## 3 Results and Discussions
### Photovoltaic Panel  
The preliminary design of the solar PV array is based on PV-SYST 7.0, which is one useful software for the design of photovoltaic system anywhere in the market [20]. It allows defining an independent system or a general electric grid. In this work, the system is independent, since it is a one-family house, which must be electrically isolated. Figure 2: Flowchart of design. The electrical charge (shown in Figure 1) was introduced in the software for the initial calculation of the number of PV modules and the energy storage system in chemical form with a battery. The type of PV module is chosen from a list provided by the software, considering the maximum current of the module and the electrolyzer [26]. Hence, taking into account that the maximum current point of the electrolyzer is 4 A, according to the experimental polarization curve obtained in our group, the selected PV is the model Solartec SST72 110 24 106W module with a maximum current of 3.3 A. In agreement with this, the PV module to choose would have a maximum current point (I\({}_{\text{MPP}}\)) lower than 4 A. This PV selected module is based on mono-crystalline silicon (c-Si), which is the most common ones with standard dimensions of 1303 \(\times\) 666 mm [24; 25]. The I-V characteristic curves for the selected module at different solar radiation levels are also displayed by the software as shown in Figure S2 of the Supplementary Materials. On the other hand, the battery system should also be considered at this time. According to the design basis of 4 consecutive days without any PV production and the electrical energy charges of our case of study, a battery with a power capacity higher than 30.54 kWh must be selected. In this case, from the list provided by the software, the selected battery is one with 32.3 kWh of power capacity. The model is Cell HTCFR26650-3800 mAh-3.2V. The capacity is 749 Ah, and the voltage is 48 V. Note that the software warns if the battery is appropriate or not for the application. Once the specific types of PV module and battery are chosen, the number of PV modules displayed in series in the solar PV array is introduced in the PV-SYST 7.0 software following an optimization procedure, as described below. In this case, the aim is to find the minimum number of PV modules that allows providing enough electrical energy for all the days of January to avoid the energy running out with the combined photovoltaic-battery system. This optimization procedure is performed according to the curves displayed by the software, which shows the electrical power demand covered by the system and the loss of energy associated with the fully charged battery (Figure 3). In this case, special attention should be paid to find the lowest number of PV modules, which avoids the loss of power demand (green line, secondary axis of Figure 3) for different temporal horizons. This optimization has started with sixteen PV modules in series (Figure 3a). In this case, it can be observed that for the temporal horizon of one day (1 st January), the system can self-supply the house, and the battery is not full, since a loss of energy is not shown in the graph. On the other hand, as can be observed from Figure 3b, keeping this number of PV modules, the electrical energy demand of the house for a whole week is not covered (the first week of January). Hence, on the seventh day, the house does not receive any electricity, since the battery has not received enough energy to be used later. Therefore, the number of PV modules should be increased to completely charge the battery for its further use. In this sense, the optimization continues with twenty-two PV modules. In this case (as can be observed in Figure 3c), the electrical demand is fully covered for self- supporting the house for the first week, but it seems not to be enough for the second one, since the power demands fall to zero after the ninth day (as shown in the Figure 3d).