Ain Shams University ,Faculty of Engineering
Electrical power & Machines Department
Electrical Drive Systems (EPM451s)
ASSIGNMENT “2”
STUDENT NAME:
STUDENT ID:
SECTION:
SUBMITTED TO: PROF. DR. MOSTAFA MAREI
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Ain Shams University ,Faculty of Engineering
Electrical power & Machines Department
Electrical Drive Systems (EPM451s)
1- Rotor resistance control using DC chopper:
Speed control by means of slip variation can be achieved by employing a variable
resistance Chopper
Resistance in the Rotor
Circuit. From the equations
the maximum value of
torque does not depend
upon the value of rotor
resistance. However, the
rotor resistance influences
the slip at which maximum
torque occurs. A family of
curves has been depicted in
Fig. 4.9 for variable
resistance in the rotor circuit.
For given load conditions the
speed can be varied. The slip
of the motor at any given value
of rotor resistance is given by:
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Ain Shams University ,Faculty of Engineering
Electrical power & Machines Department
Electrical Drive Systems (EPM451s)
MATLAB CODE:
clear; clc;
%motor parameters
Vs = 460/sqrt(3);
ws = 120*60/4;
ws_rad = 2*pi*ws/60;
Rr = 0.23;
wm = 0:1:ws;
slip = ((ws - wm) / ws);
slip_square = slip.^2;
% Initialize torque values
Td = zeros;
% Plot torque for different resistances
resistances = 0.1:0.1:0.4;
%resistance is effective resistance = (1dutyCycle)*R_external
figure;
legend_labels = cell(1, length(resistances));
for j = 1:length(resistances)
for i = 1:length(wm)
Td(i, j) = (3 * (Rr + resistances(j)) * Vs^2) / (slip(i) * ws_rad *
(((Rr + resistances(j))^2 / slip_square(i)) + 0.64));
end
plot(fliplr(slip), Td(:, j));
hold on;
legend_labels{j} = sprintf('R=%.1f', resistances(j));
end
hold off;
% Labels, title, legend
xlabel('Slip');
ylabel('Torque');
title('Torque vs Slip');
legend(legend_labels);
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Ain Shams University ,Faculty of Engineering
Electrical power & Machines Department
Electrical Drive Systems (EPM451s)
SCREENSHOTS:
4|Page
Ain Shams University ,Faculty of Engineering
Electrical power & Machines Department
Electrical Drive Systems (EPM451s)
2- Stator current control
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Ain Shams University ,Faculty of Engineering
Electrical power & Machines Department
Electrical Drive Systems (EPM451s)
MATLAB CODE:
clear; clc;
%motor parameters
ws = 120*60/4;
wm = 0:0.5:ws;
Xm = 43.5;
Xr = 1.94;
Rr = 0.69;
Rs = 1.01;
R = Rr + Rs;
slip = ((ws - wm) / ws);
slip_squared = power(slip,2);
current_values = 20:20:100;
hold on;
% Plot torque for different currents
for c = current_values
Tq = zeros;
i = 1;
while i <= 2*ws+1
Tq(i) = (3 * R * (Xm * c)^2) / (slip(i) * ws * ((R * R) /
slip_squared(i) + (Xm + Xr)^2));
i = i + 1;
end
plot(fliplr(slip), Tq);
end
hold off;
xlabel('Slip');
ylabel('Torque');
legend('current = 20 A', 'current = 40 A', 'current = 60 A' ,'current = 80 A'
, 'current = 100 A');
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Ain Shams University ,Faculty of Engineering
Electrical power & Machines Department
Electrical Drive Systems (EPM451s)
SCREENSHOTS:
7|Page
Ain Shams University ,Faculty of Engineering
Electrical power & Machines Department
Electrical Drive Systems (EPM451s)
3- Sta c Kramer Drive (Bonus)
Defini on: The static Kramer-drive is the method of controlling the speed of an
induction motor by injecting the opposite-phase voltage in the rotor circuit. The
injected voltage increases the resistance of the rotor, thus controlled the speed of the
motor. By changing the injected voltage, the resistance and speed of an induction
motor are controlled.
The static Kramer-drive converts the slip power of an induction motor into AC power
and supply back to the line. The slip power is the air gap power between the stator and
the rotor of an induction motor which is not converted into mechanical power. Thus,
the power is getting wasted. The static Kramer drives fed back the wasted power into
the main supply. This method is only applicable when the speed of the drive is less
than the synchronous speed.
Static Kramer Drive Working
The rotor slip power is converted into DC by a diode bridge. This DC power is now
fed into DC motor which is mechanically coupled to an induction motor. The torque
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Ain Shams University ,Faculty of Engineering
Electrical power & Machines Department
Electrical Drive Systems (EPM451s)
supplied to the load is the total sum of the torque produced by the induction and DC
motor drive.
The figure shown below represents the variation of Vd1 and Vd2 with a speed of two
values of DC motor field current. When the value of Vd1 is equal to the value of
Vd2 then the steady state operation of the drive is obtained, i.e., at A and B for field
current of If1 and If2.
The speed control is possible only when speed is less or half of the synchronous
speed. When the large range speed is required, the diode bridge is replaced by the
thyristor bridge. The relationship between the Vd1 and the speed can be altered by
controlling the firing angle of thyristor amplifier. Speed can now be controlled up to
stand still.
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Ain Shams University ,Faculty of Engineering
Electrical power & Machines Department
Electrical Drive Systems (EPM451s)
MATLAB CODE:
clear; clc;
vs= 460/sqrt(3);
ws = 120 * 60 / 4;
% synchronous speed
wm = 0:1:6000;
% motor speed
Trated = 1000; %assumed;
nc = 1; % transformer turns ratio
nm = 1; % motor turns ratio
a = nc/nm;
Rr= 0.1;
alphas = [90,105, 120, 135]; % Values of alpha
hold on;
ylim([0 inf])
% Initialize Td array
Td = zeros(length(wm), length(alphas));
% Calculate torque for different alpha values
for j = 1:length(alphas)
alpha = alphas(j);
Td(:, j) = (((-(wm / ws)) + 1 + a*cosd(alpha)) /
((ws*Rr)/(2.339*a*vs^2)^2));
% Plot each torque curve
plot(sqrt(wm / ws), Td(:, j) / Trated);
end
hold off;
xlabel('sqrt(wm/ws)'); %because torque is proportional to the speed squared
ylabel('per unit Torque');
legend('alpha = 135','alpha = 120', 'alpha = 105', 'alpha = 90');
10 | P a g e
Ain Shams University ,Faculty of Engineering
Electrical power & Machines Department
Electrical Drive Systems (EPM451s)
SCREENSHOTS:
11 | P a g e