Question

Problem A 460-V, four-pole, 60-Hz, Y components R,-0.15 Ω Xi=0.852 Ω X2 = 1.066 Ω Pmech 400 w -connected induction motor has the following equivalent circuit R2 0.154 Ω Pmise 150 Pcore 400 w Write MATLAB script to plot on two separate figures: a) b) the torque versus speed of the motor. the converted power versus speed of the motor

Answer 1

--------The code to plot is as follows-----------------------------------------

% M-file create a plot of the torque-speed curve and power speed curve of the
% induction motor
% First, initialize the values needed in this program.
r1 = 0.15; % Stator resistance
x1 = 0.852; % Stator reactance
r2 = 0.154; % Rotor resistance
x2 = 1,066; % Rotor reactance
xm = 20; % Magnetization branch reactance
f=60; %frequency of the supply given to machine
P=4; % no of poles of machine
v_phase = 460 / sqrt(3); % Phase voltage
n_sync = 120*f/P; % Synchronous speed (r/min)
w_sync = 2*pi*n_sync/60; % Synchronous speed (rad/s)
% Calculate the Thevenin voltage and impedance from Equations
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 of rotor in rpm
w_nm = 2*pi*n_sync/60; % Mechanical speed of rotor in rad/s
% Calculate torque
for ii = 1:51
t_ind1(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

plot(nm,t_ind1,'Color','k','LineWidth',2.0);

xlabel('\itn_{m}','Fontweight','Bold');
ylabel('\tau_{ind}','Fontweight','Bold');
title ('Induction Motor Torque-Speed Characteristic','Fontweight','Bold');
%Calculate power at different speeds
p_conv= t_ind1.*w_nm + 400+400 +150;
% Plot the power-speed curve
figure() % to bring the plot in a seperate figure without overwriting the previous figure
plot(nm,p_conv,'Color','k','LineWidth',2.0);
xlabel('\itn_{m}','Fontweight','Bold');
ylabel('p_conv','Fontweight','Bold');
title ('Induction Motor Power-Speed Characteristic','Fontweight','Bold');

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the outputs obtained are

Induction Motor Torque-Speed Characteristic 300 250 200 드 150 ド 100 50 0 200 400 600 800 1000 1200 1400 1600 1800

x 104 6 Induction Motor Power-Speed Characteristic 4 2 0 200 400 600 800 1000 1200 1400 1600 1800