# Assessing the Impact of an EV Battery Swapping Station on the Reliability of Distribution Systems
## 2 Overview of Battery Swapping Station
### Charging Strategy  
The charging behavior of the power station is not only related to the behavior and habits of EV users, but it is also greatly affected by the price. Different from the plug-in EV charging station, the charging object of a BSS is the EV battery, which means that the charging time cannot be affected by the arrival and stay time of the EV owners, but the charging time and power can be flexibly scheduled. BSS needs to purchase electricity from the grid to charge batteries, while the current electricity market often uses time-of-use (TOU) electricity prices or peak-to-valley electricity prices. Taking into account the economics of the overall operation of BSSs, based on the peak-to-valley price of electricity, we design the following charging strategy. The core idea is to charge as much as possible during the valley time  
Figure 1: The structure of a battery swapping station (BSS).  
Figure 2: Illustration on the work-flow of a BSS.  
when the electricity price is lower and to reduce the charging demand as much as possible during the peak time of the higher electricity price [13]. It can be expressed as:  
\[\begin{array}{l}\textit{during peak time},P_{k,t}^{ch}=0.5P_{\textit{rated}}^{ ch},k\in\Omega_{1,t}\\ \textit{during shoulder peak time},P_{k,t}^{ch}=0.8P_{\textit{rated}}^{ ch},k\in\Omega_{1,t}\\ \textit{during off peak time},P_{k,t}^{ch}=P_{\textit{rated}}^{ch},k\in\Omega_{1,t} \end{array} \tag{1}\]  
where \(P_{k,t}^{ch}\) denotes the charging power of battery \(k\) in time \(t\); and \(P_{\textit{rated}}^{ch}\) denotes the rated charging power of batteries.  
However, adopting the above-mentioned charging strategy only guarantees the economy of BSS operation, but it cannot guarantee that BSS has sufficient battery reserves at every moment \(t\), so that every EV user can replace the empty battery with a fully charged battery. In order to solve this problem, we introduce inventory management theory [19]. Define the minimum limit of the number of batteries that BSS can be used for replacement (namely the number of batteries in the waiting queue and also the number of set \(\Omega_{2,t}\) elements) at time \(t\) as \(S_{0}\). When the number of available batteries at that time is lower than the minimum value, all charging slots work at full power to charge all HB so that the number of batteries in the waiting queue reaches a certain value \(S\) higher than \(S_{0}\). Among them, (\(S_{0}\), \(S\)) is defined as the buffer zone, and the lowest limit \(S_{0}\) is used to ensure the normal operation of the battery swapping service without interruption due to lack of available batteries. So far, the battery charging strategy in this article can be expressed as:  
\[\begin{array}{l}\textit{if}\left|\Omega_{2,t}\right|<S_{0}\\ P_{k,t}^{ch}=P_{\textit{rated}}^{ch},k\in\Omega_{1,t}\\ \textit{else}\\ \textit{during peak time},P_{k,t}^{ch}=0.5P_{\textit{rated}}^{ch},k\in\Omega_{1,t} \\ \textit{during shoulder peak time},P_{k,t}^{ch}=0.8P_{\textit{rated}}^{ ch},k\in\Omega_{1,t}\\ \textit{during off peak time},P_{k,t}^{ch}=P_{\textit{rated}}^{ch},k\in\Omega_{1,t} \end{array} \tag{2}\]  
Then the SOC of HB during the charging period can be calculated as follows:  
\[SOC_{k,t+1}=SOC_{k,t}+\frac{P_{k,t}^{ch}\Delta t\eta^{c}}{E_{rated}},\,k\in \Omega_{1,t}. \tag{3}\]  
where \(SOC_{k,t}\) denotes the SOC of battery \(k\) in time \(t\); \(\eta^{c}\) and \(E_{rated}\) denote the charging efficiency and rated capacity of EV batteries, respectively; \(\Delta t\) denotes the unit time interval.