Effect of Slip on Induction Motor - Frequency, Induced EMF, Current, Reactance, Resistance, Power Factor


Slip :


     The slip is defined as the difference between the synchronous speed ( Ns ) and the actual speed of the motor ( N ), expressed of fraction of synchronous speed.

Thus slip,

S  =  Ns – N / Ns

Percentage slip,

% S  =   ( Ns – N / Ns ) × 100


Check out more about slip here  -  Slip in Induction Motor



Rotor Frequency :


     The relation between synchronous speed, supply frequency and the number of stator poles is given by,

f  =   Ns P / 120    Hz    ...(1)

     When the rotor rotates at a speed ' N ' then the rotor conductor cut the rotating magnetic field at the relative speed i.e., N-  N. The frequency of the rotor induced emf or current ' f' can expressed as

fr  =   ( Ns – N ) P / 120    Hz    ...(2)

Dividing equation ( 2 ) by ( 1 ), we get

Effect of Slip on Induction Motor

Therefore,

      fr   s f    in running condition

So rotor frequency in running condition is slip times the supply frequency.

At start, N = 0 and slip = 1, Hence  fr   =  f

Under normal running condition, the rotor frequency is very small as slip is very small.



Rotor Induced EMF :


     When the rotor is stationary or Stand still i.e., slip = 1, the emf induced in the rotor is maximum. This is due to the rate of cutting the flux by rotor is maximum as the relative speed between rotor and rotating magnetic field is maximum.


     As rotor gains speed, the relative speed decreases. This reduces the magnitude of induced emf in the rotor, proportionality. The relative speed is ' N-  N ' rpm, when motor is running at speed ' N ' rpm.


At Stand still : 


Rotor induced emf / phase at stand still,

E2r  α  Ns  ( Since N = 0 start )


Under Running Condition :


Rotor induced emf / phase under running condition,

E2r  α  ( Ns – N )

Dividing equation ( 1 ) by ( 2 ), we get

Therefore,

     Rotor induced EMF under running condition will be slip times the rotor induced EMF at stand still.



Rotor Reactance :


     The rotor reactance depends upon the frequency. At slip s, the frequency of the rotor induced emf     fr   =  s f

Let, 

L2  =  Inductance of the rotor per phase


At standstill :

fr   =   f

Hence, 

    Rotor reactance / phase at stand still,

X2   =  2 π fr L2  2 π f L2



Under Running Condition :

fr   =  s f

Hence

Rotor reactance / phase under running condition,

X2r   =  2 π fr L2  2 π sf L


Therefore,

X2r  =  s X2

     Rotor reactance under running condition will be slip times the rotor reactance at stand still.



Rotor Resistance :


Let,  

   R2  =   Stand still rotor resistance / phase

      Rotor resistance is independent of frequency and hence rotor resistance remains same as ' R2 '  Ω / phase at stand still and in running condition.



Rotor Impedance :


     The rotor impedance / phase at stand still and under running condition is given by


Z2  =  R2 + JX2

( R2 + X2 )2   at stand still

And

Z2r  =  R2 + J sX2

( R2 + (sX2) )2   at slip 's'



Rotor Current :


At Stand still :


Let 

   I2  =  Stand still rotor current / phase

  Cos φ2  =  Power factor of the rotor at stand still

Then the equivalent circuit of the rotor at stand still is shown in below figure.

Effect of Slip on Induction Motor

Therefore,

Where, 

   E2  =  Stand still rotor induced emf / phase


Under Running Condition :


   The equivalent circuit of the rotor under running condition is shown in below figure.

Effect of Slip on Induction Motor

Therefore,

   Rotor current / phase under running condition,

  



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1 Comments

  1. Yes sir I was check it yeah absolute correct fraction

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