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ELECTRIC
MACHINERY
FUNDAMENTALS
ELECTRIC
MACHINERY
FUNDAMENTALS
FOU
RTH
EDITION
Stephen J. Chapman
B
AE
SYSTEMS Australia
Higher
Education
Boston Burr Ridge,
IL
Dubuque, IA Madison, WI New
York
San
Francisco
SI.
l ouis Bangkok Bogota Caracas Kuala l umpur
Lisbon London Madrid Mexico City
Mi
l
an
Montreal New
De
lhi
Santiago
Seou
l Singapore Sydney Taipei
Toronto
•
Higher
Education
ELE
CTR
IC M
AC
HIN
ERY
RJNDAMENTALS.
FOURT
H
EDITION
Published by McGraw-Hill. a business unit
of
The McGraw-Hill Companies. Inc., 1221 Avenue
of
the
Americas, N
ew
Yort. NY 10020. Copyright 0 2005, 1999. 1991. 1985 by
The
McGraw,Hill
Companies. Inc. All rights reserved. No part
of
this publication
may
be
reproduced or distributed
in
any
form
or
by
any
means.
or
stored
in
a database
or
retrieval system. without the prior written
con'
sent
of
The McGraw-Hill Companies. Inc., including. but not limited to,
in
any
network
or
other
electronic storage
or
transmission.
or
broadcast for distan
ce
learning.
Some
ancillaries. including electronic
and
prim components.
may
not be available to customers
out,
side the Unit
ed
States.
Thi
s
book
is printed
on
acid'free
paper.
1234567890DOaDOC09876543
ISBN 0--07- 246523--9
Publisher: Elizabeth
A.
Jones
Senior
spo
nsoring editor: Carlise Paulson
Managing developmental editor:
EmilyJ.
Lupash
Marketing manager: Val'
'""
R.
Bercier
Senior project manager: Sheila
M.
Frank
Senior production supervisor: Laura
Fu
ller
Senior media project manager: Tammy Juran
Senior designer: Da\·id
W.
Hash
Lead photo research coordinator: Carrie
K.
Burger
Compositor:
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- Indianapolis
Typeface:
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Times Rotnlln
Printer:
R. R.
Donnelley Crawfordsville. IN
Libmry
of
Co
n
~r
ess
Gl
talo~in~-in-l'ublic:ltion
Data
Chapman. Stephen J.
Electric machinery fundamentals / Stephen
Chapman.
- 4th ed.
p. em.
Includes index.
IS
BN
0-07
- 246523--9
I.
Electric machinery. I. Title.
TK2000.C46
2005
621.31 ·042---dc22
www.mhhe.oom
2003065174
C
IP
THIS WORK IS DEDICATED WITH LOVE TO
MY MOTHER, LOUISE
G.
CHAPMAN,
ON
THE OCCASION
OF
HER
EIGHTY-RFfH
BIRTHD
AY.
ABOUT THE AUTHOR
Ste
ph
en
J.
Chapman received a B.S. in
El
ec
tri
ca
l Engin
ee
ring from Lo
ui
siana
State University (1975) and an M.S.E. in Electri
ca
l Engineering from the Univer-
sity of Central Florida ( 1979), and pursued further graduate studies
at
Rice
University.
From 1975 to
1980, he served
as
an o
ffi
ce
r in the U.S. Navy, assigned to
teach electrical engineering
at
the U.S. Naval Nucl
ea
r P
owe
r School in Orlando,
Florida. From
1980 to 1982, he was affiliated with the Univers
it
y
of
Houston,
where he ran
the power systems program in the College of T
ec
hnology.
From 1982 to 1988 and from
1991
to 1995, he served as a member of the
te
c
hnical
s
tafT
of
til
e
Ma
ssachusetts Institute of
Te
c
hnolo
gy's
Lin
co
ln
Lab
ora
tory
,
both at the main facility in Lexington,
Ma
ssachuse
tt
s,
and
at
the
fi
e
ld
site on Kwa-
jalein Atoll in the Republic of the Marshall Islands. While
th
ere, he did research
in
radar sig
nal
processing systems. He ultimate
ly
became
th
e leader of four large
opera
ti
onal range instrumentation radars
at
the Kwajalein field s
it
e (TRADEX,
ALTAIR, ALCOR, and
MMW
).
From 1988 to
1991
,
Mr.
Chapman was a research engineer
in
Shell Devel-
opme
nt
Company
in
Houston, Texas, where he did seis
mi
c signal processing re-
search. He was also affiliated with the University of Houston, where he
co
ntinu
ed
to teach on a part-time basis.
Mr.
Chapman is currently mana
ge
r
of
systems modeling and operational
analysis for BAE SYSTEMS Australia,
in
Me
lb
ourne.
Mr.
Chapman is a se
ni
or me
mber
of the Institute of Electri
ca
l and Elec-
tronic Eng
in
eers (and several
of
its
co
mp
onent societies) . He is also a member
of
th
e Association for Computing Machinery and
th
e Institution of Eng
in
eers
(Australia).
vu
BRIEF CONTENTS
Chapter 1 Introduction to Machinery Principles
Chapter 2 Transformers 65
Chapter 3 Introduction to Power Electronics 152
Chapter 4
AC
Machinery Fundamentals 230
Chapter 5 Synchronolls Generators
267
Chapter 6 Synchronolls Motors 346
Chapter 7 Induction Motors 380
Chapter 8 DC Machinery Fundamentals 473
Chapter 9 DC Motors and Generators 533
Chapter 10 Single-Phase and Special-Purpose Motors 633
Appendix A Three-Phase Circuits
68
1
Appendix B Coil Pitch and Distributed Windings
707
Appendix C Salient-Pole Theory ofSynchronolls Machines 727
Appendix D Tables
of
Constants and Conversion Factors 737
"
TABLE OF CONTENTS
Chapter 1 Introduction
to
Machinery Principles
1.1
Electrical Machines, Transfo
rm
ers, and Daily Life
1.2 A Note on Units and Notation
Notation
2
1
.3
Rotational Mo
ti
on, N
ew
ton
's
Law, and Power Relationships 3
A
ng
ul
ar
Position
(J
I
An
gular Velocity w / A
ng
ul
ar
Acceleration a / Torque T / Newton
's
Law
o/
Rot
at
ion I
Wo
rk
W Power P
I..
The Magne
ti
c Field 8
Production
of
a Magnetic Field / Magnetic Circuits /
Magnetic
Behavior 01 Ferromagnetic Mate
ri
als I
En
er
gy
Losses in a Ferromagnetic Core
1.
5
Faraday's Law
-I
ndu
ce
d Voltage from a Time-Changing
Magne
ti
c Field
28
1.
6 Produc
ti
on of Induced Force on a Wire 32
1.
7
Indu
ced
Vo
lt
age on a Conductor Moving in a Magnetic Field
34
I."
The
Lin
ear
OC
M
ac
hine- A Simple Example
36
Starting the Linear DC Machine / The
line
ar
DC
Machine as a Motor
I The Linear DC M
ac
hine as a
Genera
to
r I Starting Problems with the Li
ne
ar
Machine
I..
Real, Reactive, and Apparent Power in AC Circuits
47
Alternative Fonns
of
the P
owe
r Equations I Complex
Power I
Th
e Relationships beflt'een Impedance
An
gle,
C
ur
rent Angle, and P
owe
r I
Th
e P
owe
r
Tr
iangle
1.10
Summary
53
Questions
54
Probl
ems
55
Refe
re
nces
64
"
XII TABLE OF
CO
NTENTS
Cha
pt
er 2 Transformers 65
2.1
Why Transfo
nn
ers Are Important to Modern Life
66
2.2
Types and Construc
ti
on of Transformers 66
2.3
The Ideal Transfo
nn
er 68
Power in an Ideal Transformer I Impedance
TransfornUltion throu
gh
a Transfo
rn
ler I Analysis
of
Circuits Containing Ideal Transformers
2.4
Th
eory of
Ope
ration of R
ea
l Single-Phase Transformers
76
The Voltage Ratio across a Transformer I
The
Magnetization
Cu
rrent
in
a Real Transformer I T
he
Cu
rrent Ratio on a Transfor
me
r
and
the D
ot
Conrention
2.5
Th
e Equivale
nt
Ci
rc
uit of a Transformer
86
The Exact Equivalent Circuit
of
a Real Transformer I
ApproxinUlte Equivalent Circuits
of
a Transformer I
Determining the
Val
ues
of
Components
in
the Transfonner
Model
2.6 The Per-Unit System of Measureme
nt
s 94
2.7
Transfo
nn
er Vo
lt
age Regula
ti
on a
nd
Efficiency
1
00
The Transformer Phasor Diagram I Transfonner Efficiency
2.8
Transfo
nn
er Taps and Voltage Reg
ul
a
ti
on
108
2.
9 The Autotransfo
nn
er 109
Voltage
an
d Current Relationships
in
an
Au
totransformer I
The
Apparent Power Rating Advantage
of
Au
totransfornlers I
The
Internal Impedance
of
an
Au
totransformer
2.10 Three-Phase Transfo
nn
ers
11
6
Three-Phase Transfo
rm
er Connections I
The
Per-Unit
System
fo
r Three-Phase
Tr
ansformers
2.
11
Three-Phase Transfo
nn
a
ti
on Using Two Transformers 1
26
The Open-
il
(or V-V) Connection I
The
Open-"3'e-Open-
Delta Connection I
The
Scott-T Connection I T
he
Three-
Phase T Connection
2.
12
Transfo
nn
er Ratings and Related Problems 134
The Voltage
and
Frequency Ratings
of
a Transformer I
The Apparent Power Rating
of
a Transfornler I
Th
e
Problem
of
Cu
rrent In
rn
sh
I The Transformer Nameplate
2.13 Instnune
nt
Transformers 1
40
2.14 Swnmary 1
42
Questions 1
43
P
rob
lems 1
44
Re
fe
rences
15
1
C
hapt
er 3
3
.1
3.2
3.3
3.4
3.5
3.6
3.7
3.'
3
.'
C
hapt
er 4
4.1
TABLE OF CONTENTS
XlU
Introduction
to
Power
Electronics
Power Electronic Components
The
Diode / The
Two-
Wire
Th
yristor
or
PNPN Diode / The
Three-Wire Thyristor
of
SCR /
The
Gate Turnoff Thyristor /
The
DlAC
/ The
TRIA
C /
The
Power
Tra
nsistor /
The
Insulated-Gate Bipolar Transistor / Power atui Speed
Comparison
of
Power Electronic Components
Basic Rectifier Circuits
Th
e Half-Wave Rectifier / The Full-Wave Rectifier /
The
Three-Phase Half-Wave Rectifier /
Th
e Three-Phase Full-
Wave
Rectifier / Filtering
Re
ctifier Output
Pulse Circuits
A Relaxation Oscillator Using a
PNPN
Diode / Pulse
Synchronization
Voltage
Variation by
AC
Ph
ase Control
AC
Phase
Controlfora
DC
Load Drivenfrom an
AC
Source /
AC
Phase
An
gle Control
for
an
AC
Load / T
he
Effe
ct
of
Inductive Loads on Phase Angle Control
DC
-to-DC Power Contro
l-Ch
oppers
Forced Commutation in Chopper Circuits /
Series-
Capacitor Commutation Circuits / Parallel-Capacitor
Commutation Circuits
Inverters
The
Rectifier / External Commutation lnverters / Self-
Commutation Inverters / A Single-Phase Current Source
Inverter / A Three-Phase Current Source lnverter /
A
Thre
e-
Phase Voltage Source Inverter / Pulse-Width
Modulation lnverters
Cycloconverters
Basic Concepts / Noncirculating Current
Cycloconverters / Circulating Current Cycloconverters
Hannonic Pr
ob
lems
Summary
Questions
Problems
References
AC
Machinery
Fundamentals
A Simple Loop
in
a Uniform Magnetic
Fi
e
ld
The
Voltage Indu
ced
in a Simple Rotating Loop / T
he
Torque lnduced
in
a
Cu
rrent-Cart}'ing Loop
152
152
1
63
171
177
186
1
93
209
218
221
223
223
229
230
230
XIV
TABLEOF
CO
NTENT
S
4.
2 The Rotating Magnetic
Fi
eld 238
Pr
oof
of
the Rotating Magnetic Fi
eld
Concept I The
Relationship
between Electrical
Fre
quency and the Speed
of
Magnetic Field Rotation I Reversing the Direction
of
Magnetic Field Rotation
4.3
Magnetomotive Force and Flux
Di
stribution on AC Machines 246
4.4
Induced Voltage
in
AC
Ma
chines
250
Th
e I
nd
uced Voltage
in
a Coil
on
a Two-Pole Stator I
The
I
nd
uced Voltage
in
a
Th
ree-Phase Set
of
Coils I
The
RMS
Voltage
in
a Three-Phase Stator
4.5
Induced Torque
in
an AC M
ac
hine 255
4
.•
Wmding Insulation
in
an
AC
Ma
chine
258
4.7
AC Machine Power Flows and Losses
261
The Losses
in
AC
Machines I The Power-Flow Diagram
4.S
Voltage Regulation and Speed Regulation
262
4.9
Swnmary 264
Qu
es
tions 265
P
rob
lems 265
References 266
Cha
pt
er 5 Synchronous
Ge
nerators 267
5.
1 Synchronous Generator Construction 267
5
.2
Th
e Speed
of
Rotation of a Synchronous Generator 272
5.3
The I
nt
ernal Generated Voltage of a Synchronous Generator
273
5.4
The Equivale
nt
Circuit of a Synchronous Generator 274
5.5
The Phasor Diagram of a Synchronous Generator 279
5
.•
Power and Torque in Synchronous Generators 280
5.7 Measuring Synchronous Generator Model Parameters 283
The Short-Circuit Ratio
5.8 The Synchronous Generator Operating Alone 288
Th
e Effect
of
Load Changes
on
Synchronous Generator
Operating Alone
I Example Problems
5.9 Parallel Operation of AC Generators
299
The
Conditions Requiredfor Paralleling I The General
Procedure for Paralleling Generators I Frequ
ency-
Power
and Voltage-Reactive P
owe
r Characteristics
of
a Synchronous
Generator I Operation
of
Generators
in
Parallel with Large
Power Systems I
Op
eration
of
Generators
in
Parallel with
Other Generators
of
the Same Size
5.
10
Synchronous Generator Transie
nt
s 319
Tra
nsient Stability
of
Synchronous Generators I
Short-Circuit
Tra
nsients in Synchronous Generators
5
.11
5. 12
C
hapt
er 6
6.1
6.2
6.3
6.4
6.5
6.6
C
hapt
er 7
7
.1
7.2
7.3
TABLE OF CONTENTS
XV
Synchronous Generator Ratings
The
Voltage, Speed,
and
Frequency Ratings / Apparent
Power atui Power-Factor Ratings / Synchronous
Generator Capability
CUf1Jes
/ Short-Time Operation
and
Sef1Jice
Factor
Summary
Questions
Problems
Ref
ere
nces
Synchronous Motors
Basic Principles
of
Motor Operation
The
Equiralent Circuit
of
a Synchronous Motor /
The
Synchronous Motor from a Magnetic Field Perspective
Steady-State
Synchronous Motor Operation
The
Synchronous Motor Torque-Speed Characteristic
CUf1Je
/
The
Effect
of
Load Changes on a Synchronous Motor /
Th
e
Effect
of
Field Changes on a Synchronous Motor /
The
Synchronous Motor atui Power,
Fa
ctor Correction /
The
Synchronous Capacitor or Synchronous Condenser
Starting Synchronous Motors
Motor
Starting by Reduced Elect
ri
cal Frequency / Motor
Starting with an
utemal
Prime Mo
ve
r / Motor Starting
by Using Amortisseur Windings / T
he
Effect
of
Amortisseur Windings
on
Motor Stability
Synchronous Generators and Synchronous Motors
Synchronous Motor Ratings
Summary
Questions
Problems
Ref
ere
nces
Induction Motors
Induction Motor Construction
Basic Induction Motor Concepts
The
Development
of
Indu
ced
Torque
in
an ltuiuction
Motor /
The
Concept
of
Rotor Slip / The Electrical
Frequency on the Rotor
The Equivalent Circuit
of
an Induction Motor
The
Tran
sformer Model
of
an Induction Motor /
The
Rotor
Circuit
Model/The
Final Equiralent Circuit
326
336
337
338
345
346
346
350
364
37
1
372
373
374
374
379
380
380
384
388
XVI
TABLE
OF
CONTENTS
7.4
Power and Torque in Induction Motors
394
Losses
and
the Pml'er-Flow Diagram I Power atui Torque
in
an
Induction Motor I Separating
th
e Rotor Copper
Lo
sses and the
Pmwr
Converted
in
an lnduction Motor S
Equivalent Cirr:uit
7.5
Induction Motor Torque-Speed Characteristics
401
lndu
ced
Torque from a Physical Statuipoint
IThe
Derivation
of
the lnduction Motor ltuiuced-Torque Equation I
Comments on
th
e Induction Motor Torque-Speed Cun'e I
Maximum (Pullout) Torque
in
an ltuiuction Motor
7
.•
Variations in Induction Motor Torque-Speed Characteristics
416
Control
of
Motor Characteristics by Cage Rotor Design I
Deep-Bar
and
Double-Cage Rotor Designs I lnduction
Motor Design Classes
7.7 Trends in Induction Motor Design 426
7.8
Starting Induction Motors 430
lnduction Motor Starting Circuits
7.9 Speed Control
of
Induction Motors
434
lnduction Motor Speed Control by Pole Changing I Speed
Control
by Changing the Line Frequency I Speed Control
by
Changing the Line Voltage I Speed Control by
Changing the Rotor Resistance
7.10 Solid-State Induction Motor Drives
444
Fr
equency (Speed) Adjustment I A Choice
of
Voltage
and
Fr
equency Patterns I Independently Adjustable
Acceleration
atui Deceleration Ramps I Motor Protection
7.
11
Detennining Circuit Model Parameters
452
The No-Load
Test
I
The
DC
Test
for
Stator Resistan
ce
I
The Locked-Rotor Test
7.
12
The Induction Generator 460
The lnduction Generator Operating Alone I lnduction
Generator Applications
7.13 Induction Motor Ratings
464
7.14 Swnmary 466
Questions
467
P
rob
lems
468
Rererences
472
C
hapt
er 8 DC Machinery Fundamentals
473
8.
1
A Simple Rotating Loop between Curved Pole Faces
473
TABLE OF CONTENTS
XVU
The
lliltage lnduced
in
a Rotating Loop / Getting DC
Voltage out
of
the Rotating Loop / The I
nd
uced Torque
in
the Rotating Loop
8.2
Commuta
ti
on in a Simple Four-Loop
IX
M
ac
hine 485
8.3
Commutation and Armature Cons
tru
c
ti
on
in
R
ea
l
DC M
ac
hines 490
The
Rotor Coils / Connections
to
the Commutator
Segments /
The
Lap Winding /
Th
e Wave Winding / The
Frog-Leg
Win
ding
8.4
Pr
oblems with Conunutation
in
Real M
ac
hines
502
Ar
mature Reaction / L dildt Voltages / Solutions to the
Problems with Commutation
8.5
The
Int
ernal Generated
Vo
lt
age and Induced Torque
Equ
a
ti
ons of R
ea
l DC M
ac
hines 514
8.6
The Construc
ti
on of DC M
ac
hin
es 518
Pole
and
Frame Construction / Rotor or
Ar
mature
Const
rn
ction / Commutator
and
Br
ushes / Winding
Insulation
8.7
Power Fl
ow
and Losses
in
DC Machines
524
The
Losses
in
DC Machines / The Power-Flow Diagram
8.8
Summary 527
Qu
estions 527
Problems 527
References 530
C
hapt
er 9 DC Motors and Generators 533
9
.1
Intro
du
c
ti
on to DC Motors 533
9.2
The Equiv
al
e
nt
C
ir
cuit of a
IX
Motor 535
9.3
The Magnetiza
ti
on Curve of a DC M
ac
hine 536
9.4
Se
parately
Ex
ci
t
ed
and Shunt
IX
Motors 538
Th
e Tenninal Characterist
ic
of
a Shunt DC Motor /
Nonlinear Analysis
of
a Shunt DC Motor / Speed Control
of
Shu
nt
DC Motors / The Effect
of
an Open Field
Ci
rcuit
9.5
The Pe
nn
ane
nt
-Magnet DC Motor 559
9.6
The
Se
ri
es
IX
Motor 562
Induced Torque
in
a Series DC Motor /
The
Terminal
Characteristic
of
a Series DC Motor / Speed Control
of
Series DC Motors
9.7
The Compo
un
ded DC Motor 568
The
Torque
-S
peed Characteristic
of
a Cumulatively
Compounded DC M
otor
/ The Torque- Speed
XVIII TABLE OF CONTENTS
Characteristic
of
a Differentially Compoutuied DC Motor /
The Nonlinear Analysis
of
Compou
nded
DC Motors /
Speed Control
in
the Cumulatively Compoutuied DC Motor
9.8 DC Motor Starters
9.9
9.10
9.
11
9.12
9.13
9.14
9.15
9.16
9.17
Cha
pt
er
10
10.1
DC Motor Problems
on
Starting / DC Motor Starting
Circuits
The Ward-Leonard System and Solid-State Speed
Co
nt
rollers
Protection Ci
rc
uit Section / StartlStop Circuit Section /
High.Power Electronics Section /
Lo
w-Power Electronics
Section
DC Motor Efficiency Calcula
ti
ons
Introduc
ti
on to
IX
Generators
Th
e Separately
Ex
cit
ed
Ge
nerator
The Terminal Characteristic
of
a Separately Excited DC
Generator / Control
of
Terminal Voltage / Nonlinear
Analysis
of
a Separately Excited DC Generator
The Shunt DC Generator
Voltage Buildup
in
a
Sh
unt Generator /
The
Tenninal
Characteristic
of
a
Sh
u
nt
DC Generator / Voltage Control
fo
r a Shunt DC Generator /
The
Analysis
of
Shunt DC
Generators
The Se
ri
es DC Generator
The
Te
rminal Cha racteristic
of
a Series Generator
The Crunul a
ti
ve
ly Compo
un
ded DC Generator
The
Te
rminal Characteristic
of
a Cumulatively
Compounded DC Generator / Voltage Control
of
Cumulatively Compou
nded
DC Generators / Analysis
of
Cumulatively Compou
nded
DC Generators
The Differentially
Co
mpo
lUld
ed DC Generator
The
Te
rminal Cha racteristic
of
a Differentially
Compound
ed
DC Generator / Voltage Control
of
Differentially Compou
nded
DC Generators / Graphical
Analysis
of
a Differentially Compounded DC Generator
Srunmary
Questions
P
rob
lems
Re
fe
rences
S
in
gle-Phase a
nd
Special-Purpose Motors
The Uni
ve
rsal Motor
Applications
of
Universal Motors / Speed Control
of
Universal Motors
573
582
592
594
596
602
608
6
11
615
619
620
621
631
633
634

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