The various losses in the stator of three phase induction motor are stator copper losses and stator iron losses. The stator iron losses consist of eddy current loss and hysteresis loss.

In rotor the losses are rotor iron loss and rotor copper loss. The other losses on the rotor side are friction losses at bearing and slip rings etc and the windage losses.

The stator iron losses depend upon the two factors namely flux density and the supply frequency. The rotor iron loss depends on the frequency of the rotor current. The frequency of the rotor current depends on the slip or speed of the rotor (f^’=sf). The iron losses of the rotor are negligible, since the frequency of the rotor current is very small.

 

 

 

i. Rotor copper loss is determined by using the formula 3I²₂R₂.

ii. Stator copper loss is calculate by using the formula 3I²₁R₁

iii. Input to the motor on load is equal to √3V_LI_L cosΦ watts.

 
  Slip Torque characteristics of an induction Motor

In an induction motor is supplied to the stator winding. The power to the rotor circuit is transferred entirely by induction. The output available at the rotor shaft is mechanical energy.

During the power conversion, certain losses take place at various stages. The rotor output of an induction motor is given as follows:

Stator output = Stator input – stator losses

Stator output = Rotor Input

Rotor Output = Rotor Input – Rotor copper losses

Rotor output = Mechanical Energy

Mechanical Energy ----> Gross Torque T_g

Gross Torque T_g = (useful torque or shaft torque T_sh) + (Winding and friction losses in the motor)

Rotor output = 2πN_rT_g

Where, N_r = actual speed of the motor in r.p.m

           T_g = Gross torque in NM

From this T_g = Rotor output in watts / 2πN_r  --------> 1

For an ideal case, assuming no copper losses in the rotor circuit.

Rotor Output = rotor Input

For this condition, the motor should run at synchronous speed.

Then the torque,

T_g = Rotor Input / 2πN_s  --------> 2

Using the eqn 1 & 2

Rotor output = 2πN_rT_g  --------> 3

Rotor input 2πN_sT_g  --------> 4

 

But in actual case

(Rotor input – Rotor output) = Rotor copper losses.

using the eqn 3 & 4

(2πN_sT_g - 2πN_rT_g) = Rotor copper losses.

That is Rotor copper losses = T_g. 2π(N_s – N_r)   --------> 5

Using the eqn 4&5

Rotor copper losses/Rotor input = T_g2π(N_s-N_r) / 2πN_rsT_g

                                               = (N_s-N_r) / N_s

                                               = Slip S  --------> 6

Thus , from the equation 6, Rotor copper losses equal to 

                                               s x Rotor input   --------> 7

But Rotor Gross Output = Rotor input – Rotor copper losses

Using equation 7

Rotor gross output = (Rotor input – s) x Rotor input

                            = (1-s) Rotor input

Or

Rotor gross output/Rotor input = (1-s)  --------> 8

Using s, (N_s – N_r) /N_s

Rotor gross output/Rotor input = {1- (N_s – N_r) /N_s}

                                              = (N_s-N_s+N_r) / N_s

                                              =N_r/N_s

That is,

Rotor gross output/Rotor input = Actual speed of the motor / Synchronous speed

Hence this can be expressed as

Rotor efficiency = N_r/N_s

Using the expression (6 and 8), (6+8) gives

Rotor copper losses/Rotor Gross input = s/(1-s)

 

The induction motor receives power from the supply mains through the stator windings. The input power is electrical power. The power from the stator winding is transferred to rotor, via air gap by induction principle. The output power is a mechanical power. The mechanical power is obtained at the shaft of the motor to perform mechanical work.

During this power transfer, some losses such as copper losses in stator winding, copper losses in rotor winding, core losses in stator winding, frictional losses and windage losses take place.

Then the efficiency is determined by knowing the input power and the output power.

Efficiency of any machine is the ratio of output power and input power. The efficiency of an induction motor is obtained as

Efficiency η = Output power / input power

                   = Output power / (Output power + losses)