ENE3201ELECTRICAL MACHINES AND CONTROL TUTORIAL 5 – INDUCTION MACHINES

ENE3201ELECTRICAL MACHINES AND CONTROL TUTORIAL 5 – INDUCTION MACHINES




VEE3001-Introduction to Electrical Machines

ENE3201-Electrical Machines and Control

Tutorial 5 – Induction Machines


Q1.

When rated voltage of 440 V is applied to the stator terminals of a poly-phase induction motor, it develops a starting torque equal to 1.5 times the rated torque. At what voltage will the staring torque be exactly equal to the rated torque?

(359 V)



Q2.

A 6-pole 60 Hz polyphase induction motor has a full-load speed of 1155 rpm.

a) What is the slip in rpm.?

b) What is the slip in rad/s?

c) What is the percent slip?

(45 rpm, 4.71 rad/sec, 3.75%)



Q3.

A 60 Hz polyphase induction motor has an operating speed of 575 rpm.

a) For how many poles is the stator wound?

b) What is the slip at this load?

(12 poles, 0.0417)


Q4.

A 50 Hz induction motor has a no-load speed of 2990 rpm and a full-load speed of 2880 rpm. Calculate a) the frequency of the rotor induced e.m.f at the instant of starting. b) rotor frequencies at no-load and at full-load.

(50 Hz, 0.167 Hz, 2 Hz)


Q5.

A 6-pole, 60Hz induction motor has a rotor induced emf of 55 V at the instant of starting. If this motor with its stator excited is driven by another motor in the same direction as the stator field what is the rotor induced emf when the rotor speed is at

a) synchronous speed? b) 1204 rpm? c) 1250 rpm d) 2400 rpm. e) when the rotor is driven at synchronous speed but in the opposite direction to the stator field.

( (a) . 0V, (b) 0.183V, (c) 2.29 V (d) 55 V (e) 110V)


Q6.

A 2-pole 60 Hz induction motor has a full-load speed of 3450 rpm. Calculate the approximate speeds at loads of ¼, ½, ¾, and 1 ¼ times full load.

(3563 rpm, 3525 rpm, 3488 rpm, 3413 rpm)


Q7.

An 8-pole, 60 Hz induction motor develops maximum torque at a speed of 73 rad/sec. If the rotor resistance per phase is 0.50 ohm, calculate the rotor reactance per phase at standstill. (2.22 ohm)

Q8.

A 10-pole 60 Hz wound-rotor induction motor has a full load speed of 690 rpm. The rotor resistance per phase is 0.3 Ω, and the standstill reactance per phase is 1.1Ω. a) with the rotor short-circuited, at what speed will the pull-out occur? b) If maximum starting torque needs to be obtained, what rotor resistance per phase need to be added? c) What is the full load speed with the added resistance?

(524 rpm, 0.8 ohm, 590 rpm)


Q9.

A 22.5 kW, 60 Hz three-phase wound-rotor induction motor has a no-load speed of 125 rad/sec, full-load speed of 120 rad/sec, and pulls out at 88 rad/sec. The rotor resistance is 0.25 Ω.

a) What is the stand-still reactance of the rotor?

b) What additional resistance per phase should be added to the rotor to obtain a full load speed of 113 rad/sec.?

c) What is the no-load speed with the added resistance?

d) What is the new speed regulation?

e) At what speed will the maximum torque occur with the resistance added?

(0.833, 0.28,124.2rad/sec, 9.91%, 45.71 rad/sec)


Q10

A large 3-phase, 4000V, 50 Hz squirrel-cage induction motor draws a current of 385 A and a total active power of 2344 kW when operating at full-load. The corresponding speed is accurately measured to be 591 rpm. The stator is connected in wye and the resistance between two stator terminals is 0.10 Ω. The total iron losses are 23.4 kW and the windage and friction losses are 12 kW. Calculate the following:

a) The power factor at full load.

b) The active power supplied to the rotor.

c) The copper losses in the rotor.

d) The load mechanical power (kW), the torque (kN-m) and efficiency (%).

(0.878, 2298 kW, 34.47 kW, 2251 kW, 30.31 kN-m, 96%)


Q11.

A 3-phase, 5000 hp, 6000 V, 60 Hz, 12-pole wound-rotor induction motor has the following characteristics:



Calculate:

  1. Rotor and stator resistances at 75oC.

  2. Voltage and frequency induced in rotor at 200 rpm and 594 rpm.

  3. Reactive power absorbed by the motor to create the revolving field at no-load.

  4. Copper loss in stator when the motor runs at no-load (75oC).

  5. Active power supplied to the rotor at no-load.


( (a) 0.00449 Ω(dc), 0.0689 Ω(dc), (b) 1067V, 40 Hz, 16V 0.6 Hz, (c) 1035 kvar, (d) 2.274 kW, (e) 49.73 kW )


Q12.

Refering to the motor in Q11, calculate under full-voltage, locked-rotor conditions:


  1. Reactive power absorbed by motor.

  2. Copper loss in stator

  3. Active power supplied to the rotor.

  4. Mechanical power output.

  5. Torque developed by rotor.


(18.6Mvar, 737 kW, 1431 kW, zero, 22.8kN-m)



Q13.

Referring to the motor in Q11, the motor speed is to be controlled by inserting series resistors with the rotor. If the motor is to develop 20 kN-m at a speed of 450 rpm, calculate:

  1. voltage between slip-rings

  2. rotor resistance per phase and total power dissipated in rotor.

  3. Rotor current.


(400V; 0.509, 314kW; 454 A)



Q14.

Determine the efficiency and output horse-power of a 3-phase 400 V, delta-connected induction motor running on load with a fractional slip of 0.04 and taking a current of 50 A at a power factor of 0.86. When running light at 400 V, the motor has an input current of 15 A and the power taken is 2000 W of which 650 W represents the friction, windage and rotor core losses. The resistance per phase of the stator winding is 0.5 ohm.

(85.8%, 34.2hp)






Q15

.

The full-voltage starting current taken by a poly-phase, 440 V, induction motor is 5.5 times the rated current and the starting torque developed is 1.5 times the rated torque. Determine a) the applied voltage to the motor terminals in order to limit the staring current to 3 times the rated current. b) the starting torque under these conditions.

(240V, 0.446TFL)







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