## 3 Numerical Experiments
### Comparison of Results between Modular BSS and Traditional BSS  
One of the critical features of ET BSS is the demand-based battery rental mode to match individual travel behaviors. In this subsection, we will explore the advantages of this feature by comparing the costs and charging scheduling of the modular BSS with that of the traditional BSS.  
There are some differences between traditional BSS and modular BSS in terms of parameter settings. ET drivers can only choose to rent a fixed capacity battery in traditional BSSs. We assume the battery's rated capacity in the traditional BSS is equal to that of the summation of two battery blocks in the modular BSS. Except for that, the other parameters are the same as in modular BSS. Since the input of the data-driven model in our study, i.e., the daily travel patterns of ETs, are the same in both experiments, the daily _BSD_s differ due to the different operating modes of the two BSSs, which does not lead to unfair experimental comparisons.  
Table 4 represents the comparison results of annual costs of two BSS operational strategies.  
The results show that modular BSS can save investment and operating costs significantly. Under the modular battery swapping service scenario, modular BSS's annual investment cost of battery blocks is 27,609.14 USD, which is 16,921.74 USD (38%) less than the traditional battery swapping service. Specifically, we convert the batteries purchased by the traditional BSS into equivalent battery blocks, and the modular BSS can purchase 19 fewer battery blocks than the traditional BSS. Therefore, a modular BSS's annual investment cost of battery blocks is less than that of a traditional BSS. It follows that modular BSSs can reduce battery inventory at BSS by considering ET drivers' heterogeneous driving range requirement and by providing a demand-based battery rental mode to match individual travel behaviors.  
As for the electricity cost, modular BSS purchases 84,049.78 USD of electricity from the grid, which is 39,401.36 USD (31.92%) less than the traditional BSS. We next analyze the operational stage. Figure 6 shows the total number of battery blocks in the charging state in each hour of a day over a year using the two operational strategies of modular BSS and traditional BSS. We can see that ET battery blocks in both BSSs are mainly charged during periods of flat and valley prices. This suggests that BSSs can reduce the burden of uncontrolled charging on the grid compared to EVs charging stations. In addition, the percentage of battery blocks in the modular BSS charged during the period of valley price is 53.7%, much higher than the 36.30% in the traditional BSS. Conversely, the percentage of battery blocks charged during peak price periods in the modular BSS is 3%, which is much smaller than the 12.86% in the traditional BSS. This indicates that modular BSSs perform better than traditional BSSs in terms of peak shaving and valley filling.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Annual Costs** & \begin{tabular}{c} **Annual Investment** \\ **Cost of Battery** \\ **Blocks (USD)** \\ \end{tabular} & \begin{tabular}{c} **Annual Operation** \\ **and Maintenance** \\ **Costs (USD)** \\ \end{tabular} & \
\begin{tabular}{c} **Electricity** \\ **Cost (USD)** \\ \end{tabular} &
\begin{tabular}{c} **Number of Purchased** \\ **Equivalent Battery Blocks** \\ \end{tabular} \\ \hline Traditional BSS & 170,234.52 & 44,530.88 & 2252.50 & 123,451.14 & 50 \\ Modular BSS & 113,055.47 & 27,609.14 & 1396.55 & 84,049.78 & 31 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison results of two BSS operational strategies.