## 1 Introduction
Furthermore, while active SoC management strategies are essential for extending battery lifespan and improving power quality, most studies [12; 14] evaluate these methods in simplified or idealized scenarios, overlooking the severe fluctuations and high penetration of PV energy typical of weak grids. Finally, although hybrid storage components have been increasingly integrated into energy systems [4], their deployment remains limited due to the absence of experimental validation that reflects real-world grid dynamics and operational complexities. This paper directly addresses these gaps by developing and experimentally validating three advanced power smoothing methods--V2 GGlide, V2 GSUN, and V2 GSmooth--optimized with fuzzy logic and designed explicitly for weak low-voltage grids with high renewable penetration. Unlike previous studies, these methods are systematically compared under varying SoC conditions, revealing their relative strengths and limitations in addressing power fluctuations and grid instability. The proposed approach also introduces an innovative strategy for active SoC management in hybrid energy storage systems, ensuring consistent energy quality, maximizing battery lifespan, and optimizing energy utilization across different operating scenarios. Furthermore, the methods are validatedexperimentally in a low-voltage microgrid laboratory connected to a public distribution network, demonstrating their practical feasibility and scalability. This validation bridges the gap between theoretical advancements and real-world implementation, offering a robust framework for enhancing grid reliability and renewable energy integration. The contributions of this paper extend beyond theoretical development, addressing critical challenges in energy management and system optimization. By providing a comprehensive comparative analysis of power smoothing methods, introducing a novel SoC management strategy, and validating these approaches under realistic conditions, the study documented in this paper establishes a practical foundation for deploying V2G systems in weak grids with high PV penetration. These contributions pave the way for more reliable, sustainable, and scalable integration of renewable energy into modern power networks. The remainder of this paper is organized as follows: Section 2 describes the materials and methods, including the system configuration, the fuzzy logic-based smoothing methods (V2 GGlide, V2 GSUN, and V2 GSmooth), and the modeling of membership functions for the lithium-ion battery energy storage system (LI-ION BESS). Section 3 presents the results, analyzing the performance of each smoothing method under three SoC conditions--high, medium, and low--using key metrics such as variance reduction, standard deviation, and energy delivery. Section 4 provides a detailed discussion of the results, highlighting the comparative performance of the methods, their dependence on SoC levels, and their implications for grid stability and battery management. Additionally, the limitations of the proposed approach and potential areas for future work are discussed. Section 5 concludes the paper by summarizing the main findings, emphasizing the effectiveness of the proposed methods, and outlining recommendations for improving power smoothing strategies in weak low-voltage networks.