Losses and Efficiency of Induction Motor

A three phase induction motor turns electrical input into shaft output. The difference is losses, in two groups:

1. Constant or fixed losses,
2. Variable losses.

Constant or Fixed Losses

Constant losses are taken as nearly constant over the normal running range of an induction motor. A no-load test on a three phase induction motor is the usual way to find them. They split as:

1. Iron or core losses,
2. Mechanical losses,
3. Brush friction losses.

Iron or Core Losses

Iron or core losses split into hysteresis and eddy current losses. Laminating the core raises resistance in the eddy path and cuts eddy currents. High-grade silicon steel is used to keep hysteresis loss down. Core loss also depends on flux density and on supply frequency. Stator frequency is the supply frequency. Rotor frequency is slip times supply frequency, so it is much lower in normal running. At 50 Hz with a typical 3% full-load slip, rotor frequency is about 1.5 Hz. Rotor core loss is then usually neglected next to stator core loss.

Mechanical and Brush Friction Losses

Mechanical losses occur at the bearings. Brush friction occurs only on wound-rotor machines. Both are small at standstill and rise with speed. On a fixed-frequency three phase induction motors, speed stays close to synchronous speed, so these losses are treated as nearly constant.

Variable Losses

Variable losses are the copper losses from current in the stator and rotor windings. They rise and fall with load current. A blocked-rotor test gives the short-circuit impedance, from which those winding copper losses at a given current are estimated. A smaller stray-load term also grows with load. The job of an induction motor is to convert electrical power into mechanical power, and that conversion has several power-flow stages.

The power-flow diagram shows those stages. Input to the three phase induction motor is a three-phase supply to the stator.
Let P_in = electrical power supplied to the stator of three phase induction motor,
V_L = line voltage supplied to the stator of three phase induction motor,
I_L = line current,
Cosφ = power factor of the three phase induction motor.
Electrical power input to the stator, P_in = √3V_LI_Lcosφ
Stator iron loss and stator copper loss are taken from that input. The remainder is the air-gap (rotor) input.
So, rotor input P₂ = P_in – stator losses (stator copper loss and stator iron loss).
The rotor cannot turn all of this rotor input into mechanical power. It must cover rotor losses. Those are rotor iron loss and rotor copper loss. Rotor iron loss tracks rotor frequency, which is small once the rotor is up to speed, so it is usually neglected. Rotor copper loss remains. After that copper loss is subtracted, the rest of P₂ is gross mechanical power P_m.

Let P_c be the rotor copper loss,
I₂ be the rotor current under running condition,
R₂ is the rotor resistance,
P_m is the gross mechanical power developed.
P_c = 3I₂²R₂
P_m = P₂ – P_c
Friction and windage still come out of that gross mechanical power before the shaft. Net shaft output to the load is P_out.
P_out = P_m – Mechanical losses (friction and windage losses).
P_out is the shaft power, the useful output.

Efficiency of Three Phase Induction Motor

Efficiency is output divided by input,

Rotor efficiency of the three phase induction motor ,

= Gross mechanical power developed / rotor input

Three phase induction motor efficiency,

Three phase induction motor efficiency