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The document outlines calculations for a motor's rotor side impedance, combined referred rotor impedance, line current, stator copper losses, air gap power, power conversion, induced torque, load torque, overall efficiency, and motor speed. It provides detailed formulas and results for each calculation, including values for electrical and mechanical power, torque, and efficiency. The calculations are based on given parameters such as resistance, reactance, voltage, and slip.

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Ibrahim Hussain
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52 views2 pages

Q1

The document outlines calculations for a motor's rotor side impedance, combined referred rotor impedance, line current, stator copper losses, air gap power, power conversion, induced torque, load torque, overall efficiency, and motor speed. It provides detailed formulas and results for each calculation, including values for electrical and mechanical power, torque, and efficiency. The calculations are based on given parameters such as resistance, reactance, voltage, and slip.

Uploaded by

Ibrahim Hussain
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as TXT, PDF, TXT or read online on Scribd
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% Initialize all the values

r1 = 0.40;
r2 = 0.25;
x1 = 0.85;
x2 = 0.85;
xm = 25;
P_rot = 300;
V = 415;
V_phase = 415/sqrt(3);
slip = 0.08;
toD = 180/pi;

% Calculate the rotor side impedance


Za = r2 + x2*j + r2*( (1/slip) - 1 );
str = ['disp: Za = ' num2str(Za)];
disp(str);
fprintf('Za = %0.4f + j %0.4f\n', real(Za), imag(Za));
fprintf('Za = %0.4f cis %0.2f (in degree)\n\n', abs(Za), angle(Za)*toD);

% Calculate the combined referred rotor impedance with the magnetization


% branch
Zb = (Za*xm*j) / (Za+xm*j);
str = ['disp: Zb = ' num2str(Zb)];
disp(str);
fprintf('Zb = %0.4f + j %0.4f\n', real(Zb), imag(Zb));
fprintf('Zb = %0.4f cis %0.2f (in degree)\n\n', abs(Zb), angle(Zb)*toD);

% a) Calculate the line current


I_line = V_phase / (Zb + r1 + x1*j);
str = ['disp: line current = ' num2str(I_line)];
disp(str);
fprintf('a) line current = (%0.4f + j %0.4f) A\n', real(I_line), imag(I_line));
fprintf(' line current = (%0.4f cis %0.2f (in degree)) A\n\n', abs(I_line),
angle(I_line)*toD);

% b) Calculate the stator copper losses


P_scl = 3 * ( abs(I_line)^2 ) * r1;
fprintf('b) Stator copper losses = %0.4f w\n\n', P_scl);

% c) Calculate the air gap power


t = angle(I_line);
P_in = sqrt(3) * V * abs(I_line) * cos(t);
P_ag = P_in-P_scl;
fprintf('c) Air gap power = %0.4f kW\n\n', P_ag/1000);

% d) Calculate the power converted from electrical to mechanical form


P_conv = ( (1-slip) * P_ag );
fprintf('d) Power converted = %0.4f kW\n\n', P_conv/1000);

% e) Calculate the induced torque


f = 50;
p = 4;
ssrpm = (120*f)/p;
ssrps = ssrpm * ( (2*pi)/60 );
T_ind = P_ag/ssrps;
fprintf('e) Torque induced = %0.4f Nm\n\n', T_ind);

% f) Calculate the load torque


mssrpm = (1-slip) * ssrpm;
mssrps = mssrpm * ( (2*pi)/60 );
P_out = P_conv - P_rot;
T_load = P_out/mssrps;
fprintf('f) Load torque = %0.4f Nm\n\n', T_load);

% g) Calculate the overall efficiency


E = (P_out/P_in)*100;
fprintf('g) Overall efficiency = %0.0f percent\n\n', E);

% h) Calculate the motor speed

% in rpm
fprintf('h) motor speed in revolutions per minutes = %0.0f rpm\n\n', mssrpm);

% in rad/s
fprintf(' motor speed in radians per second = %0.2f rad/s\n\n', mssrps);

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