#### The induction motor and transformer both are singly energized devices. The stator and rotor of an induction motor can be compared to the primary and secondary windings of the transformer. Similarly, from the e.m.f. equation of transformer we can derive the equations for EMF induced in stator and rotor of the motor.

Thus, when a 3-phase supply is fed to the stator, a rotating field will set up and emf's ( E_{1} & E_{2} ) are induced in the stator and rotor.

#### Where kW_{1} and kW_{2} are winding factors for the stator and rotor windings respectively. Therefore,

#### The above 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. There also exist leakage fluxes in the induction motor as seen in the transformer. The behavior of both devices is similar to load conditions also.

Thus, we can say that the behavior of an induction motor is same as 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 emf's in the stator and rotor. These emf's under running conditions are E_{1} and sE_{2} respectively lagging 'φ' by 90°. Since the rotor winding is a short circuit, the voltage sE_{2} sets up the rotor current I_{2} lagging behind by an angle φ_{2,} and sE_{2} will be equal to rotor impedance drop.

#### From the above, the phasor diagram of induction motor on load condition can be drawn as,

#### The current flowing in the stator winding i.e., stator current is
*I*_{o} = I_{o} + I'_{2}
Where- I
_{o} = No-load current of the induction motor. - I'
_{2} = Rotor current referred to the stator.

The phasor sum of E_{1}, I_{1} R_{1}, and I_{1} X_{1} gives the applied voltage V_{1}. Cos φ_{1} is the p.f. of the stator and Cos φ_{1} is the p.f. of the rotor circuit.

*I*

_{o}= I_{o}+ I'_{2}_{o}= No-load current of the induction motor._{2}= Rotor current referred to the stator.