Fractional Order Systems with Application to Electrical Power Engineering, 3rd Edition

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: 20 January 2026 | Viewed by 1155

Special Issue Editors

Department of Energy, Aalborg University, 9220 Aalborg, Denmark
Interests: power electronics; power systems; smart grid; AC/DC microgrid; intelligent control; fractional order system
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Guest Editor
Department of Electrical and Computer Engineering, Aarhus University, 8000 Aarhus, Denmark
Interests: power systems; microgrid; cyber-physical system; machine learning; optimal control; fractional order system

Special Issue Information

Dear Colleagues,

As the Guest Editors, we invite scientists and professionals  to submit their theoretical and applied contributions, as well as review articles, to this Special Issue of Fractal and Fractional on the subject of “Fractional Order Systems with Application to Electrical Power Engineering, 3rd Edition”. This Special Issue aims to advance the modeling, design, analysis, and control of fractional order systems for energy and power engineering applications, such as power electronics and electric motor drives, power systems, distributed generation, and multi-energy systems.

Fractional calculus plays a crucial role in accurately describing practical dynamic behaviors in engineering systems using fractional-order models. As a non-standard operator, fractional-order calculus addresses the limitations of classical differential equations, which cannot accurately describe the dynamic behavior of complex systems. It provides an effective tool for describing practical models with memory properties and historical dependence, offering additional degrees of freedom and enhancing design flexibility. The fractal nature of fractional calculus enables the formulation of more accurate mathematical models compared to those based on integer calculus.

Topics of interest for this Special Issue include, but are not limited to, the following:

  • Development of fractional order modeling of energy systems;
  • Fractional order simulation of energy systems with power electronic topologies;
  • Fractional order modeling and analysis of hybrid energy storage systems;
  • Artificial intelligence application in fractional order energy systems;
  • Robust control of fractional order energy systems;
  • Energy efficiency in fractional order energy systems;
  • Grid integration of fractional order power converters;
  • Power quality issues in fractional order energy systems;
  • Reliability and resilience issues in fractional order energy systems;
  • Intelligent control of fractional order energy systems;
  • Stability issues in fractional order energy systems;
  • Application of fractional order control strategies;
  • Fractional control design of renewable energy systems.

Dr. Arman Oshnoei
Dr. Soroush Oshnoei
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. Fractal and Fractional is an international peer-reviewed open access monthly 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 2700 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

  • fractional order system
  • distributed energy resources
  • energy storage system
  • multi-energy systems
  • power electronic systems
  • power converters
  • renewable energy systems
  • artificial intelligence
  • stability analysis
  • intelligent control
  • fractional calculus
  • reliability and resiliency

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Published Papers (1 paper)

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Research

23 pages, 5273 KB  
Article
Federated Learning Detection of Cyberattacks on Virtual Synchronous Machines Under Grid-Forming Control Using Physics-Informed LSTM
by Ali Khaleghi, Soroush Oshnoei and Saeed Mirzajani
Fractal Fract. 2025, 9(9), 569; https://doi.org/10.3390/fractalfract9090569 - 29 Aug 2025
Cited by 1 | Viewed by 863
Abstract
The global shift toward clean production, like using renewable energy, has significantly decreased the use of synchronous machines (SMs), which help maintain stability and control, causing serious frequency stability issues in power systems with low inertia. Fractional order controller-based virtual synchronous machines (FOC-VSMs) [...] Read more.
The global shift toward clean production, like using renewable energy, has significantly decreased the use of synchronous machines (SMs), which help maintain stability and control, causing serious frequency stability issues in power systems with low inertia. Fractional order controller-based virtual synchronous machines (FOC-VSMs) have become a promising option, but they rely on communication networks to work together in real time, causing them to be at risk of cyberattacks, especially from false data injection attacks (FDIAs). This paper suggests a new way to detect FDI attacks using a federated physics-informed long short-term memory (PI-LSTM) network. Each FOC-VSM uses its data to train a PI-LSTM, which keeps the information private but still helps it learn from a common model that understands various operating conditions. The PI-LSTM incorporates physical constraints derived from the FOC-VSM swing equation, facilitating residual-based anomaly detection that is sensitive to minor deviations in control dynamics, such as altered inertia or falsified frequency signals. Unlike traditional LSTMs, the physics-informed architecture minimizes false positives arising from benign disturbances. We assessed the proposed method on an IEEE 9-bus test system featuring two FOC-VSMs. The results show that our method can successfully detect FDI attacks while handling regular changes, proving it could be a strong solution. Full article
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