## 4 Results and Discussion
### Analysis of Metrics for the Implementation of V2G with Power Smoothing Methods
#### 4.4.5 Coefficient of Variation  
The coefficient of variation (see Figure 15), which evaluates relative variability to the mean, also showed a general decrease with smoothing methods. Again, the ramp-rate method with a variable rate of change using fuzzy logic stood out by providing greater relative consistency in energy generation. In summary, the metrics analysis suggests that the V2 GSmooth method can be considered the most effective option for smoothing energy generation in the context of V2G. This method reduces variability, improves stability, and offers more consistent energy generation compared to the other evaluated methods. The innovative power smoothing technique proposed in this study, utilizing an enhanced version of the \"ramp-rate\" method with fuzzy logic control, demonstrates promising results in mitigating the impact of renewable energy fluctuations on the grid. Integrating electric vehicle batteries during charging, mainly through the V2G system, is a valuable resource in enhancing grid performance and stability. The experimental validation conducted in the Micro-Grid Laboratory at the University of Cuenca, Ecuador, showcases the effectiveness of the proposed method in a real-world isolated microgrid utility. The case studies presented in this paper provide a comprehensive evaluation of the proposed power smoothing enhancement under various operational conditions. The results highlight the method's adaptability to different SoC values of the Li-Ion BESS, demonstrating its effectiveness in maintaining the operation within safe SoC values (20-80%). The proposed method significantly reduces power variance, indicating its capability to smooth out fluctuations in renewable energy generation. Furthermore, the prioritization of the electric vehicle charging station (EVCS) in the second case study demonstrates the versatility of the proposed method in addressing specific operational objectives. The results indicate a substantial reduction in power variance and highlight the potential of the enhanced V2 GSmooth method in optimizing EVCS, achieving high power stabilization effectiveness while preserving an adequate SoC of EV batteries for future usage and overall system reliability. The comparative analysis with conventional power smoothing methods (MA and R-R) suggests that the proposed method balances power smoothing and energy delivery. While the MA and R-R methods outperform in energy delivery, the enhanced V2 GSmooth method provides a more stable power profile. The choice between these methods depends on the specific requirements and priorities of the renewable energy-electric vehicle system. Finally, the evaluation of various metrics, including standard deviation, crest factor, form factor, ripple index, and coefficient of variation, supports the superiority of the proposed method in smoothing energy generation within the context of V2G. The V2 GSmooth method consistently demonstrates a significant reduction in variability, improved stability, and more consistent energy generation compared to alternative methods. However, while our study has shed light on the immediate technical and operational benefits of implementing the V2G concept using BEV batteries, it is imperative to highlight the necessity of a more extensive and comprehensive examination. Specifically, a thorough investigation into the long-term effects of BEV aging and remuneration policies for EV owners is crucial. Successfully implementing any V2G strategy hinges on a deeper understanding of how these factors evolve over an extended period. Therefore, we strongly advocate for future research endeavors that delve into the multifaceted impacts of BEV aging and associated compensation policies, providing invaluable insight for the sustainable integration of V2G technologies.