Initial LFC studies stem from the Proportional-Integral (PI) control era, valued for their simplicity and computational ease (Wang et al., 1993). Integrated into LFC, PI controls split into steady-state integral and transient proportional parts. The PI control’s widespread use in LFC hinges on its non-differential regulation efficacy in fundamental power setups. However, as power systems grow and face more stochastic disruptions, PI’s static nature limits its dynamic stability, threatening frequency equilibrium and risking failures (Wang et al., 1994). Scholars have since sought to improve PI for LFC, with (Chen et al., 2022) incorporating sliding mode control for disturbance resilience. The rise of complex, nonlinear, and interconnected power systems demands control strategies that address these traits. Long et al. (2021) introduces a tri-layer LFC model for detailed power system dynamics, with a control strategy for nonlinear management. Yet, its reliance on specific parameters and a model-centric approach limits broad use. This shift from PI to adaptive, interconnected strategies reflects the ongoing effort to manage modern power systems’ complexities. The ongoing evolution of LFC methods highlights the necessity for flexible, robust, and efficient controls to maintain the stability and reliability of our increasingly intricate and interconnected power grids.

Model Predictive Control (MPC) uses dynamic models, typically linear empirical ones, to predict and optimize system behavior over a future time span, adjusting the present state with future constraints in mind (Peng et al., 2023). This allows for real-time feedback and corrections. A distributed MPC algorithm promotes collaborative LFC between wind and thermal plants, improving overall system performance through dynamic cooperation.

Adaptive Control (AC), on the other hand, adjusts its parameters and rules in response to changing system conditions, maintaining stability despite uncertainties and significant disturbances without needing known variability bounds (Yan et al., 2022). AC in LFC, via adaptive dynamic programming, minimizes frequency deviations in grids, requiring less reliance on prior knowledge than MPC. However, AC systems tend to be more complex and costly.

Traditional controls often lack adaptability, affecting the performance and cost of frequency control in islanded microgrids. AI algorithms offer a solution, handling nonlinear complexities and improving operational efficiency and stability. AI learns and adapts to changing conditions, refining LFC strategies, enhancing energy efficiency, and ensuring reliable power supply. AI’s predictive abilities also help prevent system failures, increasing microgrid resilience to uncertainties and disturbances.

In the modern era of islanded microgrids, which significantly integrate renewable energy resources, the complexity and interconnectedness of information flow across various regions necessitate a systematic approach for prioritizing the use of novel energy sources. Traditional LFC strategies face challenges in navigating the intricate decision-making processes required for efficient energy management. Within the realm of computer science, Artificial Intelligence (AI) emerges as a critical field, striving to emulate human cognitive abilities, including learning, decision-making, and problem-solving. The inherent capability of AI to engage with and learn from its environment independently positions it as a formidable tool for addressing complex challenges in energy systems.

The integration of AI with LFC mechanisms represents a pioneering effort to transcend the limitations of conventional LFC methods. For example, the work of Jia et al. (2019) showcases the successful application of Q-learning to LFC, significantly enhancing system adaptability through the ongoing refinement of the state-action matrix for comprehensive power control in simplified models. Furthermore, Yu et al. (2012) have introduced an innovative imitation learning strategy that integrates eligibility traces into reinforcement learning, yielding improved LFC performance in islanded systems through faster convergence and enhanced dynamic capabilities. In another notable advancement, Yu et al. (2015) have developed a cooperative reinforcement learning strategy, employing multiple intelligent agents to devise an optimal unified control strategy, effectively addressing the challenges posed by the interconnectivity of disparate control regions.

Additionally, Zhang et al. (2023a) have constructed a tri-level architecture for a multi-agent system, enabling coordinated control over LFC and Automatic Voltage Control (AVC). This architecture leverages the autonomous, independent, and collaborative nature of intelligent agents to ensure logical consistency while decentralizing control functions physically. In a groundbreaking approach, Xi et al. (2018) propose the Evolutionary Population Cooperative Control (EPCC) strategy, utilizing a win-lose criterion and space-time tunneling concept to quickly achieve Nash equilibrium within a multi-agent system (MIS) framework. This strategy, rooted in the Multi-Agent System Stochastic Consensus Game (MAS-SCG), promotes frequent information exchanges among intelligent agents, demonstrating the potential of AI to enhance decision-making and operational efficiency in complex energy systems.

Reinforcement Learning (RL) is a key machine learning paradigm that focuses on devising strategies for agents to make optimal decisions to meet set objectives through interactions with environmental states. Utilizing a Markov decision process, RL entails recognizing states and selecting actions guided by rewards, leading to state transitions. Studies have investigated applying power system’s instantaneous frequency and transmission line power flow as RL environmental states, with power allocation directives as action decisions, tackling power allocation challenges effectively. (Yu et al., 2011; Shangguan et al., 2021; Zhang et al., 2023b).

Zhang et al. (2020) have considered the total profit of power generation companies, incorporating dispatch mileage compensation into power command allocation to enhance the economic efficiency of power generation. Li et al. (Zhang et al., 2021) introduced an adaptive distributed auction algorithm for optimizing LFC power command allocation, minimizing the deviation between total and allocated power commands. This method is praised for its rapid convergence and model-free nature, ensuring precise generator power control. Moreover, Li et al. (2021) proposed a double-delay deep deterministic policy gradient algorithm, augmented by a multi-experience pool probabilistic replay strategy, improving controller training efficiency, action instruction quality, and mitigating stochastic perturbations in systems incorporating new energy sources, highlighting the evolving applications of RL in power system optimization.

In the dynamically evolving context of islanded microgrids, enriched with a diverse array of renewable energy resources, the exploration of AI control strategies combined with RL distribution tactics is underway to realize an intelligently integrated LFC system across multiple regions. This research endeavor has led to the development of multi-regional, multi-layered distributed LFC frameworks, enabling intelligence dissemination from macro to micro levels (Xi et al., 2016a; Xi et al., 2016b). To address these limitations and enhance generalizability, Xi et al. (2021) replaced the traditional wolf climbing LFC algorithm with PDWoLF-PHC, proposing a VWPS-HDC method that offers improved performance through time-consistent climbing. Additionally, to overcome the drawbacks of the WPH algorithm, Xi et al. (2022) introduced a cost-consistent VWPC-HDC method, achieving faster dynamic optimization, enhanced robustness, and reduced generation costs.

However, the practicality of these methodologies, based on the wolf pack hunting principle, is constrained by their reliance on extensive knowledge systems. To mitigate these limitations.

The challenge of ensuring wide-ranging applicability in the domain of standalone microgrid Load Frequency Control (LFC) remains a critical issue. It necessitates the creation of control frameworks and algorithms that can effectively operate in diverse scenarios beyond the scope of their original design. This adaptability is essential for managing the dynamic operational landscapes and the variability in demand that are characteristic of isolated microgrids. The integration of a diverse set of techniques, alongside reinforcement learning, is vital for enhancing the robustness and adaptability required to navigate changes in the environment.

This paper introduces the Data-Enhanced Optimum Load Frequency Control (DEO-LFC) methodology, which is designed to achieve a harmonious balance between generation costs and frequency stability in microgrids with a substantial integration of renewable energy sources. The Soft Graph Actor Critic (SGAC) algorithm is presented as a groundbreaking fusion of deep reinforcement learning and graph sequence neural network models, tailored to manage the intricacies of adaptive frequency regulation. By employing a Markov decision process for system modeling and a graph to sequence neural network for policy function approximation, the DEO-LFC approach highlights its potential impact. Its application to the isolated island city microgrid model within the China Southern Grid serves as a testament to its effectiveness in modern electrical grid settings.

The main contributions of this paper are summarized as follows.

1) Introduction to the DEO-LFC Methodology: The DEO-LFC methodology signifies a paramount advancement in the realm of frequency stability enhancement and cost minimization in isolated microgrids, especially those with substantial renewable energy sources integration. This methodological shift toward employing agent-based systems, which utilize reinforcement learning algorithms, marks a departure from conventional control strategies. The DEO-LFC framework presents an innovative, adaptive approach to managing frequency control challenges in complex operational contexts. It specifically targets the issues arising from the fluctuating nature of renewable energy sources, thereby facilitating a more reliable and cost-effective energy management system.

The organisation of this manuscript is as follows: Section 2 delineates the configuration of the islanded microgrid system. Subsequently, Section 3 introduces a groundbreaking approach, detailing its structural framework. Section 2 delineates the configuration of the islanded microgrid system. Section 4 is dedicated to the execution of case studies designed to evaluate the proposed method’s efficacy. Finally, Section 5 concludes the document by providing a comprehensive summary and discussing the principal outcomes derived from the research conducted. Finally, Section 5 concludes the document by providing a comprehensive summary and discussing the principal outcomes derived from the research conducted.

In microgrids, integration of Distributed Generation (DG) units such as Photovoltaic (PV), Wind Power (WP), and Energy Storage (ES) systems is achieved via grid-connected inverter interfaces, which allow these units to align with desired power outputs through specific control mechanisms. A simplified model for these inverters is used to explain the Load Frequency Control (LFC) framework, highlighting the role of traditional, renewable, and storage energy sources in frequency regulation.

Figure 1 illustrates an autonomous microgrid setup featuring diverse generation sources like diesel engines, micro gas turbines, fuel cells, PV, wind turbines, ES systems, and consumer loads. Here, diesel engines and ES systems play a crucial role in frequency regulation, while renewables focus on maximizing power output through Maximum Power Point Tracking (MPPT), offering limited frequency support. The control system of the microgrid dynamically distributes power to match demand, prioritizing efficiency, sustainability, and stability.

For independent operation, microgrids require self-adjusting power generation for voltage and frequency stability, incorporating Primary Frequency Control (PFC) and LFC mechanisms. PFC deals with immediate power output adjustments in response to frequency changes, whereas LFC involves coordinated efforts across multiple sources to correct frequency discrepancies, typically managed by centralized controllers and communication systems. ES and diesel generators are key to microgrid frequency stability, with PV and WP units focusing on MPPT due to their variable output.

Recent research suggests strategies for integrating wind and solar into frequency regulation by reserving part of their output to improve system response. Yet, the focus remains on PFC. This study explores how diesel and ES significantly contribute to frequency stability, managing variances in power supply. Wind and solar, despite their fluctuating nature, are considered less reliable for maintaining balance and stability in microgrids.

This paper introduces a DEO-LFC method designed to optimize generation costs while ensuring frequency stability in microgrids rich in renewables. The DEO-LFC strategy balances cost-efficiency with the critical need for frequency stability, addressing the challenges posed by high renewable energy integration in isolated microgrids.

The framework employs advanced algorithms for adaptive frequency regulation, adept at navigating the complex dynamics characteristic of such systems. It promises improved performance, especially in mitigating the unpredictability associated with renewable energy sources. By integrating data-driven insights and knowledge-based control, the DEO-LFC approach enhances the reliability and efficiency of frequency management in microgrids, aligning operational expenditures with the overarching goal of frequency stabilization. This methodological innovation stands to significantly advance the operational robustness of isolated microgrids, ensuring stability amidst the fluctuating nature of renewable energy contributions.

The formulation of generation cost within the electricity production sphere is articulated via a sophisticated mathematical model, meticulously capturing the comprehensive economic obligations of power generation firms. This model is all-encompassing, amalgamating crucial operational cost elements integral to the generation process. It assimilates direct costs, such as fuel expenses encompassing a spectrum from fossil to renewable sources, and extends to cover the wide range of maintenance demands for generation infrastructure, encompassing routine checks, parts replacement, and emergency repairs. Furthermore, the model includes labor expenses covering wages, training, and health and safety measures for personnel, along with various indirect costs. These indirect expenses encompass regulatory compliance charges, environmental levies, and investments in technological innovation, essential for the electricity generation continuum.

Crafted with precision, the model reflects the intricate dynamics prevalent in the energy sector by integrating both variable costs, which alter with production levels and operational intensity, and fixed costs, which are invariant to output volume. This dual approach offers a comprehensive perspective on the economic terrain of electricity generation, covering the spectrum from initial capital outlay to incremental operating expenses.

Merging such varied economic components into a unified model provides stakeholders with an in-depth view of the critical economic considerations vital for prudent and sustainable power generation management. It facilitates a detailed comprehension of the interplay between different cost determinants and their collective influence on the cost-efficiency and -effectiveness of power plants. Ultimately, this model transcends being a mere cost inventory, evolving into a dynamic tool that underpins strategic decision-making and future-oriented planning, pivotal for the advancement of the power generation industry. The cost of power generation is as follows: C i P G i = a i P G i 2 + b i P G i + c i (9) where P _Gi is the output of the ith unit, a _i , b _i ,c _i are constants, and C _i is the cost of the ith unit. C i P G i , actual = C i P G i , plan + Δ P G i = α i Δ P G i 2 + β i Δ P G i + γ i (10) α i = a i β i = 2 a i P G i , plan + b i γ i = a i P G i , plan 2 + b i P G i , plan + c i (11) where ΔP _Gi is the output of ith unit, P _Gi,actual is the output of ith unit,α _i , β _i , γ _i are coefficients.

The Differential Evolution Optimization for Load Frequency Control (DEO-LFC) framework represents a vanguard methodology in the domain of electrical grid management, specifically engineered to fortify frequency stability across power networks—a critical factor for ensuring uninterrupted service and superior power quality within microgrid configurations. Achieving and maintaining an exact frequency balance is of paramount importance, as deviations from the established frequency spectrum can lead to detrimental effects, such as the deterioration of infrastructure, compromised quality of electricity, and a heightened risk of grid instability. Within the realm of microgrid management, the economic aspects of power generation take on a significant role, deeply influencing the operational dynamics and the economic viability of these systems. The implementation of efficacious frequency control measures is indispensable for reducing superfluous energy consumption and operational expenses, thereby enhancing the economic efficiency of microgrids, optimizing the use of resources, and improving the cost-efficiency of power generation initiatives.

Islanded microgrids, characterized by their compact scale and increased susceptibility to fluctuations in load demand, encounter unique challenges in achieving consistent frequency control. These standalone power systems require intricate and flexible management strategies that can effectively align the twin goals of cost minimization and optimization of system performance. The DEO-LFC approach addresses these challenges by deploying an innovative multi-objective optimization framework, carefully crafted to strike a balance between cost-effectiveness and dependable system performance. This framework is designed to minimize the adverse effects of operational constraints while preserving the integrity of economic and performance objectives, thus embodying a holistic strategy that caters to both economic and operational performance imperatives.

Incorporating multi-objective optimization techniques, the DEO-LFC methodology skillfully manages the intricate interplay between grid stability and economic factors in power generation. It delivers a refined solution that adeptly adjusts the equilibrium between ensuring grid stability and contemplating the economic dimensions of power generation. This versatile and comprehensive approach is uniquely suited to address the fluctuating demands of microgrid settings, guaranteeing frequency stability alongside a commitment to operational efficiency and fiscal judiciousness. The strategic formulation of objective functions and constraints under this methodology underscores its capacity to navigate the complexities of modern power systems, providing a robust framework for the sustainable and efficient management of energy resources in microgrids. Through the meticulous design of its optimization processes, the DEO-LFC strategy exemplifies an advanced paradigm in grid management, advocating for a harmonious integration of technical and economic considerations to foster resilient and economically viable microgrid ecosystems. The objective functions and constraints are as follows. min ∑ t = 1 T Δ f + ∑ t = 1 T ∑ i = 1 n α i Δ P Gi 2 + β i Δ P Gi + γ i (9a) ∑ i = 1 n Δ P i in = Δ P order − ∑ Δ P order − ∑ * Δ P i in ≥ 0 Δ P i min ≤ Δ P i in ≤ Δ P i max Δ P G i t − Δ P G i t + 1 ≤ Δ P i rate (10a) where ΔP _order-∑ is the total command, ΔP _i ^max and ΔP _i ^min are the limits of the ith unit, ΔP _i ⁱⁿ is the command of the ith unit.

In Reinforcement Learning (RL), the dynamic interaction between an agent and its environment is conceptualized through a Markov Decision Process (MDP), serving as both the mathematical foundation and a key modeling instrument for RL challenges. An MDP framework typically encapsulates a state space, action space, state transition probabilities, and a reward function. Within this structure, the agent selects actions in accordance with the present state at each discrete time step, while the environment responds by presenting a subsequent state and associated reward, as dictated by the state transition probability function and the reward function. The MDP framework posits that state transitions in the decision-making process adhere to the Markov property—meaning the forthcoming state is contingent solely on the current state and the executed action, devoid of any historical influence. The quintessential components of an MDP include.

1) State space: the set of all possible states.

In MDP, the goal of an agent is to find an optimal strategy, i.e., to choose an optimal action in each state to maximize the expected cumulative reward.

In the present investigation, step disturbances were systematically introduced into the Case study to meticulously evaluate the system’s response and resilience under perturbed conditions. The outcomes of this experimental setup are comprehensively documented and presented through a series of visual representations and quantitative data analyses, spanning Figure 4. The outcomes of this experimental setup are comprehensively documented and presented through a series of visual representations and quantitative data analyses, spanning Figure 4 and including the detailed numerical results compiled in Table 1. This approach was deliberately chosen to facilitate a nuanced understanding of the system’s dynamics and its capability to maintain stability or adapt to sudden changes in operating conditions. This approach was deliberately chosen to facilitate a nuanced understanding of the system’s dynamics and its capability to maintain stability or adapt to sudden changes in operating conditions.

The inclusion of step disturbances serves as a critical methodological tool to simulate real-world operational challenges, providing insights into The inclusion of step disturbances serves as a critical methodological tool to simulate real-world operational challenges, providing insights into the system’s robustness and the efficacy of implemented control strategies. This structured presentation of findings, leveraging both graphical and This structured presentation of findings, leveraging both graphical and tabular formats, is designed to provide a comprehensive overview of the experimental results, fostering an in-depth analysis of the system’s response patterns. The empirical evidence gathered through this methodology is instrumental in validating the theoretical models and hypotheses posited in the study, thereby contributing to the advancement of the system. The empirical evidence gathered through this methodology is instrumental in validating the theoretical models and hypotheses posited in the study, thereby contributing to the advancement of knowledge in the field. Furthermore, the detailed exposition of results in this manner adheres to rigorous scientific communication standards, ensuring clarity, precision, and replicability of the research findings.

Table 1’s analysis provides a detailed comparison of the SGAC algorithm against other algorithmic models, focusing on frequency deviation and generation cost metrics. The findings reveal that the frequency deviations with other strategies were 1.089–4.155 times greater than with the SGAC algorithm. Additionally, the SGAC algorithm demonstrated a reduction in generation costs by 0.31%–1.28% over its counterparts, underscoring its superior efficiency and control in microgrid management. A deeper investigation into frequency response and diesel generator outputs across different control strategies highlights the variance in performance and the efficacy of each control mechanism. The SGAC algorithm emerges as the top performer, with soft Q-learning noted as a strong alternative.

The standout performance of both the SGAC and soft Q-learning algorithms is linked to their use of maximum entropy exploration mechanisms, enabling precise adjustments in learning rates and importance weighting through an updated experience-sharing framework. This adaptability allows for customized control strategies in various zones, enhancing operational flexibility. Particularly, the SGAC algorithm excels in making decisions based on dynamic joint trajectories and historical data, bypassing traditional policy evaluation methods and improving its responsiveness to learning adjustments.

The SGAC algorithm’s adaptability and control effectiveness across diverse system conditions firmly establish its role as a leader in the field of reinforcement learning, distinguished by its straightforward and universally applicable parameters. However, applying reinforcement learning broadly faces challenges, such as setting a shared exploration goal for multiple agents in complex tasks and dealing with the instability from agents needing to respond to each other.

The introduction of multi-agent reinforcement learning approaches, focusing on collective characteristics, marks a significant advancement in overcoming these challenges, steering reinforcement learning towards achieving dynamic tasks through autonomous decision-making and agent exploration.

Further examination of operational dynamics, as shown in Figure 3B, reveals the system’s ability to closely follow load disturbances, including negative and square wave perturbations. The LFC units’ power outputs adjust to address unpredictable power changes effectively. An in-depth look at the regulation curves of various LFC units in Figure 3A shows a strategic allocation based on regulation costs and disturbance types, leading to optimized frequency control. The uniform micro-increment rate principle guides power distribution among LFC units, resulting in an economically efficient power output, contrasting with other DRL models that lack refinement mechanisms and heavily rely on theoretical models, thus limiting their control accuracy.

In the research delineated within this document, a sophisticated smart distribution grid model, replete with a plethora of renewable energy sources, is meticulously constructed to facilitate an in-depth analysis of the SGAC algorithm’s operational performance amidst a highly stochastic environment. The model is enriched with an array of renewable energy sources, encompassing electric vehicles, wind turbines, small-scale hydropower plants, micro-gas turbines, fuel cells, photovoltaic systems, and other energy sources. The model is enriched with an array of renewable energy sources, encompassing electric vehicles, wind turbines, small-scale hydropower plants, micro gas turbines, fuel cells, photovoltaic systems, and biomass energy solutions. Notably, certain renewable energy sources such as electric vehicles, wind power, and photovoltaic power generation exhibit considerable variability and unpredictability in their output. Consequently, these sources are modelled as sources of random load disturbances, their power outputs being incorporated into the system without contributing to the frequency Consequently, these sources are modelled as sources of random load disturbances, their power outputs being incorporated into the system without contributing to the frequency regulation mechanisms.

The variability inherent in wind power generation is captured through the application of finite bandwidth white noise as the input signal for the wind turbine model, thereby replicating the stochastic nature of wind speeds. The variability inherent in wind power generation is captured through the application of finite bandwidth white noise as the input signal for the wind turbine model, thereby replicating the stochastic nature of wind speeds. Similarly, the active power output for the photovoltaic generation model is derived by emulating the diurnal variations in solar irradiance. Characteristic of these renewable energy sources, thereby providing a robust framework for evaluating the efficacy of the SGAC algorithm under conditions that closely mimic real-world operational challenges.

Comprehensive details pertaining to the specifications and operational parameters of each energy unit incorporated within this model can be found in This extensive cataloguing of parameters is instrumental in underpinning the simulation exercises with a high degree of accuracy and relevance. This extensive cataloguing of parameters is instrumental in underpinning the simulation exercises with a high degree of accuracy and relevance, ensuring that the insights gleaned from this study are both valid and applicable to the design. This extensive cataloguing of parameters is instrumental in underpinning the simulation exercises with a high degree of accuracy and relevance, ensuring that the insights gleaned from this study are both valid and applicable to the design and optimization of future smart distribution grids. Through this meticulously constructed model, the paper aims to shed light on the adaptability and control capabilities of the SGAC algorithm, particularly in managing the complexities introduced by the SGAC algorithm. Particularly in managing the complexities introduced by the integration of a diverse mix of renewable energy sources within smart grid infrastructures.

This paper presents a detailed examination of the integration of random white noise as a proxy for load disturbances within a sophisticated smart distribution network model. This model is intentionally crafted to mimic the erratic load fluctuations commonly observed in power systems that are extensively integrated with novel energy resources. The primary objective of this research is to conduct a comprehensive evaluation of the Soft Graph Actor Critic (SGAC)’s efficacy and resilience when faced with environments characterized by substantial stochastic disturbances. A key component of this investigation involves conducting simulations that introduce 24-h cycles of random white noise disturbances, thereby allowing for an in-depth analysis of the SGAC algorithm’s robustness and long-term operational integrity under scenarios of severe random load fluctuations.

Figure 4 delineates the proficiency of the SGAC algorithm in accurately and promptly tracking random disturbances, thereby highlighting its precision in real-time disturbance management. The outcomes of these simulations, systematically compiled in Table 2, offer a quantitative assessment of the generation costs incurred, representing a cumulative analysis of the total regulatory expenses accumulated by all generating units over a 24-h period. A comparative evaluation reveals that the frequency deviation experienced with alternative control algorithms ranges from 1.388 to 3.711 times higher than that encountered when employing the SGAC algorithm. Moreover, the generation costs associated with the SGAC algorithm exhibit a nominal decrease, spanning from 0.0006% to 0.019%. These statistics underscore the SGAC algorithm’s superior economic efficiency, advanced self-adaptive capabilities, and its distinguished performance in executing coordinated optimal control compared to other intelligent algorithms.

To further substantiate the SGAC algorithm’s performance efficacy, an assortment of disturbances, including step waves, square waves, and random waves, were systematically introduced into the system. The resulting data underscore the SGAC’s exceptional convergence properties and its elevated learning efficiency, underscoring its unmatched adaptability and robustness within stochastic operational environments. The algorithm’s prowess in attenuating random disturbances and enhancing dynamic control effectiveness across interconnected grid landscapes is emphatically validated through these findings.

Figure 4 provides insight into how the output power from various units aligns with load demand across a 24-h cycle, showcasing the system’s adeptness at matching load fluctuations and achieving optimal operational states through the synchronized management of multiple energy sources under a cohesive power command strategy. The Energy Storage System (ESS) is identified as a pivotal element, demonstrating its capability to swiftly and accurately modulate power output, thereby contributing significantly to the balance of supply and demand through its flexible charging and discharging functionalities. The real-time optimization conducted by the system controller enables a smoother and more stable regulation process, facilitating rapid and efficient cooperative responses to abrupt load changes within the power system. This, in turn, validates the SGAC algorithm’s capacity to support swift and optimal cooperative operations amidst fluctuating system conditions, thereby enhancing the overall operational efficiency and reliability of the power system in managing dynamic and unpredictable environments.