## 3 Results
### Power Smoothing Evaluation Using the Mean Average (V2 GSUN) Filter Under Vari SoC Conditions  
Figure 4 illustrates the response of the LI-ION BESS to PV power fluctuations using the MA (V2 GSUN) filter across three SoC conditions:  
* **Case 1 (SoC > 80%):** With the LI-ION BESS fully charged, the smoothed power (red line) closely follows the PV power fluctuations (blue line), showing a significant reduction in the variations of power delivered to the grid. Meanwhile, the LI-ION BESS power (yellow line) efficiently adjusts to compensate for these fluctuations, resulting in highly effective smoothing. * **Case 2 (SoC \(\approx\) 50%):** With a mid-range SoC, the smoothing capacity remains effective; however, more pronounced fluctuations appear due to storage limitations. This leads to a slower response in compensating for power peaks, which is slightly less effective than in Case 1. * **Case 3 (SoC < 20%):** With a low SoC, the LI-ION BESS lacks sufficient energy to absorb all fluctuations. As a result, the smoothed power (red line) exhibits larger variations, reflecting the system's difficulty in compensating for PV power variability. Figure 5 highlights the variability in the SoC of the LI-ION BESS across the three different SoC conditions:  
* **Case 1 (SoC > 80%):** The LI-ION BESS maintains a high SoC, ensuring ample capacity to absorb PV power fluctuations. This results in highly efficient and stable power smoothing with minimal SoC variability, indicating optimal system operation. Figure 4: Results of response of LI-ION BESS to input PV power fluctuations \(P_{PV}\) with MA (V2 GSUN) filter and its compensated PV solar power response \(P_{PVC}\). **(a)** Case 1, **(b)** Case 2, and **(c)** Case 3. * **Case 2 (SoC \(\approx\) 50%):** The SoC exhibits more pronounced fluctuations due to the charging and discharging demands required to balance PV power variations. While the smoothing remains effective, the compensation capacity is slightly reduced, resulting in less stable behavior compared to Case 1. * **Case 3 (SoC < 20%):** With the SoC dropping below 20%, the LI-ION BESS's ability to absorb fluctuations without deep discharges is significantly limited. This leads to greater SoC variability and less effective smoothing of PV power fluctuations. Table 1 presents the results of power smoothing using the MA (V2 GSUN) filter under three different SoC conditions for the LI-ION BESS. * **Case 1:** When the initial SoC of the LI-ION BESS is above 80%, the V2 GSUN filter achieves a significant reduction in PV power variability, decreasing the variance by 4.4%. Without the LI-ION BESS, the variance of PV power is 15.70, but with the LI-ION BESS, it is reduced to 13.44, indicating efficient fluctuation compensation. Additionally, the MA filter delivers 0.27 kWh more energy to the system compared to the scenario without the LI-ION BESS. However, the total energy delivered (8.15 kWh) is slightly lower than in the case without the LI-ION BESS (8.42 kWh). * **Case 2:** At an intermediate SoC (approximately 50%), the filter remains effective but less so than in the previous case. The variance without the LI-ION BESS is 15.83, and with the LI-ION BESS, it reduces to 13.58, indicating a reduction in power delivered fluctuations, although the fluctuations are more noticeable than in Case 1. The energy difference is 0.26 kWh more with the LI-ION BESS, but the total energy delivered (8.23 kWh) remains slightly lower compared to the scenario without the LI-ION BESS (8.49 kWh). * **Case 3:** When the SoC of the LI-ION BESS is low (below 20%), the filter still reduces the variance, but with reduced effectiveness due to storage limitations. The variance without the LI-ION BESS is 15.45, and with the LI-ION BESS, it decreases to 12.99. This suggests that the system is still able to smooth some fluctuations, albeit less efficiently. In terms of energy delivered, the LI-ION BESS provides 0.14 kWh more to the