Electric Machinery Fundamentals 5th edition

Chapter 4 (Code examples)

Example 4-4

Plot the terminal characteristics of the generator of Example 4-3 with a 0.8 PF leading and lagging load.

Import the PyLab namespace (provides set of useful commands and constants like Pi) and reduce the displayed precision to four digits.



In [1]:

    
%pylab notebook
%precision 4









    



Populating the interactive namespace from numpy and matplotlib

First, initialize the current amplitudes (21 values in the range 0-60 A):



In [2]:

    
i_a = linspace(0, 60, 21)   # syntax: linspace(start, end, NumberOfValues)

Now initialize all other values:



In [3]:

    
#v_phase = zeros(1,21);
e_a = 277.0   # armature voltage
x_s = 1.0     # sychronous reactance
PF=0.8        # power factor



In [4]:

    
theta_rad = arccos(PF)                        # in radians
theta_lead = degrees(theta_rad)               # angle for leading power factor
theta_lagg = - degrees(theta_rad)             # angle for lagging power factor
theta = radians([[theta_lead], [theta_lagg]]) # combine both angles in an array
theta # let's see what it looks like









    Out[4]:





array([[ 0.6435],
       [-0.6435]])



In [5]:

    
theta_lead   # let's see what the angles look like









    Out[5]:





36.8699



In [6]:

    
theta_lagg   # let's see what the angles look like









    Out[6]:





-36.8699

Now calculate v_phase for each current level using: $$E_A^2 = (V_\phi - X_S I_A \sin(\theta))^2 + (X_S I_A \cos(\theta))^2$$ which can be solved for the phase voltage: $$ V_\phi = \sqrt{E_A^2 - (X_S I_A \cos(\theta))^2} + X_S I_A \sin(\theta)$$



In [7]:

    
v_phase = sqrt(e_a**2 -(x_s * i_a * cos(theta))**2) + (x_s * i_a * sin(theta))

Calculate terminal voltage from the phase voltage:



In [8]:

    
v_t = v_phase * sqrt(3)

Plot the terminal characteristic, remembering that the line current is the same as i_a:



In [9]:

    
plot(i_a, v_t[0], i_a, v_t[1], lw=2)  # ATTENTION! Python starts array count at 0
xlabel('Line Current (A)')
ylabel('Terminal voltage (V)')
title ('Terminal characteristic for 0.8 PF lagging and leading load')
legend(('$PF = 0.8$ leading', '$PF = 0.8$ lagging'), loc=7) # loc=7 stands for centre right
grid()