Power flow in an Induction Motor

Induction motor coverts an electrical power supplied it to into mechanical power. The various stages in this conversion is called Power flow in an induction motor.

The three phase supply is given to the stator is the net electrical input to the motor. If the power factor is Cos Φ and V1 , I1 are phase values of supply voltage and current.

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Pin = V1 I1 Cos Φ (Power input per phase)

By using phasor Diagram

V1 Cos Φ = [(-E1) Cos Φ1 + I1 R1 Cos 0 + j I1 X1 Cos90]

Pin  = [(-E1) Cos Φ1 + I1 R1 Cos 0 + j I1 X1 Cos90] I1

Pin = -(E1) [ Io CosΦo + (-I2 CosΦ2) ] + I21 R1

Pin = - E1Io CosΦo + EI2 CosΦ+ I21 R1

Stator Core losses = E1Io CosΦo and Stator Cu losses =  I21 R1

Air Gap power (P2) = Pin - (Stator Core losses + Stator Cu losses )

P2 =  EI2 CosΦ2

P2 = ( E2 I2 CosΦ2 ) / s
P2 = [ ( I2 )2 R2 ] / s

 P2  = Pc / s

 Pc  = Rotor Cu loss

 Gross mechanical Power (Pg) = P2  - Pc

 P2 :  Pc :  Pg = 1 : s :1 - s  

 Brake Horse Power (Power available at the shaft) = Pg - [ mechanical losses]
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