Question

1. At a location in Europe, it is necessary to supply 1000 kW of 60-Hz power. Only power sources available operate at 50 Hz. It is decided to generate the power by means of a motor-generator set consisting of a 20- pole synchronous motor (its electrical rotating frequency is 50 Hz) driving a synchronous generator. How many poles should the synchronous generator have in order to convert 50-Hz power to 60-Hz power

Answer 1

Answer:

Explanation:

From the given information:

The speed of a synchronous motor in relation to its frequency can be represented with the formula:

$n_{sm}= \dfrac{120f_{se}}{P}$

where,

the electrical frequency $f_{se}$ is measured in Hz

the number of poles = P

For us to estimate the number of poles to have 50 Hz - 60 Hz Power, then we need to relate the frequencies of the above equation.

i.e

$\dfrac{120(50 \ Hz)}{P_1}= \dfrac{120( 60 \Hz)}{P_2} \\ \\ \dfrac{6000 \ Hz}{P_1}= \dfrac{7200 \ Hz}{P_2} \\ \\ \dfrac{P_2}{P_1}=\dfrac{7200}{6000} \\ \\ \\ \dfrac{P_2}{P_1}= \dfrac{12}{10}$

Thus, we can conclude that 10 poles synchronous motor is attached with 12 poles synchronous generator in order to convert 50 Hz to 60 Hz power.