## 4 Results and Discussion
### Performance Validation  
The training and testing analysis for the accumulated battery-data are performed in MATLAB software by accomplishing the BPNN algorithm. In this concern as shown in Figure 13, the overall regression for training, validation and testing is brought about 99.507%. Moreover, at the initial experiment, the actual SOC was calculated using Coulomb counting (CC) method. Figure 14 shows that though the initialization disparity of the estimated SOC is high relating to the actual SOC in consequence of the random accessed weights of BPNN algorithm, the inconsistency is minimized after some moments as a result of weight adjustment tactics. Along with this regard, Figure 15 indicates the RMSE (0.082%) of the estimated SOC. Table 1 shows an accuracy comparison of the proposed method for lead-acid battery (LAB) with other techniques, i.e., support vector machine for regression (SVR), Kalman filter (KF), dual extended Kalman filter--auto regressive exogenous (DEKF-ARX), particle swarm optimization (PSO) and Open Circuit Voltage (OCV) published in the literature. The table shows that the proposed model results in the least MSE. The other principle of the proposed BMS controller is to elongate the working-life of the battery storage.  
Figure 11: Experimental analysis for Day 4: 322 W/m\({}^{2}\), 21 \({}^{\circ}\)C.  
Figure 12: (**a**) Generation of AC voltage density; (**b**) Pure AC sine wave; (**c**) Modified AC sine wave production in Oscilloscope.  
Figure 10: Experimental analysis for Day 3: 372 W/m\({}^{2}\), 23 \({}^{\circ}\)C.  
Figure 14: Comparison between Actual and Estimation SOC.  
Figure 13: Training, Testing, and Validation results with regression.  
Figure 15: Root mean square error (RMSE) of the system.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Year** & **Ref.** & **Battery** & **SOC Algorithm** & **Error (\%)** \\ \hline
2015 & [36] & LAB & SVR & 0.95 \\
2016 & [37] & LAB & KF & 1.7 \\
2017 & [38] & LAB & DEKF-ARX & 4.58 \\
2018 & [39] & LAB & PSO & 3.46 \\
2019 & [40] & LAB & OCV & 3.78 \\
2019 & [41] & LIB & BPNN & 1.2 \\
2019 & [42] & LIB & BPNN & 1.15 \\
2020 & Proposed Model & LAB & BPNN & 0.082 \\ \hline \end{tabular}
\end{table}
Table 1: Comparison of SOC estimation accuracy.  
Conventionally, load conducts the battery energy supply for all day-night that diminishes the storage lifespan. The projected model monitors the operation of PV supply, load, and battery by maintaining the SOC in the safest range. Moreover, the battery is discharged when the PV supply is insufficient to support the load demand only that assists to achieve the aforementioned goal. By following this novel method, a comparison between the conventional and projected model of the battery-lifetime is shown in Figure 16, of which it can be observed that the proposed model enhance battery lifetime compared to the conventional model. The selected battery is able to afford the 5 W light for around seven hours. To validate the robustness of the proposed model, a comparison between simulated and experimented modified AC sine wave is conducted as shown in Figure 17 which reveals good agreement between the experimental and simulation results. The proposed approach is easy to implement for already installed and new PV systems. It can be also adopted in many applications of the flexible ac transmission system (FACTS) devices and wind energy conversion systems [43; 44; 45; 46; 47; 48; 49; 50; 51].