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Preface xii About the Companion Website xv 1 Introduction to Harmonic Balance Finite Element Method (HBFEM) 1 1.1 Harmonic Problems in Power Systems 1 1.1.1 Harmonic Phenomena in Power Systems 2 1.1.2 Sources and Problems of Harmonics in Power Systems 3 1.1.3 Total Harmonic Distortion (THD) 4 1.2 Definitions of Computational Electromagnetics and IEEE Standards 1597.1 and 1597.2 7 1.2.1 The Building Block of the Computational Electromagnetics Model 7 1.2.2 The Geometry of the Model and the Problem Space 8 1.2.3 Numerical Computation Methods 8 1.2.4 High-Performance Computation and Visualization (HPCV) in CEM 9 1.2.5 IEEE Standards 1597.1 and 1597.2 for Validation of CEM Computer Modeling and Simulations 9 1.3 HBFEM Used in Nonlinear EM Field Problems and Power Systems 12 1.3.1 HBFEM for a Nonlinear Magnetic Field With Current Driven 13 1.3.2 HBFEM for Magnetic Field and Electric Circuit Coupled Problems 14 1.3.3 HBFEM for a Nonlinear Magnetic Field with Voltage Driven 14 1.3.4 HBFEM for a Three-Phase Magnetic Tripler Transformer 14 1.3.5 HBFEM for a Three-Phase High-Speed Motor 15 1.3.6 HBFEM for a DC-Biased 3D Asymmetrical Magnetic Structure Simulation 15 1.3.7 HBFEM for a DC-Biased Problem in HV Power Transformers 16 References 17 2 Nonlinear Electromagnetic Field and Its Harmonic Problems 19 2.1 Harmonic Problems in Power Systems and Power Supply Transformers 19 2.1.1 Nonlinear Electromagnetic Field 19 2.1.2 Harmonics Problems Generated from Nonlinear Load and Power Electronics Devices 21 2.1.3 Harmonics in the Time Domain and Frequency Domain 25 2.1.4 Examples of Harmonic Producing Loads 28 2.1.5 Harmonics in DC/DC Converter of Isolation Transformer 28 2.1.6 Magnetic Tripler 33 2.1.7 Harmonics in Multi-Pulse Rectifier Transformer 35 2.2 DC-Biased Transformer in High-Voltage DC Power Transmission System 38 2.2.1 Investigation and Suppression of DC Bias Phenomenon 38 2.2.2 Characteristics of DC Bias Phenomenon and Problems to be Solved 40 2.3 Geomagnetic Disturbance and Geomagnetic Induced Currents (GIC) 41 2.3.1 Geomagnetically Induced Currents in Power Systems 42 2.3.2 GIC-Induced Harmonic Currents in the Transformer 46 2.4 Harmonic Problems in Renewable Energy and Microgrid Systems 47 2.4.1 Power Electronic Devices Harmonic Current and Voltage Sources 48 2.4.2 Harmonic Distortion in Renewable Energy Systems 50 2.4.3 Harmonics in the Microgrid and EV Charging System 52 2.4.4 IEEE Standard 519-2014 56 References 58 3 Harmonic Balance Methods Used in Computational Electromagnetics 60 3.1 Harmonic Balance Methods Used in Nonlinear Circuit Problems 60 3.1.1 The Basic Concept of Harmonic Balance in a Nonlinear Circuit 60 3.1.2 The Theory of Harmonic Balance Used in a Nonlinear Circuit 63 3.2 CEM for Harmonic Problem Solving in Frequency, Time and Harmonic Domains 65 3.2.1 Computational Electromagnetics (CEM) Techniques and Validation 65 3.2.2 Time Periodic Electromagnetic Problems Using the Finite Element Method (FEM) 66 3.2.3 Comparison of Time-Periodic Steady-State Nonlinear EM Field Analysis Method 71 3.3 The Basic Concept of Harmonic Balance in EM Fields 73 3.3.1 Definition of Harmonic Balance 73 3.3.2 Harmonic Balance in EM Fields 73 3.3.3 Nonlinear Medium Description 75 3.3.4 Boundary Conditions 76 3.3.5 The Theory of HB-FEM in Nonlinear Magnetic Fields 76 3.3.6 The Generalized HBFEM 83 3.4 HBFEM for Electromagnetic Field and Electric Circuit Coupled Problems 85 3.4.1 HBFEM in Voltage Source-Driven Magnetic Field 85 3.4.2 Generalized Voltage Source-Driven Magnetic Field 86 3.5 HBFEM for a DC-Biased Problem in High-Voltage Power Transformers 91 3.5.1 DC-Biased Problem in HVDC Transformers 91 3.5.2 HBFEM Model of HVDC Transformer 91 References 95 4 HBFEM for Nonlinear Magnetic Field Problems 96 4.1 HBFEM for a Nonlinear
Junwei Lu, Professor, Griffith School of Engineering, Griffith University, Australia. Professor Lu has developed Harmonic Balance FEM techniques for nonlinear magnetics and Time Domain FEM techniques for wave propagation problems, and has been working in this area since 1985. He has taught numerical techniques in EM, power electronics and electric machines, power transmission and distribution, advanced communications systems since 1993. He holds over 10 international patents related to smart antennas arrays, high frequency transformers and inductor, and other high frequency magnetic devices. His research interests include Computational Electromagnetics, EMC computer modelling and simulation, high frequency magnetics, smart mobile terminal antennas, MEMS devices, and smart transformer used in renewable energy system and smart grid, and EV technology. Xiaojun Zhao is researcher at the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Source, North China Electric Power University, China. His main research interests are engineering electromagnetic field analysis, DC bias phenomena in power transformers, and modeling properties of magnetic material. Sotoshi Yamada received the B.E. and M.E. degrees from the Department of Electrical Engineering, Kanazawa University, Kanazawa, Japan, in 1972 and 1974, respectively. He received the Dr. Eng. degree from Kyushu University, Fukuoka, Japan, in 1985. From 1974 to 1992, he was with the Department of Electrical and Computer Engineering, Faculty of Engineering, Kanazawa University. He has been Professor at Laboratory of Magnetic Field Control and Applications since 1992 and is engaged in research on power magnetic devices, the numerical electromagnetic field calculation, biomagnetics, etc.