10 January 2018

Effect of Frequency on Rotor Parameter in the Three Phase Induction Motor

Rotor emf

  • When the three phase supply is given to the three phase induction motor, the rotating magnetic field is produced which rotates at synchronous speed.

Starting condition

  • The speed of the rotor during starting condition is zero therefore the relative speed between stator rotating magnetic field and rotor speed is
        Ns – N = Ns
  • When the rotor conductors cut the rotating magnetic field, an emf will be induced in it. 
  • Let us consider that the induced emf in the rotor is E2

Running condition

  • Let us assume that the induced emf in the rotor is E2’. The relative speed between stator rotating magnetic field and rotor speed is Ns – N. 
  • The induced emf in the rotor condition is

                    Relative speed                     Rotor emf
                         Ns                                             E2
                         Ns – N                                      E2
                         E2’ = [ Ns – N / N] E2
                         E2’ = s E2
  • The slip at starting is unity therefore the rotor induced emf is same as that of starting condition. 
  • However the rotor induced emf decreases as the speed increases or slip decreases.

Effect of slip on rotor Parameters

  • The effect of slip on rotor parameter is summarized as below. As the slip decreases during running condition, all the parameter decreases during running condition.

Rotor parameter

Starting condition
Running condition
Frequency of rotor emf

f
f’ = sf
Rotor induced emf

E2
E2’= s E2
Rotor resistance

R2
R2
Rotor reactance

X2 = 2πfL
X2 = s X2 =  s( 2πfL )
Rotor impedance


Z2 = √ R22 + X22

Z2’ = √ R22 + X22
= √ R22 + ( sX2 )2

Rotor current



I2 = E2 / Z2

I2 = E2 / √ R22 + X22





I2’ = E2’/Z2


I2’= s E2 / √ R22 + ( sX2 )2
Rotor power factor
Cos F2 = R2 / Z2
= R2 / √ R22 + X22
Cos F2 = R2 / Z2
= R2 / √ R22 + ( sX2 )2


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