Page 178 - Solutions Manual to accompany Electric Machinery Fundamentals

x1 = 0.852; % Stator reactance
r2 = 0.154; % Rotor resistance
x2 = 1.066; % Rotor reactance
xm = 20; % Magnetization bran ch reactance
v_phase = 460 / sqrt(3); % Phase voltage
n_sync = 1800; % Synchronous speed (r/min)
w_sync = 188.5; % Synchronous spe ed (rad/s)
p_mech = 400; % Mechanical losses (W)
p_core = 400; % Core losses (W)
p_misc = 150; % Miscellaneous losses (W )

% Calculate the Thevenin voltage and impedance from Equa tions
% 6-41a and 6-43.
v_th = v_phase * ( xm / sqrt(r1^2 + (x1 + xm)^2) );
z_th = ((j*xm) * (r 1 + 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 0.1. Note that the first slip value
% is set to 0.001 instead of exactly 0 to avoid divide-
% by-zero problems.
s = (0:0.001:0.1); % Slip
s(1) = 0.001;
nm = (1 - s) * n_sync; % Mechan ical speed
wm = nm * 2*pi/ 60; % Mechanical speed

% Calculate torque, P_conv, P_out, and efficiency
% versus speed
for ii = 1:length(s)

% Induced torque
t_ind(ii) = (3 * v_th^2 * r2 / s(ii)) / ...
(w_sync * ((r_th + r2/s(ii))^2 + (x_th + x2)^2) );

% Power converted
p_conv(ii) = t_ind(ii) * wm(ii);

% Power output
p_ out(ii) = p_conv(ii) - p_mech - p_core - p_misc;

% Power input
zf = 1 / ( 1/(j*xm) + 1/(r2/s(ii)+j*x2) );
ia = v_phase / ( r1 + j*x1 + zf );
p_in(ii) = 3 * v_phase * abs(ia) * cos(atan( imag(ia)/real(ia)));

% Efficiency
ef f(ii) = p_out(ii) / p_in(ii) * 100;

end

% Plo t the torque-speed curve
fi gure(1);
plot(nm,t_ind,'b-','LineWidth', 2.0);
xlabel('\bf\ itn_{m} \rm\bf(r/min)');
ylabel('\bf\tau_{ind} \rm\bf(N-m)');
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