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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 31 August 2025 | Viewed by 16416

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Special Issue Editors

Prof. Dr. Helga Silaghi

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Guest Editor

Department of Control Systems Engineering and Management, University of Oradea, 410087 Oradea, Romania
Interests: mathematical modelling of electrical machines; numerical simulation of electrical machines; modelling and simulation in electrical drives; control of electric drive systems; control systems engineering; mathematical modelling and control of robotic systems; intelligent control of electric vehicles

Dr. Claudiu Raul Costea

E-Mail Website
Guest Editor

Department of Control Systems Engineering and Management, University of Oradea, 410087 Oradea, Romania
Interests: modelling and simulation in electrical drives; control of electric drive systems; identification methods; control systems engineering; intelligent control of electric vehicles

Special Issue Information

Dear Colleagues,

This Special Issue, “Applied Mathematics and Intelligent Control in Electrical Engineering”, addresses researchers working in the field of mathematical methods applied in electrical engineering. The main aim of this Special Issue is to collect research articles in which the latest advances in the mathematical methods and procedures applied in electrical engineering are approached. The problem of highlighting the efficiency of the proposed solutions by applying them in the case of practical applications is also covered. This Special Issue is dedicated to a large range of scientific subjects, including mathematical modelling, numerical methods, numerical simulation of electrical machines, modelling and simulation in electrical drives, modelling and simulation in power electronics, control of electric vehicles, mathematical modelling and control of robotic systems, applied mathematics in energy systems and electrical engineering applications. Mathematical methods and procedures represent some of the most efficient solutions for improving the design of electrical machines and drives in order to obtain better performances.

Potential topics include, but are not limited to, the following areas:

Mathematical modelling in electrical engineering;
Numerical methods in electrical engineering;
Numerical simulation of electrical machines;
Applied mathematics in electrical drive systems;
Artificial intelligence in electrical drive systems;
Modelling and simulation in electrical drives;
Modelling and simulation in power electronics;
Mathematical modelling and control of robotic systems;
Applied mathematics in energy systems;
Special electric drives;
Control of electric drive systems;
Intelligent control of electric vehicles;
Industrial drive applications.

Prof. Dr. Helga Silaghi
Dr. Claudiu Raul Costea
Guest Editors

Manuscript Submission Information

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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.

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Keywords

applied mathematics
mathematical modelling
numerical methods
numerical simulation
electrical engineering
electrical machines
electrical drive systems
artificial intelligence
power electronics
industrial applications
special electric drives
control of electric vehicles
energy systems
robotic systems

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Published Papers (9 papers)

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Research

20 pages, 1810 KiB

Open AccessArticle

The Application of Transformers with High-Temperature Superconducting Windings Considering the Skin Effect in Mobile Power Supply Systems

by Vadim Manusov, Inga Zicmane, Ratmir Galeev, Svetlana Beryozkina and Murodbek Safaraliev

Mathematics 2025, 13(5), 821; https://doi.org/10.3390/math13050821 - 28 Feb 2025

Viewed by 594

Abstract

The active and passive components of transformer electrical equipment have reached their limits regarding modernization and optimization, leading to the implementation of innovative approaches. This is particularly relevant for mobile and autonomous energy complexes due to the introduction of increased frequency, which can be advantageous, especially in geoengineering, where the energy efficiency of electrical equipment is crucial. The new design of transformer equipment utilizing cryogenic technologies incorporates high-temperature superconducting (HTS) windings, a dielectric filler made of liquid nitrogen, and a three-dimensional magnetic system based on amorphous alloys. The finite element method showed that the skin effect does not impact HTS windings compared to conventional designs when the frequency increases. The analysis and synthesis of the parameters of the magnetic system made from amorphous iron and HTS windings in an HTS transformer with a dielectric medium of liquid nitrogen at a temperature of 77 K were performed, significantly reducing the mass and size characteristics of the HTS transformer compared to traditional counterparts while eliminating environmental and fire hazards. Based on these studies, an experimental prototype of an industrial HTS transformer with a capacity of 25 kVA was designed and manufactured. Full article

(This article belongs to the Special Issue Applied Mathematics and Intelligent Control in Electrical Engineering)

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23 pages, 1477 KiB

Open AccessArticle

Sensitivity Analysis of MTPA Control to Angle Errors for Synchronous Reluctance Machines

by Martin Petrun and Jernej Černelič

Mathematics 2025, 13(1), 38; https://doi.org/10.3390/math13010038 - 26 Dec 2024

Cited by 2 | Viewed by 741

Abstract

This study investigated the sensitivity of maximum torque per ampere (MTPA) control in synchronous reluctance machines (SynRMs) to angle errors, examining specifically how deviations in the reference control trajectory affected performance. Analytical and numerical methods were employed to analyze this sensitivity systematically, including the impact of magnetic saturation. Two MTPA control implementation schemes were evaluated, with torque and current amplitude as the reference variables, using a template SynRM from the open-source simulation tool SyR-e. The results indicated that performance sensitivity to angle errors was moderately low near the MTPA trajectory, allowing for significant angle deviations with minimal performance loss. Although magnetic saturation increased this sensitivity slightly, reducing the allowable error range by up to 25%, the maximum angle deviation for up to 1% of the performance decrease still corresponded to approximately

\pm 3^{\circ}

around the MTPA trajectory. The findings of this study suggest potential for simplifying control implementations, reducing component costs through less precise position determination (sensor-based or sensorless), and achieving additional control objectives such as torque ripple reduction. Full article

(This article belongs to the Special Issue Applied Mathematics and Intelligent Control in Electrical Engineering)

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39 pages, 3488 KiB

Open AccessArticle

Parameter Extraction for Photovoltaic Models with Flood-Algorithm-Based Optimization

by Yacine Bouali and Basem Alamri

Mathematics 2025, 13(1), 19; https://doi.org/10.3390/math13010019 - 25 Dec 2024

Cited by 2 | Viewed by 1055

Abstract

Accurately modeling photovoltaic (PV) cells is crucial for optimizing PV systems. Researchers have proposed numerous mathematical models of PV cells to facilitate the design and simulation of PV systems. Usually, a PV cell is modeled by equivalent electrical circuit models with specific parameters, which are often unknown; this leads to formulating an optimization problem that is addressed through metaheuristic algorithms to identify the PV cell/module parameters accurately. This paper introduces the flood algorithm (FLA), a novel and efficient optimization approach, to extract parameters for various PV models, including single-diode, double-diode, and three-diode models and PV module configurations. The FLA’s performance is systematically evaluated against nine recently developed optimization algorithms through comprehensive comparative and statistical analyses. The results highlight the FLA’s superior convergence speed, global search capability, and robustness. This study explores two distinct objective functions to enhance accuracy: one based on experimental current–voltage data and another integrating the Newton–Raphson method. Applying metaheuristic algorithms with the Newton–Raphson-based objective function reduced the root-mean-square error (RMSE) more effectively than traditional methods. These findings establish the FLA as a computationally efficient and reliable approach to PV parameter extraction, with promising implications for advancing PV system design and simulation. Full article

(This article belongs to the Special Issue Applied Mathematics and Intelligent Control in Electrical Engineering)

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28 pages, 7546 KiB

Open AccessArticle

Signatures and Mechanism Analysis of Converter-Grid Subsynchronous Oscillations

by Alisher Askarov, Yuly Bay, Ruslan Ufa, Pavel Radko, Pavel Ilyushin and Aleksey Suvorov

Mathematics 2024, 12(24), 3884; https://doi.org/10.3390/math12243884 - 10 Dec 2024

Viewed by 959

Abstract

In the last decade, a rather new phenomenon related to subsynchronous oscillations (SSO) in a wide frequency range has emerged in modern power grids with power converters. The consequences of these oscillations can be severe system accidents, which have already occurred in various power systems. Taking into account the importance of studying such oscillations for effective mitigation and the existing gaps in understanding the mechanisms of SSO occurrence due to different combinations of used controllers in the inverter control system, as well as the grid parameters, a frequency analysis of simplified grid inverter models is performed. As a result, five different mechanisms of SSO occurrence, the affecting factors and the level of inverter model detail required for the adequate study of SSO are justified. The developed detailed state–space model allowed for verifying the obtained results, as well as identifying an additional sixth mechanism of SSO occurrence. The common condition for the occurrence of all the identified SSO mechanisms is a weak grid with a short-circuit ratio of less than two. The results of control hardware-in-the-loop testing confirmed the conclusions drawn. As a result, a classification of SSO occurrence mechanisms was formed, reflecting their causes and distinctive features. Full article

(This article belongs to the Special Issue Applied Mathematics and Intelligent Control in Electrical Engineering)

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14 pages, 1572 KiB

Open AccessArticle

Artificial Neural Network-Based Data-Driven Parameter Estimation Approach: Applications in PMDC Motors

by Faheem Ul Rehman Siddiqi, Sadiq Ahmad, Tallha Akram, Muhammad Umair Ali, Amad Zafar and Seung Won Lee

Mathematics 2024, 12(21), 3407; https://doi.org/10.3390/math12213407 - 31 Oct 2024

Cited by 1 | Viewed by 1514

Abstract

The optimal performance of direct current (DC) motors is intrinsically linked to their mathematical models’ precision and their controllers’ effectiveness. However, the limited availability of motor characteristic information poses significant challenges to achieving accurate modeling and robust control. This study introduces an approach employing artificial neural networks (ANNs) to estimate critical DC motor parameters by defining practical constraints that simplify the estimation process. A mathematical model was introduced for optimal parameter estimation, and two advanced learning algorithms were proposed to efficiently train the ANN. The performance of the algorithms was thoroughly analyzed using metrics such as the mean squared error, epoch count, and execution time to ensure the reliability of dynamic priority arbitration and data integrity. Dynamic priority arbitration involves automatically assigning tasks in real-time depending on their relevance for smooth operations, whereas data integrity ensures that information remains accurate, consistent, and reliable throughout the entire process. The ANN-based estimator successfully predicts electromechanical and electrical characteristics, such as back-EMF, moment of inertia, viscous friction coefficient, armature inductance, and armature resistance. Compared to conventional methods, which are often resource-intensive and time-consuming, the proposed solution offers superior accuracy, significantly reduced estimation time, and lower computational costs. The simulation results validated the effectiveness of the proposed ANN under diverse real-world operating conditions, making it a powerful tool for enhancing DC motor performance with practical applications in industrial automation and control systems. Full article

(This article belongs to the Special Issue Applied Mathematics and Intelligent Control in Electrical Engineering)

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32 pages, 13207 KiB

Open AccessArticle

Mathematical Modelling of Traction Equipment Parameters of Electric Cargo Trucks

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

Mathematics 2024, 12(4), 577; https://doi.org/10.3390/math12040577 - 14 Feb 2024

Cited by 12 | Viewed by 1764

Abstract

Electric vehicles are one of the most innovative and promising areas of the automotive industry. The efficiency of traction equipment is an important factor in the operation of an electric vehicle. In electric vehicles, the energy stored in the battery is converted into mechanical energy to drive the vehicle. The higher the efficiency of the battery, the less energy is lost in the conversion process, which improves the overall energy efficiency of the electric vehicle. Determining the performance characteristics of the traction battery of an electric vehicle plays an important role in the selection of the vehicle and its future operation. Using mathematical modelling, it is shown that battery capacity, charging rate, durability and efficiency are essential to ensure the comfortable and efficient operation of an electric vehicle throughout its lifetime. A mathematical model of an electric truck including a traction battery has been developed. It is shown that, with the help of the developed mathematical model, it is possible to calculate the load parameters of the battery in standardised driving cycles. The data verification is carried out by comparing the data obtained during standardised driving with the results of mathematical modelling. Full article

(This article belongs to the Special Issue Applied Mathematics and Intelligent Control in Electrical Engineering)

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23 pages, 5801 KiB

Open AccessArticle

Moving Discretized Control Set Model Predictive Control with Dominant Parameter Identification Strategy for Dual Active Bridge Converters

by Tan-Quoc Duong and Sung-Jin Choi

Mathematics 2024, 12(4), 563; https://doi.org/10.3390/math12040563 - 13 Feb 2024

Viewed by 1739

Abstract

The dual active bridge (DAB) converter has grown significantly as one of the most important units for energy distribution, connecting various types of renewable energy sources with the DC microgrid. For controlling the DAB converter, moving discretized control set model predictive control (MDCS-MPC) is considered one of the most effective methods because of its advantages, such as high dynamic performance and multiobjective control. However, MDCS-MPC strongly depends on the accuracy of system parameters. Meanwhile, the system parameters can be changed due to temperature drift, manufacturing tolerance, age, and operating circumstances. As a result, the steady-state performance of the output voltage of MDCS-MPC is affected. Motivated by this, this paper proposes MDCS-MPC combined with the parameter identification technique to improve the steady-state performance of the output voltage of the DAB converter. Then, analysis of the percentage of the steady-state error of the output voltage is defined on six model parameters, and sensitivity analysis of two dominant parameters is chosen. After that, a straightforward least-squares analysis (LSA) technique is used to identify the two parameters online. The proposed method is verified through simulation in several different operating scenarios to verify its effectiveness. Full article

(This article belongs to the Special Issue Applied Mathematics and Intelligent Control in Electrical Engineering)

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28 pages, 5648 KiB

Open AccessArticle

Applied Mathematics in the Numerical Modelling of the Electromagnetic Field in Reference to Drying Dielectrics in the RF Field

by Viorica Spoiala, Helga Silaghi and Dragos Spoiala

Mathematics 2024, 12(4), 526; https://doi.org/10.3390/math12040526 - 8 Feb 2024

Cited by 1 | Viewed by 982

Abstract

The processing of dielectric materials in the radio frequency field continues to be a concern in engineering. This procedure involves a rigorous analysis of the electromagnetic field based on specific numerical methods. This paper presents an original method for analysing the process of drying wooden boards in a radio frequency (RF) installation. The electromagnetic field and thermal field are calculated using the finite element method (FEM). The load capacity of the installation is also calculated, since the material being heated in the radio frequency heating installations is placed in a capacitor-type applicator. A specific method is created in order to solve the problem related to mass, a quantity which tends to change during the drying of the dielectric. In addition, special consideration is given to issues regarding the coupling of the electromagnetic field and the thermal field, along with aspects pertaining to mass. These are implemented numerically using a program written in the Fortran language, which takes the distribution of finite elements from the Flux2D program, the dielectric thermal module, intended only for the study of RF heating. The results obtained after running the program are satisfactory and they represent a support for future studies, especially if the movement of the dielectric is taken into account. Full article

(This article belongs to the Special Issue Applied Mathematics and Intelligent Control in Electrical Engineering)

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35 pages, 2444 KiB

Open AccessArticle

Privacy Preservation Using Machine Learning in the Internet of Things

by Sherif El-Gendy, Mahmoud Said Elsayed, Anca Jurcut and Marianne A. Azer

Mathematics 2023, 11(16), 3477; https://doi.org/10.3390/math11163477 - 11 Aug 2023

Cited by 12 | Viewed by 5609

Abstract

The internet of things (IoT) has prepared the way for a highly linked world, in which everything is interconnected, and information exchange has become more easily accessible via the internet, making it feasible for various applications that enrich the quality of human life. Despite such a potential vision, users’ privacy on these IoT devices is a significant concern. IoT devices are subject to threats from hackers and malware due to the explosive expansion of IoT and its use in commerce and critical infrastructures. Malware poses a severe danger to the availability and reliability of IoT devices. If left uncontrolled, it can have profound implications, as IoT devices and smart services can collect personally identifiable information (PII) without the user’s knowledge or consent. These devices often transfer their data into the cloud, where they are stored and processed to provide the end users with specific services. However, many IoT devices do not meet the same security criteria as non-IoT devices; most used schemes do not provide privacy and anonymity to legitimate users. Because there are so many IoT devices, so much malware is produced every day, and IoT nodes have so little CPU power, so antivirus cannot shield these networks from infection. Because of this, establishing a secure and private environment can greatly benefit from having a system for detecting malware in IoT devices. In this paper, we will analyze studies that have used ML as an approach to solve IoT privacy challenges, and also investigate the advantages and drawbacks of leveraging data in ML-based IoT privacy approaches. Our focus is on using ML models for detecting malware in IoT devices, specifically spyware, ransomware, and Trojan horse malware. We propose using ML techniques as a solution for privacy attack detection and test pattern generation in the IoT. The ML model can be trained to predict behavioral architecture. We discuss our experiments and evaluation using the “MalMemAnalysis” datasets, which focus on simulating real-world privacy-related obfuscated malware. We simulate several ML algorithms to prove their capabilities in detecting malicious attacks against privacy. The experimental analysis showcases the high accuracy and effectiveness of the proposed approach in detecting obfuscated and concealed malware, outperforming state-of-the-art methods by 99.50%, and would be helpful in safeguarding an IoT network from malware. Experimental analysis and results are provided in detail. Full article

(This article belongs to the Special Issue Applied Mathematics and Intelligent Control in Electrical Engineering)

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