Electric Machinery Fundamentals 5th edition

Chapter 2 (Code examples)

Example 2-5

Calculate and plot the voltage regulation of a transformer as a function of load for power factors of 0.8 lagging, 1.0, and 0.8 leading.

Import the PyLab namespace (provides set of useful commands and constants like Pi)



In [1]:

    
%pylab notebook









    



Populating the interactive namespace from numpy and matplotlib

Define all the parameters:



In [2]:

    
VS = 230.0                   # Secondary voltage (V)
amps = arange(0, 65.2, 6.52) # Current values (A)
Req = 0.0445                 # Equivalent R (ohms)
Xeq = 0.0645                 # Equivalent X (ohms)

Calculate the current values for the three power factors. The first row of I contains the lagging currents, the second row contains the unity currents, and the third row contains the leading currents.



In [3]:

    
I = amps * array ([[0.8 - 0.6j],   # Lagging
                   [1.0],          # Unity
                   [0.8 + 0.6j]])  # Leading

Calculate VP/a:



In [4]:

    
VPa = VS + Req * I + 1j * Xeq * I

Calculate voltage regulation:



In [5]:

    
VR = (abs(VPa) - VS) / VS * 100;

Plot the voltage regulation:



In [6]:

    
rc('text', usetex=True)   # enable LaTeX commands for plot
plot(amps,VR[0,])
plot(amps,VR[1,])
plot(amps,VR[2,])
title(r'\textbf{Voltage Regulation Versus Load}');
xlabel(r'\textbf{Load (A)}');
ylabel(r'\textbf{Voltage Regulation (\%)}');
legend(('0.8 PF lagging','1.0 PF','0.8 PF leading'), loc=2);
grid()