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Scientific Reports volume 15, Article number: 32455 (2025) Cite this article
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This paper introduces a novel fault-clearing strategy for large-scale hybrid photovoltaic/wind/battery power systems (HPVWBPS). A modified fault-clearing strategy (MFCS) is developed using the Manta ray foraging optimization (MRFO) algorithm and a fuzzy logic controller (FLC). The FLC enhances decision-making in fault-clearing, while MRFO determines the optimal FLC gains for photovoltaic (PV) and wind turbine (WT)-based power plants, ensuring maximum power point tracking (MPPT). Additionally, MRFO optimizes power dispatch during faults by considering solar and wind resource availability, battery energy levels, and load demand. By mimicking the foraging behavior of manta rays, the algorithm efficiently balances power generation and consumption, minimizing fault impact. The proposed strategy is evaluated through extensive simulations on a large-scale HPVWBPS using MATLAB/SIMULINK 2022(b). The proposed method enhances system stability and fault recovery by determining optimal controller gains using the MRFO algorithm. A detailed comparison of key performance metrics, rise time (RT), settling time (ST), maximum overshoot (MOST), and optimal gains was conducted for both voltage and current regulators under four configurations: PI-based GWO, PI-based MRFO, FLC-based GWO, and FLC-based MRFO. This assessment isolates the effects of both the controller type and the optimization algorithm. The results show that MRFO consistently outperforms GWO in both PI and FLC frameworks. MRFO provides faster convergence, reduced overshoot, and shorter settling times. For the current regulator, the MRFO-FLC combination achieves an ST of 1.0020 ms, compared to 1.0033 ms for the PI-GWO controller, marking a 1.3% improvement. The RT is reduced from 3.2755 μs to 2.1885 μs, a 33.2% decrease. MOST is also lowered from 143.22% to 140.12%, a 2.17% reduction. These improvements enhance the regulator’s dynamic performance and reduce component stress. The voltage regulator shows similar trends. The ST drops slightly from 1.0052 ms to 1.0051 ms. RT improves from 8.1978 μs to 8.1878 μs. MOST decreases from 86.79% to 86.57%. Though the changes are smaller, they remain consistent across all metrics. FLC-based controllers outperform PI-based controllers in terms of dynamic response and stability. They better handle system nonlinearities and delays, making them more suitable for hybrid renewable energy systems. Among all configurations tested, the FLC-MRFO setup delivers the best overall performance. Its superior adaptability, reduced overshoot, and faster response validate its effectiveness for robust and efficient power system control.
The motivation behind developing a modified fault-clearing strategy (MFCS) for large-scale hybrid PV/wind/battery power systems (HPVWBPS) based on Manta ray foraging optimization (MRFO) and fuzzy logic control (FLC) stems from the increasing integration of renewable energy sources and energy storage systems into power grids. While these systems offer numerous environmental and economic benefits, they also introduce uncertainties and challenges, particularly during fault conditions^1,2,3, such as uncertainties in renewable energy generation: Photovoltaic (PV) and wind power generation are inherently intermittent and affected by various uncertainties such as weather conditions, cloud cover, wind speed, and direction. These uncertainties can lead to fluctuations in power output, making fault clearing and system stability more challenging^4,5. Energy Storage Systems (ESS) play a vital role in integrating renewable energy sources into power grids, but they also come with several uncertainties. One key uncertainty is the state of charge (SoC), which refers to the energy available in the storage system at any given moment. Accurate real-time estimation of SoC can be challenging due to factors like environmental conditions and battery degradation. Inaccurate SoC estimation can lead to inefficient charging or discharging, potentially shortening the system’s lifespan. Another significant uncertainty involves energy degradation and aging. ESS, especially batteries, degrade over time, losing capacity and efficiency. This degradation depends on factors like temperature, depth of discharge, and usage patterns, making it hard to predict how long the system will function optimally. Uncertainty in degradation rates complicates long-term planning and maintenance schedules, affecting the system’s reliability. The unpredictable nature of both energy demand and renewable energy supply adds another layer of uncertainty. Renewable energy sources, such as solar and wind, fluctuate due to weather conditions and time of day, while energy demand can vary unpredictably. These fluctuations make it difficult to optimize the charging and discharging cycles of ESS, which need to respond dynamically to these changes.
Additionally, the lifespan and performance of ESS are inherently uncertain. Various factors, such as usage patterns, operating temperatures, and charging cycles, affect how long an energy storage system can last and how efficiently it operates. Predicting when a system will need to be replaced or repaired is difficult, which complicates cost estimates and operational planning. Market and policy uncertainties also play a significant role. Regulations, incentives, and market dynamics can change over time, impacting the financial viability of ESS projects. For instance, future policy shifts regarding energy tariffs or subsidies may alter the economic landscape, making it difficult to forecast long-term returns on investment in energy storage systems. Another area of uncertainty is the efficiency of charging and discharging. The efficiency of energy storage depends on factors like the type of storage technology, temperature, and usage cycles. Variability in these conditions leads to uncertainty in how much energy can be stored and how efficiently it can be used, affecting the overall performance of the system. Technological advancements also contribute to uncertainty. The pace of innovation in energy storage technologies, such as developing new battery chemistries, is unpredictable. A technological breakthrough could make existing systems obsolete or offer more efficient solutions, creating uncertainty for investors and planners in choosing the right technology for long-term use. Cost uncertainties further complicate decision-making. The capital costs, operational expenses, and maintenance costs of ESS can fluctuate due to market forces, changes in raw material prices, and technological advancements. Uncertainty in these costs makes it difficult to accurately project the return on investment and the financial feasibility of energy storage projects. The environmental and temperature sensitivity of ESSs also introduces uncertainty. ESSs, particularly batteries, are sensitive to temperature changes, and extreme temperatures can negatively impact performance and lifespan. Uncertainty in future climate conditions and local weather patterns makes it difficult to predict how an ESS will perform over time, especially in outdoor settings. Lastly, the increasing digitization of energy systems introduces cybersecurity and data integrity risks. Energy storage systems rely on sophisticated control systems vulnerable to cyberattacks or data corruption. Uncertainty regarding the security of these systems can pose risks to their reliable and safe operation^6,7.
These interactions introduce additional uncertainties, including variations in power demand, system configuration, and network topology, which can affect fault-clearing strategies and system stability^8,9,10.
Addressing these challenges is essential to ensure large-scale hybrid power systems’ reliable and stable operation¹¹. Therefore, the development of an advanced fault-clearing strategy that considers uncertainties becomes crucial. The proposed approach combines the MRFO algorithm and FLC to optimize power dispatch and decision-making during fault conditions. The MRFO algorithm’s ability to adaptively explore and exploit the solution space, considering uncertain renewable energy generation and storage availability, assists in efficient power dispatch optimization. With its linguistic rule-based decision-making and adaptability to uncertainties, the FLC enhances the control actions during fault conditions¹².
By considering uncertainties explicitly in the fault-clearing strategy, the proposed approach aims to improve the resilience and reliability of large-scale HPVWBPS^13,14. This research contributes to developing intelligent and adaptive strategies to effectively handle uncertainties, ensuring optimal fault management and system stability in renewable energy integration. The hybrid renewable energy system (HRES) comprises multiple components: PV panels, wind turbines (WTs), batteries, inverters, and loads. FLC receives inputs from sensors that measure the power output of the PV and wind sources, the state of charge of the battery, and the power consumption of the loads. The controller uses these inputs to generate control signals that adjust the power flow between the components of the system^15,16.
The uncertainties associated with the PV and wind power sources can significantly impact the performance of the hybrid power system. For example, the changes in weather conditions can cause fluctuations in the power output of the sources, which can result in instability and inefficiency in the system^17,18,19. The FLC-based control system is designed to mitigate these uncertainties and ensure the reliability and stability of the system. In addition, this work focuses on using the MRFO to enhance the performance of the FLC in the presence of uncertainties associated with the PV and wind power sources. In the context of the HRES, the MRFO algorithm is used to optimize the parameters of the FLC controller, such as the membership functions of the input and output variables. The objective is to improve the control system’s performance by reducing the impact of uncertainties associated with the PV and wind power sources. The MRFO algorithm is used to explore the solution space and find the optimal values of the parameters that maximize the control system’s performance.
In this study, the performance of two control strategies is compared to verify the effectiveness of the suggested controller. The first strategy employs a proportional-integral (PI) controller optimized using the grey wolf optimizer (GWO), a powerful optimization algorithm inspired by the social hunting behavior of grey wolves. Introduced by Mirjalili et al. in 2014, GWO simulates grey wolves’ leadership hierarchy and hunting tactics, leveraging their social dynamics to explore the solution space effectively and converge on optimal solutions²⁰. The algorithm comprises three main steps: exploration, exploitation, and encircling prey, which allow it to balance global search capabilities with local refinement efficiently. The second strategy utilizes FLC optimized with the MRFO algorithm. MRFO, inspired by the foraging behavior of manta rays, offers a unique approach to optimization by simulating their natural foraging patterns to explore and exploit the solution space. By integrating the MRFO with FLC, the proposed controller aims to improve decision-making processes and enhance system responsiveness to dynamic changes in operating conditions. By comparing the two approaches, GWO-optimized PI controller and MRFO-optimized FLC, the study aims to assess the efficacy of the FLC in managing uncertainties and improving system stability, particularly in the context of HRESs. This comparison seeks to highlight the advantages of MRFO in optimizing control actions, thereby enhancing the balance of power generation, storage, and load demand more effectively than the traditional PI controller optimized by GWO. This evaluation provides insights into the strengths and weaknesses of each approach, informing the selection of optimal control strategies for renewable energy applications.
HRES combining PV, wind, and battery storage technologies offers significant potential for enhancing energy reliability and sustainability. However, their integration into the grid introduces challenges related to fault management. Efficient fault-clearing strategies are crucial to maintaining system stability and protecting equipment²¹. Lu et al. used an electrical time series graph and a convolutional neural network (CNN) to develop a defect diagnosis approach for PV arrays. This approach leverages the pattern recognition capabilities of CNNs to identify and diagnose faults in PV arrays accurately. The method demonstrates improved diagnostic accuracy and reliability, significantly enhancing the maintenance and operational efficiency of PV systems. Simulation results highlight the effectiveness of the proposed method in promptly detecting and diagnosing faults, thereby reducing downtime and optimizing energy conversion management²². Through optimization of the kernel extreme learning machine (KELM) algorithm, Chen et al. perform a modified technique that improves the diagnostic speed and accuracy, making it very useful for real-time fault identification in PV arrays. The approach leverages the current–voltage (I-V) characteristics to precisely identify various types of faults, significantly improving the reliability and efficiency of PV system operations. The results demonstrate the method’s robustness and potential for practical application in enhancing the maintenance and performance of PV systems²³. Harrou et al. created an unsupervised monitoring method that uses a one-class support vector machine (OCSVM) to find anomalies in PV systems. This method effectively identifies deviations from normal operating conditions without requiring labeled fault data. The approach enhances the reliability of PV systems by providing early detection of anomalies, which allows for timely maintenance and reduces system downtime. The results indicate that the OCSVM-based method is robust and efficient in identifying various anomalies, thereby improving the overall performance and dependability of PV system monitoring²⁴. Dhouib et al. carried out a fault-based study on a small hybrid PV/wind farm system connected to the grid. The study focused on identifying and characterizing various faults within the hybrid system (HS) to enhance its reliability and efficiency. The analysis utilized advanced simulation tools to assess the system’s fault response and the impact on overall performance. Results demonstrated that understanding fault behaviors in such HSs is crucial for improving fault management strategies and ensuring stable and efficient grid integration. The findings provide valuable insights for optimizing HRESs and enhancing their fault resilience²⁵.
Jimenez-Aparicio et al. conducted a study that assessed the effectiveness of the protection scheme in accurately detecting and isolating faults in distribution networks influenced by the intermittent nature of solar PV. The machine-learning algorithm was integrated with traveling-wave principles to enhance fault detection precision and response times. Results showed that the proposed protection scheme significantly improved fault management in distribution systems, ensuring excellent stability and reliability despite the variable penetration of solar PV. The findings highlight the potential of combining advanced machine-learning techniques with traditional protection methods to optimize the performance of modern power distribution networks²⁶. Jeong, Lee, and Kim conducted a study on developing various scenarios to evaluate the performance and feasibility of integrating renewable energy sources in green buildings. The study utilized simulation tools to analyze energy efficiency, cost-effectiveness, and environmental impact under different configurations. The results demonstrated that a well-designed renewable energy supply system could significantly reduce energy consumption and greenhouse gas emissions in green buildings. The findings provide valuable insights for optimizing renewable energy integration, contributing to developing sustainable and energy-efficient building designs²⁷. Chen and Wang conducted a study aimed at enhancing the efficiency and sustainability of green buildings by integrating renewable energy sources, such as solar and hydrogen energy, into a hybrid power system. Optimization involved assessing various design parameters to balance energy efficiency, cost-effectiveness, and environmental impact. Results indicated that the optimized hybrid power system significantly improved the building’s energy performance and reduced its carbon footprint. The study provides valuable insights for developing advanced hybrid energy solutions for green buildings, promoting sustainable urban development²⁸.
The available literature has shown that these studies collectively highlight the advancements and ongoing research efforts in developing effective fault-clearing strategies for large-scale hybrid PV/wind/battery power systems. Each approach offers unique benefits and addresses specific challenges associated with integrating renewable energy sources into the grid. As illustrated in Fig. 1, the primary objectives of this paper are given as follows:
The paper addresses the challenges posed by the intermittent nature of HPVWBPS in maintaining system stability, especially during fault conditions in large-scale HSs.
It introduces a novel fault-clearing strategy designed for large-scale HPVWBPS to ensure the system’s stability during faults.
The paper aims to optimize the fault-clearing process by using MRFO to determine the optimal gains of the FLC and enhance decision-making in MPPT for the power system.
It seeks to optimize the power dispatch of the HS during fault conditions, considering solar and wind resource availability, battery energy levels, and load demand.
Through simulations, the paper evaluates the proposed strategy’s effectiveness in improving fault management and overall system stability, intending to reduce overshooting and settling time compared to conventional methods.
Summary of the proposed strategy.
To highlight the quality of this study, a detailed comparison of its merits and results with those of previous publications was conducted. A comparative analysis of this work and prior research is presented in Table 1.
The following is a summary of the article’s main contributions:
The paper introduces a novel hybrid fault-clearing strategy combining MRFO and FLC techniques. This combination leverages the optimization capabilities of MRFO and the adaptability of FLC to enhance fault-clearing performance in hybrid power systems. The use of MRFO optimizes the parameters of the FLC to ensure the MPPT of the HPVWBPS and to ensure optimal fault detection and clearing actions. This optimization enhances the efficiency and effectiveness of the fault-clearing process, reducing fault response times and minimizing potential damage to system components.
The proposed strategy explicitly considers uncertainties inherent in large-scale HPVWBPS. These include variations in renewable energy generation and unforeseen system disturbances. By addressing these complexities, the plan aims to improve system reliability and robustness.
Simulations are conducted on a large-scale HPVWBPS using MATLAB/SIMULINK 2022(b). The proposed strategy’s performance is compared to a conventional controller.
In this study, the performance of the PI controller based on the GWO and the FLC based on the MRFO algorithm is compared to verify the efficacy of the suggested controller.
The proposed procedure improves the overall stability and reliability of large-scale HPVWBPS by integrating MRFO and FLC. The proposed strategy ensures quick and accurate fault detection and isolation, maintaining the power system’s continuous and stable operation. The FLC component of the strategy allows for adaptive fault management. This adaptability ensures that the system can respond dynamically to changing conditions and fault characteristics, providing a more flexible and resilient fault-clearing mechanism. The work adds to the existing body of knowledge by presenting a fault-clearing strategy that addresses specific challenges associated with large-scale HRES. It provides a detailed methodology for integrating MRFO and FLC and simulation results that validate the approach. The proposed strategy shows potential for real-world application in large-scale hybrid renewable energy installations. By demonstrating its effectiveness through simulations, the paper lays the groundwork for future experimental validation and possible implementation in actual power systems. The MRFO-FLC-based strategy enhances the hybrid power system’s fault tolerance. It ensures that the system can continue to operate effectively even in the presence of faults, thereby increasing the power supply’s overall resilience and reliability.
The manuscript has been segmented into the subsequent chapters: Section “Introduction” provides an overview and a literature review. Furthermore, the system configuration and modeling are shown in Sect. “PV/wind/battery hybrid power system configuration (HPVWBPS)“. Sect. “Control strategy management for the HS” goes on to detail the control plan. Furthermore, Sect. “Control strategy management for the HS” presents the MRFO. Furthermore, Sect. “Manta ray foraging optimization (MRFO)” presents the FLC optimized by MRFO (FLC-MRFO). Furthermore, the comparative statistical analysis, simulation findings, and discussion are presented in Sect. “Fuzzy logic controller (FLC) optimized by MRFO (FLC-MRFO)“. Sect. “Simulation results and discussion” finally determines the conclusions.
An HPVWBPS configuration is a type of HRES that combines PV and wind energy sources with a battery storage system. This configuration is becoming increasingly popular due to its ability to generate more consistent power output throughout the day and year compared to a single renewable energy source system. The configuration typically includes PV panels, WTs, and a battery storage system. The significant elements of PVWBHS are depicted in Fig. 2^29,30.
HPVWBPS components.
The PV panels and WT are connected to a common DC bus through a charge controller and a DC-DC converter. The DC bus is then connected to an inverter that converts the DC power to AC power for consumption by the loads. The battery storage system is connected to the same DC bus through a battery charger and a DC-DC converter, and it is used to store excess energy generated by the PV panels and WT’s for later use³¹. The battery storage system serves several functions in the HPVWBPS configuration. First, it stores excess energy generated by the PV panels and WTs when the energy demand is lower than the energy generation. Second, it supplies energy to the loads when the energy demand exceeds the energy generation. Third, it helps to smooth out the power output of the PV and wind sources, reducing the need for backup power generation or grid connection. Fourth, it provides backup power in case of power outages or emergencies³². The PV panels and WT have complementary characteristics. The battery storage system also helps to maintain the balance between the energy generated by the sources and the energy consumed by the loads³³. This means that the HPVWBPS configuration is an effective way to enable the more consistent and reliable use of renewable energy while maintaining energy storage capabilities. It is a viable option for remote areas or off-grid applications where the grid connection is not available, and it can be used as a backup power source for grid-connected applications. It has many applications, including residential, commercial, and industrial sectors³⁴.
Mathematical models are used to simulate and optimize the performance of HSs under different environmental and operational conditions. These models involve equations describing the energy generation, storage, and consumption processes and the interaction between different components. Let’s explore some key aspects of mathematical modeling for each component:
The power output of a solar PV panel is a function of solar irradiance, panel temperature, and the characteristics of the PV module. The power output ({P}_{PV})​ is given by:
where:
({A}_{PV} 🙂 surface area of the PV panel, ({eta }_{PV} 🙂 efficiency of the PV panel, and (Ileft(tright) 🙂 solar irradiance at time (left(text{t}right)).
The temperature of the PV panel also affects efficiency, which is incorporated into the model using temperature coefficients.
The wind speed and turbine characteristics determine wind power. The power generated by a wind turbine, ({P}_{wt}left(tright))​, is a function of the wind speed (nu left(tright)), the air density (rho), and the rotor swept area ({A}_{rotor}).
where:
(rho) is the air density,
({A}_{rotor})​ is the rotor swept area,
(nu left(tright)) is the wind speed at time (left(tright)),
({eta }_{wt})​ is the wind turbine efficiency.
The power output is also limited by the turbine’s cut-in and cut-out speeds.
The battery stores excess energy when production exceeds demand and discharges when energy is needed. The energy stored in the battery at any time, ({E}_{bat}left(tright)), can be expressed as:
where:
({E}_{bat}left(tright)) is the stored energy at (t)
({eta }_{ch} &)​({eta }_{dis}) are the charging and discharging efficiencies of the battery
({P}_{excess}left(tright)) is the excess power available at t
({P}_{demand}left(tright)) is the power demand at (t)
The battery also has operational constraints such as maximum storage capacity and minimum/maximum state of charge.
The fundamental equation governing the operation of HPVWBPS is the power balance:
This equation ensures that the total power generated by the PV panels, wind turbines, and discharging batteries at any time equals the total load demand plus the power being stored in the battery.
HPVWBPS control strategy controls the power flow between a PV array, a wind turbine, a battery bank, and a load in a hybrid power system that uses renewable energy sources^35,36,37. The strategy aims to optimize the power flow between these components to minimize power losses and ensure a stable energy supply while also considering uncertainties and variability associated with renewable energy sources³⁸. One of the critical challenges in controlling an HPVWBPS is the variability and uncertainty of renewable energy sources, which can lead to fluctuations in the power output. To address this challenge, the control strategy typically employs a combination of techniques, such as FLC, proportional-integral (PI) control, and artificial intelligence (AI) algorithms like neural networks or evolutionary algorithms^39,40,41,42. The control strategy monitors the power output of the PV array and the WT, as well as the SOC of the battery bank. It uses this information to decide how to allocate the power among these components to meet the load demand. The strategy may also take into account other factors such as weather conditions, time of day, and the cost of electricity⁴³. One of the advantages of an HPVWBPS control strategy is its ability to improve the power system’s stability and efficiency while reducing reliance on fossil fuels and minimizing greenhouse gas emissions⁴⁴. Additionally, the strategy can help increase the battery bank’s lifespan by optimizing its charge and discharge cycles. Hence, the HPVWBPS manages the power flow in the HRES that uses renewable energy sources. By optimizing the power flow, the strategy can help to ensure a stable and reliable energy supply while also contributing to a sustainable and cleaner energy future⁴⁵. To manage the power supplied by the HRES to meet the load and charge the lead acid battery during surplus energy, the HPVWBPS controller strives to guarantee that the power delivered by the HS is managed⁴⁶. Figure 3 uses the power management approach flowchart. If more energy is needed, it will be used to charge the battery. To provide the load with the necessary power, WTs and PV arrays are used. On the other hand, the battery will provide the load if renewable energy sources are inadequate to match the demand. Maintaining SoC_min at 30% will be the control variable utilized in the system design^47,48.
Power management plan of HPVWBPS.
To ensure that the proposed control and fault-clearing strategies are suitable for real-world applications, the system has been evaluated against key national and international grid codes governing distributed and hybrid renewable energy systems. This evaluation provides a benchmark for technical compliance and operational reliability. The selected standards include IEEE 1547–2018, IEC 61727, ENTSO-E grid requirements, and FERC Order 842^49,50. The IEEE 1547–2018 standard governs the interconnection and interoperability of distributed energy resources (DER) within U.S. electric power systems. It outlines performance requirements related to voltage and frequency regulation, ride-through behavior, and communication protocols. IEC 61727 defines the essential interface requirements for photovoltaic systems connected to utility grids, addressing power quality, protection, and system behavior under abnormal conditions. ENTSO-E grid code requirements focus on the European transmission system and specify critical performance metrics for fault ride-through, frequency response, and post-fault recovery. FERC Order 842 mandates primary frequency response for grid-connected resources in the U.S. bulk power system, emphasizing rapid and autonomous control actions during frequency deviations^51,52. Key controller functions were benchmarked against these grid codes to confirm the system’s compliance. First, the fault ride-through (FRT) performance of the proposed system exceeds the minimum duration thresholds (150–250 ms) prescribed by IEEE 1547 and ENTSO-E. The system successfully maintains connectivity during both symmetrical and asymmetrical voltage sags, preserving power delivery and avoiding unnecessary disconnections^53,54. Second, voltage recovery behavior was tested following fault clearance. The system’s post-fault voltage restoration aligns with the envelope curves defined in the referenced standards, confirming its ability to recover voltage levels within acceptable time frames and maintain grid stability. Third, the system supports frequency response within 500 ms of a frequency deviation. This rapid adjustment is achieved through the integration of the battery energy storage system and fast-acting control algorithms. The response time meets the expectations outlined in IEEE 1547 and FERC Order 842, ensuring active support for frequency stabilization during disturbances. Finally, while synthetic inertia was not explicitly modeled, the combined action of the FLC controller and the battery system introduces sufficient damping to mitigate frequency variations. This functional behavior provides inertia-like support, which enhances system resilience during grid events and aligns with emerging expectations for inertia emulation in renewable systems^53,54. These validations confirm that the proposed control system not only manages hybrid energy flow efficiently under steady-state conditions but also fulfills essential grid-support roles during dynamic and fault scenarios. The controller’s design and response characteristics are consistent with the performance standards required for integration into modern grid-connected renewable energy infrastructures.
In optimization algorithms, researchers strive to develop efficient methods that mimic the behavior of organisms in the natural world. These algorithms are inspired by various species’ adaptation and survival strategies. One such algorithm is the MRFO, which emulates the foraging patterns of manta rays. Researchers have identified a unique approach for optimizing complex problems by observing these majestic creatures. This essay will delve into the principles and applications of MRFO, shedding light on its potential as a powerful tool for various domains^12,55. Manta rays are known for their impressive foraging capabilities, enabling them to find and consume large quantities of plankton efficiently. Several researchers have studied their behavior extensively and identified fundamental principles that make MRFO an effective optimization algorithm. Manta rays exhibit a zigzag swimming pattern while foraging, which maximizes their chances of encountering prey. Similarly, MRFO employs a search mechanism that explores different regions of the solution space, increasing the likelihood of finding optimal solutions. The chain Foraging mathematical model is represented by the following equation, where the agent ({Z}_{i}) can be updated at iteration (i)^12,55.
where the current and maximum iterations are denoted by the letters t, respectively and i. r represents a random vector within the range of [0, 1]. (alpha) represents a weight coefficient, and N indicates the total number of agents. The MRFO algorithm comprises several stages that simulate the foraging behavior of manta rays. Initially, the algorithm initializes a population of potential solutions known as “rays.” It then evaluates the fitness of each ray based on the problem-specific objective function. This evaluation is akin to the manta rays assessing the abundance of plankton in a particular region^12,55. After evaluating the rays, the algorithm divides them into distinct groups, analogous to how real manta rays form schools. Each group corresponds to a promising solution, and their movement patterns simulate the swimming behavior of manta rays. The algorithm then carries out an iterative process known as “foraging.” During foraging, the rays within each group explore the solution space by adjusting their positions using predefined movement equations. This movement is influenced by the best solutions found in previous iterations, encouraging convergence towards the optimal solution^12,55. The agent’s position is updated depending on where the best agent and its front agent are located. The procedure for updating ({Z}_{i}).is shown in the following equation^12,55.
The following equation is used to update the weighting factor, where it is denoted by (beta).
where ({r}_{1}) is a uniform random number in [0, 1]. Additionally, agents in the stage of cyclone foraging can alter their positions in accordance with the randomly generated location in the search space, which enhances MRFO detection. The following equation is used to update the location of the current agent^12,55.
where (Lb) and (Ub) are the search space bounds.
Somersault foraging is the third and final stage in the MRFO. The agents swim both towards and away from the food during this stage, and the formula below is used to update the agents’ locations^12,55.
S stands for the somersault factor, which is used to calculate the manta rays’ somersault range. Also, ({r}_{2}) and ({r}_{3}) refers to random numbers. Figure 4 depicts the MRFO flowchart.
Flowchart of the MRFO.
FLC is a type of control system that uses fuzzy logic instead of traditional binary logic (true/false) to handle imprecise, uncertain, or ambiguous information. FLCs are particularly effective in systems where the relationships between variables are complex or not well-defined. FLCs are widely used in various applications, including control systems for renewable energy sources, due to their ability to handle nonlinearities and uncertainties effectively. The membership functions of the input and output variables are represented as fuzzy sets, which allow for handling uncertainties more robustly and flexibly^56,57,58,59. Combining an FLC with MRFO involves using the MRFO algorithm to optimize the parameters of the FLC. This hybrid approach leverages the strengths of both techniques to achieve better control performance in complex systems like large-scale HPVWBPS. This work uses FLC-MRFO to assure MPPT of the HPVWBPS in PV and WT-based power plants. Additionally, the FLC-MRFO is implemented to enhance the decision-making process of the fault-clearing strategy. The FLC utilizes expert knowledge and linguistic rules to determine the appropriate control actions in response to different fault scenarios. The strategy exhibits robustness and adaptability to varying system conditions by incorporating fuzzy logic into the control scheme.
When the point where operation begins is far from the maximum power point (MPP), FLC-MRFO can use an extended step length; when the technique approaches MPP, it can use a reduced step length. It should be noted that FLC can change its step based on the conditions surrounding the energy input. The maximum power transmission requirements of the circuit dictate the MPPT for the solar subsystem of a PV farm; the goal is to ascertain the point at which the PV cell’s output resistance equals the load resistance. In this work, the authors used the Tsukamoto fuzzy logic system (TFLS), where TFLS uses the weighted average to calculate the crisp output. The pulse width modulation (PWM) block’s MPPT controller manages the duty cycle. This regulates the DC-DC power converter to supply the DC load bus with the maximum possible power. The FLC structure is employed in the solar subsystem; Fig. 5 illustrates it. Users can manage this structure and generate fuzzy rules using the FLC toolbox in the MATLAB/SIMULINK 2022b environment.
Simulink model of the FLC-MRFO of the solar subsystem.
Fuzzification, rule base, and defuzzification are the three steps that make up a controller based on an FLC-MRFO. During fuzzification, the power and voltage of PV that indicate the input variables are transformed into linguistic variables using a membership function (MF). A block for computing the error (E) and the change of the error (dE), which are described, respectively, in (12) and (13), is present at sampling moment k^53,54.
where (Pleft(kright)) and (Vleft(kright)) represent the power and terminal voltage that a PV module delivers, respectively.
The same block error inputs are used to operate the MPPT in the second wind subsystem example, where P(k) is the wind output power and k denotes the wind speed. The MPPT controller may choose the required wind speed variation (ref) based on the sign of E(k). Figure 6 depicts the physical layout of the MPPT of the FLC MRFO that will regulate the wind subsystem.
Simulink model of the FLC-MRFO of the wind subsystem.
Also, the member function of the FLC-MRFO for the solar and wind subsystem is represented in Fig. 7, where Fig. 7a depicts the MF of the error signal, and Fig. 7b depicts the MF of the change of input signals. The membership functions used in this research work are triangular, as depicted in Fig. 7, for mathematical simplicity.
Membership functions for FLC-MRFO: (a) Membership function of the error signal (E); and (b) Membership function of the change of input signals (dE).
Triangular membership functions are widely used in FLC due to several distinct advantages. One of the primary benefits is their simplicity and ease of implementation. Since these functions are defined by straight lines, they require less computational effort compared to more complex shapes like Gaussian or trapezoidal functions. This linearity ensures faster processing, making triangular membership functions ideal for real-time systems or embedded applications where processing speed is crucial. Another key advantage is their efficient computational performance. Because they are composed of linear segments, triangular membership functions are computationally lightweight, reducing the burden on system resources. This makes them particularly useful in applications where quick decision-making is required, such as dynamic control systems in renewable energy or industrial automation. Triangular membership functions also offer a good degree of flexibility in design. Despite their simplicity, they can be easily adjusted by modifying their base width and peak positions, allowing for effective modeling of various system behaviors. This flexibility enables designers to represent different levels of uncertainty without the need for more complex membership functions, which may be overkill for certain applications. The clear and precise representation provided by triangular membership functions is another advantage. The peak of the triangle signifies the core or most accurate value of the fuzzy set, while the sloping sides indicate the degree of membership to the set. This makes them effective for modeling gradual transitions between fuzzy states, ensuring that changes in the input are reflected smoothly in the system’s output. Furthermore, triangular membership functions facilitate smooth transitions between adjacent fuzzy sets, which is important in control systems that require a proportional response to gradual changes in input. The sharpness of the triangular shape prevents abrupt jumps in the output, contributing to system stability. Additionally, because triangular membership functions are widely used across various applications, there is ample design knowledge and examples available. This makes it easier to implement and tune FLC systems, especially in domains such as power systems, robotics, and automated control, where simplicity and computational efficiency are often prioritized. Finally, the simplicity of triangular membership functions also simplifies the construction of the rule base in FLC systems. With fewer parameters to tune compared to more complex membership functions, the design and maintenance of the control rules are more straightforward, making these functions particularly practical for engineers and developers. To conclude, triangular memberships offer a balance of simplicity, flexibility, and computational efficiency, making them a popular choice in many fuzzy logic-based control systems. The membership degree is always between 0 and 1, where 0 means it is not a member of the fuzzy set, and 1 means it is a member of the fuzzy set.
The total of the factors that propel schedule optimization is known as the cost function. The optimizer optimizes the schedule by minimizing the value of the cost function for each action in the schedule. The cost function computes the cost of doing the tasks in a timetable indirectly.
The Membership function values are allocated to the linguistic variables using seven fuzzy subsets: NS (Negative Small), PM (Positive Medium), NL (Negative Large), PL (Positive Large), PS (Positive Small), NM (Negative Medium), and ZE (zero). The input error (E) and change of error (CE) values were standardized using the input scaling factor. The triangular shape of the membership function of this arrangement assumes that there is only one dominant fuzzy subset for any input. The process used to generate the regulated output is called the composition operation. The Max–Min technique is applied. Each rule for the output membership function is given by the Minimum. The FLC’s rule base is displayed in Table 2.
Figure 8 represents the Simulink block diagram used to operate the PVWBHS system. The error signal, which serves as the input to the FLC-MRFO, is generated by comparing the reference load with the produced power. By applying the rules on the HPVWBPS, the FLC-MRFO generates the resulting output for each pair (E, dE), as depicted in Fig. 9.
Simulink block diagram of FLC-MRFO for HPVWBPS.
3D surface of HPVWBPS system output created by FLC-MRFO.
In this study, HPVWBPS, with a capacity of 38 MW, has been implemented in MATLAB/SIMULINK 2022(b). The system has three main components: a 20 MW solar farm, an 18 MW wind farm, and a battery storage system connected to a reversible chopper. The battery system is crucial in powering the station’s monitoring and control systems when solar and wind resources are unavailable. Additionally, it enhances both the dynamic and steady-state behavior of the overall system. All three components are interconnected through an AC converter, which converts DC to AC before integrating with the electrical network. The HPVWBPS has been tested under two case studies. The first case study (Case#1) evaluates the system under standard test conditions (STC), as illustrated in Fig. 10. The second case study (Case#2) assesses the system based on solar radiation and temperature data specific to Ras Ghareb–Red Sea, Egypt, as shown in Fig. 11. The weather data for this location were obtained from NASA⁶⁰ and the New and Renewable Energy Authority (NREA)⁶¹. To evaluate the effectiveness of the FLC optimized by the MRFO algorithm in the HPVWBPS, the system is tested under two distinct scenarios: one operating without failure and the other under fault conditions.
Testing conditions of Case #1: (a) solar radiation, (b) temperature, at STC 1000 W/m² and 25 °C and (c) wind speed = 15 m/s.
Realistic waveforms on a winter day showcasing: (a) solar radiation, (b) temperature, and (c) wind speed at Ras Ghareb-Red Sea, Egypt.
To validate the effectiveness of the proposed controller, we conducted a comprehensive performance comparison involving four configurations: PI-based GWO, PI-based MRFO, FLC-based GWO, and FLC-based MRFO. Figure 12 presents the system’s output power during a disturbance scenario, confirming its ability to maintain a stable 38 MW power output. The results show that the MRFO-optimized FLC controllers reach the maximum power point (MPP) more rapidly, with shorter settling times, lower overshoot, and improved tracking precision compared to the other configurations. In particular, the FLC-MRFO setup demonstrates superior dynamic response, reduced settling time by approximately 1.4%, and power harvesting efficiency exceeding 98%. It also effectively suppresses the effects of partial shading and voltage fluctuations in the power-voltage (P–V) curve, confirming its robustness and enhanced control capability under varying operating conditions. Table 3 provides a detailed comparison of key performance metrics, rise time (RT), settling time (ST), maximum overshoot (MOST), and optimal gains for both the voltage and current regulators under four configurations: PI-based GWO, PI-based MRFO, FLC-based GWO, and FLC-based MRFO. This comprehensive assessment isolates the effects of both the controller type and the optimization algorithm. The results indicate that MRFO consistently outperforms GWO in both PI and FLC frameworks, demonstrating faster convergence, reduced overshoot, and shorter settling times. Additionally, FLC-based controllers show improved dynamic response and stability compared to PI controllers, confirming their superior handling of system nonlinearity and delays. Among all tested configurations, the FLC-MRFO combination delivers the best overall performance, validating its suitability for robust and efficient control in hybrid renewable energy systems.
Total power of PVWBHS in Case#1.
Figure 13 presents the convergence curves generated by the GWO and the MRFO algorithms. It indicates that the GWO algorithm gets stuck in local optima earlier than the MRFO algorithm. Additionally, the MRFO algorithm provides more accurate data than the GWO algorithm, with corresponding mean fitness values of 2.166 for GWO and 2.161 for MRFO.
Convergence curves provided by both GWO for the PI controller and MRFO for FLC tuning.
The output of the PV solar farm in Case #1 is shown in Fig. 14. The voltage generated by the PV solar cell array is applied to the boost converter, which increases the voltage from 0.74 pu (666 V) to 0.91 pu (825 V) at the inverter input, as shown in Fig. 14a. The current output from the PV solar cell arrays is 0.97 pu (924 A), as shown in Fig. 14b, and the output power is 1 pu (20 MW), as shown in Fig. 14c. The battery storage system does not operate at STC because, as illustrated in Fig. 15, the power generated by the PV array matches the load demand. At full power, a DC-DC boost converter increases the voltage from 0.74 pu (666 V) DC to 0.91 pu (825 V) DC, as shown in Fig. 16. The voltage source converter (VSC), a 3-level, three-phase converter operating at 1990 Hz, maintains a unity power factor while converting the 0.91 pu (825 V) DC voltage to 0.33 pu (300 V) AC^62,63. The inverter operates using PWM controlled by an FLC-MRFO-driven pulse generator. Figure 17 shows the voltage output of an inverter using PWM. PWM is a technique used to simulate an AC waveform by switching a DC voltage on and off rapidly. The waveform is characterized by square pulses with high-frequency switching. This modulation introduces high-frequency harmonics, which are undesirable in many applications as they can cause interference and inefficiency. The zoomed-in section highlights the square-modulated nature of the waveform, clearly showing the high-frequency switching components that give the waveform its stepped appearance. Figure 18 illustrates the inverter’s voltage output after passing through an LC (inductor-capacitor) filter. The LC filter smooths out the high-frequency harmonics from the PWM waveform, resulting in a more sinusoidal waveform, which is more suitable for typical AC applications. The filtered waveform retains the fundamental frequency but significantly reduces the high-frequency components⁶⁴, providing a cleaner, smoother output. The zoomed-in section in this figure shows a more regular sinusoidal pattern compared to the sharp transitions seen in the unfiltered PWM waveform. The LC filter’s role is crucial in converting the PWM-modulated waveform into a form that closely resembles a pure sine wave, improving the quality of the power supplied to the load. The output power of the WF in the HPVWBPS, demonstrated to be 18 MW, is depicted in Fig. 19a. The DC voltage is controlled at 0.95 pu (1145 V), and the reactive power is maintained at 0 MVAR, as shown in Figs. 19b and c, respectively. Additionally, the WT of the HPVWBPS operates at a speed of 1.2 pu, as shown in Fig. 19d. The WF, equipped with double-fed induction generators (DFIGs), initially generates 18 MW. The generator’s synchronous speed divided by the corresponding WT speed is 1.2 pu. Figure 20 shows a point-of-common-connection (PCC) bus with a peak voltage per line of 11 kV. The current at the PCC bus was injected three times, as depicted in Fig. 21. Interestingly, the HPVWBPS under Case#1 operates flawlessly, achieving exactly 38 MW of power. Furthermore, the results validate that the quality of the proposed HS in Case#1 remains unchanged when the WF is connected to the PV farm.
PV farm output in the HPVWBPS in Case#1: (a) voltage, (b) current, and (c) power.
Battery output in the HPVWBPS in Case #1: (a) voltage, (b) power, and (c) state of charge.
DC-link voltage in the HPVWBPS in Case #1.
The inverter generated voltage in Case #1.
The inverter generated voltage after filtering in HPVWBPS in Case #1.
Wind farm output in the HPVWBPS in Case #1: (a) the output active power; (b) DC voltage; (c) the output reactive power; and (d) the wind speed.
PCC bus voltage in the HPVWBPS in Case #1.
PCC bus current in the HPVWBPS in Case#1.
Figure 22 illustrates the output power of the HPVWBPS under a disturbance in Case#2, which was evaluated using realistic solar radiation, temperature, and wind speed data from Ras Ghareb-Red Sea, Egypt. In Case #2, the output power from the PV array is insufficient to meet the demand due to varying radiation and temperature levels. To maintain the system’s power balance, the battery storage system regulates the rate at which its power is discharged, as shown in Fig. 23. The PV solar farm’s output in HPVWBPS during Case# 2 is depicted in Fig. 24.
Total output power in the HPVWBPS in Case #2.
Battery output in the HPVWBPS in Case #2: (a) voltage, (b) power, and (c) state of charge.
PV farm output in the HPVWBPS in Case #2: (a) voltage, (b) current, and (c) power.
Figure 25 presents the results of the wind farm (WF) in the HPVWBPS Case# 2 through four-line graphs, each representing a different parameter. Figure 25a shows the active power of the WF, revealing fluctuations over 24 h, with a prominent peak around the 10th hour, indicating a period of high energy generation. Figure 25b depicts the wind speed at the WF, demonstrating a general decrease over the 24 h, with minor fluctuations, indicating a gradual decrease in wind intensity. Figure 25c illustrates the DC bus voltages of the WTs, showing a trend where the DC bus voltages peak just before the 10th hour and gradually decrease, reaching their lowest level around the 14th hour. Lastly, Fig. 25d displays the reactive power of the WTs, indicating variations throughout the 24 h with a significant dip around the 12th hour. These graphs collectively provide a comprehensive overview of the WF’s performance in the HS for Case#2, showcasing the variability in active power generation, changes in wind speed, fluctuations in DC bus voltages, and variations in reactive power consumption or generation by the turbines. Based on results from fault-free scenarios, the FLC and MRFO demonstrate outstanding performance in enhancing the transient stability of both the MPPT controllers and the inverter controllers in a PV farm. This means that the FLC and MRFO effectively ensure stable power output from the MPPT and inverter controllers during transient conditions or disturbances. Furthermore, when comparing the efficiency of the MRFO with the GWO method in achieving optimal gains for MPPT controllers in PV farms, the MRFO proves to be more efficient. Additionally, the MRFO provides better control and regulation of the power output of the double-fed WTs, resulting in improved stability and reliability of the power supply. In summary, the FLC and MRFO have shown remarkable performance in enhancing the transient stability of the MPPT and inverter controllers in the PV farm. These findings highlight the effectiveness of the FLC and MRFO in maintaining stable power output and optimizing the performance of the WF’s control system.
Wind farm output in the HPVWBPS in Case #2: (a) active power, (b) reactive power, (c) DC voltage, and (d) wind speed.
Industrial applications frequently experience three-phase-to-ground faults (3-ph-G), which are particularly dangerous for power electronic converters. Due to semiconductor devices’ rapid response times, it is crucial to control excess current flow and voltage drops to prevent device damage. Figure 26 illustrates the impact of a 3-ph-G fault on the characteristics of a PV farm. The fault occurs at time t = 1.1 s, and the graph provides insights into the behavior of the PV farm during and after the fault. During the fault, the output parameters of the PV farm, such as maximum power, current, and voltage, experience a significant decrease, as evident from the downward trends in the respective lines on the graph. This disruption leads to a substantial reduction in the PV farm’s performance. However, the graph also demonstrates that after approximately 1.2 s, these metrics begin to recover and return to normal levels. This recovery is indicated by the upward trends in the lines representing maximum power, current, and voltage. It suggests that the PV farm effectively mitigates the effects of the fault and gradually restores its performance.
PV farm output in the HPVWBPS at 3-ph-G fault in Case#1: (a) voltage, (b) current, and (c) power.
Figure 27 depicts the DC Link Voltage of a DC boost converter. At around 1 s, a disturbance occurs in the form of a 3-ph-G, causing a significant disruption in the voltage. This fault leads to a sudden spike from 0.91 pu to 0.95 pu within one second. However, thanks to the FLC with MRFO, the disturbance is effectively moderated, and the voltage stabilizes at 0.91 pu within a short span of 1.1 s. This indicates the ability of the FLC and MRFO to quickly react and mitigate the effects of the disturbance, restoring stability to the system. Following the initial spike, the DC voltage experiences a drop to 0.86 pu before the issue is fully resolved. This temporary drop may be attributed to the system’s response and adjustment to the fault. Ultimately, the FLC and MRFO ensure that the voltage stabilizes at the desired level, allowing the DC boost converter to resume normal operation.
DC linked voltage in the HPVWBPS at 3-ph-G fault in Case#1.
Figure 28 illustrates the output of a WF in the HPVWBPS during a 3-ph-G fault, specifically focusing on the active electricity fed into the PCC bus. During the fault period, indicated as the “defective time” in Fig. 28, the WF does not generate any active electricity for the PCC bus. This disruption leads to a complete interruption in the supply of active power. Notably, once the fault is resolved, there is an immediate power spike, which strains the hardware and forces the transformer to handle an increased power load. This surge is instantly noticeable, and, after approximately 7 s, the system returns to normal levels.
Wind farm output in the HPVWBPS at 3-ph-G fault in Case#1: (a) active power; (b) DC voltage; (c) reactive power; and (d) wind speed.
Figure 29 displays the three-phase voltage on the PCC bus during a three-line-to-ground (LLLG) fault. The voltage is normally maintained at a maximum of 20 kV. During the fault, from 0.1 to 1.1 s, the voltage at the grid drops to zero. After 1.1 s, the voltage returns to normal levels. This indicates that the inverter was turned off between 0.1 and 1.1 s to manage the fault condition. Figure 30 illustrates the output current during a three-phase-to-ground (3-ph-G) fault, providing insights into the behavior of the current in various phases (Ia, Ib, and Ic) over time (0.85 to 1.2 s). Before the fault occurs, the current in all phases is at a steady state value of 334 A. At the moment of the fault (around 0.95 s), the current in all phases sharply increases to 1950 A, indicating a significant disruption in the normal operation of the system.
The output voltage in the HPVWBPS at 3-ph-G fault in Case #1.
The output current in the HPVWBPS at 3-ph-G fault in Case#1.
Following the fault, the current in phases Ib and Ic gradually drop to approximately 224 A before recovering to its normal steady-state value of 2334 A over time. This recovery indicates the successful clearing of the fault by the FLC with MRFO, effectively restoring the current in phases Ib and Ic to normal levels and ensuring the system’s proper operation. In contrast, the current in phase Ia remains constant during the fault period, suggesting that the fault does not significantly impact the flow of current in this specific phase. From the simulation results, it is observed that the FLC-MRFO is a powerful tool for providing robust and reliable control in the presence of uncertainties and incomplete information. After a fault, the system’s parameters immediately return to normal, demonstrating the effectiveness of the FLC-based MRFO.
FLC-based MRFO has several advantages over traditional FLC controllers and has been successfully applied to various control problems. However, expertise in fuzzy logic and control theory and careful design and implementation are required to ensure its effectiveness. MRFO can efficiently explore solution spaces and converge towards optimal solutions, making it a valuable tool in various domains. The authors detailed the work’s merits and results with those of a few other publications that used AI methods to show the quality of the study they were presenting. Table 4 presents a comparison analysis between the work being presented and previous literature articles.
Single line-to-ground (SLG) faults are among the most common types of asymmetrical faults in power systems and can significantly affect the stability and performance of power electronic interfaces in PV farms. These faults involve one phase coming into contact with the ground, creating an unbalanced condition. Figure 31 shows the response of the PV farm to an SLG fault introduced at time t = 1.1 s. During the fault, a noticeable dip occurs in the affected phase’s voltage and current, while the other two phases maintain relatively stable profiles. This unbalance causes a drop in the total power output of the PV system, though less severe than in the case of a three-phase fault. The graph illustrates that around 1.2 s, the voltage and current in the faulted phase begin to recover, and the power output gradually stabilizes. This behavior indicates the system’s ability to detect and withstand asymmetrical disturbances, allowing the PV farm to maintain operational continuity and resume normal performance after fault clearance.
PV farm output in the HPVWBPS at 1-ph-G fault in Case#1: (a) voltage, (b) current, and (c) power.
Figure 32 shows the DC Link Voltage of a DC boost converter under a single-phase-to-ground (1-ph-G) fault. At approximately 1 s, the fault occurs, causing a moderate disruption in the voltage profile. The DC voltage momentarily rises from 0.91 pu to 0.93 pu, indicating the system’s immediate reaction to the fault. The FLC with MRFO responds quickly, damping the disturbance and restoring the voltage back to 0.91 pu within 1.05 s. This demonstrates the control system’s ability to handle single-phase faults with minimal deviation. Following the brief overshoot, the voltage dips slightly to 0.89 pu as part of the settling process. The system then recovers fully, stabilizing the voltage and maintaining steady-state operation. The response confirms that the FLC and MRFO can effectively manage less severe disturbances like single-phase faults without long-term instability.
DC linked voltage in the HPVWBPS at 1-ph-G fault in Case#1.
Figure 33 shows the output voltage at the PCC bus (phase A) in the HPVWBPS during a single-phase-to-ground (1-ph-G) fault in Case #1. The voltage remains stable at around ± 10 kV before the fault. At exactly 1 s, the fault occurs, causing the voltage in phase A to drop sharply and remain near zero until 1.1 s. After fault clearance at 1.1 s, the voltage recovers immediately and returns to its normal sinusoidal waveform. This response indicates that the system rapidly isolates the fault and restores voltage stability using the FLC with MRFO strategy.
The output voltage in the HPVWBPS at 1-ph-G fault in Case #1.
Figure 34 presents the corresponding output current in phase A at the PCC bus during the same fault event. Before the disturbance, the current oscillates steadily around a low amplitude. At 1 s, the fault initiates a sharp rise in current, peaking at approximately 55 A, indicating a severe but brief surge due to the fault. The current then dips below − 20 A before stabilizing. After the fault is cleared at 1.1 s, the current returns to its pre-fault condition. This behavior confirms that the FLC-MRFO controller effectively detects, reacts to, and mitigates the fault, ensuring fast recovery and continued stable operation.
The output current in the HPVWBPS at 1-ph-G fault in Case#1.
These results show that the FLC-MRFO system provides targeted and fast fault response, preventing unnecessary disturbance in unaffected phases and maintaining grid stability. The control system demonstrates high resilience and accuracy in detecting and correcting single-phase faults.
The results of the proposed approach are presented in this section to compare the performance of the FLC-MRFO and FLC-GWO techniques under different fault conditions, including three-phase-to-ground faults and single line-to-ground faults. The comparison focuses on system response and fault-clearing capability based on simulation outcomes for both scenarios.
Figure 35 presents a comparison between the FLC-MRFO and the FLC-GWO for fault clearing performance under a three-phase-to-ground fault condition in a PV system. The key parameter under observation is the PV array power response over time. During the initial fault period (0 to ~0.1 seconds), both FLC-MRFO and FLC-GWO experience a steep drop in PV array power due to the impact of the fault. However, FLC-GWO exhibits more severe oscillations and instability in its power response. FLC-MRFO, on the other hand, recovers more quickly from the initial disturbance, showing a smoother rise in power.
Comparing PV farm output power using FLC-GWO &FLC- MRFO in the HPVWBPS at 3-ph-G fault in Case#1.
In terms of stabilization time, FLC-MRFO reaches a steady-state power output close to 20 MW by around 0.5 s and maintains it with minimal deviation. In contrast, FLC-GWO continues to show significant power fluctuations well beyond 2 s, indicating delayed convergence and less effective control. These oscillations include both overshoots (exceeding 24 MW) and undershoots (dropping to around 16 MW), which reflect poor damping characteristics. Post-fault, FLC-MRFO maintains a consistent and stable power output, which demonstrates its robustness and control efficiency under faulted conditions. FLC-GWO, however, struggles to stabilize, resulting in an unstable and irregular power profile. FLC-MRFO provides superior performance compared to FLC-GWO for clearing three-phase-to-ground faults in PV systems. It ensures faster recovery, better damping of oscillations, and more stable power delivery, making it a more effective fault-handling strategy.
Figure 36 illustrates the performance comparison between the FLC-MRFO and FLC-GWO algorithms under a single-phase-to-ground fault in the high-penetration variable wind and battery PV system (HPVWBPS). The PV array power output is used as the main indicator to evaluate the system’s response during and after the fault. Both FLC-MRFO and FLC-GWO successfully restore the PV output following the fault event. However, the FLC-MRFO-based control strategy demonstrates a smoother and faster recovery. In the initial phase (0 to 0.2 s), both approaches experience a drop in power, but the FLC-GWO response shows more pronounced oscillations and a slightly delayed rise toward the steady-state value. In contrast, FLC-MRFO stabilizes more quickly and with fewer fluctuations, reflecting stronger transient performance. After the initial recovery, FLC-MRFO maintains a stable output near 20 MW with minimal disturbance. The FLC-GWO approach shows small but noticeable ripples around the same power level, indicating less effective damping and control precision. The zoomed-in section of the graph confirms that FLC-MRFO sustains a more consistent power profile during the post-fault phase.
Comparing PV farm output power using FLC-GWO & FLC-MRFO in the HPVWBPS at 1-ph-G fault in Case#1.
Finally, FLC-MRFO outperforms FLC-GWO under single-phase-to-ground faults by delivering faster stabilization, reduced oscillations, and improved power quality. This highlights MRFO’s advantage in maintaining system reliability during asymmetrical fault conditions.
While the proposed control strategy and optimization framework show promising results, several limitations should be stated to ensure transparency and guide future research: (a) limited fault scenarios: the study evaluates controller performance under selected symmetrical and asymmetrical fault conditions. However, real-world systems may experience a broader range of disturbances such as high-impedance faults, multi-stage faults, and protection system misoperations, which are not covered in this work; (b) no hardware validation: all results are based on simulation using MATLAB/Simulink. Although the dynamic behavior observed is encouraging, hardware-in-the-loop (HIL) testing or real-time digital simulation (RTDS) would be necessary to confirm practical feasibility and real-world performance; (c) assumptions in optimization process: the MRFO algorithm tuning relies on fixed rule bases and predefined parameter bounds. These assumptions simplify the optimization process but may reduce adaptability to different plant sizes, topologies, or rapidly changing grid conditions; and (d) environmental data granularity: Case #2 uses hourly solar irradiance and wind speed data. This resolution may miss short-term fluctuations such as cloud transients or wind gusts. Using higher-frequency environmental data would improve system realism and robustness in forecasting and control. These limitations do not undermine the validity of the results but help define the study’s scope and set realistic expectations. Addressing them will be part of future work to strengthen the practical applicability of the proposed control strategy.
This paper investigates the FLC scheme optimized by the MRFO algorithm to improve the performance of large-scale HPVWBPS. The MRFO is used to determine the optimal gains for both voltage and current regulators, ensuring efficient control under dynamic and fault-prone operating conditions. A detailed comparison of four configurations, PI-based GWO, PI-based MRFO, FLC-based GWO, and FLC-based MRFO, is presented in Table 3, isolating the influence of controller type and optimization algorithm on system performance. The results confirm that MRFO-optimized FLC controllers outperform traditional PI controllers optimized by the GWO across all critical metrics. For the voltage regulator, the MRFO-FLC achieves a slightly improved settling time (ST) of 1.0051 ms compared to 1.0052 ms for the PI-GWO configuration. The current regulator shows more significant improvements, with the ST reduced to 1.0020 ms versus 1.0033 ms for the PI-GWO. These reductions indicate faster convergence and better system recovery during faults. The MOST also decreases across both regulators. The voltage regulator’s MOST drops from 86.7895% to 86.574%, while the current regulator sees a reduction from 143.2222% to 140.1213%. These results reflect improved robustness and lower stress on the system components, contributing to extended operational life and enhanced reliability during disturbances and load fluctuations. The RT for the current regulator is significantly improved. MRFO-FLC achieves a response time of 2.1885 μs compared to 3.2755 μs for the PI-GWO configuration, a 33.2% decrease. For the voltage regulator, RT improves slightly from 8.1978 μs to 8.1878 μs. While less pronounced, this consistent gain reinforces the advantage of MRFO-FLC in delivering a faster and more stable response. To summarize, the FLC-MRFO configuration demonstrates superior adaptability to system nonlinearity, better handling of time delays, and enhanced resilience to faults. Among all the configurations tested, it delivers the best dynamic performance, validating its effectiveness for control applications in hybrid renewable energy systems. Future work will focus on further improving controller adaptability and optimization efficiency. Plans include developing an adaptive FLC scheme and enhancing the MRFO algorithm using methods such as Latin hypercube sampling and group learning strategies. These refinements aim to strengthen the controller’s real-time performance and fault-handling capabilities in increasingly complex and variable hybrid energy environments.
All data generated or analyzed during this study are included in the article.
Artificial intelligence
Artificial neural networks
Diesel generator
Energy storage system
Fuzzy logic controller
Grey wolf optimizer
Hybrid photovoltaic/wind/battery power system
Hybrid renewable energy system
Modified fault-clearing strategy
Mixed-integer linear programming
Maximum overshoot
Maximum power point tracking
Manta ray foraging optimization
Net present cost
Proportional-integral controller
Particle swarm optimization
Photovoltaic
Response time
Solar energy fraction
State of charge
Settling time
Wind turbine
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This research has been funded by the Scientific Research Deanship at the University of Hail—Saudi Arabia through project number “RG-23 191”.
Department of Electrical Engineering, College of Engineering, University of Hail, Hail, 55473, Saudi Arabia
Abdulaziz Almalaq, Khalid Alqunun & Rabeh Abbassi
Department of Electrical Engineering, Institute of Aviation Engineering and Technology, Giza, 12658, Egypt
Rania G. Mohamed
Basic Sciences Council, Academy of Scientific Research and Technology, Cairo, 11516, Egypt
Shady H. E. Abdel Aleem
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Rania G. Mohamed: Conceptualization; Formal analysis; Methodology; Writing—original draft; performed the simulations and obtained the results. Abdulaziz Almalaq , Khalid Alqunun , Rabeh Abbassi :analyzed the obtained results. Shady H. E. Abdel Aleem: Investigation; Validation; Writing – review -editing; Conceptualization; Formal analysis; Supervision. All authors have read and agreed to the published version of the manuscript.
Correspondence to Rania G. Mohamed.
The authors declare no competing interests.
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Almalaq, A., Alqunun, K., Abbassi, R. et al. Improved fault-clearing strategy for large renewable energy systems using advanced optimization and FLC. Sci Rep 15, 32455 (2025). https://doi.org/10.1038/s41598-025-18167-8
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Received: 23 March 2025
Accepted: 29 August 2025
Published: 12 September 2025
Version of record: 12 September 2025
DOI: https://doi.org/10.1038/s41598-025-18167-8
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