Page 194 - Solutions Manual to accompany Electric Machinery Fundamentals

(b) If a transmission line with an impedance of 0.50 + j0.35  per phase is used to connect the
induction motor to the infinite bus, its impedance will be in series with the motor’s impedances, and the
starting current will be
V
 I  I  ,bus
L A
R line  jX line  R  1 jX  1 R  F jX F

266 0 V
 I  I
L A
0.50   j 0.35   0.54   j 2.093   0.435   j 2.90 

 I  I 48.0  74.6 A
L A
The voltage at the terminals of the motor will be
V   A R  I 1 jX  1 R  F jX F 

V   48.0  74.6 A 0.54   j 2.093  0.435  j 2.90  


V   244.2 4.3 V

Therefore, the terminal voltage will be 3 244.2 V  423 V . Note that the terminal voltage sagged by
about 9.2% during motor starting.
(c) If an ideal 1.4:1 step-down autotransformer is connected between the transmission line and the
motor, the motor’s impedances will be referred across the transformer by the square of the turns ratio a =
1.4. The referred impedances are

R  1 a R  2 1 1.96 0.058   0.1137 

X   1 a X  2 1  1.96 0.32    0.627
R  F a R  2 F 1.96 0.435    0.853 

X   F a X  2 F  1.96 2.90   5.684  

Therefore, the starting current referred to the primary side of the transformer will be
V
  I   I  ,bus
L A R line  jX line  R  1 jX   1 R  F  jX  F

   I  I 266 0 V

L A 0.50   j 0.35   0.1137   j 0.627 0.853   j 5.684 

   I  I 39.0  77.6 A

L A
The voltage at the motor end of the transmission line would be the same as the referred voltage at the
terminals of the motor
 V  R   jX  I R    jX  
 A 1 1 F F



V   39.0  77.6 A 0.1137  j 0.627 0.853  j 5.684  


 V 249 3.7 V



Therefore, the line voltage at the motor end of the transmission line will be 3 249 V  431 V . Note
that this voltage sagged by 6.3% during motor starting, which is less than the 9.2% sag with case of
across-the-line starting.
6-25. In this chapter, we learned that a step-down autotransformer could be used to reduce the starting current
drawn by an induction motor. While this technique works, an autotransformer is relatively expensive. A
much less expensive way to reduce the starting current is to use a device called Y- starter (described
earlier in this chapter). If an induction motor is normally -connected, it is possible to reduce its phase

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