## 4 Economic Analysis of the Solar ORC System
### Economic Analysis of Solar ORC System  
For the economic analysis purposes, the construction period for the system has been assumed to be one year. The economic lifetime is assumed to be 20 years and has no salvage value at the end of 20 years. An interest rate of 6% is used for the analysis. The operating hours for the system is considered to be 2084 h that corresponds to the average total annual sunlight hours in Ottawa, Canada [42]. Using the above parameters, the annual cash flow, present values, and annual equivalent cost (AEC) can be calculated [43]. Annual equivalent cost is a crucial parameter to evaluate the cost of electricity per kWh. It can be evaluated as follows:  
\[AEC=\frac{IC_{c}\times i}{1-\left(1+i\right)^{-n}} \tag{21}\]  
where \(IC_{c}\) is the initial investment, \(i\) is the interest rate, and \(n\) is the economic lifetime of the system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Equipment** & **Cost** \\ \hline \multicolumn{2}{c}{_Thermal energy generation_} \\ Installation of solar collectors & CAD 3565.00 \\ Solar collectors (15 collectors @ CAD 900) & CAD 15,525.00 \\ Collectors pump & CAD 517.50 \\ \hline \multicolumn{2}{c}{_ORC unit_} \\ Evaporator & CAD 517.50 \\ Condenser & CAD 1897.50 \\ Regenerator & CAD 1200.00 \\ Scroll expander & CAD 4542.50 \\ Pump & CAD 862.50 \\ Refrigerant tank and piping & CAD 287.50 \\ Labor cost & CAD 230.00 \\ \hline \multicolumn{2}{c}{_Power block_} \\ Generator & CAD 632.50 \\ Control systems & CAD 345.00 \\ \hline \multicolumn{2}{c}{_Others_} \\ Water tank & CAD 172.50 \\ Measuring devices & CAD 230.00 \\ Miscellaneous & CAD 172.50 \\ \hline \multicolumn{2}{c}{_Total_} \\ \hline \hline \multicolumn{2}{c}{Price is in CAD (Canadian dollars) \(\sim\) 0.76 USD (United States dollars).} \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Cost of Common Equipment Among the Mixtures. \begin{table}
\begin{tabular}{c c} \hline \hline
**Working Fluid** & **Cost** \\ \hline R245 fa/R152a (0.9/0.1) & USD 1730.00 \\ R245 fa/propane (0.4/0.6) & USD 832.00 \\ Butane/propane(0.8/0.2) & USD 184.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Working fluid mixture costs. The net present value of all the cash flows can be evaluated as follows:  
\[NPV=(B-C)*\left(\frac{1-\left(1+i\right)^{-n}}{i}\right)-IC_{c} \tag{22}\]  
where \(NPV\) is the net present value of the investment, \(B\) is benefit of the investment each year and \(C\) is the cost of investment each year. The benefit-cost ratio is an index of the ratio of the present values of the benefit cash flows and cost cash flows. It is evaluated as follows:  
\[BCR=\frac{B*\left(\frac{1-\left(1+i\right)^{-n}}{i}\right)}{C*\left(\frac{1- \left(1+i\right)^{-n}}{i}\right)+IC_{C}} \tag{23}\]  
The payback period \(PB\) is the total years required for NPV to reach 0. It is evaluated by solving the expression below:  
\[NPV=0=(B-C)*\left(\frac{1-\left(1+i\right)^{-PB}}{i}\right)-IC_{c} \tag{24}\]  
The internal rate of return (IRR) is the critical rate of interest where NPV = USD 0. For investment to be economically feasible, IRR has to be more than or equal to the interest rate. It is evaluated by solving the expression below:  
\[NPV=0=(B-C)*\left(\frac{1-\left(1+IRR\right)^{-n}}{IRR}\right)-IC_{c} \tag{25}\]  
The annual cost of electricity is evaluated using two methods. One uses annual benefit and the other uses EAC as minimum benefit required to sustain the investment. \[Annual\ Cost\ of\ Electricity(B)=\frac{W_{N}*2084\frac{hr}{year}}{B} \tag{26}\]  
\[Annual\ Cost\ of\ Electricity(EAC)=\frac{W_{N}*2084\frac{hr}{year}}{EAC} \tag{27}\]  
For this economic analysis, the payback period is assumed to be equal to the economic life cycle of the system i.e., 20 years since it is being considered as a community benefit investment. Figure 22a,b present the annual cash flow and net present value during the life cycle of the ORC system for various working fluid mixtures. The cash flows and NPV for the three different mixtures are almost identical to each other.