## 3 Results
### SAPV System Case Study  
In order to evaluate the proposed design method, an installation located at the Energy Engineering Institute of the UPV [48] is considered for a typical demand of a house with a power demand of up to 4.6 kW. The most recent PVGIS irradiance data for the year 2020 have been taken. The parameters considered for this case study are shown in Table 2.  
The price of the regulator for the installation is not considered since a combined inverter with a regulator oriented to PV installations has been chosen for the study. Several of these inverters can work in parallel to support the power of the installation. The performance and other technical parameters, as well as the prices, have been obtained either from the technical datasheets of this equipment, from market analysis, directly from the distributor, or from documents from recognized institutions [49,50]. The power of the PV modules and the nominal capacity of the battery modules are used for the discretization of the results. The generator consumption has been estimated from the power produced and the fuel consumption at a 75% load. To determine the data to be entered into the reliability simulator and optimizer, a study has been carried out where data have been collected from four local distributors and one national distributor of photovoltaic modules and batteries for these systems. Data have been obtained for five of the ten largest capacity PV module manufacturers in the world [51]. In order to normalize the different technologies of each manufacturer and the nominal generation power of the panel, the price of each module has been normalized by dividing it by its nominal power and finding the weighted average of all the modules collected, for a total of 51 modules (Figure 14). An average price with a VAT of 0.488 EUR/Wp (0.403 EUR/Wp without VAT) has been obtained. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**InitialPglInstalled (W)** & **Initial Qb,max (Wh)** & **EndPgInstalled (W)** & **Final Qb,max (Wh)** & **Time(s)** & **Total iterations** \\ \hline
6050 & 10,000 & 6050 & 13,000 & 126.5 & 7 \\
9900 & 9500 & 6050 & 13,000 & 279.2 & 16 \\
11,000 & 20,000 & 6050 & 13,000 & 432.0 & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimization method comparison. Figure 13: Simulation time versus iterations of the optimization algorithm. A similar procedure has been followed for batteries. Currently, there are different battery technologies with different characteristics that are used for self-consumption systems. The main technologies are lead acid, AGM, GEL and lithium (LFP lithium steel phosphate), which are being introduced due to their progressive price reduction. Assessing the differences between different technologies [52] and given its stability in maintaining the charge and discharge voltage, its low maintenance, its suitability for deep cycle applications, and its progressive decrease in price, LFP technology has been chosen. The developed method also allows consideration of data for batteries from other technologies that could be used in the installation. The procedure followed was similar to the previous one, taking data from different distributors for the main lithium battery models, for a total of 120 items, obtaining an average price with a VAT of 0.597 EUR/Wh (0.493 EUR/Wh without VAT) (Figure 15).