Page 201 - Solutions Manual to accompany Electric Machinery Fundamentals


 I  I 381.7  82.4 A
L A
The starting kVA of the motor is

S start  3V  A  I   3 266 V 381.7 A   304.6 kVA
The locked rotor kVA/hp is

304.6 kVA
kVA/hp   4.06
75 hp

Therefore this motor is Starting Code Letter D.
6-29. Plot the torque-speed characteristic of the motor in Problem 6-28. What is the starting torque of this
motor?
SOLUTION A MATLAB program to calculate the torque-speed characteristic of this motor is shown below:

% M-file: prob6_29.m
% M-file create a plot of the torque-speed curve of the
% induction motor of Problem 6-28.

% First, initialize the values needed in this program.
r1 = 0.058; % Stator resistance
x1 = 0.320; % Stator reactance
r2 = 0.037; % Rotor resistance
x2 = 0.386; % Rotor reactance
xm = 9.24; % Magnetization branch reactance
v_phase = 460 / 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 = (0:0.05:50) / 50; % Slip
s(1) = 0.001;
nm = (1 - s) * n_sync; % Mechanical speed

% Calculate torque versus speed
for ii = 1:length(s)
t_ind(ii) = (3 * v_th^2 * r2 / s(ii)) / ...
(w_sync * ((r_th + r2/s(ii))^2 + (x_th + x2)^2) );
end

% Plot the torque-speed curve
figure(1);
plot(nm,t_ind,'b-','LineWidth',2.0);
xlabel('\bf\itn_{m}');

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