# Economic Routing of Electric Vehicles using Dynamic Pricing in Consideration of System Voltage
## 3 Charging Strategy for Charging Stations  
The operator determines the charging price according to the state of the system and sends this information to the CS. The CS then updates the charging price. The inter-layer communication shown in Figure 2 can be described as follows: \(P_{demand}\) is the charging schedule of the CS, \(DP_{i,t}\) is the additional charging price signal of the \(i\)th CS at time \(t\), \(P_{i,schedule}\) is the charging schedule of the EV, and \(\overline{TOU_{i,t}}\) is the updated charging price of the \(i\)th CS at time \(t\). Figure 1: Flowchart of [PERSON]’s algorithm. The following equations describe the objective function of the EV's route selection. \[\mathrm{argmin}(w_{jk}(i)) \tag{1}\]  
\[w_{jk}(i)=\sum_{t=t_{ji}}^{T_{i,t}}(E_{jk}(i)\times\overline{TOU_{i,t}}) \tag{2}\]  
\[E_{jk}(i)=S_{jk}(i)/\eta \tag{3}\]  
\[T_{i,t}=\frac{E_{ik}(i)}{P}+t_{ji} \tag{4}\]  
\[\overline{TOU_{i,t}}=T\mathrm{O}U_{i,t}+DP_{i,t} \tag{5}\]  
\[0<\overline{TOU_{i,t}} \tag{6}\]  
where  
\(i\): charging station;  
\(j\): starting point;  
\(k\): destination point;  
\(w_{jk}(i)\): sum of the weights from \(j\) to \(k\) through charging station \(i\);  
\(T_{i,t}\): charging time from \(t\) to the charging station \(i\);  
\(t_{ji}\): time from \(j\) to charging station \(i\);  
\(E_{jk}(i)\): amount of energy required to go from \(j\) to \(k\) through charging station \(i\);  
\(E_{ik}(i)\): amount of energy required to go from charging station \(i\) to \(k\);  
\(S_{jk}(i)\): distance from \(j\) to \(k\) through charging station \(i\);  
\(\eta\): driving power efficiency of EVs (km/kWh); and  
Figure 2: Operation scheme of the system. _P_: rapid charging power. The EV uses [PERSON]'s algorithm to determine the route with the minimum cost, as shown in Equation (1). Equations (2)-(6) are constraints. Equation (2) is a measure of the weight value of each route calculated by multiplying the energy required for driving by the charge price. Equation (3) is the required energy calculation for the driving distance considering charging station \(i\). Equation (4) is a formula for the time spent charging at charging station \(i\). Since the charging power of the CS is a constant, it was used to check the charging time of the EV arriving at the charging station and apply it to the charging schedule. Equations (5) and (6) are constraints on dynamic prices as the dynamic pricing signal. The dynamic pricing signal should be added or subtracted to the existing TOU (Time-of-Use) price, and the reflected price should be positive. Figure 3 shows the operating algorithm of the system operator. First, EV driving data is developed as a probability model based on actual highway data. These data are the number of vehicles that pass-through toll gates on inter-hourly highways and are modelled with the probability that vehicles have passed during each time period. The route will be selected considering the price information for charging the battery, driving distance of the vehicle, normal speed for the road on which it is driven, starting time, and destination. The route selection algorithm is shown in Equation (1) and is performed by individual EVs. The cost of charging the battery will act as a weight in the route selection algorithm, and the charging price will determine the route that can be driven at the minimum cost. It is assumed that when an EV user selects a driving route, it passes through a charging station once. Charging stations that receive the time the vehicle arrives at the charging station incorporate the information to schedule the charging demand. The charging station shares the charging schedule with the system operator. The price information of the reflected charging station shares information with the vehicle in real time, and the vehicle that sets the driving route sets the route with the updated price information. Figure 3: Flowchart of the system operator. The CS transmits the schedule obtained from the electric vehicle to the system operator.