Page 82 - Solutions Manual to accompany Electric Machinery Fundamentals

3-7. Modify the MATLAB in Example 3-1 by swapping the currents flowing in any two phases. What
happens to the resulting net magnetic field?
SOLUTION This modification is very simple—just swap the currents supplied to two of the three phases.

% M-file: mag_field2.m
% M-file to calculate the net magetic field produced
% by a three-phase stator.

% Set up the basic conditions
bmax = 1; % Normalize bmax to 1
freq = 60; % 60 Hz
w = 2*pi*freq; % angluar velocity (rad/s)

% First, generate the three component magnetic fields
t = 0:1/6000:1/60;
Baa = sin(w*t) .* (cos(0) + j*sin(0));
Bbb = sin(w*t+2*pi/3) .* (cos(2*pi/3) + j*sin(2*pi/3));
Bcc = sin(w*t-2*pi/3) .* (cos(-2*pi/3) + j*sin(-2*pi/3));

% Calculate Bnet
Bnet = Baa + Bbb + Bcc;

% Calculate a circle representing the expected maximum
% value of Bnet
circle = 1.5 * (cos(w*t) + j*sin(w*t));

% Plot the magnitude and direction of the resulting magnetic
% fields. Note that Baa is black, Bbb is blue, Bcc is
% magneta, and Bnet is red.
for ii = 1:length(t)

% Plot the reference circle
plot(circle,'k');
hold on;

% Plot the four magnetic fields
plot([0 real(Baa(ii))],[0 imag(Baa(ii))],'k','LineWidth',2);
plot([0 real(Bbb(ii))],[0 imag(Bbb(ii))],'b','LineWidth',2);
plot([0 real(Bcc(ii))],[0 imag(Bcc(ii))],'m','LineWidth',2);
plot([0 real(Bnet(ii))],[0 imag(Bnet(ii))],'r','LineWidth',3);
axis square;
axis([-2 2 -2 2]);
drawnow;
hold off;

end
When this program executes, the net magnetic field rotates clockwise, instead of counterclockwise.
3-8. If an ac machine has the rotor and stator magnetic fields shown in Figure P3-1, what is the direction of the
induced torque in the machine? Is the machine acting as a motor or generator?

76