Power Systems Harmonics Computer Modelling and Analysis

by Acha, Enrique; Madrigal, Manuel

• ISBN13: 9780471521754
• ISBN10: 0471521752
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-06-11
• Publisher: WILEY

Summary

Deregulation has presented the electricity industry with many new challenges in power system planning and operation. Power engineers must understand the negative effect of harmonics on an electrical power network resulting from the extensive use of power electronics-based equipment. Serving as a complete reference to harmonics modelling, simulation and analysis, this book lays the foundations for optimising quality of power supply in the planning, design and operation phases. Features Include: * MATLAB function codes to aid the development of harmonic software and provide a hands-on approach to the theory presented. * Insight into the use of alternative, increased efficiency, harmonic domain techniques. * Examination of the harmonic modelling and analysis of FACTS, along with conventional and custom power plant equipment. * Clear presentation of the basic analytical approaches to harmonic theory and techniques for the resolution of harmonic distortion. Advanced undergraduate and postgraduate students in electrical engineering will benefit from the unique combination of practical examples and theoretical grounding. Practising power engineers, managers and consultants will appreciate the detailed coverage of engineering practice and power networks world-wide.

Author Biography

Enrique Acha is the author of Power Systems Harmonics: Computer Modelling and Analysis, published by Wiley. Manuel Madrigal is the author of Power Systems Harmonics: Computer Modelling and Analysis, published by Wiley.

Table of Contents

Foreword	xi
Preface	xv
I FUNDAMENTAL THEORY	1	(172)
Introduction	3	(8)
Background	3	(1)
Harmonic in Power System	4	(1)
Power Quality	5	(1)
Custom Power	5	(1)
Engineering Tools and Methods	6	(2)
Software tools	6	(1)
Hardware tools	7	(1)
Hardware-in-the-loop	7	(1)
Avenues of Research on Harmonic Analysis	8	(1)
Bibliography	8	(3)
Orthogonal Series Expansion	11	(24)
Introduction	11	(1)
Orthogonal Function	11	(1)
Periodic Functions	12	(4)
Even and Odd Functions	13	(1)
Half-wave symmetry	14	(1)
Quarter-wave symmetry	15	(1)
Hidden symmetry	16	(1)
The Fourier Series	16	(4)
Trigonometric form	16	(2)
Exponential form	18	(2)
Summary of waveform symmetry in a Fourier Series	20	(1)
The Fourier Transform	20	(6)
Fundamental equation	20	(1)
Discrete Fourier transform	21	(4)
East Fourier transform	25	(1)
Convolutions	26	(2)
Time convolutions	26	(1)
Frequency convolution	26	(2)
The Hartley Transform	28	(6)
From Fourier to Hartley series	28	(1)
Properties of the cas (.) function	28	(1)
The Hartley transform	29	(1)
Properties of the Hartley transform	30	(1)
Discrete Hartley transform	30	(2)
Fast Hartley transform	32	(2)
Summary	34	(1)
Bibliography	34	(1)
Electric Circuit Analysis Under Non-sinusoidal Conditions	35	(40)
Introduction	35	(1)
Key Periodic Electrical Relations	36	(12)
Non-sinusoidal functions	38	(5)
Sinusoidal functions	43	(3)
Symmetry and power definitions	46	(2)
Phasor Analysis	48	(2)
Symmetrical Components	50	(3)
Three-phase sinusoidal systems	51	(1)
Three-phase non-sinusoidal systems	51	(2)
Linear Circuit Analysis	53	(11)
Harmonic propagation studies in large networks	55	(9)
Passive Filters	64	(8)
Single-tuned first-order filters	65	(1)
High-pass second-order filters	65	(1)
Single-tuned first-order harmonic filter design	66	(6)
Summary	72	(1)
Bibliography	72	(3)
Harmonic Evaluation of Non-linear Functions	75	(24)
Introduction	75	(1)
Polynomial Evaluation by Hand Calculations	76	(3)
Convolutions in the Complex Fourier Harmonic Domain	79	(10)
Polynomial evaluation	79	(5)
Rational polynomial evaluation	84	(3)
Switching function evaluation	87	(2)
Numeric Evaluation of Non-linear Functions	89	(1)
Analytical Approximation of Saturation	89	(8)
Piecewise linear approximation	90	(1)
Rational fraction approximation	90	(1)
Hyperbolic approximation	91	(1)
Cubic splines interpolation	92	(2)
Simple polynomial approximation	94	(3)
Summary	97	(1)
Bibliography	97	(2)
Linearisation in Harmonic Domain	99	(26)
Introdoction	99	(1)
Linearisation of a Simple Non-linear Relation	99	(3)
Dynamic Relations	102	(6)
Norton and Thevenin Circuit equivalents	104	(3)
Linear relations in dynamic elements	107	(1)
Linear Relations	108	(7)
Multi-variable Relations	115	(4)
An Application to an Industrial Test Case	119	(4)
Summary	123	(1)
Bibliography	124	(1)
Real Fourier Harmonic Domain	125	(12)
Introduction	125	(1)
Direct Frequency Domain Evaluations	125	(4)
Linearisation in the Real Fourier Harmonic Domain	129	(2)
Dynamic Relations	131	(1)
Linear Elements	132	(4)
Summary	136	(1)
Bibliography	136	(1)
Hartley Harmonic Domain	137	(14)
Introduction	137	(1)
Direct Frequency Domain Evaluations	137	(4)
Liearisation in the Hartley Harmonic Domain	141	(2)
Dynamic Relations	143	(1)
Linear Elements	144	(4)
Computational Advantage	148	(1)
General Remarks about the Hartley Harmonic Domain	149	(1)
Summary	149	(1)
Bibliography	150	(1)
Interactive Solutions of Non-linear Power Plant Components	151	(22)
Introduction	151	(1)
Harmonic Domain Newton--Raphson Techniques	152	(4)
Point-by-point evaluation of the non-linear characteristic	155	(1)
The Non-linear Inductor in the Harmonic Domain	156	(3)
Harmonic Domain Convergence Characteristics	159	(10)
Full Newton--Raphson method	167	(1)
Single-valued Newton--Raphson method	168	(1)
Gauss--Seidel method	168	(1)
Quasi-Newton--Raphson method	169	(1)
Summary	169	(1)
Bibliography	170	(3)
II CONVENTIONAL POWER PLANT EQUIPMENT	173	(100)
Synchronous Generator	175	(18)
Introduction	175	(1)
Synhronous Machine under Non-sinusoidal Conditions	175	(10)
Machine's harmonic admittance matrix in the dq0 axes	176	(3)
Machine's harmonic admittance matrix in the αβγ	179	(4)
Machine's harmonic admittance matrix in abc axes	183	(2)
Saturation in the Synchronous Machine	185	(5)
Experimental Results	190	(1)
Summary	190	(2)
Bibliography	192	(1)
Transmission Lines	193	(34)
Introduction	193	(1)
Evaluation of Lumped Parameters	194	(8)
Matrix of potential coefficients P	194	(1)
Impedance matrix AG--E	195	(2)
Skin effect impedance matrix ZSkin	197	(2)
Reduced equivalent matrices Zabc and Yabc	199	(2)
500 kV power transmission line configuration	201	(1)
Evaluation of Distributed Parameters	202	(4)
Harmonic Voltage Wave Propagation in Transmission Lines	206	(3)
Transmission Line Transpositions	209	(5)
VAR Compensation	214	(2)
Network nodal analysis	214	(2)
Single-Phase Transmission Line Equivalents	216	(7)
Summary	223	(1)
Bibliography	224	(3)
Magnetic Non-linearities	227	(28)
Introduction	227	(1)
Inrush Currents	228	(3)
Single-phase Transformer	231	(5)
Lattice equivalent circuit representation	232	(3)
Transformer parameters in per unit values	235	(1)
Three-phase Transformer Bank	236	(7)
Laminated Iron Cores	243	(10)
Modelling of Cores	243	(8)
Modelling of hysteresis	251	(1)
Calculation of iron losses	251	(1)
External system	252	(1)
Summary	253	(1)
Bibliography	253	(2)
Electric Arcs	255	(18)
Introduction	255	(1)
Electric Arc Furnaces: Overview	256	(2)
Electric Furnace Installations	258	(1)
Electric Arc Furnace Modelling	259	(2)
Static electric arc model	260	(1)
Harmonic Domain Equation of the Electric Arc	261	(5)
Dynamic Characteristic	262	(3)
Static characteristic	265	(1)
Electric Arc Lamps: Overview	266	(3)
Arc Discharge Lamps	269	(2)
Summary	271	(1)
Bibliography	272	(1)
III POWER ELECTRONICS EQUIPMENT	273	(88)
Static VAR Compensator	275	(24)
Introduction	275	(2)
Single-Phase TCR Basic Operation	277	(10)
Voltage zero-crossing reference	279	(3)
Thyristor turn-on and turn-off	282	(4)
Single-phase TCR Modelling	286	(1)
Three-Phase TCR Modelling	287	(8)
Summary	295	(1)
Bibliography	296	(3)
Thyristor-controlled Series Compensator	299	(16)
Introduction	299	(3)
TCSC Operation	302	(4)
TCSC model	302	(4)
TCSC Impedance Response	306	(6)
SUmmary	312	(1)
Bibliography	312	(3)
Three-phase, Six-pulse Rectifier	315	(22)
Introduction	315	(3)
Rectifier Operation Using Switching Functions	318	(4)
Effect of the AC side inductance	319	(3)
Thyristor switching functions	322	(1)
Model in the Harmonic Domain	322	(7)
Harmonic in Electrical Power Networks	329	(5)
Harmonic in Electrical Power Networks	329	(1)
Harmonics produced by single-phase converters	329	(4)
Harmonic in distribution systems	333	(1)
Summary	334	(1)
Bibliography	335	(2)
Static Compensator with PWM Converters	337	(24)
Introduction	337	(1)
STATCOM Operation	338	(1)
STATCOM Based on PWM Converters	338	(1)
Analytical Model	339	(3)
PWM Converter Switching Functions	342	(6)
Selective harmonic elimination	342	(3)
Multi-module PWM technique	345	(3)
Implementation of the Thevenin Equivalent of the STATCOM	348	(5)
Analysis of the equivalent model	349	(4)
Active Filters	353	(5)
Basic principles of operation	353	(1)
Shunt active filter	353	(4)
Series active filter	357	(1)
Hybrid filter	357	(1)
Universal active filter	357	(1)
Summary	358	(1)
Bibliography	359	(2)
Index	361