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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: IEEE Press Series on Power Engineering
- Sprache: Englisch
The only book on the market that emphasizes machine design beyond the basic principles of AC and DC machine behavior AC electrical machine design is a key skill set for developing competitive electric motors and generators for applications in industry, aerospace, and defense. This book presents a thorough treatment of AC machine design, starting from basic electromagnetic principles and continuing through the various design aspects of an induction machine. Introduction to AC Machine Design includes one chapter each on the design of permanent magnet machines, synchronous machines, and thermal design. It also offers a basic treatment of the use of finite elements to compute the magnetic field within a machine without interfering with the initial comprehension of the core subject matter. Based on the author's notes, as well as after years of classroom instruction, Introduction to AC Machine Design: * Brings to light more advanced principles of machine design--not just the basic principles of AC and DC machine behavior * Introduces electrical machine design to neophytes while also being a resource for experienced designers * Fully examines AC machine design, beginning with basic electromagnetic principles * Covers the many facets of the induction machine design Introduction to AC Machine Design is an important text for graduate school students studying the design of electrical machinery, and it will be of great interest to manufacturers of electrical machinery.
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Veröffentlichungsjahr: 2017
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IEEE Press445 Hoes Lane Piscataway, NJ 08854
IEEE Press Editorial BoardTariq Samad, Editor in Chief
Giancarlo Fortino
Xiaoou Li
Ray Perez
Dmitry Goldgof
Andreas Molisch
Linda Shafer
Don Heirman
Saeid Nahavandi
Mohammad Shahidehpour
Ekram Hossain
Jeffrey Nanzer
Zidong Wang
INTRODUCTION TO AC MACHINE DESIGN
THOMAS A. LIPO
Emeritus Professor University of Wisconsin Madison, WI
Research Professor Florida State University
Copyright © 2017 by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.
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Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
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Library of Congress Cataloging-in-Publication Data is available.
ISBN: 978-1-119-35216-7
This book is dedicated to my many students who have taken the course ECE 713 Electromagnetic Design of AC Machines over the past 35+ years. You have helped prove that such a course remains a vital, important issue in a modern power systems/power electronics graduate program.
We are as dwarfs seated on the shoulders of giants that we might see more and further than they. Yet not by virtue of the keenness of our eyesight nor the breadth of our vision but alone because we are raised aloft on that giant mass.
Bernard of Chartres d. ca. 1130 AD
CONTENTS
Preface and Acknowledgments
List of Principal Symbols
About the Author
CHAPTER 1
MAGNETIC CIRCUITS
1.1 Biot–Savart Law
1.2 The Magnetic Field
B
1.3 Example—Computation of Flux Density
B
1.4 The Magnetic Vector Potential
A
1.5 Example—Calculation of Magnetic Field from the Magnetic Vector Potential
1.6 Concept of Magnetic Flux
1.7 The Electric Field
E
1.8 Ampere's Law
1.9 Magnetic Field Intensity
H
1.10 Boundary Conditions for
B
AND
H
1.11 Faraday's Law
1.12 Induced Electric Field Due to Motion
1.13 Permeance, Reluctance, and the Magnetic Circuit
1.14 Example—Square Toroid
1.15 Multiple Circuit Paths
1.16 General Expression for Reluctance
1.17 Inductance
1.18 Example—Internal Inductance of a Wire Segment
1.19 Magnetic Field Energy
1.20 The Problem of Units
1.21 Magnetic Paths Wholly in Iron
1.22 Magnetic Materials
1.23 Example—Transformer Structure
1.24 Magnetic Circuits with Air Gaps
1.25 Example—Magnetic Structure with Saturation
1.26 Example—Calculation for Series–Parallel Iron Paths
1.27 Multiple Winding Magnetic Circuits
1.28 Magnetic Circuits Applied to Electrical Machines
1.29 Effect of Excitation Coil Placement
1.30 Conclusion
Reference
CHAPTER 2
THE MMF AND FIELD DISTRIBUTION OF AN AC WINDING
2.1 MMF and Field Distribution of a Full-Pitch Winding for a two Pole Machine
2.2 Fractional Pitch Winding for a Two-Pole Machine
2.3 Distributed Windings
2.4 Concentric Windings
2.5 Effect of Slot Openings
2.6 Fractional Slot Windings
2.7 Winding Skew
2.8 Pole Pairs and Circuits Greater than One
2.9 MMF Distribution for Three-Phase Windings
2.10 Concept of an Equivalent Two-Phase Machine
2.11 Conclusion
References
CHAPTER 3
MAIN FLUX PATH CALCULATIONS USING MAGNETIC CIRCUITS
3.1 The Main Magnetic Circuit of an Induction Machine
3.2 The Effective Gap and Carter's Coefficient
3.3 The Effective Length
3.4 Calculation of Tooth Reluctance
3.5 Example 1—Tooth MMF Drop
3.6 Calculation of Core Reluctance
3.7 Example 2—MMF Drop Over Main Magnetic Circuit
3.8 Magnetic Equivalent Circuit
3.9 Flux Distribution in Highly Saturated Machines
3.10 Calculation of Magnetizing Reactance
3.11 Example 3—Calculation of Magnetizing Inductance
3.12 Conclusion
References
CHAPTER 4
USE OF MAGNETIC CIRCUITS IN LEAKAGE REACTANCE CALCULATIONS
4.1 Components of Leakage Flux in Induction Machines
4.2 Specific Permeance
4.3 Slot Leakage Permeance Calculations
4.4 Slot Leakage Inductance of a Single-Layer Winding
4.5 Slot Leakage Permeance of Two-Layer Windings
4.6 Slot Leakage Inductances of a Double-Cage Winding
4.7 Slot Leakage Inductance of a Double-Layer Winding
4.8 End-Winding Leakage Inductance
4.9 Stator Harmonic or Belt Leakage
4.10 Zigzag Leakage Inductance
4.11 Example 4-–Calculation of Leakage Inductances
4.12 Effective Resistance and Inductance Per Phase of Squirrel-Cage Rotor
4.13 Fundamental Component of Rotor Air Gap MMF
4.14 Rotor Harmonic Leakage Inductance
4.15 Calculation of Mutual Inductances
4.16 Example 5-–Calculation of Rotor Leakage Inductance Per Phase
4.17 Skew Leakage Inductance
4.18 Example 6-–Calculation of Skew Leakage Effects
4.19 Conclusion
References
CHAPTER 5
CALCULATION OF INDUCTION MACHINE LOSSES
5.1 Introduction
5.2 Eddy Current Effects in Conductors
5.3 Calculation of Stator Resistance
5.4 Example 7—Calculation of Stator and Rotor Resistance
5.5 Rotor Parameters of Irregularly Shaped Bars
5.6 Categories of Electrical Steels
5.7 Core Losses Due to Fundamental Flux Component
5.8 Stray Load and No-Load Losses
5.9 Calculation Of Surface Iron Losses Due To Stator Slotting
5.10 Calculation Of Tooth Pulsation Iron Losses
5.11 Friction And Windage Losses
5.12 Example 8—Calculation of Iron Loss Resistances
5.13 Conclusion
References
CHAPTER 6
PRINCIPLES OF DESIGN
6.1 Design Factors
6.2 Standards for Machine Construction
6.3 Main Design Features
6.4 The
D
2
L
Output Coefficient
6.5 The
D
3
L
Output Coefficient
6.6 Power Loss Density
6.7 The D
2.5
L Sizing Equation
6.8 Choice of Magnetic Loading
6.9 Choice of Electric Loading
6.10 Practical Considerations Concerning Stator Construction
6.11 Rotor Construction
6.12 The Design Process
6.13 Effect of Machine Performance by a Change in Dimension
6.14 Conclusion
References
CHAPTER 7
THERMAL DESIGN
7.1 The Thermal Problem
7.2 Temperature Limits and Maximum Temperature Rise
7.3 Heat Conduction
7.4 Heat Convection on Plane Surfaces
7.5 Heat Flow Across the Air Gap
7.6 Heat Transfer by Radiation
7.7 Cooling Methods and Systems
7.8 Thermal Equivalent Circuit
7.9 Example 10-–Heat Distribution of 250 HP Induction Machine
7.10 Transient Heat Flow
7.11 Conclusion
References
CHAPTER 8
PERMANENT MAGNET MACHINES
8.1 Magnet Characteristics
8.2 Hysteresis
8.3 Permanent Magnet Materials
8.4 Determination of Magnet Operating Point
8.5 Sinusoidally FED Surface PM Motor
8.6 Flux Density Constraints
8.7 Current Density Constraints
8.8 Choice of Aspect Ratio
8.9 Eddy Current Iron Losses
8.10 Equivalent Circuit Parameters
8.11 Temperature Constraints and Cooling Capability
8.12 Magnet Protection
8.13 Design for Flux Weakening
8.14 PM Motor with Inset Magnets
8.15 Cogging Torque
8.16 Ripple Torque
8.17 Design using Ferrite Magnets
8.18 Permanent Machines with Buried Magnets
8.19 Conclusion
Acknowledgment
References
CHAPTER 9
ELECTROMAGNETIC DESIGN OF SYNCHRONOUS MACHINES
9.1 Calculation of Useful Flux Per Pole
9.2 Calculation of Direct and Quadrature Axis Magnetizing Inductance
9.3 Determination of Field Magnetizing Inductance
9.4 Determination of
d
-Axis Mutual Inductances
9.5 Calculation of Rotor Pole Leakage Permeances
9.6 Stator Leakage Inductances of a Salient Pole Synchronous Machine
9.7 The Amortisseur Winding Parameters
9.8 Mutual and Magnetizing Inductances of the Amortisseur Winding
9.9 Direct Axis Equivalent Circuit
9.10 Referral of Rotor Parameters to the Stator
9.11 Quadrature Axis Circuit
9.12 Power and Torque Expressions
9.13 Magnetic Shear Stress
9.14 Field Current Profile
9.15 Conclusion
References
CHAPTER 10
FINITE-ELEMENT SOLUTION OF MAGNETIC CIRCUITS
10.1 Formulation of The Two-Dimensional Magnetic Field Problem
10.2 Significance of The Vector Potential
10.3 The Variational Method
10.4 Nonlinear Functional and Conditions for Minimization
10.5 Description of the Finite-Element Method
10.6 Magnetic Induction and Reluctivity in the Triangle Element
10.7 Functional Minimization
10.8 Formulation of the Stiffness Matrix Equation
10.9 Consideration of Boundary Conditions
10.10 Step-By-Step Procedure for Solving the Finite-Element Problem
10.11 Finite-Element Modeling of Permanent Magnets
10.12 Conclusion
10.A Appendix
References
Appendix A
Computation of Bar Current
Appendix B
Fem Example
Index
EULA
List of Tables
Chapter 1
Table 1.1
Chapter 2
Table 2.1
Table 2.2
Table 2.3
Table 2.4
Table 2.5
Table 2.6
Chapter 5
Table 5.1
Chapter 6
Table 6.1
Table 6.2
Table 6.3
Table 6.4
Table 6.5
Table 6.6
Table 6.7
Table 6.8
Table 6.9
Table 6.10
Table 6.11
Chapter 7
Table 7.1
Table 7.2
Table 7.3
Table 7.4
Table 7.5
Table 7.6
Table 7.7
Table 7.8
Table 7.9
Table 7.10
Table 7.11
Table 7.12
Chapter 8
Table 8.1
Guide
Cover
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Preface and Acknowledgments
THE MATERIAL IN THIS BOOK is derived from notes for a graduate level course on the design of AC electrical machines that I taught semi-annually at the University of Wisconsin since 1980. These notes were produced prior to this text in limited distribution form for teaching purposes over these many years. Upon retirement, the evolution of this material has now come to an end.
While given short shrift in most engineering curricula, electrical machine design remains one of the most challenging disciplines within electrical engineering. Since literally all of the significant texts dealing with this subject have long been out of print, it was decided to offer this material as a means to enable those interested in this subject to acquire the necessary basic knowledge.
It is the belief of the writer that, while the finite element method is a powerful analytic technique, the basic principles of machine theory cannot be taught well if finite elements are introduced too early. In this spirit, the subject of finite elements has been included only at the end of the book. Hopefully, with a deeper understanding of the basic principles garnered from this book, the student can go forth with modern mathematical tools such as finite elements and put them to work in a more enlightened manner.
It will be evident to the reader from the outset that the author has been deeply influenced by the writings of Alger, Liwschitz-Garik, and many others. Hopefully, sufficient new material exists to warrant the writer as being an “author” and not simply the “editor” of profound insights from these titans of the past.
My special thanks to four of my students, Michael Klabunde, Xiaogang Luo, Wenbo Liu, and Wen Ouyang, who made important contributions to Chapters 5, 6, 9, and 10, respectively. Also, I wish to thank Professor Katsuji Shinohara of Kagoshima University, Japan and his colleagues for their careful reading of an earlier version of this manuscript. Finally, special thanks to Rich Schiferl for his masterful editing of the final manuscript.
THOMAS A. LIPO
Madison, WI
List of Principal Symbols
Note: Additional subscripts s and r generally denote stator and rotor values of the quantity, respectively. The subscript 1 denotes the fundamental component. Boldface denotes a three-dimensional vector.
Symbol
Meaning
A
magnetic vector potential vector (Wb/m)
A
area (m
2
)
B
magnetic field or magnetic flux density vector (Wb/m
2
)
b
1/3
breadth of slot 1/3 of the way from narrow portion (m)
B
c
core flux density (Wb/m
2
)
B
g
flux density in the air gap (Wb/m
2
)
B
g,ave
average value of air gap flux density over one tooth and slot (Wb/m
2
)
B
gm
flux density in the gap produced by the magnet (Wb/m
2
)
B
gm1
fundamental component of air gap flux density produced by the magnet (Wb/m
2
)
B
g1
peak fundamental air gap flux density (Wb/m
2
)
b
o
slot opening (m)
B
top
,
B
mid
,
B
root
flux density at top, midpoint, and root of a tooth (Wb/m
2
)
C
number of parallel circuits
C
f
number of parallel field winding circuits
C
s
number of parallel stator circuits
C
h
thermal capacitance (J/°K)
C
ir
loss coefficient (W/m
3
)
c
p
specific heat (J/kg-°K)
cos
φ
gap
power factor as measured at the air gap
d
cs
,
d
cr
depth of the stator, rotor core (m)
d
e
equivalent depth of solid copper (m)
d
p
penetration constant (m)
d
m
magnet depth (magnet thickness) (m)
D
is
,
D
ir
inner diameter of stator, rotor punching (m)
D
os
,
D
or
outer diameter of stator, rotor punching (m)
d
ss
,
d
sr
depth of stator, rotor slot (m)
d
t
depth of tooth (m)
E
electric field intensity vector (V/m)
e
b
induced voltage in a rotor bar (V)
F
force vector (N)
magnetomotive force (MMF) (A-turn)
rotor core MMF drop (A-turn)
stator core MMF drop (A-turn)
f
e
stator applied frequency (Hz)
air gap MMF drop (A-turn)
peak fundamental component of stator MMF
MMF drop over the entire length of a tooth (A-turn)
stator, rotor tooth MMF drop (A-turn)
g
mechanical gap (m)
g
e
equivalent gap including fringing and saturation (m)
h
harmonic index
h
k
slot harmonics
H
magnetic field intensity vector (A/m)
H
top
,
H
mid
,
H
root
magnetic field intensity at the top, midpoint, and bottom section of a tooth (A/m)
H
t(ave)
average field intensity over entire length of a tooth (A/m)
I
steady (DC) current (A)
i
a
,
i
b
,
i
c
instantaneous current in phases a, b, and c (A)
i
b
current in a rotor bar (A)
i
e
current in an end-ring segment (A)
I
d
,
I
q
direct and quadrature current components
I
mr
peak rotor bar current (A)
I
r,har
equivalent current accounting for rotor space harmonics
I
s
peak AC stator current (A)
J
current density vector (A/m
2
)
J
m
volumetric polarization current (A/m
2
)
k
c
Carter factor
k
ch
winding factor for harmonic
h
for concentrated windings
k
cu
copper space factor
k
dh
distribution factor for
h
th harmonic
k
h
winding factor for
h
th harmonic
k
hys
Steinmetz coefficient
k
i
lamination space factor
K
m
surface polarization current
K
p
factor to include the effect of slot leakage flux on saturation of the core
K
pf
pole face factor
k
ph
pitch factor for
h
th harmonic
k
sr
ratio of rotor to stator surface current density
k
s
,
k
m
,
k
sl
slot factors
k
d
,
k
q
,
k
f
pole face factors
k
sh
skew factor for
h
th harmonic
K
surface current density vector (A/m)
K
s
,
K
r
stator, rotor surface current density (A/m)
K
s(rms)
stator surface current density assuming rms amps (Arms/m)
K
s1
peak fundamental component of stator surface current density (A/m)
k
χh
