# A460-V. 30-hp. 60-Hz. four-pole. Star-connected induction motor has two possible rotor designs. a single-cage rotor and a double-cage rotor. (The stator is identical for either rotor design.) The motor with the single-cage rotor may be modeled by the following impedances in ohms per phase referred to the stator circuit: R1= 0.641 Ω X1 = 0.750 Ω R2 = 0.3 Ω X2 = 0.5 Ω Xm= 26.3 Ω The motor with the double-cage rotor may be modeled as a tightly coupled. High resistance outer cage in parallel with a loosely coupled. Low resistance inner cage The stator and magnetization resistance and reactances will be identical with those in the single-cage design. The resistance and reactance of the rotor outer cage are: R2o, = 3.2 Ω X2o, = 0.5 Ω The resistance and reactance of the inner cage are R2i = 0.4 Ω X2i = 3.3 Ω Write a MATLAB script to calculate and plot the two torque-speed characteristics with the two rotor designs. How do they compare?

A460-V. 30-hp. 60-Hz. four-pole. Star-connected induction motor has two possible rotor designs. a single-cage rotor and a double-cage rotor. (The stator is identical for either rotor design.) The motor with the single-cage rotor may be modeled by the following impedances in ohms per phase referred to the stator circuit:

R1= 0.641 Ω X1 = 0.750 Ω R2 = 0.3 Ω X2 = 0.5 Ω Xm= 26.3 Ω

The motor with the double-cage rotor may be modeled as a tightly coupled. High resistance outer cage in parallel with a loosely coupled. Low resistance inner cage The stator and magnetization resistance and reactances will be identical with those in the single-cage design. The resistance and reactance of the rotor outer cage are:

R2o, = 3.2 Ω X2o, = 0.5 Ω The resistance and reactance of the inner cage are R2i = 0.4 Ω X2i = 3.3 Ω

Write a MATLAB script to calculate and plot the two torque-speed characteristics with the two rotor designs. How do they compare?

r1 = 0.641; % Stator resistance

x1 = 0.750; % Stator reactance

r2 = 0.300; % Rotor resistance for single-

% cage motor

r2i = 0.400; % Rotor resistance for inner

% cage of double-cage motor

r2o = 3.200; % Rotor resistance for outer

% cage of double-cage motor

x2 = 0.500; % Rotor reactance for single-

% cage motor

x2i = 3.300; % Rotor reactance for inner

% cage of double-cage motor

x2o = 0.500; % Rotor reactance for outer

% cage of double-cage motor

xm = 26.3; % Magnetization branch reactance

v_phase = 460 / sqrt(3); % Phase voltage

n_sync = 1800; % Synchronous speed (r/min)

w_sync = 188.5; % Synchronous speed (rad/s)

% Calculate the Thevenin voltage and impedance from Equations

% 7-41a and 7-43.

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 motor speed 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; % Avoid division-by-zero

nm = (1 - s) * n_sync; % Mechanical speed

% Calculate torque for the single-cage rotor.

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

% Calculate resistance and reactance of the double-cage

% rotor at this slip, and then use those values to

% calculate the induced torque.

for ii = 1:51

y_r = 1/(r2i + j*s(ii)*x2i) + 1/(r2o + j*s(ii)*x2o);

z_r = 1/y_r; % Effective rotor impedance

r2eff = real(z_r); % Effective rotor resistance

x2eff = imag(z_r); % Effective rotor reactance

% Calculate induced torque for double-cage rotor.

t_ind2(ii) = (3 * v_th^2 * r2eff / s(ii)) / ...

(w_sync * ((r_th + r2eff/s(ii))^2 + (x_th + x2eff)^2) );

end

% Plot the torque–speed curves

% Plot the torque–speed curves

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

hold on;

plot(nm,t_ind2,'Color','k','LineWidth',2.0,'LineStyle','-.');

xlabel('\itn_{m}','Fontweight','Bold');

ylabel('\tau_{ind}','Fontweight','Bold');

title ('Induction motor torque–speed characteristics', ...

'Fontweight','Bold');

legend ('Single-Cage Design','Double-Cage Design');

grid on;

hold off;