Power System Harmonics

by Arrillaga, Jos; Watson, Neville R.

• ISBN13: 9780470851296
• ISBN10: 0470851295
• Edition: 2nd
• Format: Hardcover
• Copyright: 2003-11-21
• Publisher: WILEY

Summary

Harmonic distortion problems include equipment overheating, motor failures, capacitor failure and inaccurate power metering. The topic of power system harmonics was covered for the first time 20 years ago and the first edition has become a standard reference work in this area. Unprecedented developments in power electronic devices and their integration at all levels in the power system require a new look at the causes and effects of these problems, and the state of hardware and software available for harmonic assessment. Following the successful first edition, this second edition of Power System Harmonics maintains the practical approach to the subject and discusses the impact of advanced power electronic technology on instrumentation, simulation, standards and active harmonic elimination techniques. Features include: A new chapter on modern digital instrumentation techniques. Added sections on active filters and modern distorting devices such as FACTS devices, multilevel conversion, current source, voltage source inverters and turn-OFF-related power electronic devices. References to international standards for harmonics and inter-harmonics. Numerical examples of technique application. Offering a comprehensive understanding of power systems, this book is an asset to power engineers involved in the planning, design and operation of power system generation, transmission and distribution. Researchers and postgraduate students in the field will also benefit from this useful reference.

Author Biography

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.

Table of Contents

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