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Mathematical Modelling and Numerical Analysis in Electrical Engineering, 2nd Edition
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Mathematical Modelling and Numerical Analysis in Electrical Engineering, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 28 February 2025 | Viewed by 4591

Special Issue Editors

Dr. Udochukwu B. Akuru

E-Mail Website
Guest Editor
Department of Electrical Engineering, Tshwane University of Technology, Pretoria 0183, South Africa
Interests: electrical machines; power engineering; renewable energy
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ogbonnaya I. Okoro

E-Mail Website
Guest Editor
Department of Electrical and Electronic Engineering, College of Engineering and Engineering Technology (CEET), Michael Okpara University of Agriculture Umudike, 440001 Umuahia, Abia State, Nigeria
Interests: electrical power; machines
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yacine Amara

E-Mail Website
Guest Editor
GREAH, Université Le Havre Normandie, 76600 Le Havre, France
Interests: electrical power engineering; engineering, applied and computational mathematics; design engineering; electrical and electronics engineering; power systems analysis; MATLAB simulation; power electronics; finite element modeling; finite element analysis; renewable energy technologies
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematics and electrical engineering have always existed mutually. Mathematics is the science of studying numbers, quantities, geometry, and shapes, while electrical engineering deals with, among other things, the practical application of mathematical theory in circuit design, electromagnetics, and electronics. To bridge the gap between mathematical problems and real-world solutions, numerical processes have evolved to solve complex mathematical models based on high-end computations. This Special Issue is focused on “Mathematical and Numerical Analysis in Electrical Engineering”, and we kindly request you to submit an article. This Special Issue will cover mathematical methods and techniques in electrical engineering, analytical, semi-numerical, and numerical-based computational modelling, the analysis of electrical engineering problems, and mathematical and numerical designs for industrial-based electrical engineering devices and systems.

Suggested Topics for the Special Issue:

  • Numerical and analytical methods and simulation of electromagnetic fields, devices, and systems;
  • Mathematical and numerical modelling in electrical power engineering;
  • Computational techniques for efficient numerical analysis of electrical devices and networks;
  • Fast numerical modelling and analysis techniques for prototyping of electrical machines;
  • Mathematical and numerical processes in power system and electrical machines optimization;
  • Applied mathematics in power engineering theory and design;
  • Thermal analysis and control of electrical machines based on mathematical modelling and simulations;
  • Finite element analyses for industrial design feasibility of renewable energy devices.

Dr. Udochukwu B. Akuru
Prof. Dr. Ogbonnaya Okoro
Prof. Dr. Yacine Amara
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 submissions that pass pre-check are 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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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.

Keywords

  • applied mathematics
  • finite element analysis
  • numerical modelling and analysis
  • analytical modelling
  • electrical power engineering
  • electrical machines
  • electrical networks
  • renewable energy devices
  • design optimisation
  • power systems
  • electromagnetic fields
  • mathematical modelling
  • computer-aided design and modelling
  • industrial design and prototyping

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (5 papers)

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Research

18 pages, 6191 KiB  
Article
Fast Analysis and Optimization of a Magnetic Gear Based on Subdomain Modeling
by Manh-Dung Nguyen, Woo-Sung Jung, Duy-Tinh Hoang, Yong-Joo Kim, Kyung-Hun Shin and Jang-Young Choi
Mathematics 2024, 12(18), 2922; https://doi.org/10.3390/math12182922 - 20 Sep 2024
Viewed by 532
Abstract
This study presents a two-dimensional analytical method for fast optimization, taking into consideration the influence of the eddy current in a magnet and iron loss within a coaxial magnetic gear. Subdomain modeling was utilized to obtain vector potentials in the air-gap, magnet, and [...] Read more.
This study presents a two-dimensional analytical method for fast optimization, taking into consideration the influence of the eddy current in a magnet and iron loss within a coaxial magnetic gear. Subdomain modeling was utilized to obtain vector potentials in the air-gap, magnet, and modulation regions by solving Maxwell’s equations. After that, the magnet, rotor, and modulation losses were predicted and then compared using a finite element method simulation within three topologies with gear ratios ranging from five to six. The authors improved the machine performance, specifically the torque density, by employing a multi-objective function with particle swarm optimization. The flux density obtained using subdomain modeling in just 0.5 s benefits the optimization process, resulting in a torque-density optimal model after around 3 h. A 3/19/16 prototype targeting a low-speed, high-torque, permanent generator application was fabricated to verify the analytical and simulation results. Full article
(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering, 2nd Edition)
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25 pages, 6867 KiB  
Article
Derivation of Analytical Expressions for Fast Calculation of Resistance Spot Welding System Currents
by Robert Brezovnik and Jožef Ritonja
Mathematics 2024, 12(16), 2454; https://doi.org/10.3390/math12162454 - 7 Aug 2024
Viewed by 588
Abstract
The paper deals with the dynamics of a resistance spot welding system. At the core of this system is a transformer, which is powered on the primary side by a pulse-width modulated inverter and has a full-wave output rectifier on the secondary side [...] Read more.
The paper deals with the dynamics of a resistance spot welding system. At the core of this system is a transformer, which is powered on the primary side by a pulse-width modulated inverter and has a full-wave output rectifier on the secondary side that provides a direct welding current. The entire system is nonlinear, due to magnetic hysteresis and electronics. The electronics prevent the current from flowing in all parts of the welding transformer at separate time intervals during the voltage supply period; therefore, not all the parameters affect the dynamic of currents and voltages all the time so the system is also time-variant. To design a high-performance welding system and to predict the maximum possible welding current at a specific load, it is necessary to know the welding and primary currents. The leakage inductances of the system can reduce the maximum welding current significantly at higher frequencies and the same load. There are several methods to determine these currents, each with its drawbacks. Measurements are time-consuming, using professional software is expensive and requires time to learn and free open-source software has many limitations and does not guarantee the correctness of the results. The article presents a new, fourth option—a theoretical derivation of analytical expressions that facilitate straightforward and rapid calculation of the welding and primary currents of the resistance spot welding system with symmetrical secondary branches. The derivation of the mathematical expressions is based on the equivalent circuits that describe the system in different operating states. The results of the numerical simulations confirmed the derived expressions completely. Full article
(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering, 2nd Edition)
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22 pages, 147962 KiB  
Article
Developing and Evaluating the Operating Region of a Grid-Connected Current Source Inverter from Its Mathematical Model
by Carlos R. Baier, Pedro E. Melin, Miguel A. Torres, Roberto O. Ramirez, Carlos Muñoz and Agustin Quinteros
Mathematics 2024, 12(12), 1775; https://doi.org/10.3390/math12121775 - 7 Jun 2024
Cited by 2 | Viewed by 898
Abstract
Grid-connected power inverters are indispensable in modern electrical systems, playing a pivotal role in enhancing the integration of renewable energies into power grids. Their significance, primarily when functioning as grid-forming inverters, extends to maintaining the grid’s inertia and strength—a distinct advancement over traditional [...] Read more.
Grid-connected power inverters are indispensable in modern electrical systems, playing a pivotal role in enhancing the integration of renewable energies into power grids. Their significance, primarily when functioning as grid-forming inverters, extends to maintaining the grid’s inertia and strength—a distinct advancement over traditional grid-following operations. As grid-forming inverters, these devices emulate the characteristics of synchronous generators and can act as robust voltage sources, providing essential ancillary services. This behavior is particularly relevant when integrating energy storage systems on the converters’ direct current side. Among the various inverter topologies, the current source inverter (CSI) has emerged as a promising yet underexplored alternative for grid-forming applications. CSIs, when paired with their AC output filters, can effectively operate as voltage sources, utilizing control strategies that facilitate the integration of renewable energies into the electrical system. Their design inherently manages output current fluctuations, reducing the need for restrictive current limitations or additional protective measures. This paper examines the operational region of CSIs, obtained through detailed modeling, to explore their advantages, challenges, and potential for enhancing grid-connected systems. Analyzing the operating region from the converter model verifies the limits of where the converter can operate in a plane of active and reactive powers. For a small prototype model operating with 7 amperes in DC and 120 V in AC, it is possible to supply or absorb active power exceeding 1000 W and manage maximum reactive power values around 500 VAr, as determined by its operating region. Simulations also confirm that small changes in the control reference, as little as 5%, towards the region’s right limits cause significant oscillations in the dynamic control responses. This research aims to deepen our understanding of CSIs’ operational capabilities and highlight their unique benefits in advancing grid-connected systems and promoting the integration of renewable energy using this technology. Full article
(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering, 2nd Edition)
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25 pages, 2927 KiB  
Article
Optimization of an IPMSM for Constant-Angle Square-Wave Control of a BLDC Drive
by Mitja Garmut, Simon Steentjes and Martin Petrun
Mathematics 2024, 12(10), 1418; https://doi.org/10.3390/math12101418 - 7 May 2024
Cited by 1 | Viewed by 767
Abstract
Interior permanent magnet synchronous machines (IPMSMs) driven with a square-wave control (i.e., six-step, block, or 120° control), known commonly as brushless direct current (BLDC) drives, are used widely due to their high power density and control simplicity. The advance firing (AF) angle is [...] Read more.
Interior permanent magnet synchronous machines (IPMSMs) driven with a square-wave control (i.e., six-step, block, or 120° control), known commonly as brushless direct current (BLDC) drives, are used widely due to their high power density and control simplicity. The advance firing (AF) angle is employed to achieve improved operation characteristics of the drive. The AF angle is, in general, applied to compensate for the commutation effects. In the case of an IPMSM, the AF angle can also be adjusted to exploit reluctance torque. In this paper, a detailed study was performed to understand its effect on the drive’s performance in regard to reluctance torque. Furthermore, a multi-objective optimization of the machine’s cross-section using neural network models was conducted to enhance performance at a constant AF angle. The reference and improved machine designs were evaluated in a system-level simulation, where the impact was considered of the commutation of currents. A significant improvement in the machine performance was achieved after optimizing the geometry and implementing a fixed AF angle of 10°. Full article
(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering, 2nd Edition)
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24 pages, 4977 KiB  
Article
Analysis of Higher-Order Bézier Curves for Approximation of the Static Magnetic Properties of NO Electrical Steels
by Ermin Rahmanović and Martin Petrun
Mathematics 2024, 12(3), 445; https://doi.org/10.3390/math12030445 - 30 Jan 2024
Viewed by 832
Abstract
Adequate mathematical description of magnetization curves is indispensable in engineering. The accuracy of the description has a significant impact on the design of electric machines and devices. The aim of this paper was to analyze the capability of Bézier curves systematically, to describe [...] Read more.
Adequate mathematical description of magnetization curves is indispensable in engineering. The accuracy of the description has a significant impact on the design of electric machines and devices. The aim of this paper was to analyze the capability of Bézier curves systematically, to describe the nonlinear static magnetic properties of non-oriented electrical steels, and to compare this approach versus the established mathematical descriptions. First, analytic functions versus measurements were analyzed. The Bézier curves were then compared systematically with the most adequate analytic functions. Next, the most suitable orders of Bézier curves were determined for the approximation of nonlinear magnetic properties, where the influence of the range of the input measurement dataset on the approximation process was analyzed. Last, the extrapolation capabilities of the Bézier curves and analytic functions were evaluated. The general conclusion is that Bézier curves have adequate flexibility and significant potential for the approximation and extrapolation of nonlinear properties of non-oriented electrical steels. Full article
(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering, 2nd Edition)
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