Page 183 - Solutions Manual to accompany Electric Machinery Fundamentals

I A
R 1 jX 1 jX 2 R 2

+ 0.105 ? j0.211 ? j0.317 ? 0.071 ? I 2

 1  s
j4.789 ? jX M R  
V ? 2  s 

-

A MATLAB program to calculate the torque-speed characteristic of this motor is shown below:

% M-file: prob6_20.m
% M-file create a plot of the torque-speed curve of the
% induction motor of Problem 6-20.

% First, initialize the values needed in this program.
r1 = 0.105; % Stator resistance
x1 = 0.211; % Stator reactance
r2 = 0.071; % Rotor resistance
x2 = 0.317; % Rotor reactance
xm = 4.789; % Magnetization branch reactance
v_phase = 208 / sqrt(3); % Phase voltage
n_sync = 1200; % Synchronous speed (r/min)
w_sync = 125.7; % Synchronous speed (rad/s)

% Calculate the Thevenin voltage and impedance from Equations
% 6-41a and 6-43.
v_th = v_phase * ( xm / sqrt(r1^2 + (x1 + xm)^2) );
z_th = ((j*xm) * (r1 + j*x1)) / (r1 + j*(x1 + xm));
r_th = real(z_th);
x_th = imag(z_th);

% Now calculate the torque-speed characteristic for many
% slips between 0 and 1. Note that the first slip value
% is set to 0.001 instead of exactly 0 to avoid divide-
% by-zero problems.
s = (0:1:50) / 50; % Slip
s(1) = 0.001;
nm = (1 - s) * n_sync; % Mechanical speed

% Calculate torque versus speed
for ii = 1:51
t_ind(ii) = (3 * v_th^2 * r2 / s(ii)) / ...
(w_sync * ((r_th + r2/s(ii))^2 + (x_th + x2)^2) );
end

% Plot the torque-speed curve
figure(1);
plot(nm,t_ind,'b-','LineWidth',2.0);
xlabel('\bf\itn_{m}');
ylabel('\bf\tau_{ind}');
title ('\bfInduction Motor Torque-Speed Characteristic');

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