## 4 Discussion
### Climatological Year  
First, the variation in the optimal system will be verified depending on the year used in the climatology data extracted from the PVGIS database. It is carried out for the records from 2015 to 2019, comparing them with the previous results for the year 2020 (Table 4). In all of them, the installation presents the same characteristics, and it is assumed that the market prices are the same. It can be seen in Figure 16 that there are differences in the results. Although the ideal battery capacity is not affected, the necessary installed power does vary by up to 2750 W in the discretized calculations (corresponding to five modules). The interpretation of this may be due to a greater or lesser concentration of days of low PV production (cloudy or rainy days) at times of the year with lower irradiance. With the same energy storage capacity, it is possible to supply the demand in this period. A greater frequency of these low PV production days implies greater installed PV power to be able to store enough energy. Figure 15: Quantity of battery models per normalized price range. \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Iterative Heuristic Algorithm** & **Continuous PSO Algorithm** & **Discretized PSO** \\ \hline Installed power (W) & 9900 & 9525 & 9900 \\ \hline Battery capacity (Wh) & 17,760 & 17,668 & 17,760 \\ \hline Reliability (\%) & 93.78 & 93.65 & 93.65 \\ \hline Approximate annual cost (EUR/year) & 1828.24 & 1825.99 & 1828.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the design optimization of the SAPV system for 2020 climatological data. Taking information from AEMET [53], the reason for these variations can be analyzed from the data represented in Figures 17 and 18. The data have been taken from the datosclima.es website (accessed on 10 October 2023), which obtains the data directly from the AEMET OpenData API ([[https://www.aemet.es/en/datos_abiertos/AEMET_OpenData](https://www.aemet.es/en/datos_abiertos/AEMET_OpenData)]([https://www.aemet.es/en/datos_abiertos/AEMET_OpenData](https://www.aemet.es/en/datos_abiertos/AEMET_OpenData))) (accessed on 10 October 2023), which has national climatological data records available to any user. The data have been taken for the closest weather station to the location of the SAPV installation (Table 5). It can be seen that 2016 is the year with the fewest hours of sunshine among those analyzed. This, although not conclusive, gives clues as to why this is the year that presents an optimal system with greater power compared to the rest, although it disagrees with the fact that 2017 is the year with the highest installed power, being one of the years that more solar hours were accumulated. Next, if we pay attention to the distribution of solar hours in Figure 18, a prolonged period of lower radiation is observed in both, which explains this fact. In both years, there is a prolonged period of lower solar incidence, with brief peaks that are in line with the average for the time. This temporary distribution explains the profitability of a greater installed capacity to cover the cost of fuel consumption in those specific periods. In the case of having the calculations for all the years, the solution for 2016 would be the one to apply; however, the system provided in 2020 is a compromise solution between all of them. Another solution would be to take the data for the TMY in PVGIS and convert them to the desired inclined plane, although this solution would also give an averaged system. Comparing the optimal system for each year with the meteorological data of 2016, these being the most critical among those analyzed, the reliability parameters obtained are shown in Table 6.