# Power System Harmonics and Passive Filter Designs

ISBN: 978-1-118-86162-2
872 pages
March 2015, Wiley-IEEE Press

## Description

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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FOREWORD xv

PREFACE xix

CHAPTER 1 POWER SYSTEM HARMONICS 1

1.2 Increases in Nonlinear Loads 3

1.3 Effects of Harmonics 4

1.4 Distorted Waveforms 4

1.5 Harmonics and Sequence Components 7

1.6 Harmonic Indices 9

1.7 Power Factor, Distortion Factor, and Total Power Factor 11

1.8 Power Theories 13

1.9 Amplification and Attenuation of Harmonics 27

References 28

CHAPTER 2 FOURIER ANALYSIS 31

2.1 Periodic Functions 31

2.2 Orthogonal Functions 31

2.3 Fourier Series and Coefficients 33

2.4 Odd Symmetry 35

2.5 Even Symmetry 36

2.6 Half-Wave Symmetry 37

2.7 Harmonic Spectrum 41

2.8 Complex form of Fourier Series 41

2.9 Fourier Transform 43

2.10 Dirichlet Conditions 52

2.11 Power Spectrum of a Function 54

2.12 Convolution 56

2.13 Sampled Waveform: Discrete Fourier Transform 57

2.14 Fast Fourier Transform 64

References 69

CHAPTER 3 HARMONIC GENERATION-1 71

3.1 Harmonics in Transformers 71

3.2 Energization of a Transformer 79

3.3 Delta Windings of Three-Phase Transformers 82

3.4 Harmonics in Rotating Machine Windings 92

3.5 Cogging and Crawling of Induction Motors 97

3.6 Synchronous Generators 102

3.7 Saturation of Current Transformers 104

3.8 Ferroresonance 105

3.9 Power Capacitors 111

3.10 Transmission Lines 112

References 112

CHAPTER 4 HARMONIC GENERATION-II 115

4.1 Static Power Converters 115

4.2 Single-Phase Bridge Circuit 115

4.3 Reactive Power Requirements of Converters 122

4.4 Three-Phase Bridge Circuit 124

4.5 Harmonics on Output (DC) Side 133

4.6 Inverter Operation 135

4.7 Diode Bridge Converters 139

4.8 Switch-Mode Power (SMP) Supplies 142

4.9 Home Appliances 143

4.10 Arc Furnaces 144

4.11 Cycloconverters 147

4.12 Thyristor-Controlled Reactor 150

4.13 Pulse Width Modulation 154

4.14 Voltage Source Converters 158

4.15 Wind Power Generation 162

4.16 Fluorescent Lighting 165

4.18 Pulse Burst Modulation 174

4.19 Chopper Circuits and Electric Traction 175

4.20 Slip Frequency Recovery Schemes 177

4.21 Power Semiconductor Devices 178

References 181

CHAPTER 5 INTERHARMONICS AND FLICKER 183

5.1 Interharmonics 183

5.2 Sources of Interharmonics 183

5.3 Arc Furnaces 192

5.4 Effects of Interharmonics 196

5.5 Reduction of Interharmonics 198

5.6 Flicker 198

5.7 Flicker Testing 202

5.8 Control of Flicker 205

5.9 Tracing Methods of Flicker and Interharmonics 208

5.10 Torsional Analysis 210

5.11 Subsynchronous Resonance 217

References 225

CHAPTER 6 HARMONIC REDUCTION AT THE SOURCE 229

6.1 Phase Multiplication 230

6.2 Varying Topologies 230

6.3 Harmonic Cancellation: Commercial Loads 232

6.4 Input Reactors to the PWM ASDs 235

6.5 Active Filters 237

6.6 Active Current Shaping 248

6.7 Hybrid Connections of Active and Passive Filters 251

6.8 Impedance Source Inverters 255

6.9 Matrix Converters 259

6.10 Mutilevel Inverters 262

6.11 Switching Algorithms for Harmonic Control 270

6.12 Theory of Resultants of Polynomials 271

References 277

CHAPTER 7 ESTIMATION AND MEASUREMENTS OF HARMONICS 281

7.1 Waveform without Ripple Content 282

7.2 Waveform with Ripple Content 288

7.3 Phase Angle of Harmonics 298

7.4 Measurements of Harmonics 304

7.5 Measuring Equipment 309

7.6 Transducers for Harmonic Measurements 312

7.7 Characterizing Measured Data 314

7.8 Probabilistic Concepts 316

7.9 Summation of Harmonic Vectors with Random Angles 323

7.10 Central Limit Theorem 326

7.11 Kalman Filtering 326

References 329

CHAPTER 8 EFFECTS OF HARMONICS 331

8.1 Rotating Machines 332

8.2 Effect of Negative Sequence Currents on Synchronous Generators 335

8.3 Insulation Stresses 337

8.4 Transformers 345

8.5 Cables 359

8.6 Capacitors 361

8.7 Voltage Notching 362

8.8 EMI (Electromagnetic Interference) 363

8.10 Protective Relays and Meters 369

8.11 Circuit Breakers and Fuses 372

8.12 Telephone Influence Factor 372

References 377

CHAPTER 9 HARMONIC RESONANCE 379

9.1 Two-Port Networks 379

9.2 Resonance in Series and Parallel RLC Circuits 383

9.3 Practical LC Tank Circuit 391

9.4 Reactance Curves 396

9.5 Foster's Networks 397

9.6 Harmonic Resonance 400

9.7 Harmonic Resonance in a Distribution System 404

9.8 Elusiveness of Resonance Problems 405

9.9 Resonance Due to Single-Tuned Filters 408

9.10 Switched Capacitors for Power Factor Improvement 410

9.11 Secondary Resonance 411

9.12 Multiple Resonances in a Distribution Feeder 415

9.13 Part-Winding Resonance in Transformer Windings 416

9.14 Composite Resonance 419

9.15 Resonance in Transmission Lines 421

9.16 Zero Sequence Resonance 421

9.17 Factors Affecting Harmonic Resonance 423

References 424

CHAPTER 10 HARMONIC DISTORTION LIMITS ACCORDING TO STANDARDS 427

10.1 Standards for Limitation of Harmonics 427

10.2 IEEE 519 Harmonic Current and Voltage Limits 429

10.3 Point of Common Coupling (PCC) 432

10.4 Applying IEEE 519 Harmonic Distortion Limits 433

10.5 Time Varying Characteristics of Harmonics 435

10.6 IEC Harmonic Current Emission Limits 436

10.7 Voltage Quality 440

10.8 Commutation Notches 444

10.9 Applying Limits to Practical Power Systems 449

References 450

CHAPTER 11 APPLICATION OF SHUNT CAPACITOR BANKS 453

11.1 Shunt Capacitor Banks 453

11.2 Location of Shunt Capacitors 458

11.3 Ratings of Capacitors 459

11.4 Shunt Capacitor Bank Arrangements 465

11.5 Fusing 468

11.6 Connections of Banks 476

11.7 Unbalance Detection 479

11.8 Destabilizing Effect of Capacitor Banks 481

11.9 Switching Transients of Capacitor Banks 483

11.10 Control of Switching Transients 486

11.11 Switching Capacitors with Motors 489

11.12 Switching Devices 490

11.13 Switching Controls 498

References 501

CHAPTER 12 MODELING OF SYSTEM COMPONENTS FOR HARMONIC ANALYSIS 503

12.1 Transmission Lines 503

12.2 Cables 532

12.3 Zero Sequence Impedance of OH Lines and Cables 538

12.4 Filter Reactors 539

12.5 Transformers 540

12.6 Induction Motors 554

12.7 Synchronous Generators 556

12.9 System Impedance 559

12.10 Three-Phase Models 561

12.11 Uncharacteristic Harmonics 563

12.12 Converters 564

References 566

CHAPTER 13 HARMONIC MODELING OF SYSTEMS 569

13.1 Electrical Power Systems 569

13.2 Extent of Network Modeling 572

13.3 Impact of Loads and Generation 573

13.4 Short-Circuit and Fundamental Frequency Load Flow Calculations 574

13.5 Industrial Systems 578

13.6 Distribution Systems 582

13.7 Transmission Systems 589

13.8 Compensation of Transmission Lines 593

13.9 Commercial Buildings 598

13.11 HVDC Transmission 599

References 605

CHAPTER 14 HARMONIC PROPAGATION 607

14.1 Harmonic Analysis Methods 608

14.2 Frequency Domain Analysis 608

14.3 Frequency Scan 610

14.4 Voltage Scan 611

14.5 Harmonic Analysis Methods 612

14.6 Time Domain Analysis 620

14.7 Sensitivity Methods 620

14.8 Unbalanced AC System and HVDC Link 622

14.9 Hybrid Frequency and Time Domain Concept 623

14.10 Probabilistic Concepts 626

14.11 Computer-Based Programs 631

14.12 Harmonic Analyses of a Large Industrial System 632

14.13 Long Transmission Line 653

14.14 34.5 kV UG Cable 673

14.15 5-Bus Transmission System 673

References 682

CHAPTER 15 PASSIVE FILTERS 685

15.1 Filter Types 685

15.2 Single-Tuned Filters 690

15.3 Harmonic Filter Detuning and Unbalance 699

15.4 Relations in an ST Filter 699

15.5 Selection of Q Factor 701

15.6 Double-Tuned Filter 702

15.7 Bandpass Filters 704

15.8 Damped Filters 705

15.9 Type C Filter 710

15.10 Zero Sequence Traps 716

15.11 Series-Type Low-Pass Filter 717

15.12 Transfer Function Approach for Filter Designs 718

15.13 Optimization Techniques of Filter Designs 723

15.14 Genetic Algorithms for Filter Designs 728

15.15 HVDC-DC Filters 731

15.16 Limitations of Passive Filters 734

15.17 Flowchart for Design of Filters 735

15.18 Filter Components 735

15.19 Failure of Harmonic Filters 741

References 741

CHAPTER 16 PRACTICAL PASSIVE FILTER DESIGNS 745

16.1 Study 1: Small Distribution System with Major Six-Pulse Loads 745

16.2 Study 2: Filters for Arc Furnance Loads 756

16.3 Study 3: Filters for Two 8000-Hp ID Fan Drives 770

16.4 Study 4: Double-Tuned filter on a Three-Winding Transformer 782

16.5 Study 5: PV Solar Generation Plant 785

16.6 Study 6: Impact of Harmonics at a Distance 799

16.7 Study 7: Wind Generation Farm 804

INDEX 829

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## Author Information

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.
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## Reviews

“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)

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