## 3 Methodology
### System Analysis of Energy and Exergy
Calculating \(\dot{\mathrm{E_{Q}}}\) and \(\dot{\mathrm{E_{w}}}\) is determined as follows:  
\[\sum\dot{\mathrm{E}}_{\mathrm{in}}=\sum\dot{\mathrm{E}}_{\mathrm{out}} \tag{2}\]6  
\[\sum\dot{\mathrm{E}}_{\mathrm{in}}=\sum\dot{\mathrm{E}}_{\mathrm{out}} \tag{2}\]7  
The indicated hybrid system's components exergy and energy balance equations are shown in \[\sum\dot{\mathrm{E}}_{\mathrm{in}}=\sum\dot{\mathrm{E}}_{\mathrm{out}} \tag{2}\]8  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Elements** & **Energy Equation’s Balance** & **Energy Equation’s Balances** \\ \hline Compressor & \(\dot{\mathrm{W}}_{\mathrm{AC}}=\dot{\mathrm{m}}_{\mathrm{22}}\)\((\mathrm{h}_{\mathrm{23}}-\mathrm{h}_{\mathrm{22}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,AC}}=\dot{\mathrm{W}}_{\mathrm{AC}}+\dot{\mathrm{ E}}_{\mathrm{22}}-\dot{\mathrm{E}}_{\mathrm{23}}\) \\ \hline Combustion chamber & \(\dot{\mathrm{m}}_{\mathrm{23}}\mathrm{h}_{\mathrm{23}}+\dot{\mathrm{m}}_{\mathrm{24 }}\mathrm{L}\mathrm{H}\mathrm{V}=\dot{\mathrm{m}}_{\mathrm{25}}\mathrm{h}_{ \mathrm{25}}\) & \(\dot{\mathrm{E}}_{\mathrm{D,CC}}=\left(\dot{\mathrm{E}}_{\mathrm{23}}+\dot{ \mathrm{E}}_{\mathrm{24}}\right)-\dot{\mathrm{E}}_{\mathrm{25}}\) \\ \hline Gas turbine & \(\dot{\mathrm{W}}_{\mathrm{GT}}=\dot{\mathrm{m}}_{\mathrm{25}}(\mathrm{h}_{ \mathrm{25}}-\mathrm{h}_{\mathrm{26}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,GT}}=\left(\dot{\mathrm{E}}_{\mathrm{25}}-\dot{ \mathrm{E}}_{\mathrm{26}}\right)-\dot{\mathrm{W}}_{\mathrm{GT}}\) \\ \hline HRSG & \(\dot{\mathrm{Q}}_{\mathrm{HRSG}}=\dot{\mathrm{m}}_{\mathrm{26}}(\mathrm{h}_{ \mathrm{26}}-\mathrm{h}_{\mathrm{27}})+\) & \(\dot{\mathrm{E}}_{\mathrm{D,HRSG}}=\dot{\mathrm{E}}_{\mathrm{26}}-\dot{ \mathrm{E}}_{\mathrm{27}}+\dot{\mathrm{E}}_{\mathrm{19}}-\dot{\mathrm{E}}_{ \mathrm{20}}-\dot{\mathrm{E}}_{\mathrm{14}}-\dot{\mathrm{E}}_{\mathrm{1}}\) \\ \hline HPST & \(\dot{\mathrm{W}}_{\mathrm{HPST}}=\dot{\mathrm{m}}_{\mathrm{1}}(\mathrm{h}_{ \mathrm{1}}-\mathrm{h}_{\mathrm{2}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,HPST}}=\dot{\mathrm{E}}_{\mathrm{1}}-\dot{\mathrm{ E}}_{\mathrm{2}}-\dot{\mathrm{W}}_{\mathrm{HPST}}\) \\ \hline IPST & \(\dot{\mathrm{W}}_{\mathrm{IPST}}=\dot{\mathrm{m}}_{\mathrm{3}}(\mathrm{h}_{ \mathrm{3}}-\mathrm{h}_{\mathrm{5}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,IPST}}=\dot{\mathrm{E}}_{\mathrm{3}}-\dot{\mathrm{ E}}_{\mathrm{5}}-\dot{\mathrm{W}}_{\mathrm{IPST}}\) \\ \hline LPST & \(\dot{\mathrm{W}}_{\mathrm{L}\mathrm{PST}}=\dot{\mathrm{m}}_{\mathrm{6}}(\mathrm{h}_ {\mathrm{6}}-\mathrm{h}_{\mathrm{8}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,LPST}}=\dot{\mathrm{E}}_{\mathrm{6}}-\dot{\mathrm{ E}}_{\mathrm{8}}-\dot{\mathrm{W}}_{\mathrm{LPST}}\) \\ \hline Condenser1 & \(\dot{\mathrm{Q}}_{\mathrm{Con}}=\dot{\mathrm{m}}_{\mathrm{15}}(\mathrm{h}_{ \mathrm{16}}-\mathrm{h}_{\mathrm{15}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,Con}}=\dot{\mathrm{E}}_{\mathrm{8}}-\dot{\mathrm{ E}}_{\mathrm{9}}+\dot{\mathrm{E}}_{\mathrm{15}}-\dot{\mathrm{E}}_{\mathrm{16}}\) \\ \hline Condenser2 & \(\dot{\mathrm{Q}}_{\mathrm{Con2}}=\dot{\mathrm{m}}_{\mathrm{34}}(\mathrm{h}_{ \mathrm{35}}-\mathrm{h}_{\mathrm{34}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,Con}}=\dot{\mathrm{E}}_{\mathrm{31}}-\dot{ \mathrm{E}}_{\mathrm{32}}+\dot{\mathrm{E}}_{\mathrm{34}}-\dot{\mathrm{E}}_{\mathrm{ 35}}\) \\ \hline Pump & \(\dot{\mathrm{W}}_{\mathrm{Pump}}=\dot{\mathrm{m}}_{\mathrm{20}}(\mathrm{h}_{ \mathrm{21}}-\mathrm{h}_{\mathrm{20}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,P}}=\dot{\mathrm{W}}_{\mathrm{P1}}+\dot{\mathrm{E}}_{ \mathrm{20}}-\dot{\mathrm{E}}_{\mathrm{21}}\) \\ \hline Pump1 & \(\dot{\mathrm{W}}_{\mathrm{Pump1}}=\dot{\mathrm{m}}_{\mathrm{9}}(\mathrm{h}_{ \mathrm{10}}-\mathrm{h}_{\mathrm{9}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,P1}}=\dot{\mathrm{W}}_{\mathrm{P1}}+\dot{\mathrm{E}}_{ \mathrm{9}}-\dot{\mathrm{E}}_{\mathrm{10}}\) \\ \hline Pump2 & \(\dot{\mathrm{W}}_{\mathrm{Pump2}}=\dot{\mathrm{m}}_{\mathrm{11}}(\mathrm{h}_{ \mathrm{12}}-\mathrm{h}_{\mathrm{11}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,P2}}=\dot{\mathrm{W}}_{\mathrm{P2}}+\dot{\mathrm{E}}_{ \mathrm{11}}-\dot{\mathrm{E}}_{\mathrm{12}}\) \\ \hline Pump3 & \(\dot{\mathrm{W}}_{\mathrm{Pump3}}=\dot{\mathrm{m}}_{\mathrm{13}}(\mathrm{h}_{ \mathrm{14}}-\mathrm{h}_{\mathrm{13}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,P3}}=\dot{\mathrm{W}}_{\mathrm{P1}}+\dot{\mathrm{E}}_{ \mathrm{13}}-\dot{\mathrm{E}}_{\mathrm{14}}\) \\ \hline OFWH1 & \(\dot{\mathrm{Q}}_{\mathrm{OFWH1}}=\dot{\mathrm{m}}_{\mathrm{10}}\mathrm{h}_{ \mathrm{10}}+\dot{\mathrm{m}}_{\mathrm{7}}\mathrm{h}_{\mathrm{7}}=\dot{ \mathrm{m}}_{\mathrm{11}}\mathrm{h}_{\mathrm{11}}\) & \(\dot{\mathrm{E}}_{\mathrm{D,OFWH1}}=\dot{\mathrm{E}}_{\mathrm{7}}+\dot{\mathrm{E}}_{ \mathrm{10}}-\dot{\mathrm{E}}_{\mathrm{11}}\) \\ \hline OFWH2 & \(\dot{\mathrm{Q}}_{\mathrm{OFWH2}}=\dot{\mathrm{m}}_{\mathrm{21}}\mathrm{h}_{ \mathrm{21}}+\dot{\mathrm{m}}_{\mathrm{4}}\mathrm{h}_{\mathrm{4}}=\dot{ \mathrm{m}}_{\mathrm{13}}\mathrm{h}_{\mathrm{13}}\) & \(\dot{\mathrm{E}}_{\mathrm{D,OFWH2}}=\dot{\mathrm{E}}_{\mathrm{4}}+\dot{\mathrm{E}}_{ \mathrm{12}}-\dot{\mathrm{E}}_{\mathrm{13}}\) \\ \hline ORT & \(\dot{\mathrm{W}}_{\mathrm{ORT}}=\dot{\mathrm{m}}_{\mathrm{29}}(\mathrm{h}_{ \mathrm{29}}-\mathrm{h}_{\mathrm{30}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,ST}}=\dot{\mathrm{E}}_{\mathrm{29}}+\dot{ \mathrm{E}}_{\mathrm{30}}-\dot{\mathrm{W}}_{\mathrm{ORT}}\) \\ \hline Heat exchanger & \(\dot{\mathrm{Q}}_{\mathrm{HE}}=\dot{\mathrm{m}}_{\mathrm{30}}(\mathrm{h}_{ \mathrm{30}}-\mathrm{h}_{\mathrm{31}})\) & \(\dot{\mathrm{E}}_{\mathrm{D,HE}}=\dot{\mathrm{E}}_{\mathrm{30}}  
The energy performance denoted as \(\eta_{\rm th}\) can be estimated using the following equation:  
\[\sum\dot{\mathrm{E}}_{\mathrm{in}}=\sum\dot{\mathrm{E}}_{\mathrm{out}} \tag{2}\]9  
The amount of heat supplied to the cycle was estimated from  
\[\dot{\mathrm{Q}}_{\mathrm{in}}+\dot{\mathrm{W}}_{\mathrm{in}}+\sum\dot{\mathrm{ m}}_{\mathrm{in}}\mathrm{h}_{\mathrm{in}}=\dot{\mathrm{Q}}_{\mathrm{out}}+\dot{ \mathrm{W}}_{\mathrm{out}}+\sum\dot{\mathrm{m}}_{\mathrm{out}}\mathrm{h}_{ \mathrm{out}} \tag{3}\]0  
Moreover, the exergy efficiency (\(\eta_{\rm ex}\)) serves as an indicator of system's quality and is calculable by means of the following formula:  
\[\dot{\mathrm{Q}}_{\mathrm{in}}+\dot{\mathrm{W}}_{\mathrm{in}}+\sum\dot{\mathrm{ m}}_{\mathrm{in}}\mathrm{h}_{\mathrm{in}}=\dot{\mathrm{Q}}_{\mathrm{out}}+\dot{ \mathrm{W}}_{\mathrm{out}}+\sum\dot{\mathrm{m}}_{\mathrm{out}}\mathrm{h}_{ \mathrm{out}} \tag{3}\]1  
where E is the exergy of the fuel that was supplied to the cycle combustion chamber.