**3.2 Charging station model descriptions**

We focus on the urban electric vehicle fast charging infrastructure planning model and investigate the positioning aspects of fast charging stations in the dense residential areas road network. It supports city trips, where charging infrastructure and BEVs both play an important role in optimizing electric vehicle charging station locations. Consider a metropolitan road network where all vehicles in the network are assumed to be battery electric vehicles. This assumption is not necessarily restrictive as the model proposed below can be easily extended to accommodate both electric and regular vehicles. Let G(N,A) be a transportation network of the electric vehicles system, where N is the set of nodes (i.e., origins, destination, junctions) and A is the set of directed links (arcs). While all nodes in N are eligible candidate sites for stations, the set of O-D nodes can be a subset of N. Thus, an unpopulated road junction can be included as a candidate site but need not be included as an O-D node. Next, given a set of O-D pairs (Q) with a nonnegative traffic flow (fq), the set of nodes visited while traveling on path q (Nq), and vehicle range (R), the FRLM is defined as the problem of locating p facilities on the network G(N,A) to maximize the total traffic flow refueled. Traffic flow between an O-D pair q is considered as refueled only when vehicles leaving the origin can reach the destination and return back to the origin without running out of fuel. Before presenting the problem definition, we discuss related assumptions and present additional notation, subsequently. It is assumed that the traffic and path between the O-D pairs are known in advance. Traffic assigned a unique path is usually the shortest path determined by the Disktra algorithm [18]. From a problem formulation perspective, the proposed model can easily be extended to multiple avenues; therefore, this assumption is not restrictive. Although in some cases flow information may not be available, it can be obtained from the traffic demand matrix or through O-D estimation methods. Therefore, it is also reasonable to assume that the traffic volume is known in advance.

This work applied and extended the flow-refueling location model (FRLM) developed by Capar et al. (2013) [19, 20] as a basis. The formulation of the problem is as follows.

$$\text{Max}\left[\sum\_{q\in Q} f\_q \mathbb{y}\_q\right] \tag{1}$$

Subject to:

$$\sum\_{i \in K^q\_{j,k}} z\_i \ge \mathcal{Y}\_q \forall q \in \mathcal{Q}\_\* a\_{j,k} \in A\_q \tag{2}$$

$$\sum\_{i \in N} z\_i = p \tag{3}$$

$$z\_i, \boldsymbol{y}\_q \in \{0, 1\} \forall q \in Q, i \in N \tag{4}$$

Where,

*f <sup>q</sup>*: Traffic volumes on the shortest path between O-D pair *q*.

*a <sup>j</sup>*,*<sup>k</sup>*: A directional arc starting from node j and ending at the node *k*.

*Aq*: Set of directional arcs on path q, sorted from origin to destination and back to origin.

*Kq <sup>j</sup>*,*<sup>k</sup>*: Set of candidate nodes, which can refuel the directional arc *a <sup>j</sup>*,*<sup>k</sup>* in *Aq*. *M*: Set of O-D nodes where *M* ∈ *N*.

*N*: Set of nodes which constitute the network, *N* ¼ f g 1, 2, … , *n* .

*p*: The number of stations to be located.

*q*: Index of O-D pairs.

*Q*: Set of O-D pairs.

*yq* and *zi* are decision variables. =1 if the flow on path q is recharged (and feasible), and equal 0 if not; *zi* =1 if a service station is built at node i, and *zi* =0 if not.

*i*; *j*; *k*: Indexes for potential facilities at nodes.

The set of candidate sites accessible from the mth candidate site on a path q can be calculated from [10]:

$$K\_{j,k}^{q} = \begin{cases} \left[ N\_q \middle| d\_{j,r}^q \le R, r > j \right] & \forall q \in \mathcal{Q}, j = 1, 2, \dots, M\_q, k = 1 \\\\ \left[ N\_q \middle| d\_{j,r}^q < R, r > j \right] & \forall q \in \mathcal{Q}, j = 2, \dots, M\_q, k = 0 \\\\ \left[ N\_q \middle| d\_{j,r}^q \le R/2, r > j \right] & \forall q \in \mathcal{Q}, j = 1, k = 0 \end{cases} \tag{5}$$

Where,

*Kq <sup>j</sup>*,*<sup>k</sup>*: is the set of candidate sites accessible from the mth candidate site on a path *q*.

*Nq*: is the set of candidate sites on a path q, now sorted in sequential order from origin to destination.

*Mq*: the number of candidate sites on path q beyond the origin but not within half the range R of the destination of path q, that is, in the distance interval 0, *Dq* � *<sup>R</sup>=*<sup>2</sup> � � on path *<sup>q</sup>*; if *Dq* � *<sup>R</sup>=*<sup>2</sup> <sup>≤</sup><sup>0</sup> � � then *Mq* =0, with *Dq* is the length of the shortest path of an O-D pair *q*.

*R*: the range of electric vehicle.

The battery range of an EV trip represents the maximum length an EV can travel without charging, which is imposed by the battery technology. Here, "charging" is used to broadly represent battery recharge, battery exchange, or any other option to obtain a fully charged battery for the EV to continue its travel. To develop a widely applicable fast-charging station location optimisation method that considers the several relevant variables of the electromobility systems, which are as follows: trafic flow volume, the usual range of battery electric vehicle, general user demand, and especially taking into account the effect of traffic congestion; however, trafic flow volume, range of electric vehicle, and the number of EVs are the most critical parameters. The outlined method first computes static ranking variables based on statistics and spatial relations (getting and summing close attribute values). Then the selection of those candidate sites that fit the scenario goals was performed by GIS scripting.

In fast-charging infrastructure location optimization method, the set of candidate sites *K<sup>q</sup> <sup>j</sup>*,*<sup>k</sup>* (Eq. (5)) was combined with the vehicle traffic data from the EV trajectory was grouped into charging demand clusters through clustering analysis to determine the optimal locations for charging stations.

#### **3.3 Traffic congestion coefficient**

The energy consumption of an electric vehicle depends not only on the distance it travels, but also on the density of vehicle traffic on the road. Traffic congestion at different times of the day plays an important part in the energy consumption of an electric vehicle. We use a traffic congestion coefficient [21] to analyze the interlink

*Fast-Charging Infrastructure Planning Model for Urban Electric Vehicles DOI: http://dx.doi.org/10.5772/intechopen.100011*

between traffic and energy consumption. This coefficient is calculated as the ratio of actual energy consumed by an electric vehicle to cover a certain distance during particular hour of the day, to the energy consumed by it during the same period to cover the same distance on an empty road under ideal conditions. The coefficient varies between 0 to 1, with 1 reflecting an empty road condition and 0 being standstill traffic. This traffic congestion coefficient might vary from place to place. This coefficient takes into consideration the energy loss due to frequent breaking and accelerating and extra energy consumed during vehicle ignition. All other minor inefficiencies are included in this coefficient.

$$
\pi = \frac{d\_{\text{act}}}{d\_{\text{idc}}} \tag{6}
$$

Where,

*τ*: Traffic congestion coefficient.

*dact*: Actual distance travellled by an electric vehicle.

*didc*: Distance travellled by an electric vehicle under ideal condition.

Before scheduling the next trip for EV, its state of charge has to be assessed to evaluate whether the remaining battery level is sufficient enough to take the next trip or to travel to the nearest charging station. A general equation for the distance that an EV can travel during a certain hour of the day can be derived as [22]:

$$D = \sum\_{i}^{i+1} (I\_{\text{SoC}\_i} - \text{SoC}\_{\text{min}}) \times R \times \pi\_i \tag{7}$$

Where,

*D*: Distance traveled over the operating period per day, (km).

*ISoCi* : Initial State of Charge of the Battery at the start of an hour, (%).

*SoC*min: Minimum State of Charge of the battery, (%).

*R*: Range of an electric vehicle under ideal conditions, with low traffic and no obstacles, in a single charge, (km).

*τ*: Traffic Congestion Coefficient.

### **4. Application: a case study**

The geographical information of the transport system was extracted from OpenStreetMap [23]. The survey area is in Cau Giay district, Hanoi city (Vietnam). It is comprised of 166 nodes (geographical points) and approximately 500 sections of roads (straight lines connecting two nodes) with lengths ranging from a few meters up to 10 km. Office/work hours are based on the Vietnam legislation are from 8 am to 17 pm. This information is used to create the vehicles' plans.

This network has 363 arcs and 166 junctions (vertices), each of which serves as a candidate site. The OD flow of electric vehicles and the distance between the OD points in Cau Giay district during a working day are provided. There are 166 candidate sites and 5000 O-D pairs were tested in a working day. Note that because the model ensures that the return trip is rechargable, by extension so are the round trips starting at either end. For illustration purposes, **Figure 2** shows, the transportation system indicating roads, as bold lines. In the transportation network shown in **Figure 2**, there are 166 candidate sites for the fast-charging station. These were locations where fast-charging stations can be deployed, highlighted in green, and numbered from 1 to 166. However, not all of them have been selected for

**Figure 2.** *Transportation network in Cau Giay District, Hanoi, Vietnam.*

fast-charging station deployment. The selection depends on the vehicles traffic flow through the candidate sites' locations. Therefore, the vehicle traffic flows through nodes were evaluated, the node with high traffic will be prioritized for selection to deploy the fast-charging station. The three candidate nodes circled in red in **Figure 2** (nodes 76, 90, and 135) are nodes with high media flow as assessed through simulation. These nodes are located on arterial traffic routes which vehicles from outside enter the center and vice versa. The traffic flow profiles for nodes 76, 90, and 135 of intense vehicle movement, surveyed during the average 1-day period, was shown in **Figure 5**.

Before the traffic flow simulation, the routes of each vehicle must be defined, i.e. the shortest path between the points in their plans (Dijkstra's algorithm [18]). After each traffic flow simulation, vehicles facing traffic jams have their routes recalculated. The travel time of each vehicle depends on the length of the section of road belonging to its route and the actual velocity. All vehicles perform their routes concurrently. This process is repeated for a pre-defined number of iterations to reduce the travel times individually [24].

It can be noted from **Figure 3** that most of the trips are shorter than 35 km. Generally, the travel modes of trips consist of walking, riding a bicycle, using public transit, and using a private car. The walk and bicycle travel modes have short trip lengths mainly under 10 km. Therefore, the daily trips whose length is over 20 km are assumed to be EV trips in this survey, and these trips were used to generate basic travel demand.

The hourly travel demand was imported into SUMO (Simulation of Urban Mobility) [25] for vehicle traffic flow analysis to generate the trajectory of the EVs. Since the EVs may have multiple trips in a day, the time sequenced trajectories between different activity locations for one EV were merged to reconstruct the complete daily trip. **Figure 4** illustrates an EV trajectory example, trajectory 1 illustrates the route from home to work, while trajectory 2 illustrates a different route since the EV traveled to other purpose activity place during the trip from work to home. Both trajectory 1 and trajectory 2 make up the complete daily trip for one EV.

*Fast-Charging Infrastructure Planning Model for Urban Electric Vehicles DOI: http://dx.doi.org/10.5772/intechopen.100011*

**Figure 3.** *Distribution of trip frequencies by cumulative trip length.*

**Figure 4.** *An example of EV trajectory with other purpose trip.*

In traffic flow analysis, we applied to the 166 nodes in the traffic network, one O-D flow contains the information about how many vehicles are driving from O to D and back in a day, a week or a certain period of time. The set of locations of nodes with high traffic is determined through simulation data analysis which are preferred locations in the fast-charging station selection.

**Table 1** shows an exemplary O-D pair from node (76) to node (90). The distance from node (76) to node (90) is 32 km. The path of this O-D flow shown in the table starts at node (76) and continues all the way crossing nodes (77), (80), and (91) until it reaches node (90) and come back. Traffic flow through all nodes are evaluated. The high traffic flow sections of roads are considered to be potential fast charging stations locations. The traffic flow profiles of nodes locations (76), (90) and (135) are plotted on **Figure 5**. Each profile is unique, consequence of vehicles


#### **Table 1.**

*Table entries for the O-D pair 76–90.*

**Figure 5.** *Traffic flow profiles for three roads of intense vehicle movement.*

flowing towards city centre in the morning and the other way around after work. High and thin peaks indicate possible traffic jams.

Characteristics of electric vehicles used in this survey are shown in **Table 2**. Fast-charging stations are assumed to be immediately available to EVs that arrive for charging, i.e. EVs do not wait to charge.

The travel times of EVs can be translated into cost. Thus, initially, fast-charging stations locations are selected using the most used routes of regular vehicles based on traffic flows. So, the selected fast-charging stations locations might be suitable for some EVs, it will not necessarily be aligned with the routes of all EVs. Several EVs go to charge in this fast charging stations causing traffic jams, leads to larger travel times within the region. This highlights the importance of evaluating the selected locations. Besides, traffic congestion is quite a serious problem in developing cities, especially with mixed traffic characteristics like in Hanoi. Traffic congestion affects the distance traveled by EVs, and this must be taken into account when planning electric vehicle charging stations. **Figure 6** shows the variations in the traffic congestion coefficient over the day, calculated using the Eq. (6). Survey time is from 7 am to 10 pm.

From all candidate sites, the top 18 busiest sections of roads are considered to be potential fast-charging station locations (red circle in **Figure 7**). Most of these fastcharging station locations are outside the city centre, on the northern and western areas due to the population distribution. With the fast-charging station locations identified, the traffic flow analysis is performed for each of the fast-charging station cases: from one to 18 fast-charging station locations.

*Fast-Charging Infrastructure Planning Model for Urban Electric Vehicles DOI: http://dx.doi.org/10.5772/intechopen.100011*


#### **Table 2.**

*Characteristics (average) of EVs [26].*

**Figure 6.** *Traffic congestion coefficient variation.*

**Figure 7.** *Potential fast-charging station locations with high traffic flow of EVs.*
