## 2 Methodology
### Advanced Exergetic (AdvEx) Analysis
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Components**} & **Unavoidable** & **Ideal** & **Parameters Used** & **Components** & **Unavoidable** & **Ideal** & **Parameters Used** \\  & **Conditions** & **Conditions** & **Unavoidable costs** & **Conditions** & **Conditions** & **Conditions** & **Unavoidable Costs** \\ \hline \multicolumn{7}{c}{_LEVEL 1_} & \multicolumn{7}{c}{_LEVEL 1_} \\ \hline \multirow{2}{*}{VAP 1} & \(\Delta T_{pinch}=6\) K & \(\Delta T_{min}=0\) K & \(\Delta T_{min}=15\) K & \multirow{2}{*}{VAP 2} & \(\Delta T_{pinch}=5\) K & \(\Delta T_{min}=0\) K & \(\Delta T_{min}=15\) K \\  & \(\Delta P_{min}=10\) kPa & \(\Delta P_{min}=0\) kPa & \(\Delta P_{min}=\Delta P_{ml}\) & & \(\Delta P_{min}=10\) kPa & \(\Delta P_{min}=0\) kPa & \(\Delta P_{min}=\Delta P_{ml}\) \\ \hline \multirow{2}{*}{PRE-HE 1} & \(\Delta T_{pinch}=43\) K & \(\Delta T_{pinch}=0\) K & \(\Delta T_{min}=15\) K & \multirow{2}{*}{PRE-HE 2} & \(\Delta T_{pinch}=5\) K & \(\Delta T_{pinch}=0\) K & \(\Delta T_{min}=15\) K \\  & \(\Delta P_{min}=10\) kPa & \(\Delta P_{min}=0\) kPa & \(\Delta P_{min}=\Delta P_{ml}\) & & & & & \\ \hline \multirow{2}{*}{CON 1} & \(\Delta T_{pinch}=3\) K & \(\Delta T_{pinch}=0\) K & \(\Delta T_{min}=15\) K & \multirow{2}{*}{CON 2} & \(\Delta T_{pinch}=3\) K & \(\Delta T_{pinch}=0\) K & \(\Delta T_{min}=15\) K \\  & \(\Delta P_{min}=10\) kPa & \(\Delta P_{min}=0\) kPa & \(\Delta P_{min}=0\) kPa & \(\Delta P_{min}=\Delta P_{ml}\) & & & & \\ \hline \multirow{2}{*}{TURB 1} & \(\eta_{in}=93\%\) & \(\eta_{in}=100\%\) & \(\eta_{inch}=100\%\) & \multirow{2}{*}{75\% of \(\dot{Z}_{TURB\ 1}\)} & \multirow{2}{*}{TURB 2} & \(\eta_{in}=93\%\) & \(\eta_{in}=100\%\) & \multirow{2}{*}{75\% of \(\dot{Z}_{TURB\ 2}\)} \\  & \(\eta_{mch}=100\%\) & \(\eta_{mch}=100\%\) & & & & & \\ \hline \multirow{2}{*}{PU 1} & \(\eta_{in}=82\%\) & \(\eta_{in}=100\%\) & \multirow{2}{*}{75\% of \(\dot{Z}_{TURB\ 1}\)} & \multirow{2}{*}{PU 2} & \(\eta_{in}=77\%\) & \(\eta_{in}=100\%\) & \multirow{2}{*}{75\% of \(\dot{Z}_{TURB\ 2}\)} \\  & \(\eta_{mch}=100\%\) & \(\eta_{mch}=100\%\) & & & & & \\ \hline \multirow{2}{*}{RECUP} & \(\Delta T_{pinch}=5\) K & \(\Delta T_{pinch}=0\) K & \(\Delta T_{min}=15\) K & \multirow{2}{*}{} & \multirow{2}{*}{} & \multirow{2}{*}{} \\  & \(\Delta P_{min}=10\) kPa & \(\Delta P_{min}=0\) kPa & \(\Delta P_{min}=\Delta P_{ml}\) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters utilized for the AdvExEcon analysis of the Sinem GPP. Thus, the unavoidable amount of exergy destruction for the \(k\)th component is calculated as shown below [33]:  
\[\dot{E}^{UN}_{D,k}=\dot{E}^{R}_{P,k}\Bigg{(}\frac{E_{D}}{E_{P}}\Bigg{)}^{UN}_{k} \tag{2}\]  
After the inevitable amount of exergy destruction is determined, the amount of avoidable exergy destruction amount is determined by subtracting the amount of exergy destruction of the \(k\)th component operating under real conditions from the amount of avoidable exergy destruction. Equation (3) is as follows:  
\[\dot{E}^{AV}_{D,k}=\dot{E}^{R}_{D,k}-\dot{E}^{UN}_{D,k} \tag{3}\]  
Separated parts of the exergy destruction amount can be further separated again, so the interaction and improvement potentials between components can be made more understandable. Thus, the enhanced decomposed parts listed below are obtained as follows [14; 34]:  
\[\dot{E}^{UN,EN}_{D,k}=\dot{E}^{EN}_{P,k}\Bigg{(}\frac{E_{D}}{E_{P}}\Bigg{)}^{UN}_ {k} \tag{4}\]  
\[\dot{E}^{UN,EX}_{D,k}=\dot{E}^{UN}_{D,k}-\dot{E}^{UN,EN}_{D,k} \tag{5}\]  
\[\dot{E}^{AV,EN}_{D,k}=\dot{E}^{EN}_{D,k}-\dot{E}^{UN,EN}_{D,k} \tag{6}\]  
\[\dot{E}^{AV,EX}_{D,k}=\dot{E}^{EX}_{D,k}-\dot{E}^{UN,EX}_{D,k} \tag{7}\]  
where \(\dot{E}^{UN,EN}_{D,k}\) and \(\dot{E}^{UN,EX}_{D,k}\) are the avoidable and inevitable parts of the inevitable exergy breakdown, while \(\dot{E}^{AV,EN}_{D,k}\) and \(\dot{E}^{AV,EX}_{D,k}\) are the avoidable and inevitable parts of the avoidable exergy destruction.