Numerical Methods for Energy Applications (Power Systems)

✍ Scribed by Naser Mahdavi Tabatabaei (editor), Nicu Bizon (editor)

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 1033
• Category: Library

✦ Synopsis

This book provides a thorough guide to the use of numerical methods in energy systems and applications. It presents methods for analysing engineering applications for energy systems, discussing finite difference, finite element, and other advanced numerical methods. Solutions to technical problems relating the application of these methods to energy systems are also thoroughly explored. Readers will discover diverse perspectives of the contributing authors and extensive discussions of issues including:
• a wide variety of numerical methods concepts and related energy systems applications;• systems equations and optimization, partial differential equations, and finite difference method;• methods for solving nonlinear equations, special methods, and their mathematical implementation in multi-energy sources;• numerical investigations of electrochemical fields and devices; and• issues related to numerical approaches and optimal integration of energy consumption.
This is a highly informative and carefully presented book, providing scientific and academic insight for readers with an interest in numerical methods and energy systems.

✦ Table of Contents

Foreword
Preface
Contents
Contributors
Advanced Numerical Methods
Advanced Numerical Methods for Equations, Systems Equations and Optimization
1 Introduction
2 Generation and Propagation of Errors
3 Approximating Functions
3.1 Polynomial Interpolation
3.2 Numerical Differentiation
4 Numerical Methods for Solving Equations and Systems Equations
4.1 Numerical Methods for Solving Equations
4.2 Numerical Methods for Solving the System of Equations
5 Optimization Methods
6 Application to Matlabs
7 Conclusion
References
Analysis of Partial Differential Equations in Time Dependent Problems Using Finite Difference Methods and the Applications on Electrical Engineering
1 Introduction
2 Finite Difference Methods for Time-Dependent Problems
2.1 Basic Concepts
2.2 Properties of Finite Difference Schemes
2.3 Von Neumann Stability
2.4 The Leapfrog Scheme
2.5 Dissipative Schemes
2.6 Difference Schemes for Hyperbolic Systems in One Dimension
3 Finite Difference Time Domain Applications in Electrical Engineering
4 Conclusions
References
Theoretical Approaches of Finite Elements Method (FEM)
1 Introduction
2 The Principle of Finite Elements Method (FEM)
3 Galerkin Method
3.1 Weak Form of Equations of the Steady-State Magnetic Field
3.2 The Principle of the Galerkin Method
3.3 Approximation Using Finite Elements
3.4 Galerkin Method Using the Scalar Magnetic Potential
3.5 Galerkin Method Using the Magnetic Potential Vector
4 Numerical Example
5 Conclusions
References
Advanced Numerical Methods Based on Artificial Intelligence
1 Introduction
2 Genetic Algorithms
2.1 Structure of a Genetic Algorithm
2.2 Chromosome Structure of an Individual
2.3 Selection Operator
2.4 Crossover Operator
2.5 Mutation Operator
3 Fuzzy Logic
3.1 Fuzzification
3.2 Inference
3.3 Defuzzification
4 Neural Networks
4.1 Activation Functions
4.2 Neuronal Networks Architecture
4.3 Training of Neural Networks
5 Identification of the Proper Equivalent Multi-layer Earth Structure Through a Genetic Algorithm Based AI Technique
5.1 Description of the Presented Application
5.2 Implemented Genetic Algorithm
5.3 Computed Equivalent Soil Models
6 Neural Network Implementation to Evaluate the Inductive Coupling Matrix in Case of a HVPL – MGP Electromagnetic Interference Problem
6.1 Description of the Studied Problem
6.2 Proposed Neural Network Solution
6.3 Matlab Implementation of Proposed Neural Network
6.4 Obtained NN Results
7 Conclusions
References
Numerical Methods for Solving Nonlinear Equations
1 Introduction
2 One-Variable Nonlinear Equations
2.1 One-Point Methods
2.2 Multi-point Methods
3 System of Nonlinear Equations
3.1 Gauss–Seidel Method
3.2 Fixed-Point Method
3.3 Newton Method
3.4 Quasi-Newton Method
3.5 Steepest Descent Method
3.6 Leven-Marquardt Method
3.7 Multi-step Method
3.8 Picard Method
3.9 Newton–Krylov Method
4 Discussion
5 Conclusion
References
Theoretical Approach to Element Free Galerkin Method and Its Mathematical Implementation
1 Introduction
2 Mathematical Formulation
2.1 Moving Least Square Method
2.2 Choice of Weight Function
2.3 Imposition of Boundary Conditions
3 Numerical Problems
3.1 Circular Bar Subjected to Body Force
3.2 Two-Dimensional Timoshenko Beam Subjected to Traction at Tip
4 Numerical Results and Discussions
4.1 Circular Bar Subjected to Body Forces
4.2 Two-Dimensional Timoshenko Beam Subjected to Traction at Tip
5 Conclusion
References
Theoretical Approach to Chebyshev Spectral Collocation Method and Its Mathematical Implementation
1 Introduction
2 Chebyshev Method
2.1 Application of Spectral Collocation Method in Fluid Dynamic Problems
3 Problem Formulation
3.1 Boundary Conditions
4 Base Flow Solution
5 Code Validation
6 Results and Discussions
6.1 Effect of Radius Ratio (η)
6.2 Effect of Viscous Heating
6.3 Effect of Buoyancy
7 Conclusions
References
Advanced Numerical Methods Based on Optimization
1 Introduction
2 Formulation of the Optimization Problem
3 Classification of the Optimal Problems
4 Types of Optimizations
5 Unconstrained Optimization Problems
6 Nonlinear Optimization Without Constraints
6.1 Unconstraint Optimization Problems
6.2 Optimization Problems with Linear Constraints and Nonlinear Objective Function
7 The Problems of Convex Programming
8 The Problems of Separable Programming
9 The Problems of Non-convex Programming
10 Nonlinear Optimization Without Constraints. The Convex Case
11 Optimization Methods with Constraints
11.1 Convex Programming. Kuhn—Tucker Optimality Conditions
11.2 Semi-defined Programming (SDP)
12 Mixed Integer Nonlinear Programming (MINLP)
13 Heuristic Methods
14 Genetic Algorithms (GAs)
15 Ant Colony Optimization
16 Simulated Annealing (SA)
17 Particle Swarm Optimization (PSO)
18 The Model of the Bee Swarm
19 The Firefly Model
20 Very Large Scale Neighborhood Search
21 Security-Constrained Unit Commitment (SCUC)
22 Conclusion
References
Ill-Posed Inverse Problems in Electrical Engineering Applications
1 Introduction
2 Fredholm Integral Equation
3 Key Performance Indicators in Inverse Problems Regularization
3.1 Own Observations on the Spectrum of Singular Values
3.2 Characterization of Stability as Disturbances with the Spectrum of Singular Values
3.3 Picard’s Condition as Performance Indicator
3.4 Conditioning Number as a Performance Indicator
4 Conditioning and Regularization in Power Flow Case Study
5 Intermediate Methods
5.1 Normal Pseudo Solution
5.2 Method of Collocation
5.3 Tikhonov Regularization Methods
6 Special Methods of Regularization
6.1 Mixed Tikhonov—TSVD
6.2 SVD Preconditioning
6.3 Conjugate Gradient Regularization Method
6.4 Algebraic Reconstruction Technique (ART)
7 Regularization as a Harmonic Reconstruction of Signals
8 Conclusions
References
Advanced Energy Systems
Advanced Energy Systems Based on Energy Hub Concept
1 Introduction
2 Concept of Energy Hub
2.1 Basic Concept
2.2 Elements of Hub
2.3 Potential Benefits
3 Different Types of Energy Hubs
3.1 Micro Energy Hubs
3.2 Macro Energy Hubs
4 Conclusion
References
Sustainable Energy Systems Based on the Multi-energy Sources
1 Introduction
2 Non-sustainable Energy Sources
3 Sustainable Energy Sources
3.1 Solar Energy Systems
3.2 Wind Energy Systems
3.3 Hydroelectric Energy Systems
3.4 Geothermal Energy Systems
3.5 Biomass Energy Systems
3.6 Water Wave Energy Systems
3.7 Hydrogen Energy Systems
4 Sustainable Energy Systems Created on the Multi-energy Sources in Silifke District of Turkey
5 Renewable Power Plant Created in Silifke District of Turkey
6 Sustainable Energy Management Model
7 Conclusion
References
Modeling of Energy Systems for Smart Homes
1 Introduction
2 Energy Systems
2.1 Smart Homes
3 Modeling of Smart Home Energy Devices
3.1 Home Appliances
3.2 Home Renewable Energy Units
4 Optimizing Method of Smart Home Devices
4.1 Objective Function
4.2 Constraints
4.3 Intelligent Algorithm
5 Numerical Results
6 Conclusion
References
Finite Volume Method Used for Numerical Investigations of Electrochemical Devices
1 Introduction
2 Basics of Finite Volume Method
3 Numerical Methods for Solving Linear Systems
4 Computational Fluid Dynamics
5 Numerical Investigation of an Electrochemical Device—A Study Case for PEM Fuel Cells
5.1 Finite Volume Method Applied for PEM Fuel Cells Investigation
5.2 Numerical Modeling—CFD Implementation
6 Conclusions
References
Night Operation of a Solar Chimney Integrated with Spiral Heat Exchanger
1 Introduction
2 System Description and Basic Principle
2.1 Conventional Solar Chimney
2.2 Hybrid Power Plant
3 Thermal Modeling of the Heat Exchanger
4 Mathematical Model
4.1 Conventional Solar Chimney
4.2 Hybrid Geothermal-Solar Chimney
5 Numerical Approach and Boundary Conditions
6 Results and Discussions
6.1 Validation
6.2 The Impact of Collector Radius on the Plant Performance
6.3 Investigation of Coil Pitch
6.4 Investigation of Tube Diameter
6.5 Geothermal Water Flow Investigation
6.6 Effect of Water Inlet Temperature
6.7 Variation of Internal Air and Geothermal Water Temperatures
6.8 Collector Heat Losses
7 Conclusion
References
Incorporating of IPFC in Multi-machine Power System Phillips-Heffron Model
1 Introduction
2 Nonlinear Model of Multi-machine Power System with Embedded IPFC
3 Linearized Model
4 Power System Oscillation Damping Controller
5 Digital Simulation
5.1 Stable Power System
5.2 Unstable Power System
6 Conclusion
References
Techno-Economical Analysis of Energy Storage Systems in Conventional Distribution Networks
1 Introduction
1.1 Motivation
1.2 Literature Survey
1.3 Research Gap
1.4 Chapter Organization
2 Problem Formulation
2.1 Optimal Placement and ESS Scheduling
3 Simulation and Results
3.1 Scenario 1: Optimal Placement and Scheduling of 1 ESS
3.2 Scenario 2: Optimal Placement and Scheduling of 2 ESSs
3.3 Scenario 3: ESS Scheduling
3.4 Scenario 4: Investigating Effect of ESSE on System Cost Reduction
4 Conclusion
References
OPAL-RT Technology Used in Automotive Applications for PEMFC
1 Introduction
2 Fuel Cell in ICSI Energy
3 Mathematical Modeling
3.1 Modeling Criteria for a PEMFC Stack
3.2 Fuel Cell Mathematical Modeling (Electrochemistry)
3.3 Testing and Simulation Infrastructure
4 RT-LAB Multicore Simulator
5 Conclusions
References
Numerical Energy Applications
Theoretical Techniques for the Exploration of Piezoelectric Harvesters
1 Introduction
2 Piezoelectric Harvesters (PHs)
3 Finite Element Analysis Applications of PHs
4 Time—Dependent Analyses via MatLab
5 Optimization of Design
6 Conclusions
References
Numerical Analysis of Electromagnetic Fields
1 Introduction
1.1 Low Frequency Methods
1.2 High Frequency Methods
2 Surface Integral Equations
3 Method of Moments
3.1 Using Surface Integral Equations for MoM
3.2 Discretization of SIE Formulations
4 Physical Optics
4.1 MECA Method
5 Comparison Between Method of Moments and Modified Equivalent Current Approximation
6 Conclusions
References
Optimization Methods for Wireless Power Transfer
1 Introduction to Wireless Power Transfer
2 Theoretical Considerations
3 Parameters Identification for the Wireless Power Transfer
3.1 The Assessment of Two Parallel-Bases Helicoidally Pancake-Type Coils
3.2 The Assessment of Two Truncated Cone-Like Coils, with Parallel Bases, Configuration a
3.3 The Assessment of Two Truncated Cone-Like Coils, with Non-Parallel Bases with One Coil Rotated 450.
3.4 The Assessment of Two Truncated Cone-Like Coils, with Parallel Bases, Configuration B
4 The Optimization of Parameters
4.1 Transfer Function and Output Square Error Method Based on “fminunc” Function
5 Case Study: Optimization of Magnetically Coupled Coils
5.1 Optimization of Useful Active Power P2 = PRLDepending on the Parameters L1, L2, and M
5.2 Efficiency Optimization Function of L1, L2, and M Parameters
5.3 Structure’s Optimization Using ANSYS Q3D Extractor
6 Conclusions
References
Numerical Assessment of Electromagnetic Energy and Forces in Non-destructive Measurement Devices
1 Introduction to Non-destructive Testing
2 Non-destructive Measurement Devices
2.1 Description of the Main Devices Utilized for Characterization of the Magnetic Materials
2.2 Epstein Frame
2.3 Single Sheet Tester (SST)
2.4 Magneto-optic Investigation Methods of the Magnetic Domain Structures
2.5 Vibrating Sample Magnetometer (VSM)
3 Numerical Assessment of Electromagnetic Energy and Forces
3.1 Electromagnetic Field Energy Theorem
3.2 Electromagnetic Field Energy and Coenergy for Nonlinear Media
3.3 Warburg Theorem
3.4 The Generalized Forces Theorem in the Electromagnetic Field
4 Case of Study
4.1 The Magnetic Field Direct Problem—The Determination of Currents (i1 ,i2 )
4.2 The Magnetic Field Inverse Problem—The Reconstruction of the B-H Relationship Using Currents (i1 ,i2 )
5 Conclusions
References
Optimal Integration of Electric Vehicles in Smart Grid Energy Flow
1 Introduction
2 Electric Vehicles, Smart Grid Power System and Bi-directional Energy Flow
2.1 Wind Energy Based RES
2.2 Solar Energy Based RES
3 Requirements for PEV Charging Stations and Smart Grid Power System
4 Case Study: Modelling Individual and Compounded V2G
4.1 Battery Charging Modelling
4.2 Vehicle to Grid Modelling
4.3 Modelling of the EV Parking Lot Operation
5 Case Study: Simulations, Results and Discussion
6 Conclusion
References
Numerical Approaches of Biomass Plants Efficiency
1 Introduction
2 Structure of Biomass Plants
3 Data Acquisition System of Cogeneration Power Plants
4 Numerical Approaches of CPP Efficiency
5 Conclusion
References
Power and Energy Flow in Cvasi-Stationary Electric and Magnetic Circuits
1 Introduction
2 Advanced Numerical Analysis Applied to Determination of Power and Energy Functionals Extreme
2.1 Variational Method
2.2 Lagrange’s Method
3 Equilibrium State of DC and AC Circuits and Minimum Power Flow. Examples
3.1 Principle of Minimum Consumed Power for DC Circuits and Variational Method
3.2 Principle of Minimum Consumed Power for AC Circuits and Variational Method
4 Equilibrium State of Linear Magnetic and Minimum Energy Flow. Example
5 Conclusion
References
Numerical Methods for Analysis of Energy Consumption in Drying Process of Wood
1 Introduction
1.1 The Current State of Dielectric Processing in the Radiofrequency Field
1.2 The Current State of Dielectric Processing in the Microwave Field
2 General Aspects of Processing of Dielectrics in a High Frequency Field
2.1 Radiofrequency Heating
2.2 Microwave Heating
2.3 Dielectric Properties. Complex Dielectric Constant
2.4 Material Parameters of Wood
2.5 Radiofrequency Electrothermal Installations
2.6 Microwave Electrothermal Installations
3 Numerical Modeling of Dielectric Heating in RF and MW Field
3.1 3D Calculation Programs for Numerical Analysis of the Drying Process Using Electromagnetic Field Coupling—Thermal Field—Mass Problems—Movement Problems
3.2 Numerical Modeling of Heating in the Electromagnetic Field Using the Comsol Multiphysics Software
4 Conclusions
References
Design and Energy Analysis for Fuel Cell Hybrid Electric Vehicle
1 Introduction
2 Description and Modelling of the Components of a Fuel Cell Hybrid Electric Vehicle
2.1 Proton Exchange Membrane Fuel Cell
2.2 Battery
2.3 Ultracapacitor
2.4 DC/DC Converter
3 EMS Control Strategies
4 Experimental Validation
5 Analysis of Experimental Results in Respect to Electrical Vehicle Efficiency
6 Conclusion
References
Finite Element Solutions for Magnetic Shielding Power Applications
1 Introduction
2 Time Harmonic Magnetic Shields
2.1 Basics of Magnetic Shielding Mechanisms
2.2 The Cylindrical Shield in Transversal Time Harmonic Magnetic Field
3 Finite Element Formulations for Magneto Static and Time Harmonic Magnetic Field
3.1 Finite Element Analysis of Magneto Static Field Using a Variational Formulation
3.2 Finite Element Galerk in Formulation a Time Harmonic Magnetic Field
4 Case Study: Determination of the Magnetic Field Produced by a High Voltage Electrical Overhead Line Near a Shielded Building Using Finite Element Method
5 Conclusions
References
Regression Analysis-Based Load Modelling for Electric Distribution Networks
1 Introduction
2 Correlation and Regression Analysis
2.1 Correlation Methods
2.2 Intensity of the Relationship Between Two Variables
3 Case Studies in the Electric Distribution Networks
3.1 Power Correlation Problem
3.2 Peak Load Estimation Using Power Correlation
3.3 Residential Load Estimation Using a Regression—Correlation-Based Method
4 Conclusions
References
Finite Element Analysis of Electromagnetic Fields Emitted by Overhead High-Voltage Power Lines
1 General
2 2D ANSYS Maxwell Model for Computing ELF Electric and Magnetic Fields Around OHVPLs
2.1 Model Development
2.2 Model Validation
3 Finite Element Analysis of ELF-EMFs from Typical OHVPLs Used in the Romanian Power Grid
3.1 ELF-EMFs from the 110 kV Double-Circuit OHVPL
3.2 ELF-EMFs from the 220 kV Double-Circuit OHVPL
3.3 ELF-EMFs from the 400 kV Single-Circuit OHVPL
4 Conclusions
References
Design and Finite Element Analysis of Permanent Magnet Synchronous Generator for Wind Turbine Application
1 Introduction
2 A Literature Review of PMSGs
3 Design and Modelling of PMSG
4 Electromagnetic Transient Analysis
4.1 ANSYS/Maxwell Program
4.2 Performance Results
5 Conclusion
References
Power and Energy System Modeling Based on Modified Tellegen Principle
1 Introduction
2 Modified Tellegen’s Theorem
3 Similarity Transformation
4 Modeling Based on Modified Tellegen’s Theorem
5 Examples of Power and Energy Calculation Based on Modified Tellegen’s Theorem
6 Conclusions
Appendix
References
Self-tuning Yaw Control Strategy of a Horizontal Axis Wind Turbine Based on Machine Learning
1 Introduction
2 Objectives and Applications
3 Machine Learning and Artificial Intelligence Techniques
3.1 Reinforcement Learning
3.2 Artificial Neural Networks
3.3 Optimization Algorithms
4 Machine Learning Based Wind Turbine Yaw Control
4.1 Yaw Control RL
4.2 Yaw Control MLP-BP
4.3 Yaw Control PSO and PoF
4.4 Yaw Control DM
5 Conclusions
References
Numerical Methods of Electric Power Flow in Interconnected Systems
1 Introduction
2 Type of Buses
3 The Power Flow Problem PFP
3.1 The Operating Area for Unit Generator
3.2 The 4 Bus System Model
3.3 The Problem Formulation of Power Flow
3.4 Power Flow Problem
4 Newton–Raphson Iterative Method
4.1 Power Flow Solution by Using Newton Raphson Method
4.2 NR Power Flow. Case Study
5 Fast Power Flow Method
6 The Gauss Seidel Method Applied to a Network
7 GS Power Flow. Case Study
8 Conclusion
References
Numerical Methods in Selecting Location of Distributed Generation in Energy Network
1 Introduction
2 Types of DG Resources
2.1 PV System
2.2 WTs
2.3 FCs
2.4 MTs
2.5 Synchronous and Asynchronous Generators
3 The Effect of DGs on Power Networks
3.1 The Effect of DGs on Voltage Profile
3.2 The Effect of DG Resources on Network Power Losses
3.3 The Effect of DGs on Harmonics
3.4 The Effect of DGs on the Short Circuit Level in the Network
3.5 The Effect of DGs on the Self-healing of the Distribution System
4 The Economic Aspects of Low Voltage Networks, Especially Micro-grids (MGs)
5 Placement of DG Resources
5.1 Introduction
5.2 Problem Modeling
5.3 Solution Methods
6 Conclusions
References
Numerical Methods for Power System Analysis with FACTS Devices Applications
1 Introduction
2 Numerical Technique
2.1 Bisection Method [5–9]
2.2 Regula Falsi Method [5–9]
2.3 Simple Repetition or Fixed Point Method [5–9]
2.4 Newton Raphson Method [5–9]
2.5 Secant Method [5–9]
3 FACTS Devices
3.1 Power System Modeling
3.2 SVC Modeling
3.3 TCSC Modeling
3.4 UPFC Modeling
4 Formulation the Problem of FACTS Devices Placement
4.1 Objective Functions
4.2 Constraints
4.3 Optimal Placement of TCSC, SVC, and UPFC
5 Conclusions
References
Index
503912_1_En_36_Chapter_OnlinePDF.pdf
Correction to: Numerical Methods for Energy Applications
Correction to: N. Mahdavi Tabatabaei and N. Bizon (eds.), Numerical Methods for Energy Applications, Power Systems, https://doi.org/10.1007/978-3-030-62191-9
503912_1_En_36_Chapter_OnlinePDF.pdf
Correction to: Numerical Methods for Energy Applications
Correction to: N. Mahdavi Tabatabaei and N. Bizon (eds.), Numerical Methods for Energy Applications, Power Systems, https://doi.org/10.1007/978-3-030-62191-9