Phasor Diagram of Induction Motor

       The phasor diagram of loaded induction motor is similar to the loaded transformer. The only difference is the secondary of induction motor is rotating and short circuited while transformer secondary is stationary and connected to load. The load on induction motor is mechanical while load on transformer is electrical. Still by finding electrical equivalent of mechanical load on the motor, the phasor diagram of induction motor can be developed.

       Let              Φ = Magnetic flux links with both primary and secondary.

       There is self induced e.m.f. E₁ in the stator while a mutually induced e.m.f. E_2r in the rotor.

       Let               R₁ = Stator resistance per phase.

                           X₁ = Stator reactance per phase

       The stator voltage per phase V₁ has to counter balance self induced e.m.f. E₁ and has to supply voltage drops I₁ R₁ and I₁ X₁. So on stator side we can write,

        The rotor induced e.m.f. in the running condition has to supply the drop across impedances as rotor short circuited.

      The value of E_2r depends on the ratio of rotor turns to stator turns.

      The rotor current in the running condition is I_2r which lags E_2r by rotor p.f. angle Φ_2r.

       The reflected rotor current I_2r' on stator side is the effect of load and is given by,

                             I_2r' = K I_2r

       The induction motor draws no load current I_o which is phasor sum of I_c and I_m. The total stator current drawn from supply is,

                              Ī₁ = Ī_o + Ī_2r'

       The Φ₁ is angle between V₁ and I₁ and cos Φ₁ gives the power factor of the induction motor.

       Thus using all above relations the phasor diagram of induction motor on load can be obtained.

       The steps to draw phasor diagram are,

1. Takes Φ as reference phasor.

2. The induced voltage E₁ lags Φ by 90^o.

3. Show - E₁ by reversing voltage phasor.

4. The phasor E_2r is in phase with E₁. So I_2r show lagging E_2r i.e. E₁ direction by Φ_2r.

5. Show I_2r R₂  in phase with I_2r and I_2r  X_2r  leading the resistive drop by 90^o, to get exact location of.

6. Reverse I_2r to get I_2r'.

7. I_m is in phase with Φ while Ic is at leading with. Add I_m and Ic to get I_o.

8. Add I_o and I_2r' to get I₁.

9. From tip of - E₁ phasor, add I₁ R₁  in phase with I₁ and I₁X₁  at 90^o leading to I₁ to V₁ get phasor.

10. Angle between V₁ and I₁ is Φ₁.

       The phasor diagram is shown in the Fig. 1.

Fig. 1  On load phasor diagram of induction motor

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