Page 203 - Solutions Manual to accompany Electric Machinery Fundamentals

V 460 V
I ,     TH  2 R ,    R   2  TH   X TH  2 R j X  X 2  TH
 R 
j X
But the line current in a  connection is 3 times the phase current, so

3V 797 V
I , L   3I ,     TH  2 R j  R  ,   TH  2  X   X TH  2 R j  R  TH  X 2  X

After (in Y):

V 266 V
I  I   ,Y 
L ,Y  ,Y  TH  2 R j  R  TH  2  X  X TH  2 R j  R  TH  X 2  X
Therefore the line current will decrease by a factor of 3 when using this starter. The starting current with
a -Y starter is

703 A
I start   234 A
3
(c) A 1.25:1 step-down autotransformer reduces the phase voltage on the motor by a factor 0.8. This
reduces the phase current and line current in the motor (and on the secondary side of the transformer) by a
factor of 0.8. However, the current on the primary of the autotransformer will be reduced by another
factor of 0.8, so the total starting current drawn from the line will be 64% of its original value. Therefore,
the maximum starting current drawn from the line will be

  I 0.64 703 A  450 A
start
6-31. When it is necessary to stop an induction motor very rapidly, many induction motor controllers reverse
the direction of rotation of the magnetic fields by switching any two stator leads. When the direction of
rotation of the magnetic fields is reversed, the motor develops an induced torque opposite to the current
direction of rotation, so it quickly stops and tries to start turning in the opposite direction. If power is
removed from the stator circuit at the moment when the rotor speed goes through zero, then the motor has
been stopped very rapidly. This technique for rapidly stopping an induction motor is called plugging.
The motor of Problem 6-21 is running at rated conditions and is to be stopped by plugging.
(a) What is the slip s before plugging?
(b) What is the frequency of the rotor before plugging?

(c) What is the induced torque  ind before plugging?

(d) What is the slip s immediately after switching the stator leads?
(e) What is the frequency of the rotor immediately after switching the stator leads?
(f) What is the induced torque  ind immediately after switching the stator leads?

SOLUTION

(a) The slip before plugging is 0.02 (see Problem 6-21).
(b) The frequency of the rotor before plugging is f  r sf  e 0.02 60 Hz  1.2 Hz

(c) The induced torque before plugging is 39.2 Nm in the direction of motion (see Problem 6-21).

(d) After switching stator leads, the synchronous speed becomes –1800 r/min, while the mechanical
speed initially remains 1764 r/min. Therefore, the slip becomes

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