
Harmonic Balance Finite Element Method
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Content
- Intro
- Title Page
- Copyright
- Contents
- Preface
- About the Companion Website
- Chapter 1 Introduction to Harmonic Balance Finite Element Method (HBFEM)
- 1.1 Harmonic Problems in Power Systems
- 1.1.1 Harmonic Phenomena in Power Systems
- 1.1.2 Sources and Problems of Harmonics in Power Systems
- 1.1.3 Total Harmonic Distortion (THD)
- 1.2 Definitions of Computational Electromagnetics and IEEE Standards 1597.1 and 1597.2
- 1.2.1 ``The Building Block´´ of the Computational Electromagnetics Model
- 1.2.2 The Geometry of the Model and the Problem Space
- 1.2.3 Numerical Computation Methods
- 1.2.4 High-Performance Computation and Visualization (HPCV) in CEM
- 1.2.5 IEEE Standards 1597.1 and 1597.2 for Validation of CEM Computer Modeling and Simulations
- 1.3 HBFEM Used in Nonlinear EM Field Problems and Power Systems
- 1.3.1 HBFEM for a Nonlinear Magnetic Field With Current Driven
- 1.3.2 HBFEM for Magnetic Field and Electric Circuit Coupled Problems
- 1.3.3 HBFEM for a Nonlinear Magnetic Field with Voltage Driven
- 1.3.4 HBFEM for a Three-Phase Magnetic Tripler Transformer
- 1.3.5 HBFEM for a Three-Phase High-Speed Motor
- 1.3.6 HBFEM for a DC-Biased 3D Asymmetrical Magnetic Structure Simulation
- 1.3.7 HBFEM for a DC-Biased Problem in HV Power Transformers
- References
- Chapter 2 Nonlinear Electromagnetic Field and Its Harmonic Problems
- 2.1 Harmonic Problems in Power Systems and Power Supply Transformers
- 2.1.1 Nonlinear Electromagnetic Field
- 2.1.2 Harmonics Problems Generated from Nonlinear Load and Power Electronics Devices
- 2.1.3 Harmonics in the Time Domain and Frequency Domain
- 2.1.4 Examples of Harmonic Producing Loads
- 2.1.5 Harmonics in DC/DC Converter of Isolation Transformer
- 2.1.6 Magnetic Tripler
- 2.1.7 Harmonics in Multi-Pulse Rectifier Transformer
- 2.2 DC-Biased Transformer in High-Voltage DC Power Transmission System
- 2.2.1 Investigation and Suppression of DC Bias Phenomenon
- 2.2.2 Characteristics of DC Bias Phenomenon and Problems to be Solved
- 2.3 Geomagnetic Disturbance and Geomagnetic Induced Currents (GIC)
- 2.3.1 Geomagnetically Induced Currents in Power Systems
- 2.3.2 GIC-Induced Harmonic Currents in the Transformer
- 2.4 Harmonic Problems in Renewable Energy and Microgrid Systems
- 2.4.1 Power Electronic Devices - Harmonic Current and Voltage Sources
- 2.4.2 Harmonic Distortion in Renewable Energy Systems
- 2.4.3 Harmonics in the Microgrid and EV Charging System
- 2.4.4 IEEE Standard 519-2014
- References
- Chapter 3 Harmonic Balance Methods Used in Computational Electromagnetics
- 3.1 Harmonic Balance Methods Used in Nonlinear Circuit Problems
- 3.1.1 The Basic Concept of Harmonic Balance in a Nonlinear Circuit
- 3.1.2 The Theory of Harmonic Balance Used in a Nonlinear Circuit
- 3.2 CEM for Harmonic Problem Solving in Frequency, Time and Harmonic Domains
- 3.2.1 Computational Electromagnetics (CEM) Techniques and Validation
- 3.2.2 Time Periodic Electromagnetic Problems Using the Finite Element Method (FEM)
- 3.2.3 Comparison of Time-Periodic Steady-State Nonlinear EM Field Analysis Method
- 3.3 The Basic Concept of Harmonic Balance in EM Fields
- 3.3.1 Definition of Harmonic Balance
- 3.3.2 Harmonic Balance in EM Fields
- 3.3.3 Nonlinear Medium Description
- 3.3.4 Boundary Conditions
- 3.3.5 The Theory of HB-FEM in Nonlinear Magnetic Fields
- 3.3.6 The Generalized HBFEM
- 3.4 HBFEM for Electromagnetic Field and Electric Circuit Coupled Problems
- 3.4.1 HBFEM in Voltage Source-Driven Magnetic Field
- 3.4.2 Generalized Voltage Source-Driven Magnetic Field
- 3.5 HBFEM for a DC-Biased Problem in High-Voltage Power Transformers
- 3.5.1 DC-Biased Problem in HVDC Transformers
- 3.5.2 HBFEM Model of HVDC Transformer
- References
- Chapter 4 HBFEM for Nonlinear Magnetic Field Problems
- 4.1 HBFEM for a Nonlinear Magnetic Field with Current-Driven Source
- 4.1.1 Numerical Model of Current Source to Magnetic Field
- 4.1.2 Example of Current-Source Excitation to Nonlinear Magnetic Field
- 4.2 Harmonic Analysis of Switching Mode Transformer Using Voltage-Driven Source
- 4.2.1 Numerical Model of Voltage Source to Magnetic System
- 4.2.2 Example of Voltage-Source Excitation to Nonlinear Magnetic Field
- 4.3 Three-Phase Magnetic Frequency Tripler Analysis
- 4.3.1 Magnetic Frequency Tripler
- 4.3.2 Nonlinear Magnetic Material and its Saturation Characteristics
- 4.3.3 Voltage Source-Driven Connected to the Magnetic Field
- 4.4 Design of High-Speed and Hybrid Induction Machine using HBFEM
- 4.4.1 Construction of High-Speed and Hybrid Induction Machine
- 4.4.2 Numerical Model of High-Speed and Hybrid Induction Machine using HBFEM, Taking Account of Motion Effect
- 4.4.3 Numerical Analysis of High Speed and Hybrid Induction Machine using HBFEM
- 4.5 Three-Dimensional Axi-Symmetrical Transformer with DC-Biased Excitation
- 4.5.1 Numerical Simulation of 3-D Axi-Symmetrical Structure
- 4.5.2 Numerical Analysis of the Three-Dimensional Axi-Symmetrical Model
- 4.5.3 Eddy Current Calculation of DC-Biased Switch Mode Transformer
- References
- Chapter 5 Advanced Numerical Approach using HBFEM
- 5.1 HBFEM for DC-Biased Problems in HVDC Power Transformers
- 5.1.1 DC Bias Phenomena in HVDC
- 5.1.2 HBFEM for DC-Biased Magnetic Field
- 5.1.3 High-Voltage DC (HVDC) Transformer
- 5.2 Decomposed Algorithm of HBFEM
- 5.2.1 Introduction
- 5.2.2 Decomposed Harmonic Balanced System Equation
- 5.2.3 Magnetic Field Coupled with Electric Circuits
- 5.2.4 Computational Procedure Based on the Block Gauss-Seidel Algorithm
- 5.2.5 DC-Biasing Test on the LCM and Computational Results
- 5.2.6 Analysis of the Flux Density and Flux Distribution Under DC Bias Conditions
- 5.3 HBFEM with Fixed-Point Technique
- 5.3.1 Introduction
- 5.3.2 DC-Biasing Magnetization Curve
- 5.3.3 Fixed-Point Harmonic-Balanced Theory
- 5.3.4 Electromagnetic Coupling
- 5.3.5 Validation and Discussion
- 5.4 Hysteresis Model Based on Neural Network and Consuming Function
- 5.4.1 Introduction
- 5.4.2 Hysteresis Model Based on Consuming Function
- 5.4.3 Hysteresis Loops and Simulation
- 5.4.4 Hysteresis Model Based on a Neural Network
- 5.4.5 Simulation and Validation
- 5.5 Analysis of Hysteretic Characteristics Under Sinusoidal and DC-Biased Excitation
- 5.5.1 Globally Convergent Fixed-Point Harmonic-Balanced Method
- 5.5.2 Hysteretic Characteristic Analysis of the Laminated Core
- 5.5.3 Computation of the Nonlinear Magnetic Field Based on the Combination of the Two Hysteresis Models
- 5.6 Parallel Computing of HBFEM in Multi-Frequency Domain
- 5.6.1 HBFEM in Multi-Frequency Domain
- 5.6.2 Parallel Computing of HBFEM
- 5.6.3 Domain Decomposition
- 5.6.4 Reordering and Multi-Coloring
- 5.6.5 Loads Division in Frequency Domain
- 5.6.6 Two Layers Hybrid Computing
- References
- Chapter 6 HBFEM and Its Future Applications
- 6.1 HBFEM Model of Three-Phase Power Transformer
- 6.1.1 Three-Phase Transformer
- 6.1.2 Nonlinear Magnetic Material and its Saturation Characteristics
- 6.1.3 Voltage Source-Driven Model Connected to the Magnetic Field
- 6.1.4 HBFEM Matrix Equations, Taking Account of Extended Circuits
- 6.2 Magnetic Model of a Single-Phase Transformer and a Magnetically Controlled Shunt Reactor
- 6.2.1 Electromagnetic Coupling Model of a Single-Phase Transformer
- 6.2.2 Solutions of the Nonlinear Magnetic Circuit Model by the Harmonic Balance Method
- 6.2.3 Magnetically Controlled Shunt Reactor
- 6.2.4 Experiment and Computation
- 6.3 Computation Taking Account of Hysteresis Effects Based on Fixed-Point Reluctance
- 6.3.1 Fixed-Point Reluctance
- 6.3.2 Computational Procedure in the Frequency Domain
- 6.3.3 Computational Results and Analysis
- 6.4 HBFEM Modeling of the DC-Biased Transformer in GIC Event
- 6.4.1 GIC Effects on the Transformer
- 6.4.2 GIC Modeling and Harmonic Analysis
- 6.4.3 GIC Modeling Using HBFEM Model
- 6.5 HBFEM Used in Renewable Energy Systems and Microgrids
- 6.5.1 Harmonics in Renewable Energy Systems and Microgrids
- 6.5.2 Harmonic Analysis of the Transformer in Renewable Energy Systems and Microgrids
- 6.5.3 Harmonic Analysis of the Transformer Using a Voltage Driven Source
- 6.5.4 Harmonic Analysis of the Transformer Using a Current-Driven Source
- References
- Appendix
- Appendix I & II
- Matlab Program and the Laminated Core Model for Computation
- Appendix III
- FORTRAN-Based 3D Axi-Symmetrical Transformer with DC-Biased Excitation
- Index
- EULA
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