# Excercises Electric Machinery Fundamentals

## Problem 6-10



In [1]:

%pylab inline




Populating the interactive namespace from numpy and matplotlib



### Description

A three-phase 60-Hz two-pole induction motor runs at a no-load speed of 3580 r/min and a full-load speed of 3440 r/min.

• Calculate the slip and the electrical frequency of the rotor at no-load and full-load conditions.
• What is the speed regulation of this motor?


In [2]:

fe = 60     # [Hz]
p  = 2
n_nl = 3580 # [r/min]
n_fl = 3440 # [r/min]



### SOLUTION

The synchronous speed of this machine is:

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


In [3]:

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




n_sync = 3600 r/min



The slip and electrical frequency at no-load conditions is:

$$S_\text{nl} = \frac{n_\text{sync} - n_\text{nl}}{n_\text{sync}} \cdot 100\%$$


In [4]:

s_nl = (n_sync - n_nl) / n_sync
print('''
s_nl = {:.2f} %
============='''.format(s_nl*100))




s_nl = 0.56 %
=============


$$f_\text{r,nl} = sf_e$$


In [5]:

f_rnl = s_nl * fe
print('''
f_rnl = {:.2f} Hz
==============='''.format(f_rnl))




f_rnl = 0.33 Hz
===============



The slip and electrical frequency at full load conditions is:

$$S_\text{fl} = \frac{n_\text{sync} - n_\text{fl}}{n_\text{sync}} \cdot 100\%$$


In [6]:

s_fl = (n_sync - n_fl) / n_sync
print('''
s_fl = {:.2f} %
============='''.format(s_fl*100))




s_fl = 4.44 %
=============


$$f_\text{r,fl} = sf_e$$


In [7]:

f_rfl = s_fl * fe
print('''
f_rfl = {:.2f} Hz
==============='''.format(f_rfl))




f_rfl = 2.67 Hz
===============



The speed regulation is:

$$SR = \frac{n_\text{nl} - n_\text{fl}}{n_\text{fl}} \cdot 100\%$$


In [8]:

SR = (n_nl - n_fl) / n_fl
print('''
SR = {:.2f} %
==========='''.format(SR*100))




SR = 4.07 %
===========