**induction motor equivalent circuit**with the help of equivalent circuit of the transformer.

The basic

*equivalent circuit of induction motor*is shown in Fig. which is very similar to that of a transformer.

Here R_{1} and X_{1} are the per phase values of stator resistance and stator leakage reactance.

E_{1} is per phase stator voltage and N_{1} the number of stator turns per phase whereas R_{2} rotor resistance per phase and sX_{2} is rotor reactance per phase in running condition.

The resistance R_{o} is the no-load resistance per phase, that represents the resistance for core losses and X_{o }represents the magnetizing component of the no-load stator current similar to the magnetizing component of the no-load primary current of the transformer.

V_{1} is the per phase stator supply voltage. E_{1} is the per phase stator induced voltage

E_{2r} = sE_{2} is the per phase rotor induced EMF (in running condition)

- where, s = slip, E
_{2}= induced EMF in rotor at standstill.

The rotor current I_{2r} is given by,

I_{2r} = sE_{2}/ [R_{2}^{2} + (sX_{2})^{2}]^{1/2}

= E_{2}/ [(R_{2}/s)^{2} + X_{2}^{2}]^{1/2}

From the above expression, it is clear that the rotor circuit actually consists of a fixed resistance R_{2} and a variable reactance sX_{2}, connected across E_{2r} = sE_{2 } is equivalent to a rotor circuit having a fixed reactance X_{2} connected in series with a variable resistance R_{2}/s and supplied with constant voltage E_{2}.

We can express resistance R_{2}/s in two parts as follows:

R_{2}/s = R_{2} + R_{2}(1/s – 1)

- were, the first part R
_{2}is the rotor resistance and represents the rotor copper losses. **and the second part R**. It is the electrical power that is converted into the mechanical power by the motor._{2}(1/s – 1) is the load resistance R_{L}. It is the electrical equivalent of the mechanical load on the motor

Hence equivalent rotor circuit of the induction motor can be drawn as under.

# Equivalent Circuit of Induction Motor Referred to Stator

We can draw the equivalent circuit of induction motor referred to stator or rotor side like that of a transformer.

The

*equivalent circuit of 3 phase induction motor referred to the stator*is shown in Fig. Here, all the parameters are referred to the stator winding.

We know that,

transformation ratio, k = E

_{2}/E

_{1}

All the rotor parameters are transferred to the stator side as follows:

E

_{2r}’ = E

_{2r}/k

I’

_{2}r = kI

_{2r}

X’

_{2}= X

_{2}/k

^{2}and R’

_{2}= R

_{2}/k

^{2}

## Approximate Equivalent Circuit of Three Phase Induction Motor

The no-load circuit components R_{o} and X_{o} can be shifted to the left of R_{1} and X_{1} to obtain the approximate equivalent circuit of the induction motor.

Here, R_{o1 }= R_{1} + R’_{1}

is equivalent resistance of induction motor referred to the stator and X_{o1} = X_{1} + X’_{1} is equivalent reactance of induction motor referred to the stator.

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