Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.6
2.2
Journals
Mathematics
Special Issues
Mathematical Methods Applied in Power Systems, 2nd Edition
share announcement

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 2026 | Viewed by 4211

Special Issue Editors

Prof. Dr. Gheorghe Grigoras

E-Mail Website
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

E-Mail Website
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

E-Mail Website
Guest Editor
Department of Electrotechnics and Measurements, Faculty of Electrical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Interests: energy analytics and numerical tools; energy efficiency in buildings and industry; renewable energy; numerical methods; EMF; EMC
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

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 250 words) can be sent to the Editorial Office for assessment.

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

  • 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

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (4 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

27 pages, 3490 KB  
Article
A Weighted Mean of Vectors-Based Mathematical Optimization Framework for PV-STATCOM Deployment in Distribution Systems Under Time-Varying Load Conditions
by Ghareeb Moustafa, Hashim Alnami, Badr M. Al Faiya and Sultan Hassan Hakmi
Mathematics 2026, 14(8), 1351; https://doi.org/10.3390/math14081351 - 17 Apr 2026
Viewed by 208
Abstract
The increasing penetration of photovoltaic (PV) systems in distribution networks has introduced new challenges in voltage regulation and energy loss mitigation, particularly under time-varying loading conditions. This paper presents a constrained multi-objective mathematical optimization framework for the optimal allocation and sizing of PV-STATCOM [...] Read more.
The increasing penetration of photovoltaic (PV) systems in distribution networks has introduced new challenges in voltage regulation and energy loss mitigation, particularly under time-varying loading conditions. This paper presents a constrained multi-objective mathematical optimization framework for the optimal allocation and sizing of PV-STATCOM devices in radial distribution systems. The problem is formulated as a nonlinear optimization model that minimizes the daily energy losses over a 24 h operating horizon while satisfying network operational constraints, inverter capacity limits, and renewable penetration restrictions. To efficiently solve the resulting non-convex optimization problem, a metaheuristic algorithm based on the weighted mean of vectors (WMV) is employed. The WMV method integrates wavelet-based weighting mechanisms, mean-driven update rules, vector combination strategies, and a local refinement operator to balance global exploration and local exploitation within the feasible search domain. Constraint violations are handled through a penalty-based mathematical transformation of the objective function. The proposed framework is validated on the IEEE 33-bus and IEEE 69-bus distribution systems under realistic daily load variations. The numerical results demonstrate significant reductions in daily energy losses compared to differential evolution, particle swarm optimization, artificial rabbits optimization, and golden search optimization algorithms. Furthermore, convergence analysis confirms the robustness and computational efficiency of the WMV approach in solving large-scale constrained power system optimization problems. Full article
(This article belongs to the Special Issue Mathematical Methods Applied in Power Systems, 2nd Edition)
►▼ Show Figures

Figure 1

25 pages, 990 KB  
Article
An Adaptive Fitness-Guided Starfish Optimization Framework for Optimal Power Flow Operation
by Sulaiman Z. Almutairi and Abdullah M. Shaheen
Mathematics 2026, 14(5), 909; https://doi.org/10.3390/math14050909 - 7 Mar 2026
Cited by 1 | Viewed by 446
Abstract
Optimal Power Flow Operation (OPFO) is a large-scale, nonlinear, and highly constrained optimization problem that plays a central role in achieving economical, reliable, and environmentally sustainable power system operation. Despite the widespread use of metaheuristic algorithms for OPFO, many methods primarily depend on [...] Read more.
Optimal Power Flow Operation (OPFO) is a large-scale, nonlinear, and highly constrained optimization problem that plays a central role in achieving economical, reliable, and environmentally sustainable power system operation. Despite the widespread use of metaheuristic algorithms for OPFO, many methods primarily depend on global-best updates or complex hybrid operators, leading to issues like premature convergence and diminished population diversity. Furthermore, recent literature tends to focus on numerical improvements without sufficiently addressing the underlying interaction structures that ensure stability in convergence. To address these limitations, this paper proposes an Improved Starfish Optimization (ISFO) algorithm incorporating a hybrid fitness-aware population-based search mechanism for solving OPFO problems involving the simultaneous regulation of synchronous generator outputs, on-load tap-changing transformer ratios, and reactive power compensation devices. The proposed method introduces an adaptive Fitness-Aware Collective (FAC) interaction strategy that systematically models pairwise fitness relationships to guide attraction toward superior solutions and repulsion from inferior ones, thereby strengthening exploitation while preserving diversity through controlled stochastic peer-based perturbations. A dual-mode search framework further balances global exploration and local intensification without introducing additional control parameters, enhancing robustness and scalability. The OPFO problem is formulated as a constrained nonlinear optimization model, where equality constraints enforce power flow balance equations and inequality constraints represent operational limits of generators, transformers, voltages, and transmission lines. The proposed ISFO is validated on the IEEE 57-bus power system under three operating scenarios: fuel cost minimization, transmission loss minimization, and emission minimization. Comparative results demonstrate consistent superiority over the standard Starfish Optimization Algorithm (SFOA). In cost minimization, ISFO reduces the total generation cost from 41,697.85 $/h to 41,669.34 $/h while simultaneously decreasing real power losses by 5.22%. Under loss minimization, ISFO achieves a minimum transmission loss of 10.77 MW, corresponding to a 9.23% reduction relative to SFOA, with improved convergence stability. For emission minimization, ISFO attains the lowest emission level of 1.474 ton/h, representing a 6.65% reduction compared to SFOA, alongside an additional 5.67% reduction in system losses. Statistical evaluations based on 30 independent runs further confirm the robustness and reliability of the proposed approach, demonstrating reduced variance, narrower confidence intervals, and statistically significant improvements across all investigated objectives. Full article
(This article belongs to the Special Issue Mathematical Methods Applied in Power Systems, 2nd Edition)
►▼ Show Figures

Figure 1

34 pages, 1593 KB  
Article
Enhancing Radial Distribution System Performance Through Optimal Allocation and Sizing of Photovoltaic and Wind Turbine Distribution Generation Units with Rüppell’s Fox Optimizer
by Yacine Bouali and Basem Alamri
Mathematics 2025, 13(15), 2399; https://doi.org/10.3390/math13152399 - 25 Jul 2025
Cited by 4 | Viewed by 1308
Abstract
Renewable energy sources are being progressively incorporated into modern power grids to increase sustainability, stability, and resilience. To ensure that residential, commercial, and industrial customers have a dependable and efficient power supply, the transmission system must deliver electricity to end-users via the distribution [...] Read more.
Renewable energy sources are being progressively incorporated into modern power grids to increase sustainability, stability, and resilience. To ensure that residential, commercial, and industrial customers have a dependable and efficient power supply, the transmission system must deliver electricity to end-users via the distribution network. To improve the performance of the distribution system, this study employs distributed generator (DG) units and focuses on determining their optimal placement, sizing, and power factor. A novel metaheuristic algorithm, referred to as Rüppell’s fox optimizer (RFO), is proposed to address this optimization problem under various scenarios. In the first scenario, where the DG operates at unity power factor, it is modeled as a photovoltaic system. In the second and third scenarios, the DG is modeled as a wind turbine system with fixed and optimal power factors, respectively. The performance of the proposed RFO algorithm is benchmarked against five well-known metaheuristic techniques to validate its effectiveness and competitiveness. Simulations are conducted on the IEEE 33-bus and IEEE 69-bus radial distribution test systems to demonstrate the applicability and robustness of the proposed approach. Full article
(This article belongs to the Special Issue Mathematical Methods Applied in Power Systems, 2nd Edition)
►▼ Show Figures

Graphical abstract

36 pages, 6279 KB  
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
Cited by 5 | Viewed by 1158
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)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-4
Back to TopTop