FOREWORD xv PREFACE xix ABOUT THE AUTHOR xxi CHAPTER 1 POWER SYSTEM HARMONICS 1 1.1 Nonlinear Loads 2 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 4.17 Adjustable Speed Drives 167 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 8.9 Overloading of Neutral 367 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 12.8 Load Models 557 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 13.10 Residential Loads 599 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.