## 4 Discussion  
Considering the typical PV-battery standalone systems, with large battery banks with enough energy to supply more than 2 days of autonomy (in many cases 3 or 4 days, or even more), the charge/discharge rates were very low, typically around C20 (current in A roughly 5% of the nominal capacity in Ah). In these cases, for lead-acid batteries, the equivalent full cycles model or the rainflow cycle counting model overestimated the battery lifetime, being necessary to use [PERSON] et al. 's [30] model, obtaining in the case studied a lifetime of roughly 12 years for the Pyrenees and 5 years for Tindouf. Using Li-ion batteries, models that just consider cycle aging are not correct--it is necessary to consider both cycle and calendar aging, as the model of [PERSON] et al. [43] combined with the calendar aging model of [PERSON] et al. does [44]. For the studied standalone PV-battery system with Li-ion batteries and low temperatures (much lower than 20 \({}^{\circ}\)C), the typical value of 20 years for stationary battery systems can be considered as the battery lifetime. However, if the average temperature is higher than 20 \({}^{\circ}\)C (as in Tindouf), the battery life is significantly reduced to 13.7 years. Summarizing, comparing a similar battery bank size in a PV-battery standalone system, the LiFePO\({}_{4}\) battery life is expected to be around two times the OpzS lead-acid one. As the LiFePO\({}_{4}\) battery cost at the end of 2020 can be around two times the OpzS cost, this means that economically LiFePO\({}_{4}\) batteries can be competitive with the OpzS technology. Considering the expected reduction in Li-ion battery cost, we can expect that Li-ion batteries will be widely installed in PV-battery standalone systems in a few years. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Eq. Full Cycles** & **Groot** & **Wang + Petit** & **Value Selected** \\ \hline Pyrenees 8 \({}^{\circ}\)C & 67.2 & 162.1 & 66.5 & 20 \\ Pyrenees 12 \({}^{\circ}\)C & 67.2 & 141.1 & 41.4 & 20 \\ Tinduf 23.1 \({}^{\circ}\)C & 68.9 & 118.2 & 13.7 & 13.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results. Battery lifetime estimation (years) for Li-ion batteries. **Author Contributions:** Conceptualization, R.D.-L.; methodology, R.D.-L. and T.C.-A. ; software, R.D.-L.; validation, J.S.A.-S., T.C.-A. and R.D.-L.; formal analysis, J.L.B.-A. and R.D.-L.; investigation, R.D.-L. and T.C.-A. ; resources, J.S.A.-S. and J.L.B.-A. ; data curation, T.C.-A. and R.D.-L.; writing--original draft preparation, R.D.-L. and T.C.-A. ; writing--review and editing, J.S.A.-S., R.D.-L. and J.L.B.-A. ; visualization, R.D.-L. and T.C.-A. ; supervision, R.D.-L. and J.L.B.-A. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported by the Universidad de Zaragoza programme \"Proyectos de investigacion-proyectos puente-convocatoria 2019\", project \"Modelos de envejecimiento de baterias de litio para suplicacion en simulacion y optimizacion de sistemas aislados de la red electrica\" [grant number: UZ2020-TEC03]. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Data available on request. **Conflicts of Interest:** The authors declare no conflict of interest. **Abbreviations**