Page 163 - Solutions Manual to accompany Electric Machinery Fundamentals

jX  10 j  


V  M V     120 0 V  117.5 0.6 V
TH 
R  1  1 X M  j X  0.1   j   10   0.23 
The slip at pullout torque is
R
s max  2
R 2    X  X 2
TH TH 2
0.070 
s max   0.164
 0.0959  2   0.2066  0.210    2

The pullout torque of the motor is
3V 2
 max  TH
  sync    R TH R TH   TH  X 2  X 2 
2


  3 117.5 V 2
 max 
  188.5 rad/s 0.0959        0.0959  2   0.2066    0.210  2   


 max  210 N m
6-7. (a) Calculate and plot the torque-speed characteristic of the motor in Problem 6-5. (b) Calculate and plot
the output power versus speed curve of the motor in Problem 6-5.
SOLUTION
(a) A MATLAB program to calculate the torque-speed characteristic is shown below.

% M-file: prob6_7a.m
% M-file create a plot of the torque-speed curve of the
% induction motor of Problem 6-5.

% First, initialize the values needed in this program.
r1 = 0.100; % Stator resistance
x1 = 0.210; % Stator reactance
r2 = 0.070; % Rotor resistance
x2 = 0.210; % Rotor reactance
xm = 10.0; % Magnetization branch reactance
v_phase = 208 / 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
% 6-41a and 6-43.
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 torque-speed characteristic 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;

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