at full load is 96 percent.
(a) What is the input power to the motor at rated conditions?
(b) What is the line current of the motor at rated conditions? What is the phase current of the motor
at rated conditions?
(c) What is the reactive power consumed by or supplied by the motor at rated conditions?

(d) What is the internal generated voltage E of this motor at rated conditions?
A
(e) What are the stator copper losses in the motor at rated conditions?

(f) What is P conv at rated conditions?

(g) If E is decreased by 10 percent, how much reactive power will be consumed by or supplied by
A
the motor?
SOLUTION
(a) The input power to the motor at rated conditions is

P 100 hp 746 W/hp 
P  OUT   77.7 kW
 0.96
IN
(b) The line current to the motor at rated conditions is
P 77.7 kW
I  L   120 A

3 V T PF   3 440 V 0.85 

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