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Mathematical Methods Applied in Power Systems, 2nd Edition
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Mathematical Methods Applied in Power Systems, 2nd Edition

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 663

Special Issue Editors

Prof. Dr. Gheorghe Grigoras

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Guest Editor
Faculty of Electrical Engineering, Energetics and Applied Informatics, "Gheorghe Asachi" Technical University of Iasi, 700050 Iasi, Romania
Interests: smart grids; applications of artificial intelligence in analysis; operation; control and management; optimization techniques; energy efficiency
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Radu Porumb

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Guest Editor
Department of Electric Power Systems, University Politehnica of Bucharest, 060042 Bucharest, Romania
Interests: power quality; energy efficiency; electrical and electronics; power system control; distributed generation; load forecasting; smart grid; energy storage systems; renewable energy; education
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Dan Doru Micu

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Guest Editor
Department of Electrotechnics and Measurements, Faculty of Electrical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Interests: numerical methods and modelling techniques in electromagnetics; artificial intelligence algorithms and inverse problems; electromagnetic field analysis; synthesis and optimization; energy efficiency solutions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The latest research directions in the power engineering field were motivated by the current technological developments and the gradual implementation of the “Smart Grids” concept. The planning and operation of a modern power system requires efficient management of large databases, enabling one to obtain the best solutions, essential in the decision-making process. Thus, improving routine calculations focused on data classification and complex tasks (selective analysis, multiobjective optimization, optimal online control, etc.) is fundamental. Consequently, the practical issues related to the optimal planning and operation of power systems can be solved by combining classical algorithms with the facilities offered by artificial intelligence algorithms. These approaches are used in all stages of the decision-making process, but especially for overcoming difficulties in multi-objective modeling, handling of constraints, and uncertainty considerations (load estimation, costs, electricity demands, etc.). The second edition of the Special Issue, entitled “Mathematical Methods Applied in Power Systems”, was proposed to highlight the innovative solutions obtained using the latest models and techniques developed in the planning and operation of modern power systems.

Prof. Dr. Gheorghe Grigoras
Prof. Dr. Radu Porumb
Prof. Dr. Dan Doru Micu
Guest Editors

Manuscript Submission Information

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Keywords

  • modeling and simulation
  • applied numerical methods
  • computational techniques
  • performance analysis and forecasting
  • optimization and operational research
  • data mining and soft computing
  • statistics
  • evolutionary computation
  • fuzzy logic
  • expert systems

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Published Papers (1 paper)

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Research

36 pages, 6279 KiB  
Article
Eel and Grouper Optimization-Based Fuzzy FOPI-TIDμ-PIDA Controller for Frequency Management of Smart Microgrids Under the Impact of Communication Delays and Cyberattacks
by Kareem M. AboRas, Mohammed Hamdan Alshehri and Ashraf Ibrahim Megahed
Mathematics 2025, 13(13), 2040; https://doi.org/10.3390/math13132040 - 20 Jun 2025
Viewed by 338
Abstract
In a smart microgrid (SMG) system that deals with unpredictable loads and incorporates fluctuating solar and wind energy, it is crucial to have an efficient method for controlling frequency in order to balance the power between generation and load. In the last decade, [...] Read more.
In a smart microgrid (SMG) system that deals with unpredictable loads and incorporates fluctuating solar and wind energy, it is crucial to have an efficient method for controlling frequency in order to balance the power between generation and load. In the last decade, cyberattacks have become a growing menace, and SMG systems are commonly targeted by such attacks. This study proposes a framework for the frequency management of an SMG system using an innovative combination of a smart controller (i.e., the Fuzzy Logic Controller (FLC)) with three conventional cascaded controllers, including Fractional-Order PI (FOPI), Tilt Integral Fractional Derivative (TIDμ), and Proportional Integral Derivative Acceleration (PIDA). The recently released Eel and Grouper Optimization (EGO) algorithm is used to fine-tune the parameters of the proposed controller. This algorithm was inspired by how eels and groupers work together and find food in marine ecosystems. The Integral Time Squared Error (ITSE) of the frequency fluctuation (ΔF) around the nominal value is used as an objective function for the optimization process. A diesel engine generator (DEG), renewable sources such as wind turbine generators (WTGs), solar photovoltaics (PVs), and storage components such as flywheel energy storage systems (FESSs) and battery energy storage systems (BESSs) are all included in the SMG system. Additionally, electric vehicles (EVs) are also installed. In the beginning, the supremacy of the adopted EGO over the Gradient-Based Optimizer (GBO) and the Smell Agent Optimizer (SAO) can be witnessed by taking into consideration the optimization process of the recommended regulator’s parameters, in addition to the optimum design of the membership functions of the fuzzy logic controller by each of these distinct algorithms. The subsequent phase showcases the superiority of the proposed EGO-based FFOPI-TIDμ-PIDA structure compared to EGO-based conventional structures like PID and EGO-based intelligent structures such as Fuzzy PID (FPID) and Fuzzy PD-(1 + PI) (FPD-(1 + PI)); this is across diverse symmetry operating conditions and in the presence of various cyberattacks that result in a denial of service (DoS) and signal transmission delays. Based on the simulation results from the MATLAB/Simulink R2024b environment, the presented control methodology improves the dynamics of the SMG system by about 99.6% when compared to the other three control methodologies. The fitness function dropped to 0.00069 for the FFOPI-TIDμ-PIDA controller, which is about 200 times lower than the other controllers that were compared. Full article
(This article belongs to the Special Issue Mathematical Methods Applied in Power Systems, 2nd Edition)
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