## 1 Introduction
This study proposed an adaptive PMS using fuzzy logic to ensure smooth transitions between different operating modes, showing significant improvements in PV generator efficiency and system stability. In DC-bus MG, energy stability and quality have been improved using FLC-ESS [28]. This study investigated the use of superconducting magnetic energy storage (SMES) and battery systems controlled by FLC to mitigate voltage and power fluctuations, demonstrating improved stability and rapid response to climate and load variations. Finally, optimal regulation of energy flow in PV systems with BESS has been achieved using adaptive FLC [29; 30], highlighting FLC robustness and smooth performance in DC-bus voltage regulation and efficient energy flow management among PV systems, BESS, and loads. Similarly, studies [31; 32] demonstrate that fuzzy logic applied to improve the quality of renewable systems is promising. The literature review reveals various studies focused on mitigating power fluctuations in electrical grids caused by intermittent renewable sources. Studies such as [5] have evaluated spline-based control methods and S-G filters for PV power smoothing, showing significant reductions in variability with minimal additional storage capacity. However, there is an opportunity to optimize these methods specifically for integration into vehicle-to-grid (V2G) systems in isolated networks, better adapting them to variable load and solar generation conditions [5; 6]. Moreover, while lithium-ion batteries from electric vehicles (EVs) have been used to stabilize the grid, as seen in studies like [7], there is still room to maximize their responsiveness and efficiency in isolated MG. Solutions could improve charge/discharge management to optimize ESS, adapting to variable demand and generation patterns thereby enhancing V2G integration [7; 12]. Furthermore, while methods like MA and ramp rate techniques for frequency control and power smoothing have been compared, as outlined in studies such as [13], a more detailed and comprehensive comparison of these strategies in specific MG environments could provide additional insights into their effectiveness and adaptability. This exploration would be crucial for optimizing energy management strategies in variable network and weather conditions [13; 14]. Additionally, although results are validated in MG laboratories, as demonstrated in studies like [15], there is an urgent need to investigate how these results translate and validate in real operational scenarios outside the controlled laboratory environment. This approach would allow for more robust validation of proposed strategies and a deeper understanding of operational challenges in real networks and variable climate conditions [15; 16]. Finally, while methods such as MA filters and fuzzy logic-based control for power smoothing and grid stability have been explored, specific studies have not adapted and optimized these techniques for simultaneous integration into V2G systems in isolated MG by adjusting the ramp rate in real time. To overcome these challenges, this study presents an innovative adaptive strategy to improve the stability of isolated networks by integrating renewable PV generation and energy management using V2G technology (V2 GSUN method). The original contribution of this study lies in implementing an adaptive strategy that integrates PV energy, energy management, and V2G technology to stabilize isolated networks using an enhanced adaptive MA filter with fuzzy logic. This allows lithium-ion batteries in EVs to act as dynamic units for ESS and supply, leveraging their high energy density and rapid response capabilities.