# Mathematics-Driven Analysis of Offshore Green Hydrogen Stations
## 3 Results  
As part of the results presented in this paper, the previously described mathematics-based technical model is adapted and applied to a case study involving a green hydrogen production station powered by solar energy, intended to be installed in the town of Santona (Cantabria, Spain). This site is an ideal location for testing marine energy prototypes due to several key characteristics. Firstly, its location on the Cantabrian coast provides direct access to the open sea (Figure 4). Secondly, the Santona Bay, covering an area of 28 km\({}^{2}\), offers a protected yet representative environment for conducting initial testing [42]. Lastly, the presence of the \"Parque Natural de las Marismas de Santona y Noja\" highlights the importance of developing environmentally friendly energy technologies in the region [44]. With the objective of calculating the average level of \(I_{n\_total}\) received on the photovoltaic panels, the following model parameters are configured and summarized in Table 2: location, time definition, atmospheric and marine conditions, and photovoltaic panels input parameters. Once these input parameters are configured and the technical model is executed in Python, the results include the estimations of the following variables: \(\frac{\text{mol}_{\text{H}_{2}}}{\text{s}\times\text{m}^{2}}\) (Equation (43)), \(\frac{\text{kg}_{\text{H}_{2}}}{\text{s}\times\text{m}^{2}}\) (Equation (44)), and \(\frac{\text{h}_{\text{H}_{2}0}}{\text{s}\times\text{m}^{2}}\) (Equation (45)), as well as the photovoltaic panel surface area required for the production of 1 \(\frac{\text{mol}_{\text{H}_{2}}}{\text{s}}\) (Equation (46)) and 1 \(\frac{\text{kg}_{\text{H}_{2}}}{\text{s}}\) (Equation (47)), and the consumption of 1 \(\frac{\text{h}_{\text{H}_{2}0}}{\text{s}}\) (Equation (48)). Figure 5 presents the average value of \(I_{n\_total}\) (Equation (27)), calculated for all hours of the day (a) and for all days of the year (b). Using the average value simplifies the analysis and sizing of the station, allowing it to be conducted from a statistical perspective. However, the technical model of the station also enables the calculation of the estimated natural values of \(I_{n\_total}\) for each hour of the day and each day of the year. Figure 5a illustrates that the average levels of \(I_{n\_total}\) are equal to 0 during the hours of the day when \(\alpha_{solar\_elevation}\) (Equation (8)) is either 0 or negative and greater than 0 when \(\alpha_{solar\_elevation}\) is positive. The maximum value is reached when \(\alpha_{solar\_elevation}\) is also at its highest within the same day. This occurs at 12 p.m. local time. Figure 5b shows the influence of the hours without solar radiation (nighttime). As a result, the obtained values exhibit a smoother evolution compared to Figure 5a. Since it represents an average of the total solar radiation density received throughout the day, its minimum value is always greater than 0. The maximum daily average value is reached \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline GPS position of the installation: & Santóna, Spain \\ Year under study (_year_): & 2025 \\ Total number of days in the year \(\left(N_{days}\right)\): & 365 \\ Day of the year under study (N): & All \\ Local time (\(h_{local}\)): & All \\ Atmospheric state/quality: & Normal \\ Radiation losses due to marine surface irregularities (\(K_{marine}\)): & 0 \\ Panel inclination and azimuth relative to the sun’s & Perfect alignment with the \\ position (\(\beta_{inclination}\)) and (\(\beta_{azimuth}\)): & estimated sun position \\ Photovoltaic panel conversion efficiency \(\left(K_{pands}\right)\): & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Case-specific configuration of mathematics-based technical model parameters: location, time definition, atmospheric and marine conditions, and photovoltaic panels. Figure 4: Project site location: Santóna (Cantabria, Spain).