Problems #7

1. A three-phase induction motor has a starting torque of 100% and a maximum torque of 250% of the full load torque. Neglecting stator resistance, compute (i) the slip at maximum torque, (ii) full-load slip, and (iii) the rotor current at starting in terms of the full-load current.

2. A 10kW, 400V, three-phase, 50Hz wound-rotor induction motor develops rated output at rated voltage and frequency and with its slip rings short-circuited. The maximum torque equal to twice the full-load torque occurs at a slip of 10% with its slip rings short-circuited. Neglect stator resistance and rotational losses. Determine,

(i) slip and rotor speed at full load torque,

(ii) rotor copper loss at full load,

(iii) starting torque at rated voltage and frequency,

The rotor resistance is now doubled by inserting external resistance in the rotor circuit. Find,

(i) the slip at maximum torque,

(ii) full-load slip and rotor speed,

(iii) starting torque.

3. A 100kW, 460V, three-phase, 60Hz, six-pole wound rotor induction motor develops its rated output at a speed of 1158 rpm when operated at rated voltage and frequency with its slip rings short-circuited. The maximum torque it can develop at rated voltage and frequency is 310% of full-load torque. The resistance of the rotor winding is 0.17 ohm/phase Y. Neglect any effects of rotational and stray load loss and stator resistance.

(i) Compute the rotor copper loss at full-load.

(ii) Compute the speed at maximum torque in rpm.

(iii) How much rotor resistance must be inserted in series with the rotor windings to produce maximum starting torque.

With the rotor winding short-circuited, the motor is now run from a 50Hz supply with the applied voltage adjusted so that the air-gap flux wave is essentially equal to that at rated 60Hz operation.

(i) Compute the applied voltage at 50Hz.

(ii) Compute the speed at which the motor will develop a torque equal to its rated 60Hz value with slip rings short-circuited.

4. A 10kW, 400V, three-phase, 4-pole, delta-connected, squirrel-cage induction motor gave the following test results:

No-load test: 400V, 8A, 250W

Blocked-rotor test: 90V, 34A, 1345W

The dc resistance of the stator winding per phase is 0.6 ohm. Calculate the rotational losses and the equivalent circuit parameters.