Special Issue "Mathematical Models for the Design of Electrical Machines"

A special issue of Mathematical and Computational Applications (ISSN 2297-8747). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: 31 December 2019

Special Issue Editors

Guest Editor
Assoc. Prof. Dr. Frédéric Dubas

Département ENERGIE, FEMTO-ST, CNRS, University Bourgogne Franche-Comté, F90000 Belfort, France
Website | E-Mail
Interests: applied mathematics; partial differential equations, separation of variables method; principle of superposition; (semi-)analytical modeling; subdomain technique; magnetic equivalent circuit; electrical machines
Guest Editor
Prof. Dr. Kamel Boughrara

Laboratoire de Rcherche en Electrotechnique (LRE-ENP), 16200 Algiers, Algeria
E-Mail
Interests: electromagnetic field; electrical machines; analytical methods; numerical methods

Special Issue Information

Dear Colleagues,

Electrical machines are used in many electrical engineering applications, viz., transports (e.g., electric/hybrid/fuel cell vehicles, railway traction, aerospace, etc.), energy harvesting (e.g., flywheel, etc.), renewable energy (e.g., wind power turbine, hydroelectric power plant, etc.), magnetic refrigeration device, etc. For decades, numerical methods (i.e., the finite-element, finite-difference or boundary-element analysis) have been widely used in R&D departments for their accuracy as compared to measurements. Nevertheless, mainly in 3-D, these approaches are time-consuming and not suitable for the optimization problems. Nowadays, in order to reduce the computation time, R&D engineers must develop full computer-aided-design for electrical machines with accurate and fast models in simulations. Hence, the main objective of this Special Issue is to bring the latest advances and developments in mathematical modeling and design of electrical machines for different applications. The main models discussed will be based on the:

  • Equivalent circuits (e.g., electrical, thermal, magnetic, etc.);
  • Schwarz-Christoffel mapping method;
  • Maxwell-Fourier (i.e., multi-layers models, eigenvalues models, subdomain technique).

The interest topics in the mathematical models include, but are not restricted to:

  • 2-D, quasi 3-D and 3-D;
  • Global/local saturation, slotting and/or eddy-current effects;
  • Adaptive Generic models;
  • Multi-physic modeling with new materials;
  • Hybrid models.

The numerical method as well as the experimental tests will be used as comparisons or validations.

Assoc. Prof. Dr. Frédéric Dubas
Prof. Dr. Kamel Boughrara
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematical and Computational Applications is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 300 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (7 papers)

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Research

Open AccessArticle
Combining the Magnetic Equivalent Circuit and Maxwell–Fourier Method for Eddy-Current Loss Calculation
Math. Comput. Appl. 2019, 24(2), 60; https://doi.org/10.3390/mca24020060
Received: 27 March 2019 / Revised: 31 May 2019 / Accepted: 2 June 2019 / Published: 4 June 2019
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Abstract
In this paper, a hybrid model in Cartesian coordinates combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and [...] Read more.
In this paper, a hybrid model in Cartesian coordinates combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series) is developed. This model coupling has been applied to a U-cored static electromagnetic device. The main objective is to compute the magnetic field behavior in massive conductive parts (e.g., aluminum, magnets, copper, iron) considering the skin effect (i.e., with the eddy-current reaction field) and to predict the eddy-current losses. The magnetic field distribution for various models is validated with 2-D and three-dimensional (3-D) finite-element analysis (FEA). The study is also focused on the discretization influence of 2-D generic MEC on the eddy-current loss calculation in conductive regions. Experimental tests and 3-D FEA have been compared with the proposed approach on massive conductive parts in aluminum. For an operating point, the computation time is divided by ~4.6 with respect to 3-D FEA. Full article
(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
Open AccessFeature PaperArticle
Study of a Hybrid Excitation Synchronous Machine: Modeling and Experimental Validation
Math. Comput. Appl. 2019, 24(2), 34; https://doi.org/10.3390/mca24020034
Received: 1 February 2019 / Revised: 20 March 2019 / Accepted: 21 March 2019 / Published: 27 March 2019
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Abstract
This paper deals with a parallel hybrid excitation synchronous machine (HESM). First, an expanded literature review of hybrid/double excitation machines is provided. Then, the structural topology and principles of operation of the hybrid excitation machine are examined. With the aim of validating the [...] Read more.
This paper deals with a parallel hybrid excitation synchronous machine (HESM). First, an expanded literature review of hybrid/double excitation machines is provided. Then, the structural topology and principles of operation of the hybrid excitation machine are examined. With the aim of validating the double excitation principle of the topology studied in this paper, the construction of a prototype is presented. In addition, both the 3D finite element method (FEM) and 3D magnetic equivalent circuit (MEC) model are used to model the machine. The flux control capability in the open-circuit condition and results of the developed models are validated by comparison with experimental measurements. The reluctance network model is created from a mesh of the studied domain. The meshing technique aims to combine advantages of finite element modeling, i.e., genericity and expert magnetic equivalent circuit models, i.e., reduced computation time. It also allows taking the non-linear characteristics of ferromagnetic materials into consideration. The machine prototype is tested to validate the predicted results. By confronting results from both modeling techniques and measurements, it is shown that the magnetic equivalent circuit model exhibits fairly accurate results when compared to the 3D finite element method with a gain in computation time. Full article
(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
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Open AccessArticle
Exact Two-Dimensional Analytical Calculations for Magnetic Field, Electromagnetic Torque, UMF, Back-EMF, and Inductance of Outer Rotor Surface Inset Permanent Magnet Machines
Math. Comput. Appl. 2019, 24(1), 24; https://doi.org/10.3390/mca24010024
Received: 7 January 2019 / Revised: 8 February 2019 / Accepted: 13 February 2019 / Published: 17 February 2019
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Abstract
This paper presents a two-dimensional analytical model of outer rotor permanent magnet machines equipped with surface inset permanent magnets. To obtain the analytical model, the whole model is divided into the sub-domains, according to the magnetic properties and geometries. Maxwell equations in each [...] Read more.
This paper presents a two-dimensional analytical model of outer rotor permanent magnet machines equipped with surface inset permanent magnets. To obtain the analytical model, the whole model is divided into the sub-domains, according to the magnetic properties and geometries. Maxwell equations in each sub-domain are expressed and analytically solved. By using the boundary/interface conditions between adjacent sub-regions, integral coefficients in the general solutions are obtained. At the end, the analytically calculated results of the air-gap magnetic flux density, electromagnetic torque, unbalanced magnetic force (UMF), back-electromotive force (EMF) and inductances are verified by comparing them with those obtained from finite element method (FEM). One of the merits of this method in comparison with the numerical model is the capability of rapid calculation with the highest precision, which made it suitable for optimization problems. Full article
(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
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Open AccessFeature PaperArticle
Magnetic Field Analytical Solution for Non-homogeneous Permeability in Retaining Sleeve of a High-Speed Permanent-Magnet Machine
Math. Comput. Appl. 2018, 23(4), 72; https://doi.org/10.3390/mca23040072
Received: 9 October 2018 / Revised: 6 November 2018 / Accepted: 7 November 2018 / Published: 10 November 2018
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Abstract
This work presents a novel solution for magnetic field calculation in two-dimensional problems in which one region is defined with space-varying magnetic parameter. The proposed solution extends the well-established Maxwell–Fourier method for calculating magnetic fields in surface-mounted cylindrical high-speed permanent-magnet machines. This contribution [...] Read more.
This work presents a novel solution for magnetic field calculation in two-dimensional problems in which one region is defined with space-varying magnetic parameter. The proposed solution extends the well-established Maxwell–Fourier method for calculating magnetic fields in surface-mounted cylindrical high-speed permanent-magnet machines. This contribution is effective to evaluate more realistic magnetic parameters, where measurements of a high-speed permanent-magnet generator prototype indicate saturation in the retaining sleeve due to pole-to-pole leakage flux. The saturation profile is a function of mechanical angle and can be modeled with the aid of a space-varying relative permeability, expressed in terms of a Fourier series. As an example, the presented solution has been applied to a surface-mounted PM machine at no-load condition. Magnetic field calculations show that a simple saturation profile, with low order space-varying permeability in the retaining sleeve significantly affects the magnetic flux density distribution in the air-gap. The analytical solution is confronted with finite-element method, which confirms validity of the proposed methodology. Full article
(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
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Open AccessFeature PaperArticle
Memory Efficient Method for Electromagnetic Multi-Region Models Using Scattering Matrices
Math. Comput. Appl. 2018, 23(4), 71; https://doi.org/10.3390/mca23040071
Received: 25 October 2018 / Revised: 6 November 2018 / Accepted: 7 November 2018 / Published: 9 November 2018
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Abstract
This paper describes the scattering matrix approach to obtain the solution to electromagnetic field quantities in harmonic multi-layer models. Using this approach, the boundary conditions are solved in such way that the maximum size of any matrix used during the computations is independent [...] Read more.
This paper describes the scattering matrix approach to obtain the solution to electromagnetic field quantities in harmonic multi-layer models. Using this approach, the boundary conditions are solved in such way that the maximum size of any matrix used during the computations is independent of the number of regions defined in the problem. As a result, the method is more memory efficient than classical methods used to solve the boundary conditions. Because electromagnetic sources can be located inside the regions of a configuration, the scattering matrix formulation is developed to incorporate these sources into the solving process. The method is applied to a 3D electromagnetic configuration for verification. Full article
(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
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Open AccessFeature PaperArticle
Two-Dimensional Exact Subdomain Technique of Switched Reluctance Machines with Sinusoidal Current Excitation
Math. Comput. Appl. 2018, 23(4), 59; https://doi.org/10.3390/mca23040059
Received: 18 September 2018 / Revised: 9 October 2018 / Accepted: 10 October 2018 / Published: 11 October 2018
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Abstract
This paper presents a two-dimensional (2D) exact subdomain technique in polar coordinates considering the iron relative permeability in 6/4 switched reluctance machines (SRM) supplied by sinusoidal waveform of current (aka, variable flux reluctance machines). In non-periodic regions (e.g., rotor and/or stator slots/teeth), magnetostatic [...] Read more.
This paper presents a two-dimensional (2D) exact subdomain technique in polar coordinates considering the iron relative permeability in 6/4 switched reluctance machines (SRM) supplied by sinusoidal waveform of current (aka, variable flux reluctance machines). In non-periodic regions (e.g., rotor and/or stator slots/teeth), magnetostatic Maxwell’s equations are solved considering non-homogeneous Neumann boundary conditions (BCs). The general solutions of magnetic vector potential in all subdomains are obtained by applying the interface conditions (ICs) in both directions (i.e., r- and θ-edges ICs). The global saturation effect is taken into account, with a constant magnetic permeability corresponding to the linear zone of the nonlinear B(H) curve. In this investigation, the magnetic flux density distribution inside the electrical machine, the static/dynamic electromagnetic torques, the magnetic flux linkage, the self-/mutual inductances, the magnetic pressures, and the unbalanced magnetic forces (UMFs) have been calculated for 6/4 SRM with two various non-overlapping (or concentrated) windings. One of the case studies is a M1 with a non-overlapping all teeth wound winding (double-layer winding with left and right layer) and the other is a M2 with a non-overlapping alternate teeth wound winding (single-layer winding). It is important to note that the developed semi-analytical model based on the 2D exact subdomain technique is also valid for any number of slot/pole combinations and for non-overlapping teeth wound windings with a single/double layer. Finally, the semi-analytical results have been performed for different values of iron core relative permeability (viz., 100 and 800), and compared with those obtained by the 2D finite-element method (FEM). The comparisons with FEM show good results for the proposed approach. Full article
(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
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Open AccessArticle
An Analytical Expression for Magnet Shape Optimization in Surface-Mounted Permanent Magnet Machines
Math. Comput. Appl. 2018, 23(4), 57; https://doi.org/10.3390/mca23040057
Received: 16 July 2018 / Revised: 2 October 2018 / Accepted: 2 October 2018 / Published: 5 October 2018
Cited by 1 | PDF Full-text (3811 KB) | HTML Full-text | XML Full-text
Abstract
Surface-mounted permanent magnet machines are widely used in low and medium speed applications. Pulsating torque components is the most crucial challenge, especially in low-speed applications. Magnet pole shape optimization can be used to mitigate these components. In this research, an analytical model is [...] Read more.
Surface-mounted permanent magnet machines are widely used in low and medium speed applications. Pulsating torque components is the most crucial challenge, especially in low-speed applications. Magnet pole shape optimization can be used to mitigate these components. In this research, an analytical model is proposed to calculate the magnetic vector potential in surface-mounted permanent magnet machines. A mathematical expression is also derived for optimal the magnet shape to reduce the cogging torque and electromagnetic torque components. The presented model is based on the resolution of the Laplace’s and Poisson’s equations in polar coordinates by using the subdomain method and applying hyperbolic functions. The proposed method is applied to the performance computation of a surface-mounted permanent magnet machine, i.e., a 3-phase 12S-10P motor. The analytical results are validated through the finite element analysis (FEA) method. Full article
(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
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