Phasor Diagram of Induction Motor


     The induction motor like a transformer is singly energized device. The stator and rotor of an induction motor can be compared to primary and secondary of transformer.


     When a 3-phase supply is fed to the stator, a rotating field is set up and emfs are induced in stator and rotor

E1  =  4.44 kW1 f1 N1 φ

E2  =  4.44 kW2 f2 N2 φ

Where kW1 and kW2 are winding factors for the stator and rotor windings respectively.

Therefore,


     The expression is similar to the voltage transformation ratio of the transformer. The slight difference in these equations is due to the use of distributed winding for the induction motor as compared to the concentrated coils used in the transformer.


     An induction motor at standstill exhibits the characteristics of a transformer on no-load. In induction motor also the leakage fluxes as in a transformer. The behaviour of both the devices is similar under load conditions also.


     Thus behaviour of an induction motor is similar to that of a transformer. Therefore, the vector or phasor diagram of the induction motor can be developed similar to that of a transformer. The phasor diagram is drawn on a per phase basis.



Phasor or Vector Diagram of Induction Motor :


     let us take the mutual flux φ between the stator and rotor windings as the reference phasor. This flux induces emfs in stator and rotor. These, emfs under running conditions are E1 and sE2 respectively lagging ''φ'' by 90°. Since the rotor winding is short circuit, the voltage sE2 sets up the rotor current I2 lagging behind by an angle φ2  =  Tan-1 ( sX2 / R2 ). sE2 is equal to rotor impedance drop i.e.,

sE2  =  I2 ( R2 + j sX2 )


Phasor Diagram of Induction Motor

The above figure shows the phasor diagram of induction motor on load.

The current flowing in the stator winding i.e., stator current is

Io  =  Io + I'2  

Where 

Io  =  No. load current of the induction motor

I'2  =  Rotor current referred to stator


     The phasor sum of E1I1 R1 and I1 X1 gives the applied voltage V1Cos φ1 is the p.f. of the stator and Cos φ2 is the p.f. of the rotor circuit.

V1  =  E1 + I1 ( R1 + J X1 )


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