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

Step-by-step explanation:

From the given information:

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

`n_(sm)= (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

`(120(50 \ Hz))/(P_1)= (120( 60 \Hz))/(P_2) \\ \\ (6000 \ Hz)/(P_1)= (7200 \ Hz)/(P_2) \\ \\ (P_2)/(P_1)=(7200)/(6000) \\ \\ \\ (P_2)/(P_1)= (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.