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Mathematical Applications in Electrical Engineering
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Mathematical Applications in Electrical Engineering

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

Deadline for manuscript submissions: closed (30 September 2024) | Viewed by 9175

Special Issue Editor

Prof. Dr. Fausto Sargeni

E-Mail Website
Guest Editor
Department of Electronic Engineering, University of Rome “Tor Vergata”, Via del Politecnico 1, 00133 Rome, Italy
Interests: mathematical problems in electrical engineering
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to "Mathematical Applications in Electrical Engineering" and focuses on areas of the application of mathematics and numerical methods to electrical engineering problems. The areas covered include circuit theory, materials simulations, electromagnetic characterization of materials, finite element modeling, optimization techniques, mathematical application in circuits and algorithms for the extraction, processing, and transmission of information, artificial intelligence techniques, electromagnetic fields, neural networks, and circuits and algorithms for classification, recognition, and prediction.

This Special Issue aims to provide mathematical methods and applications in electrical engineering problems.

We invite authors to contribute original research articles addressing significant issues and contributing to developing new concepts, methodologies, applications, trends, and knowledge in science. Review articles describing the current state-of-the-art are also welcome.

Prof. Fausto Sargeni
Guest Editor

Manuscript Submission Information

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Published Papers (10 papers)

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Research

23 pages, 2739 KiB  
Article
Neural Network Architectures and Magnetic Hysteresis: Overview and Comparisons
by Silvia Licciardi, Guido Ala, Elisa Francomano, Fabio Viola, Michele Lo Giudice, Alessandro Salvini, Fausto Sargeni, Vittorio Bertolini, Andrea Di Schino and Antonio Faba
Mathematics 2024, 12(21), 3363; https://doi.org/10.3390/math12213363 - 26 Oct 2024
Viewed by 682
Abstract
The development of innovative materials, based on the modern technologies and processes, is the key factor to improve the energetic sustainability and reduce the environmental impact of electrical equipment. In particular, the modeling of magnetic hysteresis is crucial for the design and construction [...] Read more.
The development of innovative materials, based on the modern technologies and processes, is the key factor to improve the energetic sustainability and reduce the environmental impact of electrical equipment. In particular, the modeling of magnetic hysteresis is crucial for the design and construction of electrical and electronic devices. In recent years, additive manufacturing techniques are playing a decisive role in the project and production of magnetic elements and circuits for applications in various engineering fields. To this aim, the use of the deep learning paradigm, integrated with the most common models of the magnetic hysteresis process, has become increasingly present in recent years. The intent of this paper is to provide the features of a wide range of deep learning tools to be applied to magnetic hysteresis context and beyond. The possibilities of building neural networks in hybrid form are innumerable, so it is not plausible to illustrate them in a single paper, but in the present context, several neural networks used in the scientific literature, integrated with various hysteretic mathematical models, including the well-known Preisach model, are compared. It is shown that this hybrid approach not only improves the modeling of hysteresis by significantly reducing computational time and efforts, but also offers new perspectives for the analysis and prediction of the behavior of magnetic materials, with significant implications for the production of advanced devices. Full article
(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering)
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16 pages, 3913 KiB  
Article
Harmonic Mitigation in Multi-Pulse Rectification: A Comparative Study of 12-, 18-, and 24-Pulse Systems
by Hani Albalawi, Abdul Wadood, Shahbaz Khan and Aadel Mohammed Alatwi
Mathematics 2024, 12(20), 3257; https://doi.org/10.3390/math12203257 - 17 Oct 2024
Viewed by 471
Abstract
In the evolution of the modern “More Electric Aircrafts” (MEAs) concept, higher-pulse rectification systems using differential fork autotransformers play a pivotal role. These systems align with the MEAs concept, which aims to replace traditional hydraulic and pneumatic systems with electric alternatives. The reason [...] Read more.
In the evolution of the modern “More Electric Aircrafts” (MEAs) concept, higher-pulse rectification systems using differential fork autotransformers play a pivotal role. These systems align with the MEAs concept, which aims to replace traditional hydraulic and pneumatic systems with electric alternatives. The reason is that MEAs prioritize weight reduction to enhance fuel efficiency and reduce emissions. Higher-pulse rectifiers achieve this by minimizing losses and optimizing power conversion. Additionally, they mitigate harmonics, ensuring a clean power supply to critical avionic components. These systems also regulate voltage effectively, contributing to overall system stability. Furthermore, their compliance with IEEE-519 standards ensures their safe and efficient operation. Keeping in view the above applications, a comparative study of 12-, 18-, and 24-pulse rectification systems was carried out using different autotransformer topologies. The simulation and hardware results are presented for validation. The voltage and current waveforms were meticulously analyzed for each topology, emphasizing the pivotal role played by the differential fork autotransformer design. By quantifying the total harmonic distortion (THD) levels using MATLAB simulations, intriguing insights were revealed. Notably, the 24-pulse system emerged as the clear winner in harmonic mitigation, showcasing its superior waveform quality and reduced harmonic content. However, the 18-pulse configuration also exhibited a commendable performance, surpassing the 12-pulse counterpart. Full article
(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering)
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13 pages, 4182 KiB  
Article
Application of Weighting Algorithm for Enhanced Broadband Vector Network Analyzer Measurements
by Sang-hee Shin and James Skinner
Mathematics 2024, 12(18), 2871; https://doi.org/10.3390/math12182871 - 14 Sep 2024
Viewed by 626
Abstract
A weighting algorithm for application in the Thru-Reflect-Line (TRL) calibration technique is presented to enhance the accuracy and reliability of vector network analyzer (VNA) measurements over broad frequency bands. The method addresses the inherent limitations of the traditional TRL calibration, particularly the step [...] Read more.
A weighting algorithm for application in the Thru-Reflect-Line (TRL) calibration technique is presented to enhance the accuracy and reliability of vector network analyzer (VNA) measurements over broad frequency bands. The method addresses the inherent limitations of the traditional TRL calibration, particularly the step changes observed in banded-TRL approaches when multiple Line standards are used. By introducing a bespoke weighting function that assigns phase-dependent weights to each Line standard, smoother transitions and improved S-parameter measurements can be achieved. Experimental validation using measurements of both 3.5 mm and Type-N devices demonstrates the effectiveness of the weighted-TRL method in eliminating discontinuities and calibration artifacts across a wide range of frequencies. The results reveal the improved calibration of S-parameters this approach can yield compared to traditional TRL calibration methods. The developed weighted-TRL calibration technique offers a significant advancement in metrology-grade measurements, enabling more precise characterization of high-frequency devices across broad frequency bands. By mitigating a key limitation of the TRL calibration, this method provides a valuable tool for enhancing the accuracy and reliability of VNA measurements for precision metrology applications. Full article
(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering)
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10 pages, 2733 KiB  
Article
Use of the Adaptive Cross Approximation for the Efficient Computation of the Reduced Matrix with the Characteristic Basis Function Method
by Eliseo García, Carlos Delgado and Felipe Cátedra
Mathematics 2024, 12(10), 1565; https://doi.org/10.3390/math12101565 - 17 May 2024
Viewed by 724
Abstract
A technique for the reduction in the CPU-time in the analysis of electromagnetic problems using the Characteristic Basis Function Method (CBFM) is presented here, allowing for analysis of electrically large cases where an iterative solution process cannot be avoided. This technique is based [...] Read more.
A technique for the reduction in the CPU-time in the analysis of electromagnetic problems using the Characteristic Basis Function Method (CBFM) is presented here, allowing for analysis of electrically large cases where an iterative solution process cannot be avoided. This technique is based on the use of the Adaptive Cross Approximation (ACA) for the fast computation of the coupling matrix between CBFs belonging to adjacent blocks, as well as the Multilevel Fast Multipole Method (MLFMM) for the computation of matrix−vector products in the solution of the full system. This combination allows for a noticeable reduction in the computational resources during the analysis of electrically large and complex scenarios while maintaining a very good degree of accuracy. A number of test cases serve to validate the presented approach in terms of accuracy, memory and CPU-time compared with conventional techniques. Full article
(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering)
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16 pages, 1142 KiB  
Article
Energy Mutual Aid Device of Electric Vehicles: Quadratic Boost Converter with Modified Voltage-Mode Controller
by Jun Xiao, Shuo Zhai, Wei Jia, Weisheng Wang, Zhiyuan Zhang and Baining Guo
Mathematics 2024, 12(10), 1531; https://doi.org/10.3390/math12101531 - 14 May 2024
Cited by 1 | Viewed by 868
Abstract
Electric vehicles are becoming a mainstay of road transport. However, the uneven distribution of the electric vehicle charging piles in cities has led to the problem of “mileage anxiety”. This has become a significant concern of consumers in purchasing electric vehicles. At the [...] Read more.
Electric vehicles are becoming a mainstay of road transport. However, the uneven distribution of the electric vehicle charging piles in cities has led to the problem of “mileage anxiety”. This has become a significant concern of consumers in purchasing electric vehicles. At the same time, it also hinders the development of the electric vehicle industry. For this reason, this paper designs an electric vehicle energy mutual aid device. In the event that the power battery of an electric vehicle is low on energy and there are no suitable charging piles around, the device can also seek energy supplementation from surrounding electric vehicles with sufficient energy. This device should satisfy the characteristics of wide gain, high power, small size, and light weight. Firstly, the quadratic boost converter and its state space model are constructed. It uses only one electrical switching element to realize the light weight of the device, and it also provides wide voltage gain to fulfill the needs of electric vehicle charging. Secondly, an improved voltage mode controller is proposed to address the shortcomings of the conventional voltage mode controller of the quadratic boost converter. It avoids the tradeoff between the transient and steady-state performance due to the integration action of the conventional voltage mode controller. Also, this controller uses less feedback to make the controlled system output the required DC power, reducing the weight of the device. Finally, the effectiveness of the proposed energy mutual aid device is verified by simulations and experiments. Full article
(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering)
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12 pages, 1380 KiB  
Article
Simplification of Electrode Profiles for Piezoelectric Modal Sensors by Controlling Gap-Phase Length
by Marta Martín-Nieto, Damián Castaño, Sergio Horta Muñoz and David Ruiz
Mathematics 2024, 12(10), 1525; https://doi.org/10.3390/math12101525 - 14 May 2024
Viewed by 732
Abstract
This paper presents a method to optimize and simplify the electrode profile of a piezoelectric modal sensor. At the same time that the electrode profile is optimized to maximize the charge, a null-polarity phase is introduced. This gap-phase is modeled using the normalized [...] Read more.
This paper presents a method to optimize and simplify the electrode profile of a piezoelectric modal sensor. At the same time that the electrode profile is optimized to maximize the charge, a null-polarity phase is introduced. This gap-phase is modeled using the normalized norm of the spatial gradient of the polarity profile along with a two-step filtering and projection technique. High-order vibration modes generate a complex polarization profile that makes the manufacturing process difficult. The novelty of the proposed method is the addition of a constraint on the length of the interface in the topology optimization problem. This constraint simplifies the optimal designs and facilitates the fabrication process. Several examples show the simplified electrode profile that maximizes the electrical charge produced by a vibration mode, while reducing the number of different polarization regions by means of the gap-length constraint. Full article
(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering)
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13 pages, 1830 KiB  
Article
Analysis of an Interface Crack between Piezoelectric Semiconductor Coating and Elastic Substrate Structure
by Xiangru Tian, Yali Zhang, Hailiang Ma, Xing Li and Shenghu Ding
Mathematics 2024, 12(8), 1208; https://doi.org/10.3390/math12081208 - 17 Apr 2024
Viewed by 849
Abstract
Piezoelectric semiconductor materials possess a unique combination of piezoelectric and semiconductor effects, exhibiting multifaceted coupling properties such as electromechanical, acoustic, photoelectric, photovoltaic, thermal, and thermoelectric capabilities. This study delves into the anti-plane mechanical model of an interface crack between a strip of piezoelectric [...] Read more.
Piezoelectric semiconductor materials possess a unique combination of piezoelectric and semiconductor effects, exhibiting multifaceted coupling properties such as electromechanical, acoustic, photoelectric, photovoltaic, thermal, and thermoelectric capabilities. This study delves into the anti-plane mechanical model of an interface crack between a strip of piezoelectric semiconductor material and an elastic material. By introducing two boundary conditions, the mixed boundary value problem is reformulated into a set of singular integral equations with a Cauchy kernel. The details of carrier concentration, current density, and electric displacement near the crack are provided in a numerical analysis. The findings reveal that the distribution of the current density, carrier concentration, and electric displacement is intricately influenced by the doping concentration of the piezoelectric semiconductor. Moreover, the presence of mechanical and electric loads can either expedite or decelerate the growth of the crack, highlighting the pivotal role of external stimuli in influencing material behavior. Full article
(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering)
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19 pages, 1309 KiB  
Article
Energy-Management Strategy of Battery Energy Storage Systems in DC Microgrids: A Distributed Fuzzy Output Consensus Control Considering Multiple Cyber Attacks
by Xu Tian, Weisheng Wang, Liang Zou, Shuo Zhai, Bin Hai and Rui Wang
Mathematics 2024, 12(6), 887; https://doi.org/10.3390/math12060887 - 18 Mar 2024
Viewed by 994
Abstract
Distributed renewable sources are one of the most promising contributors for DC microgrids to reduce carbon emission and fuel consumption. Although the battery energy storage system (BESS) is widely applied to compensate the power imbalance between distributed generators (DGs) and loads, the impacts [...] Read more.
Distributed renewable sources are one of the most promising contributors for DC microgrids to reduce carbon emission and fuel consumption. Although the battery energy storage system (BESS) is widely applied to compensate the power imbalance between distributed generators (DGs) and loads, the impacts of disturbances, DGs, constant power loads (CPLs) and cyber attacks on this system are not simultaneously considered. Based on this, a distributed fuzzy output consensus control strategy is proposed to realize accurate current sharing and operate normally in the presence of denial of service (DoS) attacks and false data injection (FDI) attacks. Firstly, the whole model of the BESS in DC microgrids embedded into disturbance items, DGs, CPLs and resistive loads, is firstly built. This model could be further transformed into standard linear heterogeneous multi-agent systems with disturbance, which lays the foundation for the following control strategy. Then the model of FDI and DoS attacks are built. Meanwhile, the fuzzy logic controller (FLC) is applied to reduce the burden of communication among batteries. Based on these, a distributed output consensus fuzzy control is proposed to realize accurate current sharing among batteries. Moreover, the system under the proposed control in different cases is analyzed. Finally, the feasibility of the proposed control strategy is verified by numerical simulation results and experiment results. Full article
(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering)
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18 pages, 18820 KiB  
Article
A Frequency/Phase/Amplitude Estimator for Three-Phase Applications Operating at a Low Sampling Rate
by Abdullah M. Abusorrah and Hamed Sepahvand
Mathematics 2024, 12(3), 363; https://doi.org/10.3390/math12030363 - 23 Jan 2024
Cited by 1 | Viewed by 818
Abstract
A frequency/phase/amplitude estimator is arguably one of the most crucial components in the control and synchronization of grid-connected equipment. Such an estimator may also be useful for monitoring and protection purposes in power systems. In this paper, an open-loop (and therefore unconditionally stable) [...] Read more.
A frequency/phase/amplitude estimator is arguably one of the most crucial components in the control and synchronization of grid-connected equipment. Such an estimator may also be useful for monitoring and protection purposes in power systems. In this paper, an open-loop (and therefore unconditionally stable) estimator for the accurate and rapid extraction of the grid voltage phase, frequency, and amplitude is presented. In designing the proposed technique, special focus is given to applications operating at a low sampling rate. Examples of such applications include high-power converters, where both switching and sampling frequencies are very low. The study concludes with a comprehensive evaluation of the proposed estimator, demonstrating its effectiveness in accurately and swiftly estimating the fundamental parameters of grid voltage under low sampling rates. It highlights the estimator’s enhanced performance in scenarios of distorted grid conditions and its superiority in filtering capabilities compared to traditional methods. These findings underline the estimator’s potential for broad applicability in power system monitoring, protection, and control. Full article
(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering)
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17 pages, 1019 KiB  
Article
Mathematical Calculation of Synchronous Electric Motors Dynamic Stability
by Valery Pupin and Victor Orlov
Mathematics 2023, 11(21), 4465; https://doi.org/10.3390/math11214465 - 28 Oct 2023
Cited by 1 | Viewed by 1221
Abstract
This paper considers the equipment and power supply schemes for urban water supply, heat supply and sewerage pumping stations. Mathematical calculations of the impact of the static and full centrifugal pumps pressure ratio on the dynamic stability of synchronous electric motors were carried [...] Read more.
This paper considers the equipment and power supply schemes for urban water supply, heat supply and sewerage pumping stations. Mathematical calculations of the impact of the static and full centrifugal pumps pressure ratio on the dynamic stability of synchronous electric motors were carried out. An analysis of the influence of pump parameters and engine load on the run-down parameters and drive stability during power shutdowns was carried out. It has been theoretically proven and practically confirmed that ensuring the stability of pumping station drives and the reduction in enterprise losses during various short-term disruptions in power supply networks can be provided by means of a high-speed backup source with a response time of less than 9 ms, dynamic voltage dip compensators with a response time of less than 3 ms and uninterruptible power supply sources. Full article
(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering)
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