Excercises Electric Machinery Fundamentals

Chapter 1 Problem 1-18



In [1]:

    
%pylab inline









    



Populating the interactive namespace from numpy and matplotlib

Description

Assume that the voltage applied to a load is $\vec{V} = 208\,V\angle -30^\circ$ and the current flowing through the load $\vec{I} = 2\,A\angle 20^\circ$.

(a)

Calculate the complex power $S$ consumed by this load.

(b)

Is this load inductive or capacitive?

(c)

Calculate the power factor of this load?

(d)

Calculate the reactive power consumed or supplied by this load.
Does the load consume reactive power from the source or supply it to the source?



In [2]:

    
V = 208.0 * exp(-1j*30/180*pi)  # [V]
I =   2.0 * exp( 1j*20/180*pi)  # [A]

SOLUTION

(a)

The complex power $S$ consumed by this load is:

$$ S = V\cdot I^* $$



In [3]:

    
S = V * conjugate(I)   # The complex conjugate of a complex number is
                       # obtained by changing the sign of its imaginary part.
S_angle = arctan(S.imag/S.real)    
print('S = {:.1f} VA ∠{:.1f}°'.format(*(abs(S), S_angle/pi*180)))
print('====================')









    



S = 416.0 VA ∠-50.0°
====================

(b)

This is a capacitive load.

(c)

The power factor of this load is leading and:



In [4]:

    
PF = cos(S_angle)  
print('PF = {:.3f} leading'.format(PF))
print('==================')









    



PF = 0.643 leading
==================

(d)

This load supplies reactive power to the source. The reactive power of the load is:

$$ Q = VI\sin\theta = S\sin\theta$$



In [5]:

    
Q = abs(S)*sin(S_angle)
print('Q = {:.1f} var'.format(Q))
print('==============')









    



Q = -318.7 var
==============