Induction Motor Equivalent Circuit

The induction motor is equivalent to a rotating transformer. Hence, we can draw the 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.
 

induction motor equivalent circuit graphic

 
Here R1 and X1 are the per phase values of stator resistance and stator leakage reactance.
 
E1 is per phase stator voltage and N1 the number of stator turns per phase whereas R2 rotor resistance per phase and sX2 is rotor reactance per phase in running condition.

The resistance Ro is the no-load resistance per phase, that represents the resistance for core losses and Xo represents the magnetizing component of the no-load stator current similar to the magnetizing component of the no-load primary current of the transformer.

 
V1 is the per phase stator supply voltage. E1 is the per phase stator induced voltage
 
E2r = sE2 is the per phase rotor induced EMF (in running condition)

  • where, s = slip, E2 = induced EMF in rotor at standstill.

The rotor current I2r is given by,
 
I2r = sE2/ [R22 + (sX2)2]1/2
      = E2/ [(R2/s)2 + X22]1/2
 
From the above expression, it is clear that the rotor circuit actually consists of a fixed resistance R2 and a variable reactance sX2, connected across E2r = sE2 is equivalent to a rotor circuit having a fixed reactance X2 connected in series with a variable resistance R2/s and supplied with constant voltage E2.
 
We can express resistance R2/s in two parts as follows:
R2/s = R2 + R2(1/s – 1)

  • were, the first part R2 is the rotor resistance and represents the rotor copper losses.
  • and the second part R2(1/s – 1) is the load resistance RL. It is the electrical equivalent of the mechanical load on the motor. It is the electrical power that is converted into the mechanical power by the motor.

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

equivalent circuit of induction motor rotor image

 

Induction Motor Equivalent Circuit Referred to Stator

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

induction motor equivalent circuit image

 
The equivalent circuit of 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 = E2/E1
All the rotor parameters are transferred to the stator side as follows:
E2r’ = E2r/k
I’2r = kI2r
X’2 = X2/k2 and R’2 = R2/k2
 

Approximate Equivalent Circuit of Induction Motor

 
The no-load circuit components Ro and Xo can be shifted to the left of R1 and X1 to obtain the approximate equivalent circuit of the induction motor.
 

approximate equivalent circuit of induction motor

 
Here, Ro1 =  R1 + R’1
 
is equivalent resistance of induction motor referred to the stator and  Xo1 = X1 + X’1 is equivalent reactance of induction motor referred to the stator.

 

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