# 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.

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 + (-I’2 CosΦ2) ] + I21 R1

Pin = - E1Io CosΦo + E1 I’2 CosΦ2 + 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 =  E1 I’2 CosΦ2

P2 = ( E’2 I’2 CosΦ2 ) / s```
```P2 = [ ( I’2 )2 R’2 ] / 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]```