Operating principle of 3-phase induction motor

A 3-phase induction motor works on the principle of electromagnetic induction: the rotating magnetic field set up by the stator induces current in the rotor, and the force between this current and the field turns the rotor. It is like a transformer with a rotating secondary.

1. Production of the rotating magnetic field

A balanced 3-phase supply is fed to three stator windings placed 120° apart in space. Their currents are 120° apart in time:

$$\phi_R = \phi_m\sin\omega t,\quad \phi_Y = \phi_m\sin(\omega t - 120^\circ),\quad \phi_B = \phi_m\sin(\omega t - 240^\circ)$$

Adding these at any instant gives a resultant flux of constant magnitude $\phi_r = 1.5\phi_m$ whose axis rotates uniformly. For example, at $\omega t = 0^\circ, 60^\circ, 120^\circ$ the resultant has the same size but has turned by 60°, 120° of electrical angle. The field rotates at synchronous speed

$$N_s = \frac{120 f}{P}$$

2. Induced emf and current in the rotor

At start the rotor is stationary. The RMF cuts the rotor conductors at speed $N_s$ and induces an emf (Faraday's law). Since the rotor conductors are short-circuited by end rings (cage) or through slip rings and resistors (wound rotor), a rotor current flows.

3. Production of torque

The current-carrying rotor conductors lie in the stator field and experience a force $F = BIl$. The forces on all conductors add up to a torque. By Lenz's law the rotor current opposes its cause — the relative motion between field and rotor — so the rotor turns in the same direction as the field, trying to catch it.

   Stator RMF at Ns  -->
   ---------------------
   x  x  x  rotor conductors (current)
   ---------------------
   Force on rotor    -->   rotor speed N < Ns

4. Slip

The rotor can never reach $N_s$: at $N_s$ there would be no relative motion, no induced emf, no current and no torque. It runs at $N$ slightly less than $N_s$:

$$s = \frac{N_s - N}{N_s}, \qquad N = N_s(1 - s)$$

Typical slip: 0.5% at no load, 2–5% at full load.

5. Rotor frequency and emf

The rotor sees the field at the relative speed $N_s - N = sN_s$, so

$$f_2 = s f, \qquad E_{2r} = sE_2, \qquad X_{2r} = sX_2$$

6. Effect of load

When load increases, the rotor slows slightly, slip increases, rotor emf and current increase, and torque increases until it matches the load. Thus the motor runs at almost constant speed.

Example: 6-pole, 50 Hz motor: $N_s = 1000$ rpm; at 4% slip, $N = 960$ rpm and $f_2 = 2$ Hz.

Reversal: interchanging any two supply terminals reverses the RMF and so the direction of rotation.