Phasor Diagram of Induction Motor

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. Ej in the stator while a mutually induced e.m.f. E2r 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 impedance as rotor is 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 hr 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 Im. The total stator current I₁ drawn from supply is,

The ϕ₁ is angle between V₁ and I₁ and cos ϕ₁ gives the power factor of the inductor 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. Take ϕ as reference phasor.

2. The induced voltage E₁ lags ϕ by 90°.

3. Show – E₁by reversing voltage phasor E₁.

4. The phasor E_2r is in phase with E₁. So show I_2r 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°, to get exact location of E_2r

6. Reverse I_2r to get I_2r.

7. I_m is in phase with ϕ while I_c is at 90° leading with . Add I_m and I_c to get Io.

8. Add I_o and I_2r to get I₁.

9. From tip of – E₁ phasor, add I₁ R₁ in phase with I₁ and I₁ X₁ at 90° leading to I₁ to get V₁ phasor.

10. Angle between V₁ and I₁ is ϕ₁.

The phasor diagram is shown in the Fig. 5.19.1

Review Question

1. Draw and explain the phasor of diagram of a three phase induction motor.