# Working of Three-phase Induction Motor Induction machine is also known as Asynchronous machine. Induction motor operates on the principle of mutual inductance. The induction motor is a device to convert electrical energy into mechanical energy.

As we have seen in the construction of induction motor, there are two main parts; stator and rotor. The stator is a stationary part and rotor is a rotating part. The stator has three main components; frame, core, and winding.

## Working of a Three-phase Induction Motor

Three-phase AC supply is given to the stator winding and a magnetic flux is set up. The magnitude of the magnetic flux is constant and rotating at synchronous speed. The rotor conductors cut magnetic flux. At starting condition, the rotor is stationary. Due to the relative speed between the rotating flux and stationary conductors an EMF induced in the rotor conductors.

The magnitude of induced EMF is proportional to the relative velocity and its direction is given by Fleming’s formula. Frequency of the induced EMF is same as supply frequency. The rotor conductors make a loop (closed path) and current pass through the rotor conductor. According to the Lenz’s law, rotor current tries to oppose the relative speed. So, rotor starts rotating in the direction of flux and tries to catch the flux. The direction of EMF determines by Fleming’s right-hand rule. The rotor current circulates in the rotor conductors and produces its own flux. The force produces in the rotor conductors and the rotor starts rotating in the direction of the rotating magnetic field. The rotor tries to catch up the stator field, but it never catches up the stator field because of friction and inertia of the rotor.

Due to this, the induction motor always runs at a slightly less than the synchronous speed. Difference between the actual speed of the rotor and the synchronous speed is known as slip. The direction of rotation of the induction motor can be changed by changing the phase sequence of the supply.

## Production of Rotating Magnetic Field (RMF) using three-phase supply

There are two conditions must satisfy to produce a rotating magnetic field.

1. Three-phase stator winding displaces by 120˚ electrical with respect to the space angle θ.
2. Current in the winding should be displaced by 120˚ electrical with respect to the time angle ω.

Let us consider that, each phase of three-phase winding has N number of turns and space angle is θ.

For, phase-a: Nph cos θ
Phase-b: Nph cos (θ-120˚)
Phase-c: Nph cos (θ-240˚)

Similarly, the current with respect to time angle ω

Phase-a: Ia = Im cos ωt
Phase-b: Ib = Im cos (ωt-120˚)
Phase-c: Ic = Im cos (ωt-240˚)

The MMF produce in the machine due to phase-a is

Fa = Nph cos θ Im cos ωt = Nm cos θ cos ωt

Similarly,

Fb = Nph cos (θ-120˚) Im cos (ωt-120˚) = Nm cos (θ-120˚) cos (ωt-120˚)
Fc = Nph cos (θ-240˚) Im cos (ωt-240˚) = Nm cos (θ-240˚) cos (ωt-240˚)

The resultant MMF in the machine is

Fr = Fa + Fb + Fc = 1.5Fm cos (θ-ωt)

The amplitude of resultant MMF is 1.5Fm; where Fm = NphIm

The resultant MMF Fr = 1.5Fm cos (θ-ωt)

At ω = 0, Fr = 1.5 Fm cos θ
ω = 45˚, Fr = 1.5 Fm cos (θ-45˚)
ω = 90˚, Fr = 1.5 Fm sin θ

Resultant MMF wave depends on both θ and ωt. It means resultant MMF wave not only varies with respect to time but also with space angle θ. Hence, it is traveling MMF wave or Rotating MMF wave.

#### Synchronous speed

The speed of rotating resultant MMF wave is ω electrical rad/sec,

ωe = p/2 x ωm
2πf = p/2 x (2πN/60)
N = 120f/p

This speed is synchronous speed. The speed of resultant MMF is synchronous speed and flux produce by this MMF is also rotating at synchronous speed, because of flux=MMF/reluctance.

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