Question

Problem 3 A three-phase, 230-V, 60-Hz, 12-kW, four-pole wound-rotor induction motor has the following parameters expressed in Ω/phase. R 0.095; 0.680; Xs 0.672; Xm 18.7. Using MATLAB, plot the electromagnetic torque as a function of rotor speed in rot/min for rotor resistances of R -0.1, 0.2,0.5, 1.0 and 1.5 .

Answer 1

The following code is used to get the desired characteristics.

% First, initializing the values needed in the program.

Rs = 0.095; % Stator resistance

Xs = 0.680; % Stator reactance

Xr = 0.672; % Rotor reactance

Xm = 18.7; % Magnetization branch reactance

v_phase = 230 / sqrt(3); % Phase voltage

N_sync = 1800; % Synchronous speed (r/min)

w_sync = 188.5; % Synchronous speed (rad/s)

% Calculate the Thevenin voltage and impedance from Equations

V_th = v_phase * ( Xm / sqrt(Rs^2 + (Xs+ Xm)^2) );

Z_th = ((j*Xm) * (Rs+ j*Xs)) / (Rs+ j*(Xs+ 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
  
Rr = 0.1;

% Calculating torque

for ii = 1:51

t_ind(ii) = (3 * V_th^2 * Rr/ s(ii)) / (w_sync * ((R_th + Rr/s(ii))^2 + (X_th + Xr)^2) );

end

% Plot the torque-speed curve for R2=0.1

plot(nm,t_ind);

hold on;

Rr = 0.2;

% Calculating torque

for ii = 1:51

t_ind(ii) = (3 * V_th^2 * Rr/ s(ii)) / (w_sync * ((R_th + Rr/s(ii))^2 + (X_th + Xr)^2) );

end

% Plot the torque-speed curve for R2=0.2

plot(nm,t_ind);

Rr = 0.5;

% Calculating torque

for ii = 1:51

t_ind(ii) = (3 * V_th^2 * Rr/ s(ii)) / (w_sync * ((R_th + Rr/s(ii))^2 + (X_th + Xr)^2) );

end

% Plot the torque-speed curve for R2=0.5

plot(nm,t_ind);

Rr = 1;

% Calculating torque

for ii = 1:51

t_ind(ii) = (3 * V_th^2 * Rr/ s(ii)) / (w_sync * ((R_th + Rr/s(ii))^2 + (X_th + Xr)^2) );

end

% Plot the torque-speed curve for R2=1

plot(nm,t_ind);

Rr = 1.5;

% Calculating torque

for ii = 1:51

t_ind(ii) = (3 * V_th^2 * Rr/ s(ii)) / (w_sync * ((R_th + Rr/s(ii))^2 + (X_th + Xr)^2) );

end

% Plot the torque-speed curve for R2=1.5

plot(nm,t_ind);

xlabel('N_m(RPM)','Fontweight','Bold');

ylabel('\tau_{ind}(Nm)','Fontweight','Bold');

title ('Induction Motor Torque-Speed Characteristic','Fontweight','Bold');

legend ('R2=0.1','R2=0.2','R2=0.5','R2=1','R2=1.5');

grid on;

hold off;

By executing the above code in MATLAB we get following plot.

100 Induction Motor Torque-Speed Characteristic R2-0.1 R2-0.5 ーR2-1.5 90 -R2-0.2 80 70 60 弖50 30 20 10 200 600 800 1000 1400 1600 1800 N(RPM)