## 4 Configuration of BESS
### Configuration Method  
For the fast-charging stations with the BESS, the investment and profit are affected by the cost of the lithium-ion batteries, converters of the BESS, charging equipment, and purchasing electricity cost. Because of the established charging station, the distribution capacity and the transformer type can be confirmed. The research of this paper only considers the BESS capacity cost and revenue based on the time-of-use electricity price. The compared subjects were two configurations with the original load and optimized load. The economic models of the relevant factors were established as follows.  
(1) Full lifetime cost of BESS  
\[W_{tol}=W_{E}+W_{P} \tag{10}\]  
\[W_{E}=(1+\pi\%)\cdot C_{E}\cdot E\cdot\frac{\gamma(1+\gamma)^{T}}{\left(1+ \gamma\right)^{T}-1} \tag{11}\]  
\[W_{P}=(1+\
u\%)\cdot C_{P}\cdot P\cdot\frac{\gamma(1+\gamma)^{T}}{\left(1+ \gamma\right)^{T}-1} \tag{12}\]  
\[N_{ch,day}=\frac{\sum_{t=1}^{T}P_{BESS,t}\times\Delta t}{E},(P_{BESS,t}>0) \tag{13}\]  
\[N_{disch,day}=\frac{\sum_{t=1}^{T}P_{BESS,t}\times\Delta t}{E},(P_{BESS,t}<0) \tag{14}\]  
\[T=\frac{N_{sum}}{N_{disch,day}} \tag{15}\]  
where \(W_{tol}\) is the full lifetime cost of BESS, \(W_{E}\) and \(W_{P}\) are the translated daily costs with the estimated lifetime, which are the BESS battery costs and the connected converter costs in accordance with the  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Explanation** \\ \hline \(x\%\) & Ratio of operation and maintenance cost of the batteries \\ \(y\%\) & Ratio of operation and maintenance cost of the converters \\ \(C_{\rm E}\) & Cost of the BESS’s unit battery energy \\ \(C_{\rm P}\) & Costs of the BESS’s unit converter power \\ \(E\) & Rated capacity of BESS \\ \(p\) & Rated power of BESS \\ \(\gamma\) & Discount rate \\ \(P_{BESS,t}\) & Total charging power of BESS on time \(t\) \\ \(N_{sum}\) & Total number of charge–discharge cycle of BESS \\ \(\mathrm{SOE_{min}}\) & Minimum state of energy (SOE) of BESS \\ \(\mathrm{SOE_{max}}\) & Maximum SOE of BESS \\ \(P_{ch,t}\) & Charging power of BESS on time \(t\) \\ \(P_{\mathrm{dis},t}\) & Discharging power of BESS on time \(t\) \\ \(-P_{\mathrm{max}}\) & Maximum discharging power of BESS \\ \(P_{\mathrm{max}}\) & Maximum charging power of BESS \\ \(n\) & Number of sample of BESS configuration simulation \\ \(T_{n}\) & Sampling period of BESS configuration simulation \\ \(Q(n)\) & Energy of BESS at each time of the sample \\ \hline \hline \end{tabular}
\end{table}
Table 5: List of some symbols used in the battery energy storage system (BESS) configuration.  
initial investment. \(N_{ch,day}\) and \(N_{disch,day}\) are the charging and discharging number of the BESS in each day, respectively, which are also used to calculate the using lifetime of the BESS. \(T\) is the estimated lifetime of the BESS.  
(2) Electricity cost  
\[W_{ele}=\sum_{t=1}^{T^{*}}E_{t}\cdot c_{ele} \tag{16}\]  
where \(E_{t}\) is the electricity consumption on time \(t\), and \(W_{ele}\) is the electricity cost in the BESS configuration  
(3) Objective function of configuration  
\[\text{minimize}(W_{E}+W_{P}+W_{ele}) \tag{17}\]  
where \(W_{\text{E}}\), \(W_{P}\), and \(W_{ele}\) are all related to \(E\), the size of the BESS. \(E\) is the main variable of the function.