# Mathematics-Driven Analysis of Offshore Green Hydrogen Stations
## 4 Discussion
### Solar Irradiation and Green Hydrogen Station Capacity
However, the impact of the compressor on hydrogen production is lower compared to the effect of selecting the appropriate hydrogen heating value constant. In the case under analysis, green hydrogen production capacity--expressed in \(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s}\mathrm{<m^{2}}}\)--shows a 3.1% improvement at an output pressure of 200 bars compared to 1000 bars. Under the same pressure conditions, the photovoltaic surface area required in the 200 bar configuration is 3% lower. Figure 12: Contribution of hydrogen heating value to system performance and photovoltaic panel surface area: (**a**) \(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s\times m^{2}}}\) shown in days–year, (**b**) \(\mathrm{m^{2}@1}\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s}}\) shown in days–year. Figure 13: Contribution of hydrogen output pressure to system performance and photovoltaic panel surface area: (**a**) \(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s\times m^{2}}}\) shown in days–year, (**b**) \(\mathrm{m^{2}@1}\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s}}\) shown in days–year. The electrical energy generation capacity at the output of the photovoltaic panels depends not only on \(I_{n\_total}\) but also on \(K_{pends}\). Figure 14 illustrates the effect of \(K_{pends}\) on the hydrogen production capacity of the station. As the value of \(K_{pends}\) increases, the value of \(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s\times m^{2}}}\) also increases, while the required \(M_{pends}\) decreases. Higher solar panel conversion efficiency results in a lower \(M_{pends}\) value needed to maintain the same electrical generation capacity. The effects of \(K_{pends}\) are more pronounced in areas where \(\alpha_{solar\_elevation}\) is lower, corresponding to lower \(I_{n\_total}\) values. In the case under analysis, and for a constant value of received total irradiance \(I_{n\_total}\), a twofold improvement in photovoltaic panel efficiency results in a twofold increase in green hydrogen production capacity and, equivalently, a 50% reduction in the photovoltaic surface area required to produce \(1\,\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s}}\). The hydrogen production capacity of the station also depends on \(K_{electrolyte_{2}\_i}\) and \(K_{compressor}\) (Equation (43)). Figure 15 illustrates the effect of \(K_{electrolyte_{2}\_i}\) on the station's hydrogen production capacity. As the value of \(K_{electrolyte_{2}\_i}\) increases, the value of \(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s\times m^{2}}}\) also increases, while the required \(M_{pends}\) decreases. In the case under analysis, an improvement in the efficiency of the ALK-type electrolyzer from 0.637 to 0.849 results in a 32.28% increase in green hydrogen production capacity. This, in turn, leads to a 32.28% reduction in the required photovoltaic surface area to produce \(1\,\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s}}\). Figure 16 illustrates the effect of \(K_{compressor}\) on the hydrogen production capacity of the station. As the value of \(K_{compressor}\) increases, the value of \(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s\times m^{2}}}\) also increases, while the required \(M_{pends}\) decreases. In the case under analysis, an improvement in the efficiency of the adiabatic compressor from 0.6 to 0.8 results in a 0.81% increase in green hydrogen  
Figure 14: Contribution of photovoltaic efficiency to system performance and photovoltaic panel surface area: (a) \(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s\times m^{2}}}\) shown in days–year, (b) \(\mathrm{m^{2}@1\,\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s}}}\) shown in days–year. Figure 15: Contribution of electrolyzer efficiency to system performance and photovoltaic panel surface area: (a) \(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s\times m^{2}}}\) shown in days–year, (b) \(\mathrm{m^{2}@1\,\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s}}}\) shown in days–year. production capacity. This, in turn, leads to a 0.81% reduction in the required photovoltaic surface area to produce \(1\over 8\).