# Toward Efficient Mobile Electric Vehicle Charging under Heterogeneous Battery Switching Technology
## 3 System Model
### Heterogeneous BSS Selection Concerning BS Reservation and Load Balancing across BSS
#### 3.4.2 Selection of BSS Phase for BS Service
* For the purpose of estimation ATS such information is additionally needed (\(R_{V}\)ID, \(B_{type}\), \(R_{vt}^{arr}\), \(C_{SOC}\), \(C_{L}\)). Thus, for accounting and identifying each and every requested vehicle reach to selected BSS or not, the optimizing equation is given below (line 12 to 14 Algorithm 1). \[T_{2}=\frac{r_{BSS}-r_{vi}}{d_{km}^{hour}}\] (3) where \(T_{2}\) is time that obtained the flow and distance of each vehicle, the term \(r_{BSS}\) is the position vector of selected BSS and \(r_{vi}\) is the position vector of the requested vehicle, Similarly, the term \(d_{km}^{hour}\) is obtaining the results of time that taken by \(R_{V}\) from current to final location (line 15). * After confirming the selection of BSS and reservation response back to GC, the vehicle may need extra time and cannot reach the selected BSS on required time because of road uncertainties including traffic jam signals, road congestion, and accident. By accounting uncertainty time for each \(R_{V}\) the Equation is given below (line 16 Algorithm 1). \[T_{3}=T_{1}+T_{2}+B_{f}^{t}\] (4) The arrival time of the vehicle can be accounted for according to the above Equation (4). The term \(B_{f}^{t}\) is refer to buffer time which is considering 10 min for each vehicle to address roadside uncertainties. Where \(T_{3}\) is representing the approximate time (along with buffer time) which is taken by vehicle up to BSS from current location(line 17 Algorithm 1). Similarly, for accounting total time which is taken by vehicle for reaching to selected BSS and time taken while battery switching process including \(Q_{t}\) and \(S_{t}\) at the station, the Equation of problem is refined below (line 16 Algorithm 1). \[EST=T_{3}\] (5) After accounting the EST, if the \(R_{V}\) reach the selected BSS on current SOC and confirm the reservation. The GC allocate battery in the station when \(R_{V}\) reach on required ATS to selected BSS switch the battery with fully charged. BSS decrease by 1 \(M_{B}^{S}\) and update the status of the switching station (line 17 to 21 Algorithm 1). * Upon sending request by \(R_{V}\) to GC some time the required battery type is not readily available (\(M_{B}^{S}=0\), \(X\in B_{type}\)) but available on charge. In this case, the vehicle will wait when the required battery type is fully charged according to Equation (6) when \(M_{ battery}^{EL}=C_{ battery}^{EL}\). The switching station will change the status of the number of \(M_{B}^{S}>0\), \(X\in B_{type}\)) and the update status (line 21 to 24 Algorithm 1). \[E_{cha}^{time}=M_{ battery}^{EL}-C_{ battery}^{EL}\] (6)
where the term \(E_{cha}^{time}\) denote the expected charging time of the drained battery, \(M_{battery}^{EL}\) represent the maximum battery energy level mean that how much power will get the battery to fully recharge again and \(C_{battery}^{EL}\) shows that the current battery energy level of the required battery. Along with this time again EST to find that the \(R_{V}\) reach to selected \(BBS\) on below Equation (7) (line 24 Algorithm 1). \[EST=T_{3}+E_{cha}^{time} \tag{7}\]  
In this equation the EST refer to \(W_{t}\). However, when \(R_{V}\) reaches selected BSS and the required battery type is readily available (\(M_{B}^{S}>0\)), the vehicle will switch the battery with a fully charged battery. After the switching process is completed, BSS decreases the number of \(M_{B}^{S}\) for the required battery type by \(1\). Similarly, the depleted battery of the vehicle is added to the charging queue to recharge. Updating the status of \(M_{B}^{S}\) and sharing procedure with GC are described in line 26 Algorithm 1). As such, expected energy consumption of the entire system is refined by the following equation.