Q:

A P _out = 100 hp, V _{L-L _rat} = 480 V, f = 60 Hz, p = 6 pole, three-phase induction motor runs at full load and rated voltage with a slip of 3%. Under conditions of stress on the power system, the line-to-line voltage drops to V _{L-L _low} = 430 V. If the load is of the constant torque type, compute for the lower voltage:

1. Slip s _low (use small-slip approximation).

2. Shaft speed n _{m _low} in rpm.

3. Output power P _{out_low}.

4. Rotor copper loss in terms of the rated rotor copper loss at rated voltage.

Q:

Solution

1. Based on the small-slip approximation , the new slip at the low voltage is

   
   

2. With the synchronous speed rpm one calculates the shaft speed at low voltage as

   
   

3. The output power at low voltage is P _out = ? _m T _m. For constant mechanical torque one gets

   
   

4. Due to the relation (where P _g is the air-gap power), the torque is proportional to P _g, and therefore, for constant torque operation the air-gap power is constant. Thus the rotor loss is

   
   

One concludes that a decrease of the terminal voltage increases the rotor loss (temperature) of an induction motor.