## 3 Results
### Power Smoothing Evaluation Using the Ramp Rate (V2 GSmooth) Filter Under Varied SoC Conditions  
Figure 6 illustrates the profiles for PV power (blue line), stored power in the LI-ION BESS (yellow line), and the smoothed power delivered to the grid (red line) using the ramp rate (V2 GSmooth) filter under three distinct SoC conditions for the LI-ION BESS. * **Case 1 (SoC \(\approx\) 90%):** At a high SoC, the LI-ION BESS is fully charged and effectively compensates for PV power fluctuations. The smoothed power demonstrates exceptional stability, closely following the desired ramp rate. The system operates efficiently, achieving a significant reduction in variability while maintaining grid stability. * **Case 2 (SoC \(\approx\) 50%):** With a mid-range SoC, the smoothing performance remains effective but shows slightly more significant power variations compared to Case 1. The intermediate storage capacity limits the system's ability to fully compensate for abrupt fluctuations, resulting in a less stable output profile. Figure 6: Results of response of LI-ION BESS to input PV power fluctuations \(\mathbf{P_{PV}}\) with RR (V2 GSmooth) filter and its compensated PV solar power response \(\mathbf{P_{PVC}}\). (**a**) Case 1, (**b**) Case 2 and (**c**) Case 3. * **Case 3 (SoC < 20%):** At a low SoC, the effectiveness of the V2 GSmooth filter diminishes considerably. The energy available in the LI-ION BESS is insufficient to absorb the full extent of PV power variations, leading to greater variability in the smoothed power output. The system struggles to adhere to the defined ramp rate, highlighting the limitations of energy storage under deep discharge conditions. Complementarily, Figure 7 shows the behavior of the LI-ION BESS SoC in each of the studied cases, confirming that the system operates within a safe charge range (between 20% and 80%). Maintaining this range is essential to ensure the system's longevity and operational efficiency. These results emphasize the effectiveness of the ramp rate (V2 GSmooth) filter in reducing PV power fluctuations. However, its performance declines as the SoC of the LI-ION BESS decreases. Despite this limitation, the system continues to perform well in compensating for power variations, particularly when the storage operates at higher charge levels. Table 2 presents the results obtained by applying the ramp rate (V2 GSmooth) filter for power smoothing under three different initial SoC conditions of the LI-ION BESS. * **Case 1 (SoC > 80%):** The filter achieves a reduction in the variability of PV power generation, with the variance decreasing from 15.81 to 13.23, representing a 16.32% reduction. The energy delivered to the grid without the LI-ION BESS is 8.49 kWh, while with the LI-ION BESS, it is 8.36 kWh, indicating a slight difference of 0.14 kWh. This result suggests that at high SoC levels, the system efficiently compensates for fluctuations, albeit with a minor reduction in the total energy delivered. * **Case 2 (SoC \(\approx\) 50%):** The filter shows an even more significant reduction in variability, with the variance decreasing from 15.74 to 13.03, representing a 17.22% improvement. The energy delivered to the grid without the LI-ION BESS is 8.47 kWh, while with the LI-ION BESS, it is 8.43 kWh, showing a negligible difference of 0.04 kWh. This indicates that the system remains effective in smoothing fluctuations, with minimal energy loss when operating at intermediate SoC levels.