## 4 Results and Discussion
### Case 1: Comparison and Validation of the Proposal against Conventional R-R and MA Filters  
The experimental results are summarized in Figure 10, illustrating the emulated profiles of generated power (blue line), the Li-Ion BESS power (purple line), and the smoothed power output to the grid (red line). In Figure 10a, the smoothing response using the MA method is observed; in Figure 10b, the smoothing response using the R-R method with a fixed ramp-rate is depicted; and in Figure 10c, the smoothing response using the proposed R-R method with a variable ramp-rate through FLC is shown. Figure 11 provides an overview of the Li-Ion BESS's SoC behavior for each power smoothing methodology in this study. Figure 11 represents the SoC status with MA, R-R, V2 GSmooth, demonstrating satisfactory performance as the system maintained its operation within safe values (20-80%). This highlighted the effectiveness of the proposed method in this particular case.  
Figure 12 depicts the resulting smoothing factor, expressed as a variable percentage of the ramp-rate (%R-R), at the output of the FLC. A detailed analysis revealed proper alignment with the fuzzy rules established in Table 1 and illustrated in Figure 4. The graph in Figure 12 provides insight into how well the obtained smoothing factor adhered to the predefined fuzzy rules.  
Table 2 presents the results of various proposed methodologies for power smoothing, aiming to mitigate the variability of RES by applying a condition based on the initial SoC of the Li-Ion BESS. Each test began with a preset initial SoC at 50%. The generated energy was smoothed by implementing these methodologies, providing more or less energy depending on the SoC percentage within the specified range.  
Figure 9: Total power delivered to the isolated system by renewable energy sources.  
The results indicated that the enhanced R-R filter method through FLC achieved a variance reduction of 12.99%. The variance without Li-Ion was 8.84, while it decreased to 7.43 with Li-Ion. Furthermore, the method resulted in a marginal improvement in energy delivery, with an additional 0.13 kWh of energy injection compared to the case without Li-Ion. In exploring the V2G power smoothing strategies, we meticulously assessed three key methodologies. The MA method emerged as a standout performer, boasting a remarkably high Utilized Life Cycles of 2.803. This emphasized its commendable efficiency in adeptly mitigating temporal variations. Conversely, the R-R method demonstrated resilience to shifts in energy demand, showcasing a slightly lower helpful Utilized Life Cycles of 1.459, indicative of diminished battery wear.  
Figure 10: Power response results using V2G with Li-Ion BESS to PV and WP power fluctuations, employing: (**a**) MA filter, (**b**) R-R filter, and (**c**) R-R filter using FLC (proposed V2 GSmooth method).  
The introduction of V2 GSmooth, a modified version of R-R incorporating fuzzy logic, achieved a refined equilibrium, attaining a reduced Utilized Life Cycles of 1.369. These findings underscored the importance of choosing smoothing strategies that minimize the number of Utilized Life Cycles. This approach ensures enhanced durability and sustainable battery performance, highlighting a pivotal consideration in selecting effective V2G strategies.