## 2 Material and Methods
### Parametric Analysis of the System  
#### 3.2.1 Thermodynamic Parametric Analysis  
For the thermodynamic calculations, the parameters that are taken into account are the electricity input to the electrolyzer and the solar beam irradiation. When the default irradiation value of 700 W/m\({}^{2}\) is considered, the PEM electrolyzer power input varies from 0 to 22.92 kW, which is the case when the whole ORC electricity production is used to power the PEM water electrolyzer and the hydrogen compressor, so there is no net electricity generation. Consequently, the main plant outputs, which are the net electricity production, the overall system energy, and exergy efficiency, are included in this section,  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Design ambient temperature (\(\mathbf{T_{amb}}\)) & 25 \({}^{\circ}\)C \\ Solar beam irradiation (\(\mathbf{G_{bn}}\)) & 700 W/m\({}^{2}\) \\ Incident angle (0) & 30\({}^{\circ}\) \\ Collector aperture (\(\mathbf{A_{a}}\)) & 195 m\({}^{2}\) \\ Ratio of collector aperture to the tank volume (\(\hat{\
abla}_{\mathbf{r}}\)) & 80 m\({}^{2}\)/m\({}^{3}\) \\ Ratio of the ORC high pressure to the critical pressure (\(\alpha\)) & 0.9 \\ Heat recovery system inlet temperature definition parameter (b) & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Design parameters of the system.  
Figure 5: Overall system exergy efficiency depending on the parameter (\(\alpha\)) for different working fluids, considering only electricity production through the ORC.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Outputs** & **Values** \\ \hline Solar energy input (\(\mathbf{Q_{solar}}\)) & 136.5 kW \\ ORC heat input (\(\mathbf{Q_{in}}\)) & 78.04 kW \\ ORC electricity production (\(\mathbf{P_{el,ORC}}\)) & 24.78 kW \\ ORC thermal efficiency (\(\mathbf{n_{ORC}}\)) & 31.75\% \\ System energy efficiency (\(\mathbf{n_{en}}\)) & 18.15\% \\ System exergy efficiency (\(\mathbf{n_{ex}}\)) & 19.49\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: System outputs when only electricity is produced.  
depending on the electrolyzer power input and the solar beam irradiation. As it is shown in Figure 6, the net electricity generation has a linear decreasing rate depending on the electricity input to the electrolyzer. The maximum value is equal to 17.15 kW when solar beam irradiation is equal to 500 W/m\({}^{2}\), 24.78 kW when this value is equal to 700 W/m\({}^{2}\), and 32.40 kW when this value is equal to 900 W/m\({}^{2}\). These are the cases of zero hydrogen production and compression, while the minimum values are equal to zero when the installation does not provide electricity and the entire power is utilized for hydrogen production and compression. In Figures 7 and 8, it is illustrated that both energy and exergy efficiency decrease when the electricity feeds to the PEM water electrolyzer, and the hydrogen production rate increase. When the plant provides only electricity to the grid, the energy and exergy efficiency are determined at 18.46% and 19.83%, respectively, in the case of the solar beam irradiation that is equal to 900 W/m\({}^{2}\). However, in the case of maximum hydrogen generation, these rates are equal to 9.6% and 10.07%, respectively. Finally, according to the results, the net power production, as well as the overall energy and exergy efficiencies increase with the increase of solar beam irradiation. The calculated values of both energy and exergy efficiency are greater than the corresponding ones defined by [PERSON] et al. [19]. The authors of this study investigated a similar system that is based on the PTC-powered ORC, as well as provides electricity and hydrogen, leading to an energy efficiency of 5.85%, and an exergy efficiency of 8.27%. In the present work, it is assumed that both the pump and turbine achieve high isentropic efficiency, enhancing the overall ORC performance.