Equivalent Circuit of an Induction Motor


     The equivalent circuit of an induction motor is similar to a transformer equivalent circuit because the energy is transferred from stator to rotor is essentially a transformer operation.


     Equivalent circuit enables the performance characteristics of the induction motor. All per phase quantities are used in representing the equivalent circuit.


 Following are the parameters of the equivalent circuit

(i). R1  &  X1   :  Stator windinq resistance and leakage reactance.

(ii). R2  &  X2   :   Rotor winding resistance and leakage reactance at standstill ( i.e., s = 1 ).

(iii). sX2   :   Rotor leakage reactance at slip 's' ( under running condition ).

(iv). Ro   :     No-load branch resistance and it carries working component ( I) of no-load current I account for the losses on no-load.

(v). Xo  :   No-load branch reactance and it carries magnetising component ( Iµ ) of no-load to produce the flux.

(vi). E1 and sE2    :   Stator induced emf and rotor induced emf at slip 's'.


The figure below represents the equivalent circuit.

Equivalent Circuit of an Induction Motor

OR

Equivalent Circuit of an Induction Motor

Now let us consider Actual rotor circuit and Equivalent rotor circuit,

Equivalent Circuit of an Induction Motor

Equivalent Circuit of an Induction Motor

Then the rotor current,


Dividing Nr and Dr, by 'S'


     The rotor input, P2 is the sum of rotor copper losses Pc and mechanical power developed Pm. Thus it is possible to represent the electrical equivalent of mechanical power developed as follows :

Therefore,


R2 / S can be expressed as,


' RL ' represents the equivalent mechanical load. 

i.e.,

RL  =  R2 ( 1 - s / s )

So that the rotor equivalent circuit can be modified as shown in figure below

Equivalent Circuit of an Induction Motor

The rotor side parameters can be transferred to stator side as


R'2 = R2 / K2

X'2 = X2 / K2 

R'L = RL  / K2

E'2 = E2 / K = E1  

I'2 = K I2

Where

     K = Ratio of effective rotor to stator turns per phase.


The equivalent circuit shown in below figure is called Exact Equivalent circuit as referred to stator.    

Equivalent Circuit of an Induction Motor

     The approximate equivalent circuit is obtained by shifting the shunt branch ( consists of Ro & Xo ) to the supply terminals as shown in below figure.

Equivalent Circuit of an Induction Motor


Therefore, the total resistance and reactance referred to stator side are   

R01  =  R1 + R'2  

=  R1 + R2 / K2


X01  =  X1 + X'2  

=  X1 + X2 / K2



Calculation of Rotor Output and Torque Using the Equivalent Circuit :


     From the equivalent circuit, expression for output power and torque can be derived thus,

Rotor output power, 


Rotor input power,


We can write

  Pi   =  S Pi + P - S Pi     ( by adding and subtracting )

OR

 Pi   =  S Pi + P - S Pi  ( 1 – S Pi )


     This shoes that rotor input, Pis utilised in the rotor resistance as  S Pi and the equivalent resistance representing  mechanical load ( 1 - S ) Pi  

Rotor power output,          

Pr   =  ( 1 - S ) Pi 


=  ( 1 - S )  *  I2 R2 / S

 Pr  =  I22 R2 ( 1 - s / s )    . . . ( 1 )


Rotor current


Substituting the value of  I2  in equation ( 1 ), 


Again

Equating equations ( 2 ) and ( 3 ) we get


Or

Substituting Nr  as  Ns ( 1 – S ),


     Using the equivalent circuit concept and the expressions for power and torque developed above, calculations for the performance of an induction motor can be made. 


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