Question

A certain application requires power at a frequency of 16.67 Hz, while the available grid frequency is 50 Hz. A 3-phase synchronous motor connected to the 50 Hz, 3-phase grid, driving a synchronous generator, is used for this application.

Which one of the following combinations is a suitable choice for the number of poles in the motor and generator, respectively?

• A. 2, 6
• B. 6, 2
• C. 4, 6
• D. 6, 4

Hint:

Both machines share the same shaft speed; set the two synchronous-speed formulas equal and solve for the pole ratio, then check which option gives that ratio.

Answer 1

The Correct Option is B

Another way to approach this is to test each option's shaft speed directly and see which one produces exactly 16.67 Hz at the generator.

The motor's synchronous speed on the 50 Hz grid, for pole count $P_m$, is $N_s=\dfrac{120\times50}{P_m}=\dfrac{6000}{P_m}$.

Testing option (A), $P_m=2$: $N_s=6000/2=3000$ rpm. Generator frequency with $P_g=6$: $f_g=\dfrac{N_sP_g}{120}=\dfrac{3000\times6}{120}=150$ Hz. Far too high.

Testing option (B), $P_m=6$: $N_s=6000/6=1000$ rpm. Generator frequency with $P_g=2$: $f_g=\dfrac{1000\times2}{120}=16.67$ Hz. This matches the required output frequency exactly.

Testing option (C), $P_m=4$: $N_s=6000/4=1500$ rpm. Generator frequency with $P_g=6$: $f_g=\dfrac{1500\times6}{120}=75$ Hz. Too high.

Testing option (D), $P_m=6$: $N_s=1000$ rpm. Generator frequency with $P_g=4$: $f_g=\dfrac{1000\times4}{120}=33.3$ Hz. Still too high.

Only option (B) reproduces the required 16.67 Hz output.

\[ \boxed{6\text{ poles (motor)},\ 2\text{ poles (generator)}} \]