*4.2. Route Guidance Strategy Based on Vehicle Balance in Charging Stations*

In real-world traveling situations, several charging demands may be simultaneously made in road networks. In every time slot, the heuristic suggested charging stations need to be selected for all charging demands. Reachability is the most critical factor for charging station selection in an EV trip. Furthermore, compared with the increasing number of EVs, charging infrastructure is often insufficient. Given the limited charging technology at present and for the foreseeable future [47,48], increasing charging demands and insufficient charging infrastructure may lead to queuing in charging stations. The increasing number of EVs in charging stations affects the charging stations operation. Mass EV charging may increase the operating burden of charging stations, and the queuing time in charging stations may increase as the vehicle number increases. The number of vehicles at each charging station should be considered when addressing stochastic charging demands to ensure the operation efficiency of charging stations. However, in the actual situation, the chance of being selected for charging stations differs if the number of EVs in charging stations is overlooked. For example, the charging stations located in central areas may accept more EVs with charging demands than other stations. Neglecting the number of EVs in charging stations would increase the number of EVs in the charging stations located in central areas.

In this study, we define the charging service system as stable if all charging stations have a sustainable number of EVs in every time slot. In real-world situations, the sustainable number of EVs that could be queued in a charging station is limited due to resource constraints. Thus, balancing the vehicle number at different charging stations effectively reduces the negative influence of mass EV charging on charging stations, which refers to keeping the number of EVs at different charging stations at a relatively similar level. For this reason, the route guidance strategy based on vehicle balance in charging stations is established. An effective method to realize this goal is to direct an EV to the reachable charging station with a minimum number of vehicles during the time slot. In this way, the charging stations with fewer EVs have more chances to accept charging demands. It is also worth noting that such a strategy may increase the travel cost of individual drivers in some cases, especially for the drivers who can select a closer charging station with extra capacity for charging. However, this strategy is focused on the long-term transportation scenario, and it is able to ensure the stability of charging service system in the situation with a long time horizon. In addition, even though the suggested charging station is not the nearest one, its reachability could be ensured based on Assumption 7. The performance of the strategy is discussed in Section 5. To simplify the description, the route guidance strategy based on the vehicle balance in charging stations is represented by the charging station balance (CSB) strategy.

As mentioned in Section 3, the charging service provider would receive charging demands in every time slot. The energy and time consumed to traverse each link, that is, *Et <sup>a</sup>* and τ*<sup>t</sup> <sup>a</sup>*, are known at the beginning of each time slot. The output of the CSB strategy includes heuristic suggested charging stations, corresponding routes and driving time for the charging demands at every time slot. The operating steps of the CSB strategy are detailed as follows:


$$j^\* = \arg\min\_{j^\*} \{ \! \! \! \! \! / \! \! \! \! / \! \! \! \! / \! \! \! \/ \! \! \! \/ \! \! \/ \}. \tag{5}$$

The values of decision variable *xt ij* can be determined as follows:

$$\mathbf{x}\_{ij}^{t} = \begin{cases} \ 1, \ j = j^\* \\ \ 0, \ j \neq j^\* \end{cases} \tag{6}$$

If multiple charging stations with the same and minimum EV number exist, then one is randomly selected as the heuristic suggested charging station for *Ct i* .


Figure 3 illustrates the flowchart of the CSB strategy.

**Figure 3.** Flowchart of the charging station balance (CSB) strategy.

### *4.3. Route Guidance Strategy Based on the Travel Cost of Individual Drivers*

EV drivers are the decision-makers for travel activities and the service objectives of smart charging services. Therefore, the travel demands of EV drivers should be considered when planning the selection strategy of charging stations. On the premise of charging station reachability, EV drivers often want to reduce their travel cost as much as possible. Travel cost is generally regarded as the optimization criterion for choosing travel routes [50,51]. Travel cost minimization is one of the critical factors for travel demands. Travel cost has multidimensional components during an EV trip, such as travel time, energy consumption, and charging cost [20]. The driving time and energy consumption are closely correlated with the driving distance, with the former being typically proportional to the driving distance with a constant driving speed and the latter having a significant linear relationship with driving distance [52], as well as a significant influence on charging cost; hence, the charging cost would be affected by the driving distance. The driving distance can be used to reflect the integration of travel cost components. Thus, driving distance is minimized to establish the route guidance strategy based on drivers' travel demands.

Unlike driving time and energy consumption, driving distance is a static factor in a time-varying road network. Adopting driving distance as a selection criterion can utilize such an advantage and avoid complicated prediction. The driving distance from charging stations to destinations is considered in the route guidance strategy. For the routes from origins to charging stations, we assume that EV drivers prefer to focus on reachability rather than distance as mentioned in Assumption 7. As a matter of fact, the driving distance from origins to charging stations is unable to fully reflect the travel direction consistency between charging stations and destinations, but it could be reflected by the driving distance from charging stations to destinations to a certain extent [53]. Furthermore, such an assumption could reduce computing burden and ensure the feasibility of solution. Thus, the driving distance between origins and charging stations is not involved in the strategy. To simplify the description, the route guidance strategy based on the travel cost of individual drivers is represented by the shortest driving distance (SDD) strategy.

As mentioned above, the SDD strategy aims to identify all reachable charging stations, and it directs EVs to the ones with nearest to their destinations. Similar to the CSB strategy, the output of the SDD strategy also includes heuristic suggested charging stations, corresponding routes, and driving time for all charging demands at every time slot. The operating steps of the SDD strategy are detailed as follows:


$$l\_{(j\star,d\_i^t)} = \min\_{j'} \|l\_{(j',d\_i^t)}\|.\tag{7}$$

The values of decision variable can be determined on the basis of Equation (6). If multiple charging stations with the same and minimum driving distance exist between them and *dt i* , then one is randomly selected as the heuristic suggested charging station for *Ct i* .


The flowchart of the SDD strategy is given in Figure 4.

**Figure 4.** Flowchart of the shortest driving distance (SDD) strategy.
