Question

A motor generator set used for providing variable frequency AC supply consist of a three-phase, 10-pole synchronous motor and a 24-pole, three-phase synchronous generator. The motor-generator set is fed from a 25 Hz, three-phase AC supply. Determine the frequency of the generated voltage of the synchronous generator.
1. 40 Hz
2. 50 Hz
3. 25 Hz
4. 60 Hz

Answer 1

Correct Answer - Option 4 : 60 Hz

Concept:

Motor Generator (MG) Set:

• A motor-generator (M-G) set refers to a composite device consisting of a motor and a generator mechanically coupled through the common shaft.
• A motor-generator set is used to convert voltage, phase, and frequency of power.
• They also find application in isolation of electrical loads from the supply line, Ward-Leonard speed control of DC Shunt motor.
• When MG set connected together then it will be operated at the same speed.
   

For the AC machine, Speed is given as,

\(N = \frac{{120f}}{P} \)

Where N is the speed in rpm, f is the operating frequency in Hz and P is the number of poles.

Since Speed of motor = speed of the generator

\(\frac{{120{f_m}}}{{{P_m}}} = \frac{{120{f_g}}}{{{P_g}}}\)

∴ f_mP_g = f_gP_m

Where, f_m, P_m is frequency, number of poles of motor respectively.

And, f_g, P_g is frequency, a number of poles of generator respectively.

Calculation:

Given,

f_m = 25 Hz

P_m = 10

P_g = 24

We know that,

f_g P_m = f_mP_g

10f_g = 25 × 24

∴ f_g = 60 Hz