# Equivalent circuit of Induction Machine

As we have seen differences between Induction machine and Transformer. It can be seen at Difference b/w Induction Machines and Transformers.

• The energy transfer from stator to rotor of the induction motor takes place entirely with the help of a flux mutually linking the two. Thus stator acts as a primary while the rotor acts as a rotating secondary when induction motor is treated as a transformer.

If    E1 = Induced voltage in stator per phase.

E2 = Rotor induced emf per phase on standstill

K = Rotor turns / Stator turns

K= E2 / E1

• Thus if Vis the supply voltage per phase to stator, it produces the flux which links with both stator and rotor. Due to self induction, E1 is the induced emf in stator per phase while E2 is the induced emf in rotor due to mutual induction, at standstill. In running condition the induced emf in rotor becomes E2r which is sE2.

E2r = Rotor induced emf in running condition per phase

R2 = Rotor resistance per phase

R1 = Stator resistance per phase

X2r = Rotor reactance per phase in running condition

X1 = Stator reactance per phase

So induction motor can be represented as a transformer as shown in the figure

• When the induction motor is on no load, it draws a current from the supply to produce the flux in air gap and to supply iron losses.

This current Io has two components.

1. Iw or Ic = Working or active component which supplies no load losses.
2. Im = Magnetising component which sets up flux in core and air gap.

• It is important to note that as load on the motor changes, the motor speed changes, thus slip changes. As slip changes the reactance X2r changes.

• So it can be assumed that equivalent rotor circuit in the running condition has fixed reactance X2, fixed voltage E2 but a variable resistance R2/s, as indicated in the above equation.

• So the variable resistance R2/s has two parts :
1. Rotor resistance R2 itself which represents copper loss.
2. R2 (1-s) / s which represents load resistance. So it is electrical equivalent of mechanical load on the motor.

So rotor equivalent circuit can be shown as

Now equivalent circuit referred to Stator

Approximate equivalent Circuit