Page 206 - Solutions Manual to accompany Electric Machinery Fundamentals

% 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 = (0:0.1:50) / 50; % Slip
s(1) = 0.001;
nm = (1 - s) * n_sync; % Mechanical speed

% Calculate torque for the single-cage rotor.
for ii = 1: length(s)
t_ind1(ii) = (3 * v_ th^2 * r2 / s(ii)) / ...
(w_sync * ((r_th + r2/s(ii))^2 + (x_t h + x2)^2) );
end

% Calculate resistance and reactance of the double-cage
% rotor at this slip, and then use those values to
% calculate the induced torque.
for ii = 1: length(s)
y_r = 1/(r2a + j*s(i i)*x2a) + 1/(r2b + j*s(ii)*x2b);
z_r = 1/y_r; % Effective rotor impedance
r2eff = real(z_r); % Effective rotor resistance
x2eff = imag(z_r); % Effective rotor reactance

% Convert the reactace back t Xo, the reactance at
% synchronous speed.
x2eff = x2eff/s(ii); % Effective rotor reactance

% Calculate induced torque for double-cage rotor.
t_ind2(ii) = (3 * v_th^2 * r2eff / s(ii)) / ...
(w_sync * ((r_th + r2eff/s(ii))^2 + (x_t h + x2eff)^2) );
end

% Plot the torque-speed curve
figure(1);
% Plot the t orque-speed curves
plot(nm,t_ind1,'b-','LineWidth', 2.0);
hold on;
plot(nm,t_ ind2,'k-.','LineWidth',2.0);
xlabel('\bf\itn_{m}');
ylabel('\bf\tau_{ind}');
title ('\bfInduction Motor Torque-Speed Characteristic');
legend ('Single-cage design','Double-cage design');
grid on;
hold off;

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