15/12/2019

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

Rotor emf

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

Cos F2 = R2 / Z2
= R2 / √ R22 + X22
Cos F2 = R2 / Z2
= R2 / √ R22 + ( sX2 )2

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