**3. Charging station model description and method**

From the point of view of modern city planning, the location of EVs charging stations must meet the requirements of the city transportation network layout. While from the perspective of power system planning, the location of EVs charging stations should be in accordance with the current situation in short-term as well as long-term planning of the distribution system involved. EVs charging stations must be close to load centers and respect constraints on load balance, power quality, and power supply reliability of urban. From the perspective of EVs' owners, the sites of EV charging stations should be in locations which are convenient for EV's owners and near the charging demands. Furthermore, other factors, such as the location adaptability and land price, should also be considered. Thus, the initial candidate sites of EV charging stations can be determined with the aforementioned factors properly considered.

#### **3.1 Illustrative example and electric vehicle data collection**

We first use a simple illustrative example to highlight the importance of considering the trip sequence in describing the travel and charging behaviors in a common use case of electric vehicles. In **Figure 1**, assuming network nodes (1), (2), (3), (4) and (5) are candidate locations for charging station placement. Node 1 was set as origin and node (5) was set as destination. The distance of each link are also shown

**Figure 1.** *An example network with a single O-D.*

in the Figure. A full journey would be (1,2), (2,3), (3,4), (4,5) to reach the destination, and then back (5.4), (4, 3), (3,2), (2,1) to return to the original position. We first assume that the vehicle battery range R ¡40 km when the tour starts, there is no chance for vehicles to complete the trip between the O-D pair because vehicles cannot complete the trip (2,3). When R = 40, the charging station can choose one of two alternatives with (1,2,3,4) or (1,2,3,5). Under both solutions, electric vehicles will be charged at nodes (1), (2) and (3). If at (4) is placed a charging station, vehicles charged at (4) can reach the destination and return to (4). Next, after being fully charged at (4), the vehicle can return to the origin by charging again at (3) and (2). Similarly, we can see that when R = 50, it does not need to place the charging station at (1) anymore because a fully charged vehicale at (2) (while returning from the destination) can reach the origin and have enough electric capacity to travel to (2) when a new trip is next start. When R = 200 km, a single charging station at any node is sufficient to charge the entire journey because even after a full charge at (1), the vehicles will have enough battery capacity to reach (5) and go back to (1).

Through the above simple example, we see that the range of battery electric vehicle plays a decisive role in the distribution of charging stations on the traffic network in the city. First, if there is no charging station built at the origin then there should be at least one charging station was built within the R/2 distance to the origin node. Second, if there is a charging station was built at a location, the next charging station should be within the range R. Finally, if the vehicle range is greater than or equal to two times the path length, a single charging station at any node can provide electrical power whole journey. Thus, if there is a charging station at the origin node, the model will start the round trip with a fully charged state (State of Charge - SoC = 100%). If there is no charging station at the origin node, vehicles will start with the remaining battery SoC observed at the end of the previous trip. With the assumption of constant energy consumption and roundtrips it is secured that each trip will at least start with SoC of 50%.

The problem of placing charging stations for electric vehicles involves finding the optimal location of charging stations in the transport network so that the operating parameters of the vehicle network are least affected. Real-world vehicle travel patterns, especially for electric vehicles, provide abundant information to investigate charging demand. Nevertheless, it is impractical to adopt the travel information from all private vehicles. Therefore, GPS location data and vehicle's trace collection was considered to provide the travel information.

Besides the commute trips, the other purpose trips were also considered in this model. The purpose of activity locations was determined by the time of day. For instance, the "home" location is defined as the place with the most visits between 8 pm and 8 am for each day during the observation period, while the "work" location is defined as the place with the most visits on weekdays between 8 am and 8 pm during the observation period. The rest of the locations are regarded as the "other", such as shopping and recreation. With the activity location and purpose inferred from the vehicle's traces, the 24-hour travel demand for the electric vehicle is able to generate based on the time sequence of each activity.
