## 3 Results
### Power Smoothing Evaluation Using the Low-Pass Filter (V2 GGlide) Under Varied SoC Conditions  
Figure 8 presents the response of the LI-ION BESS when applying the low-pass filter (V2 GGlide) under three different SoC conditions (see Figure 9). The results demonstrate how the PV power fluctuations (blue line) are mitigated by the LI-ION BESS power response (yellow line) to produce a smooth output to the grid (red line). The analysis considers three scenarios: Case 1 (SoC \(\approx\) 90%), Case 2 (SoC \(\approx\) 50%), and Case 3 (SoC \(<\) 20%). Figure 8: Results of response of LI-ION BESS to input PV power fluctuations \(P_{PV}\) with LP (V2 GGlide) filter and its compensated PV solar power response \(P_{PVC}\). (**a**) case 1, (**b**) case 2, and (**c**) case 3. In Case 1, with the LI-ION BESS, charged to a high level (above 80%), the smoothing capability is most effective. The system absorbs significant power fluctuations without considerable impact on the output. The red line, representing the smoothed power, closely matches the variations in PV power, achieving near-optimal performance with minimal oscillations. In Case 2, where the SoC is around 50%, the system continues to perform well in compensating for power fluctuations. However, minor variations appear more visible in the smoothed output due to the intermediate storage capacity of the LI-ION BESS. Although the filter remains efficient, the system's ability to absorb larger fluctuations is slightly reduced, resulting in minor oscillations in the output. In Case 3, with the SoC below 20%, the smoothing capability is significantly limited. At this low charge level, the LI-ION BESS struggles to handle substantial power variations. This limitation is reflected in the increased variability of the smoothed output (red line). The system's response becomes less effective, as the LI-ION BESS cannot absorb fluctuations without engaging in deep discharges, which amplifies the presence of pronounced oscillations in the output. Table 3 presents the results obtained using the V2 GGlide filter, which reduces PV power generation variability through power smoothing under three different SoC levels of the LI-ION BESS. The results show a significant reduction in power variability, evidenced by a decrease in variance across all evaluated cases:  
* **Case 1 (SoC > 80%)**: The filter achieves a 22.24% reduction in variance, decreasing from 15.69 without the LI-ION BESS to 12.20 with the LI-ION BESS. This result demonstrates that when the LI-ION BESS is fully charged, the system efficiently smooths PV power fluctuations, delivering a more stable output to the grid. Additionally, there is a slight improvement in energy delivery to the system, with a difference of 0.27 kWh between the scenarios with and without the LI-ION BESS. Figure 9: Response of LI-ION BESS to LP (V2 GGlide) filter under its three \(SoC_{LI}\), conditions: Case 1 with \(SoC_{LI}\) around 90%, Case 2 with \(SoC_{LI}\) around 50%, and Case 3 with \(SoC_{LI}\) lower than 20%. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} [\%]\(SoC_{SC}\) \\ **Initial** \\ \end{tabular} } & \begin{tabular}{c} **Variance** \\ **Without** \\ **LI-ION BESS** \\ \end{tabular} & \begin{tabular}{c} **Variance with** \\ **LI-ION BESS** \\ \end{tabular} & \begin{tabular}{c} **PV Energy** \\ **Variance** \\ **Reduction [\%]** \\ \end{tabular} & \begin{tabular}{c} **Delivered** \\ **Without LI-ION** \\ **BESS [kWh]** \\ \end{tabular} & \
\begin{tabular}{c} **Delivered** \\ **Compensated** \\ **PV Energy** \\ **with LI-ION** \\ **BESS [kWh]** \\ \end{tabular} &
\begin{tabular}{c} **Utilized** \\ **Life Cycles** \\ **Life Cycles** \\ \end{tabular} \\ \hline \(SoC_{SC}>80\) & 15.69 & 12.20 & 22.24 & 8.49 & 8.22 & 2.63 \\ \(SoC_{SC}=50\) & 15.76 & 12.31 & 21.89 & 8.48 & 8.28 & 2.64 \\ \(SoC_{SC}<20\) & 15.78 & 12.98 & 17.74 & 8.48 & 8.36 & 2.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of PV power output with and without LP (V2 GGlide) filter for power smoothing.