Page 286 - Solutions Manual to accompany Electric Machinery Fundamentals

P  1 s P   1 0.778 978.3 W  217.2 W
conv,F AG,F
P    1 s P   1  0.778 623.8 W  138.5 W
conv,B AG,B

P  P  P  217.2 W 138.5 W  78.7 W
conv conv,F conv,B
The output power is


P OUT  P conv  P  rot 78.7 W 51 W  27.7 W
The induced torque is

P 354.5 W
 ind  AG   1.88 N m


sync  1800 r/min   2 rad      1 min  
 1 r   60 s 
Assuming that the rotational losses are still 51 W, this motor will still be able to speed up because P conv is
78.7 W, while the rotational losses are 51 W, so there is more power than it required to cover the
rotational losses. The motor will continue to speed up.
9-4. Use MATLAB to calculate and plot the torque-speed characteristic of the motor in Problem 9-1, ignoring
the starting winding.
SOLUTION This problem is best solved with MATLAB, since it involves calculating the torque-speed
values at many points. A MATLAB program to calculate and display both torque-speed characteristics is
shown below. Note that this program shows the torque-speed curve for both positive and negative
directions of rotation. Also, note that we had to avoid calculating the slip at exactly 0 or 2, since those
numbers would produce divide-by-zero errors in Z and Z respectively.
B
F

% M-file: prob9_4.m
% M-file create a plot of the torque-speed curve of the
% single-phase induction motor of Problem 9-4.

% First, initialize the values needed in this program.
r1 = 2.00; % Stator resistance
x1 = 2.56; % Stator reactance
r2 = 2.80; % Rotor resistance
x2 = 2.56; % Rotor reactance
xm = 60.5 % Magnetization branch reactance
v = 120; % Single-Phase voltage
n_sync = 1800; % Synchronous speed (r/min)
w_sync = 188.5; % Synchronous speed (rad/s)

% Specify slip ranges to plot
s = 0:0.01:2.0;

% Offset slips at 0 and 2 slightly to avoid divide by zero errors
s(1) = 0.0001;
s(201) = 1.9999;

% Get the corresponding speeds in rpm
nm = ( 1 - s) * n_sync;

% Caclulate Zf and Zb as a function of slip
zf = (r2 ./ s + j*x2) * (j*xm) ./ (r2 ./ s + j*x2 + j*xm);
zb = (r2 ./(2-s) + j*x2) * (j*xm) ./ (r2 ./(2-s) + j*x2 + j*xm);

% Calculate the current flowing at each slip
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