## 3 Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Standard** & \multicolumn{2}{c}{**Pyrenees**} & **Tinduf** \\ \hline
**Average temperature (\({}^{\circ}\)C)** & **20** & **8** & **12** & **23.1** \\ \hline Battery float life (years) & 20 & 46.1 & 35.1 & 16.1 \\ \hline \hline \end{tabular}  
* Irradiation over the optimal slope (south orientation) for both locations is shown in Table 2.  
\end{table} 
Table 1: Float life at different temperatures considering Arrhenius law. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & **Jan.** & **Feb.** & **Mar.** & **Apr.** & **May** & **Jun.** & **Jul.** & **Aug.** & **Sep.** & **Oct.** & **Nov.** & **Dec.** \\ \hline Pyrenees, 65\({}^{\circ}\) slope & & & & & & & & & & & \\ irradiation & 3.31 & 2.69 & 3.92 & 4.71 & 4.76 & 4.49 & 5.03 & 5.17 & 4.93 & 3.87 & 3.68 & 3.87 \\ (kWh/m\({}^{2}\)/day) & & 6.75 & 7.54 & 7.7 & 7.41 & 7.36 & 7.02 & 6.65 & 6.5 & 6.64 & 5.85 & 7.07 & 6.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Monthly average irradiation data from Photovoltaic Geographical Information System (PVGIS) [52], year 2015. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Pyrenees**} & \multicolumn{2}{c}{**Tindouf**} \\ \hline
**Battery Type** & **Lead-acid** & **Li-ion** & **Lead-acid** & **Li-ion** \\ \hline Load (kWh/yr) & 1318 & 1318 & 1318 & 1318 & 1318 \\ PV generation (kWh/yr) & 2804 & 2804 & 3944 & 3944 \\ Battery charge/discharge energy & & 740 & 717 & 767 & 669 \\ (kWh/yr) & & 57.1 & 70 & 53.6 & 65.3 \\ Equivalent full cycles per year & 2261 & 2151 & 3102 & 2399 \\ Hours of battery discharge per year & 5757 & 5792 & 5050 & 5050 \\ Average charge rate (\% of C\({}_{\text{N}}\)) & 3.77 & 4.67 & 4.15 & 4.88 \\ Average discharge rate (\% of C\({}_{\text{N}}\)) & 0.97 & 1.23 & 1.03 & 1.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the simulation during a whole year for the different systems. Figure 5: \(Cont\). Figure 5: Hourly simulation of the Pyrenees—lead-acid battery: load (W) (**a**), PV generation (W) (**b**), battery bank discharge rate (% of Cn) (**c**), charge rate (% of Cn) (**d**) and state of charge (SOC) (%) (**e**). Figure 6: _Cont_. The estimated battery lifetimes obtained by the different models are shown in Table 4 (lead-acid) and Table 5 (Li-ion). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Eq. Full Cycles** & **Rainflow** & **Schiffer** & **Value Selected** \\ \hline Pyrenees 8 \({}^{\circ}\)C & 22.7 & 24.2 & 12.2 & 12.2 \\ Pyrenees 12 \({}^{\circ}\)C & 22.7 & 24.2 & 11.8 & 11.8 \\ Tinduf 23.1 \({}^{\circ}\)C & 23.0 & 26.8 & 4.8 & 4.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results. Battery lifetime estimation (years) for lead-acid batteries. Figure 6: Hourly simulation of Tindouf—Li-ion battery: load (W) (**a**), PV generation (W) (**b**), battery bank discharge rate (% of Cn) (**c**), charge rate (% of Cn) (**d**) and SOC (%) (**e**). For the Pyrenees and lead-acid batteries (Table 4), lifetime estimation using the equivalent full cycles model or rainflow model is higher than float life at 20\({}^{\circ}\) (20 years) but lower than expected float lifetime considering temperature (Table 1). For Tindouf and lead-acid, both models obtained values much higher than the expected float life. However, the more accurate Schiffer model obtained values much lower than the expected float life, and these results are the selected ones (marked in green in Table 4). For the Pyrenees and Li-ion batteries (Table 5), all the models obtained values much higher than the float life at the average temperature considered. The selected values are 20 years, marked in green in Table 4, as it is the value usually considered for stationary battery systems, although at low temperatures than 20 \({}^{\circ}\)C higher lifetimes could be achieved [51]. For Tindouf and Li-ion, the equivalent full cycles model and Groot model obtained overestimated values, as they do not consider the calendar aging.