Multi‐objective locating of electric vehicle charging stations considering travel comfort in urban transportation system

Correspondence Maryam Ramezani, Faculty of Electrical and Comp. Eng. , University of Birjand, P.O.B. 97175/376, Birjand, Iran Email: mramezani@birjand.ac.ir Abstract Environmental concerns of using fossil fuel vehicles and recent developments in electric vehicle (EV) technology have attracted the attention of the international community to use EVs. A design strategy is proposed by simultaneously considering a distribution network and an urban transportation network, that maximises drivers’ travel comfort in urban trips and reduces costs of both charging station (CS) installation and losses. The proposed strategy meets various constraints such as, properly locating CSs in the city, considering traffic volume, taking the shortest route, reducing charging waiting time, limits of bus voltages, power balance, the permissible loading of lines. The travel comfort index corresponds to a situation in which the driver does not experience a depleted battery and successfully finish the trip. Since the movement of vehicles over the course of a day does not follow any particular pattern, unscented transformation is used to investigate the uncertainty in different probabilistic parameters of EVs. Moreover, by clustering the locations of EVs, the optimal locations of EV CSs are determined over the course of the day (in several time steps) using a multi-objective function based on a GA. The simulation results of the sample urban transportation and distribution networks confirm the efficacy of the proposed method.

urban transportation system. The main method of probability studies is Monte Carlo simulation (MCS). In [9,10], MCS was used for studying EVs. In [3], normal distributions were used for the variables of travel distance, the initial state of charge and the starting time of charging. In this study, the decongestion of urban traffic was considered in addition to investigating the distribution network. Although the Monte Carlo method is an accurate technique for studying statistical phenomena, it requires a large number of iterations for large networks. In statistical studies for siting charging stations, the number of statistical variables is large, and the transportation network is complicated [11].
In [12], the unscented transformation (UT) was used to perform statistical studies. The number of iterations required to investigate the statistical problem was very small in this method. For example, for three variables, four or five iterations are required [13], while the Monte Carlo method requires more than 1000 iterations. In [14], the optimal siting of EV parking lots was proposed to reduce the voltage deviations and network losses, and the demand curve was flattened using vehicle-to-grid (V2G) technology. In [15], a method was presented for optimal siting and sizing of plug-in hybrid electric vehicle (PHEV) charging stations, and this optimisation was accompanied by the optimal siting of renewable energy sources (RES). The multi-objective optimisation function includes the cost of charging and discharging and V2G technology was available in these stations. The objective functions of the problem were the costs of charging and discharging, voltage and network losses. In [16], a multi-objective algorithm was proposed to optimally allocate a number of renewable energy systems, including PHEV parking lots, to the distribution system. The proposed algorithm determined the number, siting and sizing of RES and parking lots. In these studies, the distance traveled by the vehicles and successful trip were not considered. Furthermore, statistical variables were not included precisely and clearly.
In [17], an operation scheduling model was presented that prevented price jump in the electricity market dominating the distribution network with a relatively significant demand of EVs. Therefore, in this study, EV charging controllers minimised the charging cost. The proposed method in [17] was limited only to EV parking lots. In [18], EV charging stations were studied based on a cost-benefit analysis. The method for implementing this strategy was smart charging of EVs. This study used V2G technology to flatten the daily load curve, besides minimising the costs in the design horizon. Applying the smart charging method definitely increases the complexity and investment cost. In [19], sizing and siting of EV fast-charging stations were investigated in the transportation and distribution networks. In this study, the limitations of drivers for charging EVs were considered. Since this method studied outside of the urban area, the complexities of the urban transportation network were not considered, so the method is not applicable to urban transport. In [20], sizing and siting of EV charging stations were investigated by considering the transportation network. This study focused on the location of connecting the high voltage sub transmission lines to the transportation network. This paper considered the uncertainty of the problem and had the limitations of the previous study [19]. In [21], a new approach based on possibilistic uncertainty was used to define the desired variables and optimal locating of EV charging stations. One of the features of this study was problem investigation through grey theory in which the data shortage cannot disturb the solution process. Reference [22] focused on the dynamic charging network design, that is, how to optimise the charging station locations and the number of chargers in each station at different time stages with an increasing EV penetration ratio. Reference [23] used genetic algorithms (GAs) to identify profit-maximising station placement and design details, with applications that reflect the costs of installing, operating and maintaining service equipment, including land acquisition. Reference [24] proposed a public charging station locating and sizing method based on the discrete distribution of EV charging demand. In most of the above studies, the trip success rate and driver comfort have not been considered. Additionally, in these studies, no traffic constraints have been considered for the city and behavioural model of the drivers.
The purpose of the present study is to propose a new method for optimal siting EV charging stations by considering the transportation system and distribution network with the help of a multi-objective GA. The first objective function of the optimisation problem includes the costs of installing charging stations and distribution network losses, and the second one includes the success rate of EVs in terms of taking the shortest route and providing drivers comfort. The constraints of the problem involve travelable distance limitation, traffic volume, limitation of the number and capacity of charging stations, limits of bus voltages, as well as, limits of power line loading and electrical power balance etc. A simplex UT method is employed for statistical studies of probabilistic parameters of EVs; instead of studying a large number of different states, few specific samples are studied.
The novelties of this paper can be summarised as follows: • Designing EV charging stations in urban transportation and distribution networks under uncertainty • Reducing the complexity of the problem of locating charging stations using a probabilistic UT technique • An operational approach to the problem of designing charging stations besides maintaining the uncertain nature of the problem • Consider the volume of traffic for higher routes This paper is organised as follows. Section 2 deals with the charging model of EVs and their probabilistic (random) parameters. Section 3 presents the objective functions of the optimisation problem, which is divided into two parts of the costs and the trip success rate. In Section 4, EVs are modelled in the network considering time steps; moreover, this section describes k-means clustering for EV locations and UT for probabilistic parameters, equations and the proposed strategy. The network under study, the proposed strategy and the simulation results are presented in Section 5, and finally, concluding remarks are presented in Section 6.

ELECTRIC VEHICLE AND PROBABILISTIC PARAMETERS
Due to their random nature, EVs have different random parameters that can be used depending on the modelling type. Some of these parameters are: Locations of EVs, the trip start/finish time, route length (travel distance), initial state of charge (SOC), EV batteries capacity and drivers' behavioural pattern. Therefore, different statistical distributions are used to model the EVs [3].
In this paper, four random parameters are considered for EVs. The probability distribution function of each random variable depends on its behaviour type.
1. The state of charge of EVs is one of the random parameters that can be expressed in percentage or a number between 0 and 1; 0 indicates a depleted battery and 1 means a fully charged one. Accordingly, a normal distribution is considered for SOC as shown in Figure 1 2. The initial locations of EVs in the transportation network are different depending on the network type, routes type and traffic volume on the routes at different points of the network. Therefore, the locations of EVs can be determined as geographical coordinates by a uniform distribution function in the studied network 3. The travel distance of EVs in their daily trips is considered as another random variable that determines the destination of EVs. For this parameter, a uniform distribution function is used to obtain a number that indicates the travel distance, and therefore, the destination of an EV 4. The start time of EV trip within the interval under study is also considered as a random variable. Since trips are generally started in the morning, a logarithmic normal distribution function is used ( Figure 2). The trip start time is defined as a variable that determines the time step as will be further described (Section 4.1)

OBJECTIVE FUNCTIONS OF CHARGING STATION SITING PROBLEM
The purpose of this paper is to optimal siting EV charging stations in the network under study as a multi-objective function. In this way, the cost objective functions of the distribution network and the charging stations are minimised, and EV trip success rate is maximised. These two objective functions and the corresponding equations will be explained in the following subsections.

Cost objective functions of charging stations and distribution network
EVs for transportation derive their required power from the electricity distribution network at charging stations. In determining candidate locations for charging stations, besides economic considerations, some other aspects should also be considered for meeting the drivers' expectations. These aspects include availability, access to the distribution network, impacts on traffic congestion and other electrical and non-electrical considerations. The charging capacity of a charging station depends on the capacities of the feeder and charging equipment, as well as, the physical extent of the stations. To reduce the charging waiting time, charging stations are equipped with level 3 fast charging systems. However, in the long run, fast charging can cause rapid batteries to wear and reduce their lifetime. Therefore, at some charging stations, batteries are slowly charged, or the depleted batteries are replaced with fully charged ones [25]. The focus of this paper is more on the driver comfort, and the capacity of the charging stations is depended number of EVs. The costs of charging stations include the cost of land, the cost of charging equipment and the variable costs depending on the charging station capacity. Moreover, when the distribution network is considered, the cost of power losses can be considered; thus, the cost objective function is given as follows: where IC i is the investment cost of the ith charging station; C chi is the cost of installing the ith EV charging device per unit capacity and C EVi is the ith charging station capacity; the third term corresponds to the cost of the distribution network losses. P L is the network losses, which can be calculated as described in Equation (2), and LSF is the loss factor of the distribution network [26].
where V f and V j are the voltage amplitudes of buses f and j at the ends of line k; δ f and δ j are the voltage angles of buses f and j at the ends of line k (these are obtained from forward/backward sweep load flow); N L is the total number of lines, and g k denotes the conductivity of line k [27]. Problem constraints are as follows: 1. Constraint on charging stations capacity: Since the optimisation problem covers a specific time interval, the maximum EV capacity of charging stations is considered within this interval. In this case, the number of EVs using a charging station determines the variable costs of the station within the corresponding interval. Assuming four charging devices in each charging station and about 10 min charging time, approximately 200 EVs can charge their batteries within an 8-h interval.
where C is the maximum allowable capacity for EV charging stations at any candidate location.
1. Bus voltage limits: Bus voltage must be within the allowable range.
where |V n | is the voltage amplitude of bus n; V min = 0.9 and V max = 1.05 are, respectively, the upper and lower voltage limits, and M is the number of network buses.
1. Loading constraint of feeders: The current through the feeder conductor should be less than the maximum allowable loading.
where I Lk is the current passing through the kth feeder conductor [17,18].

Modelling travel comfort of driver and objective function of trip success
For the successful replacement of EV technology with conventional fossil fuel vehicles, this new technology needs to satisfy the basic demands of drivers. One of these demands is the travel comfort. In this paper, travel comfort is defined as in-city trip success without the charging shortage and reaching the destination through the shortest route in a freely flowing traffic. Each EV travels the distance L 1 (in km), which depends on the initial state of charge (SOC 0 ) of its battery. After traveling distance L 1 , SOC 0 drops to a minimum value, SOC min ; SOC min denotes the minimum amount of battery charge required only for reaching a charging station.
where P cap is the EV battery capacity in kWh (in this paper, P cap is a constant value) and P s is the power consumption in kWh km −1 . The EV with a minimum state of charge should then be directed to the nearest charging station to maximise battery state of charge (SOC max ). Then, the EV continues its trip and travels another distance (L 2 ).
Since the network under study corresponds to a city and urban trips of EVs, it is assumed that an EV can complete its trip by only one instance of charging along its route. Now, the total distance traveled by the vehicle in km is obtained as follows: Consequently, if D t (in km) is defined as the distance traveled by an EV from origin to destination, then the trip of the EV is successful when the traveled distance is less than the length of the route the EV can travel. If D t ≤ L t then trip is successful.
The optimal locations of charging stations should be chosen in a way that the trip success rate is maximised over the course of a day after different trips over several time steps. Therefore, Equation (9) is defined as the second objective function of the problem such that the number of unsuccessful trips is minimised.
where N succes is the number of EVs with successful trips, and N T is the total number of EVs in the network. For this problem, some constraints on traffic volume, the capacity of charging stations, route length and so on are considered. The traffic volume on any route should not exceed a permissible limit, and the EV should travel the shortest distance between the origin and destination. For achieving the shortest waiting time, the EV should use a charging station with available capacity.
In this paper, the constraint of traffic volume on the routes is included. The traffic volume on the transportation network routes is modelled using the data from previous years. Accordingly, some popular routes are identified as default routes with certain allowable traffic volume. For their daily trips, EVs have to choose these default routes depending on their traffic volume so that the traffic can always be controlled. Furthermore, the shortest possible route is chosen between the origin and destination.
where T Lb is the traffic volume on the bth route, T maxb is the maximum allowable traffic volume on the bth route and B is the total number of routes.

ELECTRIC VEHICLES MODELING
In previous studies, for simplification, EV charging stations have been designed for specific time periods during the day [28][29][30]. However, in the present study, for a better and more accurate modelling, the optimal locations of charging stations are determined based on the cost and trip success over 24 h in several time steps. A multi-objective GA is used to optimise the objective function of the problem. The proposed chromosome, which shows the candidate locations of the charging stations, is fitted at all-time steps. The final objective function value is the consequence of the objective functions values at different time steps.

Time steps for electric vehicle trips
To verify the accuracy of the designed EV charging stations in an urban transportation network, it is necessary to study the charging/discharging performance over a given period. Since no specific pattern is repeated for in-city trips of EVs, and random patterns are used for the operation, a 24-h interval is appropriate to verify the accuracy of the study. As a result, the design is based on the 24-h random operation. Of course, each EV may need charging at any given time of 24 h depending on its initial state of charge and the length of the traveled distance, so it would be helpful if the operation was investigated with a 1-min resolution. However, for solving the operation-based problem of locating charging stations with a large number of EVs with one-minute resolution in 24 h, the number of steps is very large and causes heavy computational burden, which is troublesome.
In this paper, a design with time steps is proposed to reduce computation volume and to eliminate duplicate states. Accordingly, a 24-h study period is divided into several time steps, and over each time step, EVs complete their trips. Moreover, over each time step, EVs can travel trips that have origin and destination; that is, in the first time step, an EV starts its trip from the origin and (depending on its SOC 0 and charging stations on the route) reaches its destination, so its trip is successful. In the next stage, the destination that has been reached by the EV is defined as the origin in the next time step, and the EV starts a new trip with a new destination. As can be seen in Figure 3, this is similar to driving a car in the early morning to work and back from work in the afternoon. During the course of the day and within several time steps, the trip of those EVs that reach the destination successfully in all time steps will be considered as successful.
Therefore, to simulate the real traffic behaviour in routes for urban trips, it is not appropriate to use a single traffic pattern since traffic patterns change over the course of a day. This is due to the choices of the drivers who drive for different reasons. As shown in Figure 3, the purposes of trips are different.

K-means clustering and reducing statistical calculations
A number of EVs are considered in the simulation to model the behaviour of the EVs and to calculate the values of the objective functions. For each EV, four random variables including SOC 0 (initial state of charge), EV location in the network, trip length (which determines the destination) and the trip start time are modelled. It should be noted that SOC 0 , destination and travel route have random nature. Therefore, the use of Monte Carlo or an enumeration method will be complex and time consuming due to the huge computational volume.
In this paper, the initial locations of EVs are randomly determined, and using the k-means clustering method, the locations are divided into some clusters. For generating the random variable samples of initial charge and travel distance, a spherical unscented method is employed [31]. The output of UT contains several samples with given weighting coefficients instead of all random variables. Each cluster has a specific representative and probability.
Finally, after clustering the EVs, for each cluster representative and each sample generated by the UT, the chromosome of the problem algorithm is fitted for the multi-objective cost function and trip success to determine the optimal locations of charging stations. As a result, the output is the locations of charging stations in the network under study; these locations are found so that, besides having freely flowing traffic, EVs travel the shortest route, the cost of charging stations is minimised and the trip success is maximised, so the driver comfort is realised. Moreover, if the distribution network is considered, the corresponding constraints are included and the cost of losses is optimised.

Unscented transformation
In probabilistic studies, the most comprehensive method of investigation is the MCS. This exact statistical method runs across all possible states of probability variables, and in some power system studies, the number of iterations may amount up to several thousand or tens of thousands. However, in research works with a large number of probabilistic variables, the simulation will be very complex to achieve convergence. The powerful UT method ensures low processing volume while providing high accuracy. In this paper, due to a large number of probabilistic variables, the spherical UT method is used for probabilistic studies. The steps of probabilistic studies by using the spherical UT method are described as follows [32]: a. Using the input information of random variables to calculate the mean-value vector (m) and calculating the covariance matrix of the input variables (COV). b. Selecting the weighting factor g k according to Equation (11): where 0≤g 0 ≤1.
a. Generating vectors U recursively according to Equation (12).
By specifying the samples and weighting factors, the outputs can be calculated using Equation (14) As can be seen, for n variables, a number of n+2 samples are obtained by using the spherical UT method.
where COV(Y) is the covariance of the output variables.

Proposed scenarios
Due to the randomness of initial EV locations and the possibility of taking different routes in the network, two different scenarios are considered to model the proposed method ( Figure 4). Since the traffic volume in each route is known, the routes with the heaviest traffic are defined as the default routes. In scenario 1, an EV is assigned to one of the routes based on its destination and the traffic volume of the default routes. Depending on the initial state of charge (SOC 0 ), the EV travels a part of its trip, its location is updated and it can use a charging station if needed. In scenario 2, EVs locations are distributed across the

FIGURE 5
Transportation network under study [34] entire city transportation network (including roads, alleys and houses) to improve network reliability using V2G possibility, so this scenario can be potentially used in a future study that considers V2G. Then, each EV starts its trip based on its destination, the traffic volume of default routes and its SOC 0 , and uses a charging station if needed. In both scenarios, EVs are k-means clustered at each time step by considering the EVs locations in the transportation network, and the representatives of the clusters are determined [33]. It is worth mentioning that, in scenario 1, the clustering is performed for updating the locations of EVs after applying UT to the probabilistic parameters. However, in scenario 2, the clustering is performed before determining the random variables.

SYSTEM UNDER STUDY
For performing simulations and comparison with other articles, the test transportation network of Figure 5 (ref. [34]) is considered. As shown in this figure, the network includes 20 nodes (intersections) and 31 streets. Eight heavy-traffic routes are considered for the network. During the simulation, EVs are assigned to these routes according to the explained scenarios. In this way, the EVs travel along the routes, and if needed, they stop at charging stations to supply the energy needed for the rest of the routes. Figure 6 shows a number of heavy-traffic routes and candidate locations for constructing charging stations. The parameters related to EV are shown in Table 1.
Charging stations should be optimally located to supply EVs in the transportation network for successful trips. For this purpose, eight nodes of the network, including nodes 1, 4, 6, 8, 13, 15, 17 and 20 (Figure 6), are considered as candidate locations. The GA is then implemented to optimise the locations of the charging stations based on the EVs trip success (Equa-   Table 2. According to Figures 7 and 9, the EV locations are k-means clustered into 12 clusters throughout the network. The representative of each cluster is shown by a star symbol, and the number of UT samples is four.

Scenario 1
In Scenario 1, the initial locations of EVs are along the default routes (previous section); after traveling distances based on UT samples, the locations are updated and then clustered. In this scenario, the proposed chromosome is two-dimensional (Figure 8). The horizontal dimension shows the candidate locations  of the charging stations, and the vertical dimension shows the locations of the representatives of the clusters. The sum of the elements in each row must be equal to unity; this implies that all out-of-charge EVs are driven to charging stations. The sum of the elements in each column must be smaller than the capacity of the station (here, 200 EVs). Based on this sum, the number of charging stations is determined so that the constraint is satisfied. It is worth mentioning that the weighting factors of UT samples and the probability of representatives of k-means clusters are applied at each stage.   The optimal locations of charging stations in this scenario for the best answer are points 1, 4 and 17, with a trip success rate of 95.8%.

Scenario 2
In Scenario 2, the locations of EVs are uniformly distributed across the entire urban transportation network. These locations are sorted in terms of distance by using k-means clustering, and the cluster representatives make their trips for each UT sample. In this scenario, the proposed chromosome is one-dimensional ( Figure 10) and contains the candidate locations of the charging stations. That is, each element indicates the presence or absence of the charging station at the respective location. The results suggest points 1, 13, 15 and 17 for installing EV charging stations with a trip success rate of 98.3%. Compared to scenario 1, scenario 2 increases the trip success by 2.5% by adding one additional charging station to the network. This is because in the presence of EVs, which are uniformly distributed throughout the network, the travelable distance increases and EVs need more available charging stations.

Considering time steps for scenario 2
In this section, for locating EV charging stations, scenario 2 is used over 24 h in three time steps; that is, each EV makes multiple trips during the day, each with a different origin, destination and route. Accordingly, time steps are involved and the problem is iterated in this scenario. Then, the output of the objective function gives the installation points 8, 13, 15 and 17 with a trip success rate of 94.3%. The lower trip success than previous results is due to the involvement of three time steps during the course of the day, and consequently, an increase in the number of trips and less successful trips. For example, an EV may make a successful trip in the first step but unsuccessful trips in the next steps. Table 3 shows a comparison between the optimisation results of the charging stations in the three scenarios.

Considering distribution network for scenario 2
To validate the proposed method, scenario 2 deals with the optimal location of charging stations in the presence of the distribution network [35]. In Figure 11, the distribution and transportation networks are presented next to each other [36]. Considering the distribution network and using forward/backward sweep load flow, the cost of losses is added to the cost function of the previous steps (Equation 1). Moreover, the constraints related to the distribution network, such as voltage constraint, power balance and line loading, are considered. The results of this part of the optimisation problem, which are presented in Table 4 and Figure 12, are compared with the results of refs. [34,2]. Figure 13 shows the Pareto front responses of the multiobjective optimisation problem.  Table 4 and Figure 10 compares the two references and the proposed method. In the proposed method, fewer charging stations are optimised, but the cost of charging stations is reduced, and thus, the trip success rate is also reduced.
Besides the optimal solution of the proposed method, there are two other Pareto front solutions, which show the minimum cost and the maximum trip success rate. As can be seen, if the minimum cost is considered, the charging station will not be located, so the trip success will depend on the initial charge, which will be a small value. However, if increasing the trip success rate is intended, by reducing the importance of cost, the number of charging stations will increase and the trip success rate will be close to 100%.
In [34], there are three optimal locations for charging stations, while in the proposed method, two optimal locations are found because by reducing the costs of the charging stations, the trip success is considered as a criterion for choosing the optimal locations.
Moreover, the costs of charging and losses of the stations are higher in [33] compared to the proposed method. In [2], there are five optimal locations for charging stations with lower capacity, so the trip success rate is higher than the proposed method. However, in this reference, by ignoring the costs, there are no limitations in choosing even more locations for charging stations, while this is not rational.
Actually, the proposed method simultaneously considers the objective functions in the two mentioned references, and ultimately determines the locations of charging stations with both lower costs and acceptable trip success rate.

Sensitivity analysis
Given that the candidate locations are considered for the charging stations and that the technical and economic limitations are also included, so the maximum success rate of the trip is 95.4%. This value of maximum success rate corresponds to four charging stations. It is clear that by increasing the number of charging stations and relocating their candidate locations in the network, the trip success rate can easily be increased to approximately 100%. A sensitivity analysis for the simulation of trip success rate was performed by considering the number of charging stations; the analysis results are shown in Table 5.
According to the results of this table, with increasing the number of charging stations, the trip success rate increases, but this increase is not rational due to the charging stations cost. Moreover, from Table 5, for five charging stations, a trip success rate of 98.1% is obtained, which can be compared to the result of [2], with a success rate of 96.5% for the same number of stations; consequently, the quality of the proposed method is confirmed.

CONCLUSION
In this paper, the optimal locating of EV charging stations was studied considering the trip success index, and costs were minimised using a multi-objective GA. Some effective variables, including the initial state of charge and distance traveled in the urban transportation network, are completely random. These variables behave according to statistical distributions, so the UT method was used to simplify the calculations and the siting process of charging stations based on the optimal operation. To increase the accuracy of the results, the inclusion of time steps in the simulations was proposed. Accordingly, besides considering the probabilistic parameters, such as the traveling route and the batteries initial state of charge, the 24-h operation period was also taken into account. For this purpose, two scenarios were proposed so that, by clustering the locations of EVs and simplifying the calculations, these scenarios could be used for network reliability studies. According to the results of this paper, the proposed method can simultaneously take account of the urban transportation system and distribution network for the optimal siting of EV charging stations. Moreover, the proposed method costs less than the previously studied siting strategies (by conforming to electric and traffic control constraints), improves trip success, and consequently, leads to the travel comfort of the drivers. The numerical results of the test network under study verify the proposed approach.