# Mathematics-Driven Analysis of Offshore Green Hydrogen Stations
## 5 Conclusions  
This paper presents a mathematical model designed as a generic framework applicable to any location worldwide and developed to analyze the integration of solar energy generation and green hydrogen production. It evaluates the impact of key factors such as solar irradiance, atmospheric conditions, water surface flatness, as well as the parameters of photovoltaic panels, electrolyzers, and adiabatic compressors, on both energy generation and hydrogen production capacity. The innovative proposed model serves as a promising tool for conducting multivariable parametric analyses, selecting optimal design configurations based on specific solar energy and/or hydrogen production requirements, and performing a range of additional assessments including, but not limited to, risk evaluations, cause-effect analyses, and/or degradation studies. As demonstrated throughout this study, the increase in the value of solar irradiance received perpendicularly by the photovoltaic panels, the improvement in the efficiencies of the components involved in converting solar energy into electricity and in producing green hydrogen (namely, the electrolyzer and the compressor), as well as the proper selection of the remaining configuration parameters according to specific production requirements, have a significant impact on the total photovoltaic surface area required to power the green hydrogen production station. Efficiency improvement is understood in this context as encompassing two scenarios: (i) achieving the maximum green hydrogen production capacity for a given photovoltaic surface area or (ii) minimizing the required photovoltaic surface area for a specified hydrogen production target. Both cases reflect an increase in the operational efficiency of the solar-powered green hydrogen production station. Using Python as the programming and simulation language and applying the station model to the specific case of Santofa  
Figure 18: Multivariable parametric simulation: misalignment correction factors on \(I_{n\_total}\). (a) \(\beta_{inclination}\) offset and (b) \(\beta_{ximinth}\) offset. (Cantabria, Spain) in the year 2025, the position and trajectory of the sun relative to the photovoltaic panels powering the green hydrogen station were estimated. Due to the reflective effect of sunlight on the marine surface, an average increase in solar irradiance density received perpendicularly on the panel surface was observed: 18.2% when averaged over the course of a typical day (hourly basis) and 10.54% when averaged across the entire year (daily basis). Under the conditions of this study, the superior operating efficiency of the ALK-type electrolyzer--compared to PEM--for an equivalent level of solar irradiance, results in an estimated 4.19% increase in green hydrogen production capacity. This difference is expected to diminish over time as the efficiency gap between the two technologies narrows. In terms of photovoltaic surface area, this same condition translates into an estimated 4.03% reduction in favor of the ALK-based configuration. Hydrogen production requirements can be expressed either in \(\frac{\text{kg}_{\text{H}_{2}}}{\text{s}}\) or \(\frac{\text{mol}_{\text{H}_{2}}}{\text{s}}\). According to model outputs, the photovoltaic surface area required to produce 1 \(\frac{\text{kg}_{\text{H}_{2}}}{\text{s}}\) and 1 \(\frac{\text{mol}_{\text{H}_{2}}}{\text{s}}\) follows a ratio of 500 to 1, respectively. Additionally, under theoretical atmospheric quality conditions--which should be adapted to each specific case--the effects of degraded air quality on solar irradiance received by the photovoltaic panels, and, consequently, on hydrogen production capacity and the required photovoltaic surface area, were also modeled. For the case under analysis, average atmospheric attenuation values of 31.16% (hourly basis) and 25.25% (daily basis) were estimated. However, all simulations in this study were performed assuming standard atmospheric quality, as the station will be located offshore.