Final answer:
To convert 50 Hz to 60 Hz power using a synchronous motor-generator set with constant speed, the motor should have 10 poles and the generator should have 12 poles, allowing the frequency conversion in the required ratio of 5:6.
Step-by-step explanation:
To convert a 50 Hz power supply to a 60 Hz power supply using a synchronous motor-generator set, each machine must have a specific number of poles. The relationship between the frequency (f), the number of poles (P), and the speed of the motor (N) is given by the formula f = (P/2) × (N/60), where N is the speed in revolutions per minute (rpm). To convert from 50 Hz to 60 Hz, keeping the motor speed constant (which we would assume to be the same for both generator and motor for direct coupling), the generator must have a greater number of poles than the motor so that:
50 Hz = (Pmotor/2) × (N/60) and 60 Hz = (Pgenerator/2) × (N/60)
Ratio of frequencies is equal to the inverse ratio of the number of poles: 50/60 = Pgenerator/Pmotor.
Since we want a whole number of poles, which are typically even, you can use 10 for the motor, which results in 12 poles required for the generator: 10/12 = 5/6, which is the inverse of the frequency ratio 50/60.
Therefore, the synchronous motor should have 10 poles, and the synchronous generator should have 12 poles to convert 50 Hz power to 60 Hz power.