# Mathematics-Driven Analysis of Offshore Green Hydrogen Stations
## 2 Materials and Methods
### PHASE V: Integration of All Components into a Cohesive System  
Once \(N_{mol}\), \(P_{out}\), and the electrolyzer technology type--ALK or PEM--are defined, it is possible to estimate the total energy consumption required for the green hydrogen production and compression processes (\(PW_{Total\_i}\)), where \(i\) represents the type of technology used by the electrolyzer. This energy consumption, expressed in \(\frac{\mathrm{k}}{\mathrm{s}}\) or kw, is calculated as the sum of the individual consumption of the electrolyzer and the compressor (Equation (41)):  
\[PW_{Total\_i}=PW_{i}+\frac{PW_{COM}}{10^{3}} \tag{41}\]  
It is also possible to size the photovoltaic station so that the entire green hydrogen production and compression process can be continuously and sustainably powered by solar energy (Equation (41)). To achieve this, the expression for photovoltaic panel electricity generation capacity (Equation (28)) was set equal to the expression for total energy consumption (Equation (41)), allowing for the calculation of the required photovoltaic panel surface area (\(M_{panels}\)) needed to power the entire station (Equation (42)) and maintain the energy balance. Here, \(M_{panels}\) is expressed in square meters (m\({}^{2}\)). \[M_{panels}=\frac{PW_{Total\_i}\times 10^{3}}{I_{n\_total}\times K_{panels}} \tag{42}\]  
Although equation (Equation (42)) allows for calculating the required photovoltaic panel surface area to implement a green hydrogen station that operates at a specific location (Equation (1)), for a given hydrogen flow rate (\(\frac{\mathrm{mol}}{\mathrm{s}}\)) and at a defined output pressure (\(P_{out}\)), it is recommended to determine the contribution of each unit of panel surface area (1 m\({}^{2}\)) to the amount of hydrogen produced and stored by the station. To achieve this, equation (Equation (42)) is expanded and expressed in terms of \(\frac{\mathrm{mol}}{\mathrm{s}\times\mathrm{m}^{2}}\):  
\[\frac{\mathrm{mol}}{\mathrm{s}\times\mathrm{m}^{2}}=\frac{I_{n\_total}\times K _{panels}}{\frac{HV}{K_{electrolaser\_i}}\times 1000+\left|\frac{R\times(T_{mat}-T_{in})}{K_{ compact\_i}\times(1-T)}\right|} \tag{43}\]  
As can be observed, the numerator represents the photovoltaic station's electricity generation capacity per square meter of surface area, while the denominator represents the electrical consumption required for the production and storage of 1 \(\frac{\mathrm{mol}}{\mathrm{s}}\) of hydrogen. Considering that the theoretical molecular mass of hydrogen (\(m_{h2}\)) is a constant with a value of 2 \(\times\) 10\({}^{-3}\)\(\frac{\mathrm{kg}}{\mathrm{mol}}\), equation (Equation (43)) can be expressed in terms of the \(\frac{\mathrm{kg}}{\mathrm{s}}\) of hydrogen produced and stored per square meter of panel surface area:  
\[\frac{\mathrm{kg}}{\mathrm{s}\times\mathrm{m}^{2}}=\left(\frac{\mathrm{mol}} {\mathrm{s}\times\mathrm{m}^{2}}\right)\times m_{h2} \tag{44}\]  
Green hydrogen production is achieved by dissociating the water molecule (\(H_{2}O\)) through the process known as electrolysis, consuming one mole of water for every mole of hydrogen produced.