## 4 Discussion  
The evaluation of the three methods--V2 GGlide (low-pass filter), V2 GSUN (moving average filter), and V2 GSmooth (ramp rate filter)--under varied SoC levels of the LI-ION BESS provides a comprehensive understanding of their applicability and performance in mitigating PV power variability. All methods demonstrated notable effectiveness in reducing power variance compared to the scenario without the LI-ION BESS, underscoring the critical role of energy storage systems in stabilizing renewable energy generation. Among the methods, V2 GGlide proved to be the most effective, achieving a variance reduction of 22.24% at high SoC levels (SoC \(>\) 80%), which highlights its superior ability to smooth out power fluctuations when ample storage capacity is available. This result reinforces the suitability of the low-pass filter for scenarios requiring a stable and reliable power output under high storage availability. In contrast, V2 GSUN exhibited moderate performance, with a variance reduction of 17.82% at low SoC levels (SoC \(<\) 20%), maintaining its effectiveness even under partial charge conditions. However, its performance slightly lagged behind V2 GGlide, particularly at lower SoC levels, emphasizing its sensitivity to the storage state. The V2 GSmooth filter demonstrated results similar to V2 GSUN but offered a slight advantage in energy delivery, particularly under medium and low SoC conditions, indicating its relatively consistent performance in scenarios with moderate power fluctuations. This highlights the recursive filter's potential as a balanced method for maintaining stable energy output while optimizing energy delivery. Across all methods, the improvement in energy delivery, particularly with V2 GGlide and V2 GSUN, reflects the active compensation of PV power variability, ensuring a smoother and more reliable supply to the grid. Additionally, the ability of all filters to keep the LI-ION BESS within the optimal SoC range (20-80%) reveals the significance of efficient SoC management to preserve battery longevity and maximize overall system effectiveness.  
The V2 GGlide method demonstrates superior performance in reducing variance at high state-of-charge (\(SOC_{LI}\)) levels compared to V2 GSUN and V2 GSmooth. This performance is mainly due to the implementation of a dynamic low-pass filter, whose smoothing factor (\(\alpha\)) is adjusted in real-time by a fuzzy logic system that considers the PV power (\(P_{PV}\)) and the lithium batteries' state-of-charge (\(SOC_{LI}\)). This dynamic adjustment allows the system to optimize the stability of the power output, mitigating rapid fluctuations and ensuring stable operation even in scenarios with high renewable energy penetration. As shown in the results (Table 3), the V2 GGlide achieves a variance reduction of 22.24% in the case of \(SOC_{LI}\) > 80%, significantly outperforming the other methods evaluated. This result highlights the fundamental role of the low-pass filter in improving system performance.  
The V2 GSmooth method stands out for its focus on mitigating power fluctuations through a power ramp control strategy. By employing predefined rules to limit oscillations, this method eliminates the need for real-time dynamic adjustments, simplifying its implementation while enhancing stability in networks with high renewable energy penetration. Moreover, its robust design effectively minimizes relative energy losses across all \(SOC_{LI}\) levels, even in scenarios where storage capacity is limited. These characteristics make V2 GSmooth a reliable and efficient approach for maintaining grid stability. Additionally, its features can be seamlessly integrated into other methodologies by combining them with dynamic systems, such as adaptive fuzzy logic controllers, to enhance further system flexibility and responsiveness under diverse and variable operating conditions.