(Modified problem 3-11 in Chapman) In later years, motors improved and could be run directly from a 50 Hz power supply. As a result, 16.67 Hz power systems shrank and disappeared. However, there were many perfectly good working 16.67 Hz motors in factories around the country that owners were not ready to discard. To keep them running, some users created their own 16.67 Hz power in the plant using motor-generator sets. A motor-generator set consists of two machines connected on a common shaft, one acting as a motor and the other acting as a generator. If the two machines have different numbers of poles but exactly the same shaft speed, then the electrical frequency of the two machines will be different due to relationship fse = nsm⋅P/120. What combination of poles on the two machines could convert 50 Hz power to 16.67 Hz power?

Hence to get the same speed, the ratio of poles of generator to motor should be 3.

Explanation:

We are given that the speeds of the motor-generator sets are same.

In case of motors we have operating frequency 16.67 Hz and now we need to define the number of poles of generator set so that we can get the same speed.

For the case of motor, we write an equation;

f m = speedm x Pm / 120

speedm = fm x 120 / Pm

For the case of generator we write an equation;

speedg = fg x 120 /Pg

Now we know that speedm = speedg

fm x 120 / Pm = fg x 120 /Pg

fm / Pm = fg  /Pg

16.67 / Pm = 50 / Pg

Pg / Pm = 50 / 16.67

Pg / Pm = 3

Hence to get the same speed, the ratio of poles of generator to motor should be 3.

For example;

If motor has 2 poles, then generator will have 6 poles

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