## 3 Methodology
### System Analysis of Energy and Exergy  
The system's mass, exergy, and energy equations are expressed individually for all components and the overall system. In a constant flow of the open system, the total mass inside the control volume remains constant over time. As per the principle of mass conservation, the total mass incoming to cv must be identical to the total mass exiting it. Moreover, in a constant flow open system, emphasis is placed on the mass flow rate (\(\dot{\rm m}\)) per unit of time more than the total mass entering and leaving the system above a specific duration. Thus, the conservation of mass principle in generic constant flow systems with several inlets and outputs is represented as follows:  
\[\sum\dot{\rm m}_{\rm in}=\sum\dot{\rm m}_{\rm out} \tag{1}\]  
In constant-flow open systems, the control volume's overall energy content does not change (\(\rm E_{cv}=constant\)). Consequently, the control volume's overall energy variation is zero (\(\rm\Delta E_{cv}=0\)), indicating that the energy incoming to the cv equals the energy that exits it. \begin{table}
\begin{tabular}{l l l} \hline \hline  & **Parameter** & **Value** \\ \hline \multirow{8}{*}{GT cycle} & Number of gas turbine unit & 1 \\  & GTT, K & 1376 \\  & Mass flow rate of air, kg/s & 438 \\  & Compression ratio & 9 \\  & Ambient temperature, K & 306 \\  & LHV of fuel, (kJ/kg) & 50,056 \\  & RH & 0.63 \\  & \(\rm\eta_{GT}\), \% & 90 \\  & \(\rm\eta_{AC}\), \% & 80 \\ \hline \multirow{8}{*}{RC cycle} & Inlet pressure for HPST, bar & 100 \\  & Inlet pressure for IPST, bar & 40 \\  & Inlet pressure for LPST, bar & 10 \\  & Condenser temperature, K & 313 \\  & \(\rm\eta_{ST}\), \% & 90 \\  & \(\rm\eta_{Pump}\), \% & 85 \\ \hline \multirow{8}{*}{ORCs} & Inlet temperature for ORCs, K & 471 \\  & Inlet pressure for ORCs, bar & 8 \\ \cline{1-1}  & Working fluid & R123 \\ \cline{1-1}  & \(\rm\eta_{ORT}\), \% & 88 \\ \cline{1-1}  & \(\rm\eta_{ORP}\), \% & 80 \\ \hline \multirow{8}{*}{TES system and solar field} & Lat. (deg.) & 35.47\({}^{\circ}\) N \\ \cline{1-1}  & Long. (deg.) & 44.39\({}^{\circ}\) E \\ \cline{1-1}  & Position & Kirkuk/Iraq \\ \cline{1-1}  & Solar field area (m\({}^{2}\)) & 510,120 \\ \cline{1-1}  & HTF’s outlet temperature (\({}^{\circ}\)C) & 565 \\ \cline{1-1}  & HTF’s inlet temperature (\({}^{\circ}\)C) & 287 \\ \cline{1-1}  & Working fluid & Salt (60\% NaNo\({}_{3}-40\%\) KNo\({}_{3}\)) \\ \cline{1-1}  & Area of collectors (m\({}^{2}\)) & 400,000 \\ \cline{1-1}  & DNI & 8.02 \\ \cline{1-1}  & Reflection coefficient & 0.94 \\ \cline{1-1}  & Receiver’s absorption coefficient & 0.92 \\ \cline{1-1}  & Transmission coefficient of the glass cover & 0.92 \\ \cline{1-1}  & Incidence angle modifier & 1 \\ \cline{1-1}  & \(\rm\eta_{PTC}\) & 85 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input readings were utilized for the proposed hybrid system [35; 36; 37]. The energy conservation concept for an open system with continuous flow is expressed by the following equations [38; 39]:  
\[\sum\dot{\mathrm{E}}_{\mathrm{in}}=\sum\dot{\mathrm{E}}_{\mathrm{out}} \tag{2}\]  
\[\dot{\mathrm{Q}}_{\mathrm{in}}+\dot{\mathrm{W}}_{\mathrm{in}}+\sum\dot{\mathrm{ m}}_{\mathrm{in}}\mathrm{h}_{\mathrm{in}}=\dot{\mathrm{Q}}_{\mathrm{out}}+\dot{ \mathrm{W}}_{\mathrm{out}}+\sum\dot{\mathrm{m}}_{\mathrm{out}}\mathrm{h}_{ \mathrm{out}} \tag{3}\]  
The following formula represents the energy-conservation principle for an open system with constant flow or the first law of thermodynamics.