J.C. Das is a consultant of electrical power systems at Power Systems Studies, Inc., USA. He is Life Fellow of IEEE (UK), Fellow of IET (India), and has authored approximately sixty technical papers and published 190 study reports of real-world power systems. He is the author of three books including ARC Flash Hazard Analysis and Mitigation. He is a registered P.E. in the states of Georgia and Oklahoma, C.Eng. in UK, and Eur Ing in Europe. J. C. Das is also a member of CIGRE, Federation of European Engineers, and other technical associations and organizations.

“Students and professionals will definitely find this book an essential resource that will be referenced for many years.”  (IEEE Electrical Engineering magazine, 1 January 2016)

• FOREWORD xvPREFACE xixABOUT THE AUTHOR xxiCHAPTER 1 POWER SYSTEM HARMONICS 11.1 Nonlinear Loads 21.2 Increases in Nonlinear Loads 31.3 Effects of Harmonics 41.4 Distorted Waveforms 41.5 Harmonics and Sequence Components 71.6 Harmonic Indices 91.7 Power Factor, Distortion Factor, and Total Power Factor 111.8 Power Theories 131.9 Amplification and Attenuation of Harmonics 27References 28CHAPTER 2 FOURIER ANALYSIS 312.1 Periodic Functions 312.2 Orthogonal Functions 312.3 Fourier Series and Coefficients 332.4 Odd Symmetry 352.5 Even Symmetry 362.6 Half-Wave Symmetry 372.7 Harmonic Spectrum 412.8 Complex form of Fourier Series 412.9 Fourier Transform 432.10 Dirichlet Conditions 522.11 Power Spectrum of a Function 542.12 Convolution 562.13 Sampled Waveform: Discrete Fourier Transform 572.14 Fast Fourier Transform 64References 69CHAPTER 3 HARMONIC GENERATION-1 713.1 Harmonics in Transformers 713.2 Energization of a Transformer 793.3 Delta Windings of Three-Phase Transformers 823.4 Harmonics in Rotating Machine Windings 923.5 Cogging and Crawling of Induction Motors 973.6 Synchronous Generators 1023.7 Saturation of Current Transformers 1043.8 Ferroresonance 1053.9 Power Capacitors 1113.10 Transmission Lines 112References 112CHAPTER 4 HARMONIC GENERATION-II 1154.1 Static Power Converters 1154.2 Single-Phase Bridge Circuit 1154.3 Reactive Power Requirements of Converters 1224.4 Three-Phase Bridge Circuit 1244.5 Harmonics on Output (DC) Side 1334.6 Inverter Operation 1354.7 Diode Bridge Converters 1394.8 Switch-Mode Power (SMP) Supplies 1424.9 Home Appliances 1434.10 Arc Furnaces 1444.11 Cycloconverters 1474.12 Thyristor-Controlled Reactor 1504.13 Pulse Width Modulation 1544.14 Voltage Source Converters 1584.15 Wind Power Generation 1624.16 Fluorescent Lighting 1654.17 Adjustable Speed Drives 1674.18 Pulse Burst Modulation 1744.19 Chopper Circuits and Electric Traction 1754.20 Slip Frequency Recovery Schemes 1774.21 Power Semiconductor Devices 178References 181CHAPTER 5 INTERHARMONICS AND FLICKER 1835.1 Interharmonics 1835.2 Sources of Interharmonics 1835.3 Arc Furnaces 1925.4 Effects of Interharmonics 1965.5 Reduction of Interharmonics 1985.6 Flicker 1985.7 Flicker Testing 2025.8 Control of Flicker 2055.9 Tracing Methods of Flicker and Interharmonics 2085.10 Torsional Analysis 2105.11 Subsynchronous Resonance 217References 225CHAPTER 6 HARMONIC REDUCTION AT THE SOURCE 2296.1 Phase Multiplication 2306.2 Varying Topologies 2306.3 Harmonic Cancellation: Commercial Loads 2326.4 Input Reactors to the PWM ASDs 2356.5 Active Filters 2376.6 Active Current Shaping 2486.7 Hybrid Connections of Active and Passive Filters 2516.8 Impedance Source Inverters 2556.9 Matrix Converters 2596.10 Mutilevel Inverters 2626.11 Switching Algorithms for Harmonic Control 2706.12 Theory of Resultants of Polynomials 271References 277CHAPTER 7 ESTIMATION AND MEASUREMENTS OF HARMONICS 2817.1 Waveform without Ripple Content 2827.2 Waveform with Ripple Content 2887.3 Phase Angle of Harmonics 2987.4 Measurements of Harmonics 3047.5 Measuring Equipment 3097.6 Transducers for Harmonic Measurements 3127.7 Characterizing Measured Data 3147.8 Probabilistic Concepts 3167.9 Summation of Harmonic Vectors with Random Angles 3237.10 Central Limit Theorem 3267.11 Kalman Filtering 326References 329CHAPTER 8 EFFECTS OF HARMONICS 3318.1 Rotating Machines 3328.2 Effect of Negative Sequence Currents on Synchronous Generators 3358.3 Insulation Stresses 3378.4 Transformers 3458.5 Cables 3598.6 Capacitors 3618.7 Voltage Notching 3628.8 EMI (Electromagnetic Interference) 3638.9 Overloading of Neutral 3678.10 Protective Relays and Meters 3698.11 Circuit Breakers and Fuses 3728.12 Telephone Influence Factor 372References 377CHAPTER 9 HARMONIC RESONANCE 3799.1 Two-Port Networks 3799.2 Resonance in Series and Parallel RLC Circuits 3839.3 Practical LC Tank Circuit 3919.4 Reactance Curves 3969.5 Foster's Networks 3979.6 Harmonic Resonance 4009.7 Harmonic Resonance in a Distribution System 4049.8 Elusiveness of Resonance Problems 4059.9 Resonance Due to Single-Tuned Filters 4089.10 Switched Capacitors for Power Factor Improvement 4109.11 Secondary Resonance 4119.12 Multiple Resonances in a Distribution Feeder 4159.13 Part-Winding Resonance in Transformer Windings 4169.14 Composite Resonance 4199.15 Resonance in Transmission Lines 4219.16 Zero Sequence Resonance 4219.17 Factors Affecting Harmonic Resonance 423References 424CHAPTER 10 HARMONIC DISTORTION LIMITS ACCORDING TO STANDARDS 42710.1 Standards for Limitation of Harmonics 42710.2 IEEE 519 Harmonic Current and Voltage Limits 42910.3 Point of Common Coupling (PCC) 43210.4 Applying IEEE 519 Harmonic Distortion Limits 43310.5 Time Varying Characteristics of Harmonics 43510.6 IEC Harmonic Current Emission Limits 43610.7 Voltage Quality 44010.8 Commutation Notches 44410.9 Applying Limits to Practical Power Systems 449References 450CHAPTER 11 APPLICATION OF SHUNT CAPACITOR BANKS 45311.1 Shunt Capacitor Banks 45311.2 Location of Shunt Capacitors 45811.3 Ratings of Capacitors 45911.4 Shunt Capacitor Bank Arrangements 46511.5 Fusing 46811.6 Connections of Banks 47611.7 Unbalance Detection 47911.8 Destabilizing Effect of Capacitor Banks 48111.9 Switching Transients of Capacitor Banks 48311.10 Control of Switching Transients 48611.11 Switching Capacitors with Motors 48911.12 Switching Devices 49011.13 Switching Controls 498References 501CHAPTER 12 MODELING OF SYSTEM COMPONENTS FOR HARMONIC ANALYSIS 50312.1 Transmission Lines 50312.2 Cables 53212.3 Zero Sequence Impedance of OH Lines and Cables 53812.4 Filter Reactors 53912.5 Transformers 54012.6 Induction Motors 55412.7 Synchronous Generators 55612.8 Load Models 55712.9 System Impedance 55912.10 Three-Phase Models 56112.11 Uncharacteristic Harmonics 56312.12 Converters 564References 566CHAPTER 13 HARMONIC MODELING OF SYSTEMS 56913.1 Electrical Power Systems 56913.2 Extent of Network Modeling 57213.3 Impact of Loads and Generation 57313.4 Short-Circuit and Fundamental Frequency Load Flow Calculations 57413.5 Industrial Systems 57813.6 Distribution Systems 58213.7 Transmission Systems 58913.8 Compensation of Transmission Lines 59313.9 Commercial Buildings 59813.10 Residential Loads 59913.11 HVDC Transmission 599References 605CHAPTER 14 HARMONIC PROPAGATION 60714.1 Harmonic Analysis Methods 60814.2 Frequency Domain Analysis 60814.3 Frequency Scan 61014.4 Voltage Scan 61114.5 Harmonic Analysis Methods 61214.6 Time Domain Analysis 62014.7 Sensitivity Methods 62014.8 Unbalanced AC System and HVDC Link 62214.9 Hybrid Frequency and Time Domain Concept 62314.10 Probabilistic Concepts 62614.11 Computer-Based Programs 63114.12 Harmonic Analyses of a Large Industrial System 63214.13 Long Transmission Line 65314.14 34.5 kV UG Cable 67314.15 5-Bus Transmission System 673References 682CHAPTER 15 PASSIVE FILTERS 68515.1 Filter Types 68515.2 Single-Tuned Filters 69015.3 Harmonic Filter Detuning and Unbalance 69915.4 Relations in an ST Filter 69915.5 Selection of Q Factor 70115.6 Double-Tuned Filter 70215.7 Bandpass Filters 70415.8 Damped Filters 70515.9 Type C Filter 71015.10 Zero Sequence Traps 71615.11 Series-Type Low-Pass Filter 71715.12 Transfer Function Approach for Filter Designs 71815.13 Optimization Techniques of Filter Designs 72315.14 Genetic Algorithms for Filter Designs 72815.15 HVDC-DC Filters 73115.16 Limitations of Passive Filters 73415.17 Flowchart for Design of Filters 73515.18 Filter Components 73515.19 Failure of Harmonic Filters 741References 741CHAPTER 16 PRACTICAL PASSIVE FILTER DESIGNS 74516.1 Study 1: Small Distribution System with Major Six-Pulse Loads 74516.2 Study 2: Filters for Arc Furnance Loads 75616.3 Study 3: Filters for Two 8000-Hp ID Fan Drives 77016.4 Study 4: Double-Tuned filter on a Three-Winding Transformer 78216.5 Study 5: PV Solar Generation Plant 78516.6 Study 6: Impact of Harmonics at a Distance 79916.7 Study 7: Wind Generation Farm 804INDEX 829

J.C. Das is a consultant of electrical power systems at Power Systems Studies, Inc., USA. He is Life Fellow of IEEE (UK), Fellow of IET (India), and has authored approximately sixty technical papers and published 190 study reports of real-world power systems. He is the author of three books including ARC Flash Hazard Analysis and Mitigation. He is a registered P.E. in the states of Georgia and Oklahoma, C.Eng. in UK, and Eur Ing in Europe. J. C. Das is also a member of CIGRE, Federation of European Engineers, and other technical associations and organizations.

“Students and professionals will definitely find this book an essential resource that will be referenced for many years.”  (IEEE Electrical Engineering magazine, 1 January 2016)

• FOREWORD xvPREFACE xixABOUT THE AUTHOR xxiCHAPTER 1 POWER SYSTEM HARMONICS 11.1 Nonlinear Loads 21.2 Increases in Nonlinear Loads 31.3 Effects of Harmonics 41.4 Distorted Waveforms 41.5 Harmonics and Sequence Components 71.6 Harmonic Indices 91.7 Power Factor, Distortion Factor, and Total Power Factor 111.8 Power Theories 131.9 Amplification and Attenuation of Harmonics 27References 28CHAPTER 2 FOURIER ANALYSIS 312.1 Periodic Functions 312.2 Orthogonal Functions 312.3 Fourier Series and Coefficients 332.4 Odd Symmetry 352.5 Even Symmetry 362.6 Half-Wave Symmetry 372.7 Harmonic Spectrum 412.8 Complex form of Fourier Series 412.9 Fourier Transform 432.10 Dirichlet Conditions 522.11 Power Spectrum of a Function 542.12 Convolution 562.13 Sampled Waveform: Discrete Fourier Transform 572.14 Fast Fourier Transform 64References 69CHAPTER 3 HARMONIC GENERATION-1 713.1 Harmonics in Transformers 713.2 Energization of a Transformer 793.3 Delta Windings of Three-Phase Transformers 823.4 Harmonics in Rotating Machine Windings 923.5 Cogging and Crawling of Induction Motors 973.6 Synchronous Generators 1023.7 Saturation of Current Transformers 1043.8 Ferroresonance 1053.9 Power Capacitors 1113.10 Transmission Lines 112References 112CHAPTER 4 HARMONIC GENERATION-II 1154.1 Static Power Converters 1154.2 Single-Phase Bridge Circuit 1154.3 Reactive Power Requirements of Converters 1224.4 Three-Phase Bridge Circuit 1244.5 Harmonics on Output (DC) Side 1334.6 Inverter Operation 1354.7 Diode Bridge Converters 1394.8 Switch-Mode Power (SMP) Supplies 1424.9 Home Appliances 1434.10 Arc Furnaces 1444.11 Cycloconverters 1474.12 Thyristor-Controlled Reactor 1504.13 Pulse Width Modulation 1544.14 Voltage Source Converters 1584.15 Wind Power Generation 1624.16 Fluorescent Lighting 1654.17 Adjustable Speed Drives 1674.18 Pulse Burst Modulation 1744.19 Chopper Circuits and Electric Traction 1754.20 Slip Frequency Recovery Schemes 1774.21 Power Semiconductor Devices 178References 181CHAPTER 5 INTERHARMONICS AND FLICKER 1835.1 Interharmonics 1835.2 Sources of Interharmonics 1835.3 Arc Furnaces 1925.4 Effects of Interharmonics 1965.5 Reduction of Interharmonics 1985.6 Flicker 1985.7 Flicker Testing 2025.8 Control of Flicker 2055.9 Tracing Methods of Flicker and Interharmonics 2085.10 Torsional Analysis 2105.11 Subsynchronous Resonance 217References 225CHAPTER 6 HARMONIC REDUCTION AT THE SOURCE 2296.1 Phase Multiplication 2306.2 Varying Topologies 2306.3 Harmonic Cancellation: Commercial Loads 2326.4 Input Reactors to the PWM ASDs 2356.5 Active Filters 2376.6 Active Current Shaping 2486.7 Hybrid Connections of Active and Passive Filters 2516.8 Impedance Source Inverters 2556.9 Matrix Converters 2596.10 Mutilevel Inverters 2626.11 Switching Algorithms for Harmonic Control 2706.12 Theory of Resultants of Polynomials 271References 277CHAPTER 7 ESTIMATION AND MEASUREMENTS OF HARMONICS 2817.1 Waveform without Ripple Content 2827.2 Waveform with Ripple Content 2887.3 Phase Angle of Harmonics 2987.4 Measurements of Harmonics 3047.5 Measuring Equipment 3097.6 Transducers for Harmonic Measurements 3127.7 Characterizing Measured Data 3147.8 Probabilistic Concepts 3167.9 Summation of Harmonic Vectors with Random Angles 3237.10 Central Limit Theorem 3267.11 Kalman Filtering 326References 329CHAPTER 8 EFFECTS OF HARMONICS 3318.1 Rotating Machines 3328.2 Effect of Negative Sequence Currents on Synchronous Generators 3358.3 Insulation Stresses 3378.4 Transformers 3458.5 Cables 3598.6 Capacitors 3618.7 Voltage Notching 3628.8 EMI (Electromagnetic Interference) 3638.9 Overloading of Neutral 3678.10 Protective Relays and Meters 3698.11 Circuit Breakers and Fuses 3728.12 Telephone Influence Factor 372References 377CHAPTER 9 HARMONIC RESONANCE 3799.1 Two-Port Networks 3799.2 Resonance in Series and Parallel RLC Circuits 3839.3 Practical LC Tank Circuit 3919.4 Reactance Curves 3969.5 Foster's Networks 3979.6 Harmonic Resonance 4009.7 Harmonic Resonance in a Distribution System 4049.8 Elusiveness of Resonance Problems 4059.9 Resonance Due to Single-Tuned Filters 4089.10 Switched Capacitors for Power Factor Improvement 4109.11 Secondary Resonance 4119.12 Multiple Resonances in a Distribution Feeder 4159.13 Part-Winding Resonance in Transformer Windings 4169.14 Composite Resonance 4199.15 Resonance in Transmission Lines 4219.16 Zero Sequence Resonance 4219.17 Factors Affecting Harmonic Resonance 423References 424CHAPTER 10 HARMONIC DISTORTION LIMITS ACCORDING TO STANDARDS 42710.1 Standards for Limitation of Harmonics 42710.2 IEEE 519 Harmonic Current and Voltage Limits 42910.3 Point of Common Coupling (PCC) 43210.4 Applying IEEE 519 Harmonic Distortion Limits 43310.5 Time Varying Characteristics of Harmonics 43510.6 IEC Harmonic Current Emission Limits 43610.7 Voltage Quality 44010.8 Commutation Notches 44410.9 Applying Limits to Practical Power Systems 449References 450CHAPTER 11 APPLICATION OF SHUNT CAPACITOR BANKS 45311.1 Shunt Capacitor Banks 45311.2 Location of Shunt Capacitors 45811.3 Ratings of Capacitors 45911.4 Shunt Capacitor Bank Arrangements 46511.5 Fusing 46811.6 Connections of Banks 47611.7 Unbalance Detection 47911.8 Destabilizing Effect of Capacitor Banks 48111.9 Switching Transients of Capacitor Banks 48311.10 Control of Switching Transients 48611.11 Switching Capacitors with Motors 48911.12 Switching Devices 49011.13 Switching Controls 498References 501CHAPTER 12 MODELING OF SYSTEM COMPONENTS FOR HARMONIC ANALYSIS 50312.1 Transmission Lines 50312.2 Cables 53212.3 Zero Sequence Impedance of OH Lines and Cables 53812.4 Filter Reactors 53912.5 Transformers 54012.6 Induction Motors 55412.7 Synchronous Generators 55612.8 Load Models 55712.9 System Impedance 55912.10 Three-Phase Models 56112.11 Uncharacteristic Harmonics 56312.12 Converters 564References 566CHAPTER 13 HARMONIC MODELING OF SYSTEMS 56913.1 Electrical Power Systems 56913.2 Extent of Network Modeling 57213.3 Impact of Loads and Generation 57313.4 Short-Circuit and Fundamental Frequency Load Flow Calculations 57413.5 Industrial Systems 57813.6 Distribution Systems 58213.7 Transmission Systems 58913.8 Compensation of Transmission Lines 59313.9 Commercial Buildings 59813.10 Residential Loads 59913.11 HVDC Transmission 599References 605CHAPTER 14 HARMONIC PROPAGATION 60714.1 Harmonic Analysis Methods 60814.2 Frequency Domain Analysis 60814.3 Frequency Scan 61014.4 Voltage Scan 61114.5 Harmonic Analysis Methods 61214.6 Time Domain Analysis 62014.7 Sensitivity Methods 62014.8 Unbalanced AC System and HVDC Link 62214.9 Hybrid Frequency and Time Domain Concept 62314.10 Probabilistic Concepts 62614.11 Computer-Based Programs 63114.12 Harmonic Analyses of a Large Industrial System 63214.13 Long Transmission Line 65314.14 34.5 kV UG Cable 67314.15 5-Bus Transmission System 673References 682CHAPTER 15 PASSIVE FILTERS 68515.1 Filter Types 68515.2 Single-Tuned Filters 69015.3 Harmonic Filter Detuning and Unbalance 69915.4 Relations in an ST Filter 69915.5 Selection of Q Factor 70115.6 Double-Tuned Filter 70215.7 Bandpass Filters 70415.8 Damped Filters 70515.9 Type C Filter 71015.10 Zero Sequence Traps 71615.11 Series-Type Low-Pass Filter 71715.12 Transfer Function Approach for Filter Designs 71815.13 Optimization Techniques of Filter Designs 72315.14 Genetic Algorithms for Filter Designs 72815.15 HVDC-DC Filters 73115.16 Limitations of Passive Filters 73415.17 Flowchart for Design of Filters 73515.18 Filter Components 73515.19 Failure of Harmonic Filters 741References 741CHAPTER 16 PRACTICAL PASSIVE FILTER DESIGNS 74516.1 Study 1: Small Distribution System with Major Six-Pulse Loads 74516.2 Study 2: Filters for Arc Furnance Loads 75616.3 Study 3: Filters for Two 8000-Hp ID Fan Drives 77016.4 Study 4: Double-Tuned filter on a Three-Winding Transformer 78216.5 Study 5: PV Solar Generation Plant 78516.6 Study 6: Impact of Harmonics at a Distance 79916.7 Study 7: Wind Generation Farm 804INDEX 829

J.C. Das is a consultant of electrical power systems at Power Systems Studies, Inc., USA. He is Life Fellow of IEEE (UK), Fellow of IET (India), and has authored approximately sixty technical papers and published 190 study reports of real-world power systems. He is the author of three books including ARC Flash Hazard Analysis and Mitigation. He is a registered P.E. in the states of Georgia and Oklahoma, C.Eng. in UK, and Eur Ing in Europe. J. C. Das is also a member of CIGRE, Federation of European Engineers, and other technical associations and organizations.

“Students and professionals will definitely find this book an essential resource that will be referenced for many years.”  (IEEE Electrical Engineering magazine, 1 January 2016)

• FOREWORD xvPREFACE xixABOUT THE AUTHOR xxiCHAPTER 1 POWER SYSTEM HARMONICS 11.1 Nonlinear Loads 21.2 Increases in Nonlinear Loads 31.3 Effects of Harmonics 41.4 Distorted Waveforms 41.5 Harmonics and Sequence Components 71.6 Harmonic Indices 91.7 Power Factor, Distortion Factor, and Total Power Factor 111.8 Power Theories 131.9 Amplification and Attenuation of Harmonics 27References 28CHAPTER 2 FOURIER ANALYSIS 312.1 Periodic Functions 312.2 Orthogonal Functions 312.3 Fourier Series and Coefficients 332.4 Odd Symmetry 352.5 Even Symmetry 362.6 Half-Wave Symmetry 372.7 Harmonic Spectrum 412.8 Complex form of Fourier Series 412.9 Fourier Transform 432.10 Dirichlet Conditions 522.11 Power Spectrum of a Function 542.12 Convolution 562.13 Sampled Waveform: Discrete Fourier Transform 572.14 Fast Fourier Transform 64References 69CHAPTER 3 HARMONIC GENERATION-1 713.1 Harmonics in Transformers 713.2 Energization of a Transformer 793.3 Delta Windings of Three-Phase Transformers 823.4 Harmonics in Rotating Machine Windings 923.5 Cogging and Crawling of Induction Motors 973.6 Synchronous Generators 1023.7 Saturation of Current Transformers 1043.8 Ferroresonance 1053.9 Power Capacitors 1113.10 Transmission Lines 112References 112CHAPTER 4 HARMONIC GENERATION-II 1154.1 Static Power Converters 1154.2 Single-Phase Bridge Circuit 1154.3 Reactive Power Requirements of Converters 1224.4 Three-Phase Bridge Circuit 1244.5 Harmonics on Output (DC) Side 1334.6 Inverter Operation 1354.7 Diode Bridge Converters 1394.8 Switch-Mode Power (SMP) Supplies 1424.9 Home Appliances 1434.10 Arc Furnaces 1444.11 Cycloconverters 1474.12 Thyristor-Controlled Reactor 1504.13 Pulse Width Modulation 1544.14 Voltage Source Converters 1584.15 Wind Power Generation 1624.16 Fluorescent Lighting 1654.17 Adjustable Speed Drives 1674.18 Pulse Burst Modulation 1744.19 Chopper Circuits and Electric Traction 1754.20 Slip Frequency Recovery Schemes 1774.21 Power Semiconductor Devices 178References 181CHAPTER 5 INTERHARMONICS AND FLICKER 1835.1 Interharmonics 1835.2 Sources of Interharmonics 1835.3 Arc Furnaces 1925.4 Effects of Interharmonics 1965.5 Reduction of Interharmonics 1985.6 Flicker 1985.7 Flicker Testing 2025.8 Control of Flicker 2055.9 Tracing Methods of Flicker and Interharmonics 2085.10 Torsional Analysis 2105.11 Subsynchronous Resonance 217References 225CHAPTER 6 HARMONIC REDUCTION AT THE SOURCE 2296.1 Phase Multiplication 2306.2 Varying Topologies 2306.3 Harmonic Cancellation: Commercial Loads 2326.4 Input Reactors to the PWM ASDs 2356.5 Active Filters 2376.6 Active Current Shaping 2486.7 Hybrid Connections of Active and Passive Filters 2516.8 Impedance Source Inverters 2556.9 Matrix Converters 2596.10 Mutilevel Inverters 2626.11 Switching Algorithms for Harmonic Control 2706.12 Theory of Resultants of Polynomials 271References 277CHAPTER 7 ESTIMATION AND MEASUREMENTS OF HARMONICS 2817.1 Waveform without Ripple Content 2827.2 Waveform with Ripple Content 2887.3 Phase Angle of Harmonics 2987.4 Measurements of Harmonics 3047.5 Measuring Equipment 3097.6 Transducers for Harmonic Measurements 3127.7 Characterizing Measured Data 3147.8 Probabilistic Concepts 3167.9 Summation of Harmonic Vectors with Random Angles 3237.10 Central Limit Theorem 3267.11 Kalman Filtering 326References 329CHAPTER 8 EFFECTS OF HARMONICS 3318.1 Rotating Machines 3328.2 Effect of Negative Sequence Currents on Synchronous Generators 3358.3 Insulation Stresses 3378.4 Transformers 3458.5 Cables 3598.6 Capacitors 3618.7 Voltage Notching 3628.8 EMI (Electromagnetic Interference) 3638.9 Overloading of Neutral 3678.10 Protective Relays and Meters 3698.11 Circuit Breakers and Fuses 3728.12 Telephone Influence Factor 372References 377CHAPTER 9 HARMONIC RESONANCE 3799.1 Two-Port Networks 3799.2 Resonance in Series and Parallel RLC Circuits 3839.3 Practical LC Tank Circuit 3919.4 Reactance Curves 3969.5 Foster's Networks 3979.6 Harmonic Resonance 4009.7 Harmonic Resonance in a Distribution System 4049.8 Elusiveness of Resonance Problems 4059.9 Resonance Due to Single-Tuned Filters 4089.10 Switched Capacitors for Power Factor Improvement 4109.11 Secondary Resonance 4119.12 Multiple Resonances in a Distribution Feeder 4159.13 Part-Winding Resonance in Transformer Windings 4169.14 Composite Resonance 4199.15 Resonance in Transmission Lines 4219.16 Zero Sequence Resonance 4219.17 Factors Affecting Harmonic Resonance 423References 424CHAPTER 10 HARMONIC DISTORTION LIMITS ACCORDING TO STANDARDS 42710.1 Standards for Limitation of Harmonics 42710.2 IEEE 519 Harmonic Current and Voltage Limits 42910.3 Point of Common Coupling (PCC) 43210.4 Applying IEEE 519 Harmonic Distortion Limits 43310.5 Time Varying Characteristics of Harmonics 43510.6 IEC Harmonic Current Emission Limits 43610.7 Voltage Quality 44010.8 Commutation Notches 44410.9 Applying Limits to Practical Power Systems 449References 450CHAPTER 11 APPLICATION OF SHUNT CAPACITOR BANKS 45311.1 Shunt Capacitor Banks 45311.2 Location of Shunt Capacitors 45811.3 Ratings of Capacitors 45911.4 Shunt Capacitor Bank Arrangements 46511.5 Fusing 46811.6 Connections of Banks 47611.7 Unbalance Detection 47911.8 Destabilizing Effect of Capacitor Banks 48111.9 Switching Transients of Capacitor Banks 48311.10 Control of Switching Transients 48611.11 Switching Capacitors with Motors 48911.12 Switching Devices 49011.13 Switching Controls 498References 501CHAPTER 12 MODELING OF SYSTEM COMPONENTS FOR HARMONIC ANALYSIS 50312.1 Transmission Lines 50312.2 Cables 53212.3 Zero Sequence Impedance of OH Lines and Cables 53812.4 Filter Reactors 53912.5 Transformers 54012.6 Induction Motors 55412.7 Synchronous Generators 55612.8 Load Models 55712.9 System Impedance 55912.10 Three-Phase Models 56112.11 Uncharacteristic Harmonics 56312.12 Converters 564References 566CHAPTER 13 HARMONIC MODELING OF SYSTEMS 56913.1 Electrical Power Systems 56913.2 Extent of Network Modeling 57213.3 Impact of Loads and Generation 57313.4 Short-Circuit and Fundamental Frequency Load Flow Calculations 57413.5 Industrial Systems 57813.6 Distribution Systems 58213.7 Transmission Systems 58913.8 Compensation of Transmission Lines 59313.9 Commercial Buildings 59813.10 Residential Loads 59913.11 HVDC Transmission 599References 605CHAPTER 14 HARMONIC PROPAGATION 60714.1 Harmonic Analysis Methods 60814.2 Frequency Domain Analysis 60814.3 Frequency Scan 61014.4 Voltage Scan 61114.5 Harmonic Analysis Methods 61214.6 Time Domain Analysis 62014.7 Sensitivity Methods 62014.8 Unbalanced AC System and HVDC Link 62214.9 Hybrid Frequency and Time Domain Concept 62314.10 Probabilistic Concepts 62614.11 Computer-Based Programs 63114.12 Harmonic Analyses of a Large Industrial System 63214.13 Long Transmission Line 65314.14 34.5 kV UG Cable 67314.15 5-Bus Transmission System 673References 682CHAPTER 15 PASSIVE FILTERS 68515.1 Filter Types 68515.2 Single-Tuned Filters 69015.3 Harmonic Filter Detuning and Unbalance 69915.4 Relations in an ST Filter 69915.5 Selection of Q Factor 70115.6 Double-Tuned Filter 70215.7 Bandpass Filters 70415.8 Damped Filters 70515.9 Type C Filter 71015.10 Zero Sequence Traps 71615.11 Series-Type Low-Pass Filter 71715.12 Transfer Function Approach for Filter Designs 71815.13 Optimization Techniques of Filter Designs 72315.14 Genetic Algorithms for Filter Designs 72815.15 HVDC-DC Filters 73115.16 Limitations of Passive Filters 73415.17 Flowchart for Design of Filters 73515.18 Filter Components 73515.19 Failure of Harmonic Filters 741References 741CHAPTER 16 PRACTICAL PASSIVE FILTER DESIGNS 74516.1 Study 1: Small Distribution System with Major Six-Pulse Loads 74516.2 Study 2: Filters for Arc Furnance Loads 75616.3 Study 3: Filters for Two 8000-Hp ID Fan Drives 77016.4 Study 4: Double-Tuned filter on a Three-Winding Transformer 78216.5 Study 5: PV Solar Generation Plant 78516.6 Study 6: Impact of Harmonics at a Distance 79916.7 Study 7: Wind Generation Farm 804INDEX 829