Question

(a) List the factors that determine the starting torque of the three-phase Induction motor. How does this torque generally compare with the value of the rated torque? (6)

(b) A 3 ph, 440 V, 60 Hz 8 pole induction motor runs at a power factor of 0.85 lag and drives a load of 8 kW at a speed of 14.4 rev/sec. The stator loss is 1 kW and the rotational losses (windage and friction) amount to 0.8 kW. Calculate EACH of the following: (10)

(i) the synchronous speed;

(ii) the rotor copper loss;

(iii) the input power to the motor;

(iv) the motor current.

Answer 1

Part (a)

Factors that determine the starting torque of a three-phase induction motor:

The square of the applied voltage (T proportional to V^2).
The rotor resistance (increasing rotor resistance increases starting torque up to a maximum).
The rotor and stator leakage reactances.
The number of poles / synchronous speed.
The supply frequency.
The air-gap flux and the winding turns ratio.
Comparison with rated torque: the starting torque of a standard squirrel-cage motor is typically about 1.5 to 2 times the full-load torque, so that the motor can start its load. It is generally greater than rated torque but not excessive.

Part (b)

3-phase, 440 V, 60 Hz, 8-pole induction motor, p.f. 0.85 lag, drives 8 kW load at 14.4 rev/s. Stator loss 1 kW, rotational losses 0.8 kW.

(i) Synchronous speed: Ns = 120 f / P = 120 x 60 / 8 = 900 rev/min = 15 rev/s.
(ii) Rotor copper loss:
Slip s = (Ns - N)/Ns = (15 - 14.4)/15 = 0.6/15 = 0.04.
Shaft output = 8 kW. Rotor gross mechanical power = shaft output + rotational losses = 8 + 0.8 = 8.8 kW.
Air-gap power Pg = rotor gross power / (1 - s) = 8.8 / 0.96 = 9.167 kW.
Rotor copper loss = s x Pg = 0.04 x 9.167 = 0.367 kW (367 W).
(iii) Input power to the motor = air-gap power + stator loss = 9.167 + 1 = 10.167 kW.
(iv) Motor current: I = P_in / (root 3 x V x cos phi) = 10167 / (1.732 x 440 x 0.85) = 10167 / 648.1 = 15.69 A.

So synchronous speed = 900 rev/min, rotor copper loss = 0.367 kW, input power = 10.17 kW, motor current = 15.7 A.

✓ Verified Model Answer (Text Solution)

Factors that determine the starting torque of a three-phase induction motor:

3-phase, 440 V, 60 Hz, 8-pole induction motor, p.f. 0.85 lag, drives 8 kW load at 14.4 rev/s. Stator loss 1 kW, rotational losses 0.8 kW.