## 3 Results and Discussions
### Hydrogen Tank  
Different methods have been reported for hydrogen storage as hydrogen hydrates, which have been compared in the bibliography with existing hydrogen storage technologies [47, 48]. This type of storage is useful when a large distance transport is required [49, 50]. However, for low-scale application and for single-entry production-consumption, the compressed hydrogen storage (CGH\({}_{2}\)) is the best choice. In this study, a typical mathematic method for the design of pressurized tanks has been used [51]. The main design basis is the conditions and amount of hydrogen to be stored (1.8 kg, as already mentioned). A commercial AEMWE, such as the ones commercialized, achieved the maximum hydrogen pressure conditions of 35 bars [52]. Hence, for the current study, the pressure and temperature conditions are fixed in 30 bars and 298 K. Due to this outlet pressure, a compressor is not required for this residential application. The tank volume is calculated by the equation of Mench [19, 51], which is defined as follows:  
\[\frac{\mathrm{P}}{\mathrm{n}^{3}}\cdot\mathrm{V}^{3}+\left(\text{-}\frac{ \mathrm{P}\cdot\mathrm{b}}{\mathrm{n}^{2}}\text{-}\frac{\mathrm{Ru}\cdot \mathrm{T}}{\mathrm{n}^{2}}\right)\cdot\mathrm{V}^{2}+\frac{\mathrm{a}}{ \mathrm{n}}\cdot\mathrm{V}\text{-}\mathrm{a}\cdot\mathrm{b}=0 \tag{3}\]  
where P is the pressure (3 \(\times\) 10\({}^{6}\) Pa), V is the tank volume (m\({}^{3}\)), n is the number of moles (900), Ru is the universal gas constant (8.314 J/mol K), T is the temperature (298 K), and a and b are constant calculated by Equations (4) and (5), respectively. \[\mathrm{a}=\frac{27}{64}\cdot\frac{\mathrm{R}_{\mathrm{a}}^{2}\cdot\mathrm{T}_ {\mathrm{c}}^{2}}{\mathrm{Pc}} \tag{4}\]  
Figure 7: Coupling Solartec SSW72 08 108 Wp PV module \(-\)50 cm\({}^{2}\) AEMWE developed in our lab. \[\text{b}=\frac{\text{Ru}}{8}.\frac{\text{Tc}}{\text{Pc}} \tag{5}\]  
where \(\text{Tc}\) is the critical temperature and \(\text{Pc}\) is the critical pressure of the hydrogen gas. The initial hydrogen conditions are collected in Table S2. All this allows calculating the tank volume achieving a theoretical value of 0.758 m\({}^{3}\). Considering an oversizing of 20%, a final volume of 0.91 m\({}^{3}\) is obtained for the hydrogen tank. Concerning the recipient material, carbon steel is the preferred one for indoor pressure equipment according to the ASME BPVC Section VIII code [53]. Future developments of new composite materials would increase the tensile strength above that of steel, although most of the reports use a wide range of steel types, e.g., stainless steel [54]. Then, the specific dimensions of the hydrogen tank are calculated using the Mijalev monogram (see Figure S7 in Supplementary Materials) [55], which shows two axes, reduced pressure (MPa) and tank volume (m\({}^{3}\)). Reduced pressure is estimated with Equation (6):  
\[\text{Pred}=\frac{\text{Pcal}}{10\cdot[\sigma]\cdot\text{C}} \tag{6}\]  
where \(\text{P}_{\text{red}}\) is the reduced pressure (MPa), \(\text{Pcal}\) is the calculation pressure (3.6 MPa), \([\sigma]\) is the permissible tension of carbon steel (107.1 MPa), and C is the overthickness by corrosion (0.002 m). These parameters are according to carbon steel material [52]. Once the tank volume (0.91 m\({}^{3}\)) and reduced pressure (1.6807 MPa) are calculated, the Mijalev monogram is used to know the optimal diameter, 0.7 m. As the tank is cylindrical, the height is calculated with the diameter and volume. The optimal dimensions are 2.4 m \(\times\) 0.7 m.  
As it is an indoor pressure tank, the shell is indispensable for the safety of the system [51].