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Fractional Order Systems with Application to Electrical Power Engineering

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

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 24897

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Special Issue Editors

Dr. Arman Oshnoei

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Guest Editor

Department of Energy, Aalborg University, 9220 Aalborg, Denmark
Interests: power electronics; power systems; smart grid; AC/DC microgrid; intelligent control
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Behnam Mohammadi-Ivatloo

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Guest Editor

Smart Energy Systems Laboratory, Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
Interests: smart energy systems, machine learning, uncertainty management, decision making, renewable energy sources
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As the Guest Editors, we encourage scientists and colleagues to submit their theoretical and applied contributions, as well as review articles, to this Special Issue of Fractal and Fractional on the subject “Fractional Order Systems with Application to Electrical Power Engineering”. This Special Issue aims to explore 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 can outline many practical dynamic behaviors in the engineering field into fractional-order systems. As a non-standard operator, fractional-order calculus solves the problem that the constitutive model of classical differential equations cannot accurately describe the dynamic behavior of complex systems. It provides an effective tool for defining practical models with memory properties and historical reliance, provides additional degrees of freedom, and increases design flexibility. A more accurate mathematical model of the system can be established using fractional calculus due to the nature of a fractal dimension compared to 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
Prof. Dr. Behnam Mohammadi-Ivatloo
Guest Editors

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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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Fractional Order Systems with Application to Electrical Power Engineering, 2nd Edition in Fractal and Fractional (11 articles)

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35 pages, 5306 KiB

Open AccessArticle

Optimized Multiloop Fractional-Order Controller for Regulating Frequency in Diverse-Sourced Vehicle-to-Grid Power Systems

by Amira Hassan, Mohamed M. Aly, Mohammed A. Alharbi, Ali Selim, Basem Alamri, Mokhtar Aly, Ahmed Elmelegi, Mohamed Khamies and Emad A. Mohamed

Fractal Fract. 2023, 7(12), 864; https://doi.org/10.3390/fractalfract7120864 - 5 Dec 2023

Cited by 2 | Viewed by 1644

Abstract

A reduced power system’s inertia represents a big issue for high penetration levels of renewable generation sources. Recently, load frequency controllers (LFCs) and their design have become crucial factors for stability and supply reliability. Thence, a new optimized multiloop fractional LFC scheme is provided in this paper. The proposed multiloop LFC scheme presents a two-degree-of-freedom (2DOF) structure using the tilt–integral–derivatives with filter (TIDN) in the first stage and the tilt–derivative with filter (TDN) in the second stage. The employment of two different loops achieves better disturbance rejection capability using the proposed 2DOF TIDN-TDN controller. The proposed 2DOF TIDN-TDN method is optimally designed using the recent powerful marine predator optimizer algorithm (MPA). The proposed design method eliminates the need for precise modeling of power systems, complex control design theories, and complex disturbance observers and filter circuits. A multisourced two-area interlinked power grid is employed as a case study in this paper by incorporating renewable generation with multifunctionality electric vehicle (EV) control and contribution within the vehicle-to-grid (V2G) concept. The proposed 2DOF TIDN-TDN LFC is compared with feature-related LFCs from the literature, such as TID, FOTID, and TID-FOPIDN controllers. Better mitigated frequency and tie-line power fluctuations, faster response, lower overshot/undershot values, and shorter settling time are the proven features of the proposed 2DOF TIDN-TDN LFC method. Full article

(This article belongs to the Special Issue Fractional Order Systems with Application to Electrical Power Engineering)

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22 pages, 7415 KiB

Open AccessArticle

A New Fractional-Order Virtual Inertia Support Based on Battery Energy Storage for Enhancing Microgrid Frequency Stability

by Morsy Nour, Gaber Magdy, Abualkasim Bakeer, Ahmad A. Telba, Abderrahmane Beroual, Usama Khaled and Hossam Ali

Fractal Fract. 2023, 7(12), 855; https://doi.org/10.3390/fractalfract7120855 - 30 Nov 2023

Cited by 4 | Viewed by 1787

Abstract

Microgrids have a low inertia constant due to the high penetration of renewable energy sources and the limited penetration of conventional generation with rotating mass. This makes microgrids more susceptible to frequency stability challenges. Virtual inertia control (VIC) is one of the most effective approaches to improving microgrid frequency stability. Therefore, this study proposes a new model to precisely mimic inertia power based on an energy storage system (ESS) that supports low-inertia power systems. The developed VIC model considers the effect of both the DC-DC converter and the DC-AC inverter on the power of the ESS used. This allows for more precise and accurate modeling of the VIC compared to conventional models. Moreover, this study proposes a fractional-order derivative control for the proposed VIC model to provide greater flexibility in dealing with different perturbations that occur in the system. Furthermore, the effectiveness of the proposed fractional-order VIC (FOVIC) is verified through an islanded microgrid that includes heterogeneous sources: a small thermal power plant, wind and solar power plants, and ESSs. The simulation results performed using MATLAB software indicate that the proposed VIC scheme provides fast stabilization times and slight deviations in system frequency compared to the conventional VIC schemes. The proposed VIC outperforms the conventional load frequency control by about 80% and the conventional VIC model by about 45% in tackling load/RESs fluctuations and system uncertainty. Additionally, the studied microgrid with the proposed FOVIC scheme is noticeably more stable and responds faster than that designed with integer-order derivative control. Thus, the proposed FOVIC scheme gives better performance for frequency stability of low-inertia power systems compared to conventional VIC schemes used in the literature. Full article

(This article belongs to the Special Issue Fractional Order Systems with Application to Electrical Power Engineering)

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20 pages, 1733 KiB

Open AccessArticle

Disturbance Observer-Based Event-Triggered Adaptive Command Filtered Backstepping Control for Fractional-Order Nonlinear Systems and Its Application

by Shuai Song, Xiaona Song and Inés Tejado

Fractal Fract. 2023, 7(11), 810; https://doi.org/10.3390/fractalfract7110810 - 9 Nov 2023

Cited by 4 | Viewed by 1227

Abstract

This paper considers the disturbance observer-based event-triggered adaptive fuzzy tracking control issue for a class of fractional-order nonlinear systems (FONSs) with quantized signals and unknown disturbances. To improve the disturbance rejection ability, a fractional-order nonlinear disturbance observer (FONDO) is designed to estimate the unknown composite disturbances. Furthermore, by combining an improved fractional-order command-filtered backstepping control technique and an event-triggered control mechanism, an event-triggered adaptive fuzzy quantized control scheme is established, which guarantees the desired tracking performance can be achieved even in the presence of network constraint. Finally, the validity and superiority of the theoretic results are verified by a fractional-order horizontal platform system. Full article

(This article belongs to the Special Issue Fractional Order Systems with Application to Electrical Power Engineering)

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44 pages, 17085 KiB

Open AccessArticle

First-of-Its-Kind Frequency Enhancement Methodology Based on an Optimized Combination of FLC and TFOIDFF Controllers Evaluated on EVs, SMES, and UPFC-Integrated Smart Grid

by Sultan Alghamdi, Mohammed Alqarni, Muhammad R. Hammad and Kareem M. AboRas

Fractal Fract. 2023, 7(11), 807; https://doi.org/10.3390/fractalfract7110807 - 6 Nov 2023

Cited by 4 | Viewed by 1893

Abstract

The most recent advancements in renewable energy resources, as well as their broad acceptance in power sectors, have created substantial operational, security, and management concerns. As a result of the continual decrease in power system inertia, it is critical to maintain the normal operating frequency and reduce tie-line power changes. The preceding issues sparked this research, which proposes the Fuzzy Tilted Fractional Order Integral Derivative with Fractional Filter (FTFOIDFF), a unique load frequency controller. The FTFOIDFF controller described here combines the benefits of tilt, fuzzy logic, FOPID, and fractional filter controllers. Furthermore, the prairie dog optimizer (PDO), a newly developed metaheuristic optimization approach, is shown to efficiently tune the suggested controller settings as well as the forms of the fuzzy logic membership functions in the two-area hybrid power grid investigated in this paper. When the PDO results are compared to those of the Seagull Optimization Algorithm, the Runge Kutta optimizer, and the Chaos Game Optimizer for the same hybrid power system, PDO prevails. The system model incorporates physical constraints such as communication time delays and generation rate constraints. In addition, a unified power flow controller (UPFC) is put in the tie-line, and SMES units have been planned in both regions. Furthermore, the contribution of electric vehicles (EVs) is considered in both sections. The proposed PDO-based FTFOIDFF controller outperformed many PDO-based traditional (such as proportional integral derivative (PID), proportional integral derivative acceleration (PIDA), and TFOIDFF) and intelligent (such as Fuzzy PID and Fuzzy PIDA) controllers from the literature. The suggested PDO-based FTFOIDFF controller has excellent performance due to the usage of various load patterns such as step load perturbation, multi-step load perturbation, random load perturbation, random sinusoidal load perturbation, and pulse load perturbation. Furthermore, a variety of scenarios have been implemented to demonstrate the advantageous effects that SMES, UPFC, and EV units have on the overall performance of the system. The sensitivity of a system is ascertained by modifying its parameters from their standard configurations. According to the simulation results, the suggested PDO-based FTFOIDFF controller can improve system stability despite the multiple difficult conditions indicated previously. According to the MATLAB/Simulink data, the proposed method decreased the total fitness function to 0.0875, representing a 97.35% improvement over PID, 95.84% improvement over PIDA, 92.45% improvement over TFOIDFF, 83.43% improvement over Fuzzy PID, and 37.9% improvement over Fuzzy PIDA. Full article

(This article belongs to the Special Issue Fractional Order Systems with Application to Electrical Power Engineering)

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33 pages, 5253 KiB

Open AccessArticle

Design Optimization of Improved Fractional-Order Cascaded Frequency Controllers for Electric Vehicles and Electrical Power Grids Utilizing Renewable Energy Sources

by Fayez F. M. El-Sousy, Mohammed H. Alqahtani, Ali S. Aljumah, Mokhtar Aly, Sulaiman Z. Almutairi and Emad A. Mohamed

Fractal Fract. 2023, 7(8), 603; https://doi.org/10.3390/fractalfract7080603 - 4 Aug 2023

Cited by 6 | Viewed by 1520

Abstract

Recent developments in electrical power grids have witnessed high utilization levels of renewable energy sources (RESs) and increased trends that benefit the batteries of electric vehicles (EVs). However, modern electrical power grids cause increased concerns due to their continuously reduced inertia resulting from RES characteristics. Therefore, this paper proposes an improved fractional-order frequency controller with a design optimization methodology. The proposed controller is represented by two cascaded control loops using the one-plus-proportional derivative (1 + PD) in the outer loop and a fractional-order proportional integral derivative (FOPID) in the inner loop, which form the proposed improved 1 + PD/FOPID. The main superior performance characteristics of the proposed 1 + PD/FOPID fractional-order frequency controller over existing methods include a faster response time with minimized overshoot/undershoot peaks, an ability for mitigating both high- and low-frequency disturbances, and coordination of EV participation in regulating electrical power grid frequency. Moreover, simultaneous determination of the proposed fractional-order frequency controller parameters is proposed using the recent manta ray foraging optimization (MRFO) algorithm. Performance comparisons of the proposed 1 + PD/FOPID fractional-order frequency controller with existing PID, FOPID, and PD/FOPID controllers are presented in the paper. The results show an improved response, and the disturbance mitigation is also obtained using the proposed MRFO-based 1 + PD/FOPID control and design optimization methodology. Full article

(This article belongs to the Special Issue Fractional Order Systems with Application to Electrical Power Engineering)

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18 pages, 10057 KiB

Open AccessArticle

Fractional-Order Model-Free Predictive Control for Voltage Source Inverters

by Hani Albalawi, Abualkasim Bakeer, Sherif A. Zaid, El-Hadi Aggoune, Muhammad Ayaz, Ahmed Bensenouci and Amir Eisa

Fractal Fract. 2023, 7(6), 433; https://doi.org/10.3390/fractalfract7060433 - 27 May 2023

Cited by 8 | Viewed by 1598

Abstract

Currently, a two-level voltage source inverter (2L-VSI) is regarded as the cornerstone of modern industrial applications. However, the control of VSIs is a challenging task due to their nonlinear and time-varying nature. This paper proposes employing the fractional-order controller (FOC) to improve the performance of model-free predictive control (MFPC) of the 2L-VSI voltage control in uninterruptible power supply (UPS) applications. In the conventional MFPC based on the ultra-local model (ULM), the unknown variable that includes all the system disturbances is estimated using algebraic identification, which is insufficient to improve the prediction accuracy in the predictive control. The proposed FO-MFPC uses fractional-order proportional-integral control (FOPI) to estimate the unknown function associated with the MFPC. To get the best performance from the FOPI, its parameters are optimally designed using the grey wolf optimization (GWO) approach. The number of iterations of the GWO is 100, while the grey wolf’s number is 20. The proposed GWO algorithm achieves a small fitness function value of approximately 0.156. In addition, the GWO algorithm nearly finds the optimal parameters after 80 iterations for the defined objective function. The performance of the proposed FO-MFPC controller is compared to that of conventional MFPC for the three loading cases and conditions. Using MATLAB simulations, the simulation results indicated the superiority of the proposed FO-MFPC controller over the conventional MFPC in steady state and transient responses. Moreover, the total harmonic distortion (THD) of the output voltage at different sampling times proves the excellent quality of the output voltage with the proposed FO-MFPC controller over the conventional MFPC controller. The results confirm the robustness of the two control systems against parameter mismatches. Additionally, using the TMS320F28379D kit, the experimental verification of the proposed FO-MFPC control strategy is implemented for 2L-VSI on the basis of the Hardware-in-the-Loop (HIL) simulator, demonstrating the applicability and effective performance of our proposed control strategy under realistic circumstances. Full article

(This article belongs to the Special Issue Fractional Order Systems with Application to Electrical Power Engineering)

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18 pages, 9459 KiB

Open AccessArticle

Microgrid Frequency Regulation Based on a Fractional Order Cascade Controller

by Soroush Oshnoei, Arman Fathollahi, Arman Oshnoei and Mohammad Hassan Khooban

Fractal Fract. 2023, 7(4), 343; https://doi.org/10.3390/fractalfract7040343 - 21 Apr 2023

Cited by 10 | Viewed by 1929

Abstract

Nowadays, the participation of renewable energy sources (RESs) and the integration of these sources with traditional power plants in microgrids (MGs) for providing demand-side power has rapidly grown. Although the presence of RESs in MGs reduces environmental problems, their high participation significantly affects the system’s whole inertia and dynamic stability. This paper focuses on an islanded MG frequency regulation under the high participation of RESs. In this regard, a novel fractional order cascade controller (FOCC) is proposed as the secondary frequency controller. In the proposed FOCC controller structure, a fractional order proportional-integral controller is cascaded with a fractional order tilt-derivative controller. The proposed FOCC controller has a greater degree of freedom and adaptability than integer order controllers and improves the control system’s efficiency. The adjustable coefficients of the proposed controller are tuned via the kidney-inspired algorithm. An energy storage system equipped with virtual inertia is also employed to improve the system inertia. The proposed FOCC controller efficiency is compared with proportional-integral-derivative (PID), tilt-integral-derivative (TID), and fractional order proportional-integral-derivative (FOPID) controllers under different disturbances and operating conditions. The results demonstrate that the presented controller provides better frequency responses compared to the other controllers. Moreover, the sensitivity analysis is performed to show the proposed controller robustness versus the parameters’ changes in the system. Full article

(This article belongs to the Special Issue Fractional Order Systems with Application to Electrical Power Engineering)

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23 pages, 3594 KiB

Open AccessArticle

Driver Training Based Optimized Fractional Order PI-PDF Controller for Frequency Stabilization of Diverse Hybrid Power System

by Guoqiang Zhang, Amil Daraz, Irfan Ahmed Khan, Abdul Basit, Muhammad Irshad Khan and Mirzat Ullah

Fractal Fract. 2023, 7(4), 315; https://doi.org/10.3390/fractalfract7040315 - 6 Apr 2023

Cited by 27 | Viewed by 2115

Abstract

This work provides an enhanced novel cascaded controller-based frequency stabilization of a two-region interconnected power system incorporating electric vehicles. The proposed controller combines a cascade structure comprising a fractional-order proportional integrator and a proportional derivative with a filter term to handle the frequency regulation challenges of a hybrid power system integrated with renewable energy sources. Driver training-based optimization, an advanced stochastic meta-heuristic method based on human learning, is employed to optimize the gains of the proposed cascaded controller. The performance of the proposed novel controller was compared to that of other control methods. In addition, the results of driver training-based optimization are compared to those of other recent meta-heuristic algorithms, such as the imperialist competitive algorithm and jellyfish swarm optimization. The suggested controller and design technique have been evaluated and validated under a variety of loading circumstances and scenarios, as well as their resistance to power system parameter uncertainties. The results indicate the new controller’s steady operation and frequency regulation capability with an optimal controller coefficient and without the prerequisite for a complex layout procedure. Full article

(This article belongs to the Special Issue Fractional Order Systems with Application to Electrical Power Engineering)

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29 pages, 21253 KiB

Open AccessArticle

Optimal FOPI Error Voltage Control Dead-Time Compensation for PMSM Servo System

by Fumin Li, Ying Luo, Xin Luo, Pengchong Chen and Yangquan Chen

Fractal Fract. 2023, 7(3), 274; https://doi.org/10.3390/fractalfract7030274 - 21 Mar 2023

Cited by 5 | Viewed by 1828

Abstract

This paper proposed a dead-time compensation method with fractional-order proportional integral (FOPI) error voltage control. The disturbance voltages caused by the power devices’ dead time and non-ideal switching characteristics are compensated for with the FOPI controller and fed to the reference voltage. In this paper, the actual error voltage is calculated based on the model and actual voltage of the permanent magnet synchronous motor. Considering the parameter error of the permanent magnet synchronous motor and the voltage error caused by the dead-time effect, a FOPI controller is used to calculate the compensation voltage. An improved particle swarm optimization (PSO) algorithm is utilized to design the parameters of the FOPI controller in order to eliminate the dead-time effect, and the optimal fitness function is designed. Compared with other optimization algorithms, the improved PSO algorithm can achieve faster convergence speed in the error voltage controller parameter design. The proposed dead-time compensation method can improve the performance of the current response and eliminate the dead-time effect. This method also eliminates all harmonic disturbances and has a good suppression effect on high-frequency harmonics. The simulation and experimental results show that the dead-time compensation method using optimal FOPI error voltage control makes the current ripple smaller and the response speed faster than that of the traditional optimal integer-order PI control, thus demonstrating the effectiveness and advantages of the proposed method. Full article

(This article belongs to the Special Issue Fractional Order Systems with Application to Electrical Power Engineering)

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20 pages, 10834 KiB

Open AccessArticle

Theoretical Analysis of a Fractional-Order LLCL Filter for Grid-Tied Inverters

by Xiaogang Wang, Ruidong Zhuang and Junhui Cai

Fractal Fract. 2023, 7(2), 135; https://doi.org/10.3390/fractalfract7020135 - 31 Jan 2023

Cited by 4 | Viewed by 1591

Abstract

The LLCL-filter-based grid-tied inverter performs better than the LCL-type grid-tied inverter due to its outstanding switching-frequency current harmonic elimination capability, but the positive resonance peak must be suppressed by passive or active damping methods. This paper proposes a class of fractional-order LLCL (FOLLCL) filters, which provides rich features by adjusting the orders of three inductors and one capacitor of the filter. Detailed analyses are performed to reveal the frequency characteristics of the FOLLCL filter; the orders must be selected reasonably to damp the positive resonance peak while reserving the negative resonance peak to attenuate the switching-frequency harmonics. Furthermore, the control system of the grid-tied inverter based on the FOLLCL filter is studied. When the positive resonance is suppressed by the intrinsic damping effect of the FOLLCL filter, the passive or active damper can be avoided; the grid current single close-loop is adequate to control the grid-tied inverter. For low-frequency applications, proportional-resonant (PR) controller is more suitable for the FOLLCL-type grid-tied inverter compared with the proportional-integral (PI) and fractional-order PI controllers due to its overall performance. Simulation results are consistent with theoretical expectations. Full article

(This article belongs to the Special Issue Fractional Order Systems with Application to Electrical Power Engineering)

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18 pages, 5004 KiB

Open AccessArticle

A New Intelligent Fractional-Order Load Frequency Control for Interconnected Modern Power Systems with Virtual Inertia Control

by Sherif A. Zaid, Abualkasim Bakeer, Gaber Magdy, Hani Albalawi, Ahmed M. Kassem, Mohmed E. El-Shimy, Hossam AbdelMeguid and Bassel Manqarah

Fractal Fract. 2023, 7(1), 62; https://doi.org/10.3390/fractalfract7010062 - 5 Jan 2023

Cited by 30 | Viewed by 2324

Abstract

Since modern power systems are susceptible to undesirable frequency oscillations caused by uncertainties in renewable energy sources (RESs) and loads, load frequency control (LFC) has a crucial role to get these systems’ frequency stability back. However, existing LFC techniques may not be sufficient to confront the key challenge arising from the low-inertia issue, which is due to the integration of high-penetration RESs. Therefore, to address this issue, this study proposes an optimized intelligent fractional-order integral (iFOI) controller for the LFC of a two-area interconnected modern power system with the implementation of virtual inertia control (VIC). Here, the proposed iFOI controller is optimally designed using an efficient metaheuristic optimization technique, called the gray wolf optimization (GWO) algorithm, which provides minimum values for system frequency deviations and tie-line power deviation. Moreover, the effectiveness of the proposed optimal iFOI controller is confirmed by contrasting its performance with other control techniques utilized in the literature, such as the integral controller and FOI controller, which are also designed in this study, under load/RES fluctuations. Compared to these control techniques from the literature for several scenarios, the simulation results produced by the MATLAB software have demonstrated the efficacy and resilience of the proposed optimal iFOI controller based on the GWO. Additionally, the effectiveness of the proposed controller design in regulating the frequency of interconnected modern power systems with the application of VIC is confirmed. Full article

(This article belongs to the Special Issue Fractional Order Systems with Application to Electrical Power Engineering)

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Review

Jump to: Research

31 pages, 3141 KiB

Open AccessReview

Fractional-Order Control Techniques for Renewable Energy and Energy-Storage-Integrated Power Systems: A Review

by Masoud Alilou, Hatef Azami, Arman Oshnoei, Behnam Mohammadi-Ivatloo and Remus Teodorescu

Fractal Fract. 2023, 7(5), 391; https://doi.org/10.3390/fractalfract7050391 - 9 May 2023

Cited by 18 | Viewed by 3270

Abstract

The worldwide energy revolution has accelerated the utilization of demand-side manageable energy systems such as wind turbines, photovoltaic panels, electric vehicles, and energy storage systems in order to deal with the growing energy crisis and greenhouse emissions. The control system of renewable energy units and energy storage systems has a high effect on their performance and absolutely on the efficiency of the total power network. Classical controllers are based on integer-order differentiation and integration, while the fractional-order controller has tremendous potential to change the order for better modeling and controlling the system. This paper presents a comprehensive review of the energy system of renewable energy units and energy storage devices. Various papers are evaluated, and their methods and results are presented. Moreover, the mathematical fundamentals of the fractional-order method are mentioned, and the various studies are categorized based on different parameters. Various definitions for fractional-order calculus are also explained using their mathematical formula. Different studies and numerical evaluations present appropriate efficiency and accuracy of the fractional-order techniques for estimating, controlling, and improving the performance of energy systems in various operational conditions so that the average error of the fractional-order methods is considerably lower than other ones. Full article

(This article belongs to the Special Issue Fractional Order Systems with Application to Electrical Power Engineering)

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