Page 191 - Solutions Manual to accompany Electric Machinery Fundamentals

 R 2  2  R 2 

   2.434    0.516 0
 s   s 
 R 2 
   0.2346, 2.199
 s 


R  0.0082 , 0.077 
2
These two solutions represent two situations in which the torque-speed curve would go through this
specific torque-speed point. The two curves are plotted below. As you can see, only the 0.077  solution
is realistic, since the 0.0082  solution passes through this torque-speed point at an unstable location on
the back side of the torque-speed curve.

(b) The slip at pullout torque can be found by calculating the Thevenin equivalent of the input circuit
from the rotor back to the power supply, and then using that with the rotor circuit model. The Thevenin
equivalent of the input circuit was calculated in part (a). The slip at pullout torque is

R
s max  2
R TH 2   TH  X 2  X 2
0.077 
s max   0.0846
 0.559  2   0.332  0.386    2

The rotor speed a maximum torque is

n  (1 s   ) n  1 0.0846 1800 r/min  1648 r/min
pullout sync
and the pullout torque of the motor is

3V 2
 max  TH
  sync    R TH R TH   TH  X 2  X 2 
2


185