Excercises Electric Machinery Fundamentals

Chapter 4 Problem 4-1



In [1]:

    
%pylab inline









    



Populating the interactive namespace from numpy and matplotlib

Description

At a location in Europe, it is necessary to supply 1000 kW of 60-Hz power. The 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 synchronous motor driving a synchronous generator.

How many poles should each of the two machines have in order to convert 50-Hz power to 60-Hz power?



In [2]:

    
fse1 = 50.0 # [Hz]
fse2 = 60.0 # [Hz]

SOLUTION

The speed of a synchronous machine is related to its frequency by the equation:

$$f_{se} = \frac{n_{sm}\cdot p/2}{60}$$

To make a 50 Hz and a 60 Hz machine have the same mechanical speed so that they can be coupled together, we see that:

$$n_\text{sync} = \frac{120f_{se,1}}{p_1} = \frac{120f_{se,2}}{p_2}$$



In [3]:

    
p2_p1 = (120*fse2) / (120*fse1)
print('p2_p1 = {:.2f}'.format(p2_p1))









    



p2_p1 = 1.20

$$\frac{p_2}{p_1} = \frac{120f_{se,2}}{120f_{se,1}} = \frac{60}{50} = \frac{12}{10} = \frac{24}{20}=\ldots$$

Therefore, a 10-pole synchronous motor must be coupled to a 12-pole synchronous generator to accomplish this frequency conversion.