Question 4.16: A 400 V, 50 Hz, three-phase induction motor is rotating at 9...

f = 50 Hz
P = 2, 4, 6, etc.

N_{s} = \frac{120  f}{p} = \frac{120  ×  50}{2} = 3000 rpm (for P = 2)

= \frac{120  ×  50}{4} = 1500 rpm (for P = 4)

Rotor speed is somewhat less than the synchronous speed N_{s}. Logically, here N_{s} can only be 1500 rpm, when N_{s} = 1500 rpm, P = 4.

Full load slip,             S = \frac{N_{s}  –  N_{r}} {N_{s}} = \frac{1500  –  1440}{1500} = 0.04

Frequency of rotor induced EMF f_{r} = S × f = 0.04 × 50

= 2 Hz

Speed of rotor field with respect to rotor, N is

N = \frac{120  ×   f_{r}}{P} = \frac{120  ×  2}{4} = 60 rpm

The rotor rotates at a speed of 1440 rpm. This means the speed of the rotor with respect to stator, which is stationary, is 1440 rpm.
The speed of the rotor field with respect to the rotor is 60 rpm.
Therefore, the speed of the rotor field with respect to the stator is 1440 + 60 = 1500 rpm. And, the speed of the rotating magnetic field produced by the stator rotates at synchronous speed, N_{s} with respect to the stator. In this case the speed of rotating field produced by the stator is 1500 rpm. Thus, we see that both the magnetic fields of the stator and rotor are stationary with respect to each other, which is, of course, the essential condition for production of torque.
The principle of working of a three-phase induction motor is summarized as follows: A three-phase induction motor has three-phase windings placed in slots made on the stator. The rotor, which is placed inside the stator carries a closed winding. There are two types of rotor construction, namely squirrel cage type and slip-ring type. Three-phase supply is applied to the stator windings. The rotor requires no power supply. EMF is induced in the rotor due to electromagnetic induction.
When three-phase supply is applied to the stator windings, a rotating magnetic field is produced. The speed, N_{s} of the rotating field is given by N_{s} = \frac{120  f}{P} where, f is the frequency of supply and P is the number of poles for which the winding is made. EMF is induced in the rotor winding due to electromagnetic induction. Since the rotor winding is a closed winding, current will flow through the rotor winding. Due to interaction between the rotating field and the current-carrying rotor winding, torque is developed on the rotor. The rotor starts rotating in the same direction as the rotating magnetic field. The rotor attains a speed somewhat less than the speed of the rotating field. The rotor can never rotate at the speed of the rotating magnetic field because if rotor speed N_{r} becomes equal to N_{s}, there will be no relative velocity between the rotating field and the rotor and there will be no EMF induced in the rotor due to electromagnetic induction. As a consequence, there will be no rotor current and no torque developed to rotate the rotor. The difference of N_{s} and N_{r} expressed as a percentage of N_{s} is called the slip of the motor.
The direction of rotation of a three-phase induction motor can be reversed by interchanging the supply connection of any two phases to the motor. In that case the direction of rotation of the rotating magnetic field will change and hence the direction of rotation of the rotor will also change.
Induction motor at starting takes a heavy current because an induction motor is like a short circuited transformer. By short circuiting the secondary terminals, if full voltage is applied to the primary a heavy current will flow. To avoid this, induction motors are started with reduced voltage using star–delta starters or auto-transformer starter. Only small induction motors upto 5 hp ratings are allowed to be started direct-on-line.