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 (Torquem (Tm)) is proportional to cube of the speed: Tm = (1.3×10^ -5 )*wm^3 where wm 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?

Answer #1

**MATLAB 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:**

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 Ω; r2=0.6258 Ω; 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.
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