## 4 Case Example
### Step 5. Cost-Benefit Analysis  
Once the BESS ageing for different configurations and scenarios has been calculated, a cost-benefit analysis must be performed, considering both the BESS cost and fixed term energy cost. Among the different reports found in the literature that analyse energy storage costs, the one published in [41] has been selected as the most reliable study. Moreover, electricity access fees for industrial consumption for the regulated market in Spain can be found in [42]. The fixed term of the access fee considers three time periods of time-discrimination (P1, P2, and P3). For further information about the Spanish regulated market, and time discrimination periods, the authors recommend the work published in [42]. The variable term of energy is kept constant for every scenario, i.e., the BESS is re-charged from the grid, and the BESS energy recharged form the grid plus the industrial load demand matches the total energy consumed by the industrial load in scenarios SB and WB, so the overall energy consumption remains constant. Hence, it is not included in the cost. Costs are summarized in Table 5 [42]. Considering this, the cost equation can be written as:  
\[Cost(\frac{euro}{year})=(P1+P2+P3)\cdot P_{LIMIT}+BESS_{project-cost} \tag{17}\]  
The contracted power (\(P_{LIMIT}\)) is considered constant for the three time-discrimination periods (as is requested to industrial consumption). The yearly BESS project cost has been calculated based on [43; 44; 45]. The annualized cost of the BESS project has been defined as:  
\[C_{ann}=CRF(i,R_{proj})\cdot C_{NPC} \tag{18}\]  
where \(C_{ann}\) is the annualized cost, \(C_{NPC}\) is the net present cost, and \(CRF\) is the capital recovery factor, which depends on the annual real discount rate (\(i\)) and on the project  
Figure 12: Days until \(\
abla Q=20\%\) as a function of the BESS configuration in winter. \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Cost** \\
**-** & **[6/kW and Year]** \\ \hline P1 & 59.1734 \\ P2 & 39.4906 \\ P3 & 8.3677 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summarized costs. lifetime (\(R_{proj}\)). \(C_{NPC}\) is calculated as the present value of all the costs of installing and operating the battery over the project lifetime, minus the present value of all the revenues earned over the project lifetime. Hence, the total yearly cost is calculated as follows:  
\[Cost(\frac{euro}{year})=(P1+P2+P3)\cdot P_{LIMIT}+C_{ann}=(P1+P2+P3)\cdot P_{LIMIT }+CRF(i,R_{proj})\cdot C_{NPC} \tag{19}\]  
The constants for calculating the BESS project cost are listed in Table 6[41; 43],  
where \(C_{OM}\) is the operation and maintenance cost, and \(N_{proj}\) is the number of years over which the cost is annualized. The total cost for each scenario is shown in Tables 7 and 8, where:  
\[Total(\frac{euro}{year})=Fixed-access-fee+BESS-project \tag{20}\] \begin{table}
\begin{tabular}{c c} \hline
**Item** & **Value [Unit]** \\ \hline BESS cost (\(\xi\)/kW) & 1876 \(\xi\)/kW \\ BESS cost (\(\xi\)/kWh) & 469 \(\xi\)/kWh \\ \(C_{OM}\) & 10 \(\xi\)/kW and year \\ \(i\) & 3.41\% \\ \(N_{proj}\) & 25 years \\ \hline \end{tabular}
\end{table} 
Table 6: Summarized costs for the BESS project.