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Fractal Fract
Special Issues
Fractional-Order Dynamics and Control in Green Energy Systems
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Fractional-Order Dynamics and Control in Green Energy Systems

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

Deadline for manuscript submissions: 18 April 2025 | Viewed by 1423

Special Issue Editors

Dr. Manashita Borah

E-Mail Website1 Website2
Guest Editor
1. Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720, USA
2. Department of Electrical Engineering, Tezpur University, Assam 784028, India
Interests: fractional calculus; energy storage; electric transportation; control systems; nonlinear dynamics; maglev
Dr. Christos Volos

E-Mail Website
Guest Editor
Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece
Interests: electrical and electronics engineering; mathematical modeling; control theory; engineering, applied and computational mathematics; numerical analysis; mathematical analysis; numerical modeling; modeling and simulation; robotics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional calculus has seen a rapid rise in recent applications in science and technology with improved results. The articles in this Special Issue will include the recent developments and applications of fractional calculus in green and sustainable technology to understand their inherent dynamics. Fractional-order dynamics offer several advantages over integer-order dynamics in the context of green energy systems:

  1. Enhanced accuracy: fractional-order models can capture the intricate dynamics and memory effects observed in green energy systems more effectively than integer-order models.
  2. Improved robustness: fractional-order control schemes are inherently robust to disturbances, uncertainties, and system parameter variations, which are common challenges in green energy systems.
  3. Increased flexibility: fractional-order controllers provide greater flexibility in shaping the closed-loop system response, enabling improved transient and steady-state performance.
  4. Efficient energy management: fractional-order control techniques facilitate efficient energy management, load balancing, and optimal utilization of renewable energy resources in green energy systems.

Recently, fractional-order dynamics and control have found applications in various aspects of green energy systems, including:

  1. Renewable energy generation: fractional-order control algorithms are used to enhance the performance of renewable energy sources such as solar panels, wind turbines, and hydroelectric systems; they enable better tracking of maximum power points, improved fault tolerance, and optimized energy conversion.
  2. Energy storage systems: fractional-order control can be employed in energy storage systems, such as batteries and supercapacitors, to improve their charging and discharging characteristics, extend their lifespan, and ensure efficient utilization of stored energy.
  3. Grid integration: fractional-order control techniques aid in integrating green energy systems with the electrical grid; they assist in power flow control, voltage regulation, and stability enhancement, enabling seamless integration and effective management of distributed energy resources.
  4. Demand response and energy management: fractional-order control plays a crucial role in demand response programs and energy management systems, facilitating optimal energy consumption scheduling, load forecasting, and power grid stabilization.

The purpose of this Special Issue is to offer a forum focused on the dissemination of the recent progress in fractional calculus and its potential applications in green energy systems. Topics may include, but are not limited to:

  1. Energy storage systems, supercapacitors and batteries, and hybrid energy storage;
  2. Energy efficient robots and manipulators;
  3. Fuel cells and renewable energy applications;
  4. Energy efficient biomedical devices and biological systems;
  5. Modes of green transportation, drones, electric vehicles, autonomous vehicles, and maglev vehicles;
  6. Physics-informed learning machines;
  7. Chaos control, nonlinear dynamics, and secure communication.

Dr. Manashita Borah
Dr. Christos Volos
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 100 words) can be sent to the Editorial Office for announcement on this website.

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 chaos
  • energy storage systems
  • dynamics
  • control systems
  • energy storage systems
  • biological systems
  • renewable energy applications
  • energy-efficient robots
  • green transportation

Published Papers (2 papers)

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Research

16 pages, 2615 KiB  
Article
Enhancing Transient Stability in Multi-Machine Power Systems through a Model-Free Fractional-Order Excitation Stabilizer
by Arman Fathollahi and Björn Andresen
Fractal Fract. 2024, 8(7), 419; https://doi.org/10.3390/fractalfract8070419 - 17 Jul 2024
Viewed by 424
Abstract
The effective operation of model-based control strategies in modern energy systems, characterized by significant complexity, is contingent upon highly accurate large-scale models. However, achieving such precision becomes challenging in complex energy systems rife with uncertainties and disturbances. Controlling different parts of the energy [...] Read more.
The effective operation of model-based control strategies in modern energy systems, characterized by significant complexity, is contingent upon highly accurate large-scale models. However, achieving such precision becomes challenging in complex energy systems rife with uncertainties and disturbances. Controlling different parts of the energy system poses a challenge to achieving optimal power system efficiency, particularly when employing model-based control strategies, thereby adding complexity to current systems. This paper proposes a novel model-independent control approach aimed at augmenting transient stability and voltage regulation performance in multi machine energy systems. The approach involves the introduction of an optimized model-free fractional-order-based excitation system stabilizer for synchronous generators in a multi machine energy system. To overcome the limitations associated with complex system model identification, which add degrees of simplification at defined operating conditions and assume the system model remains fixed despite high uncertainty and numerous disturbances, an optimal model-independent fractional-order-based excitation control strategy is introduced. The efficacy of the proposed approach is validated through comparative numerical analyses using the MATLAB/Simulink environment. These simulations were conducted on a two-area, 12-bus multi-machine power system. Simulation results demonstrate that the presented excitation system stabilizer outperforms conventional controllers in terms of transient and small-signal stability. It also suppresses the low-frequency electromechanical oscillations within the multimachine energy system. Full article
(This article belongs to the Special Issue Fractional-Order Dynamics and Control in Green Energy Systems)
►▼ Show Figures

Figure 1

Figure 1
<p>Single-line diagram of a two-area, four-machine power system: a representative example of a multi-machine power system.</p> Full article ">Figure 2
<p>Block diagram of the presented FCPSO algorithm (<math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mo>ℴ</mo> </msub> </mrow> </semantics></math>: global error, and <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mi mathvariant="sans-serif-italic">ℓ</mi> </msub> </mrow> </semantics></math>: local error).</p> Full article ">Figure 3
<p>Block diagram of MFESS with supplementary FCPSO parameter adaptation algorithm.</p> Full article ">Figure 4
<p>The standard block diagram of the conventional excitation system (CPSS-AVR).</p> Full article ">Figure 5
<p>Multi machine power system responses to a three-phase short-circuit fault (large disturbance).</p> Full article ">Figure 5 Cont.
<p>Multi machine power system responses to a three-phase short-circuit fault (large disturbance).</p> Full article ">
18 pages, 892 KiB  
Article
A Hybrid Approach Combining the Lie Method and Long Short-Term Memory (LSTM) Network for Predicting the Bitcoin Return
by Melike Bildirici, Yasemen Ucan and Ramazan Tekercioglu
Fractal Fract. 2024, 8(7), 413; https://doi.org/10.3390/fractalfract8070413 - 15 Jul 2024
Viewed by 497
Abstract
This paper introduces hybrid models designed to analyze daily and weekly bitcoin return spanning the periods from 18 July 2010 to 28 December 2023 for daily data, and from 18 July 2010 to 24 December 2023 for weekly data. Firstly, the fractal and [...] Read more.
This paper introduces hybrid models designed to analyze daily and weekly bitcoin return spanning the periods from 18 July 2010 to 28 December 2023 for daily data, and from 18 July 2010 to 24 December 2023 for weekly data. Firstly, the fractal and chaotic structure of the selected variables was explored. Asymmetric Cantor set, Boundary of the Dragon curve, Julia set z2 −1, Boundary of the Lévy C curve, von Koch curve, and Brownian function (Wiener process) tests were applied. The R/S and Mandelbrot–Wallis tests confirmed long-term dependence and fractionality. The largest Lyapunov test, the Rosenstein, Collins and DeLuca, and Kantz methods of Lyapunov exponents, and the HCT and Shannon entropy tests tracked by the Kolmogorov–Sinai (KS) complexity test determined the evidence of chaos, entropy, and complexity. The BDS test of independence test approved nonlinearity, and the TeraesvirtaNW and WhiteNW tests, the Tsay test for nonlinearity, the LR test for threshold nonlinearity, and White’s test and Engle test confirmed nonlinearity and heteroskedasticity, in addition to fractionality and chaos. In the second stage, the standard ARFIMA method was applied, and its results were compared to the LieNLS and LieOLS methods. The results showed that, under conditions of chaos, entropy, and complexity, the ARFIMA method did not yield successful results. Both baseline models, LieNLS and LieOLS, are enhanced by integrating them with deep learning methods. The models, LieLSTMOLS and LieLSTMNLS, leverage manifold-based approaches, opting for matrix representations over traditional differential operator representations of Lie algebras were employed. The parameters and coefficients obtained from LieNLS and LieOLS, and the LieLSTMOLS and LieLSTMNLS methods were compared. And the forecasting capabilities of these hybrid models, particularly LieLSTMOLS and LieLSTMNLS, were compared with those of the main models. The in-sample and out-of-sample analyses demonstrated that the LieLSTMOLS and LieLSTMNLS methods outperform the others in terms of MAE and RMSE, thereby offering a more reliable means of assessing the selected data. Our study underscores the importance of employing the LieLSTM method for analyzing the dynamics of bitcoin. Our findings have significant implications for investors, traders, and policymakers. Full article
(This article belongs to the Special Issue Fractional-Order Dynamics and Control in Green Energy Systems)
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Figure 1
<p>Daily bitcoin price from 18 July 2010 to 28 December 2023.</p> Full article ">Figure 2
<p>Weekly bitcoin price from 18 July 2010 to 24 December 2023.</p> Full article ">
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