Question 9.6: A six-pole, three-phase synchronous generator driven at 1000...
A six-pole, three-phase synchronous generator driven at 1000 rpm supplies power to an induction motor which runs at a speed of 1440 rpm on full load. Calculate the percentage slip of the motor and the number of poles of the motor.
The synchronous generator is rotated at a synchronous speed of 1000 rpm by a prime mover. The synchronous speed N_{s} is expressed as
N_{s}=\frac{120 f}{P} where f is the frequency of the generated EMF
\begin{aligned} \text {or,} \quad f &=\frac{N_{s} \times P}{120} \\&=\frac{1000 \times 6}{120}=50 Hz\end{aligned}This synchronous generator now supplies power to the induction motor at a frequency of 50 Hz. The synchronous speed of the rotating magnetic field produced in the motor is
N_{s}=\frac{120 \times f}{P}=\frac{120 \times 50}{2}=3000 rpm (for P = 2)
and N_{s}=\frac{120 \times 50}{4}=1500 rpm (for P = 4)
The motor speed is 1440 rpm, which should be slightly less than the synchronous speed. Logically, the number of poles of the motor must be 4.
Percentageslip, S=\frac{N_{s}-N_{r}}{N_{s}} \times 100=\frac{(1500-1440) \times 100}{1500}=4 per cent