## 3 Methodology
### Exergoeconomic and Environmental Analysis
\begin{table}
\begin{tabular}{l l l} \hline
**Component** & **Cost Balance Equation** & **Auxiliary Equation** \\ \hline AC & \(\dot{C}_{22}+\dot{C}_{W,\text{AC}}+\dot{Z}_{\text{AC}}=\dot{C}_{23}\) & \(c_{w,\text{AC}}=c_{w,\text{GT}}\) \\ \hline CC & \(\dot{C}_{23}+\dot{C}_{24}+\dot{Z}_{\text{CC}}=\dot{C}_{25}\) & \(\frac{\dot{C}_{23}}{E_{23}}=\frac{\dot{C}_{38}}{25}\), \(c_{24}=12\) \\ \hline GT & \(\dot{C}_{25}+\dot{Z}_{W,\text{GT}}=\dot{C}_{26}+\dot{C}_{\text{GT}}\) & \(\frac{\dot{C}_{25}}{E_{25}}=\frac{\dot{C}_{26}}{E_{25}}\) \\ \hline HRSG & \(\dot{C}_{26}+\dot{C}_{19}+\dot{C}_{14}+\dot{Z}_{\text{HRSG}}=\dot{C}_{1}+\dot{ C}_{27}+\dot{C}_{20}\) & \(\frac{26}{E_{25}}=\frac{\dot{C}_{27}}{E_{27}}\) \\ \hline HPST & \(\dot{C}_{1}+\dot{Z}_{W,\text{HPST}}=\dot{C}_{2}+\dot{C}_{\text{HPST}}\) & \(\frac{\dot{C}_{1}}{E_{1}}=\frac{\dot{C}_{2}}{E_{2}}\) \\ \hline IPST & \(\dot{C}_{3}+\dot{Z}_{W,\text{IPST}}=\dot{C}_{5}+\dot{C}_{\text{IPST}}\) & \(\frac{\dot{C}_{3}}{E_{3}}=\frac{\dot{C}_{3}}{E_{3}}\) \\ \hline LPST & \(\dot{C}_{6}+\dot{Z}_{W,\text{LPST}}=\dot{C}_{8}+\dot{C}_{\text{LPST}}\) & \(\frac{\dot{C}_{6}}{E_{6}}=\frac{\dot{C}_{6}}{E_{6}}\) \\ \hline Cond1 & \(\dot{C}_{8}+\dot{C}_{15}+\dot{Z}_{\text{cond1}}=\dot{C}_{9}+\dot{C}_{16}\) & \(\frac{\dot{C}_{6}}{E_{6}}=\frac{\dot{C}_{6}}{E_{6}}\) \\ \hline Pump1 & \(\dot{C}_{9}+\dot{C}_{W,\text{P1}}+\dot{Z}_{\text{P1}}=\dot{C}_{10}\) & \(c_{w,\text{P1}}=c_{w,\text{HPST}}\) \\ \hline OFWH1 & \(\dot{C}_{7}+\dot{C}_{10}+\dot{Z}_{\text{OFWH1}}=\dot{C}_{11}\) & \\ \hline Pump2 & \(\dot{C}_{11}+\dot{C}_{W,\text{P2}}+\dot{Z}_{\text{P2}}=\dot{C}_{12}\) & \(c_{w,\text{P2}}=c_{w,\text{HPST}}\) \\ \hline OFWH2 & \(\dot{C}_{12}+\dot{C}_{4}+\dot{Z}_{\text{OFWH2}}=\dot{C}_{13}\) & \\ \hline Pump3 & \(\dot{C}_{13}+\dot{C}_{W,\text{P3}}+\dot{Z}_{\text{P3}}=\dot{C}_{14}\) & \(c_{w,\text{P3}}=c_{w,\text{HPST}}\) \\ \hline PTC & \(\dot{C}_{18}+\dot{C}_{q,\text{solar}}+\dot{Z}_{\text{PTC}}=\dot{C}_{17}\) & \(\dot{C}_{q,\text{solar}}=0\) \\ \hline TES & \(\dot{C}_{17}+\dot{C}_{21}+\dot{Z}_{\text{TES}}=\dot{C}_{18}+\dot{C}_{19}\) & \\ \hline Pump4 & \(\dot{C}_{20}+\dot{C}_{W,\text{P4}}+\dot{Z}_{\text{P4}}=\dot{C}_{21}\) & \(c_{w,\text{P4}}=c_{w,\text{HPST}}\) \\ \hline Evap & \(\dot{C}_{27}+\dot{C}_{34}+\dot{Z}_{\text{Evap}}=\dot{C}_{28}+\dot{C}_{29}\) & \(\frac{\dot{C}_{27}}{E_{27}}=\frac{\dot{C}_{28}}{E_{28}}\) \\ \hline ORT & \(\dot{C}_{29}+\dot{Z}_{W,\text{ORT}}=\dot{C}_{30}+\dot{C}_{\text{ORT}}\) & \(\frac{\dot{C}_{29}}{E_{29}}=\frac{\dot{C}_{20}}{E_{29}}\) \\ \hline HE & \(\dot{C}_{30}+\dot{C}_{33}+\dot{Z}_{\text{HE}}=\dot{C}_{31}+\dot{C}_{34}\) & \(\frac{\dot{C}_{30}}{E_{29}}=\frac{\dot{C}_{31}}{E_{31}}\) \\ \hline Cond2 & \(\dot{C}_{31}+\dot{C}_{35}+\dot{Z}_{\text{cond2}}=\dot{C}_{32}+\dot{C}_{36}\) & \(\frac{\dot{C}_{31}}{E_{31}}=\frac{\dot{C}_{32}}{E_{32}}\) \\ \hline ORP & \(\dot{C}_{32}+\dot{C}_{W,\text{ORP}}+\dot{Z}_{\text{ORP}}=\dot{C}_{33}\) & \(c_{w,\text{ORP}}=c_{w,\text{ORP}}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Cost balance and auxiliary equations of the system components [52; 53]. Finally, the CO\({}_{2}\) emission rate (\(\epsilon_{\text{CO}_{2}}\)) is calculated using the following equation [54]:  
\[\epsilon_{\text{CO}_{2}}=\frac{\dot{\text{m}}_{\text{CO}_{2}}}{\dot{\text{W}}_{ \text{net}}} \tag{30}\]