Excercises Electric Machinery Fundamentals

Chapter 6 Problem 6-12



In [1]:

    
%pylab inline
%precision 4









    



Populating the interactive namespace from numpy and matplotlib






    Out[1]:





'%.4f'

Description

The power crossing the air gap of a 60 Hz, four-pole induction motor is 25 kW, and the power converted from electrical to mechanical form in the motor is 23.2 kW.

(a)

What is the slip of the motor at this time?

(b)

What is the induced torque in this motor?

(c)

Assuming that the mechanical losses are 300 W at this slip, what is the load torque of this motor?



In [2]:

    
fse   = 60     # [Hz]
p     = 4          
Pag   = 25.0e3 # [W]
Pconv = 23.2e3 # [W]
Pm    = 300    # [W]

SOLUTION

(a)

The synchronous speed of this motor is:

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



In [3]:

    
n_sync = 60 * fse // (p//2)  # // is used for integer division in Python 3
n_sync









    Out[3]:





1800

The power converted forom the electrical to the mechanical form is:

$$P_\text{conv} = (1-s)P_\text{AG}\quad \leadsto \quad s = 1 - \frac{P_\text{conv}}{P_\text{AG}} $$



In [4]:

    
s = 1 - Pconv/Pag
s









    Out[4]:





0.0720

(b)

The speed of the motor is:

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



In [5]:

    
n_m = (1-s)*n_sync
n_m









    Out[5]:





1670.4000

The induced torque of the motor is:

$$\tau_\text{ind} = \frac{P_\text{conv}}{\omega_m}$$



In [6]:

    
Tind = Pconv/(2*pi/60 * n_m)
Tind # [Nm]









    Out[6]:





132.6291

Alternately, the induced torque can be found as:

$$\tau_\text{ind} = \frac{P_\text{AG}}{\omega_\text{sync}}$$



In [7]:

    
Tind = Pag/(2*pi/60 * n_sync)
Tind # [Nm]









    Out[7]:





132.6291

(c)

The output power of this motor is:

$$ P_\text{out} = P_\text{conv} -P_\text{mech} $$



In [8]:

    
Pout = Pconv-Pm
Pout # [W]









    Out[8]:





22900.0000

And the output torque:

$$\tau_\text{out} = \frac{P_\text{out}}{\omega_m}$$



In [9]:

    
Tout = Pout / (2*pi/60 * n_m)
Tout









    Out[9]:





130.9141