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About this book

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


Correction to: Numerical Methods for Energy Applications

The original version of these chapters “Numerical Methods in Selecting Location of Distributed Generation in Energy Network” and “Numerical Methods for Power System Analysis with FACTS Devices Applications” are inadvertently published with branch name after the institution name. It has now been corrected.

Naser Mahdavi Tabatabaei, Nicu Bizon

Advanced Numerical Methods


Advanced Numerical Methods for Equations, Systems Equations and Optimization

In this chapter an overview of advanced numerical methodsNumerical methods is presented. After errors are defined, the readers are initiated with the principles of approximating functions, numerical methods for solving equations and systems equations and optimization methods. The theoretical basics of polynomial interpolationPolynomial interpolation, numerical differentiation and numerical integration are presented, and, as a natural sequel, for each method some examples are given. Numerical methods for linearLinear equation and nonlinear equationsNon-linear equation and system equations, numerical methods for computing eigenvalues and eigenvectors are discussed and examples are given. The main goal of the optimization methods is to find the maximum or minimum of the objective function by using linear or nonlinear programming as shown in this chapter. Finally, an introduction in Matlab is done to put in evidence the easy-to-use and attractiveness of this popular software. Each method is accompanied by examples to help understanding.

Horia Andrei, Dan D. Micu, Marian Gaiceanu, Marilena Stanculescu, Paul Cristian Andrei

Analysis of Partial Differential Equations in Time Dependent Problems Using Finite Difference Methods and the Applications on Electrical Engineering

Finite difference methodsFinite Difference Method are used as a numerical method in the time-dependent and time-independent solution of partial differential equationsPartial Differential Equations (PDEs) commonly encountered in many engineering problems. In this chapter the theoretical basics and practical applications of these methods and limits their scope in terms of electrical engineer applications are examined. This numerical method, which are commonly used to solve problems of electromagnetic fields that cannot be solved by analytical methods are described in detail. Among these methods, the Finite Difference Time Domain (FDTD) methodFinite Difference Time Domain (FDTD), which is widely used in the calculation of the electric and magnetic fields in electrical engineering applications is concentrated and the results, limitations and alternatives of this method for different applications are examined. Using this numerical method, nonlinear material and structural characteristics in engineering applications can be examined depending on time. Robust and accurate analysis results can be obtained by using this method, which can also be integrated with developed models and software.

Hidir Duzkaya, Suleyman Sungur Tezcan, M. Cengiz Taplamacioglu

Theoretical Approaches of Finite Elements Method (FEM)

In engineering practices, electromagnetic fieldElectromagnetic field problems are of two main types: analysis and synthesis problems. In principle, a synthesis problem can be solved by an iterative technique, repeating the solving of some analysis problems, for configurations adapted because of some preliminary results of analysis simulations. Therefore, knowing how to compute the electromagnetic field precisely is a crucial issue in most of electrical engineering problems. This chapter is dedicated to Theoretical Approaches of Finite Elements Method (FEM).

Marilena Stanculescu, Sorin Deleanu, Paul Cristian Andrei, Horia Andrei, Lavinia Bobaru, Mihai Iordache

Advanced Numerical Methods Based on Artificial Intelligence

The chapter presents some advanced numerical methods based on Artificial IntelligenceArtificial Intelligence (AI) (AI) techniques applied to specific electrical engineering problems. A theoretical description is done regarding the basic aspects of the nowadays most commonly used AI techniques: Neural NetworksNeural Networks (NN), Fuzzy LogicFuzzy Logic (FL), and Genetic AlgorithmsGenetic Algorithms (GA) respectively. The presented AI techniques are exemplified through two specific electrical engineering application implemented by the authors in their previous research projects. The first application consist in the identification of the optimal equivalent horizontally layered earth structure by means of a Genetic Algorithm according in site soil resistivity measurements. The second application provides a Neural NetworkNeural Networks (NN) alternative two evaluate the impedance matrix that describes the electromagnetic coupling between overhead powerlines and nearby underground pipelines for different separation distances and various vertically layered soil structures.

Levente Czumbil, Dan D. Micu, Andrei Ceclan

Numerical Methods for Solving Nonlinear Equations

The nonlinear description has continuously been crucial in a wide range of disciplines to provide an accurate prediction of a natural phenomenon. Thus, finding a reliable solution method for these nonlinear models is of significant importance since, in most real-life applications, direct solution methods are not feasible, even in linear cases. Moreover, an inefficient method is likely to take additional computational costComputational cost and effort. This chapter attempts to provide a fundamental description of various iterative methodsIterative methods for solving nonlinear discretized equations. In the first part, a theoretical account of nonlinear systems with different types of iterative methods are depicted. The second part deals with both one-point and multi-point iterative methodsMulti-point iterative methods; this includes a description of the method, mathematical formulations, and the weak and strong points. Different iterative methods to solve a system of nonlinear equations are then described. Some discussed methods include the family of conjugate gradient, multi-step, and Newton-like. This part also identifies intricacies regarding a system of nonlinear equations, offering different remedies to solve these issues. Finally, a comparative study of the discussed methods and their applications in solving conventional equations are outlined in brief. The iterative methodsIterative methods mentioned in this chapter can be useful not only in solving nonlinear problemsNonlinear problems but also in linear problems and optimizationOptimization.

Narges Mohammadi, Shahram Mehdipour-Ataei, Maryam Mohammadi

Theoretical Approach to Element Free Galerkin Method and Its Mathematical Implementation

Numerical methods such as FVM, FDM, FVM, and BVM are eminent for solving the physical problems in engineering and science. Mentioned numerical methods are based on the predefined topological map, generally called “mesh,” Meshes are required to establish the relations between nodes, which becomes vital for the creation of shape functions. The problems with mesh-based methods are (i) They require the qualitative mesh, which is a somewhat tedious, time-consuming & messy task (ii) Meshing & re-meshing for a sizeable computational domain is time consuming, tedious, and costly task also requires the skills (iii) In complex computational domains, the mesh-based method fails in terms of accuracy (iv) Glass hour and shear locking phenomena generally found in the traditional finite element method. In the last two and a half decades, many engineers and mathematicians have proposed a new class of numerical methods known as meshfree methods. Meshfree methods are independent of mesh and approximate the governing PDE based on the set of nodes only. This chapter seeds light on an eminent meshfree method called EFGM. Chapter deals with the introduction and background of meshfree methods, the EFGM method, and its mathematical formulations. The chapter also comprises two elastostatic numerical problems, the 1D problem of a bar with body forces and 2D Timoshenko cantilever beam with traction at the tip, numerical results have been evaluated & compared with exact results. The convergence of both 1D and 2D problems have been discussed. This work built a sound foundation on EFGM and will act as a stepping stone for novices in the field of meshfree methods. Keywords: Advanced numerical approach, Mesh-free methods, Element free Galerkin method

Bhaumik Nagevadiya, Rameshkumar Bhoraniya, Ramdevsinh Jhala, Rajendrasinh Jadeja

Theoretical Approach to Chebyshev Spectral Collocation Method and Its Mathematical Implementation

This chapter describes the linear stability investigation of the incompressible viscid flow between the two concentric counter-rotating vertical cylinders. The parallel flow assumption was considered for the base flow, and hence it is varying in the radial direction only. The flow is a shear driven, and hence the pressure gradient is zero in the stream wise direction. The Governing stability equations for the disturbance flow quantities are derived in cylindrical polar coordinates by coupling the energy equation with the Navier-stokes formulas. The stability formulas are discretized using CSC method. The discretized stability formulas, combined with appropriate boundary conditions, form a general Eigenvalues problem (EVP). The full spectrum of the eigenvalue problem is computed for the different Reynolds numbers under the effect of viscous heating, different radius ratio, and buoyancy. The axial and radial wave numbers, β and α are taken as π/2 and zero, respectively. The effect of viscosity variation due to temperature is introduced by Nahme number (Na) and Brinkman number (Br) and effect of buoyancy by Grashof number (Gr). The acute value of Re of the flow is computed for isothermal and non-isothermal Ta–Co flow including the effect of viscid heating and buoyancy at different radius ratio (η). The viscous heating and buoyancy effect destabilize the flow.

Rameshkumar Bhoraniya, Pinank Patel, Ramdevsinh Jhala, Rajendrasinh Jadeja

Advanced Numerical Methods Based on Optimization

In this chapter the unconstrainedUnconstrained and constrainedConstrained optimizationOptimization algorithms for numerical methodsNumerical methods are envisaged. The numerical solutions to the fundamental problems in energy systemsEnergy systems are provided. The recent heuristicHeuristic methods used in power systemsPower systems are highlighted, and the specific algorithms are proven by simulations. The selection of the best solution is one of the authors’ concern. Therefore, the optimization algorithms along with numerical examples are delivered in this chapter.

Marian Gaiceanu, Vasile Solcanu, Theodora Gaiceanu, Iulian Ghenea

Ill-Posed Inverse Problems in Electrical Engineering Applications

In this chapter some ill-posed inverse electromagnetic and power engineering problems are introduced, both at a theoretical introductory and mathematical modelling level and detailed regarding their numerical solving case studies based, by the application of several regularizationRegularization techniques starting from classical Tikhonov approach up to singular values decomposition procedures. Fredholm integralFredholm integral equation mathematical modelling is presented in the physical definition of the inverse electromagnetic and/or power engineering problems, accompanied by explanations regarding the physical significance.

Andrei Ceclan, Dan D. Micu, Levente Czumbil, Horia Andrei, Marian Gaiceanu, Marilena Stanculescu, Paul Cristian Andrei

Advanced Energy Systems


Advanced Energy Systems Based on Energy Hub Concept

Energy systems in the past alone were providing consumer's needs, and their management did independently. By industrialization of the lifestyle and high dependence of human societies into energy and on the other hand, a lack of fossil resources, system exploitation seeks to use multi-carrier energy to meet the needs of their consumer's needs. Therefore, the use of multi-carrier systems with the advancement of technology became possible to increase the reliability of the system in the presence of different energy sources. Of course, the critical and challenging issue in it is the way of managing these systems on a large scale. The concept of an energy hub, which is like a virtual box including production, conversion, storage, and consumption of various carriers, has been introduced and the high potential for the operation of multi-carrier systems and optimal management of them possess. This chapter aims to introduce a comprehensive energy hub and its application in the management of multi-carrier systems and express its advantages in preserving the existing resources for posterity alongside the increasing demand for consumers with the lowest cost of operation without limitation its size. Energy hub is used in various sectors such as commercial, industrial, and even agricultural, and can integrate with the integration of these small network hubs from Micro Hub, which are called Macro hub. Moreover, the management of these hubs has dealt with detail.

Hossein Shayeghi, Amir Mohammad Moghaddam

Sustainable Energy Systems Based on the Multi-energy Sources

One of the most important and indispensable needs of people is energy. Today, with the increasing population and developing technology, the energy demand has increased considerably. Currently, one of the most important problems in the world is finding new energies and ensuring its continuity. Development in the economy is possible by having cheap, sufficient, quality and reliable energy sources. Energy, an important element of international power struggles, has gained an international dimension. Energy will continue to be at the forefront of the economic and social development of the countries in the coming centuries. This chapter provides detailed information about non-renewable and renewable energy sourcesRenewable energy sources. Solar and wind energy systems are emphasized. The working principles of hydroelectric and geothermal energy systems are explained. Mas-biomass energy systems, water wave energy systems are given extensive information on. Applications on these energy systems are emphasized. Examples of sustainable energy systems with different energy sources are given. Renewable energy sources can be used directly or converted to another form of energy. Examples of direct use are solar powered appliances, geothermal heating and water or wind mills. Examples of the most direct use are wind turbinesWind turbines or photovoltaic batteries for electricity generation. The development of renewable energy is related to human use of renewable energy sources. The interest in the development of renewable energy is directly related to the waste gases that fossil fuels give to the environment and the risks of fossil fuels and the use of nuclear energy.

Mehmet Zile

Modeling of Energy Systems for Smart Homes

In the last years, smart homes have been introduced for improving the lifestyle of people. The energy system of a smart home is similar to the power network because both consumer and producer types of devices exist in the smart home. This complexity causes that manually managing the smart home becomes more difficult than a traditional home. Knowing the energy system of the smart home and automatically managing of its devices are important in increasing the efficiency of the smart home and the welfare of consumers. For this reason, analytical and mathematical modeling of devices of the smart home is investigated in this chapter. Modeling of the producer and consumer devices of the smart home’s energy system is presented analytically and mathematically. Moreover, an optimization algorithm is also presented to ponder the proposed model of the power system and select the optimal schedule of devices for having the highest operation of the energy system of smart homes. A technical-economic objective function is considered for finding the best schedule of devices. Ultimately, the proposed method is simulated in a sample smart home for evaluating the model of devices and energy system. Ultimately, the efficiency of the proposed energy system of the smart home is pondered based on the simulation results.

Hossein Shayeghi, Masoud Alilou

Finite Volume Method Used for Numerical Investigations of Electrochemical Devices

The chapter provides a general overview on the Finite Volume MethodFinite Volume Method (FVM) and on Computational Fluid DynamicComputational Fluid Dynamic (CFD). It introduces the FVM by using a general scalar transport equation and it describes the main steps of a CFD investigation. All these are applied to the mass, momentum, species, energy and potential conservation equations, equations that govern the operation of Proton Exchange Membrane (PEM) fuel cells. The importance of spatial discretizationSpatial discretization and of interpolation schemesInterpolation schemes used in CFD investigations is point out by analysing few parameters with impact on the fuel cellFuel cell operation. Two cases have been considered. First case based on a fuel cell with a simplified configuration, namely a single serpentine channel, revealed the influence of spatial discretization on the accuracy of the simulation results with regards to current density, pressure and temperature. The second case based on a lab-scale fuel cell with two configurations for channels (7 serpentine and 7 parallel) have been used to analyse the effect of three interpolation schemes (first order, second order, QUICK) on the PEM fuel cell operation; therefore, pressure, hydrogen and water mass fraction profiles were considered for comparison. It was found out that besides the differences in the results accuracy due to spatial discretization and interpolation schemes, the design/geometry used in the CFD investigation may or may not emphasize these differences. If for the 7-serpentine channels fuel cell the interpolation scheme did not show much changes in the accuracy of the results not the same conclusion was drawn for the 7-parallel channels fuel cell where the accuracy of the results improved with increasing the order of the interpolation scheme. A mesh-independent solution on a well-posed problem will provide valuable and accurate results only if the numerical methods are appropriate and the interpolation schemes are of high order. The modeling of fuel cells using CFD techniques, as of any other device, can be an important alternative to the experiment, providing information that is critical to design, operation and optimization, the requirement being to use appropriate model, assumptions and boundary conditions and, of course, an adequate numerical method.

Elena Carcadea, Mihai Varlam

Night Operation of a Solar Chimney Integrated with Spiral Heat Exchanger

Solar powerSolar power is one of the most raising and encouraging renewable source of energy generation. Solar plants are playing an important role in power supplies worldwide. Nowadays, the electrical energyElectrical energy demand is increasing rapidly due to fast-growing daily requirements. In the last few decades, scientific researchers have focused on a novel technology called the solar chimney power plant, sometimes recognized as solar updraft tower. The solar chimneySolar chimney is principally composed of three main constituents, namely, a solar collectorSolar collector, a chimney and a wind turbine. This promising technology addresses a very challenging idea of generating electricity from free solar energy. It is categorized as a viable resource of clean energy for many non developed countries. The world’s first solar chimney prototype was designed and constructed at ManzanaresManzanares in Spain, as a result of a joint project between the Schlaich Bergermann partner and the Spanish government. The plant is characterized by a tower high 195 m with a radius of 5 m. The radius and height of the collector encircling the tower are respectively 120 m and 1.85 m. The spanish prototypeSpanish prototype built by the engineer Jorg Schlaich of Schlaich Bergermann operated without significant problems for seven years. Several research projects have been conducted all over the world to design and introduce different solar towers based on experience gained from operating the 50 kW Spanish prototype. To ensure that the energy conversion is maintained at satisfactory levels to guarantee considerable power generation, an unprecedentedly high tower and an immense collector area are needed. This plant is then based on a thermal updraft movement of hot air resulting from natural convection. In this chapter, the simulations were conducted using cylindrical coordinate system. The inner fluid flow is considered turbulent and simulated with the k-ε turbulent model, by means of the CFDCFD commercial software ANSYS FluentANSYS Fluent. Numerical data were validated by comparing them with those from experiments. The agreement between simulation results and the measurements taken from the experimental plant in Manzanares is fairly good. A set of mathematical modelMathematical models of the solar updraft power plant have been developed where a model considering the kinetic energy difference within the solar collector was proposed. The operation of such a plant is strongly dependent on the amount of solar radiationSolar radiation. The main disadvantage of this system is the inability to operate constantly at night. A geothermal heating device is suggested to guarantee a continuous operation during night hours. In this chapter, an auxiliary heating system constructed of in-plane spiral coil tubesSpiral coil tubes is proposed to be placed above the ground under the collector. Thus, the computational modelComputational model is afterward combined with a mathematical model for a geothermal heat exchanger to evaluate the effect of combining both solar and geothermal energyGeothermal energy on the plant performance. A parametric study of the hybrid plant is carried out. The study focus essentially on the impact of the collector size, the meteorological conditions as well as the effectiveness of the heat exchangerHeat exchanger on the air flow rate, the temperature increase within the collector and the global performance of the solar-geothermal hybrid system.

Amel Dhahri, Ahmed Omri, Jamel Orfi

Incorporating of IPFC in Multi-machine Power System Phillips-Heffron Model

TheIPFC developmentPhillips-Heffron of power networks has led to low-frequencyLow-frequency oscillationsOscillations in the power systemPower system. The relatively small and sudden disturbances in the network cause such oscillations in the system. In the normal case, the oscillations damp rapidly and the amplitude of oscillations does not exceed a certain value. But depending on the operating point conditions and the values of the system parameters, these oscillations may continue for a long time and at worst increase their amplitude. These oscillations can affect the power transmission capability and stabilityStability of the power system. PSSPower System Stabilizers (PSS)" (Power System Stabilizer) and FACTSFACTS (Flexible AC Transmission Systems) devices are commonly used for dampingDamping low-frequency oscillations. The Interline Power Flow Controller (IPFCIPFC) among the FACTS device is suitable for the power flow control and stability of power systems. This chapter establishes an approach to derive the dynamical model of a multi-machineMulti-machine power system with embedded IPFC devices. Derivations about the stability analysis and the incorporating of IPFC to enhance the damping of low-frequency oscillations in a multi-machine power system based on Modified Phillips-HeffronPhillips-Heffron modelingModeling has been done. To demonstrate the application and efficiency of the developed models, a case study on a three-machine test power system with adding IPFC has been presented. Numerical results with MATLABMATLAB for dynamical simulations show the significant effects of IPFC on damping the low-frequency oscillations and especially validates the modeling procedure.

Nemat Talebi, Abas Moghadasi

Techno-Economical Analysis of Energy Storage Systems in Conventional Distribution Networks

Growing trend of integrating renewable energy resources in conventional Distribution NetworksConventional Distribution Network and their intermittent output increase the need for Energy Storage SystemsEnergy Storage Systems (ESS). In this chapter, a closed form equation is proposed for optimal management of multi Energy Storage System in a conventional Distribution Network, analytically. Using the proposed approach, Energy Storage System can be embedded and utilized optimally in today’s Distribution NetworkDistribution Network (DN) using the existing facilities. In order to find optimal performance of the storage system, the objective function is solved analytically and a closed form equation is achieved for storage system performance. The Energy Storage System management is performed in order to minimize total cost of daily energy lossEnergy loss and energy supply of the system. In addition, technical assessment of Energy Storage System is also taken into account to obtain a situation in which utilization of Energy Storage System is economical. In the Optimization problem, energy price, storage utilization duration, amount of load demand, power lossPower Loss of the system, costs, limits and characteristics of storage system are integrated in the objective function. The proposed approach is applied to two test systems with different load levels. Obtained results indicate that the proposed approach can be successfully applied to practical networks and enhance efficiency of the distribution systems.

Amin Foroughi Nematollahi, Abolfazl Rahiminejad, Behrooz Vahidi

OPAL-RT Technology Used in Automotive Applications for PEMFC

This chapter aims to present the implementation and real time simulation stages of a PEM fuel cell using OPAL-RT technology. The following topics are presented: OPAL-RT technology, real-time simulation, conditions regarding the implementation of a mathematical model from Simulink/MATLAB in the RT-LAB platform using the OPAL-RT technology. Through the developed mathematical models, the authors can optimize the fuel cells, but also the integration of monitoring and control systems with the purpose of real time visualization of parameters as well as data acquisition using CAN, data storage and processing. The physical mathematical equations of the model were implemented in a programming language, in the form of code or block diagram, in order to be simulated in real-time. The advantages of real-time simulation of the mathematical models developed in the research projects are characterized by three decisive factors: speed of implementation, development flexibility and results predictability. The originality of the method is that the model can be simulated in real time (HIL) using an OPAL-RT architecture.

Maria Simona Raboaca, Mihai Rata, Ioana Manta, Gabriela Rata

Numerical Energy Applications


Theoretical Techniques for the Exploration of Piezoelectric Harvesters

In this chapter, analytical and numerical techniques for the design and optimizationOptimization of piezoelectricPiezoelectric harvesterHarvester (PH) systems are handled. In the frame of chapter, initially the approaches on how to start with an initial design will be explained. Then, the techniques to improve the starting design will be described. In the working tasks, especially the applications of finite elementFinite element analysis (FEA), and time-integration schemes are focused together with the required analytical methods. There exist many tools to implement the time integration, however from the point of engineering, MatLabMatlab tool is the most preferable. In the case of FEA, mainly the MaxwellMaxwell 3D package programme is explained in the present chapter. A route to get the optimized harvesterHarvester devices is discussed gradually. In the time integration method, the description of dimensionless equations of motion, electricity and magneticMagnetic equations are given for the future possible applications. As the most studied sample in the literature—the cantilever structure of piezoelectric materials are considered under single well and double well potential magnetic regions. The time dependent solutions of the systems are given and possible future applications are underlined on the applications. Main interest areas of PH are medicine, automotive industry, space mission and military devices. Following the mechanical design, the ferromagneticFerromagnetic and non-magnetic parts should be clearly identified for the electromagnetic design if the device uses a magnetic component. Each design has its own magnetic flux path, magnetic field density values and magnetic. In order to provide a concrete device, following the analytical description, 2D or/and 3D designs should be drawn under a package programme working with FEA. MagnetostaticMagnetostatic and magnetodynamicMagnetodynamic solutions are required in order to get the voltage and current output from the system. Besides, a time-dependent solution via a MatLab code can be applied. In this chapter, there will be different harvester systems and their analyses to give comprehensive ideas to the readers for the sake of creating original harvesters. Before the practical applications on the harvesters, theoretical works on the considered harvestersHarvester give a chance to the engineers to use the budget and time efficiently.

Erol Kurt, Hatice Hilal Kurt

Numerical Analysis of Electromagnetic Fields

Classically, the solution to contour problems in electromagnetism was based on analytical techniques, looking for closed solutions. The solution, whether computational or analytical, of electromagnetic problems is extremely important for analyzing the interactions of wave emitting and receiving devices among themselves and with their environment, including both inanimate dispersing objects and living beings. There are many applications in various areas: radio frequency antennas, radar, optics, wireless communications, imaging in bioengineering, nanotechnology and metamaterials, electrical substations, etc. Such analytical or computational solutions are particularly useful to increase productivity in all these well-established areas, to provide procedures to improve existing designs before actual implementations and to facilitate the design of new processes and devices. Typically, electromagnetism problems can be formulated using Maxwell equationsMaxwell equations. However, the Maxwell equations only admit an analytical solution for some dispersing or emitting objects with canonical geometric shapes, such as the sphere, the infinite plane, elemental antennas, etc. Numerical methods broaden the spectrum of known solutions which, while to be considered approximate, in many cases can be selected to what level of precision the calculated results describe the physical reality being analyzed. In recent decades, driven by the availability of increasingly powerful computers, the area of computational electromagneticsComputational electromagnetics (CEM) (CEM) has experienced a remarkable increment as an area of research. Mathematical formulations of physical electromagnetic problems produce systems of equations that can now be solved numerically by computers. Thanks to advances in computational technology and increasingly sophisticated mathematical algorithms of electromagnetic modeling, it is a reality to simulate radiationRadiation or scatteringScattering problems containing arbitrary and complex structures for which there is no analytical solution to the Maxwell equations. There are various methods of computational electromagnetism and various classifications. Depending on the geometric model used by their formulations to characterize the dispersers, they can be classified into three types: ray tracing, surface discretizations, and volume discretizations. Depending on the precision achieved in the results and the field of application, they are classified into full-wave and asymptotic methods, also called low and high-frequency methods. Methods based on volumetric discretizations, such as finite-difference time-domain (FDTD) and frequency domainDomain finite-element methodFinite Element Method (FEM) (FEM), have the advantages that they allow for easy modeling of non-homogeneous media, and their associated 3D mathematical formulations are relatively simple. However, they suffer from the fact that the resulting system of linear equations has a number of unknowns proportional to the simulated volume, so the computational demand grows very rapidly as the electrical dimensions considered in the simulation increase. The methods based on discretizations of surfaces present characteristics that make them computationally more efficient than the volumetric ones. The formulations used in surface methods are based on surface integral equations (SIE) which, unlike volumetric formulations, are mathematically more difficult to implement in a computational code, partly due to the various types of singularities of the Green function. Another disadvantage of this type of methods is the impossibility of simulating general non-homogeneous means, although they have the great advantage that they only require discretizing the interfaces, that is to say, the two-dimensional surfaces that delimit the dispersing objects. Among the surface methods, the method-of-momentsMethod of Moments (MoM) (MoM) and its computational optimizations stand out, in exchange for introducing a controllable numerical error on the results of the pure MoM, known as fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA). The physical optics (PO) is also considered as a surface method based on SIEs since it is based on surface discretizations, although using approximations valid only for electrically large objects. The PO supports a correction method to include diffractionDiffraction, called physical theory of diffraction (PTD), although this correction is only applicable to perfect electric conductors (PEC). In this chapter, we will analyze some of the numerical methods used in electromagnetism.

Javier Bilbao, Eugenio Bravo, Olatz Garcia, Carolina Rebollar, Concepcion Varela

Optimization Methods for Wireless Power Transfer

This chapter provides an investigation of the wireless power transfer domain. It follows the description of the analysis and identification of the system’s parameters, which consist of two magnetically connected coils utilized in constructing the wireless power transfer system. A section of this chapter focuses on the optimizationOptimization aspects of the wireless energy transfer. The optimization considers a function of several parameters of the system such as the structure, the number of turns, the WPTS’s working frequency.

Lavinia Bobaru, Mihai Iordache, Marilena Stanculescu, Dragos Niculae, Sorin Deleanu

Numerical Assessment of Electromagnetic Energy and Forces in Non-destructive Measurement Devices

Non-destructive testingNon-destructive testing in the electromagnetic fieldElectromagnetic field is one of the fastest and least expensive testing techniques for pieces subject to degradation. This domain has evolved a lot in recent years, because of the increasing demands received by the scientific community from the industry. Non-destructive testing aims to detect defects (different types of cracks, structural inhomogeneity) in materials (conducting, ferromagneticFerromagnetic) without destroying the tested object. Therefore, the application of such techniques addresses many relevant domains that require high security of installations, domains such as aeronautical, nuclear, medical, or chemical industry. This chapter provides insight into the most commonly used non-destructive measurement devices, but also into the magnetic field analysis in nonlinear media. It presents the magnetizationMagnetization characteristic evaluation for ferromagnetic bodies.

Marilena Stanculescu, Paul Cristian Andrei, Horia Andrei, Sorin Deleanu, Lavinia Bobaru

Optimal Integration of Electric Vehicles in Smart Grid Energy Flow

This chapter provides an insight into the rapidly growing domain represented by the plug-in electric vehicles (PEV) in connection with the smart grid power system (SGPS) and bi-directional power flowPower flow. The chapter starts with an introductive Sect. 1, followed by Sect. 2, containing a review of the main aspects, which define and characterize the interaction between the EVs and the SGPS. The analysis regarding the integration of the EVs into the SGPS under the vehicle to gridVehicle to grid (V2G) (V2G) considered the three main directions: SGPS efficiency improvement, cost-effectiveness, and the reduction in greenhouse gases. After a presentation of the SGPS structure, Sect. 2 includes a brief description of the primary power produced by the wind turbine as well as the one produced by the photovoltaic panels. Both represent input powers to the SGPS, fact which classifies these two elements of SGPS as power sources, although with an intermittent character. Following Sect. 3 dedicated to the charging stations, the chapter continues with Sect. 4 allocated to modeling, simulation, and results. Firstly, this section contains detailed models dedicated to the analysis of battery chargingBattery charging and battery dischargingBattery discharging, with applications to individual vehicles and considering the presence of renewable energy sources. The models expanded to multiple vehicles, scenarios, and simulations, including the discussions accompanying the results. In the last Sect. 5, the authors present the conclusions. The chapter concludes with an up to date section of references.

Sorin Deleanu, Marilena Stanculescu, Dragos Niculae, Paul Cristian Andrei, Lavinia Bobaru, Horia Andrei

Numerical Approaches of Biomass Plants Efficiency

Considering the ongoing process of diversification of the types of energy production, especially those from renewable sources, one of the goals of sustainable development has become the cleanest energy production, and the monitoring and modeling of the operating parameters is a topic of great interest for researchers in the field. Thus it became an imperative condition to promote the production of electricity from renewable sources in order to support the environmental protection movement but also to obtain an energy independence. The cogeneration process is one of the solutions for obtaining energy from renewable sources because it efficiently energizes the production system by obtaining thermal and electrical energy using the same quantity of fuel. Given that biomassBiomass is the primary energy source, it is clear that it is a clean energy source. This chapter presents a factory for the production of electricity and heat in Romania, which was put into operation in 2014. Its analysis will be done by mathematical modeling of the energy consumption (biomass and biogasBiogas) necessary for the operation. Also, the most important of a biomass-based power plant, precisely the electrical output of energy, the technological usage, and the electrical energy supplied to the national distribution grid are analyzed. The result consists of and an approximation model linking factors like the biogas consumption to the electrical energy output. In Sects. 2, 3 and 4 of this chapter, the authors describe the structure of a cogeneration power plantCogeneration power plant (CPP) (CPP) and introduce an example through a case of study of the data acquisition system for the CPP’s parameters and propose some numerical approachesNumerical approaches model for the evaluation of the CPP efficiencyEfficiency. The CPP analyzed in this chapter is in Suceava County, Romania, and when it first started production, in 2014, it was the biggest running on biomass cogeneration plant in the country. The chapter includes a description of the three distinct phases of the technological process of obtaining energy from biogasBiogas, starting with the type and quantities of the raw materials used and how much energy the CPP can produce. The data acquisition system is part of a sophisticated automated system called “DIANE,” which permanently monitors, coordinates, and controls all the operations in the cogeneration power plantCogeneration power plant (CPP). Following the measurement of many parameters, the analysis focuses on electrical energy production due to each generator, biogas consumption of motors, domestic electricity consumption, and the power consumption required to operate the biogasBiogas station. The acquisition of the operating parameters from the last three years continued with the application of a numerical method of interpolation, based on the PYTHON software environment. Consequently, the authors obtained the relationship between the electrical energy output and the consumed biomassBiomass input parameters in the form of polynomial functions. The chapter ends with conclusions and many references on the topic of numerical approachesNumerical approaches model to the biomass plant technological process and overall efficiencyEfficiency.

Emil Diaconu, Alexandru Enescu, Horia Andrei, Sorin Deleanu

Power and Energy Flow in Cvasi-Stationary Electric and Magnetic Circuits

Answering the question “what is the state in which conservative systems consume less power or energy?” is fundamental. Therefore, multitudinous works were dedicated to formulate the cvasi-stationary state of many domains such as physical sciences (mechanics, thermodynamics, electromagnetic), chemistry, life science (hydrology, meteorology, global climate) in power or energy terms. Based on the variational principles in this chapter specific functionals expressed in terms of power or energy for electric respectively magnetic circuits in cvasi-stationary state are defined. The matrix equations of electro-magnetic circuits formulated in terms of electric and magnetic potentialsMagnetic potentials of nodes were used to calculate the power and energy functionals. Further used advanced numerical methods the existence of functional's minimum were demonstrated and by imposing the minimization conditions are obtained the first Kirchhoff’s law for electric currents respectively magnetic flux. Several examples prove the theoretically and practically importance of the principles of minimum consumed power and energy mainly for understanding of the power and energy flow in electromagnetic systems.

Horia Andrei, Mihai Iordache, Paul Cristian Andrei, Marilena Stanculescu, Sorin Deleanu, Lavinia Bobaru

Numerical Methods for Analysis of Energy Consumption in Drying Process of Wood

This chapter presents general aspects regarding the electromagnetic fieldElectromagnetic field in radio frequency and microwaves, the thermal field, mass problems in radio frequency drying, and the authors’ contributions to the numerical analysis of high frequency drying. The material used in numerical simulationsNumerical Simulation is wood. Wood temperatureTemperature control is very important due to cracks and loss of mechanical properties during drying. The properties of dielectric materials are very important when studying the interaction that takes place between the electromagnetic field energy and the material. The need to process and obtain products that meet market demands has led to the development of process modeling software that are aimed at simulating processes and physical phenomena as precisely and realistically as possible. In the research center (Center for Research and Technological Engineering in Electromagnetic Energy Conversion—CCITCEE) a Fortran software complex that couples electric, thermal, and mass and motion problems called FEM-BEM.3D-RF was developed. In the present study the drying processDrying process of wood was numerical simulated using FEM-BEM.3D-RF in radio frequency field and Comsol Multiphysics in microwave field.

Livia Bandici, Simina Coman, Teodor Leuca

Design and Energy Analysis for Fuel Cell Hybrid Electric Vehicle

The environmental issues impose major changes in actual technologies for vehicle manufacturers. Nowadays, further research is focused on the development technologies for the vehicles of the future. Among these technologies, the fuel cell hybrid electric vehicle (FCHEV) hasFuel Cell Hybrid Electric Vehicle (FCHEV) an important role due to the potential to improve significantly the fuel economy. FCHEVs can be more efficient than conventional internal combustion engines being an efficient and promising perspective. The lately research was focused on different configurations of FCHEVs, especially concerning the desired hybridization level involving the specific FC and batteries rules for their interconnection. Proton exchange membrane fuel cellsProton Exchange Membrane Fuel cell (PEMFC) (PEMFCs) is regarded as promising candidates for vehicle applications, mainly due to the mature technology, which can provide electrical power with high efficiency, less noise, compactness, lightness, low operating temperature, and very low emissions compared with conventional internal combustion engines. The electric efficiency usually represents 40–60% while the output power can be changed to meet quickly demanded load. The design of the power source in the FCHEVsFuel Cell Hybrid Electric Vehicle (FCHEV) is extremely attractive for transport applications. The FCHEV combines the advantage offered by PEMFCProton Exchange Membrane Fuel cell (PEMFC) with the backup system using the efficient energy management assigned by the Battery. The LiPo rechargeable battery assures a quick transfer of energy during transient responses and continuous power during the absence of reactants. In this chapter, we provide a design and energy efficiency analysis for FCHEV implemented in ICSI ENERGY Department, ICSI Rm Valcea, Romania. To ensure the required power, an energy management strategy (EMSEnergy Management Strategy (EMS)) has been proposed. The FCHEV performance obtained in simulation using standardized load cycles is validated by taking into account a real experimental speed profile and numerical analysis of the acquired data. This EMSEnergy Management Strategy (EMS) is focused on rule-based fuzzy logic control and state machine control. The developed FCHEV is mainly composed of PEMFCProton Exchange Membrane Fuel cell (PEMFC) stack, LiPo rechargeable battery, and DC/AC inverter. The LiPo rechargeable battery is the main energy source, while the PEMFC plays the role of the support system. The feeding of the electric motor is assigned by the inverter which can convert the direct current (DC) in alternate current (AC). The PEMFC supplies the stationary/slow variable load, operating close to the maximum efficiency, and the battery supplies the load transients. Moreover, the PEMFC recharges the battery when is necessary, by considering the available extra energy. In order to validate the mentioned strategy, we analyzed the efficiency obtained by using the FCHEVFuel Cell Hybrid Electric Vehicle (FCHEV) in comparison with the efficiency using an only battery (electric vehicle). The results indicated more than 90% efficiency in the first case in comparison to 75% in the second case, respectively. The reliability of our model was tested and evaluated firstly taking into consideration various results by using of Matlab/Simulink environment. The experimental study was carried out by considering a specific protocol for the extra-urban driving cycleExtra-Urban Driving Cycle (EUDC) (EUDC). Therefore, this chapter takes into account an energy management strategy in order to analyze the efficiency obtained by using the FCHEV in comparison with efficiency by using only a battery (electric vehicle).

Mircea Raceanu, Nicu Bizon, Adriana Marinoiu, Mihai Varlam

Finite Element Solutions for Magnetic Shielding Power Applications

In this chapter are presented some aspects concerning the finite element analysis of magnetic shielding for power applications. The investigation describes the physical mechanisms of magnetic shielding the magnetic field in a cylindrical shield using magnetic scalar potential and magnetic vector potential. A variational and a Galerkin finite element formulation are described. The mitigation of an OHTL magnetic field inside a shielded building placed near it is evaluated in the case study of this chapter.

Dumitru Cazacu, Elena Otilia Virjoghe, Valeriu Manuel Ionescu, Stefan Castravete

Regression Analysis-Based Load Modelling for Electric Distribution Networks

The decision making in the electric distribution systems is based on data collected from consumers and the various measurement points located in the network (transformer substations, supply points, branch points, etc.). The information obtained from a 100% integration of the smart metering to consumers comes to fill the data acquired through the Supervisory Control and Data Acquisition (SCADA) system, so that the Distribution Network Operator (DNO) can accurately estimate the state of the supervised system. However, the implementation of smart metering is in various implementation stages in different countries of the world, so that today it can be stated that there is no complete integration. The same aspect should be emphasized in the case of the SCADA system at the level of distribution networksDistribution networks, which is not 100% integrated in the low/medium voltage electric substations. In these conditions, the DNO should apply the mathematical tools that take into account the similarities between the consumers’ behaviour and respectively the structure of the load supplied from the electric substations. The regressionRegression analysis-based approaches for the load modelling from the nodes of electricity distribution networks were treated in the chapter. The approaches refer to the estimation of the required powers in the supply points with a mixt structure of the load (i.e. residential, commercial, and industrial) at the hour when the maximum value of the load is recorded and the demand of residential consumersResidential consumers which represent the highest percentage from the load structure fed from the electric substations. The proposed approaches were tested in real operation conditions of the distribution networks from Romania.

Gheorghe Grigoras, Bogdan Constantin Neagu

Finite Element Analysis of Electromagnetic Fields Emitted by Overhead High-Voltage Power Lines

The overhead high-voltage power lines (OHVPLs) are considered significant sources of extremely low frequency (ELF) electric and magnetic fields (EMFs), whose potential health effects became during the past decades a matter of scientific debate and public concern all over the world. In this chapter, a simple and yet effective finite element (FE) approach is proposed to compute and analyze—from the perspective of public exposure—both electric and magnetic fields emitted by typical configurations of OHVPLs belonging to the Romanian power grid. First, a 2D ANSYS Maxwell model is developed for the specific instance of a 110 kV double-circuit OHVPL and validated against two software tools based on quasi-static analytical methods, PowerELT and PowerMAG. Next, it will be used to investigate exposure to ELF-EMFs emitted by a selection of OHVPLs with nominal voltages of 110 kV, 220 kV and 400 kV, taking into consideration influencing factors such as loading, phasing and ground clearance. Compliance with the exposure guidelines specified by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) for general public is assessed for each particular case. As a result, all calculated magnetic fields are below the ICNIRP limit of 100 μT, while the electric fields exceed the ICNIRP limit of 5000 V/m only in limited areas beneath the 400 kV OHVPLs. The calculated field levels are in line with those reported in the scientific literature for similar OHVPLs.

Eduard Lunca, Bogdan Constantin Neagu, Silviu Vornicu

Design and Finite Element Analysis of Permanent Magnet Synchronous Generator for Wind Turbine Application

Today, the demand for renewable energy sources is increasing day by day in order to reduce fossil fuels and meet the increasing energy demand. The fact that wind energy is suitable for energy production at continuous or low wind speed depending on geographical conditions increases its importance among eco-friendly energy sources. However, energy efficiency is one of the most important issues in the renewable energy field because energy production from these energy sources is constantly changing due to climate changes. Therefore, it is very important to use renewable energy sources efficiently and to enable innovative developments that will increase energy efficiency. In this chapter, a more efficient wind turbineWind turbine alternator is modeled and analyzed in detail by using the ANSYS/MaxwellANSYS/Maxwell software program. The main objective of this chapter is to create an efficient alternator model used in both vertical and horizontal wind turbines. This alternator model is selected as a permanent magnet synchronous generatorPermanent Magnet Synchronous Generators (PMSG) (PMSG) since there is no need for external excitation, smaller in size and easy to control. Firstly, the parameters are determined by using the mathematical model of the alternator. Secondly, the alternator is modeled and designed with the help of the design parameters such as pole pair, magnetizing inductance, the stator leakage, winding properties, number of turns and slots, etc. During the design process, all materials of the alternator are designed by taking into consideration of characteristic features of them. Finally, the designed alternator is electromagnetically analyzed thanks to ANSYS/Maxwell Electromagnetic Suit program which uses the Finite Element MethodFinite Element Method (FEM) (FEM). Therefore, the electrical efficiency of the wind turbine alternator at different wind speeds is performed and the optimum design of the alternator is obtained. It is hoped that this study will guide for wind power plant operators and researchers interested in wind turbine design parameters.

Abdurrahman Yavuzdeger, Burak Esenboga, Firat Ekinci, Tugce Demirdelen

Power and Energy System Modeling Based on Modified Tellegen Principle

The chapter deals with a problem of power and energy modeling of dynamic systems and their numerical solutions. The proposed approach is based on modified Tellegen’sTellegen theorem well known from electrical circuits solving. The new of this approach is that it is based on the power calculation for different linear and nonlinear physical systems. It is supposed that system is described by state spaceState space equations and from these equations the power and energy are calculated. The results can be used for electrical circuits, but also for other real physical system e.g. mechanical systems, heat transfer etc. which are described by state space equations. Thus, mathematically as well as physically correct results are received. Certain known and often used system representation structures are used and their transformations. The theory is supported by solved examples. The mathematical origin, derivation and results of simulations are given in this chapter. It is important mark here a close relationship between first and second Kirchhoff’s laws ensuring physical rightness and link to Tellegen’sTellegen theorem. It is also important to note that inner productInner product incorporate instantaneous power dissipated on resistors and instantaneous power on inductors and capacitors. At last, let’s note that Tellegen’s principle can be used not only to electrical circuits but as well any model of a physical correct system with lumped parameters. Therefore if the system is described accurately by state spaceState space equations, currents and voltages can be substituted by state space variables and it’s derivations. In the chapter, the nonlinear differential equations of linear and nonlinear systems are numerically solved and optimization methods are used in some circumstances. The examples in chapter include also solution of chaotic systems. It is important to note that solution in this chapter is based on power and energy and therefore can be useful also for modeling some devices used in renewable power systems e.g. batteries, capacitors and ultracapacitors, photovoltaic panels etc.

Milan Stork, Daniel Mayer

Self-tuning Yaw Control Strategy of a Horizontal Axis Wind Turbine Based on Machine Learning

The design procedure of a Machine LearningMachine Learning (ML) (ML) based yaw control strategy for a Horizontal Axis Wind TurbineHorizontal Axis Wind Turbine (HAWT) (HAWT) is presented in the following chapter. The proposed yaw control strategy is based on the interaction of three different Artificial Intelligence (AI) techniques to design a ML system: Reinforcement LearningReinforcement Learning (RL) (RL), Artificial Neural Networks (ANN) and metaheuristic optimization algorithms. The objective of the designed control strategy is to achieve, after a training stage, a fully autonomous performance of the wind turbine yaw control system for different input wind scenarios while optimizing the electrical power generated by the wind turbine and the mechanical loads due to the yaw rotation. The RL algorithm is known to be able to learn from experience. The training process could be carried out online with real-time data of the operation of the wind turbine or offline, with simulation data. The use of an ANN to store the data of the matrix Q(s, a) related to the RL algorithm eliminates the large scale data management and simplifies the operation of the proposed control system. Finally, the implementation of a metaheuristic optimization algorithm, in this case a Particle Swarm OptimizationParticle Swarm Optimization (PSO) (PSO) algorithm, allows calculation of the optimal yaw control action that responds to the compromise between the generated power increment and the mechanical loads increase due to the yaw actuation.

Aitor Saenz-Aguirre, Ekaitz Zulueta, Unai Fernandez-Gamiz, Jose Antonio Ramos-Hernanz, Jose Manuel Lopez-Guede

Numerical Methods of Electric Power Flow in Interconnected Systems

In this chapter the powerPower flowPower flow problem is treated as mandatory part of the Energy Management SystemEnergy Management System. The electrical energy flowEnergy flow into power systemPower system cannot be stored. The Energy Management System balance the request between the generation and load demandLoad demand. From this point of view, the steady stateSteady state behaviour of the power system is essentially to take action in case of contingencyContingency events. The authors of this chapter takes into account the most used algorithmsAlgorithms of power flow problem, and they are presented in context of interconnectedInterconnected power systemsPower system with different type of buses: with load, generators, and reference buses, taking into consideration the limitation of the generated reactiveReactive power. The theoretical aspects of the numerical methods are related to the electric power flow in interconnected systems, and they are proved through the delivered case studies: Gauss-SeidelGauss-Seidel, and Newton RaphsonNewton-Raphson.

Marian Gaiceanu, Vasile Solcanu, Theodora Gaiceanu, Iulian Ghenea

Numerical Methods in Selecting Location of Distributed Generation in Energy Network

Integration of Distributed GenerationDistributed Generation (DG) (DG) units provide benefits to distribution systems. The presence of DG can affect various parameters of the distribution system such as reducing power losses and improving voltage profiles. But to maximize the profit from DG, the optimal location and the best amount of DG must be determined. Optimal placement and sizing of DG in the distribution network is a Complicated optimization problem. This paper presents a simple method for optimal sizing and optimal placement of distributed generators. This chapter of the book is about DG placementDG Placement using numerical and innovative methods to solve the DG placement problem and comparing the two methods with each other. These methods are performed in a radial distribution system to minimize the total real power loss and improve the voltage profile. The proposed methods are tested on the standard IEEE 33-bus test system and the results are presented and compared with different approaches.

Reza Effatnejad, Mahdi Hedayati, Keyvan Choopani, Milad Chanddel

Numerical Methods for Power System Analysis with FACTS Devices Applications

Flexible AC Transmission Systems (FACTS) is created higher controllability in power systems. Several FACTS-devices are introduced for various applications. The basic applications of FACTS-devices are including power flow control, voltage control, reactive power compensation, stability improvement, power quality improvement, flicker mitigation, interconnection of renewable and distributed generation and storages. But to achieve the maximum profit from FACTS devices, the optimal size and location of these devices must be determined. Numerical optimization method is one of the methods to achieve the optimal global solution in optimization problems. This chapter of the book is about FACTS devices placementFACTS devices placement using numerical methodNumerical Methods. This method is performed in a radial Transmission system to minimize the power losses and improve the voltage profile. The proposed method is tested on the standard IEEE 14-bus test system. The results of case studies demonstrate the effectiveness of the proposed methodology.

Mahdi Hedayati, Reza Effatnejad, Keyvan Choopani, Milad Chanddel


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