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 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?
Show 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.
Updated On: Jul 20, 2026
- 2, 6
- 6, 2
- 4, 6
- 6, 4
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Recall that the motor and generator share the same mechanical shaft speed.
Since the synchronous motor drives the synchronous generator directly, both machines rotate at the same synchronous speed \(N_s\), in rpm.
Step 2: Write the synchronous speed formula for each machine.
For the motor, running on the \(50\) Hz grid with \(P_m\) poles:
\[ N_s=\frac{120\times50}{P_m} \]
For the generator, which must produce \(16.67\) Hz with \(P_g\) poles, running at this same \(N_s\):
\[ N_s=\frac{120\times16.67}{P_g} \]
Step 3: Equate the two expressions for \(N_s\).
\[ \frac{120\times50}{P_m}=\frac{120\times16.67}{P_g} \]
Cancelling \(120\) from both sides:
\[ \frac{50}{P_m}=\frac{16.67}{P_g} \implies \frac{P_m}{P_g}=\frac{50}{16.67}\approx3 \]
Step 4: Test option (A), 2 poles motor, 6 poles generator.
\[ \frac{P_m}{P_g}=\frac{2}{6}=\frac{1}{3} \]
This is the reciprocal of what is needed; it would make the generator frequency three times the grid frequency, not one-third of it. Incorrect.
Step 5: Test option (B), 6 poles motor, 2 poles generator.
\[ \frac{P_m}{P_g}=\frac{6}{2}=3 \]
This matches the required ratio from Step 3. Checking directly: \(N_s=120\times50/6=1000\) rpm; generator frequency \(=N_s\times P_g/120=1000\times2/120=16.67\) Hz. This matches exactly. Correct.
Step 6: Rule out options (C) and (D).
Option (C), \(4\) and \(6\) poles, gives \(N_s=120\times50/4=1500\) rpm, and generator frequency \(=1500\times6/120=75\) Hz, far from \(16.67\) Hz. Option (D), \(6\) and \(4\) poles, gives \(N_s=1000\) rpm and generator frequency \(=1000\times4/120=33.3\) Hz, also not matching.
Step 7: Final Answer.
\[ \boxed{6\ \text{poles (motor)},\ 2\ \text{poles (generator)}} \]
Since the synchronous motor drives the synchronous generator directly, both machines rotate at the same synchronous speed \(N_s\), in rpm.
Step 2: Write the synchronous speed formula for each machine.
For the motor, running on the \(50\) Hz grid with \(P_m\) poles:
\[ N_s=\frac{120\times50}{P_m} \]
For the generator, which must produce \(16.67\) Hz with \(P_g\) poles, running at this same \(N_s\):
\[ N_s=\frac{120\times16.67}{P_g} \]
Step 3: Equate the two expressions for \(N_s\).
\[ \frac{120\times50}{P_m}=\frac{120\times16.67}{P_g} \]
Cancelling \(120\) from both sides:
\[ \frac{50}{P_m}=\frac{16.67}{P_g} \implies \frac{P_m}{P_g}=\frac{50}{16.67}\approx3 \]
Step 4: Test option (A), 2 poles motor, 6 poles generator.
\[ \frac{P_m}{P_g}=\frac{2}{6}=\frac{1}{3} \]
This is the reciprocal of what is needed; it would make the generator frequency three times the grid frequency, not one-third of it. Incorrect.
Step 5: Test option (B), 6 poles motor, 2 poles generator.
\[ \frac{P_m}{P_g}=\frac{6}{2}=3 \]
This matches the required ratio from Step 3. Checking directly: \(N_s=120\times50/6=1000\) rpm; generator frequency \(=N_s\times P_g/120=1000\times2/120=16.67\) Hz. This matches exactly. Correct.
Step 6: Rule out options (C) and (D).
Option (C), \(4\) and \(6\) poles, gives \(N_s=120\times50/4=1500\) rpm, and generator frequency \(=1500\times6/120=75\) Hz, far from \(16.67\) Hz. Option (D), \(6\) and \(4\) poles, gives \(N_s=1000\) rpm and generator frequency \(=1000\times4/120=33.3\) Hz, also not matching.
Step 7: Final Answer.
\[ \boxed{6\ \text{poles (motor)},\ 2\ \text{poles (generator)}} \]
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