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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: IEEE Press Series on Power Engineering
- Sprache: Englisch
As new technologies are created and advances are made with the ongoing research efforts, power system harmonics has become a subject of great interest. The author presents these nuances with real-life case studies, comprehensive models of power system components for harmonics, and EMTP simulations. * Comprehensive coverage of power system harmonics * Presents new harmonic mitigation technologies * In-depth analysis of the effects of harmonics * Foreword written by Dr. Jean Mahseredijan, world renowned authority on simulations of electromagnetic transients and harmonics
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Seitenzahl: 908
Veröffentlichungsjahr: 2015
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Table of Contents
Cover
Title Page
Series
Copyright
Foreword
Preface
About The Author
Chapter 1: Power System Harmonics
1.1 Nonlinear Loads
1.2 Increases in Nonlinear Loads
1.3 Effects of Harmonics
1.4 Distorted Waveforms
1.5 Harmonics and Sequence Components
1.6 Harmonic Indices
1.7 Power Factor, Distortion Factor, and Total Power Factor
1.8 Power Theories
1.9 Amplification and Attenuation of Harmonics
References
Chapter 2: Fourier Analysis
2.1 Periodic Functions
2.2 Orthogonal Functions
2.3 Fourier Series and Coefficients
2.4 ODD Symmetry
2.5 Even Symmetry
2.6 Half-Wave Symmetry
2.7 Harmonic Spectrum
2.8 Complex form of Fourier Series
2.9 Fourier Transform
2.10 Dirichlet Conditions
2.11 Power Spectrum of A Function
2.12 Convolution
2.13 Sampled Waveform: Discrete Fourier Transform
2.14 Fast Fourier Transform
References
Chapter 3: Harmonic Generation-1
3.1 Harmonics in Transformers
3.2 Energization of a Transformer
3.3 Delta Windings of Three-Phase Transformers
3.4 Harmonics in Rotating Machine Windings
3.5 Cogging and Crawling of Induction Motors
3.6 Synchronous Generators
3.7 Saturation of Current Transformers
3.8 Ferroresonance
3.9 Power Capacitors
3.10 Transmission Lines
References
Chapter 4: Harmonic Generation – II
4.1 Static Power Converters
4.2 Single-Phase Bridge Circuit
4.3 Reactive Power Requirements of Converters
4.4 Three-Phase Bridge Circuit
4.5 Harmonics on Output (DC) Side
4.6 Inverter Operation
4.7 Diode Bridge Converters
4.8 Switch-Mode Power (SMP) Supplies
4.9 Home Appliances
4.10 Arc Furnaces
4.11 Cycloconverters
4.12 Thyristor-Controlled Reactor
4.13 Pulse Width Modulation
4.14 Voltage Source Converters
4.15 Wind Power Generation
4.16 Fluorescent Lighting
4.17 Adjustable Speed Drives
4.18 Pulse Burst Modulation
4.19 Chopper Circuits and Electric Traction
4.20 Slip Frequency Recovery Schemes
4.21 Power Semiconductor Devices
References
Chapter 5: Interharmonics and Flicker
5.1 Interharmonics
5.2 Sources of Interharmonics
5.3 Arc Furnaces
5.4 Effects of Interharmonics
5.5 Reduction of Interharmonics
5.6 Flicker
5.7 Flicker Testing
5.8 Control of Flicker
5.9 Tracing Methods of Flicker and Interharmonics
5.10 Torsional Analysis
5.11 Subsynchronous Resonance
References
Chapter 6: Harmonic Reduction at the Source
6.1 Phase Multiplication
6.2 Varying Topologies
6.3 Harmonic Cancellation: Commercial Loads
6.4 Input Reactors to the PWM ASD
6.5 Active Filters
6.6 Active Current Shaping
6.7 Hybrid Connections of Active and Passive Filters
6.8 Impedance Source Inverters
6.9 Matrix Converters
6.10 Mutilevel Inverters
6.11 Switching Algorithms for Harmonic Control
6.12 Theory of Resultants of Polynomials
References
Chapter 7: Estimation and Measurements of Harmonics
7.1 Waveform without Ripple Content
7.2 Waveform with Ripple Content
7.3 Phase Angle of Harmonics
7.4 Measurements of Harmonics
7.5 Measuring Equipment
7.6 Transducers for Harmonic Measurements
7.7 Characterizing Measured Data
7.8 Probabilistic Concepts
7.9 Summation of Harmonic Vectors with Random Angles
7.10 Central Limit Theorem
7.11 Kalman Filtering
References
Chapter 8: Effects of Harmonics
8.1 Rotating Machines
8.2 Effect of Negative Sequence Currents on Synchronous Generators
8.3 Insulation Stresses
8.4 Transformers
8.5 Cables
8.6 Capacitors
8.7 Voltage Notching
8.8 EMI (Electromagnetic Interference)
8.9 Overloading of Neutral
8.10 Protective Relays and Meters
8.11 Circuit Breakers and Fuses
8.12 Telephone Influence Factor
References
Chapter 9: Harmonic Resonance
9.1 Two-Port Networks
9.2 Resonance in Series and Parallel RLC Circuits
9.3 Practical LC Tank Circuit
9.4 Reactance Curves
9.5 Foster's Networks
9.6 Harmonic Resonance
9.7 Harmonic Resonance in a Distribution System
9.8 Elusiveness of Resonance Problems
9.9 Resonance Due to Single-Tuned Filters
9.10 Switched Capacitors for Power Factor Improvement
9.11 Secondary Resonance
9.12 Multiple Resonances in a Distribution Feeder
9.13 Part-Winding Resonance in Transformer Windings
9.14 Composite Resonance
9.15 Resonance in Transmission Lines
9.16 Zero Sequence Resonance
9.17 Factors Affecting Harmonic Resonance
References
Chapter 10: Harmonic Distortion Limits According to Standards
10.1 Standards for Limitation of Harmonics
10.2 IEEE 519 Harmonic Current and Voltage Limits
10.3 Point of Common Coupling (PCC)
10.4 Applying IEEE 519 Harmonic Distortion Limits
10.5 Time Varying Characteristics of Harmonics
10.6 IEC Harmonic Current Emission Limits
10.7 Voltage Quality
10.8 Commutation Notches
10.9 Applying Limits to Practical Power Systems
References
Chapter 11: Application of Shunt Capacitor Banks
11.1 Shunt Capacitor Banks
11.2 Location of Shunt Capacitors
11.3 Ratings of Capacitors
11.4 Shunt Capacitor Bank Arrangements
11.5 Fusing
11.6 Connections of Banks
11.7 Unbalance Detection
11.8 Destabilizing Effect of Capacitor Banks
11.9 Switching Transients of Capacitor Banks
11.10 Control of Switching Transients
11.11 Switching Capacitors With Motors
11.12 Switching Devices
11.13 Switching Controls
References
Chapter 12: Modeling of System Components for Harmonic Analysis
12.1 Transmission Lines
12.2 Cables
12.3 Zero Sequence Impedance of OH Lines and Cables
12.4 Filter Reactors
12.5 Transformers
12.6 Induction Motors
12.7 Synchronous Generators
12.8 Load Models
12.9 System Impedance
12.10 Three-Phase Models
12.11 Uncharacteristic Harmonics
12.12 Converters
References
Chapter 13: Harmonic Modeling of Systems
13.1 Electrical Power Systems
13.2 Extent of Network Modeling
13.3 Impact of Loads and Generation
13.4 Short-Circuit and Fundamental Frequency Load Flow Calculations
13.5 Industrial Systems
13.6 Distribution Systems
13.7 Transmission Systems
13.8 Compensation of Transmission Lines
13.9 Commercial Buildings
13.10 Residential Loads
13.11 HVDC Transmission
References
Chapter 14: Harmonic Propagation
14.1 Harmonic Analysis Methods
14.2 Frequency Domain Analysis
14.3 Frequency Scan
14.4 Voltage Scan
14.5 Harmonic Analysis Methods
14.6 Time Domain Analysis
14.7 Sensitivity Methods
14.8 Unbalanced AC System and HVDC Link
14.9 Hybrid Frequency and Time Domain Concept
14.10 Probabilistic Concepts
14.11 Computer-Based Programs
14.12 Harmonic Analyses of a Large Industrial System
14.13 Long Transmission Line
14.14 34.5 kV UG Cable
14.15 5-Bus Transmission System
References
Chapter 15: Passive Filters
15.1 Filter Types
15.2 Single-Tuned Filters
15.3 Harmonic Filter Detuning and Unbalance
15.4 Relations in an ST Filter
15.5 Selection of
Q
Factor
15.6 Double-Tuned Filter
15.7 Bandpass Filters
15.8 Damped Filters
15.9 Type C Filter
15.10 Zero Sequence Traps
15.11 Series-Type Low-Pass Filter
15.12 Transfer Function Approach for Filter Designs
15.13 Optimization Techniques of Filter Designs
15.14 Genetic Algorithms for Filter Designs
15.15 HVDC–DC Filters
15.16 Limitations of Passive Filters
15.17 Flowchart for Design of Filters
15.18 Filter Components
15.19 Failure of Harmonic Filters
References
Chapter 16: Practical Passive Filter Designs
16.1 Study 1: Small Distribution System With Major Six-Pulse Loads
16.2 Study 2: Filters for arc Furnance Loads
16.3 Study 3: Filters for two 8000-Hp Id Fan Drives
16.4 Study 4: Double-Tuned filter on a Three-Winding Transformer
16.5 Study 5: PV Solar Generation Plant
16.6 Study 6: Impact of Harmonics at a Distance
16.7 Study 7: Wind Generation Farm
Index
Series
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Figure 1.1
Figure 1.2
Figure 1.3
Figure 1.4
Figure 1.5
Figure 1.6
Figure 1.7
Figure 1.8
Figure 1.9
Figure 1.10
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 2.7
Figure 2.8
Figure 2.9
Figure 2.10
Figure 2.11
Figure 2.12
Figure 2.13
Figure 2.14
Figure 2.15
Figure 2.16
Figure 2.17
Figure 2.18
Figure 2.19
Figure 2.20
Figure 2.21
Figure 2.22
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 3.8
Figure 3.9
Figure 3.10
Figure 3.11
Figure 3.12
Figure 3.13
Figure 3.14
Figure 3.15
Figure 3.16
Figure 3.17
Figure 3.18
Figure 3.19
Figure 3.20
Figure 3.21
Figure 3.22
Figure 3.23
Figure 3.24
Figure 3.25
Figure 3.26
Figure 3.27
Figure 3.28
Figure 3.29
Figure 3.30
Figure 3.31
Figure 3.32
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 4.9
Figure 4.10
Figure 4.11
Figure 4.12
Figure 4.13
Figure 4.14
Figure 4.15
Figure 4.16
Figure 4.17
Figure 4.18
Figure 4.19
Figure 4.20
Figure 4.21
Figure 4.22
Figure 4.23
Figure 4.24
Figure 4.25
Figure 4.26
Figure 4.27
Figure 4.28
Figure 4.29
Figure 4.30
Figure 4.31
Figure 4.32
Figure 4.33
Figure 4.34
Figure 4.35
Figure 4.36
Figure 4.37
Figure 4.38
Figure 4.39
Figure 4.40
Figure 4.41
Figure 4.42
Figure 4.43
Figure 4.44
Figure 4.45
Figure 4.46
Figure 4.47
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6
Figure 5.7
Figure 5.8
Figure 5.9
Figure 5.10
Figure 5.11
Figure 5.12
Figure 5.13
Figure 5.14
Figure 5.15
Figure 5.16
Figure 5.17
Figure 5.18
Figure 5.19
Figure 5.20
Figure 5.21
Figure 5.22
Figure 5.23
Figure 5.24
Figure 5.25
Figure 5.26
Figure 5.27
Figure 5.28
Figure 5.29
Figure 5.30
Figure 5.31
Figure 5.32
Figure 5.33
Figure 5.34
Figure 5.35
Figure 5.36
Figure 5.37
Figure 5.38
Figure 5.39
Figure 5.40
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8
Figure 6.9
Figure 6.10
Figure 6.11
Figure 6.12
Figure 6.13
Figure 6.14
Figure 6.15
Figure 6.16
Figure 6.17
Figure 6.18
Figure 6.19
Figure 6.20
Figure 6.21
Figure 6.22
Figure 6.23
Figure 6.24
Figure 6.25
Figure 6.26
Figure 6.27
Figure 6.28
Figure 6.29
Figure 6.30
Figure 6.31
Figure 6.32
Figure 6.33
Figure 6.34
Figure 7.1
Figure 7.2
Figure 7.3
Figure 7.4
Figure 7.5
Figure 7.6
Figure 7.7
Figure 7.8
Figure 7.9
Figure 7.10
Figure 7.11
Figure 7.12
Figure 7.13
Figure 7.14
Figure 7.15
Figure 7.16
Figure 7.17
Figure 7.18
Figure 7.19
Figure 7.20
Figure 7.21
Figure 7.22
Figure 7.23
Figure 7.24
Figure 7.25
Figure 7.26
Figure 7.27
Figure 7.28
Figure 7.29
Figure 7.30
Figure 7.31
Figure 7.32
Figure 8.1
Figure 8.2
Figure 8.3
Figure 8.4
Figure 8.5
Figure 8.6
Figure 8.7
Figure 8.8
Figure 8.9
Figure 8.10
Figure 8.11
Figure 8.12
Figure 8.13
Figure 8.14
Figure 8.15
Figure 8.16
Figure 8.17
Figure 8.18
Figure 8.19
Figure 8.20
Figure 8.21
Figure 8.22
Figure 8.23
Figure 9.1
Figure 9.2
Figure 9.3
Figure 9.4
Figure 9.5
Figure 9.6
Figure 9.7
Figure 9.8
Figure 9.9
Figure 9.10
Figure 9.11
Figure 9.12
Figure 9.13
Figure 9.14
Figure 9.15
Figure 9.16
Figure 9.17
Figure 9.18
Figure 9.19
Figure 9.20
Figure 9.21
Figure 9.22
Figure 9.23
Figure 9.24
Figure 9.25
Figure 9.26
Figure 9.27
Figure 9.28
Figure 9.29
Figure 9.30
Figure 9.31
Figure 9.32
Figure 9.33
Figure 9.34
Figure 9.35
Figure 9.36
Figure 9.37
Figure 9.38
Figure 9.39
Figure 10.1
Figure 10.2
Figure 10.3
Figure 10.4
Figure 10.5
Figure 10.6
Figure 10.7
Figure 10.8
Figure 10.9
Figure 11.1
Figure 11.2
Figure 11.3
Figure 11.4
Figure 11.5
Figure 11.6
Figure 11.7
Figure 11.8
Figure 11.9
Figure 11.10
Figure 11.11
Figure 11.12
Figure 11.13
Figure 11.14
Figure 11.15
Figure 11.16
Figure 11.17
Figure 11.18
Figure 11.19
Figure 11.20
Figure 11.21
Figure 11.22
Figure 11.23
Figure 11.24
Figure 11.25
Figure 11.26
Figure 11.27
Figure 11.28
Figure 11.29
Figure 12.1
Figure 12.2
Figure 12.3
Figure 12.4
Figure 12.5
Figure 12.6
Figure 12.7
Figure 12.8
Figure 12.9
Figure 12.10
Figure 12.11
Figure 12.12
Figure 12.13
Figure 12.14
Figure 12.15
Figure 12.16
Figure 12.17
Figure 12.18
Figure 12.19
Figure 12.20
Figure 12.21
Figure 12.22
Figure 12.23
Figure 12.24
Figure 12.25
Figure 12.26
Figure 12.27
Figure 12.28
Figure 12.29
Figure 13.1
Figure 13.2
Figure 13.3
Figure 13.4
Figure 13.5
Figure 13.6
Figure 13.7
Figure 13.8
Figure 13.9
Figure 13.10
Figure 13.11
Figure 13.12
Figure 13.13
Figure 13.14
Figure 13.15
Figure 13.16
Figure 13.17
Figure 13.18
Figure 13.19
Figure 13.20
Figure 13.21
Figure 13.22
Figure 14.1
Figure 14.2
Figure 14.3
Figure 14.4
Figure 14.5
Figure 14.6
Figure 14.7
Figure 14.8
Figure 14.9
Figure 14.10
Figure 14.11
Figure 14.12
Figure 14.13
Figure 14.14
Figure 14.15
Figure 14.16
Figure 14.17
Figure 14.18
Figure 14.19
Figure 14.20
Figure 14.21
Figure 14.22
Figure 14.23
Figure 14.24
Figure 14.25
Figure 14.26
Figure 14.27
Figure 14.28
Figure 14.29
Figure 14.30
Figure 14.31
Figure 14.32
Figure 14.33
Figure 14.34
Figure 14.35
Figure 14.36
Figure 14.37
Figure 14.40
Figure 14.41
Figure 14.44
Figure 14.45
Figure 14.46
Figure 14.47
Figure 14.48
Figure 14.49
Figure 14.50
Figure 14.51
Figure 14.52
Figure 15.1
Figure 15.2
Figure 15.3
Figure 15.4
Figure 15.5
Figure 15.6
Figure 15.7
Figure 15.8
Figure 15.9
Figure 15.10
Figure 15.11
Figure 15.12
Figure 15.13
Figure 15.14
Figure 15.15
Figure 15.16
Figure 15.17
Figure 15.18
Figure 15.19
Figure 15.20
Figure 15.21
Figure 15.22
Figure 15.23
Figure 15.24
Figure 15.25
Figure 15.26
Figure 15.27
Figure 15.28
Figure 15.29
Figure 15.30
Figure 15.31
Figure 16.1
Figure 16.2
Figure 16.3
Figure 16.4
Figure 16.5
Figure 16.6
Figure 16.7
Figure 16.8
Figure 16.9
Figure 16.10
Figure 16.11
Figure 16.12
Figure 16.13
Figure 16.14
Figure 16.15
Figure 16.17
Figure 16.18
Figure 16.19
Figure 16.20
Figure 16.21
Figure 16.22
Figure 16.23
Figure 16.24
Figure 16.25
Figure 16.26
Figure 16.27
Figure 16.28
Figure 16.29
Figure 16.30
Figure 16.31
Figure 16.32
Figure 16.33
Figure 16.34
Figure 16.35
Figure 16.36
Figure 16.37
Figure 16.38
Figure 16.39
Figure 16.40
Figure 16.41
Figure 16.42
Figure 16.43
Figure 16.44
Figure 16.45
Figure 16.46
Figure 16.47
Figure 16.48
Figure 16.49
Figure 16.50
Figure 16.51
Figure 16.52
Figure 16.53
Figure 16.54
Figure 16.55
Figure 16.56
Figure 16.57
Figure 16.58
Figure 16.59
Figure 16.60
Figure 16.61
List of Tables
Table 1.1
Table 1.2
Table 1.3
Table 1.4
Table 1.5
Table 1.6
Table 1.7
Table 2.1
Table 2.2
Table 3.1
Table 3.2
Table 3.3
Table 3.4
Table 3.5
Table 3.6
Table 4.1
Table 4.2
Table 4.3
Table 4.4
Table 4.5
Table 4.6
Table 4.7
Table 4.8
Table 4.9
Table 4.10
Table 4.11
Table 4.12
Table 5.1
Table 5.2
Table 5.3
Table 5.4
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 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
Table 8.1
Table 8.2
Table 8.3
Table 8.4
Table 8.5
Table 8.6
Table 8.7
Table 8.8
Table 8.9
Table 8.10
Table 8.11
Table 8.12
Table 8.13
Table 8.14
Table 8.15
Table 9.1
Table 9.2
Table 9.3
Table 9.4
Table 10.1
Table 10.2
Table 10.3
Table 10.4
Table 10.5
Table 10.6
Table 10.7
Table 10.8
Table 10.9
Table 10.10
Table 10.11
Table 10.12
Table 10.13
Table 10.14
Table 10.15
Table 11.1
Table 11.2
Table 11.3
Table 11.4
Table 11.5
Table 11.6
Table 12.1
Table 12.2
Table 12.3
Table 12.4
Table 12.5
Table 12.6
Table 12.7
Table 13.1
Table 13.2
Table 13.3
Table 13.4
Table 14.1
Table 14.2
Table 14.3
Table 14.4
Table 14.5
Table 14.6
Table 14.7
Table 14.8
Table 14.9
Table 14.10
Table 14.11
Table 14.12
Table 14.13
Table 14.14
Table 14.15
Table 14.16
Table 14.17
Table 14.18
Table 14.19
Table 14.20
Table 14.21
Table 14.22
Table 14.23
Table 15.1
Table 15.2
Table 15.3
Table 16.1
Table 16.2
Table 16.3
Table 16.4
Table 16.5
Table 16.6
Table 16.7
Table 16.8
Table 16.9
Table 16.10
Table 16.11
Table 16.12
Table 16.13
Table 16.14
Table 16.15
Table 16.16
Table 16.17
Table 16.18
Table 16.19
Table 16.20
Table 16.21
Table 16.22
Table 16.23
Table 16.24
Table 16.25
Table 16.26
Power System Harmonics and Passive Filter Designs
J.C. Das
Copyright © 2015 by The Institute of Electrical and Electronics Engineers, Inc.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved
Published simultaneously in Canada
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Library of Congress Cataloging-in-Publication Data:
Das, J. C., 1934-
Power system harmonics and passive filter design / J. C. Das.
pages cm
ISBN 978-1-118-86162-2 (hardback)
1. Electric power system stability. 2. Harmonics (Electric waves) 3. Electric filters, Passive. I. Title.
TK1010.D37 2015
621.31′7–dc23
2014034588
Foreword
Dr. Jean Mahseredjian
Thisx.1 book on power system harmonics and passive filter designs is a comprehensive resource on this subject, covering harmonic generation, mitigation, measurement and estimation, limitations according to IEEE and IEC standards, harmonic resonance, formation of shunt capacitor banks, modeling of power system components and systems. Harmonic penetration in the power systems, passive filters, and typical study cases, covering renewable energy sources – solar and wind power generation – are included. There are many aspects of harmonics discussed in this book, which are not covered in the current publications.
The following is a chapter-wise summary of the book content.
Chapter 1 forms a background on the subject of power system harmonics with discussions of harmonic indices and power theories. The coverage of nonsinusoidal single-phase and three-phase systems and popular instantaneous power theory of H. Akagi and A. Nabe, much used for active filter designs discussed later on in the book, leads a reader to understand the nonlinearity.
The second chapter on Fourier analysis, though much mathematical, paves the way for the applications to harmonic analysis and measurements with limitations of window functions. The examples given in the chapter help the readers to understand the transformations.
Harmonic generation from conventional power equipment, ferroresonance, and electronically switched devices, converters, home appliances, cycloconverters, PWM, voltage source converters, switch mode power supplies, wind farm generation, pulse burst modulation, chopper circuits, traction and slip recovery schemes, are well described in Chapters 3 and 4. A reader will find an interesting analysis of transformer modeling, third harmonic voltages in generators, and many EMTP simulations. Harmonics due to saturation of current transformers is an added feature. Chapter 4 is fairly exhaustive and includes harmonic generation from many sources of practical importance. The analysis and topologies of ASDs (adjustable speed drives) are well documented. Though the author provides some background, yet a reader must be conversant with elements of power electronics.
Interharmonics is a new field of research, and Chapter 5 is well written so as to provide a reader a clear concept of interharmonic generation and their effects. This is followed by a well-written work on flicker from arcing loads, arcing and induction furnaces, and tracing methods of flicker. The control of flicker through the application of a STATCOM followed by torsional analysis due to harmonics in large drives with graphics is one problem that is not so well addressed in current texts. The subsynchronous resonance in series compensated HV transmission lines and drive system cascades, with EMTP simulation results, will be of interest to special readers interested in this field.
Having discussed the generation of harmonics in previous chapters, Chapter 6 is logically placed to discuss the various strategies that can be adopted to reduce the harmonics at source itself, so that harmonic penetration in the power systems is avoided. This covers active filters, combination of active and passive filters, their controls, active current shaping matrix converters, multilevel inverters, THMI inverters and theory of harmonic reduction at source, new breed of matrix and multilevel converters, followed with the theory of the resultant of polynomials. Then, the demonstration of this theory and control of switching angles is demonstrated to reduce harmonic distortion to a very low level. Some sections of this chapter will need a prior understanding of many aspects of converters and their switching, and on first reading the mathematical treatment cannot be easily followed by an average reader. The author provides excellent references at each step for further reading.
The calculations, estimation, time stamp of harmonics are the first step before a model can be generated for study. The relevance of modeling angles of the harmonics, measuring equipment, transducers, analysis of various waveforms will be of interest to all readers, while probabilistic concepts, regression methods, Kalman filtering, and so on will be of special interest. The author provides fundamental aspects leading to these advanced concepts.
The effects of harmonics can be very deleterious on electrical power equipment, Chapter 8. Practically all power system equipment of interest, motors, insulation stresses, and traveling wave phenomena on drive system cables, common mode voltages, bearing currents, protective relaying, circuit breakers, and the like are covered. Of special interest to a reader will be derating of dry and liquid-filled transformers serving nonlinear loads, which at times may be ignored, resulting in overloads.
After this background is grasped, harmonic resonance in various forms is discussed in Chapter 9. The reactance curves, Foster networks, composite resonance, secondary resonance are illustrated, which are commonly missing topics in other texts.
The limits of harmonic distortions in Chapter 10 cover both, IEEE and IEC guidelines, with limits on interharmonics and calculations of effects of notching on harmonic distortions.
In the design of passive filters, formation of shunt capacitor banks and their grounding and protection is an important aspect, Chapter 11. Often failures on harmonic filters occur due to improper selection of the ratings of unit capacitors forming the bank, as well as ignoring their protection and switching transients. The importance of this chapter cannot be overstated for a reader involved in harmonic filter designs.
The next step in harmonic analysis is accurate modeling of power system components and power systems, depending on their nature and extent of study, which is detailed in Chapters 12 and 13. These two chapters form the backbone of harmonic analysis. The modeling described for transmission lines, transformers, loads, cables, motors, generators, and converters in Chapter 12 is followed by system modeling in industrial, distribution, and transmission systems and HVDC, which are the aspects that should be clearly grasped by a reader interested in harmonics.
Study of harmonic penetration discussed in Chapter 14 can be undertaken after the material in the previous chapters is grasped. Apart from time and frequency domain methods, the chapter covers the latest aspects of probabilistic modeling.
It may seem that in the entire book only one chapter, Chapter 15, is devoted to passive filters. However, harmonic filter designs may be called the last link of the long chain of harmonic studies. The chapter describes practically all types of passive filters commonly applied in the industry, with some new technologies such as genetic algorithms and particle swarm theories.
Lastly, Chapter 16 has many real-world studies of harmonic analysis and filters designs, including arc furnaces, transmission systems, solar and wind generation plants. A reader with adequate modeling tools and software can duplicate these studies and it will be a tremendous exercise in learning.
I conclude that the book is well written and should appeal to beginners and advanced readers, in fact, this can become a standard reference book on harmonics. Many solved examples and real-world simulations of practical systems enhance the understanding. The book is well illustrated with relevant figures in each chapter.
x.1
Dr. Jean Mahseredjian is an IEEE-Fellow and Professor of Electrical Engineering at École Polytechnique de Montréal, Montréal, Québec, Canada. He is world renowned authority on the simulation and analysis of electromagnetic transients. He was also a member of IEEE working groups on Power System Harmonics.
Preface
The power system harmonics is a subject of continuous research; this book attempts to present the state-of-art technology and advancements. It is a subject of interest of many power system professionals engaged in harmonic analysis and mitigation and the applications in the modern climate when the nonlinear loads in the utility systems are on the increase.
The book provides a comprehensive coverage of generation, effects, and control of harmonics. New harmonic mitigation technologies, detailed step-by-step design of passive filters, interharmonics, and flicker are covered. The intention is that the book can serve as a reference and practical guide on harmonics.
A beginner should be able to form a clear base for understanding the subject of harmonics, and an advanced reader's interest should be simulated to explore further. A first reading of the book followed by a detailed critical reading is suggested. The many real-world study cases, examples, and graphics strive for this objective and provide clear understanding. The subject of harmonics may not form a curriculum even for graduate studies in many universities. In writing this book, an undergraduate level of knowledge is assumed; yet, the important aspects with respect to connectivity of each chapter are not lost sight of. It has the potentiality of serving as advance undergraduate and graduate textbook. Surely, it can serve as continuing education textbook and supplementary reading material.
The effects of harmonics can be experienced at a distance, and the effect on power system components is a dynamic and evolving field. These interactions have been analyzed in terms of current thinking.
The protective relaying has been called “an art and science.” The author will not hesitate to call the passive harmonic filter designs and mitigation technologies the same. This is so because much subjectivity is involved. Leaving aside high-technology research tools such as Monte Carlo simulations, the available computer techniques invariably require iterative studies to meet a number of conflicting objectives.
A first reading of the book will indicate that the reader must understand the nature of harmonics, modeling of power system components, and characteristics of filters, before attempting a practical filter design for real-world applications. Chapter 16 is devoted to practical harmonic passive filter designs and case studies including solar and wind generation. A reader can modal and reproduce the results and get a “feel” of the complex iterative and analytical procedures.
The author acknowledges with thanks permission for republication of some work from his book: Power System Analysis: Short-Circuit Load Flow and Harmonics, CRC Press.
J.C. Das
About The Author
J.C. Das is principal and consultant with Power System Studies, Inc. Snellville, Georgia. He headed the Power System Analysis department at AMEC, Inc. for many years. He has varied experience in the utility industry, industrial establishments, hydroelectric generation, and atomic energy. He is a specialist in performing power system studies, including short circuit, load flow, harmonics, stability, arc flash hazard, grounding, switching transients, and protective relaying. He conducts courses for continuing education in power systems and has authored or coauthored about 65 technical publications nationally and internationally. He is the author of the following books:
Arc Flash Hazard Analysis and Mitigation
, IEEE Press, 2012.
Transients in Electrical Systems: Analysis Recognition and Mitigation
, McGraw-Hill, 2010
Power System Analysis: Short-Circuit Load Flow and Harmonics, Second Edition
, CRC Press, 2011.
These books provide extensive converge, running into more than 2400 pages and are well received in the technical circles. His interests include power system transients, EMTP simulations, harmonics, power quality, protection, and relaying. He has published 200 study reports on electrical power system for his clients.
Related to harmonic analysis, Mr. Das has designed some large harmonic passive filters in the industry, which are in successful operation for more than 18 years.
Mr. Das is a Life Fellow of Institute of Electrical and Electronics Engineers, IEEE (United States), Member of the IEEE Industry Applications and IEEE Power Engineering societies, a Fellow of Institution of Engineering Technology (United Kingdom), a Life Fellow of the Institution of Engineers (India), a Member of the Federation of European Engineers (France), and a member of CIGRE (France). He is a registered Professional Engineer in the States of Georgia and Oklahoma, a Chartered Engineer (C. Eng.) in the United Kingdom and a European Engineer (Eur. Ing.) in the Europe. He received meritorious award in engineering, IEEE Pulp and Paper Industry in 2005.
He received MSEE degree from the Tulsa University, Tulsa, Oklahoma, and BA (advanced mathematics) and BEE degrees from the Punjab University, India.
Chapter 1Power System Harmonics
The electrical power systems should be designed not only for the sinusoidal currents and voltages but also for nonlinear and electronically switched loads. There has been an increase in such loads in the recent times, and these can introduce harmonic pollution, distort current and voltage waveforms, create resonances, increase the system losses, and reduce the useful life of the electrical equipment. Harmonics are one of the major problems of ensuring a certain power quality. This requires a careful analysis of harmonic generation and their measurements and the study of the deleterious effects, harmonic controls, and limitation to acceptable levels. Interest in harmonic analysis dates back to the early 1990s in connection with high voltage DC (HVDC) systems and static var compensators (SVC; Reference [1]). The analytical and harmonic limitation technology has progressed much during this period (see Reference [2] for a historical overview of the harmonics in power systems).
DC power is required for a number of applications from small amount of power for computers, video equipment, battery chargers, UPS (uninterrptible power supplies) systems to large chunks of power for electrolysis, DC drives, and the like. A greater percentage of office and commercial building loads are electronic in nature, which have DC as the internal operating voltage. Fuel and solar cells and batteries can be directly connected to a DC system, and the double conversion of power from DC to AC and then from AC to DC can be avoided. A case study conducted by Department of Electrical Power Engineering, Chalmers University of Technology, Gothenburg, Sweden is presented in [3]. This compares reliability, voltage drops, cable sizing, grounding and safety: AC verses DC distribution system. In Reference [4], DC shipboard distribution system envisaged by US Navy is discussed. Two steam turbine synchronous generators are connected to 7000 V DC bus through rectifiers, and DC loads are served through DC–DC converters. However, this is not a general trend, bulk and consumer power distribution systems are AC; and we will not be discussing industrial or commercial DC distribution systems in this book, except that HVDC converter interactions with respect to harmonics and DC filters are of interest and discussed in the appropriate chapters.
Harmonics in power systems originate due to varied operations, for example, ferroresonance, magnetic saturation, subsynchronous resonance, and nonlinear and electronically switched loads. Harmonic emission from nonlinear loads predominates.
1.1 Nonlinear Loads
To distinguish between linear and nonlinear loads, we may say that linear time-invariant loads are characterized so that an application of a sinusoidal voltage results in a sinusoidal flow of current. These loads display constant steady-state impedance during the applied sinusoidal voltage. Incandescent lighting is an example of such a load. The electrical motors not supplied through electronic converters also approximately meet this definition. The current or voltage waveforms will be almost sinusoidal, and their phase angles displaced depending on power factor of the electrical circuit. Transformers and rotating machines, under normal loading conditions, approximately meet this definition. Yet, it should be recognized that flux wave in the air gap of a rotating machine is not sinusoidal. Tooth ripples and slotting in rotating machines produce forward and reverse rotating harmonics. Magnetic circuits can saturate and generate harmonics. Saturation in a transformer on abnormally high voltage produces harmonics, as the relationship between magnetic flux density and the magnetic field intensity in a magnetic material (the transformer core) is not linear. Yet, the harmonics emissions from these sources are relatively small (Chapter 3).
In a nonlinear device, the application of a sinusoidal voltage does not result in a sinusoidal flow of current. These loads do not exhibit constant impedance during the entire cycle of applied sinusoidal voltage. Nonlinearity is not the same as the frequency dependence of impedance, that is, the reactance of a reactor changes in proportion to the applied frequency, but it is linear at each applied frequency if we neglect saturation and fringing. However, nonlinear loads draw a current that may even be discontinuous or flow in pulses for a part of the sinusoidal voltage cycle.
Mathematically, linearity implies two conditions:
Homogeneity
Superposition
Consider the state of a system defined in the state equation form:
If is the solution to this differential equation with initial conditions at and input ,:
then homogeneity implies that
where is a scalar constant. This means that with input is equal to times with input for any scalar .
Superposition implies that
That is, with inputs is equal to the sum of with input and with input .Thus, linearity is superimposition plus homogeneity.
1.2 Increases in Nonlinear Loads
Nonlinear loads are continuously on the increase. It is estimated that, during the next 10 years, more than 60% of the loads on utility systems will be nonlinear. Also much of the electronic load growth involves residential sector and household appliances. Concerns for harmonics originate from meeting a certain power quality, which leads to the related issues of (1) effects on the operation of electrical equipment, (2) harmonic analysis, and (3) harmonic control. A growing number of consumer loads are sensitive to poor power quality, and it is estimated that power quality problems cost US industry tens of billion of dollars per year. Although the expanded use of consumer automation equipment and power electronics is leading to higher productivity, these heavy loads are a source of electrical noise and harmonics and are less tolerant to poor power quality. For example, adjustable speed drives (ASDs) are less tolerant to voltage sags and swells as compared to an induction motor; and a voltage dip of 10% of certain time duration may precipitate ASD shutdown. These generate line harmonics and a source containing harmonics impacts their operation, leading to further generation of harmonics. This implies that the nonlinear loads which are a source of generation of harmonics are themselves relatively less tolerant to the poor power quality that originates from harmonic emission from these loads.
Some examples of nonlinear loads are as follows:
ASD systems
Cycloconverters
Arc furnaces
Rolling mills
Switching mode power supplies
Computers, copy machines, television sets, and home appliances
Pulse burst modulation
Static var compensators (SVCs)
Thyristor-controlled reactors (TCRs)
HVDC transmission, harmonics originate in converters
Electric traction, chopper circuits
Wind and solar power generation
Battery charging and fuel cells
Slip frequency recovery schemes of induction motors
Fluorescent lighting and electronic ballasts
Electrical vehicle charging systems
Silicon-controlled rectifier (SCR) heating, induction heating, and arc welding.
The harmonics are also generated in conventional power equipment, such as transformer and motors. Saturation and switching of transformers generate harmonics. The harmonic generation is discussed in Chapters 3–5. The application of capacitor banks for power factor corrections and reactive power support can cause resonance and further distortions of waveforms (Chapter 9). Earlier rotating synchronous condensers have been replaced with modern shunt capacitors or SVCs (Chapter 4).
1.3 Effects of Harmonics
Harmonics cause distortions of the voltage and current waveforms, which have adverse effects on electrical equipment. The estimation of harmonics from nonlinear loads is the first step in a harmonic analysis, and this may not be straightforward. There is an interaction between the harmonic producing equipment, which can have varied topologies, and the electrical system. Over the course of years, much attention has been focused on the analysis and control of harmonics, and standards have been established for permissible harmonic current and voltage distortions (Chapter 10). The effects of harmonics are discussed in Chapter 8.
1.4 Distorted Waveforms
Harmonic emissions can have varied amplitudes and frequencies. The most common harmonics in power systems are sinusoidal components of a periodic waveform, which have frequencies that can be resolved into some multiples of the fundamental frequency. Fourier analysis is the mathematical tool employed for such analysis, and Chapter 2 provides an overview.
The components in a Fourier series that are not an integral multiple of the power frequency are called noninteger harmonics (Chapter 5).
The distortion produced by nonlinear loads can be resolved into a number of categories:
A distorted waveform having a Fourier series with fundamental frequency equal to power system frequency and a periodic steady state exists. This is the most common case in harmonic studies. The waveform shown in Fig. 1.1 is synthesized from the harmonics shown in Table 1.1. The waveform in Fig. 1.1 is symmetrical about the x-axis and can be described by the equation:
Figure 1.1 Simulated waveform of the harmonic spectrum shown in Table 1.1.
Table 1.1 Harmonic Content of the Waveform in Fig. 1.1
h
5
7
11
13
17
19
23
%
17
12
11
5
2.8
1.5
0.5
orders shown in percentage of fundamental current.
Chapter 4 shows that this waveform is typically of a six-pulse current source converter, harmonics limited to 23rd, though higher harmonics will be present. The harmonic emission varies over wide range of distorted waveforms. Figure 1.2 shows a typical waveform for HVDC link, DC drives, and a six-pulse voltage source inverter (VSI) ASD, Ref. [1]. Chapter 4 studies typical waveforms and distortions from various types of power electronic switching equipment. This is the most common situation in practice, and the distorted waveforms can be decomposed into a number of harmonics. The system can usually be modeled as a linear system.
A distorted waveform having a submultiple of power system frequency and a periodic steady state exists. Certain types of pulsed loads and integral cycle controllers produce these types of waveforms (Chapters
4
and
5
).
The waveform is aperiodic, but perhaps almost periodic. A trigonometric series expansion may still exist. Examples are arcing devices: arc furnaces, fluorescent, mercury, and sodium vapor lighting. The process is not periodic in nature, and a periodic waveform is obtained if the conditions of operation are kept constant for a length of time. Consider the current signature of an arc furnace during scrap melting (
Fig. 1.3
). The waveform is highly distorted and aperiodic. Yet, typical harmonic emissions from arc furnace during melting and refining have been defined in IEEE standard 519 [5].
Figure 1.2 Typical line current waveforms of HVDC, DC drive, and six-pulse ASD.
Figure 1.3 Erratic current signature of an electric arc furnace during scrap melting.
The arc furnace loads are highly polluting and cause phase unbalance, flicker, impact loading, harmonics, interharmonics, and resonance, and may give rise to torsional vibrations in rotating equipment.
1.4.1 Harmonics and Power Quality
Harmonics are one of the major power quality concerns. The power quality concerns embrace much wider concerns such as voltage sags and swells, transients, under and overvoltages, frequency variations, outright interruptions, power quality for sensitive electronic equipment such as computers. Table 3.1 summarizes some power quality problems. A reference of importance is IEEE Recommended Practice for Emergency and Standby Power Systems for Industrial and Commercial Applications, [6]. This book is not about power quality; however, some important publications are separately listed in References for the interested readers.
1.5 Harmonics and Sequence Components
The theory of sequence components is not discussed in this book and references [7–10] may be seen. In a three-phase balanced system under nonsinusoidal conditions, the -order harmonic voltage (or current) can be expressed as
Based on Eqs. (1.5–1.7) and counterclockwise rotation of the fundamental phasors, we can write
Under balanced conditions, the harmonic (frequency of times the fundamental frequency) of phase lags times behind that of the same harmonic in phase . The harmonic of phase lags times behind that of the same harmonic in phase . In the case of triplen harmonics, shifting the phase angles by three times or three times results in cophasial vectors.
Table 1.2 shows the sequence of harmonics, and the pattern is clearly positive–negative–zero. We can write
All triplen harmonics generated by nonlinear loads are zero sequence phasors. These add up in the neutral. In a three-phase four-wire system, with perfectly balanced single-phase loads between the phase and neutral, all positive and negative sequence harmonics will cancel out leaving only the zero sequence harmonics.
Table 1.2 Harmonic Order and Rotation
Harmonic Order
Forward
Reverse
Fundamental
x
2
x
4
x
5
x
7
x
8
x
10
x
11
x
13
x
14
x
16
x
17
x
19
x
20
x
22
x
23
x
25
x
26
x
28
x
29
x
31
x
Note: The pattern is repeated for higher order harmonics.
In an unbalanced three-phase system, serving single-phase load, the neutral carries zero sequence and the residual unbalance of positive and negative sequence currents. Even harmonics are absent in the line because of phase symmetry (Chapter 2), and unsymmetrical waveforms will add even harmonics to the phase conductors, for example, half-controlled three-phase bridge circuit discussed in Chapter 4.
1.5.1 Sequence Impedances of Power System Components
Positive, negative, and zero sequence impedances vary over large limits, depending on the power system equipment. For example, for transformers, positive and negative sequence impedances may be considered equal, but zero sequence impedance can be infinite depending on transformer winding connections and grounding. The zero sequence impedance of transmission lines can be two to three times that of the positive or negative sequence impedance. Even for fundamental frequency current flow, the accurate modeling of sequence impedances is important and the sequence impedances to harmonics must be modeled (Chapter 12).
1.6 Harmonic Indices
1.6.1 Harmonic Factor
An index of merit has been defined as a harmonic distortion factor [5] (harmonic factor). It is the ratio of the root mean square of the harmonic content to the root mean square value of the fundamental quantity, expressed as a percentage of the fundamental:
The most commonly used index, total harmonic distortion (THD), which is in common use is the same as .
1.6.2 Equations for Common Harmonic Indices
We can write the following equations.
RMS voltage in presence of harmonics can be written as
And similarly, the expression for the current is
The total distortion factor for the voltage is
where is the fundamental frequency voltage. This can be written as
or
Similarly,
where is the fundamental frequency current.
The total demand distortion (TDD) is defined as
where is the load demand current.
The partial weighted harmonic distortion (PWHD) of current is defined as
Similar expression is applicable for the voltage. The PWHD evaluates influence of current or voltage harmonics of higher order. The sum parameters are calculated with single harmonic current components .
1.6.3 Telephone Influence Factor
Harmonics generate telephone Influence through inductive coupling. The telephone influence factor (TIF) for a voltage or current wave in an electrical supply circuit is the ratio of the square root of the sum of the squares of the weighted root mean square values of all the sine wave components (including AC waves both fundamental and harmonic) to the root mean square value (unweighted) of the entire wave:
where is the single frequency rms current at frequency , is the single frequency TIF weighting at frequency . The voltage can be substituted for current. This definition may not be so explicit, see example in Chapter 8 for calculation. A similar expression can be written for voltage.
IT product is the inductive influence expressed in terms of the product of its root mean square magnitude I in amperes times its TIF.
kVT product is the inductive influence expressed in terms of the product of its root mean square magnitude in kV times its TIF.
The telephone weighting factor that reflects the present C message weighting and the coupling normalized to 1 kHz is given by:
where message weighting at frequency under consideration. See Section 8.12 for further details.
1.7 Power Factor, Distortion Factor, and Total Power Factor
For sinusoidal voltages and currents, the power factor is defined as kW/kVA and the power factor angle is
The power factor in presence of harmonics comprises two components: displacement and distortion. The effect of the two is combined in total power factor. The displacement component is the ratio of active power of the fundamental wave in watts to apparent power of fundamental wave in volt-amperes. This is the power factor as seen by the watt-hour and var-hour meters. The distortion component is the part that is associated with harmonic voltages and currents.
At fundamental frequency the displacement power factor will be equal to the total power factor, as the displacement power factor does not include kVA due to harmonics, while the total power factor does include it. For harmonic generating loads, the total power factor will always be less than the displacement power factor.
Continuing with the relation between power factor and displacement factor, the power factor of a converter with DC-link reactor is given by the expression from IEEE 519, Ref. [5]:
where is the number of converter pulses and is the angle in radians (see Chapter 4). This ignores commutation overlap and no-phase overlap, and neglects transformer magnetizing current. For a six-pulse converter, the maximum power factor is . A 12-pulse converter has a theoretical maximum power factor of 0.988. The power factor drops drastically with the increase in firing angle.
