E-raamat: Power System Harmonics

Preface		xi
1 Subject Definition and Objectives		1	(16)
1.1 Introduction		1	(1)
1.2 The Mechanism of Harmonic Generation		1	(4)
1.3 Definitions and Standards		5	(7)
1.3.1 Factors Influencing the Development of Standards		7	(1)
1.3.2 Existing Harmonic Standards		8	(3)
1.3.3 General Harmonic Indices		11	(1)
1.4 Relevance of the Topic		12	(3)
1.5 References		15	(2)
2 Harmonic Analysis		17	(44)
2.1 Introduction		17	(1)
2.2 Fourier Series and Coefficients		18	(2)
2.3 Simplifications Resulting from Waveform Symmetry		20	(3)
2.4 Complex Form of the Fourier Series		23	(2)
2.5 Convolution of Harmonic Phasors		25	(2)
2.6 The Fourier Transform		27	(2)
2.7 Sampled Time Functions		29	(1)
2.8 Discrete Fourier Transform (DFT)		30	(3)
2.9 The Nyquist Frequency and Aliasing		33	(2)
2.10 Fast Fourier Transform (FFT)		35	(3)
2.11 Window Functions		38	(9)
2.11.1 The Picket Fence		40	(1)
2.11.2 Spectral Leakage Reduction		41	(1)
2.11.3 Choice of Window Function		41	(3)
2.11.4 Main-Lobe Width Reduction		44	(1)
2.11.5 Application to Inter-Harmonic Analysis		45	(2)
2.12 Efficiency of FFT Algorithms		47	(5)
2.12.1 The Radix-2 FFT		47	(1)
2.12.2 Mixed-Radix FFT		48	(1)
2.12.3 Real-Valued FFTs		49	(1)
2.12.4 Partial FFTs		50	(2)
2.13 Alternative Transforms		52	(6)
2.13.1 The Wavelet Transform		53	(3)
2.13.2 Automation of Disturbance Recognition		56	(2)
2.14 Discussion		58	(1)
2.15 References		58	(3)
3 Harmonic Sources		61	(82)
3.1 Introduction		61	(1)
3.2 Transformer Magnetisation Nonlinearities		62	(5)
3.2.1 Normal Excitation Characteristics		62	(1)
3.2.2 Determination of the Current Waveshape		62	(1)
3.2.3 Symmetrical Overexcitation		63	(1)
3.2.4 Inrush Current Harmonics		64	(1)
3.2.5 D.C. Magnetisation		65	(2)
3.3 Rotating Machine Harmonics		67	(7)
3.3.1 M.m.f. Distribution of A.C. Windings		67	(1)
3.3.2 Three-Phase Winding		68	(1)
3.3.3 Slot Harmonics		69	(1)
3.3.4 Voltage Harmonics Produced by Synchronous Machines		70	(2)
3.3.5 Rotor Saliency Effects		72	(1)
3.3.6 Voltage Harmonics Produced by Induction Motors		73	(1)
3.4 Distortion Caused by Arcing Devices		74	(5)
3.4.1 Electric Arc Furnaces		74	(2)
3.4.2 Discharge-Type Lighting		76	(3)
3.5 Single-Phase Rectification		79	(6)
3.5.1 D.C. Power Supplies		79	(3)
3.5.2 Line-Commutated Railway Rectifiers		82	(3)
3.6 Three-Phase Current-Source Conversion		85	(31)
3.6.1 Basic (Six-Pulse) Configuration		88	(3)
3.6.2 Effect of Transformer Connection		91	(1)
3.6.3 Twelve-Pulse Related Harmonics		91	(1)
3.6.4 Higher-Pulse Configurations		92	(1)
3.6.5 Effect of Transformer and System Impedance		93	(4)
3.6.6 Direct Voltage Harmonics		97	(2)
3.6.7 Imperfect D.C. Voltage Smoothing		99	(5)
3.6.8 Half-Controlled Rectification		104	(1)
3.6.9 Uncharacteristic Harmonic and Inter-Harmonic Generation		104	(8)
3.6.10 Frequency Cross-Modulation in Line-Commutated Converter Systems		112	(4)
3.7 Three-Phase Voltage-Source Conversion		116	(3)
3.7.1 Multi-Level VSC Configurations		117	(2)
3.8 Inverter-Fed A.C. Drives		119	(7)
3.9 Thyristor-Controlled Reactors		126	(4)
3.9.1 The Static VAR Compensator (SVC)		126	(3)
3.9.2 Thyristor-Controlled Series Compensation (TCSC)		129	(1)
3.10 Modulated Phase Control		130	(7)
3.10.1 The Switching Function Approach		133	(2)
3.10.2 Derivation of Input Current Harmonics		135	(2)
3.11 A.C. Regulators		137	(3)
3.11.1 Single-Phase Full-Wave Controller		137	(1)
3.11.2 Integral Cycle Control		138	(2)
3.12 Discussion		140	(1)
3.13 References		141	(2)
4 Effects of Harmonic Distortion		143	(48)
4.1 Introduction		143	(1)
4.2 Resonances		143	(6)
4.2.1 Parallel Resonance		143	(1)
4.2.2 Series Resonance		144	(1)
4.2.3 Effects of Resonance on System Behaviour		145	(2)
4.2.4 Complementary and Composite Resonances		147	(2)
4.2.5 Poor Damping		149	(1)
4.3 Effects of Harmonics on Rotating Machines		149	(4)
4.3.1 Harmonic Losses		149	(2)
4.3.2 Harmonic Torques		151	(1)
4.3.3 Other Effects		152	(1)
4.4 Effect of Harmonics on Static Power Plant		153	(3)
4.4.1 Transmission System		153	(1)
4.4.2 Transformers		153	(2)
4.4.3 Capacitor Banks		155	(1)
4.5 Power Assessment with Distorted Waveforms		156	(13)
4.5.1 Single-Phase System		156	(5)
4.5.2 Three-Phase System		161	(5)
4.5.3 Power Factor Under Harmonic Distortion		166	(2)
4.5.4 Effect of Harmonics on Measuring Instruments		168	(1)
4.6 Harmonic Interference with Ripple Control Systems		169	(1)
4.7 Harmonic Interference with Power System Protection		170	(1)
4.7.1 Harmonic Problems During Fault Conditions		170	(1)
4.7.2 Harmonic Problems Outside Fault Conditions		171	(1)
4.8 Effect of Harmonics on Consumer Equipment		171	(1)
4.9 Interference with Communications		172	(15)
4.9.1 Simple Model of a Telephone Circuit		173	(1)
4.9.2 Factors Influencing Interference		173	(1)
4.9.3 Coupling to Communication Circuits		174	(3)
4.9.4 Effect on Communication Circuits (Susceptiveness)		177	(7)
4.9.5 Telephone Circuit Balance to Earth		184	(1)
4.9.6 Shielding		185	(1)
4.9.7 Mitigation Techniques		186	(1)
4.10 Audible Noise from Electric Motors		187	(1)
4.11 Discussion		187	(1)
References		187	(4)
5 Harmonic Monitoring		191	(28)
5.1 Introduction		191	(1)
5.2 Measurement Requirements		191	(4)
5.2.1 The IEC 61000 4-7 Document		191	(2)
5.2.2 Inter-Harmonics		193	(1)
5.2.3 Harmonic Phase-Angle Displacement		194	(1)
5.2.4 Harmonic Symmetrical Components		195	(1)
5.3 Transducers		195	(5)
5.3.1 Current Transformers		195	(2)
5.3.2 Voltage Transformers		197	(3)
5.4 Harmonic Instrumentation		200	(6)
5.4.1 Digital Instrumentation		202	(3)
5.4.2 Structure of a Modern Monitoring System		205	(1)
5.5 Data Transmission		206	(1)
5.6 Presentation of Harmonic Information		207	(3)
5.7 Examples of Application		210	(7)
5.7.1 Synchronised Tests		210	(5)
5.7.2 Group-Connected HVD.C. Converter Test		215	(2)
5.8 Discussion		217	(1)
5.9 References		217	(2)
6 Harmonic Elimination		219	(42)
6.1 Introduction		219	(1)
6.2 Passive Filter Definitions		219	(2)
6.3 Filter Design Criteria		221	(2)
6.3.1 Conventional Criteria		221	(1)
6.3.2 Advanced Filter Design Criteria		222	(1)
6.4 Network Impedance for Performance Calculations		223	(5)
6.4.1 Size of System Representation		223	(1)
6.4.2 Effect of A.C. Network Resistance at Low Frequencies		224	(1)
6.4.3 Impedance Envelope Diagrams		225	(3)
6.5 Tuned Filters		228	(7)
6.5.1 Graphic Approach		231	(2)
6.5.2 Double-Tuned Filters		233	(1)
6.5.3 Automatically Tuned Filters		234	(1)
6.6 Damped Filters		235	(2)
6.6.1 Types of Damped Filters		236	(1)
6.6.2 Design of Damped Filters		236	(1)
6.7 Conventional Filter Configurations		237	(5)
6.7.1 Six-Pulse Design		237	(5)
6.7.2 Twelve-Pulse Configuration		242	(1)
6.8 Band-Pass Filtering for Twelve-Pulse Converters		242	(3)
6.9 Distribution System Filter Planning		245	(1)
6.10 Filter Component Properties		246	(1)
6.10.1 Capacitors		246	(1)
6.10.2 Inductors		247	(1)
6.11 Filter Costs		247	(6)
6.11.1 Single-Tuned Filter		248	(2)
6.11.2 Band-Pass Filter		250	(3)
6.12 D.C. Side Filters		253	(2)
6.13 Active Filters		255	(4)
6.13.1 Series Connection of Active Filters		256	(1)
6.13.2 Shunt Connection of Active Filters		257	(2)
6.14 Discussion		259	(1)
6.15 References		259	(2)
7 Computation of Harmonic Flows		261	(90)
7.1 Introduction		261	(1)
7.2 Direct Harmonic Analysis		261	(5)
7.2.1 Frequency Scan Analysis		264	(1)
7.2.2 Incorporation of Harmonic Voltage Sources		264	(1)
7.2.3 Cascading Sections		265	(1)
7.3 Derivation of Network Harmonic Impedances from Field Tests		266	(3)
7.3.1 Use of Existing Sources (Online Non-Invasive Tests)		266	(2)
7.3.2 Direct Injection (Online Invasive Tests)		268	(1)
7.3.3 From Transient Waveforms (Online Non-Invasive Tests)		268	(1)
7.4 Transmission Line Models		269	(17)
7.4.1 Mutually Coupled Three-Phase Lines		273	(3)
7.4.2 Consideration of Terminal Connections		276	(1)
7.4.3 Equivalent PI Model		277	(5)
7.4.4 Evaluation of Transmission Line Parameters		282	(4)
7.5 Underground and Submarine Cables		286	(4)
7.6 Three-Phase Transformer Models		290	(5)
7.7 Generator Modelling		295	(1)
7.8 Shunt Elements		295	(2)
7.9 Series Elements		297	(1)
7.10 Distribution System Modelling		298	(1)
7.11 Load Models		299	(5)
7.11.1 Induction Motor Model		302	(1)
7.11.2 Norton Equivalents of Residential Loads		303	(1)
7.11.3 Empirical Models Based on Measurements		304	(1)
7.12 Computer Implementation		304	(7)
7.12.1 Harmonic Penetration Overview		305	(1)
7.12.2 An Advanced Program Structure		305	(2)
7.12.3 Data Structure		307	(4)
7.13 Examples of Application of the Models		311	(33)
7.13.1 Harmonic Flow in a Homogeneous Transmission Line		311	(7)
7.13.2 Impedance Loci		318	(8)
7.13.3 Harmonic Analysis of Transmission Line with Transpositions		326	(8)
7.13.4 Harmonic Analysis of Transmission Line with VAR Compensation		334	(1)
7.13.5 Harmonic Analysis of an HVD.C. Transmission Line		335	(9)
7.14 Simulation Backed by Field Tests		344	(3)
7.14.1 Post-Processing of Transmission Line Harmonics for Test Result Comparisons		346	(1)
7.15 Discussion		347	(1)
7.16 References		348	(3)
8 Advanced Harmonic Assessment		351	(40)
8.1 Introduction		351	(1)
8.2 Transfer Function Model		351	(2)
8.3 Iterative Harmonic Analysis (IHA)		353	(6)
8.3.1 Fixed-Point Iterative Method		353	(1)
8.3.2 The Method of Norton Equivalents		354	(1)
8.3.3 Hybrid Time/Frequency Domain Solution		354	(2)
8.3.4 The Harmonic Domain		356	(3)
8.4 Harmonic Power Flow		359	(6)
8.4.1 Components of a Three-Phase Newton HPF Solution		360	(5)
8.5 Harmonic State Estimation		365	(4)
8.5.1 Load and Harmonic Source Identification		368	(1)
8.6 The Electromagnetic Transients Solution		369	(18)
8.6.1 Time Step Selection		370	(1)
8.6.2 A.C. System Representation		370	(1)
8.6.3 Frequency-Dependent Network Equivalents		370	(1)
8.6.4 Case Study		371	(16)
8.7 Discussion on Advanced Harmonic Modelling		387	(1)
8.8 References		388	(3)
Index		391

Jos Arrillaga is an experienced author, now an Emeritus Professor from the Department of Electrical and Computer Engineering at the University of Canterbury, New Zealand. He has written 10 books, including five for Wiley on the topic of electrical power systems, such as Power System Harmonics, Second Edition, Computer Modelling of Electrical Power Systems, Second Edition and High Voltage Direct Current Transmission. He has also written over 350 journal and conference papers. During the course of his career he has supervised around 50 PhD and 60 MSc/ME theses, most of them on the subject of high voltage direct current transmission, and he has also participated and convened several working groups. In 1997 he was awarded the Uno Lamm medal for outstanding contributions to HVDC transmission and he was in the New Years Honours list as a member of the New Zealand order of Merit.

Neville Watson is a professor with the Department of Electrical and Computer Engineering at the University of Canterbury. His research interests include power systems, power flow and harmonics. He is a senior member of IEEE and member of Institution of Professional Engineers New Zealand.