# Financial Optimization of a Solar-Driven Organic Rankine Cycle
## 2 Material and Methods
### Procedure Description  
The first part of this work is the development of a thermodynamic model in Engineering Equation Solver (EES) [19] in order to determine the ORC efficiency. The working fluid is toluene and this is a suitable selection for high-temperature levels in the range of 300-400 \({}^{\circ}\)C. Table 2 includes the main data of the ORC and more information about these values can be found in other previous studies [14; 18; 23; 33]. The next stage in this work is the dynamic investigation of the examined system. In this analysis, a program is developed in the programming language FORTRAN. This model studies 12 different days, one for every month and then the all year period can be studied. More specifically, for every \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbols** & **Values** \\ \hline Electricity cost & (\(K_{el}\)) & 0.28485 \(\epsilon\)\(\text{kW}_{\text{hel}}\)\({}^{-1}\) \\ PTC specific cost & (\(K_{cal}\)) & 250 \(\epsilon\)\(\text{m}\)\({}^{-2}\) \\ Tank specific cost & (\(K_{\text{tank}}\)) & 1000 \(\epsilon\)\(\text{m}\)\({}^{-3}\) \\ ORC specific cost & (\(K_{\text{orc}}\)) & 3000 \(\epsilon\)\(\text{kW}_{\text{el}}\)\({}^{-1}\) \\ Project life & (\(N\)) & 25 years \\ Discount factor & (\(r\)) & 3\% \\ Equivalent project years & (\(R\)) & 17.41 \\ Operation and maintenance cost & (\(K_{\text{O\&M}}\)) & 1\% of the capital cost \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data for financial analysis [28; 33]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbols** & **Values** \\ \hline Nominal power production & (\(P_{el}\)) & 10 kW \\ Pressure level in the turbine inlet & (\(P_{4}\)) & 37.14 bar \\ Pressure level in the turbine outlet & (\(P_{3}\)) & 0.079 bar \\ Superheating in the turbine inlet & (\(\Delta T_{\text{slt}}\)) & 20 \({}^{\circ}\)C \\ Condenser temperature level & (\(T_{\text{cont}}\)) & 40 \({}^{\circ}\)C \\ Saturation temperature in the HRS & (\(T_{\text{sat}}\)) & 309.7 \({}^{\circ}\)C \\ Motor efficiency & (\(\text{n}_{motor}\)) & 80\% \\ Turbine isentropic efficiency & (\(\text{n}_{\text{ls},T}\)) & 85\% \\ Electrical generator efficiency & (\(\text{n}_{\text{r}}\)) & 98\% \\ Mechanical efficiency & (\(\text{n}_{\text{lm}}\)) & 99\% \\ Recuperator temperature & (\(\Delta T_{\text{rec}}\)) & 10 \({}^{\circ}\)C \\ difference & (\(\text{P}_{\text{rhs}}\)) & 5 \({}^{\circ}\)C \\ ORC efficiency & (\(\text{n}_{\text{tor}}\)) & 32.52\% \\ Inlet oil temperature in the HRS & (\(T_{\text{s},in}\)) & 334.7 \({}^{\circ}\)C \\ Outlet oil temperature in the HRS & (\(T_{\text{s},out}\)) & 204.6 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the organic Rankine cycle. month, the proper number of sunny days is used in order to take into consideration the proper solar potential for every month. The weather data regard the location of Athens in Greece and these data can be found in the following Refs. [21; 28]. In the developed code, the time step is selected at 1 min after sensitivity analysis. For every month, the typical day is converged after an iterative process. In this process, the day is faced as 7 identical days that are solved the one after the other. So, the last day of this set is the converged day, which corresponds to reality. The goal of this work is the optimization of the examined system. The optimization variables are the collecting area (\(A_{c}\)) and the storage tank volume (\(V\)). Table 3 includes data about the optimization variables. The collecting area is studied from 100 up to 300 m\({}^{2}\) with a step of 20 m\({}^{2}\), while the storage tank volume from 10 up to 30 m\({}^{3}\) with a step of 2 m\({}^{3}\). In total, 121 cases are examined by investigating all the possible combinations of collecting areas and storage tank volumes. These 121 cases are evaluated with different criteria, and, in every case, the optimum case is selected.