Question

The parameters of a 3-phase, 4-pole, 50 Hz, Y-connected, wound-rotor induction motor are listed below. These are the default values of the “Asynchronous Machine” model in MATLAB Simulink. r1=0.5968 ?; r2=0.6258 ?; L1=0.0003495 H; L2=0.005473 H; Lm=0.0354 H; Stator line voltage = 400 V rms. The motor for rotor speeds nm= 0 to 1500 rpm.

X1= 0.1097 ohm, X2= 1.719 ohm , Xm= 11.12 ohm, RTH = 0.5853 , XTH = 0.1395 and VTH = 230.82 V.

Suppose the motor is to rotate a fan for which the load torque is proportional to cube of the speed: ?m = (1.3×10^ -5 )*?m^3 where ?m is the fan speed in rad/s. Then use MATLAB to plot the torque-speed characteristic of the fan as the motor torque-speed characteristic. What would be the motor speed and torque?

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Answer 1

matlab script

Editable code:
r1 = 0.5968;
x1 = 0.1097;
r2 = 0.6258;
x2 = 1.719;
xm = 11.12;   
vph = 400 / sqrt(3);   
n = 1500;   
w = 157.07;
vth = vph * ( xm / sqrt(r1^2 + (x1 + xm)^2) );
zth = ((1i*xm) * (r1 +1i*x1)) / (r1 + 1i*(x1 + xm));
rth = real(zth);
xth = imag(zth);
s = (0:1:50) / 50;
s(1) = 0.001;
nm = (1 - s) * n;
for a = 1:51
t1(a) = (3 * vth^2 * r2 / s(a)) /(w * ((rth + r2/s(a))^2 + (xth + x2)^2) );
end
for a = 1:51
t2(a) = (3 * vth^2 * (2*r2) / s(a)) /(w * ((rth + (2*r2)/s(a))^2 + (xth + x2)^2) );
end
plot(nm,t1,'k','LineWidth',2.0);
hold on;
plot(nm,t2,'k','LineWidth',2.0);
xlabel('speed');
ylabel('torque');
title ('Torque-Speed Characteristic Induction Motor ');
legend ('Original R2','Doubled R');
grid on;
hold off;

output;