Excercises Electric Machinery Fundamentals

Chapter 6 Problem 6-1



In [1]:

    
%pylab inline









    



Populating the interactive namespace from numpy and matplotlib

Description

A 220-V three-phase six-pole 50-Hz induction motor is running at a slip of 3.5 percent.



In [2]:

    
fse = 50 # [Hz]
p   = 6
s   = 3.5/100

Find:

(a)

(b)

(c)

(d)

SOLUTION

(a)

The speed of the magnetic fields is:

$$n_\text{sync} = \frac{120f_{se}}{P}$$



In [3]:

    
n_sync = 120*fse / p
print('''
n_sync = {:.0f} r/min
==================='''.format(n_sync))









    



n_sync = 1000 r/min
===================

(b)

The speed of the rotor is:

$$n_m = (1-s)n_\text{sync}$$



In [4]:

    
n_m = (1 - s) * n_sync
print('''
n_m = {:.0f} r/min
==============='''.format(n_m))









    



n_m = 965 r/min
===============

(c)

The slip speed of the rotor is:

$$n_\text{slip} = s \cdot n_\text{sync}$$



In [5]:

    
n_slip = s * n_sync
print('''
n_slip = {:.0f} r/min
================='''.format(n_slip))









    



n_slip = 35 r/min
=================

(d)

The rotor frequency is:

$$f_{re} = \frac{p\cdot n_\text{slip}}{120}$$



In [6]:

    
fre = n_slip*p / 120
print('''
fre = {:.2f} Hz
============='''.format(fre))









    



fre = 1.75 Hz
=============