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

Deadline for manuscript submissions: closed (20 September 2023) | Viewed by 19524

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Dr. Udochukwu B. Akuru

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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

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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
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Prof. Dr. Yacine Amara

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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
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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 others, 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 into solving complex mathematical models based on high-end computation. This Special Issue is focused on “Mathematical and Numerical Analysis in Electrical Engineering” and we kindly request you to submit an article. The scope of the Special Issue will cover areas on mathematical methods and techniques in electrical engineering – analytical, semi-numerical, and numerical-based computational modeling and analysis of electrical engineering problems, as well as 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 optimisation;
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 I. Okoro
Prof. Dr. Yacine Amara
Guest Editors

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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

Published Papers (11 papers)

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Research

18 pages, 7690 KiB

Open AccessArticle

A Parameterized Modeling Method for Magnetic Circuits of Adjustable Permanent Magnet Couplers

by Dazhi Wang, Wenhui Li, Jiaxing Wang, Keling Song, Yongliang Ni and Yanming Li

Mathematics 2023, 11(23), 4793; https://doi.org/10.3390/math11234793 - 27 Nov 2023

Viewed by 602

Abstract

The contactless transmission between the conductor rotor and the permanent magnet (PM) rotor of an adjustable permanent magnet coupler (APMC) provides the device with significant tolerance for alignment errors, making the performance estimation complicated and inaccurate. The first proposal of an edge coefficient in this paper helps to describe the edge effect with better accuracy. Accurate equivalent magnetic circuit (EMC) models of the APMC are established for each region. Models of magnetic flux, magnetic resistance, and eddy current density are established by defining the equivalent dimensional parameters of the eddy current circuit. Furthermore, the concept of magnetic inductance is proposed for the first time, parameterizing eddy currents that are difficult to describe with physical models and achieving the modeling of the dynamic eddy current circuit. The magnetic resistance is subdivided into two parts corresponding to the output and slip according to the power relationship. Furthermore, eddy current loss and dynamic torque models are further derived. The method proposed in this paper enables the APMC to be modeled and calculated in a completely new way. The correctness and accuracy of the model have been fully demonstrated using finite element simulation and an experimental prototype. In addition, the limitations of the proposed method and the reasons are fully discussed and investigated. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering)

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24 pages, 5019 KiB

Open AccessArticle

Sizing, Modeling, and Performance Comparison of Squirrel-Cage Induction and Wound-Field Flux Switching Motors

by Chiweta E. Abunike, Udochukwu B. Akuru, Ogbonnaya I. Okoro and Chukwuemeka C. Awah

Mathematics 2023, 11(16), 3596; https://doi.org/10.3390/math11163596 - 19 Aug 2023

Cited by 1 | Viewed by 1623

Abstract

In this study, the analytical design and electromagnetic performance comparison of a squirrel-cage induction motor (SCIM) and a wound-field flux switching motor (WFFSM) for high-speed brushless industrial motor drives is undertaken for the first time. The study uses analytical sizing techniques and finite element analysis (FEA) to model and predict the performance of both motors at a 7.5 kW output power. This study includes detailed equations and algorithms for sizing and modeling of both types of motors, as well as performance calculations that aid in motor selection, design optimization, and system integration. The main findings show that the SCIM has superior torque performance for starting and overload conditions, while the WFFSM offers advantages in power factor, efficiency over a wide operating range, and potential for higher peak power output. To this end, the WFFSM is capable of high-speed and high-efficiency operation while the SCIM is suitable for applications requiring variable speed operation. The validation study shows good agreement between analytical and FEA calculations for both motors. The results provide insights into the design and performance characteristics of both motors, enabling researchers to explore innovative approaches for improving their efficiency, reliability, and overall performance. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering)

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11 pages, 4284 KiB

Open AccessArticle

A Study on Electric Potential and Electric Field Distribution for Optimal Design of Lightning Rod Using Finite Element Method

by Kyung-Hoon Jang, Sang-Won Seo and Dong-Jin Kim

Mathematics 2023, 11(7), 1668; https://doi.org/10.3390/math11071668 - 30 Mar 2023

Viewed by 1345

Abstract

In this paper, we present an electric field analysis for the optimal structural design of lightning rods for high performance with a charge transfer system (CTS). In the case of a conventional rod that is produced with an empirical design and structure without quantitative data because the design is structurally very simple, only the materials and radius of curvature of the lightning rod to concentrate the electric field at the tip part of the rod are considered. Recently, the development of new types of lightning rods, such as early streamer emission (ESE) and charge transfer system (CTS), has been introduced through simulation analysis and experiments, but detailed specifications and information about the optimal design and structure have not been fully reported. In this paper, we performed an electric field analysis of the structures and materials for the optimal structural design of lightning rods with a function of CTS through computer software analysis with consideration for the radius of curvature, the size of corona ring, and optimal position (X-axis and Y-axis) of the floating electrode. For optimal structural design of lightning rods based on electric field analysis, we used a source of lightning voltage with 1.2/50 µs based on a double exponential equation. The results revealed that the electric field on the relaxation part decreases as the radius of curvature and corona ring increases. For the radius of curvature, the electric field first decreases and then increases with increasing radius of curvature and reaches a minimum at 7 mm and a maximum above 8 mm. For the case of the corona ring, the electric field decreases with increasing corona ring, and the optimal size of the corona ring was selected as 4 mm; the size of the 4 mm corona ring uniformly formed the electric field both at the tip part of the ground current collector and the corona ring. For the electric field concentration part, we found that the optimal X-axis position of the floating electrode and the Y-axis position between the ionizer conductor and floating electrode are 7 mm and 0.1 mm, respectively. These simulation results in this paper are expected to provide useful information for the design of optimized CTS-type lightning rods. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering)

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18 pages, 3881 KiB

Open AccessArticle

Investigation of the Effect of the Voltage Drop and Cable Length on the Success of Starting the Line-Start Permanent Magnet Motor in the Drive of a Centrifugal Pump Unit

by Aleksey Paramonov, Safarbek Oshurbekov, Vadim Kazakbaev, Vladimir Prakht and Vladimir Dmitrievskii

Mathematics 2023, 11(3), 646; https://doi.org/10.3390/math11030646 - 27 Jan 2023

Cited by 4 | Viewed by 1390

Abstract

The use of Line-Start Permanent Magnet Synchronous Motors (LSPMSM) improves the efficiency of conventional direct-on-line electric motor-driven fluid machinery such as pumps and fans. Such motors have increased efficiency compared to induction motors and do not have an excitation winding compared to classical synchronous motors with an excitation winding. However, LSPMSMs have difficulty in starting mechanisms with a high moment of inertia. This problem can be exacerbated by a reduced supply network voltage and a voltage drop on the cable. This article investigates the transients during the startup of an industrial centrifugal pump with a line-start permanent magnet synchronous motor. The simulation results showed that when the voltage on the motor terminals is reduced by 10%, the synchronization is delayed. The use of the cable also leads to a reduction in the voltage at the motor terminals in a steady state, but the time synchronization delay is more significant than that with a corresponding reduction in the supply voltage. The considered simulation example shows that the line-start permanent magnet synchronous motor has no problems with starting the pumping unit, even with a reduced supply voltage. The conclusions of this paper support a wider use of energy-efficient electric motors and can be used when selecting an electric motor to drive a centrifugal pump. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering)

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17 pages, 3985 KiB

Open AccessArticle

Design Optimization of a Synchronous Homopolar Motor with Ferrite Magnets for Subway Train

by Vladimir Dmitrievskii, Vladimir Prakht and Vadim Kazakbaev

Mathematics 2023, 11(3), 589; https://doi.org/10.3390/math11030589 - 22 Jan 2023

Cited by 3 | Viewed by 1712

Abstract

Brushless synchronous homopolar machines (SHM) have long been used as highly reliable motors and generators with an excitation winding on the stator. However, a significant disadvantage that limits their use in traction applications is the reduced specific torque due to the incomplete use of the rotor surface. One possible way to improve the torque density of SHMs is to add inexpensive ferrite magnets in the rotor slots. This paper presents the results of optimizing the performances of an SHM with ferrite magnets for a subway train, considering the timing diagram of train movement. A comparison of its characteristics with an SHM without permanent magnets is also presented. When using the SHM with ferrite magnets, a significant reduction in the dimensions and weight of the motor, as well as power loss, is shown. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering)

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19 pages, 7681 KiB

Open AccessFeature PaperArticle

Mathematical Modeling of the State of the Battery of Cargo Electric Vehicles

by Nikita V. Martyushev, Boris V. Malozyomov, Svetlana N. Sorokova, Egor A. Efremenkov and Mengxu Qi

Mathematics 2023, 11(3), 536; https://doi.org/10.3390/math11030536 - 19 Jan 2023

Cited by 33 | Viewed by 3722

Abstract

In this paper, a mathematical simulation model of an electric vehicle traction battery has been developed, in which the battery was studied during the dynamic modes of its charge and discharge for heavy electric vehicles in various driving conditions—the conditions of the urban cycle and movement outside the city. The state of a lithium-ion battery is modeled based on operational factors, including changes in battery temperature. The simulation results will be useful for the implementation of real-time systems that take into account the processes of changing the characteristics of traction batteries. The developed mathematical model can be used in battery management systems to monitor the state of charge and battery degradation using the assessment of the state of charge (SOC) and the state of health (SOH). This is especially important when designing and operating a smart battery management system (BMS) in virtually any application of lithium-ion batteries, providing information on how long the device will run before it needs to be charged (SOC value) and when the battery should be replaced due to loss of battery capacity (SOH value). Based on the battery equivalent circuit and the system of equations, a simulation model was created to calculate the electrical and thermal characteristics. The equivalent circuit includes active and reactive elements, each of which imitates the physicochemical parameter of the battery under study or the structural element of the electrochemical battery. The input signals of the mathematical model are the current and ambient temperatures obtained during the tests of the electric vehicle, and the output signals are voltage, electrolyte temperature and degree of charge. The resulting equations make it possible to assign values of internal resistance to a certain temperature value and a certain value of the degree of charge. As a result of simulation modeling, the dependence of battery heating at various ambient temperatures was determined. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering)

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21 pages, 3002 KiB

Open AccessArticle

Optimal Sizing of a Photovoltaic Pumping System Integrated with Water Storage Tank Considering Cost/Reliability Assessment Using Enhanced Artificial Rabbits Optimization: A Case Study

by Abdolhamid Mazloumi, Alireza Poolad, Mohammad Sadegh Mokhtari, Morteza Babaee Altman, Almoataz Y. Abdelaziz and Mahmoud Elsisi

Mathematics 2023, 11(2), 463; https://doi.org/10.3390/math11020463 - 15 Jan 2023

Cited by 4 | Viewed by 1593

Abstract

In this paper, optimal sizing of a photovoltaic (PV) pumping system with a water storage tank (WST) is developed to meet the water demand to minimize the life cycle cost (LCC) and satisfy the probability of interrupted water (p_IW) constraint considering real region data. The component sizing, including the PV resources and the WST, is determined optimally based on LCC and p_IW using a new meta-heuristic method named enhanced artificial rabbits optimization (EARO) via a nonlinear inertia weight reduction strategy to overcome the premature convergence of its conventional algorithm. The WST is sized optimally regarding the lack of irradiation and inaccessibility of the pumping system so that it is able to improve the water supply reliability. The LCC for water extraction heights of 5 and 10 m is obtained at 0.2955 M$ and 0.2993 M$, respectively, and the p_IW in these two scenarios is calculated as zero, which means the complete and reliable supply of the water demand of the customers using the proposed methodology based on the EARO. Also, the results demonstrated the superior performance of EARO in comparison with artificial rabbits optimization (ARO) and particle swarm optimization (PSO); these methods have supplied customers’ water demands with higher costs and lower reliability than the proposed EARO method. Also, during the sensitivity analysis, the results showed that changes in the irradiance and height of the water extraction have a considerable effect on the cost and ability to meet customer demand. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering)

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15 pages, 5499 KiB

Open AccessArticle

Study of the Effect of Throttling on the Success of Starting a Line-Start Permanent Magnet Motor Driving a Centrifugal Fan

by Aleksey Paramonov, Safarbek Oshurbekov, Vadim Kazakbaev, Vladimir Prakht and Vladimir Dmitrievskii

Mathematics 2022, 10(22), 4324; https://doi.org/10.3390/math10224324 - 18 Nov 2022

Cited by 5 | Viewed by 1297

Abstract

Direct-on-line synchronous motors are a good alternative to induction motors in fluid machinery drives due to their greater energy efficiency but have the significant disadvantage of limiting the maximum moment of inertia of the loading mechanism to ensure their successful and reliable start-up. This disadvantage is critical in centrifugal fans with a massive steel impeller. In this article, using a mathematical model, the dynamics of starting and synchronizing a permanent magnet synchronous motor fed directly from the mains as part of a fan drive are studied. The simulation results show the possibility of increasing the maximum moment of inertia of the load at the successful start-up of a direct-on-line synchronous motor by adjusting the hydraulic part of the fan pipeline by means of throttling. The conclusions of this paper can be used when selecting an electric motor to drive industrial fans and can contribute to wider use of energy-efficient synchronous motors with direct start-up from the mains. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering)

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19 pages, 7387 KiB

Open AccessArticle

High Impedance Fault Detection Protection Scheme for Power Distribution Systems

by Katleho Moloi and Innocent Davidson

Mathematics 2022, 10(22), 4298; https://doi.org/10.3390/math10224298 - 16 Nov 2022

Cited by 7 | Viewed by 1457

Abstract

Protection schemes are used in safe-guarding and ensuring the reliability of an electrical power network. Developing an effective protection scheme for high impedance fault (HIF) detection remains a challenge in research for protection engineers. The development of an HIF detection scheme has been a subject of interest for many decades and several methods have been proposed to find an optimal solution. The conventional current-based methods have technical limitations to effectively detect and minimize the impact of HIF. This paper presents a protection scheme based on signal processing and machine learning techniques to detect HIF. The scheme employs the discrete wavelet transform (DWT) for signal decomposition and feature extraction and uses the support vector machine (SVM) classifier to effectively detect the HIF. In addition, the decision tree (DT) classifier is implemented to validate the proposed scheme. A practical experiment was conducted to verify the efficiency of the method. The classification results obtained from the scheme indicated an accuracy level of 97.6% and 87% for the simulation and experimental setups. Furthermore, we tested the neural network (NN) and decision tree (DT) classifiers to further validate the proposed method. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering)

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15 pages, 11057 KiB

Open AccessArticle

A 2D Multi-Layer Model to Study the External Magnetic Field Generated by a Polymer Exchange Membrane Fuel Cell

by Antony Plait and Frédéric Dubas

Mathematics 2022, 10(20), 3883; https://doi.org/10.3390/math10203883 - 19 Oct 2022

Cited by 2 | Viewed by 1063

Abstract

An original innovative two-dimensional (2D) multi-layer model based on the Maxwell–Fourier method for the diagnosis of a polymer exchange membrane (PEM) fuel cell (FC) stack is presented. It is possible to determine the magnetic field distribution generated around the PEMFC stack from the (non-)homogenous current density distribution inside the PEMFC stack. Analysis of the magnetic field distribution can indicate whether the FC is healthy or faulty. In this way, an explicit, accurate and fast analytical model can allow the health state of an FC to be studied. To evaluate the capacity and the efficiency of the 2D analytical model, the distribution of local quantities (i.e., magnetic vector potential and magnetic field) in a PEMFC stack has been validated with those obtained by the 2D finite-element analysis (FEA). The comparisons demonstrate excellent results both in terms of amplitude and waveform. The validation of this 2D analytical model is essential for the subsequent generation of an inverse model useful for the diagnosis of a PEMFC. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering)

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21 pages, 11965 KiB

Open AccessArticle

A Novel Universal Torque Control of Switched Reluctance Motors for Electric Vehicles

by Mahmoud Hamouda, Fahad Al-Amyal, Ismoil Odinaev, Mohamed N. Ibrahim and László Számel

Mathematics 2022, 10(20), 3833; https://doi.org/10.3390/math10203833 - 17 Oct 2022

Cited by 3 | Viewed by 1322

Abstract

Due to their advantages, switched reluctance motors (SRMs) are interesting solutions for electric vehicle (EV) propulsion. However, they have the main drawback of high torque ripple. This paper develops a universal torque control (UTC) technique for SRM that can fulfill all vehicle requirements under a wide range of speeds. The developed UTC involves two different control techniques. It utilizes the direct instantaneous torque control (DITC) strategy in a low speed region, and the average torque control (ATC) strategy in high speeds. The selection of DITC and ATC is made based on their performance regarding torque ripple, torque/current ratio, and efficiency. Moreover, a novel transition control between the two control techniques is introduced. The results show the ability of the proposed UTC to achieve vehicle requirements while obtaining all the benefits of torque control over the possible range of speeds. The proposed UTC provides the best performance regarding minimum torque ripple, maximum torque/current ratio, and maximum efficiency over the whole speed range. The transition control achieves a smooth operation without any disturbances. The transition control helps to simplify the overall control algorithm, aiming to have a feasible and practical UTC without a complicated control structure. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering)

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