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. 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 impedances as rotor short circuited.

      The value of E2r depends on the ratio of rotor turns to stator turns.
      The rotor current in the running condition is I2r which lags E2r by rotor p.f. angle Φ2r.
       The reflected rotor current I2r' on stator side is the effect of load and is given by,
                             I2r' = K I2r
       The induction motor draws no load current Io which is phasor sum of Ic and Im. The total stator current drawn from supply is,
                              Ī1 = Īo + Ī2r'
       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 90o.
3. Show - E1 by reversing voltage phasor.
4. The phasor E2r is in phase with E1. So I2r show lagging E2r i.e. E1 direction by Φ2r.
5. Show I2r R in phase with I2r and I2r  X2r  leading the resistive drop by 90o, to get exact location of.
6. Reverse I2r to get I2r'.
7. Im is in phase with Φ while Ic is at leading with. Add Im and Ic to get Io.
8. Add Io and I2r' to get I1.
9. From tip of - E1 phasor, add I1 R in phase with I1 and I1X at 90o 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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  1. Nice to come across your site sir.Really thankful to you sir. I have started a blog Electrical Engineering Info but could not be successful.Can you help me sir

  2. thanku so much sir.....but let me know what is Ic and Im

    1. Ic is the core current , and Im is the magnetizing current.

  3. This comment has been removed by the author.

  4. Hi...When we are changing E1 to +ve X Axis it becomes -E1....but why not rotor current becoming -I2 when it changing to Primary side?