Three Phase Induction Motors Questions and Answers

Answer: A

Both statements are true. The pole changing method of speed control changes the number of poles of the stator winding, and it is suitable for cage motors only, because the cage rotor adjusts itself to the new number of poles, while a wound rotor would need its winding changed as well.

Rotor resistance control puts external resistance into the rotor circuit through slip rings, which is possible only with a wound rotor. So the answer is 'True, True', the first option, and a 'False' for either statement would be wrong.

Answer: C

The outer cage has high resistance.

In a double squirrel cage motor the outer cage, close to the air gap, is made of thin bars of a high-resistance alloy and has little leakage reactance. At starting, when the rotor frequency is high, the deep inner cage has a high reactance, so the current flows mainly in the outer cage and its high resistance gives a large starting torque. At running speed the low-resistance inner cage carries most of the current, giving good efficiency.

Low resistance and high inductance are the properties of the inner cage, not the outer one.

Answer: B

The motor runs at 720 r.p.m.

The supply frequency comes from the alternator, the synchronous speed of the motor from that frequency, and the slip from the rotor frequency.

\[ \begin{aligned} f &= \frac{PN}{120} = \frac{6 \times 1000}{120} = 50\ \text{Hz} \\ N_{s} &= \frac{120 \times 50}{8} = 750\ \text{r.p.m.} \\ s &= \frac{f_{r}}{f} = \frac{2}{50} = 0.04 \\ N &= 750(1 - 0.04) = 720\ \text{r.p.m.} \end{aligned} \]

750 r.p.m. is the synchronous speed, which an induction motor never quite reaches, and 960 r.p.m. applies the 4% slip to the alternator's 1000 r.p.m. instead of the motor's synchronous speed.

Answer: C

Interchanging two phases reverses the direction of rotation of the field.

The rotating field produced by a three phase winding turns in the order in which the phase currents reach their maxima, the phase sequence. Swapping the supply connections of any two phases reverses that sequence (R-Y-B becomes R-B-Y), so the field, and with it an induction motor, rotates the other way. This is how three phase motors are reversed.

The field is still set up and still rotates at synchronous speed, so the first two options are wrong, and its direction does change.

Answer: A

Rotor slots are skewed to reduce the magnetic hum and the locking tendency of the rotor.

If the rotor bars ran parallel to the stator slots, the rotor teeth could lock magnetically with the stator teeth (cogging), and slot harmonics would produce noise. Skewing the bars by about one slot pitch smooths out these effects, giving quieter running and a smoother starting torque.

Skewing does not control speed, which a cage motor's construction cannot vary. It makes the rotor slightly harder to make, not easier, and it is not done to strengthen the bars.

Answer: C

The rotor emf frequency is 1.50 Hz.

Find the synchronous speed, then the slip; the rotor frequency is the slip times the supply frequency.

\[ \begin{aligned} N_{s} &= \frac{120f}{P} = \frac{120 \times 50}{8} = 750\ \text{rpm} \\ s &= \frac{750 - 727.5}{750} = 0.03 \\ f_{r} &= s f = 0.03 \times 50 = 1.5\ \text{Hz} \end{aligned} \]

1.54 Hz comes from dividing the speed difference by the rotor speed, 727.5, instead of the synchronous speed. 15 Hz is a decimal slip, and 50 Hz is the rotor frequency only at standstill.

Answer: C

The relationship is F₂ = SF.

The rotor conductors are cut by the rotating field at the slip speed, N_s - N, which is the fraction S of the synchronous speed. The frequency of the emf induced in the rotor is proportional to that relative speed, so it is the stator frequency multiplied by the slip.

At standstill S = 1 and the rotor frequency equals the supply frequency; near full speed S is small, so a 50 Hz motor with 4% slip has a rotor frequency of only 2 Hz. (1 - S)F would be proportional to the rotor's own speed, not to the slip, and F/S and the square-root form give impossible results as S approaches zero.

Answer: C

Speeds above synchronous speed are obtained by rotor slip power control.

An induction motor fed only from the stator can never reach synchronous speed, because it needs slip to induce rotor current. If a voltage of slip frequency is injected into the rotor circuit from an external source (as in slip power recovery and doubly fed arrangements), the rotor current can be maintained with negative slip, and the machine can run above the synchronous speed set by the supply.

Changing the supply frequency changes the synchronous speed itself, and the motor still runs a little below the new value. Reducing the supply voltage or adding rotor resistance only increases the slip, so both lower the speed.

Answer: A

In a double cage rotor the outer cage has high resistance and the inner cage has low resistance.

The outer cage, near the air gap, is made of small bars of high-resistance material and has low leakage reactance. The inner cage, buried deep in the iron, has low-resistance bars and high leakage reactance. At starting the rotor frequency is high, so the inner cage's reactance keeps its current small and most current flows in the outer, high-resistance cage, giving a high starting torque.

Near full speed the rotor frequency is low, reactance hardly matters, and the current flows mainly in the low-resistance inner cage, giving good efficiency. Reversing the arrangement, or making both cages alike, loses that combination.

Answer: D

The keyed answer is both harmonic induction torque and harmonic synchronous torque.

Crawling is the tendency of a squirrel cage induction motor to settle at a low speed, around one seventh of synchronous speed, instead of accelerating to full speed. It comes from space harmonics in the air-gap flux. The 5th and 7th harmonic fields act like small induction motors of their own, and the 7th harmonic torque produces a dip in the torque-speed curve near one seventh of synchronous speed, in which the motor can stick. Interaction between stator and rotor harmonics also produces harmonic synchronous torques at particular speeds, which can lock the motor there.

The standard account treats the two parasitic torques together as the cause of the motor's failure to run up, so the options naming only one of them are incomplete. 'Vibration torques' is not a recognised cause.