Question

Problem A 460-V, four-pole, 60-Hz, Y-connected induction motor has the following equivalent components R,-0.15Ω R,-0.154 Ω X2-1.066 Ω M.-20 Ω Xi-0.852 Ω /mech-400 W Pmise 150 Pcore 400 W Write MATLAB script to plot on two separate figures: a) the torque versus speed of the motor. b) the converted power versus speed of the motor.

Answer 1

Matlab Code:

clc
clear all
p=4; %no of poles
j=sqrt(-1);
f=60; %frequency
r1=0.15; %stator resistance
r2=0.154; %rotor resistance
x1=0.852; %stator reactance
x2=1.066; %rotor reactance
xm=20; %magnetizing branch reactance
v_phase= 460/sqrt(3); %phase voltage
Pmech= 400; %Mechnical losses
Pmisc= 150; % Misc losses
Pcore=400; % core losses
n_sync= (120*f)/p; %synchronous speed
w_sync= (2*pi*n_sync)/60;   
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)
s= (0:0.001:0.1);
s(1)=0.001;
nm=(1-s)*n_sync;
wm= nm*2*pi/60;
for ii=1:length(s)
% Induction torque
t_ind(ii) = (3 * v_th^2 * r2 / s(ii)) /(w_sync *((r_th + r2/s(ii))^2 + (x_th + x2)^2) );
% Converter power
p_conv(ii) = t_ind(ii) * wm(ii);
end

% Plot the torque-speed curve
figure(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)');
title ('\bfInduced Torque versus Speed');
grid on;

% Plot power converted versus speed
figure(2);
plot(nm,p_conv/1000,'b-','LineWidth',2.0);
xlabel('\bf\itn_{m} \rm\bf(r/min)');
ylabel('\bf\itP\rm\bf_{conv} (kW)');
title ('\bfPower Converted versus Speed');
grid on;

Matlab Output:
Induced Torque versus Speed 300 250 200 150ト 100 50 0 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 n (rlmin)

Power Converted versus Speed 45 40 35 30 S 25 a 20 15 10 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 m (r/min)