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Discover the history, underpinnings, and applications of one of the most important theories in electrical engineering In Reference Frame Theory, author Paul Krause delivers a comprehensive and thorough examination of his sixty years of work in reference frame theory. From the arbitrary reference frame, to the coining of the title "reference frame theory," to the recent establishment of the basis of the theory, the author leaves no stone unturned in his examination of the foundations and niceties of this area. The book begins with an integration of Tesla's rotating magnetic field with reference frame theory before moving on to describe the link between reference frame theory and symmetrical induction machines and synchronous machines. Additional chapters explore the field orientation of brushless DC drives and induction machine drives. The author concludes with a description of many of the applications that make use of reference frame theory. The comprehensive and authoritative Reference Frame Theory also covers topics like: * A brief introduction to the history of reference frame theory * Discussions of Tesla's rotating magnetic field and its basis of reference frame theory * Examinations of symmetrical induction and synchronous machines, including flux-linkage equations and equivalent circuits * Applications of reference frame theory to neglecting stator transients, multiple reference frames, and symmetrical components Perfect for power engineers, professors, and graduate students in the area of electrical engineering, Reference Frame Theory also belongs on the bookshelves of automotive engineers and manufacturing engineers who frequently work with electric drives and power systems. This book serves as a powerful reference for anyone seeking assistance with the fundamentals or intricacies of reference frame theory.
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Cover
IEE Press Series on Power Engineering
Reference Frame Theory
Copyright
About the Author
Preface
1 A Brief History of Reference Frame Theory
References
2 Tesla's Rotating Magnetic Field
2.1 Introduction
2.2 Rotating Magnetic Field for Symmetrical Two‐Phase Stator Windings
2.3 Rotating Magnetic Field for Symmetrical Three‐Phase Stator Windings
2.4 Rotating Magnetic Field for Symmetrical Two‐Phase Rotor Windings
2.5 Rotating Magnetic Field for Symmetrical Three‐Phase Rotor Windings
2.6 Closing Comments
References
3 Tesla's Rotating Magnetic Field and Reference Frame Theory
3.1 Introduction
3.2 Transformation of Two‐Phase Symmetrical Stator Variables to the Arbitrary Reference Frame
3.3 Transformation of Two‐Phase Symmetrical Rotor Variables to the Arbitrary Reference Frame
3.4 Transformation of Three‐Phase Stator and Rotor Variables to the Arbitrary Reference Frame
3.5 Balanced Steady‐State Stator Variables Viewed from Any Reference Frame
3.6 Closing Comments
References
4 Equivalent Circuits for the Symmetrical Machine
4.1 Introduction
4.2 Flux‐Linkage Equations for a Magnetically Linear Two‐Phase Symmetrical Machine
4.3 Flux‐Linkage Equations in the Arbitrary Reference Frame
4.4 Torque Expression in Arbitrary Reference Frame
4.5 Instantaneous and Steady‐State Phasors
4.6 Flux‐Linkage Equations for a Magnetically Linear Three‐Phase Symmetrical Machine and Equivalent Circuit
4.7 Closing Comments
References
5 Synchronous Machines
5.1 Introduction
5.2 Synchronous Machine
5.3 Equivalent Circuit For Three‐Phase Synchronous Generator
5.4 Closing Comment
Reference
6 Brushless dc Drive with Field Orientation
6.1 Introduction
6.2 The Permanent‐Magnet ac Machine
6.3 Instantaneous and Steady‐State Phasors
6.4 Field Orientation of a Brushless dc Drive
6.5 Torque Control of a Brushless dc Drive
6.6 Closing Comments
References
7 Field Orientation of Induction Machine Drives
7.1 Introduction
7.2 Field Orientation of a Symmetrical Machine
7.3 Torque Control of Field‐Orientated Symmetrical Machine
7.4 Closing Comments
References
8 Additional Applications of Reference Frame Theory
8.1 Introduction
8.2 Neglecting Stator Transients
8.3 Symmetrical Components Derived by Reference Frame Theory
8.4 Multiple Reference Frames
8.5 Closing Comments
References
Index
End User License Agreement
Chapter 7
Table 7.2-1 Steady‐state voltage and torque equations for field orientation o...
Chapter 2
Figure 2.2-1 Sinusoidally distributed stator winding. (a) Approximate sinuso...
Figure 2.2-2 Closed paths of integration and the plot of
.
Figure 2.2-3 Plot of sinusoidal approximation of
shown in Figure 2.2-2g.
Figure 2.2-4 Elementary symmetrical, two‐pole two‐phase sinusoidally distrib...
Figure 2.2-5 Symmetrical, two‐pole two‐phase sinusoidally distributed stator...
Figure 2.2-6 Tesla's balanced steady‐state rotating magnetic field
viewed ...
Figure 2.3-1 Elementary two‐pole three‐phase sinusoidally distributed stator...
Figure 2.4-1 Two‐phase rotating, identical, and sinusoidally distributed sym...
Figure 2.5-1 Three‐phase rotating, identical, and sinusoidally distributed s...
Chapter 3
Figure 3.2-1 Two‐pole two‐phase sinusoidally distributed fictitious windings...
Figure 3.3-1 Two‐phase rotating, identical, and sinusoidally distributed win...
Figure 3.3-2 The fictitious
qr
and
dr
windings.
Figure 3.4-1 Elementary two‐pole three‐phase sinusoidally distributed stator...
Figure 3.4-2 Elementary two‐pole three‐phase sinusoidally distributed rotor ...
Figure 3.5-1 Direction of rotation of
and the phase relation between
and...
Chapter 4
Figure 4.2-1 A two‐pole two‐phase symmetrical machine.
Figure 4.3-1 Arbitrary reference frame equivalent circuits for a two‐phase, ...
Figure 4.5-1 Equivalent circuit for a two‐phase symmetrical induction machin...
Figure 4.5-2 Steady‐state torque–speed characteristics of a symmetrical indu...
Figure 4.5-3 Equivalent circuit for steady‐state operation of a single‐fed s...
Figure 4.5-4 Phasor diagram; motor action,
s
= 0.05.
Figure 4.5-5 Phasor diagram; generator action,
s
= −0.05.
Figure 4.6-1 A two‐pole three‐phase symmetrical machine.
Figure 4.6-2 Arbitrary reference frame equivalent circuits for a three‐phase...
Chapter 5
Figure 5.2-1 Salient‐rotor two‐pole three‐phase salient‐pole synchronous mac...
Figure 5.3-1 Equivalent circuit for three‐phase synchronous machine in the r...
Figure 5.3-2 Phasor diagram for generator operation.
Chapter 6
Figure 6.2-1 Two‐pole two‐phase permanent‐magnet ac machine.
Figure 6.2-2 (a) The
and
axis equivalent of a two‐phase permanent‐magnet ...
Figure 6.3-1 Phasor diagram showing voltages, currents, and rotor and stator...
Figure 6.3-2 Phasor diagram for
and
in phase.
Figure 6.4-1 Inverter–machine drive. (
a
) Inverter configuration, (
b
) transis...
Figure 6.4-2 Two‐pole three‐phase permanent‐magnet ac machine with sensors....
Figure 6.4-3 The free‐acceleration torque–speed characteristics for a three‐...
Figure 6.4-4 Phasor diagram for brushless dc drive operation at
rad/s with...
Figure 6.4-5 Torque–speed characteristics of a three‐phase machine for free ...
Figure 6.4-6 Phasor diagram for brushless dc drive operation at
with
.
Figure 6.4-7 Torque–speed characteristics for free acceleration with
.
Figure 6.4-8 Phasor diagram for brushless dc drive operation at
with
.
Figure 6.5-1 Block diagram of constant‐torque control of a three‐phase perma...
Figure 6.5-2 Phasor diagram for operating Point 1.
Figure 6.5-3 Controlling
.
Figure 6.5-4 Phasor diagram for operating Point 2.
Chapter 7
Figure 7.2-1 Block diagram depicting field‐oriented control principles.
Figure 7.3-1 Operation of induction motor drive with field orientation for s...
Figure 7.3-2 Phasor diagram for operating Point 1.
Figure 7.3-3 Phasor diagram for operating Point 2.
Cover Page
IEE Press Series
Title Page
Copyright
About the Author
Preface
Table of Contents
Begin Reading
Index
WILEY END USER LICENSE AGREEMENT
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Series Editor: M. E. El‐Hawary, Dalhousie University, Halifax, Nova Scotia,
Canada
The mission of IEEE Press Series on Power Engineering is to publish leading‐ edge books that cover the broad spectrum of current and forward‐looking technologies in this fast‐moving area. The series attracts highly acclaimed authors from industry/academia to provide accessible coverage of current and emerging topics in power engineering and allied fields. Our target audience includes the power engineering professional who is interested in enhancing their knowledge and perspective in their areas of interest.
1. Electric Power Systems: Design and Analysis, Revised Printing
Mohamed E. El‐Hawary
2. Power System Stability
Edward W. Kimbark
3. Analysis of Faulted Power Systems
Paul M. Anderson
4. Inspection of Large Synchronous Machines: Checklists, Failure Identification,
and Troubleshooting
Isidor Kerszenbaum
5. Electric Power Applications of Fuzzy Systems
Mohamed E. El‐Hawary
6. Power System Protection
Paul M. Anderson
7. Subsynchronous Resonance in Power Systems
Paul M. Anderson, B.L. Agrawal, and J.E. Van Ness
8. Understanding Power Quality Problems: Voltage Sags and Interruptions
Math H. Bollen
9. Analysis of Electric Machinery
Paul C. Krause, Oleg Wasynczuk, and S.D. Sudhoff
10. Power System Control and Stability, Revised Printing
Paul M. Anderson and A.A. Fouad
11. Principles of Electric Machines with Power Electronic Applications,
Second Edition
Mohamed E. El‐Hawary
12. Pulse Width Modulation for Power Converters: Principles and Practice
D. Grahame Holmes and Thomas A. Lipo
13. Analysis of Electric Machinery and Drive Systems, Second Edition
Paul C. Krause, Oleg Wasynczuk, and Scott D. Sudhoff
14. Risk Assessment for Power Systems: Models, Methods, and Applications
Wenyuan Li
15. Optimization Principles: Practical Applications to the Operation of Markets
of the Electric Power Industry
Narayan S. Rau
16. Electric Economics: Regulation and Deregulation
Geoffrey Rothwell and Tomas Gomez
17. Electric Power Systems: Analysis and Control
Fabio Saccomanno
18. Electrical Insulation for Rotating Machines: Design, Evaluation, Aging,
Testing, and Repair, Second Edition
Greg C. Stone, Ian Culbert, Edward A. Boulter, and Hussein Dhirani
19. Signal Processing of Power Quality Disturbances
Math H. J. Bollen and Irene Y. H. Gu
20. Instantaneous Power Theory and Applications to Power Conditioning
Hirofumi Akagi, Edson H. Watanabe, and Mauricio Aredes
21. Maintaining Mission Critical Systems in a 24/7 Environment
Peter M. Curtis
22. Elements of Tidal‐Electric Engineering
Robert H. Clark
23. Handbook of Large Turbo‐Generator Operation and Maintenance,
Second Edition
Geoff Klempner and Isidor Kerszenbaum
24. Introduction to Electrical Power Systems
Mohamed E. El‐Hawary
25. Modeling and Control of Fuel Cells: Distributed Generation Applications
M. Hashem Nehrir and Caisheng Wang
26. Power Distribution System Reliability: Practical Methods and Applications
Ali A. Chowdhury and Don O. Koval
27. Introduction to FACTS Controllers: Theory, Modeling, and Applications
Kalyan K. Sen and Mey Ling Sen
28. Economic Market Design and Planning for Electric Power Systems
James Momoh and Lamine Mili
29. Operation and Control of Electric Energy Processing Systems
James Momoh and Lamine Mili
30. Restructured Electric Power Systems: Analysis of Electricity Markets with
Equilibrium Models
Xiao‐Ping Zhang
31. An Introduction to Wavelet Modulated Inverters
S. A. Saleh and M. Azizur Rahman
32. Control of Electric Machine Drive Systems
Seung‐Ki Sul
33. Probabilistic Transmission System Planning
Wenyuan Li
34. Electricity Power Generation: The Changing Dimensions
Digambar M. Tagare
35. Electric Distribution Systems
Abdelhay A. Sallam and Om P. Malik
36. Practical Lighting Design with LEDs
Ron Lenk and Carol Lenk
37. High Voltage and Electrical Insulation Engineering
Ravindra Arora and Wolfgang Mosch
38. Maintaining Mission Critical Systems in a 24/7 Environment, Second Edition
Peter M. Curtis
39. Power Conversion and Control of Wind Energy Systems
Bin Wu, Yongqiang Lang, Navid Zargari, and Samir Kouro
40. Integration of Distributed Generation in the Power System
Math H. J. Bollen and Fainan Hassan
41. Doubly Fed Induction Machine: Modeling and Control for Wind Energy
Generation
Gonzalo Abad, Jesús López, Miguel Rodrigues, Luis Marroyo, and Grzegorz
Iwanski
42. High Voltage Protection for Telecommunications
Steven W. Blume
43. Smart Grid: Fundamentals of Design and Analysis
James Momoh
44. Electromechanical Motion Devices, Second Edition
Paul Krause, Oleg Wasynczuk, and Steven Pekarek
45. Electrical Energy Conversion and Transport: An Interactive Computer‐Based
Approach, Second Edition
George G. Karady and Keith E. Holbert
46. ARC Flash Hazard and Analysis and Mitigation
J. C. Das
47. Handbook of Electrical Power System Dynamics: Modeling, Stability, and
Control
Mircea Eremia and Mohammad Shahidehpour
48. Analysis of Electric Machinery and Drive Systems, Third Edition
Paul Krause, Oleg Wasynczuk, Scott Sudhoff, and Steven Pekarek
49. Extruded Cables for High‐Voltage Direct‐Current Transmission: Advances in
Research and Development
Giovanni Mazzanti and Massimo Marzinotto
50. Power Magnetic Devices: A Multi‐Objective Design Approach
S. D. Sudhoff
51. Risk Assessment of Power Systems: Models, Methods, and Applications,
Second Edition
Wenyuan Li
52. Practical Power System Operation
Ebrahim Vaahedi
53. The Selection Process of Biomass Materials for the Production of Bio‐Fuels
and Co‐Firing
Najib Altawell
54. Electrical Insulation for Rotating Machines: Design, Evaluation, Aging,
Testing, and Repair, Second Edition
Greg C. Stone, Ian Culbert, Edward A. Boulter, and Hussein Dhirani
55. Principles of Electrical Safety
Peter E. Sutherland
56. Advanced Power Electronics Converters: PWM Converters Processing AC
Voltages
Euzeli Cipriano dos Santos Jr. and Edison Roberto Cabral da Silva
57. Optimization of Power System Operation, Second Edition
Jizhong Zhu
58. Power System Harmonics and Passive Filter Designs
J. C. Das
59. Digital Control of High‐Frequency Switched‐Mode Power Converters
Luca Corradini, Dragan Maksimovic, Paolo Mattavelli, and Regan Zane
60. Industrial Power Distribution, Second Edition
Ralph E. Fehr, III
61. HVDC Grids: For Offshore and Supergrid of the Future
Dirk Van Hertem, Oriol Gomis‐Bellmunt, and Jun Liang
62. Advanced Solutions in Power Systems: HVDC, FACTS, and Artificial
Intelligence
Mircea Eremia, Chen‐Ching Liu, and Abdel‐Aty Edris
63. Operation and Maintenance of Large Turbo‐Generators
Geoff Klempner and Isidor Kerszenbaum
64. Electrical Energy Conversion and Transport: An Interactive Computer‐Based
Approach
George G. Karady and Keith E. Holbert
65. Modeling and High‐Performance Control of Electric Machines
John Chiasson
66. Rating of Electric Power Cables in Unfavorable Thermal Environment
George J. Anders
67. Electric Power System Basics for the Nonelectrical Professional
Steven W. Blume
68. Modern Heuristic Optimization Techniques: Theory and Applications to
Power Systems
Kwang Y. Lee and Mohamed A. El‐Sharkawi
69. Real‐Time Stability Assessment in Modern Power System Control Centers
Savu C. Savulescu
70. Optimization of Power System Operation
Jizhong Zhu
71. Insulators for Icing and Polluted Environments
Masoud Farzaneh and William A. Chisholm
72. PID and Predictive Control of Electric Devices and Power Converters Using
MATLAB®/Simulink®
Liuping Wang, Shan Chai, Dae Yoo, Lu Gan, and Ki Ng
73. Power Grid Operation in a Market Environment: Economic Efficiency and
Risk Mitigation
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