Solution Electrical Numerical 8

Numerical 8: A three phase induction motor is wound for four poles and is supplied from a 50 Hz system. Calculate. i. The synchronous speed; ii. The speed of the rotor when the slip is 4 per cent; iii. The motor frequency when the speed of the rotor is 600 r.p.m.

Solution: Given Number of phases = 3

Pole(p) = 4

Frequency(f) =50 Hz

(i) The synchronous speed 

$\displaystyle \mathrm{N_S = \frac{120\times f}{p}}$

$\displaystyle \mathrm{N_S = \frac{120\times 50}{4}}$

$\displaystyle \mathrm{N_r\,=\,1500 }$ RPM

(ii) The speed of the rotor when the slip is 4 %.

$\displaystyle \mathrm{S = \frac{N_s-N_r}{N_s}}$ 

$\displaystyle \mathrm{0.04 = \frac{1500-N_r}{1500}}$

$\displaystyle \mathrm{N_r\,=\,1440 }$ RPM

(iii) The motor frequency when the speed of the rotor is 600 r.p.m

$\displaystyle \mathrm{f'=\,s\times f\,=\, \frac{N_s-N_r}{N_s}\times f}$ 

$\displaystyle \mathrm{f'=\, \frac{1500-600}{1500}\times 50}$ 

= 30 Hz