Question

(a) Explain the principles of A.C. Motors starting, and speed control, including the effect on efficiency. (6)

(b) A 3-phase induction motor has a 4-pole, Y-connected stator winding. The motor runs on 50-Hz supply with 200V between lines. The motor resistance and standstill reactance per phase are 0.1Ω and 0.9Ω respectively.

Calculate: (10)

(a) The total torque at 4% slip

(b) The maximum torque

(c) The speed at maximum torque if the ratio of the rotor to stator turns is 0.67.

Neglect stator impedance.

Answer 1

Part (a)

Principles of A.C. motor starting and speed control, including effect on efficiency:

Starting: an induction motor at standstill draws a high starting current (5-8 times full-load) because the back e.m.f. is zero. To limit this, reduced-voltage starting is used: star-delta, auto-transformer, or soft-start. These reduce the starting current (and starting torque, which is proportional to V^2). Slip-ring motors use rotor resistance to limit starting current and increase starting torque.
Speed control: the speed of an induction motor is N = 120 f (1 - s)/P. Speed can be controlled by:
Pole changing (discrete speeds).
Rotor resistance (slip-ring motors) - increases slip, reduces speed, but wastes power.
Variable frequency (VFD) - varying the supply frequency changes the synchronous speed; this is the most efficient method and gives smooth, continuous speed control.
Effect on efficiency: reduced-voltage starting has little effect on running efficiency. Rotor resistance speed control is inefficient because the slip power is dissipated as heat. Pole-changing is efficient at each discrete speed. VFD control is the most efficient for variable-speed operation because the motor runs at low slip at each speed, and the VFD matches the supply to the load.

Part (b)

3-phase induction motor, 4-pole, Y-connected stator, 50 Hz, 200 V between lines. Motor resistance 0.1 ohm and standstill reactance 0.9 ohm per phase. Ratio of rotor to stator turns 0.67. Neglect stator impedance.

Synchronous speed Ns = 120 x 50/4 = 1500 rev/min. Angular synchronous speed w_s = 2 pi x 1500/60 = 157.08 rad/s.
Phase voltage Vph = 200/root 3 = 115.5 V.
Refer the rotor values to the stator: turns ratio (rotor/stator) = 0.67, so referred values are divided by 0.67^2 = 0.4489.
R2' = 0.1/0.4489 = 0.2228 ohm. X2' = 0.9/0.4489 = 2.004 ohm.

Part (a)

Total torque at 4% slip:

s = 0.04. R2'/s = 0.2228/0.04 = 5.57.
T = (3/w_s) x [Vph^2 (R2'/s)] / [(R2'/s)^2 + X2'^2]
= (3/157.08) x [115.5^2 x 5.57] / [5.57^2 + 2.004^2]
= 0.01910 x [13340 x 5.57] / [31.02 + 4.016]
= 0.01910 x 74304 / 35.04 = 0.01910 x 2120.5 = 40.5 N m.

Part (b)

Maximum torque:

Slip at maximum torque s_max = R2'/X2' = 0.2228/2.004 = 0.1112.
T_max = (3/(2 w_s)) x (Vph^2 / X2') = (3/314.16) x (13340/2.004) = 0.009550 x 6656 = 63.6 N m.

Part (c)

Speed at maximum torque:

N = Ns (1 - s_max) = 1500 x (1 - 0.1112) = 1500 x 0.8888 = 1333 rev/min.

So total torque at 4% slip = 40.5 N m, maximum torque = 63.6 N m, speed at maximum torque = 1333 rev/min.

✓ Verified Model Answer (Text Solution)

Principles of A.C. motor starting and speed control, including effect on efficiency:

3-phase induction motor, 4-pole, Y-connected stator, 50 Hz, 200 V between lines. Motor resistance 0.1 ohm and standstill reactance 0.9 ohm per phase. Ratio of rotor to stator turns 0.67. Neglect stator impedance.

Total torque at 4% slip:

Maximum torque:

Speed at maximum torque: