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Instructor’s Manual
to accompany
Chapman
Electric Machinery Fundamentals
Fourth Edition
Stephen J. Chapman
BAE SYSTEMS Australia
i
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Instructor’s Manual to accompany Electric Machinery Fundamentals, Fourth Edition
Copyright  2004 McGraw-Hill, Inc.
All rights reserved. Printed in the United States of America. No part of this book may be used or reproduced in
any manner whatsoever without written permission, with the following exception: homework solutions may be
copied for classroom use.
ISBN: ???
ii
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TABLE OF CONTENTS
CHAPTER 1:
INTRODUCTION TO MACHINERY PRINCIPLES
CHAPTER 2:
TRANSFORMERS
23
CHAPTER 3:
INTRODUCTION TO POWER ELECTRONICS
63
CHAPTER 4:
AC MACHINERY FUNDAMENTALS
103
CHAPTER 5:
SYNCHRONOUS GENERATORS
109
CHAPTER 6:
SYNCHRONOUS MOTORS
149
CHAPTER 7:
INDUCTION MOTORS
171
CHAPTER 8:
DC MACHINERY FUNDAMENTALS
204
CHAPTER 9:
DC MOTORS AND GENERATORS
214
CHAPTER 10:
SINGLE-PHASE AND SPECIAL-PURPOSE MOTORS
1
270
APPENDIX A: REVIEW OF THREE-PHASE CIRCUITS
280
APPENDIX B:
288
COIL PITCH AND DISTRIBUTED WINDINGS
APPENDIX C: SALIENT POLE THEORY OF SYNCHRONOUS MACHINES
295
APPENDIX D: ERRATA FOR ELECTRIC MACHINERY FUNDAMENTALS 4/E
301
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PREFACE
TO THE INSTRUCTOR
This Instructor’s Manual is intended to accompany the fourth edition of Electric Machinery Fundamentals. To
make this manual easier to use, it has been made self-contained. Both the original problem statement and the
problem solution are given for each problem in the book. This structure should make it easier to copy pages from
the manual for posting after problems have been assigned.
Many of the problems in Chapters 2, 5, 6, and 9 require that a student read one or more values from a
magnetization curve. The required curves are given within the textbook, but they are shown with relatively few
vertical and horizontal lines so that they will not appear too cluttered. Electronic copies of the corresponding opencircuit characteristics, short-circuit characteristics, and magnetization curves as also supplied with the book. They
are supplied in two forms, as MATLAB MAT-files and as ASCII text files. Students can use these files for
electronic solutions to homework problems. The ASCII files are supplied so that the information can be used with
non-MATLAB software.
Please note that the file extent of the magnetization curves and open-circuit characteristics have changed in this
edition. In the Third Edition, I used the file extent *.mag for magnetization curves. Unfortunately, after the book
was published, Microsoft appropriated that extent for a new Access table type in Office 2000. That made it hard
for users to examine and modify the data in the files. In this edition, all magnetization curves, open-circuit
characteristics, short-circuit characteristics, etc. use the file extent *.dat to avoid this problem.
Each curve is given in ASCII format with comments at the beginning. For example, the magnetization curve in
Figure P9-1 is contained in file p91_mag.dat. Its contents are shown below:
%
%
%
%
%
%
%
%
%
%
This is the magnetization curve shown in Figure
P9-1. The first column is the field current in
amps, and the second column is the internal
generated voltage in volts at a speed of 1200 r/min.
To use this file in MATLAB, type "load p91_mag.dat".
The data will be loaded into an N x 2 array named
"p91_mag", with the first column containing If and
the second column containing the open-circuit voltage.
MATLAB function "interp1" can be used to recover
a value from this curve.
0
0
0.0132
6.67
0.03
13.33
0.033
16
0.067
31.30
0.1
45.46
0.133
60.26
0.167
75.06
0.2
89.74
iv
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0.233
0.267
0.3
0.333
0.367
0.4
0.433
0.467
0.5
0.533
0.567
0.6
0.633
0.667
0.7
0.733
0.767
0.8
0.833
0.867
0.9
0.933
0.966
1
1.033
1.067
1.1
1.133
1.167
1.2
1.233
1.267
1.3
1.333
1.367
1.4
1.433
1.466
1.5
104.4
118.86
132.86
146.46
159.78
172.18
183.98
195.04
205.18
214.52
223.06
231.2
238
244.14
249.74
255.08
259.2
263.74
267.6
270.8
273.6
276.14
278
279.74
281.48
282.94
284.28
285.48
286.54
287.3
287.86
288.36
288.82
289.2
289.375
289.567
289.689
289.811
289.950
To use this curve in a MATLAB program, the user would include the following statements in the program:
% Get the magnetization curve. Note that this curve is
% defined for a speed of 1200 r/min.
load p91_mag.dat
if_values = p91_mag(:,1);
ea_values = p91_mag(:,2);
n_0 = 1200;
Unfortunately, an error occurred during the production of this book, and the values (resistances, voltages, etc.) in
some end-of-chapter artwork are not the same as the values quoted in the end-of-chapter problem text. I have
attached corrected pages showing each discrepancy in Appendix D of this manual. Please print these pages and
distribute them to your students before assigning homework problems. (Note that this error will be corrected at the
second printing, so it may not be present in your student’s books.)
v
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(a)
To write a MATLAB simulator of this circuit, note that if vin > v x , then vu = VDC , and if vin < v x ,
then v u = 0. Similarly, if v in > v y , then v v = 0, and if v in < v y , then v v = VDC . The output voltage is
then v out = v v − vu . A MATLAB function that performs these calculations is shown below. (Note that
this function arbitrarily assumes that VDC = 100 V. It would be easy to modify the function to use any
arbitrary dc voltage, if desired.)
function [vout,vu,vv] = vout(vin, vx, vy)
% Function to calculate the output voltage of a
% PWM modulator from the values of vin and the
% reference voltages vx and vy. This function
% arbitrarily assumes that VDC = 100 V.
%
%
vin
= Input voltage
%
vx
= x reference
%
vy
= y reference
%
vout
= Ouput voltage
%
vu, vv = Components of output voltage
93
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IA
+
Vφ
R1
jX1
0.105 Ω
j0.211 Ω
j5.244 Ω
jX2
R2
j0.317 Ω
0.071 Ω
jXM
I2
1 − s 
R2 

 s 
-
A MATLAB program to calculate the torque-speed characteristic of this motor is shown below:
% M-file: prob7_18.m
% M-file create a plot of the torque-speed curve of the
%
induction motor of Problem 7-18.
% First, initialize the values needed in this program.
r1 = 0.105;
% Stator resistance
x1 = 0.211;
% Stator reactance
r2 = 0.071;
% Rotor resistance
x2 = 0.317;
% Rotor reactance
xm = 5.244;
% Magnetization branch reactance
v_phase = 208 / sqrt(3);
% Phase voltage
n_sync = 1200;
% Synchronous speed (r/min)
w_sync = 125.7;
% Synchronous speed (rad/s)
% Calculate the Thevenin voltage and impedance from Equations
% 7-41a and 7-43.
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;
nm = (1 - s) * n_sync;
% Mechanical speed
% Calculate torque versus speed
for ii = 1:51
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}');
ylabel('\bf\tau_{ind}');
title ('\bfInduction Motor Torque-Speed Characteristic');
grid on;
193
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Since the fundamental voltage is reduced by 0.985, the fifth and seventh harmonics are suppressed relative
to the fundamental by the fractions:
5th:
0.643
= 0.653
0.985
7th:
0.342
= 0.347
0.985
In other words, the 5th harmonic is suppressed by 34.7% relative to the fundamental, and the 7th harmonic is
suppressed by 65.3% relative to the fundamental frequency.
B-7.
What coil pitch could be used to completely eliminate the seventh-harmonic component of voltage in ac
machine armature (stator)? What is the minimum number of slots needed on an eight-pole winding to
exactly achieve this pitch? What would this pitch do to the fifth-harmonic component of voltage?
SOLUTION To totally eliminate the seventh harmonic of voltage in an ac machine armature, the pitch factor
for that harmonic must be zero.
k p = 0 = sin
⇒
7ρ
2
7ρ
= (180°) n , n = 0, 1, 2, …
2
2(180°) n
ρ=
7
In order to maximize the fundamental voltage while canceling out the seventh harmonic, we pick the value
of n that makes ρ as nearly 180° as possible. If n = 3, then ρ = 154.3°, and the pitch factor for the
fundamental frequency would be
k p = sin
154.3°
= 0.975
2
This pitch corresponds to a ratio of 6/7. For a two-pole machine, a ratio of 6/7 could be implemented with
a total of 14 slots. If that ratio is desired in an 8-pole machine, then 56 slots would be needed.
The fifth harmonic would be suppressed by this winding as follows:
k p = sin
B-8.
(5)(154.3°) = 0.434
2
A 13.8-kV Y-connected 60-Hz 12-pole three-phase synchronous generator has 180 stator slots with a
double-layer winding and eight turns per coil. The coil pitch on the stator is 12 slots. The conductors from
all phase belts (or groups) in a given phase are connected in series.
(a) What flux per pole would be required to give a no-load terminal (line) voltage of 13.8 kV?
(b) What is this machine’s winding factor k w ?
SOLUTION
(a)
The stator pitch is 12/15 = 4/5, so ρ = 144° , and
k p = sin
144°
= 0.951
2
293
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