Efficiency and Power Flow Diagram of Induction Motor


Power Transfer Stages of Induction Motor :


     Induction motor converts an electrical power supplied to it into mechanical power. The various stages in this conversion is called as power transfer stages in an induction motor.

     The 3-phase power input to an induction motor i.e,

Stator input,

Pin  = 3 VL IL Cos φ


     Where  VL and IL are the line values of stator supply voltage and current and Cos φ is the power factor of the motor.


     A part of this power is consumed in stator iron and copper losses. The remaining power is transferred inductively to the rotor through the air-gap. This is called as Rotor Input, P2 

So,

    P2  =  Pin  -  Stator iron and Copper losses


     The rotor losses consists of majority of copper losses and a very small rotor iron losses which are generally neglected.

    By substracting the rotor copper losses from ' P2 ', we get the gross mechanical power developed by the motor, P

     Pm  =  P-  Rotor Copper losses


     A part of  ' Pm '  is consumed as mechanical losses and the remaining is the power available to the load at the shaft. This is called as Net Output Power of the Motor, Pout


The above stages can be shown diagrammatically called as Power Flow Diagram of Induction Motor.

Efficiency and Power Flow Diagram of Induction Motor


Relation Between Rotor Input, Rotor Copper Losses and Rotor Output :


 Let,

    P2  -  Rotor input

    Pc  -  Rotor copper losses

    P  -  Gross mechanical power developed or rotor output

    Tg  -   Gross torque developed by the rotor in N-m


 The actual torque available at the shaft called as Shaft Torque or Useful torque, Tsh

    Tsh  - Gross torque,

    Tg  -  Torque lost due to the friction and windage losses

     

     Now input to the rotor is through the air-gap with the help of rotating magnetic field which is rotating at a speed of ' Ns ' rpm.


     The rotor input can be expressed in terms of gross torque Tg and speed as,

P2  =  2π Ns Tg / 60   . . . ( 1 )

   

     Now torque developed remains same, but the rotor output which is gross mechanical power developed,P is at a speed ' N ' rpm.

So from output side, we can write

Pm  =  2π N Tg / 60   watt

We know that,

Rotor copper losses,

Pc  =  P2  -  Pm

=  ( 2π N Tg / 60 ) ( Ns - N )  . . . ( 2 )


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


Therefore,

Pc  =  sP2   . . . ( 3 )


So rotor copper losses are slip times the rotor input.

Now gross mechanical power developed,

Pm  =  P2  -  Pc

=  P2  -  sP2


Therefore,

Pm  =  ( 1 - s ) P2   . . . ( 4 )


So gross mechanical power developed is ( 1 - s ) times the rotor input,


Dividing equation ( 3 ) by ( 4 ), we get

Pc / Pm  =   s / 1 - s 


From the above, it can be concluded that

P2 :  Pc :  Pm   =  1 : s : 1 - s



Gross Torque and Shaft Torque :


     The torque produced by rotor is gross mechanical torque and due to mechanical losses entire cannot be available to drive load.


The load torque is net output torque called shaft torque or useful toque.


Therefore,

 Shaft torque   


 Gross torque,

Efficiency and Power Flow Diagram of Induction Motor

where,

      Tlost  =  Torque lost due to mechanical losses

      Pout  =  Motor output

      Pm  =  Mechanical power developed

      N  =  Motor speed



Efficiency of an Induction Motor :


     The ratio of net power available at the shaft ( Pout ) and the net electrical power input (  Pin ) to the motor is called as overall Efficiency of an Induction Motor. 

% Efficiency  =  ( Pout / Pin ) × 100


The maximum efficiency occurs when variable losses become equal to constant losses.

Efficiency and Power Flow Diagram of Induction Motor

The normal efficiency curve of the motor is shown above.


Rotor Efficiency,

Efficiency and Power Flow Diagram of Induction Motor


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