Induction motor:Complete Torque/Speed Curve of a Three-Phase Machine

Complete Torque/Speed Curve of a Three-Phase Machine

We have already seen that a 3-phase machine can be run as a motor, when it takes electric power and supplies mechanical power. The directions of torque and rotor rotation are in the same direction. The same machine can be used as an asynchronous generator when driven at a speed greater than the synchronous speed. In this case, it receives mechanical energy in the rotor and supplies electrical energy from the stator. The torque and speed are oppositely-directed.

The same machine can also be used as a brake during the plugging period (Art. 34.31). The three modes of operation are depicted in the torque/speed curve shown in Fig. 34.32.

Tutorial Problem No. 34.2

1. In a 3-phase, slip-ring induction motor, the open-circuit voltage across slip-rings is measured to be 110 V with normal voltage applied to the stator. The rotor is star-connected and has a resistance of 1 W and reactance of 4 W at standstill condition. Find the rotor current when the machine is (a) at standstill with slip-rings joined to a star-connected starter with a resistance of 2W per phase and negligible reactance (b) running normally with 5% slip. State any assumptions made.

[12.7 A ; 3.11 A] (Electrical Technology-I, Bombay Univ. 1978)

2. The star-connected rotor of an induction motor has a standstill impedance of (0.4 + j4) ohm per phase and the rheostat impedance per phase is (6+j2) ohm. The motor has an induced e.m.f. of 80 V between slip-rings at standstill when connected to its normal supply voltage. Find (a) rotor current at standstill with the rheostat in the circuit (b) when the slip-rings are short-circuited and the motor is running with a slip of 3%.

[5.27 A ; 3.3 A]

3. A 4-pole, 50-Hz induction motor has a full-load slip of 5%. Each rotor phase has a resistance of 0.3 W

and a standstill reactance of 1.2 W. Find the ratio of maximum torque to full-load torque and the speed at which maximum torque occurs.

[2.6 ; 1125 r.p.m.]

4. A 3-phase, 4-pole, 50-Hz induction motor has a star-connected rotor. The voltage of each rotor phase at standstill and on open-circuit is 121 V. The rotor resistance per phase is 0.3 W and the reactance at standstill is 0.8 W. If the rotor current is 15 A, calculate the speed at which the motor is running. Also, calculate the speed at which the torque is a maximum and the corresponding value of the input power to the motor, assuming the flux to remain constant.

[1444 r.p.m.; 937.5 r.p.m.]

5. A 4-pole, 3-phase, 50 Hz induction motor has a voltage between slip-rings on open-circuit of 520 V. The star-connected rotor has a standstill reactance and resistance of 2.0 and 0.4 W per phase respectively. Determine :

(a) he full-load torque if full-load speed is 1,425 r.p.m.

(b) the ratio of starting torque to full-load torque

(c) the additional rotor resistance required to give maximum torque at standstill

[(a) 200 N-m (b) 0.82 (c) 1.6 W] (Elect. Machines-II, Vikram Univ. Ujjain 1977)

6. A 50-Hz, 8-pole induction motor has a full-load slip of 4 per cent. The rotor resistance is 0.001 W per phase and standstill reactance is 0.005 W per phase. Find the ratio of the maximum to the full- load torque and the speed at which the maximum torque occurs.

[2.6; 600 r.p.m.] (City & Guilds, London)

7. A 3-f, 50-Hz induction motor with its rotor star-connected gives 500 V (r.m.s.) at standstill between slip-rings on open circuit. Calculate the current and power factor in each phase of the rotor windings at standstill when joined to a star-connected circuit, each limb of which has a resistance of 10 W and an inductance of 0.03 H. The resistance per phase of the rotor windings is 0.2 W and inductance 0.03 H. Calculate also the current and power factor in each rotor phase when the rings are short- circuited and the motor is running with a slip of 4 per cent.

[13.6 A, 0.48; 27.0 A, 0.47] (London University)

8. A 4-pole, 50-Hz, 3-phase induction motor has a slip-ring rotor with a resistance and standstill reactance of 0.04 W and 0.2 W per phase respectively. Find the amount of resistance to be inserted in each rotor phase to obtain full-load torque at starting. What will be the approximate power factor in the rotor at this instant ? The slip at full-load is 3 per cent.

[0.084 W, 0.516 p.f.] (London University)

9. A 3-f induction motor has a synchronous speed of 250 r.p.m. and 4 per cent slip at full-load. The

rotor has a resistance of 0.02 W/phase and a standstill leakage reactance of 0.15 W/phase. Calculate

(a) the ratio of maximum and full-load torque (b) the speed at which the maximum torque is developed. Neglect resistance and leakage of the stator winding.

[(a) 1.82 (b) 217 r.p.m.] (London University)

10. The rotor of an 8-pole, 50-Hz, 3-phase induction motor has a resistance of 0.2 W/phase and runs at

720 r.p.m. If the load torque remains unchanged. Calculate the additional rotor resistance that will reduce this speed by 10%

[0.8 W] (City & Guilds, London)

11. A 3-phase induction motor has a rotor for which the resistance per phase is 0.1 W and the reactance per phase when stationary is 0.4 W. The rotor induced e.m.f. per phase is 100 V when stationary.

Calculate the rotor current and rotor power factor (a) when stationary (b) when running with a slip of 5 per cent.

[(a) 242.5 A; 0.243 (b) 49 A; 0.98]

12. An induction motor with 3-phase star-connected rotor has a rotor resistance and standstill reactance of 0.1 W and 0.5 W respectively. The slip-rings are connected to a star-connected resistance of 0.2 W per phase. If the standstill voltage between slip-rings is 200 volts, calculate the rotor current per phase when the slip is 5%, the resistance being still in circuit.

[19.1 A]

13. A 3-phase, 50-Hz induction motor has its rotor windings connected in star. At the moment of starting the rotor, induced e.m.f. between each pair of slip-rings is 350 V. The rotor resistance per phase is 0.2 W and the standstill reactance per phase is 1 W. Calculate the rotor starting current if the external starting resistance per phase is 8 W and also the rotor current when running with slip-rings short- circuited, the slip being 3 per cent.

[24.5 A ; 30.0 A]

14. In a certain 8-pole, 50-Hz machine, the rotor resistance per phase is 0.04 W and the maximum torque occurs at a speed of 645 r.p.m. Assuming that the air-gap flux is constant at all loads, determine the percentage of maximum torque (a) at starting (b) when the slip is 3%.

[(a) 0.273 (b) 0.41] (London University)

15. A 6-pole, 3-phase, 50-Hz induction motor has rotor resistance and reactance of 0.02 W and 0.1 W respectively per phase. At what speed would it develop maximum torque ? Find out the value of resistance necessary to give half of maximum torque at starting.

[800 rpm; 0.007 W] (Elect.Engg. Grad I.E.T.E. June 1988)

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