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Harmonic Balance Finite Element Method: Applications in Nonlinear Electromagnetics and Power Systems
Preface
Harmonic Problems in Power Systems
Harmonic Phenomena in Power Systems
Sources and Problems of Harmonics in Power Systems
Total Harmonic Distortion (THD)
Definitions of Computational Electromagnetics and IEEE Standards 1597.1 and 1597.2
“The Building Block” of the Computational Electromagnetics Model
The Sources of EM Energy
The Geometry of the Model and the Problem Space
Numerical Computation Methods
High-Performance Computation and Visualization (HPCV) in CEM
IEEE Standards 1597.1 and 1597.2 for Validation of CEM Computer Modeling and Simulations
HBFEM Used in Nonlinear EM Field Problems and Power Systems
HBFEM for a Nonlinear Magnetic Field With Current Driven
HBFEM for Magnetic Field and Electric Circuit Coupled Problems
HBFEM for a Nonlinear Magnetic Field with Voltage Driven
HBFEM for a Three-Phase Magnetic Tripler Transformer
HBFEM for a Three-Phase High-Speed Motor
HBFEM for a DC-Biased 3D Asymmetrical Magnetic Structure Simulation
HBFEM for a DC-Biased Problem in HV Power Transformers
References
Nonlinear Electromagnetic Field and Its Harmonic Problems
Harmonic Problems in Power Systems and Power Supply Transformers
Nonlinear Electromagnetic Field
Harmonics Problems Generated from Nonlinear Load and Power Electronics Devices
Harmonics in the Time Domain and Frequency Domain
A. Time Domain Model
B. Frequency Domain Model
Examples of Harmonic Producing Loads
Harmonics in DC/DC Converter of Isolation Transformer
A. Isolation Transformer and Excitations
B. Full-Bridge Buck-Derived Converter
C. Forward Converter
D. Flyback Converter
E. LLC Resonant Converter
Magnetic Tripler
Harmonics in Multi-Pulse Rectifier Transformer
-Pulse Rectifier Transformer
-Pulse Rectifier Transformer
DC-Biased Transformer in High-Voltage DC Power Transmission System
Investigation and Suppression of DC Bias Phenomenon
Characteristics of DC Bias Phenomenon and Problems to be Solved
Geomagnetic Disturbance and Geomagnetic Induced Currents (GIC)
Geomagnetically Induced Currents in Power Systems
QIC-Induced Harmonic Currents in the Transformer
Harmonic Problems in Renewable Energy and Microgrid Systems
Power Electronic Devices - Harmonic Current and Voltage Sources
Harmonic Distortion in Renewable Energy Systems
Harmonics in the Microgrid and EV Charging System
IEEE Standard 519-2014 [24]
Current THD limits at the PCC
Voltage THD limits at the PCC
High-frequency Current Allowance in Low Current Distortion Systems
Harmonic Distortion Evaluations and Controlling Harmonics
Reducing Load Harmonic Current
Harmonic Studies
References
Harmonic Balance Methods Used in Computational Electromagnetics
Harmonic Balance Methods Used in Nonlinear Circuit Problems
TheHarmonic Balance Methods
The Theory of Harmonic Balance Used in a Nonlinear Circuit
CEM for Harmonic Problem Solving in Frequency, Time and Harmonic Domains
Computational Electromagnetics (CEM) Techniques and Validation
Time Periodic Electromagnetic Problems Using the Finite Element Method (FEM)
A. Time Domain Approach
B. Frequency Domain Approach
C. Multi-Frequency Domain Approach Using the Harmonic Balance Method
Comparison of Time-Periodic Steady-State Nonlinear EM Field Analysis Method
The Basic Concept of Harmonic Balance in EM Fields
Definition of Harmonic Balance
Harmonic Balance in EM Fields
A. Nonlinear Magnetic Field
B. Nonlinear Electric Field
Nonlinear Medium Description
A. Magnetic Medium:
B. Electric Medium:
Boundary Conditions
A. Dirichlet Boundary Condition:
B. Neumann Boundary Condition:
The Theory of HB-FEM in Nonlinear Magnetic Fields
A. Current Source-Driven Fields
B. HBFEM Formulation
The Generalized HBFEM
HBFEM for Electromagnetic Field and Electric Circuit Coupled Problems
HBFEM in Voltage Source-Driven Magnetic Field
Generalized Voltage Source-Driven Magnetic Field
HBFEM for a DC-Biased Problem in High-Voltage Power Transformers
DC-Biased Problem in HVDC Transformers
HBFEM Model of HVDC Transformer
References
HBFEM for Nonlinear Magnetic Field Problems
HBFEM for a Nonlinear Magnetic Field with Current-Driven Source
Numerical Model of Current Source to Magnetic Field
Example of Current-Source Excitation to Nonlinear Magnetic Field
Harmonic Analysis of Switching Mode Transformer Using Voltage-Driven Source
Numerical Model of Voltage Source to Magnetic System
Example of Voltage-Source Excitation to Nonlinear Magnetic Field
Three-Phase Magnetic Frequency Tripler Analysis
Magnetic Frequency Tripler
Nonlinear Magnetic Material and its Saturation Characteristics
Voltage Source-Driven Connected to the Magnetic Field
Design ofHigh-Speed and Hybrid Induction Machine using HBFEM
Construction of High-Speed and Hybrid Induction Machine
Numerical Model of High-Speed and Hybrid Induction Machine using HBFEM, Taking Account of Motion Effect
Numerical Analysis of High Speed and Hybrid Induction Machine using HBFEM
Three-Dimensional Axi-Symmetrical Transformer with DC-Biased Excitation
Numerical Simulation of 3-D Axi-Symmetrical Structure
Numerical Analysis of the Three-Dimensional Axi-Symmetrical Model
Eddy Current Calculation of DC-Biased Switch Mode Transformer
References
Advanced Numerical Approach using HBFEM
HBFEM for DC-Biased Problems in HVDC Power Transformers
DC Bias Phenomena in HVDC
HBFEM for DC-Biased Magnetic Field
A. Basic Theory of HBFEM
B. Coupling Between Electric Circuits and the Magnetic Field
C. Epstein Frame-Like Core Model
D. Calculated and Measured Results
E. Harmonic Analysis of the Magnetizing Current
F. Harmonic Analysis of the Magnetic Field
G. Harmonic Analysis of Flux Distribution
High-Voltage DC (HVDC) Transformer
Decomposed Algorithm of HBFEM
Introduction
Decomposed Harmonic Balanced System Equation
Magnetic Field Coupled with Electric Circuits
Computational Procedure Based on the Block Gauss-Seidel Algorithm
Previous Calculation Procedure
Improved Computational Procedure
Comparison Between the Previous Method and the New Method
DC-Biasing Test on the LCM and Computational Results
B-H Curve of the LCM
DC-Biasing Test
Computational Results
Analysis of the Flux Density and Flux Distribution Under DC Bias Conditions
HBFEM with Fixed-Point Technique
Introduction
DC-Biasing Magnetization Curve
Fixed-Point Harmonic-Balanced Theory
Electromagnetic Coupling
Validation and Discussion
A. Computational Results and Analysis of the Fixed-Point Harmonic-Balanced Method
B. Discussion on the Selection of the Magnetization Curve in the Computation of the DC-Biasing Magnetic Field
Hysteresis Model Based on Neural Network and Consuming Function
Introduction
Hysteresis Model Based on Consuming Function
Hysteresis Loops and Simulation
A. Hysteresis Loops Under Sinusoidal Excitation
B. DC-Biasing Hysteresis Loops
Hysteresis Model Based on a Neural Network
Simulation and Validation
Analysis of Hysteretic Characteristics Under Sinusoidal and DC-Biased Excitation
Globally Convergent Fixed-Point Harmonic-Balanced Method
Hysteretic Characteristic Analysis of the Laminated Core
Computation of the Nonlinear Magnetic Field Based on the Combination of the Two Hysteresis Models
Parallel Computing of HBFEM in Multi-Frequency Domain
HBFEM in Multi-Frequency Domain
Parallel Computing of HBFEM
Domain Decomposition
Reordering and Multi-Coloring
Loads Division in Frequency Domain
Two Layers Hybrid Computing
References
HBFEM and Its Future Applications
HBFEM Model of Three-Phase Power Transformer
Three-Phase Transformer
Nonlinear Magnetic Material and its Saturation Characteristics
Voltage Source-Driven Model Connected to the Magnetic Field
Magnetic Medium
HBFEM Matrix Equations, Taking Account of Extended Circuits
The Equivalent Circuit of a Three-Phase Transformer
Magnetic Model of a Single-Phase Transformer and a Magnetically Controlled Shunt Reactor
Electromagnetic Coupling Model of a Single-Phase Transformer
Solutions of the Nonlinear Magnetic Circuit Model by the Harmonic Balance Method
Magnetically Controlled Shunt Reactor
Experiment and Computation
Computation Taking Account of Hysteresis Effects Based on Fixed-Point Reluctance
Fixed-Point Reluctance
Computational Procedure in the Frequency Domain
Computational Results and Analysis
HBFEM Modeling of the DC-Biased Transformer in GIC Event
GIC Effects on the Transformer
GIC Modeling and Harmonic Analysis
QIC Modeling Using HBFEM Model
HBFEM Used in Renewable Energy Systems and Microgrids
Harmonics in Renewable Energy Systems and Microgrids
Harmonic Analysis of the Transformer in Renewable Energy Systems and Microgrids
Harmonic Analysis of the Transformer Using a Voltage Driven Source
Harmonic Analysis of the Transformer Using a Current-Driven Source
References
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