## 3 Results
### Economic Optimum Systems of the Five Cases
#### 3.1.1 Components of the Economic Optimum Systems  
Table 6 shows the main technical characteristics of the economic optimum PV systems for the five cases: battery lifetime, battery capacity, and PV generator power. For each case, the first row shows the data of the optimum with lead-acid battery and the second row shows those of the optimum with Li-ion battery. Figure 4: Block diagrams: (**a**) PV systems; (**b**) hybrid systems. In both PV and hybrid systems, the choice of the type of battery affected their economic optimum, including not only the lifetime of the battery, but also its capacity and the size of the PV generator. In hybrid systems, it also affected their fuel consumption. Figure 5 shows the battery lifetimes of the optimum systems, both PV (a) and hybrid (b). In all cases, the Li-ion batteries presented a lifetime of 15 years, which corresponds to the design life specified by the manufacturer and, therefore, iHOGA took it as the maximum limit before its replacement. Despite having a longer design life, lead-acid batteries had a shorter lifetime, which differed in the five cases. As a result, the lifetime of Li-ion batteries was superior in all cases, from +18% to +113%. However, comparing the PV and hybrid systems for each case, the behavior was very similar. The cases in which lead-acid batteries had shorter lifetimes were the two homes and the pig farm. It is noteworthy that a change in the type of battery resulted in a different size of the components of the system, affecting both storage and generation, On the one hand, the Li-ion battery had a lower capacity than the lead-acid battery in all cases. Differences were between \(-7\%\) and \(-6\%\) in PV systems and between \(-21\%\) and \(-92\%\) in hybrid systems. Therefore, the variations in storage when the battery type changed showed similar behaviors in the optimal PV and hybrid systems, although they reached a greater magnitude in the latter. In this sense, it must be taken into account that in PV systems, the battery must be able to supply all nighttime consumption. This is a lower limit for the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Battery Type**} & **Battery Lifetime (Years)** & **Battery Capacity (kWh)** & **PV Field (kWp)** \\ \hline \multirow{2}{*}{Winery} & Lead-acid & 9.74 & 618.2 & 324 \\  & Li-ion & 15 & 384 & 351.2 \\ \hline \multirow{2}{*}{Irrigation pumping} & Lead-acid & 12.7 & 986.4 & 192.4 \\  & Li-ion & 15 & 322.5 & 359.2 \\ \hline \multirow{2}{*}{Pig farm} & Lead-acid & 9.5 & 1545.6 & 494 \\  & Li-ion & 15 & 998.4 & 671.2 \\ \hline \multirow{2}{*}{Single-family home} & Lead-acid & 7.79 & 65.8 & 18.4 \\  & Li-ion & 15 & 61.4 & 13.2 \\ \hline \multirow{2}{*}{Second home} & Lead-acid & 7.9 & 32.9 & 5.6 \\  & Li-ion & 15 & 15.3 & 6.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Main characteristics of the economic optimum PV systems. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Battery Type**} & **Battery Lifetime (Years)** & **Battery Capacity (kWh)** & **PV Field (kWp)** \\ \hline \multirow{2}{*}{Winery} & Lead-acid & 9.15 & 197.2 & 99.6 & 3963.4 \\  & Li-ion & 15 & 107.5 & 88.4 & 5280.1 \\ \hline \multirow{2}{*}{Irrigation pumping} & Lead-acid & 12.5 & 263 & 112 & 3200.3 \\  & Li-ion & 15 & 19.9 & 112 & 6640.1 \\ \hline \multirow{2}{*}{Pig farm} & Lead-acid & 7.34 & 540.9 & 232.8 & 5612.2 \\  & Li-ion & 15 & 430 & 222.4 & 6425 \\ \hline \multirow{2}{*}{Single-family home} & Lead-acid & 7.05 & 26.2 & 7.6 & 250.6 \\  & Li-ion & 15 & 15.3 & 7.6 & 333.6 \\ \hline \multirow{2}{*}{Second home} & Lead-acid & 8.03 & 5 & 4.4 & 64.7 \\  & Li-ion & 15 & 3.9 & 4.4 & 61.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Main characteristics of the economic optimum hybrid systems. battery capacity. In contrast, the presence of diesel generation makes that limit non-existent in hybrid systems, allowing more flexibility to use a smaller battery.