## 3 Results  
An off-grid household AC load profile from a previous publication [33] has been considered to compare the battery lifetime estimation of the PV-battery system. The average measured AC load was 3.61 kWh/day. The system is located in the Pyrenees mountains, in Aragon, Spain (latitude 42.772\({}^{\circ}\), longitude \(-\)0.334\({}^{\circ}\)) with an average outdoor annual temperature of 5.1 \({}^{\circ}\)C. For comparison, the same system is considered to be in a desertic place (Tinduf, Argelia, latitude 27.669\({}^{\circ}\), longitude \(-\)8.144\({}^{\circ}\)), with an average outdoor annual temperature of 23.1 \({}^{\circ}\)C.  
Different battery lifetime estimation models will be used. For lead-acid batteries:  
* Equivalent full cycles model;
* Rainflow cycle count model;
* [PERSON] et al. 's weighted Ah-throughput model. For LiFePO4 batteries:
* Equivalent full cycles model;
* [PERSON] et al. 's cycle aging model. [PERSON] et al. 's calendar aging model combined with [PERSON] et al. 's calendar model considered an \(I_{limit}\) of 5% of the battery bank's nominal capacity (that is, current at C-rate of 20 h, C20). The nominal voltages are 48 VDC and 230 VAC. The PV modules considered have a peak power of 100 W, 12 V nominal voltage, and short-circuit current of 6.79 A. In the Pyrenees, the PV generator is composed of four serial \(\times\) seven parallel PV modules (total 2800 W), while in Tindouf (higher irradiation) it is composed of four serial \(\times\) six parallel PV modules (total 2400 W). A loss factor of \(f_{PV\_loss}\) = 0.8 was considered. Two types of battery banks were considered for both locations. The battery bank size was selected, considering that about 2.5 days of autonomy are required. * The lead-acid battery bank, which consists of 24 \(\times\) 2 V OPzS [30] (flooded, tubular-plated, deep cycle) commercial batteries in serial, C\({}_{\rm N}\) = 270 Ah (total 12.96 kWh), 1258 equivalent full cycles (CF vs. DOD curve shown in Figure 4), float life of 20 years at 20 \({}^{\circ}\)C (manufacturer datasheet) and roundtrip efficiency of 85%. SOC to disconnect load (SOC\({}_{\rm min}\)) 20%. The parameters for the Schiffer model were the ones used in [30]. * Li-ion LFP battery consists of a commercial 48 V pack of C\({}_{\rm N}\) = 213.3 Ah (total 10.24 kWh), 5600 cycles at 80% DOD, 4022 equivalent full cycles, float life of 20 years at 20 \({}^{\circ}\)C (manufacturer datasheet does not show float life, but operating life of 20 years for stationary battery systems is usually considered [51]) and roundtrip efficiency of 90%. SOC\({}_{\rm min}\) is 10%. The nominal inverter power is 600 W, and its efficiency is shown in Figure 3.  
The annual average ambient temperature in the battery room in the Pyrenees location was estimated to be higher than the outdoor temperature. We considered two values as the average: 8 or 12 \({}^{\circ}\)C. In the desertic place of Tindouf, we considered that in the battery room, the average temperature can be similar to the average outdoor temperature, 23.1 \({}^{\circ}\)C.  
Considering [PERSON] law, corrected float life at the different temperatures considered are shown in Table 1.  
Table 3 shows the results of the simulation during a whole year for the two locations considered. It can be seen that the battery bank charge/discharge energy is very low (roughly 700 kWh/yr), which implies around 60 equivalent full cycles. The charge/discharge rates are very low, as is usual in PV-battery stand-alone systems: the average charge rate is roughly 4% of the battery's nominal capacity, while the average discharge rate is around 1%. The hourly simulation of a whole year is shown in Figure 5 (Pyrenees, lead-acid) and 6 (Tinduf, Li-ion). For Tindouf, the battery bank is almost all the time at SOC higher than 80% (Figure 6). For the Pyrenees, the battery bank is also most of the time at higher SOCs than 80%; however, in winter, there are periods with lower SOCs (Figure 5), reaching 30% during short periods.