## 2 Material and Methods
### General Thermodynamic Indexes
Additionally, the exergy rate of solar irradiation is determined according to the Petela model as below [30]:  
\[Ex_{solar}=Q_{solar}\cdot\left(1-\frac{4}{3}\cdot\frac{T_{0}}{T_{sun}}+\frac{1 }{3}\left(\frac{T_{0}}{T_{sun}}\right)^{4}\right) \tag{29}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Components** & **Energy Balance Equation** & **Exergy Balance Equation** \\ \hline PTC & \(Q_{\text{solar}}=Q_{\text{u}}+Q_{\text{loss,th}}+Q_{\text{loss,opt}}\) & \(EX_{\text{solar}}=Ex_{\text{u}}+Ex_{\text{loss}}+Ex_{\text{dest}}\) \\ TES tank & \(\dot{m}_{\text{col}}\cdot\dot{h}_{\text{col,out}}+\dot{m}_{\text{s}}\cdot\dot{h} _{\text{s,out,2}}=\dot{m}_{\text{col}}\cdot\dot{h}_{\text{col,in}}+\dot{m}_{ \text{s}}\cdot\dot{m}_{\text{col}}\cdot\dot{m}_{\text{s}}\cdot\dot{m}_{\text {col,out}}+\dot{m}_{\text{s}}\cdot\dot{m}_{\text{s,out,2}}=\dot{m}_{\text{col}} \cdot\dot{m}_{\text{col,in}}+\dot{m}_{\text{s}}\) \\  & \(h_{\text{s,in}}+Q_{\text{loss}}\) & \(\dot{m}_{\text{s,in}}+Ex_{\text{loss}}+Ex_{\text{dest}}\) \\ Heat recovery system & \(\dot{m}_{\text{s}}\cdot\dot{h}_{\text{s,in}}+\dot{m}_{\text{ORC}}\cdot\dot{h} _{\text{3}}=\dot{m}_{\text{s}}\cdot\dot{h}_{\text{s,out}}+\dot{m}_{\text{ORC}} \cdot\dot{h}_{\text{4}}+\dot{m}_{\text{is}}\cdot\dot{m}_{\text{ORC}}\cdot\dot {m}_{\text{s}}+\dot{m}_{\text{ORC}}\cdot\dot{m}_{\text{s}}+\dot{m}_{\text{ORC}} \cdot\dot{m}_{\text{s}}+\dot{m}_{\text{ORC}}\cdot\dot{m}_{\text{ORC}}\cdot \dot{m}_{\text{loss}}\) \\  & \(Q_{\text{loss}}\) & \(ex_{\text{d}}+Ex_{\text{loss}}+Ex_{\text{dest}}\) \\ ORC pump & \(\dot{m}_{\text{ORC}}\cdot\dot{h}_{\text{1}}+W_{\text{pump}}=\dot{m}_{\text{ORC }}\cdot\dot{h}_{\text{2}}\) & \(\dot{m}_{\text{ORC}}\cdot\dot{m}_{\text{1}}+Ex_{\text{pump}}=\dot{m}_{\text{ORC }}\cdot\dot{m}_{\text{ORC}}\cdot\dot{m}_{\text{ex}}+Ex_{\text{dest}}\) \\ ORC condenser & \(\dot{m}_{\text{ORC}}\cdot\dot{h}_{\text{6}}=\dot{m}_{\text{ORC}}\cdot\dot{h}_{ \text{1}}+\dot{Q}_{\text{out}}\) & \(\dot{m}_{\text{ORC}}\cdot\dot{m}_{\text{ORC}}\cdot\dot{m}_{\text{ORC}}\cdot \dot{m}_{\text{loss}}+Ex_{\text{out}}+Ex_{\text{dest}}\) \\ ORC expander & \(\dot{m}_{\text{ORC}}\cdot\dot{h}_{\text{4}}=\dot{m}_{\text{ORC}}\cdot\dot{h} _{\text{5}}+W_{\text{exp}}\) & \(\dot{m}_{\text{ORC}}\cdot\dot{m}_{\text{ORC}}\cdot\dot{m}_{\text{ORC}}\cdot \dot{m}_{\text{loss}}+\dot{m}_{\text{ORC}}\cdot\dot{m}_{\text{loss}}\) \\ ORC recuperator & \(\dot{m}_{\text{ORC}}\cdot\dot{h}_{\text{2}}+\dot{m}_{\text{ORC}}\cdot\dot{h} _{\text{5}}+\dot{m}_{\text{ORC}}\cdot\dot{h}_{\text{5}}+\dot{m}_{\text{ORC}} \cdot\dot{h}_{\text{6}}\) & \(\dot{m}_{\text{ORC}}\cdot\dot{m}_{\text{ORC}}\cdot\dot{m}_{\text{loss}}+\dot{m}_{ \text{ORC}}\cdot\dot{m}_{\text{loss}}+\dot{m}_{\text{ORC}}\cdot\dot{h}_{\text{6}}\) \\ ORC recuperator & \(\dot{m}_{\text{ORC}}\cdot\dot{h}_{\text{2}}+\dot{m}_{\text{ORC}}\cdot\dot{h}_{ \text{5}}+\dot{Q}_{\text{loss}}\) & \(\dot{m}_{\text{ORC}}\cdot\dot{m}_{\text{loss}}+Ex_{\text{loss}}+Ex_{\text{dest}}\) \\ Water preheater & \(\dot{m}_{\text{water}}\cdot\dot{h}_{\text{water,a}}+\dot{m}_{\text{s}}\cdot\dot{h} _{\text{s,out}}=\dot{m}_{\text{water}}\cdot\dot{h}_{\text{water,b}}+\dot{m}_{ \text{water}}\cdot\dot{h}_{\text{water,b}}+\dot{m}_{\text{water}}\cdot\dot{m}_{ \text{water,e}}+\dot{m}_{\text{s}}\cdot\dot{m}_{\text{s,out}}=\dot{m}_{\text{water }}\cdot\dot{m}_{\text{b}}+\dot{m}_{\text{s}}\cdot\dot{m}_{\text{s,out,2}}+\dot{m}_{ \text{s}}\cdot\dot{m}_{\text{s,out,2}}+\dot{m}_{\text{loss}}+Ex_{\text{dest}}\) \\ PEM water electrolyzer & \(\dot{m}_{\text{water}}\cdot\dot{h}_{\text{water,b}}+W_{\text{PEM}}=\dot{m}_{ \text{hydrogen}}\cdot\dot{h}_{\text{hydrogen,c}}\) & \(\dot{m}_{\text{water}}\cdot\dot{m}_{\text{water,b}}+Ex_{\text{PEM}}=\dot{m}_{ \text{hydrogen}}\cdot\dot{m}_{\text{hydrogen}}\) \\  & \(+\dot{m}_{\text{oxygen}}\cdot\dot{h}_{\text{oxygen}}\) & \(\dot{m}_{\text{oxygen}}\) & \(\dot{m}_{\text{hydrogen,c}}+\dot{m}_{\text{oxygen}}\) & \(\dot{m}_{\text{oxygen}}\cdot\dot{m}_{\text{ex oxygen}}+Ex_{\text{dest}}\) \\ Hydrogen compressor & \(\dot{m}_{\text{hydrogen}}\cdot\dot{h}_{\text{hydrogen,c}}+W_{\text{comp}}=\dot{m}_{ \text{hydrogen}}\cdot\dot{m}_{\text{hydrogen}}\cdot\dot{m}_{\text{hydrogen}}\cdot\dot{m}_{ \text{hydrogen}}\cdot\dot{m}_{\text{s}}+\dot{m}_{\text{hydrogen,d}}+Ex_{\text{dest}}\) \\  & \(\dot{m}_{\text{hydrogen}}\cdot\dot{h}_{\text{hydrogen,d}}=\dot{m}_{\text{hydrogen}}\cdot\dot{m}_{ \text{hydrogen}}\cdot\dot{m}_{\text{hydrogen}}+\dot{m}_{\text{hydrogen}}\cdot\dot{m}_{ \text{s}}+\dot{m}_{\text{hydrogen}}\cdot\dot{m}_{\text{s}}+\dot{m}_{\text{hydrogen}}\cdot\dot{m}_{ \text{hydrogen}}\cdot\dot{m}_{\text{s}}+\dot{m}_{\text{hydrogen}}\cdot\dot{m}_{ \text{s}}+\dot{m}_{\text{hydrogen(\(T_{0}\)) is the reference environment temperature which is supposed at 298.15 K (25 \({}^{\circ}\)C) and (\(T_{sun}\)) is the sun's temperature which is assumed at 5/70 K [30].