Fractional Order PI Controller Research Articles

Tracking performance optimization of balancing machine turntable servo system based on deep deterministic policy gradient fractional order proportional integral derivative control strategy

Tracking performance optimization of balancing machine turntable servo system based on deep deterministic policy gradient fractional order proportional integral derivative control strategy

Application of an Optimal Fractional-Order Controller for a Standalone (Wind/Photovoltaic) Microgrid Utilizing Hybrid Storage (Battery/Ultracapacitor) System

Nowadays, standalone microgrids that make use of renewable energy sources have gained great interest. They provide a viable solution for rural electrification and decrease the burden on the utility grid. However, because standalone microgrids are nonlinear and time-varying, controlling and managing their energy can be difficult. A fractional-order proportional integral (FOPI) controller was proposed in this study to enhance a standalone microgrid’s energy management and performance. An ultra-capacitor (UC) and a battery, called a hybrid energy storage scheme, were employed as the microgrid’s energy storage system. The microgrid was primarily powered by solar and wind power. To achieve optimal performance, the FOPI’s parameters were ideally generated using the gorilla troop optimization (GTO) technique. The FOPI controller’s performance was contrasted with a conventional PI controller in terms of variations in load power, wind speed, and solar insolation. The microgrid was modeled and simulated using MATLAB/Simulink software R2023a 23.1. The results indicate that, in comparison to the traditional PI controller, the proposed FOPI controller significantly improved the microgrid’s transient performance. The load voltage and frequency were maintained constant against the least amount of disturbance despite variations in wind speed, photovoltaic intensity, and load power. In contrast, the storage battery precisely stores and releases energy to counteract variations in wind and photovoltaic power. The outcomes validate that in the presence of the UC, the microgrid performance is improved. However, the improvement is very close to that gained when using the proposed controller without UC. Hence, the proposed controller can reduce the cost, weight, and space of the system. Moreover, a Hardware-in-the-Loop (HIL) emulator was implemented using a C2000™ microcontroller LaunchPad™ TMS320F28379D kit (Texas Instruments, Dallas, TX, USA) to evaluate the proposed system and validate the simulation results.

Power quality improvement of grid‐connected solar power plant systems using a novel fractional order proportional integral derivative controller technique

AbstractRecently, there has been a push to integrate renewable energy system (RES) into grid‐connected load system in enhancing reliability and reducing losses. However, integrating these systems introduces power quality (PQ) issues, especially with non‐linear, critical, and imbalanced loads. Addressing this, a hybrid mantis search‐reptile search algorithm (HMS‐RSA) combined with a unified power quality conditioner (UPQC) to mitigate PQ problems related to current and voltages in RES systems. In other words, the UPQC, enhanced by fractional order proportional integral derivative controller parameters tuned using the proposed HMS‐RSA assists in enhancing the power quality. The approach has been validated by connecting a non‐linear load to the system, which typically creates PQ issues. The proposed method is implemented in MATLAB/Simulink and their performance is analysed in three scenarios, such as sag, swell, and disturbance, and the total harmonic distortion is evaluated to quantify improvements in PQ. Finally, the proposed method is compared with existing approaches, such as ant colony optimization (ACO), artificial bee colony optimization (ABC), and bacterial foraging optimization (BFO). The method also outperforms ACO, ABC, and BFO in terms of convergence speed and effectiveness in mitigating PQ issues.

Spider Wasp Optimizer-Optimized Cascaded Fractional-Order Controller for Load Frequency Control in a Photovoltaic-Integrated Two-Area System

The integration of photovoltaic (PV) systems into traditional power grids introduces significant challenges in maintaining system stability, particularly in multi-area power systems. This study proposes a novel approach to load frequency control (LFC) in a two-area power system, where one area is powered by a PV grid and the other by a thermal generator. To enhance system performance, a cascaded control strategy combining a fractional-order proportional–integral (FOPI) controller and a proportional–derivative with filter (PDN) controller, FOPI(1+PDN), is introduced. The controller parameters are optimized using the spider wasp optimizer (SWO). Extensive simulations are conducted to validate the effectiveness of the SWO-tuned FOPI(1+PDN) controller. The proposed method demonstrates superior performance in reducing frequency deviations and tie-line power fluctuations under various disturbances. The results are compared against other advanced optimization algorithms, each applied to the FOPI(1+PDN) controller. Additionally, this study benchmarks the SWO-tuned controller against recently reported control strategies that were optimized using different algorithms. The SWO-tuned FOPI(1+PDN) controller demonstrates superior performance in terms of faster response, reduced overshoot and undershoot, and better error minimization.

Modeling of genetic algorithm tuned adaptive fuzzy fractional order PID speed control of permanent magnet synchronous motor for electric vehicle

This study presents a novel Genetic Algorithm-optimized Adaptive Fuzzy Fractional Order Proportional Integral Derivative (GA-AFFFOPID) controller for enhancing the speed control performance of permanent magnet synchronous motor (PMSM) drives in Electric Vehicles. The proposed GA-AFFFOPID controller, which combines the advantages of genetic algorithm optimization and adaptive fuzzy fractional-order PID control, represents a unique and innovative approach to address the control challenges associated with PMSM drives. Permanent magnet synchronous motor technology, known for its efficiency, compactness, reliability, and versatility in motion control applications, is increasingly adopted in electric vehicle drive systems. However, the inherent non-linearity, dynamics, and uncertainties of permanent magnet synchronous motors pose significant control challenges. The exceptional performance of the GA-AFFFOPID controller, demonstrated through its superior system dynamics, precise speed tracking, and robustness against parameter variations and sudden load disturbances, underscores the significant advancements enabled by the genetic algorithm optimization technique in improving the control performance of PMSM drives for electric vehicle applications. Comparative analysis with traditional control methods demonstrates the exceptional performance of the Genetic Algorithm-optimized Adaptive Fuzzy Fractional Order Proportional Integral Derivative controller. These findings highlight the significant performance improvements facilitated by the genetic algorithm optimization technique in enhancing the control performance of the adaptive fuzzy fractional order PID controller in PMSM drives for electric vehicle applications.

Golden eagle optimized fractional-order PI controller design for a PFC SEPIC converter in EV charging

The power factor correction converter is the function of the front-end converter, followed by the DC–DC converter of the electric vehicle charger. It improves the power factor and regulates the output voltage and current. This research article proposes the Golden Eagle optimization for fractional order PI (FOPI) controller for Single Ended Primary Inductor Converter (SEPIC) power factor correction. The Golden eagle optimization is based on its knowledge of hunting tactics at various degrees of spiral trajectories to catch the prey. The FOPI controller has a broad range of controller parameters that provide better control and performance of the converter. The tuning of the parameters of the FOPI controller is optimized in Golden Eagle Optimization, and the Integral Absolute error with Integral Square error is used for the objective function. The optimized parameters of FOPI compare with the conventional PI controller performance. The SEPIC converter is designed and derived from the state space model by state space averaging, and the reduced model is obtained through the moment matching method. This system is tested under MATLAB/SIMULINK, and simulation results show improved settling time, fast dynamic response, reduction of inrush current, less harmonic distortion, and stability.

A new optimal 3° of freedom fractional order proportion integral derivative controller with model predictive controller for frequency regulation in high penetrated renewable based interconnected system

The increasing use of renewable energy sources (RESs) in conventional power systems is making them more complex. RES, such as solar and wind energy, reduce system inertia, affecting power system (PS) stability and frequency aberrations. Thus, the modern PS faces new concerns that arise from integrating RESs and struggles to manage frequency and stability, which can cause power outages and blackouts and lower industry production. The intelligent control mechanism is critical to the PS's operation to ensure frequency under its complicated structure. This study suggests a new best 3-DoF fractional order proportional integral derivative-model predictive controller (3DoF-FOPIDN-MPC) for controlling frequency when there is a lot of load going on quickly. The 3DoF-FOPID controls the outer loop using the area control error (ACE) signal, while MPC controls the inner loop using the output signal from the 3DoF-FOPIDN and the area's total power output response. For optimal controller functionality, the salp swarm algorithm (SSA) extracts optimized controller settings. To validate the suggested controller, it is tested under various load-changing scenarios and compared to state-of-the-art controllers. For 1 % and 3 % load changes, the suggested controller settles in 1.1 s and 1.78 s, respectively.

Optimal nonlinear Fractional-Order Proportional-Integral-Derivative controller design using a novel hybrid atom search optimization for nonlinear Continuously stirred Tank reactor

Atom search optimization (ASO) algorithm derived from physics molecular dynamics. Lennard-Jones(L-J) and bond length potential of molecules are used to derive the model for optimization. In this paper, ASO is used for developing a nonlinear Fractional Order Proportional Integral Derivative controller (NL-FOPID) for Continuously Stirred Tank Reactor (CSTR). The convergence characteristics of ASO was improved by proposing a novel hybridization approach. The proposed hybridization approach called Hybrid ASO(HASO) guides the Atom search algorithm to optimally replace the atoms that goes out of the boundary of the search space. The designed algorithm is implemented to optimize various unimodal and multi model standard benchmark functions. From results obtained from this extensive simulation, it is indicated that proposed approach increased the convergence rate and also improved the optimization effort of conventional ASO. The proposed algorithm also tested with controller design for nonlinear CSTR. The NLPID and NL FOPID designed by HASO was better than conventional controllers found in the literature.

Enhancing Transient Response in a DC-DC Converter for Electric Vehicle DC Fast Charging Applications Using Fractional-Order PI Control

DC fast charging is critical for the widespread adoption of electric vehicles (EVs) due to its impact on convenience, economics, and environmental sustainability. Due to the critical role of DC fast charging in EV adoption, improving its efficiency and performance is paramount. This paper presents a Fractional-Order PI (FOPI) controller for obtaining a well-regulated output voltage of a Dual Active Bridge (DAB) converter, a widely used topology in EV applications. The proposed FOPI is validated to the conventional PI controller in a simulated DAB model that is relevant to DC fast charging applications. The evaluation is performed, and various time-domain parameters and performance indices to evaluate the dynamic response of the model are considered. The results are expected to demonstrate significant improvement in the converter’s transient and steady-state response using the proposed FOPI controller compared to the conventional PI controller, contributing to a more efficient and robust DC fast charging system. This improvement can translate to faster charging times, better stability, and potentially reduced stress on the EV battery during DC fast charging.

Application of DPC to improve the integration of DFIG into wind energy conversion systems using FOPI controller

While the direct power control (DPC) approach has proven effective in improving the efficiency of wind energy conversion systems (WECS) using doubly fed induction generators (DFIG), its applicability is currently confined to a single usage and has not been extended to meet numerous applications. This work aimed to modify the implementation of DPC in WECS-DFIG for several objectives. This is accomplished by updating the reference power of the conventional DPC method into an adapted one to achieve two goals independently. The first objective is to track the maximum power during wind speed variations. This tracking is performed by updating the reference power to match the maximum available power at the current wind speed. The second purpose is to ensure that the WECS remains connected to the grid and continues to operate smoothly even in the event of faults; supporting fault-ride through (FRT) capability. That is achieved by reducing the reference power during these faults. The discrimination between these two objectives is based on the voltage level at the point of connecting WECS to the grid. The controller provided is an improved fractional order PI controller developed using arithmetic optimization technique (AOA). A comparison between the AOA and cuckoo search is presented. The results demonstrate the efficacy of the suggested configuration and regulator in enhancing the performance of integrating DFIG into the WECS in the presence of wind fluctuations and short circuit faults occurring. It is worth noting that AOA is better than cuckoo search in fine-tuning the settings of the FOPI controller.

Power quality improvement of grid-tied PV systems with continuous-time adaptive LMS and FOPI control-based DSTATCOM

A control technique for the single-stage solar photovoltaic-distribution static compensator (PV-DSTATCOM) integrated to a three-phase grid is presented in this article. The continuous-time adaptive Least Mean Square (CLMS) algorithm with Fractional Order Proportional Integral (FOPI) controller has been proposed to control the DSTATCOM. Perturb and Observe-based Maximum Power Point Tracking yields peak power production from the solar photovoltaic array. The precise control of PV-DSTATCOM by the proposed CLMS with FOPI controller has improved the power quality of the grid. This is achieved by utilizing the proposed algorithm's capability to effectively track the time-varying nature of irradiance and load changes, adjust weighting factors, and minimize errors. Simulations in MATLAB/Simulink demonstrate its superior performance in optimizing system behavior under intermittent sunlight, nonlinearity, and load imbalances. The grid current has been sinusoidally balanced with reduced total harmonic distortion and meets IEEE-519 standards in both steady-state and dynamic situations. The proposed CLMS with FOPI controller performs better than other methods in the literature.

Optimal fractional PI controller-based VSC-HVDC system with LCL filter design

For decades, high voltage direct current (HVDC) has been an essential means in designing smart microgrids. Though, a control approach for Voltage Source Converter (VSC)-based HVDC, like dampening oscillations, must be established for improved operational execution, as these oscillations can cause stability issues. Considering its versatility, the Fractional order Proportional Integral (FPI) controller is used in this study's control approach instead of the PI controller. With frequency domain analysis, comprehensive modelling and design of LCL filters for harmonic reduction to improve power quality are presented. The dynamic characteristics of VSC-HVDC are comprehensively presented based on dq axis synchronous frame of reference. The VSC-HVDC improved control outcome is validated by the result analysis using PI and FPI controller using ITLBO. It is found in both frequency and time-domain simulations and analysis that the AFPI-VSC-HVDC system is capable of effectively dampening oscillations to enhance the small-signal stability.

Enhanced grid integration through advanced predictive control of a permanent magnet synchronous generator - Superconducting magnetic energy storage wind energy system

In this study, the use of an Unscented Kalman Filter as an indicator in predictive current control (PCC) for a wind energy conversion system (WECS) that employs a permanent magnetic synchronous generator (PMSG) and a superconducting magnetic energy storage (SMES) system connected to the main power grid is presented. The suggested UKF indication in the hybrid WECS-SMES arrangement is in charge of estimating vital metrics such as stator currents, electromagnetic torque, rotor angle, and rotor angular speed. To optimize control strategies, PCCs use these projected properties rather than direct observations. To control the unpredictable wind energy's nature, SMES must be regulated to minimize fluctuations in the DC-link voltage and power output to the main grid. Fractional order-PI (FOPI) controllers are used in a novel control structure for the SMES system to regulate the output power and DC-link voltage. An artificial bee colony optimization approach is employed to optimize the FOPI controllers. Three commonly utilized indicators, including sliding-mode, EKF, and Luenberger, were evaluated using “MATLAB" to evaluate the performance of the UKF estimate. Assessment criteria such as mean absolute percentage error and root mean squared error were used to gauge the accuracy of the estimates. Simulation findings showed the efficiency of fractional order-PI controllers for SMES and the proposed UKF indication for predictive current control, especially in the presence of measurement noise and over a variety of wind speeds. An improvement in estimation accuracy of up to 99.9 % was demonstrated by the UKF indicator. Moreover, the stability of the suggested UKF-based PCC control for the hybrid WECS-SMES combination was confirmed using Lyapunov stability criteria."

Global MPPT controllers for enhancing dynamic performance of photovoltaic systems under partial shading condition

This research focuses on the development and evaluation of global maximum power point tracking MPPT controllers for enhancing the dynamic performance of Photovoltaic (PV) systems under partial shading conditions. Three different controllers, namely Proportional-Integral (PI), Fractional-Order PI (FOPI), and Fuzzy Logic Controllers (FLC), are studied in conjunction with a modified Incremental Conductance (IC) and Fractional Open-Circuit Voltage (FOCV) algorithms. The proposed controllers with a novel optimization algorithm called Atom Search Optimization Algorithm (ASOA) are compared with classical control. The objective is to investigate the effectiveness of the global MPPT controllers in achieving higher tracking accuracy, faster convergence, and improved stability under varying shading conditions. The study involves extensive simulations using a representative PV system model subjected to different shading scenarios. The results demonstrate that the proposed global MPPT controllers with the ASOA algorithm, when integrated with the modified MPPT algorithms, outperform the classical control techniques in terms of dynamic performance and response to partial shading conditions. The suggested ASOA-based fuzzy IC MPPT controllers can reach the MPP more quickly with a shorter settling time and a better tracking response. Furthermore, with a reduced settling time of about 1.9 % and an average power harvesting efficiency of over 97.9 %, ASOA-based fuzzy IC MPPT controllers offer the best harvesting characteristics. The controller exhibits superior tracking accuracy and stability, mitigating the effects of shading-induced multiple peaks in the P-V curve.

A novel scheme of load frequency control for a multi-microgrids power system utilizing electric vehicles and supercapacitors

Incorporation of renewable energy sources (RESs) into power systems has recently experienced a rapid surge, primarily driven by environmental concerns and the desire for more sustainable power generation. However, the replacement of traditional generating units with RESs lowers the system inertia significantly and causes intermittent generation. These issues make frequency stability a greater concern, particularly in microgrids (MGs), and produce mechanical stress on the conventional generation units. Moreover, in interconnected MGs, the complexity is further magnified owing to interaction between microgrids through the tie power which may increase the disturbance propagation among microgrids. This paper suggests a novel control scheme based on a centralized fractional order proportional integral controller cascaded with a virtual inertia emulator (C.FOPI+VI). The virtual inertia emulation is provided using a supercapacitor (SC) along with electric vehicles (EVs) controlled through a virtual inertia controller. However, the EV is suffering from uncertainty, hence the supercapacitor can mitigate this uncertainty. The control system is applied on three interconnected microgrids, each has a thermal plant, a supercapacitor, and an electric vehicle aggregator. The performance of the system incorporating the proposed control technique is compared with five different inertia emulation topologies known as virtual inertia (VI), virtual synchronous generator (VSG), distributed fractional order proportional integral controller cascaded with virtual inertia (D.FOPI+VI), distributed fractional order proportional integral controller cascaded with virtual synchronous generator (D.FOPI+VSG), and without synthetic inertia. To optimize the parameters of different controllers, the Transit Search (TS) optimization algorithm is employed considering the frequency deviation, the restoration time, and the tie power. The proposed C.FOPI+VI has proven its superiority in providing fast frequency restoration, less stress on the conventional generation units, and minimizing the spreading of the disturbance within the system. Furthermore, the proposed controller enhances the Gain Margin (G.M) to 21.1 dB compared to operation without inertia support (0.322 dB), VI (3.38 dB), VSG (5.23 dB), DFOPI+VI (8.25), and DFOPI+VSG (8.32).

Design of fractional MOIF and MOPIF controller using PSO algorithm for the stabilization of an inverted pendulum‐cart system

AbstractThe topic of this paper is the design of two fractional order schemes, based on a state feedback for linear integer order system. In the first one of the state feedback is associated with a fractional order integral () controller. In the second structure the state feedback is associated with a fractional order proportional integral () controller. With such controllers, the closed loop system with state feedback described by the state equations splits in n‐subsystems with different fractional orders derivatives of the state variable. In order to find the optimal parameters value of both controllers () and (), a multi‐objective particle swarm optimization algorithm is used, with the integral of absolute error, the overshoot , the Buslowicz stability criterion are considered as objective functions. The multi‐objective integral fractional order controller and the multi‐objective proportional integral fractional order controller are applied to stabilize the inverted pendulum‐cart system (IP‐C), and their performance is compared to the fractional order controller. The simulation results of these innovative controllers are also compared with those obtained by conventional proportional–integral–derivative and fractional order proportional–integral–derivative controllers. The robustness of the proposed controllers against disturbances is investigated through simulation runs, considering the non‐linear model of the IP‐C system. The obtained results demonstrate that our approach not only leads to high effectiveness but also showcases remarkable robustness, supported by both simulation and experimental results.

Driving an asynchronous motor powered by PV‐MPPT using equivalent RST controller of fractional order PI and IP, based on generalized predictive control

AbstractThe article introduces a new model of a Reference Signal Tracking (RST) controller for the fractional order quantities. The controller is applied to an indirect field‐oriented control (IFOC) system used for the speed control of an asynchronous motor powered by a photovoltaic (PV) generator with a maximum power point tracking (MPPT) algorithm. This model utilizes two fractional order controllers: the fractional order proportional‐integral (FOPI) regulator and the fractional‐order integral‐proportional (FOIP) regulator. These controllers are used with the generalized predictive control (GPC) technique. The first step in the approach is to derive the equivalent digital RST controller's model from the FOPI and FOIP controller's transfer functions. The GPC technique converts the continuous‐time FOPI (and FOIP) controller into a discrete‐time version. This conversion ensures a fast response and effective disturbance rejection. Simulation tests are conducted to analyze the rotor speed and stator current ripples to evaluate the performance of the proposed method. The results demonstrate the effectiveness of the introduced scheme in achieving improved control performance in terms of response speed and disturbance rejection. The article presents a modified RST controller model based on the fractional order approach applied to an IFOC system for motor speed control driven by a photovoltaic generator. Using FOPI, FOIP controllers, and GPC contributes to enhanced control performance, as evidenced by the simulation results.

Enhancing Microgrid Inverter-Integrated Charging Station Performance through Optimization of Fractional-Order PI Controller Using the One-to-One Sine Cosine Algorithm

This paper is dedicated to optimizing the functionality of Microgrid-Integrated Charging Stations (MICCS) through the implementation of a new control strategy, specifically the fractional-order proportional-integral (FPI) controller, aided by a hybrid optimization algorithm. The primary goal is to elevate the efficiency and stability of the MICCS-integrated inverter, ensuring its seamless integration into modern energy ecosystems. The MICCS system considered here comprises a PV array as the primary electrical power source, complemented by a proton exchange membrane fuel cell as a supporting power resource. Additionally, it includes a battery system and an electric vehicle charging station. The optimization model is formulated with the objective of minimizing the integral of square errors in both the DC-link voltage and grid current while also reducing total harmonic distortion. To enhance the precision of control parameter estimation, a hybrid of the one-to-one optimizer and sine cosine algorithm (HOOBSCA) is introduced. This hybrid approach improves the exploitation and exploration characteristics of individual algorithms. Different meta-heuristic algorithms are tested against HOOBSCA in different case studies to see how well it tunes FPI settings. Findings demonstrate that the suggested method improves the integrated inverters’ transient and steady-state performance, confirming its improved performance in generating high-quality solutions. The best fitness value achieved by the proposed optimizer was 3.9109, outperforming the other algorithms investigated in this paper. The HOOBSCA-based FPI successfully improved the response of the DC-link voltage, with a maximum overshooting not exceeding 8.5% compared to the other algorithms employed in this study.

Optimized fractional order PID controller with sensorless speed estimation for torque control in induction motor

With rising concern on environmental protection, the exploitation of EV has been widely focused. The IM is said to be the best in comparing varied electric motors for EV applications due to its lower price and robustness. In addition, sensor-less controlling schemes like DTC and FOC are found to be appropriate for crucial appliances owing to their energy savings, improved efficiency, and reliability. The “Optimized Fractional Order Proportional Integral Controller (FoPID)” with a sensor-less speed estimate mechanism is proposed in this work. Additionally, the parameters of FoPID are adjusted using a brand-new hybrid method called the Wolf based Elephant Herding method (W-EHA), which combines the ideas of Grey wolf optimization (GWO) model and Elephant herding optimization (EHO). The superiority of the recommended technique is finally shown in terms of controller performance and error. The RMSE obtained by the developed model at speed = 100 is 3.344, which is 53.89 %, 24.22 %, 1.09 %, and 38.96 % superior to existing approaches like P-controller, MFI-DA + FoPID, EHO-FoPID, and GWO-FoPID respectively.

Application of Fractional Order PI/PID Voltage Controllers for Three-Phase Voltage Source Inverter with Dynamic Load

Purpose: With the depletion of fossil fuels, the landscape of electrical energy generation has witnessed a transformative shift towards alternative sources such as fuel cells and photovoltaic (PV) systems that produce direct current (DC) electricity. In the realm of distributed power generation, three-phase voltage source inverters (VSIs) are extensively utilized for converting energy from DC sources to alternating current (AC) for the grid or loads. The pivotal objective of this study is to investigate and compare the performance of fractional-order Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) control structures against their integer-order counterparts in the voltage control loop of a VSI connected to a dynamic load system.
 Materials and Methods: The research employs frequency response analysis to design and implement both fractional-order PI/PID and integer-order PI/PID control structures for the voltage control loop. The simulation of the controlled system is conducted using MATLAB/Simulink, considering two distinct test scenarios – unstable and stable dynamic load conditions. The primary focus is on analyzing the inverter output voltage in the d-q axis under these scenarios.
 Findings: The analysis of the simulation results reveals noteworthy distinctions between the fractional-order and integer-order PI/PID controllers in the context of controlling the inverter system with dynamic loads. These findings shed light on the advantages of employing fractional order controllers, particularly in dynamic load scenarios, showcasing superior performance in comparison to their integer-order counterparts.
 Implications to Theory, Practice and Policy: The study's outcomes hold significant implications for the theory and practice of voltage control in distributed power generation systems. The superiority of fractional-order PI controllers underscores their potential for enhancing power quality, especially in systems with unstable and time-varying dynamic loads. These insights can inform the development of more effective control strategies for voltage source inverters, influencing both theoretical frameworks and practical applications. Policymakers may consider these findings when formulating regulations and incentives to promote the adoption of advanced control strategies in the evolving landscape of electrical energy generation.