Question 6.4: A three-phase, 230-V, 60-Hz, 12-kW, four-pole wound-rotor in......
A three-phase, 230-V, 60-Hz, 12-kW, four-pole wound-rotor induction motor has the following parameters expressed in Ω/phase.
R_1=0.095 \quad X_1=0.680 \quad X_2=0.672 \quad X_m=18.7
Using MATLAB,^† plot the electromechanical mechanical torque T_{mech} as a function of rotor speed in r/min for rotor resistances of R_2 = 0.1, 0.2, 0.5, 1.0 \text{and} 1.5 Ω.
The desired plot is shown in Fig. 6.17.
Here is the MATLAB script:
Script File
clc
clear
%Here are the motor parameters
V1 = 230/sqrt(3) ;
nph = 3 ;
poles = 4 ;
fe = 60 ;
R1 = 0.095;
X1 = 0. 680;
X2 = 0.672;
Xm = 18.7;
%Calculate the synchronous speed
omegas = 4 * pi * fe/poles;
ns = 120 * fe/poles;
%Calculate stator Thevenin equivalent
Z1eq = j * Xm * (R1 + j * X1)/(R1 + j * (X1 + Xm)) ;
R1eq = real(Z1eq) ;
X1eq = imag(Z1eq) ;
V1eq = abs(V1 * j * Xm/ (R1 + j * (X1 + Xm))) ;
%Here is the loop over rotor resistance
for m = 1 : 5
if m == 1
R2 = 0.1;
elseif m == 2
R2 = 0.2;
elseif m == 3
R2 = 0.5 ;
elseif m == 4
R2 = 1.0 ;
else
R2 = 1.5 ;
end
%Here is the loop over slip
for n = 1 : 200
s(n) = n/200 ; %slip
rpm(n) = ns * (1 - s(n)) ; %rpm
I2 = abs(V1eq/ (Z1eq + j * X2 + R2/s(n))) ; %I2
Tmech(n) = nph * I2^2 * R2/(s(n) * omegas); %Electromechanical torque
end %End of slip loop
%Now plot
plot (rpm, Tmech)
if m == 1
hold
end
end %End of resistance loop
hold
xlabel ( ' rpm' )
ylabel ('Tmech')
