The condition for maximum efficiency in an induction motor is that the slip is zero. This means that the rotor speed is equal to the synchronous speed.
When the slip is zero, the rotor bars are not cutting any flux lines, so there is no induced voltage in the rotor. This means that there is no rotor current, and therefore no rotor copper losses.
The only losses in the motor at zero slip are the stator copper losses and the iron losses. The stator copper losses are the losses due to the resistance of the stator windings. The iron losses are the losses due to hysteresis and eddy currents in the iron core of the motor.
The stator copper losses are proportional to the square of the stator current. The iron losses are proportional to the square of the flux density.
At maximum efficiency, the stator current is at a minimum, and the flux density is at a minimum. This means that the stator copper losses and the iron losses are both at a minimum.
Therefore, the efficiency of a three-phase induction motor is maximum when the power factor is unity and the slip is zero.
