# Mathematics-Driven Analysis of Offshore Green Hydrogen Stations
## 4 Discussion  
This section discusses and justifies the proposed mathematics-based technical model used to model a green hydrogen production station powered by solar energy. To this end, a series of simulations and multivariable parametric analyses have been carried out to evaluate the model's output behavior as a function of its input configuration parameters. From a logical standpoint, as detailed in the high-level flow diagram shown in Figure 2 and in each of its associated phases, the model can predict the solar trajectory based on the station's geographic location, the day of the year, and the local time (Figure 10). Subsequently,the model estimates the total solar radiation, \(I_{n\_total}\), received on the photovoltaic panels' surface, considering the date and local time, the sun's position and path, the geographic and physical orientation of the photovoltaic panels used to power the hydrogen station, and the atmospheric attenuation experienced by solar radiation before reaching the Earth's surface (Figure 11). Finally, and equally important, the influence of the configuration parameters on the green hydrogen production rate at the station's output is also analyzed. This output is expressed as \(\frac{\mathrm{mol}_{\mathrm{H_{2}}}}{\mathrm{s}\times\mathrm{m}^{2}}\), along with the required photovoltaic panel surface area (m\({}^{2}\)) to produce \(1\)\(\frac{\mathrm{mol}_{\mathrm{H_{2}}}}{\mathrm{s}}\) of hydrogen. The equivalent hydrogen production values, expressed in \(\frac{\mathrm{kg}_{\mathrm{H_{2}}}}{\mathrm{s}\times\mathrm{m}^{2}}\) and \(\frac{\mathrm{kg}_{\mathrm{H_{2}}}}{\mathrm{s}}\), can be directly obtained by applying the expression (Equation (44)).  
It is important to emphasize that the selection of parameter values will depend entirely on the specific case study being addressed. These values may be fixed or variable, measured or estimated, and may represent average, maximum, and/or minimum conditions--used to model input uncertainty and to analyze its impact on the output of the technical model representing the green hydrogen station powered by solar energy. In any case, for a given green hydrogen production requirement, the primary objective will be to minimize the surface area of the photovoltaic panels required to meet that demand. Logically, a smaller photovoltaic surface area simplifies the design and reduces the amount of material needed for the construction of the mechanical support structure--whether floating or fixed. A smaller panel surface area also proportionally decreases the forces exerted by wind and  
Figure 11: Contribution of air quality levels to \(I_{n\_total}\) due to the atmospheric attenuation: \(I_{n\_total}\). (**a**) hours–day, (**b**) days–year.  
Figure 10: Solar analemmas calculated by the mathematics-based technical model, considering the green hydrogen station is located in Santón.  
waves on the structure. As a result, a more compact station with reduced external loads facilitates simpler installation and anchoring processes while also decreasing the total amount and surface exposure of materials in contact with seawater. This, in turn, inevitably contributes to a reduction in the Levelized Cost of Electricity (LCOE) [19; 25], as it simplifies the installation, operation, and maintenance processes of the entire system.