## 4 Data Analysis and Interpretation
### Study Scenario 1: Li-Ion Storage System with Moderate SoC Level
This underscores the ability of the proposed method to enhance grid stability by effectively managing power fluctuations. Figure 11: Implementation of the proposed “V2 GSUN” algorithm for V2G to mitigate PV intermittence: (**a**) GD power, (**b**) PV power compensated with Psc, (**c**) generator frequency, and (**d**) generator line voltages. In this analysis, we began by calculating the variance for each method: the base case variance (Equation (2)), the moving average method variance (Equation (3)), the ramp-rate method variance (Equation (4)), and the V2 GSUN method variance (Equation (5)). Then, these variance values were grouped into a variance vector (Equation (6)). Finally, the percentage reduction in variance relative to the base case variance was calculated (Equation (7)). \[Var_{cb} =Var\left(f_{GD}^{cb}\right) \tag{2}\] \[Var_{MA} =Var\left(f_{GD}^{MA}\right)\] (3) \[Var_{RR} =Var\left(f_{GD}^{RR}\right)\] (4) \[Var_{V2 GSUN} =Var\left(f_{GD}^{V2 GSUN}\right)\] (5) \[Variances =\left[Var_{cb}\text{, }Var_{MA}\text{, }Var_{RR}\text{, }Var_{V2 GSUN}\right]\] (6) Figure 9:0  
In studies related to V2G, it is common practice to examine the behavior of the SoC of the batteries to monitor their usage while implementing any control technique. Hence, the behavior of the Li-Ion BESS's state of charge for each power smoothing methodology is summarized in Figure 9:1 The black line color depicts the SoC state using the MA method, green shows the SoC response with the R-R method, and brown illustrates the SoC response to the MA method integrated with FLC (V2 GSUN). The V2 GSUN method performs satisfactorily by keeping the storage system operation within safe limits, which is crucial for prolonging the battery lifespan and ensuring efficient energy management. Figure 14 presents the resulting smoothing factor, indicated by the time window size WS generated by the FLC. An in-depth analysis shows its compliance with the fuzzy rules outlined in Figure 9:2 The graph in Figure 14 offers insights into the alignment between the  
Figure 9:3 Indicators of frequency variability reduction achieved in each case of study: MA filter using FLC (proposed V2 GSUN method), R-R filter, MA filter, and case base. Figure 9:4 The behavior of Li-Ion BESS’s SoC by implementing diferent V2G power smoothing approaches: MA filter, RR filter, and MA filter using FLC (V2 GSUN). achieved smoothing factor and the predefined fuzzy rules. This alignment ensures that the dynamic adjustments made by the FLC are consistent with the desired smoothing objectives, leading to optimal power smoothing and enhanced grid stability. The real-time adjustment feature of the V2 GSUN algorithm facilitates a responsive and adaptive approach to alleviate PV power fluctuations, further validating its applicability in real-world scenarios. Table 2 summarizes the results from various methodologies proposed for mitigating variability in renewable energy sources (RES) by considering the initial SoC conditions of the storage system. Each laboratory test started with an initial SoC set at 50%. These techniques successfully smoothed renewable power generation by adjusting the output according to the SoC percentage within the designated range. The findings reveal that using the proposed V2 GSUN method decreased variance by 19.43%, from 15.6% without Li-Ion integration to 12.58% with it. Table 3 shows that the V2 GSUN method improves the variance of the grid frequency provided by the GD from the baseline case, reducing it from 1.5617 to 1.3782. This implementation of V2 GSUN results in an improvement of 11.75%.