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Optimal charging infrastructure planning based on a charging convenience buffer
Journal Pre-proof Optimal Charging Infrastructure Planning based on a Charging Convenience Buffer
Sreten Davidov PII:
S0360-5442(19)32350-3
DOI:
https://doi.org/10.1016/j.energy.2019.116655
Reference:
EGY 116655
To appear in:
Energy
Received Date:
03 June 2019
Accepted Date:
28 November 2019
Please cite this article as: Sreten Davidov, Optimal Charging Infrastructure Planning based on a Charging Convenience Buffer, Energy (2019), https://doi.org/10.1016/j.energy.2019.116655
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Optimal Charging Infrastructure Planning based on a Charging Convenience Buffer Sreten Davidov, PhD IQ LAB, research and development, SI-1000, Ljubljana, Slovenia E-mail: [email protected] Abstract In this paper, novelty is finding the optimal mix of charging technology types to be placed at optimal locations with regards to the Time of Convenience limitation acting as a charging convenience buffer of the users’ charging behavior. It constraints the optimization with the preparedness of users to wait when in request for charging and thus effect the optimal charging technology type selection. This paper is a step forward by combining two optimization constraints in providing the charging reliability and convenience needed to engage unlimited mobility of electric vehicles. For that purpose, discrete location model based on set-covering is involved to include electric vehicle users’ behavior reflected by their mobility trajectories, the technology charging times and the wait time required by the users’ when arriving at charging location. To show the general applicability of the model, a discrete 10 × 10 road network is considered. The numeric results show the optimal locations and the charging technology type to be placed. While the charging reliability provided, the part of faster charging technology installed prevails among optimal locations if the charging convenience buffer is shorter and vice-versa for the slower charging technology types. Keywords Charging Reliability, Locations Optimization, Queue Theory, Time of Convenience
1. Introduction Electromobility is advancing in transportation due to environmental, noise and health gains. The electrification of transport rises areas for research due to the need for optimal charging infrastructure (CI) rollout and charging technology placement to fulfil the needs for charging and to propagate new kind of mobility for higher electric vehicles (EV) adoption rate. However, in the emerging development of electromobility there are consequences such as scarcity of charging locations to meet the charging reliability of the CI, disrupted charging convenience and random charging technology placement. For higher electrification of transportation there are fewer prospects being explored scientifically: underdeveloped CI without an optimal charging locations layout and charging scheduling to increase electric power system flexibility and offer ancillary services. Namely, the complexity of the CI placement problem can be seen from various aspects, such as considering only transportation network, only the distribution network and considering both transportation and distribution networks, [1]. This paper deals with the CI development i.e. optimal charging locations layout planning by using a set-covering principle with single objective function to minimize the number of selected locations while dealing with the charging reliability and the charging convenience constraints. Up until now, there is a variety of research papers using the set-covering based nodal approach for the optimal placement of charging stations including only the transport network. However, no objective function is found to be subjected to the charging reliability and the charging convenience in order to find the optimal location solution, as proposed in this paper. The research made in [2] gives an outline on locating the passenger vehicle refuelling stations by using a set-covering based nodal approach. It is a base model that is used to show the applicability of set-covering in locating charging stations and does not address any other optimization constraints with regards to electric vehicle users (EVUs). In [3] a nodal-based approach is used for the optimal planning of CI by applying grid partition method. The main focus is given on applicability of grid partition rather than EVU oriented constraints, for instance, as CI reliability and charging convenience. In [4] the set-covering principle and the Maximal Covering Location Problem (MCLP) based approach are used to locate multiple types of charging stations. With regards to this paper, reference [4] is valuable since it introduces the charging technology to be placed at charging location. However, reference [4] does not use either charging reliability or charging convenience to find the optimal solution, yet it’s charging technology type is changed based on the MCLP approach. For this paper, reference [5] is the fundament and
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background, since it is the paper that uses the set-covering approach to introduce an optimization model for the CI planning for EV based on charging reliability and quality of service (QoS). The charging reliability principle is formulated as selection of a charging location within the driving range of the EV in order to enable EVUs to complete their trajectories. Nevertheless, [5] lacks another EVU oriented constraint, which is the novelty as contribution in this paper – the charging convenience. In [6] the charging convenience is stressed to be a necessity for the optimal placement of charging stations since it lays on the grounds of the charging times of the charging technology type and charging needs. Other papers, for example, [7] and [8], study the locations where charging stations should be placed in order to minimize the construction cost with the coverage used to express the EVU’s convenience. However, the EVU’s convenience also depends on the charging technology type to be placed at charging location. In [9], the charging convenience is addressed by including the traffic network topology and the driving patterns. Although [9], is in the scope of charging convenience, it still neglects the charging time and the inclusion of the charging reliability of the CI. Recently, there is a paper shown in [10] considering the charging satisfaction seen thorough the perspective of the distance to reach the charging station i.e. to find the relationship between the charging distance and the satisfaction degree. Another paper shown in [11] discusses the distance convenience from the aspect of distance deviation. A distance criterion with an Euclidean measure is also subject to our previous research, as show in [12]. In [12], the charging reliability is introduced as an optimization criterion to engage unlimited mobility and derive an optimal planning layout of locations to face the short driving range. In [13] there is a charging V2G scheduling algorithm involved that is oriented in providing convenience and profitable gains for EVU. However, it is a paper that elaborates a scheduling algorithm that is electric system oriented, rather than oriented to include the charging behavior for the charging convenience of the EVUs. In that scope, another paper is shown in [14] where an EV charge scheduling mechanism to maximize cost efficiency and EVU convenience is presented. For the charging scheduling mechanism to work, the charging behavior in this case requests longer charging times, for instance, when in the case of parked over-night or at work. If agreed by the EVUs, in this case, the charging convenience is not interrupted. This is the main target of this paper, i.e. to model the charging convenience of EVUs by the introduction of the charging convenience buffer for candidate location to anticipate users’ involvement in a charging strategy as part of their charging behavior. In other paper, [15], the charging convenience is discussed from the perspective of using the onboard battery in increasing the electric power system flexibility and thus having an effect on EVUs’ convenience. However, it must be emphasized that control algorithms which are electric system oriented regarding the charging convenience are not a subject of this research paper. Based on the literature review shown, the main facts that were extracted as a conclusion and served as incentive for the presented research paper include: necessity to include the charging convenience in the optimal CI placement planning as a user oriented constraint, necessity to formulate the charging behavior at candidate location with the newly proposed charging convenience buffer, consideration of the charging times related with the charging technology type for the charging convenience when waiting at a charging location, necessity to combine both the charging convenience and charging reliability in a set-covering based optimization model, consideration of waiting at location for charging service as occurrence by introducing the queue theory. The paper presented fills the gap and contributes in the research area for finding the optimal mix of charging technology types to be placed at optimal locations with regards to the Time of Convenience (ToC) limitation acting as a charging convenience buffer at charging location to anticipate users’ involvement in a charging strategy as part of their charging behavior. It constraints the optimization with the preparedness of users to wait when in need for charging which is in direct concern of the queue theory – waiting as occurrence due to the charging needs of EVUs. With regards to previous relative existing studies in this research area, such as [5], [12] and [17], the main improvement or novelty in this paper is going a step forward by combining two optimization constraints in providing the charging reliability and convenience needed to engage unlimited mobility of EVs. To fulfil its purpose and offer an optimal charging placement plan, this paper uses the driving patterns of the EVUs as representative of their mobility behavior. As per the set-covering theory, the candidate locations are also part of the EVUs trajectories and due to their dual nature in the complexity of the optimization problem the model selects the minimum number of locations to cover the trajectory points in order for the EVUs to complete their mobility trips. The charging times of the charging technology
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to be placed at charging location is limited by the ToC that enables the charging behavior modelling and EVUs charging convenience satisfaction. This limitation is critical for the optimal location selection and charging technology placement since it includes both the charging reliability and charging behavior of EVUs. The model presented is a generally applicable model to any road network since it uses a set-modelling approach. Numeric results show that the charging behavior of EVUs accounted with the charging convenience buffer for the candidate locations can be integrated in a set-covering CI optimization model. For the charging behavior case where it is anticipated EVUs to participate in smart charging scheme and consequently for their charging convenience it is allowed slower charging, the proposed model gives the optimal charging locations layout with slower charging technology type placed at selected locations. Otherwise, when for the charging convenience is requested faster charging, at optimal charging locations faster charging technology types prevail. The remaining sections of the paper are organised as follows: the Optimal Charging Infrastructure Planning based on a Charging Convenience Buffer is explained in detail in Section 2. The optimisation procedure for the CI placement is presented in Section 2.2, while Section 3 presents the numerical results. The conclusion drawn from this paper is presented in Section 4.
2. Optimal Charging Infrastructure Planning based on a Charging Convenience Buffer As the EVUs are anticipated to be involved in a charging strategy, it is fundamental to be able to include the charging behavior in an optimal CI planning procedure. This paper offers the charging convenience buffer at charging location as option to include the charging convenience of the EVUs. Namely, if a longer charging time is required at candidate location as a reflection of a EVU’s charging behavior, the optimal CI planning model must place slower charging technology type at location to address the charging convenience of the EVU. Using the proposed model in this paper, the CI planners are enabled to include the anticipated participation of EVUs in charging strategies and make a step forward in modelling the real-time occurrences. For the optimal CI planning the envisioned optimisation procedure including the input data parameters, the optimization model and identification of optimal results is shown in Figure 3. As this paper is focused on optimization model including the transportation network, the input data considers the parameters of discretization modelling in form of candidate locations to place a charging stations with a charging technology. The transportation network with discrete candidate locations has dual role, since the set of candidate locations is used in formulation of EVU trajectories as representative of their mobility behavior. It can be affirmed in papers like [16], moreover our research [17], where stochastic modelling can be used to create numerous EVU trajectories in a limited grid and to extract representative trajectories. Nevertheless, that part of modelling is not subject in this paper and EVU trajectories are arbitrary selected to show the coverage principle, valuable for the charging reliability formation. For the input part, another significant component is the charging technology and the charging time, that is used in the queue structure to limit the optimization shown in Subsection 2.1.4. The ToC is the other part of the queue structure, which as previously elaborated serves as a charging convenience buffer over the charging location to constrain the optimization in selection of the charging technology with regards to the charging time to address the charging behavior. The optimization model is defined with a single objective function in finding the minimal number of locations to place a charging technology type. The constraints are clearly set: the charging reliability for selection of one candidate location within the driving range of the EV and the charging convenience at that location with the limitation of ToC. The optimization model is shown in Section 2.2. The numeric results show the optimal number of charging locations with the charging technology at a charging location to be placed. The optimal placement layout is also identified. The numeric results and the discussion are shown in Section 3. 2.1. Input data preparation The input data preparation consists of modelling in the discrete domain the transportation network and showing the candidate locations, which also take part as trajectory points in exposing the EVU mobility behavior. These trajectories are arbitrary selected and used to present the coverage principle significant for the charging reliability. It must be stressed, that the input can be any imaginable discrete formulated EVU trajectory in a discrete modelled grid. The modelling of the EVUs trajectories is not in the focus of this research. The charging convenience as part of the charging behavior is comprised by the ToC and the charging technology types with their charging times. The input data preparation is consisted of the Subsection 2.1 elaborating the discrete modelling of the transportation
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network and the using of sets to note the candidate locations. Subsection 2.1.1 discusses the discrete modelling of the EVU mobility behavior and trajectory representation as per input in optimization procedure. Subsection 2.1.2 is dedicated to the formation of the sets for the charging reliability of the CI. Subsection 2.1.3 gives an overview of the charging reliability formulation. Subsection 2.1.4 gives an outlook of the charging convenience in a queue structure. The charging times for the charging technology is presented in Subsection 2.1.5. The prepared parameters are thus input for the optimization model, where a linear programming is applied in order to identify the optimal results. The optimal CI plan provides vital information for CI planners, where the mobility and charging behaviors are accounted with the criterion to resolve the limited mobility as one of the main shortcomings of EVs. 2.1.1. Discrete modelling of the transportation network
This paper uses discrete modelling in order to use the advantage of set-covering principle in the optimization procedure. For that purpose, a set of candidate locations is formed to serve both as part of a trajectory and be part of the transportation network. The goal is to cover the trajectories in a such way that the EV can be able to complete the trajectory and to exceed the driving range limitation. Hence, the covering principle is the foundation of the charging reliability criterion elaborated in Subsection 2.1.3. The set M shown in (1) consists the discrete points to model the transportation network. M m1 , m2 , m3 , , mi , , mI ; (1) i 1, 2,3,..., I The i-th element of the set is mi and the cardinality of the set is I. Due to the sampling rate in the discretization process, the cardinality of the set is bigger when lower sampling rate is used and vice-versa in the case of bigger sampling rate. For the set M, between any pair of elements’ the Euclidean rule of equally distributed in-between distance is followed. As part of the transportation network modelling, the set formulation is a discrete approach, that creates a simple method to include and model any transportation network for optimization purposes. To give a more thorough example of the road network discretisation, Figure 1 shows I = 15 candidate locations which are part of the discrete road network, formulated as per equation (1). The empty markers represent equally spaced discrete points, part of the set M. 2.1.2. Discrete representation of the electric-mobility behavior
The elements of M further serve to represent the mobility behavior of EV users and it is the basis for the coverage optimization procedure. The mobility behavior of the EV users is noted with the individual EV movement trajectory, noted as in (2).
N v nv,1 , nv,2 ,..., nv, j ,..., nv, J v ; j 1, 2,..., J v ; v 1, 2,..., V
(2)
Nv is the finite set presenting the v-th EV trajectory within the modelled road network and nv,j is the j-th element of the finite set of the EV trajectory. Jv stands for v-th EVU overall number of elements of the trajectory, while V is the total number of EVUs. Figure 2 presents the spatial trajectory of the v-th EVU, as noted per equation (2). 2.1.3. Formation of the charging reliability constraint
At this point, it can be noticed the dual nature of the elements of M: to serve as candidate location and a trajectory point. Hence, the v-th set Nv according to the set-covering principle represents the set of demand points that are to be covered by selecting from the candidate locations. The (Euclidean) distance between the j-th trajectory point, part of the Nv, and the i-th element of the set M is calculated as shown in (3). The Euclidean distance is used as distance measure between two adjacent points, thus used as a criterion in formation of the candidate locations set in relation to the charging reliability.
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i , j ,v (mi nv, j ) 2dx (mi nv, j ) 2dy ; mi M ; nv , j N v
(3)
ξi,j,v is the Euclidean distance between the i-th candidate location point or mi and the j-th trajectory point for the v-th EVU, or nv,j. The dx and dy values represent the coordinate directions. This measurement criterion is compared with the coverage distance which is taken to be the driving range of the EV, Rv. The j-th trajectory point is covered by a candidate location i, if the criterion of coverage distance noted in (4) is fulfilled.
Sv ,i mi M : i , j ,v Rv ;
(4) j 1, 2,..., J v ; v 1, 2,..., V In equation (4), the elements of the finite set Sv,i represent all candidate location points mi, which meet the distance criterion ξi,j,v ≤ Rv. In other words, Sv,i holds the candidate locations which can cover the trajectory points j. To provide a more straightforward notation of candidate locations for the further optimization process, the following Boolean coefficient is involved, i.e. ai,j,v, which is equivalent to the set defined in equation (4). 1, if i , j ,v Rv ai , j ,v (5) 0, otherwise
The ai,j,v coefficient in equation (5) notes whether the distance from the i-th candidate location to the j-th trajectory set element for the v-th EVU falls within the scope of the defined distance criterion, ξi,j,v ≤ Rv. If this criterion is met, the ai,j,v coefficient takes the value of 1, otherwise its value equals 0. Figure 4 gives an example of the charging reliability formation criterion, by assuming a driving range distance Rv and selection of charging location at distance equal to Rv. The driving range is considered constant and no range loss impacts are considered. Figure 4 also gives an example, that the scale of the road network takes its part in formation of the number of candidate locations to be included in the optimization procedure as part of the input part due to the formulation of the charging reliability sets. 2.1.4. Charging convenience as constraint of the charging behavior
In this paper, the well-known queue theory, [18], is applied in regards to the waiting time as occurrence and user convenience accounted for the charging behavior. For the purpose of smart charging, it can be expected that the charging behavior of EVUs can prefer longer charging time, [19]. Consequently, slower charging technology type needs to be placed at charging location to address the EVUs convenience. Otherwise, at locations where charging behavior requires rapid charging, faster charging technology type needs to be selected. In this paper, the ToC is used as charging convenience buffer at a candidate location in order to anticipate the charging behavior needs of EVUs and to propose an optimal CI planning come closer to real-time occurrences. To elaborate more profoundly with regards to the queue theory, each of the candidate locations of the transportation network is assumed to act as a queuing system where the key elements are the arriving v-th EVU to require a charging service at the i-th charging location to provide the requested service based on k-th charging technology type. Figure 5 shows the j-th trajectory point for the v-th driver, nv,j, where ToC is represented as charging convenience buffer in order to limit the charging time CTk for the k-th charging technology at the charging location. The charging convenience buffer is directly correlated with the charging behavior of EVUs. In addition, ToC represents the required length of stay at charging location. For instance, if for a candidate location is anticipated that the v-th EV driver will park the vehicle over-night or for work, longer charging hours for smart charging can be expected and slower charging technology type can be placed. Otherwise, if the v-th EV driver requires short stay per candidate location, faster charging technology is to be placed. Therefore, constraining the optimization model with the charging convenience buffer with a value of ToC per candidate location, imply for changing the charging technology type to be placed at optimal location and fulfilling the charging convenience. 2.1.5. Charging time of charging technology
The charging technology dictates the charging duration, since the higher the transferred power that can be enforced by the charging technology, the shorter the charging time. In the following equation the charging time is noted with regards to the charging technology:
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Lk ,v CTk R v ;
(6) v 1, 2,..., V ; k 1, 2,..., K where CTk is the charging duration using the k-th charging technology to reach distance equal to the initial EV driving range, i.e. Rv. K is the overall number of charging technology types. Faster charging stations as implied have shorter charging times, and vice-versa. Placement of faster charging technology types at charging locations depends on the allowable charging convenience buffer exposed by ToC for a charging location. The model presented uses this constraint for the charging reliability to provide a charging location placement list to fulfil the need of engaging unlimited mobility and charging convenience. 2.2. Optimal Charging Infrastructure Planning Model The charging location set-covering model (CLSCM) objective is to minimize the number of charging locations with keeping the coverage of the trajectories used to model the EVUs mobility behavior and to place the charging technology for the charging convenience. The objective function written in equation (7), F, minimizes the overall number of charging locations and selects the charging technology to be placed at a charging location. For the k-th charging technology, k ∈ K, to be placed at i-th candidate location, i ∈ I, the Boolean integer variable xi,k, is involved which takes the value of to 1 if the k-th charging technology is placed at i-th location and 0 otherwise. I K Min F xi ,к (7) i 1 k 1 The objective function minimizes the overall number of charging locations by placing the charging technology to address the charging convenience for EVU at candidate location, driving range limitation and engaging unlimited mobility with the charging reliability criterion. The objective function is constrained as shown in equations (8)-(11).
I
K
a
i , j ,v
xi ,k 1;
i 1 k 1
(8)
j 1, 2,..., J v ; v 1, 2,...,V I
K
CT x k
i ,k
ToCi ,v
(9)
1
(10)
i 1 k 1
I
K
x
i ,k
i 1 k 1
xi , k 0,1 ; i 1, 2,..., I ; k 1, 2, , K
(11) Equation (8) is included in order to ensure the charging reliability of the charging infrastructure. The coefficient ai,j,v of equation (5) notes whether the distance from the i-th candidate location to the j-th trajectory set element for the v-th EVU falls within the scope of the defined distance criterion, ξi,j,v ≤ Rv. If this criterion is met, the ai,j,v coefficient takes the value of 1, otherwise its value equals 0. This constraint will impose the optimisation to select at least one candidate location within the driving range if the v-th EVU. As the charging reliability constraint is thoroughly elaborated in papers [5], [12], [17], and in Subsection 2.1.3 in this paper, the main focus is on involvement of the charging convenience constraint which corresponds with the desired length of stay per candidate location to address the charging convenience of the EVU. Equation (9) is involved for the charging convenience as explained in detail in Subsection 2.1.4. The involvement of this constraint is the main novelty of this research paper, since it provides vital limitation in identifying the charging technology to be placed. As per the left-hand side of the inequality in (9), the charging time CTk of the k-th charging technology type is constrained on the right-side with ToC representing the charging convenience buffer addressing the need of the v-th EV driver to wait at i-th candidate location when in request for charging and introduces the charging convenience for the EVUs. The value of ToC takes in consideration the need of faster or slower charging when arriving at candidate location. Since, this limitation gives a outlook to charging convenience of the v-th EV driver according to his charging behavior and needs. Equation (10) enforces the optimization to select the k-th charging technology out of a set of K charging technology
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types to be placed at charging location. Constraint (11) states the binary definition of the optimisation decision variable for the k-th charging technology type to be placed at i-th candidate location i.e. the binary definition of I candidate location points with K charging technology types.
3. Numerical Results For the representation of the gains in novelty of the presented paper, a methodological test transportation network is involved of I = 100 discrete points distributed in a plane 10 × 10, as shown in Figure 6a). It must be emphasized, that the proposed optimization methodology can be used for more complex and bigger transportation network, such as shown in [12] and [17]. For the transportation grid, the distance between two consecutive candidate locations is 1 p.u., and in this case study 1 p.u. equals 100 km. In addition to solving the optimization model in this paper, linear programming with the Matlab formulation of the optimization problem is used. This research paper is set to use deterministic approach for the data in the Input part of the optimization procedure, as shown on Figure 3. For instance, the components of the input data such as the charging and mobility behaviors, which will serve further to determine the optimal charging locations’ layout and charging technology to be placed at location for fulfilling the EV drivers’ needs, at this stage of the research are involved as per the deterministic approach. Hence, for the future research, it is planned to include stochastic approach for the data modelling in the input part, for example, using a previously involved procedure, [17], to find representative trajectories of the stochastic mobility behavior, constraint on stochastic Quality of Service, charging convenience, stochastic driving range for the purpose to derive the optimal results with its’ probability of occurrence, to the benefit of the stakeholders, as shown earlier in one of the SCI papers published [17] and based on which this research paper is established. Figure 6b) shows the aggregated spatial layout of the EV trajectories, where the discrete points as candidate locations are also part of the EV mobility trajectories. For this case-study, these trajectories are representative of the mobility behavior. The number of trajectories, Nv, is 3 and thus equals the number of EVs equally as in the case-study represented in [1]. As these points are part of a trajectory of the EVs, according to the charging reliability constraint of the optimization model, Subsection 2.1.3, there must be a location selected within the driving range of the EV. Above all, this constraint ensures that logistically and optimally from a CI planners perspective, there is at least one charging location selected to engage unlimited mobility for EVs. The optimization procedure is executed for the different values of the driving range, Rv equal to 200, 400 and 800 km in order to validate and confirm the importance of the constraints. It is fundamental assumption that when starting the EV is fully charged and the losses in range due to EV driver’s skills and road configuration are neglected. It must be stressed that these losses in distance are here included in Rv and any other influences in driving range distance are profoundly elaborated in research paper [12]. Above all, the proposed methodology can take any arbitrary value regarding the driving range, Rv. The overall number of charging technology types for this paper is K = 3, where the first charging technology, k=1, is a fast charge (FC) technology with charging time CT1 is 30 min, for k=2, the charging technology is medium charge (MC) technology, with charging time CT2 120 min and for k=3, slow charge (SC) technology with charging time CT3 is 300 min. To sum up for the Input data preparation part (Subsection 2.1) – a methodological discrete transportation network is introduced to show the advantages of the newly involved optimization constraint regarding the charging convenience. The i-th candidate location out of I = 100 candidate locations is subject to placing the k-th charging technology type out of K charging technology types with charging time CTk. The mobility behaviour of the EV users is involved with deterministic representative trajectories, which are arbitrary selected and stochastic modelling of mobility driving patterns as shown in [17], is not subject in this research. The charging behavior is represented with the Time of Convenience, that acts as charging convenience buffer for i-th candidate location in accordance with the needs of v-th EV driver. ToC reflects the preparedness of the EVUs to wait when arriving at charging location. Additionally, the CI planners are able to include the anticipation for the EVUs to participate in a charging strategy such as smart charging, for which longer charging times are required. Therefore, multiple values for ToC are considered in this case-study i.e. 30, 120, 450 min. For the case study to be more clear, it is simply assumed that all EV drivers require the same values for ToC when arriving at charging location; nonetheless, these values can be arbitrary changed. After execution of the optimization model, with regards to the Input data, Table 1, shows the optimal locations layout for the value of ToC, 30, 120 and 450 min and for the different values of the driving range 200, 400 and 800
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km. For the first value of ToC, 30 min and value of the driving range 200, 400 or 800 km, is the most severe case when the charging convenience buffer is shortest required for candidate location and equal to the value of the charging time of the fastest charging technology. Consequently, as shown in Table 1, for the value of 30 min, only FC technology is placed at optimal locations for all the values of the Rv. Above all, the model ensures that the EVUs complete their trajectories (charging reliability criterion). As the value of ToC increases to 120 and 450 min, the optimal layout changes and also the share in locations of FC and MC. For the value of 450 min, and for the values of the driving range 200, 400 and 800 km, it is shown that the mixture of charging technology types is different, since the constraint allows placing slower charging technology types at optimal locations. To deliver better understanding of the charging convenience buffer involved with the ToC constraint imposed by EVU, the optimization model is looped through the values starting from 30 min to 600 min with a 10 min step increasing the charging convenience buffer. Increasing the ToC would mean that when EVUs are at charging location, the waiting time is higher and thus the charging convenience is lower. It is the case, when EVUs is anticipated not to take part in any charging strategy, their charging behavior implies “charge-and-go”. It is expected that by imposing shorter ToC to push the optimization model in selection of faster charging technology types with shorter charging times, thus acting in relaxing the charging convenience buffer over the charging location. Results are shown in Table 2. Results show that the share of slower charging technology types, i.e. in this case MC and SC increase their part as the charging convenience buffer with ToC increases. This is the case, when it is anticipated that the EVUs are willing to take part in smart charging strategy, when longer charging times are required. This charging behavior, by the use of ToC can be included in the CI optimization to oversee the need for charging technology to be placed at charging location. Higher the charging convenience buffer over the charging location relaxes the constraint in the optimization and as optimal output a slower charging technology is selected. These results open the perspective of charging convenience which is provided through the involvement of ToC in this paper: The shorter the time in willingness to wait when arriving at charging location, the more would the EVU be convenient for charging at that location. Notice on the results: The model gives the optimal layout and the optimal charging technology to be placed for the value of the charging convenience limitation, ToC. It shows the optimal charging mix of technology types where are to be placed by also ensuring the charging reliability for unlimited mobility of EVs. As an added value of the contribution of this research is going one step further is increasing the value of the ToC to a significantly large number (2000 min) i.e. enormously long charging convenience buffer, and for the value of the driving range 200 km, to oversee the change in the overall optimal charging technology mix, as shown on Figure 7. Figure 7 shows that the optimal charging technology mix stays unchanged after the value of ToC reaches 450 min and the share of FC is 46.875 % MC is 25 % and SC is 28.125 %. This is due to the criterion of ensuring the charging reliability of the charging infrastructure for the minimal number of charging stations to cover the EVU trajectories in order to complete their trajectories.
4. Conclusions This paper offers an optimization procedure to develop and improve the charging infrastructure placement as a vital component of the transportation system. Using a set-covering principle and a linear programming approach, the optimal set of locations is identified and the optimal charging technology mix determined. The model is based on the engagement of the charging reliability of the charging infrastructure and the charging convenience as part of the charging behavior. As a point of discussion, the Time of Convenience is introduced, as a limitation over the charging location and acting as a charging convenience buffer to contribute in optimal charging technology selection for a charging location. Since the charging behavior can be related to wiliness to participate in smart-charging strategy where longer charging times are anticipated, the ToC is a user oriented input that involves the charging convenience of the user. If the user is willing to wait longer at charging location, slower charging technology is to be placed at that location, hence, not disrupting his charging convenience. Otherwise, when charging convenience requires placing faster charging technology, the ToC acts a shorter charging convenience buffer. The queue theory is used as fundamental methodology in regards to the waiting time to charge. The presented charging infrastructure planning optimization procedure is a generally applicable optimization solution. To show its advantages, a methodological discrete 10 × 10 road network is considered and electric vehicle trajectories included to find the optimal solution. For the shorter charging convenience buffer at location, the faster charging technology types with shorter charging times prevail and vice-versa. Additionally, the optimal charging infrastructure plan in shown, with regards to the charging behavior, mobility behavior and representative trajectories. Future research is to be made on incorporating more
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segments of queue theory in combination with set-covering theory to contribute more in the charging infrastructure planning. Stochastic approaches are expected to be applied for the tasks involved in the input data preparation part, nonetheless, the parameters regarding the accessibility, comfort and urban limitations. This paper represents the basis for the future work in the field of providing new concepts for the improvement of the transportation systems.
5. References [1] Deb, Sanchari, Kari Tammi, Karuna Kalita, and Pinakeswar Mahanta. "Review of recent trends in charging infrastructure planning for electric vehicles." Wiley Interdisciplinary Reviews: Energy and Environment 7, no. 6 (2018): e306. [2] Wang, Ying-Wei, and Chuan-Ren Wang. "Locating passenger vehicle refueling stations." Transportation Research Part E: Logistics and Transportation Review 46, no. 5 (2010): 791-801. [3] Ge, Shaoyun, Liang Feng, and Hong Liu. "The planning of electric vehicle charging station based on grid partition method." In 2011 International Conference on Electrical and Control Engineering, pp. 2726-2730. IEEE, 2011. [4] Wang, Ying-Wei, and Chuah-Chih Lin. "Locating multiple types of recharging stations for battery-powered electric vehicle transport." Transportation Research Part E: Logistics and Transportation Review 58 (2013): 7687. [5] Davidov, S., & Pantoš, M. (2016). Planning of electric vehicle infrastructure based on charging reliability and quality of service. Energy. [6] Xiong, Yanhai, Jiarui Gan, Bo An, Chunyan Miao, and Ana LC Bazzan. "Optimal electric vehicle fast charging station placement based on game theoretical framework." IEEE Transactions on Intelligent Transportation Systems 19, no. 8 (2018): 2493-2504. [7] Lam, Albert YS, Yiu-Wing Leung, and Xiaowen Chu. "Electric vehicle charging station placement: Formulation, complexity, and solutions." IEEE Transactions on Smart Grid 5, no. 6 (2014): 2846-2856. [8] Xiong, Yanhai, Jiarui Gan, Bo An, Chunyan Miao, and Ana LC Bazzan. "Optimal electric vehicle charging station placement." In Twenty-Fourth International Joint Conference on Artificial Intelligence. 2015. [9] Wang, Guibin, Zhao Xu, Fushuan Wen, and Kit Po Wong. "Traffic-constrained multiobjective planning of electric-vehicle charging stations." IEEE Transactions on Power Delivery 28, no. 4 (2013): 2363-2372. [10] Liu, Jin-peng, Teng-xi Zhang, Jiang Zhu, and Tian-nan Ma. "Allocation optimization of electric vehicle charging station (EVCS) considering with charging satisfaction and distributed renewables integration." Energy 164 (2018): 560-574. [11] Guo, Fang, Jun Yang, and Jianyi Lu. "The battery charging station location problem: Impact of users’ range anxiety and distance convenience." Transportation Research Part E: Logistics and Transportation Review 114 (2018): 1-18. [12] Davidov, Sreten, and Miloš Pantoš. "Impact of stochastic driving range on the optimal charging infrastructure expansion planning." Energy 141 (2017): 603-612. [13] Wang, Baocheng, Yafei Hu, and Fanfeng Zeng. "A user cost and convenience oriented EV charging and discharging scheduling algorithm in V2G based microgrid." In 2017 International Conference on Circuits, Devices and Systems (ICCDS), pp. 156-162. IEEE, 2017. [14] Chung, Hwei-Ming, Wen-Tai Li, Chau Yuen, Chao-Kai Wen, and Noel Crespi. "Electric vehicle charge scheduling mechanism to maximize cost efficiency and user convenience." IEEE Transactions on Smart Grid (2018). [15] Magome, Nozomu, and Shigeru Tamura. "A New Decentralized Control of EVs for Load Frequency Control Retaining EV users’ Convenience." In 2018 IEEE International Telecommunications Energy Conference (INTELEC), pp. 1-6. IEEE, 2018.
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[16] Technitis, Georgios, Walied Othman, Kamran Safi, and Robert Weibel. "From A to B, randomly: a point-to-point random trajectory generator for animal movement." International Journal of Geographical Information Science 29, no. 6 (2015): 912-934. [17] Davidov, Sreten, and Miloš Pantoš. "Stochastic expansion planning of the electric-drive vehicle charging infrastructure." Energy 141 (2017): 189-201. [18] Saaty, T. L. (1961). Elements of queueing theory: with applications (Vol. 34203). New York: McGraw-Hill. [19] Lopes, J. P., Almeida, P. M. R., Silva, A. M., & Soares, F. J. (2009). Smart charging strategies for electric vehicles: Enhancing grid performance and maximizing the use of variable renewable energy resources.
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Figure Captions Figure 1 Example of road network discretisation Figure 2 Example representation of the v-th EV user trajectory Figure 3 Principle scheme in the proposed optimal charging infrastructure planning Figure 4 An example trajectory with the charging reliability criterion presented to engage unlimited mobility of EVs Figure 5 ToC acting as charging convenience buffer to fulfil the charging time of the charging technology for the charging convenience of the charging infrastructure Figure 6 a) Discrete test road network and b) Spatial layout representation of all EVUs trajectories Figure 7 Increasing ToC to significantly large number (case of driving range 200 km)
Table Captions Table 1 Changing the optimal layout of locations due to the value of ToC for the value of range, Rv= 200 km, 400 km and 800 km....................................................................................................................................................................15 Table 2 Optimal charging technology mix as function of ToC for the different values of the driving range Rv= 200 km, 400 km and 800 km.......................................................................................................................................................18
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Figure 1 Example of road network discretisation
Figure 2 Example representation of the v-th EV user trajectory
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Figure 3 Principle scheme in the proposed optimal charging infrastructure planning
Figure 4 An example trajectory with the charging reliability criterion presented to engage unlimited mobility of EVs
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Figure 5 ToC acting as charging convenience buffer to fulfil the charging time of the charging technology for the charging convenience of the charging infrastructure
a) b) Figure 6 a) Discrete test road network and b) Spatial layout representation of all EVUs trajectories 100 FC MC SC
90
Charging technology share (%)
80 70 60 50 40 30 20 10 0
0
1000
Time of Convenience, ToC v (min)
Figure 7 Increasing ToC to significantly large number (case of driving range 200 km)
2000
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Table 1 Changing the optimal layout of locations due to the value of ToC for the value of range, Rv= 200 km, 400 km and 800 km
ToC=30 min
Rv= 200 km ToC=120 min
ToC=450 min
ToC=30 min
Rv= 400 km ToC=120 min
ToC=450
ToC=30 min
Rv= 800 km ToC=120 min
ToC=450
FC
MC
SC
FC
MC
SC
FC
MC
SC
FC
MC
SC
FC
MC
SC
FC
MC
SC
FC
MC
SC
FC
MC
SC
FC
MC
SC
1 3 6 7 9 12 14 18 20 23 26 32 34 38 40 45 46 52 54 58 60 65 72 74 78 80 83 87
/
/
1 3 7 9 12 14 16 18 20 23 32 34 36 38 40 45 52 54 56 58 60 65 72 74 80 83 87 92
78
/
1 3 12 14 32 34 45 46 52 72 74 79 88 94 95
8 10 23 30 48 50 68 97
6 26 28 54 65 70 77 83 92
4 8 20 23 26 34 48 50 52 74 78 92 96
/
/
4 9 12 34 38 40 52 70 74 92 96
26 78
/
12 34 40 52 68 74
80
4 9 26 28 92 96
30 34 78 92
/
/
10 78 92
34
/
30
34 92
78
92 94 96 98
94 96 98
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Table 2 Optimal charging technology mix as function of ToC for the different values of the driving range Rv= 200 km, 400 km and 800 km
Rv= 200 km
Rv=400 km
Rv=800 km
ToC (min)
FC (%)
MC (%)
SC (%)
FC (%)
MC (%)
SC (%)
FC (%)
MC (%)
SC (%)
100
0
0
100
0
0
100
0
0
30
100
0
0
100
0
0
100
0
0
40
100
0
0
100
0
0
100
0
0
50
100
0
0
100
0
0
100
0
0
60
100
0
0
100
0
0
100
0
0
70
100
0
0
100
0
0
100
0
0
80
100
0
0
100
0
0
100
0
0
90
100
0
0
100
0
0
100
0
0
100
100
0
0
100
0
0
100
0
0
110
96.875
3.125
0
84.615
15.385
0
75
25
0
120
96.875
3.125
0
84.615
15.385
0
75
25
0
130
96.875
3.125
0
84.615
15.385
0
75
25
0
140
96.875
3.125
0
84.615
15.385
0
75
25
0
150
96.875
3.125
0
84.615
15.385
0
75
25
0
160
96.875
3.125
0
84.615
15.385
0
75
25
0
170
96.875
3.125
0
84.615
15.385
0
75
25
0
180
96.875
3.125
0
84.615
15.385
0
75
25
0
190
96.875
3.125
0
84.615
15.385
0
75
25
0
200
96.875
3.125
0
84.615
15.385
0
75
25
0
210
96.875
3.125
0
84.615
15.385
0
75
25
0
220
96.875
3.125
0
84.615
15.385
0
75
25
0
230
96.875
3.125
0
84.615
15.385
0
75
25
0
240
96.875
3.125
0
84.615
15.385
0
75
25
0
250
96.875
3.125
0
84.615
15.385
0
75
25
0
260
96.875
3.125
0
84.615
15.385
0
75
25
0
270
96.875
3.125
0
84.615
15.385
0
75
25
0
280
96.875
3.125
0
84.615
15.385
0
75
25
0
290
81.25
18.75
0
69.231
30.769
0
75
25
0
300
81.25
18.75
0
69.231
30.769
0
75
25
0
310
81.25
18.75
0
69.231
30.769
0
75
25
0
320
81.25
18.75
0
69.231
30.769
0
75
25
0
330
81.25
18.75
0
69.231
30.769
0
75
25
0
340
81.25
18.75
0
69.231
30.769
0
75
25
0
350
81.25
18.75
0
69.231
30.769
0
75
25
0
360
81.25
18.75
0
69.231
30.769
0
75
25
0
370
81.25
18.75
0
69.231
30.769
0
75
25
0
380
81.25
18.75
0
69.231
30.769
0
75
25
0
390
81.25
18.75
0
69.231
30.769
0
75
25
0
400
81.25
18.75
0
69.231
30.769
0
75
25
0
410
81.25
18.75
0
69.231
30.769
0
75
25
0
420
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81.25
18.75
0
69.231
30.769
0
75
25
0
430
81.25
18.75
0
69.231
30.769
0
75
25
0
440
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
450
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
460
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
470
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
480
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
490
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
500
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
510
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
520
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
530
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
540
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
550
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
560
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
570
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
580
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
590
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
600
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o
This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue.
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The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript
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Journal Pre-proof Title: Optimal Charging Infrastructure Planning based on a Charging Convenience Buffer Author: Sreten Davidov, PhD Research highlights
Including the charging convenience in the charging infrastructure placement planning
Charging convenience as constraint of the charging behavior
Queue principle used for the waiting time as occurrence at optimal location
Charging reliability and behavior included in a set-covering locations selection model
Sreten Davidov PII:
S0360-5442(19)32350-3
DOI:
https://doi.org/10.1016/j.energy.2019.116655
Reference:
EGY 116655
To appear in:
Energy
Received Date:
03 June 2019
Accepted Date:
28 November 2019
Please cite this article as: Sreten Davidov, Optimal Charging Infrastructure Planning based on a Charging Convenience Buffer, Energy (2019), https://doi.org/10.1016/j.energy.2019.116655
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.
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Optimal Charging Infrastructure Planning based on a Charging Convenience Buffer Sreten Davidov, PhD IQ LAB, research and development, SI-1000, Ljubljana, Slovenia E-mail: [email protected] Abstract In this paper, novelty is finding the optimal mix of charging technology types to be placed at optimal locations with regards to the Time of Convenience limitation acting as a charging convenience buffer of the users’ charging behavior. It constraints the optimization with the preparedness of users to wait when in request for charging and thus effect the optimal charging technology type selection. This paper is a step forward by combining two optimization constraints in providing the charging reliability and convenience needed to engage unlimited mobility of electric vehicles. For that purpose, discrete location model based on set-covering is involved to include electric vehicle users’ behavior reflected by their mobility trajectories, the technology charging times and the wait time required by the users’ when arriving at charging location. To show the general applicability of the model, a discrete 10 × 10 road network is considered. The numeric results show the optimal locations and the charging technology type to be placed. While the charging reliability provided, the part of faster charging technology installed prevails among optimal locations if the charging convenience buffer is shorter and vice-versa for the slower charging technology types. Keywords Charging Reliability, Locations Optimization, Queue Theory, Time of Convenience
1. Introduction Electromobility is advancing in transportation due to environmental, noise and health gains. The electrification of transport rises areas for research due to the need for optimal charging infrastructure (CI) rollout and charging technology placement to fulfil the needs for charging and to propagate new kind of mobility for higher electric vehicles (EV) adoption rate. However, in the emerging development of electromobility there are consequences such as scarcity of charging locations to meet the charging reliability of the CI, disrupted charging convenience and random charging technology placement. For higher electrification of transportation there are fewer prospects being explored scientifically: underdeveloped CI without an optimal charging locations layout and charging scheduling to increase electric power system flexibility and offer ancillary services. Namely, the complexity of the CI placement problem can be seen from various aspects, such as considering only transportation network, only the distribution network and considering both transportation and distribution networks, [1]. This paper deals with the CI development i.e. optimal charging locations layout planning by using a set-covering principle with single objective function to minimize the number of selected locations while dealing with the charging reliability and the charging convenience constraints. Up until now, there is a variety of research papers using the set-covering based nodal approach for the optimal placement of charging stations including only the transport network. However, no objective function is found to be subjected to the charging reliability and the charging convenience in order to find the optimal location solution, as proposed in this paper. The research made in [2] gives an outline on locating the passenger vehicle refuelling stations by using a set-covering based nodal approach. It is a base model that is used to show the applicability of set-covering in locating charging stations and does not address any other optimization constraints with regards to electric vehicle users (EVUs). In [3] a nodal-based approach is used for the optimal planning of CI by applying grid partition method. The main focus is given on applicability of grid partition rather than EVU oriented constraints, for instance, as CI reliability and charging convenience. In [4] the set-covering principle and the Maximal Covering Location Problem (MCLP) based approach are used to locate multiple types of charging stations. With regards to this paper, reference [4] is valuable since it introduces the charging technology to be placed at charging location. However, reference [4] does not use either charging reliability or charging convenience to find the optimal solution, yet it’s charging technology type is changed based on the MCLP approach. For this paper, reference [5] is the fundament and
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background, since it is the paper that uses the set-covering approach to introduce an optimization model for the CI planning for EV based on charging reliability and quality of service (QoS). The charging reliability principle is formulated as selection of a charging location within the driving range of the EV in order to enable EVUs to complete their trajectories. Nevertheless, [5] lacks another EVU oriented constraint, which is the novelty as contribution in this paper – the charging convenience. In [6] the charging convenience is stressed to be a necessity for the optimal placement of charging stations since it lays on the grounds of the charging times of the charging technology type and charging needs. Other papers, for example, [7] and [8], study the locations where charging stations should be placed in order to minimize the construction cost with the coverage used to express the EVU’s convenience. However, the EVU’s convenience also depends on the charging technology type to be placed at charging location. In [9], the charging convenience is addressed by including the traffic network topology and the driving patterns. Although [9], is in the scope of charging convenience, it still neglects the charging time and the inclusion of the charging reliability of the CI. Recently, there is a paper shown in [10] considering the charging satisfaction seen thorough the perspective of the distance to reach the charging station i.e. to find the relationship between the charging distance and the satisfaction degree. Another paper shown in [11] discusses the distance convenience from the aspect of distance deviation. A distance criterion with an Euclidean measure is also subject to our previous research, as show in [12]. In [12], the charging reliability is introduced as an optimization criterion to engage unlimited mobility and derive an optimal planning layout of locations to face the short driving range. In [13] there is a charging V2G scheduling algorithm involved that is oriented in providing convenience and profitable gains for EVU. However, it is a paper that elaborates a scheduling algorithm that is electric system oriented, rather than oriented to include the charging behavior for the charging convenience of the EVUs. In that scope, another paper is shown in [14] where an EV charge scheduling mechanism to maximize cost efficiency and EVU convenience is presented. For the charging scheduling mechanism to work, the charging behavior in this case requests longer charging times, for instance, when in the case of parked over-night or at work. If agreed by the EVUs, in this case, the charging convenience is not interrupted. This is the main target of this paper, i.e. to model the charging convenience of EVUs by the introduction of the charging convenience buffer for candidate location to anticipate users’ involvement in a charging strategy as part of their charging behavior. In other paper, [15], the charging convenience is discussed from the perspective of using the onboard battery in increasing the electric power system flexibility and thus having an effect on EVUs’ convenience. However, it must be emphasized that control algorithms which are electric system oriented regarding the charging convenience are not a subject of this research paper. Based on the literature review shown, the main facts that were extracted as a conclusion and served as incentive for the presented research paper include: necessity to include the charging convenience in the optimal CI placement planning as a user oriented constraint, necessity to formulate the charging behavior at candidate location with the newly proposed charging convenience buffer, consideration of the charging times related with the charging technology type for the charging convenience when waiting at a charging location, necessity to combine both the charging convenience and charging reliability in a set-covering based optimization model, consideration of waiting at location for charging service as occurrence by introducing the queue theory. The paper presented fills the gap and contributes in the research area for finding the optimal mix of charging technology types to be placed at optimal locations with regards to the Time of Convenience (ToC) limitation acting as a charging convenience buffer at charging location to anticipate users’ involvement in a charging strategy as part of their charging behavior. It constraints the optimization with the preparedness of users to wait when in need for charging which is in direct concern of the queue theory – waiting as occurrence due to the charging needs of EVUs. With regards to previous relative existing studies in this research area, such as [5], [12] and [17], the main improvement or novelty in this paper is going a step forward by combining two optimization constraints in providing the charging reliability and convenience needed to engage unlimited mobility of EVs. To fulfil its purpose and offer an optimal charging placement plan, this paper uses the driving patterns of the EVUs as representative of their mobility behavior. As per the set-covering theory, the candidate locations are also part of the EVUs trajectories and due to their dual nature in the complexity of the optimization problem the model selects the minimum number of locations to cover the trajectory points in order for the EVUs to complete their mobility trips. The charging times of the charging technology
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to be placed at charging location is limited by the ToC that enables the charging behavior modelling and EVUs charging convenience satisfaction. This limitation is critical for the optimal location selection and charging technology placement since it includes both the charging reliability and charging behavior of EVUs. The model presented is a generally applicable model to any road network since it uses a set-modelling approach. Numeric results show that the charging behavior of EVUs accounted with the charging convenience buffer for the candidate locations can be integrated in a set-covering CI optimization model. For the charging behavior case where it is anticipated EVUs to participate in smart charging scheme and consequently for their charging convenience it is allowed slower charging, the proposed model gives the optimal charging locations layout with slower charging technology type placed at selected locations. Otherwise, when for the charging convenience is requested faster charging, at optimal charging locations faster charging technology types prevail. The remaining sections of the paper are organised as follows: the Optimal Charging Infrastructure Planning based on a Charging Convenience Buffer is explained in detail in Section 2. The optimisation procedure for the CI placement is presented in Section 2.2, while Section 3 presents the numerical results. The conclusion drawn from this paper is presented in Section 4.
2. Optimal Charging Infrastructure Planning based on a Charging Convenience Buffer As the EVUs are anticipated to be involved in a charging strategy, it is fundamental to be able to include the charging behavior in an optimal CI planning procedure. This paper offers the charging convenience buffer at charging location as option to include the charging convenience of the EVUs. Namely, if a longer charging time is required at candidate location as a reflection of a EVU’s charging behavior, the optimal CI planning model must place slower charging technology type at location to address the charging convenience of the EVU. Using the proposed model in this paper, the CI planners are enabled to include the anticipated participation of EVUs in charging strategies and make a step forward in modelling the real-time occurrences. For the optimal CI planning the envisioned optimisation procedure including the input data parameters, the optimization model and identification of optimal results is shown in Figure 3. As this paper is focused on optimization model including the transportation network, the input data considers the parameters of discretization modelling in form of candidate locations to place a charging stations with a charging technology. The transportation network with discrete candidate locations has dual role, since the set of candidate locations is used in formulation of EVU trajectories as representative of their mobility behavior. It can be affirmed in papers like [16], moreover our research [17], where stochastic modelling can be used to create numerous EVU trajectories in a limited grid and to extract representative trajectories. Nevertheless, that part of modelling is not subject in this paper and EVU trajectories are arbitrary selected to show the coverage principle, valuable for the charging reliability formation. For the input part, another significant component is the charging technology and the charging time, that is used in the queue structure to limit the optimization shown in Subsection 2.1.4. The ToC is the other part of the queue structure, which as previously elaborated serves as a charging convenience buffer over the charging location to constrain the optimization in selection of the charging technology with regards to the charging time to address the charging behavior. The optimization model is defined with a single objective function in finding the minimal number of locations to place a charging technology type. The constraints are clearly set: the charging reliability for selection of one candidate location within the driving range of the EV and the charging convenience at that location with the limitation of ToC. The optimization model is shown in Section 2.2. The numeric results show the optimal number of charging locations with the charging technology at a charging location to be placed. The optimal placement layout is also identified. The numeric results and the discussion are shown in Section 3. 2.1. Input data preparation The input data preparation consists of modelling in the discrete domain the transportation network and showing the candidate locations, which also take part as trajectory points in exposing the EVU mobility behavior. These trajectories are arbitrary selected and used to present the coverage principle significant for the charging reliability. It must be stressed, that the input can be any imaginable discrete formulated EVU trajectory in a discrete modelled grid. The modelling of the EVUs trajectories is not in the focus of this research. The charging convenience as part of the charging behavior is comprised by the ToC and the charging technology types with their charging times. The input data preparation is consisted of the Subsection 2.1 elaborating the discrete modelling of the transportation
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network and the using of sets to note the candidate locations. Subsection 2.1.1 discusses the discrete modelling of the EVU mobility behavior and trajectory representation as per input in optimization procedure. Subsection 2.1.2 is dedicated to the formation of the sets for the charging reliability of the CI. Subsection 2.1.3 gives an overview of the charging reliability formulation. Subsection 2.1.4 gives an outlook of the charging convenience in a queue structure. The charging times for the charging technology is presented in Subsection 2.1.5. The prepared parameters are thus input for the optimization model, where a linear programming is applied in order to identify the optimal results. The optimal CI plan provides vital information for CI planners, where the mobility and charging behaviors are accounted with the criterion to resolve the limited mobility as one of the main shortcomings of EVs. 2.1.1. Discrete modelling of the transportation network
This paper uses discrete modelling in order to use the advantage of set-covering principle in the optimization procedure. For that purpose, a set of candidate locations is formed to serve both as part of a trajectory and be part of the transportation network. The goal is to cover the trajectories in a such way that the EV can be able to complete the trajectory and to exceed the driving range limitation. Hence, the covering principle is the foundation of the charging reliability criterion elaborated in Subsection 2.1.3. The set M shown in (1) consists the discrete points to model the transportation network. M m1 , m2 , m3 , , mi , , mI ; (1) i 1, 2,3,..., I The i-th element of the set is mi and the cardinality of the set is I. Due to the sampling rate in the discretization process, the cardinality of the set is bigger when lower sampling rate is used and vice-versa in the case of bigger sampling rate. For the set M, between any pair of elements’ the Euclidean rule of equally distributed in-between distance is followed. As part of the transportation network modelling, the set formulation is a discrete approach, that creates a simple method to include and model any transportation network for optimization purposes. To give a more thorough example of the road network discretisation, Figure 1 shows I = 15 candidate locations which are part of the discrete road network, formulated as per equation (1). The empty markers represent equally spaced discrete points, part of the set M. 2.1.2. Discrete representation of the electric-mobility behavior
The elements of M further serve to represent the mobility behavior of EV users and it is the basis for the coverage optimization procedure. The mobility behavior of the EV users is noted with the individual EV movement trajectory, noted as in (2).
N v nv,1 , nv,2 ,..., nv, j ,..., nv, J v ; j 1, 2,..., J v ; v 1, 2,..., V
(2)
Nv is the finite set presenting the v-th EV trajectory within the modelled road network and nv,j is the j-th element of the finite set of the EV trajectory. Jv stands for v-th EVU overall number of elements of the trajectory, while V is the total number of EVUs. Figure 2 presents the spatial trajectory of the v-th EVU, as noted per equation (2). 2.1.3. Formation of the charging reliability constraint
At this point, it can be noticed the dual nature of the elements of M: to serve as candidate location and a trajectory point. Hence, the v-th set Nv according to the set-covering principle represents the set of demand points that are to be covered by selecting from the candidate locations. The (Euclidean) distance between the j-th trajectory point, part of the Nv, and the i-th element of the set M is calculated as shown in (3). The Euclidean distance is used as distance measure between two adjacent points, thus used as a criterion in formation of the candidate locations set in relation to the charging reliability.
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i , j ,v (mi nv, j ) 2dx (mi nv, j ) 2dy ; mi M ; nv , j N v
(3)
ξi,j,v is the Euclidean distance between the i-th candidate location point or mi and the j-th trajectory point for the v-th EVU, or nv,j. The dx and dy values represent the coordinate directions. This measurement criterion is compared with the coverage distance which is taken to be the driving range of the EV, Rv. The j-th trajectory point is covered by a candidate location i, if the criterion of coverage distance noted in (4) is fulfilled.
Sv ,i mi M : i , j ,v Rv ;
(4) j 1, 2,..., J v ; v 1, 2,..., V In equation (4), the elements of the finite set Sv,i represent all candidate location points mi, which meet the distance criterion ξi,j,v ≤ Rv. In other words, Sv,i holds the candidate locations which can cover the trajectory points j. To provide a more straightforward notation of candidate locations for the further optimization process, the following Boolean coefficient is involved, i.e. ai,j,v, which is equivalent to the set defined in equation (4). 1, if i , j ,v Rv ai , j ,v (5) 0, otherwise
The ai,j,v coefficient in equation (5) notes whether the distance from the i-th candidate location to the j-th trajectory set element for the v-th EVU falls within the scope of the defined distance criterion, ξi,j,v ≤ Rv. If this criterion is met, the ai,j,v coefficient takes the value of 1, otherwise its value equals 0. Figure 4 gives an example of the charging reliability formation criterion, by assuming a driving range distance Rv and selection of charging location at distance equal to Rv. The driving range is considered constant and no range loss impacts are considered. Figure 4 also gives an example, that the scale of the road network takes its part in formation of the number of candidate locations to be included in the optimization procedure as part of the input part due to the formulation of the charging reliability sets. 2.1.4. Charging convenience as constraint of the charging behavior
In this paper, the well-known queue theory, [18], is applied in regards to the waiting time as occurrence and user convenience accounted for the charging behavior. For the purpose of smart charging, it can be expected that the charging behavior of EVUs can prefer longer charging time, [19]. Consequently, slower charging technology type needs to be placed at charging location to address the EVUs convenience. Otherwise, at locations where charging behavior requires rapid charging, faster charging technology type needs to be selected. In this paper, the ToC is used as charging convenience buffer at a candidate location in order to anticipate the charging behavior needs of EVUs and to propose an optimal CI planning come closer to real-time occurrences. To elaborate more profoundly with regards to the queue theory, each of the candidate locations of the transportation network is assumed to act as a queuing system where the key elements are the arriving v-th EVU to require a charging service at the i-th charging location to provide the requested service based on k-th charging technology type. Figure 5 shows the j-th trajectory point for the v-th driver, nv,j, where ToC is represented as charging convenience buffer in order to limit the charging time CTk for the k-th charging technology at the charging location. The charging convenience buffer is directly correlated with the charging behavior of EVUs. In addition, ToC represents the required length of stay at charging location. For instance, if for a candidate location is anticipated that the v-th EV driver will park the vehicle over-night or for work, longer charging hours for smart charging can be expected and slower charging technology type can be placed. Otherwise, if the v-th EV driver requires short stay per candidate location, faster charging technology is to be placed. Therefore, constraining the optimization model with the charging convenience buffer with a value of ToC per candidate location, imply for changing the charging technology type to be placed at optimal location and fulfilling the charging convenience. 2.1.5. Charging time of charging technology
The charging technology dictates the charging duration, since the higher the transferred power that can be enforced by the charging technology, the shorter the charging time. In the following equation the charging time is noted with regards to the charging technology:
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Lk ,v CTk R v ;
(6) v 1, 2,..., V ; k 1, 2,..., K where CTk is the charging duration using the k-th charging technology to reach distance equal to the initial EV driving range, i.e. Rv. K is the overall number of charging technology types. Faster charging stations as implied have shorter charging times, and vice-versa. Placement of faster charging technology types at charging locations depends on the allowable charging convenience buffer exposed by ToC for a charging location. The model presented uses this constraint for the charging reliability to provide a charging location placement list to fulfil the need of engaging unlimited mobility and charging convenience. 2.2. Optimal Charging Infrastructure Planning Model The charging location set-covering model (CLSCM) objective is to minimize the number of charging locations with keeping the coverage of the trajectories used to model the EVUs mobility behavior and to place the charging technology for the charging convenience. The objective function written in equation (7), F, minimizes the overall number of charging locations and selects the charging technology to be placed at a charging location. For the k-th charging technology, k ∈ K, to be placed at i-th candidate location, i ∈ I, the Boolean integer variable xi,k, is involved which takes the value of to 1 if the k-th charging technology is placed at i-th location and 0 otherwise. I K Min F xi ,к (7) i 1 k 1 The objective function minimizes the overall number of charging locations by placing the charging technology to address the charging convenience for EVU at candidate location, driving range limitation and engaging unlimited mobility with the charging reliability criterion. The objective function is constrained as shown in equations (8)-(11).
I
K
a
i , j ,v
xi ,k 1;
i 1 k 1
(8)
j 1, 2,..., J v ; v 1, 2,...,V I
K
CT x k
i ,k
ToCi ,v
(9)
1
(10)
i 1 k 1
I
K
x
i ,k
i 1 k 1
xi , k 0,1 ; i 1, 2,..., I ; k 1, 2, , K
(11) Equation (8) is included in order to ensure the charging reliability of the charging infrastructure. The coefficient ai,j,v of equation (5) notes whether the distance from the i-th candidate location to the j-th trajectory set element for the v-th EVU falls within the scope of the defined distance criterion, ξi,j,v ≤ Rv. If this criterion is met, the ai,j,v coefficient takes the value of 1, otherwise its value equals 0. This constraint will impose the optimisation to select at least one candidate location within the driving range if the v-th EVU. As the charging reliability constraint is thoroughly elaborated in papers [5], [12], [17], and in Subsection 2.1.3 in this paper, the main focus is on involvement of the charging convenience constraint which corresponds with the desired length of stay per candidate location to address the charging convenience of the EVU. Equation (9) is involved for the charging convenience as explained in detail in Subsection 2.1.4. The involvement of this constraint is the main novelty of this research paper, since it provides vital limitation in identifying the charging technology to be placed. As per the left-hand side of the inequality in (9), the charging time CTk of the k-th charging technology type is constrained on the right-side with ToC representing the charging convenience buffer addressing the need of the v-th EV driver to wait at i-th candidate location when in request for charging and introduces the charging convenience for the EVUs. The value of ToC takes in consideration the need of faster or slower charging when arriving at candidate location. Since, this limitation gives a outlook to charging convenience of the v-th EV driver according to his charging behavior and needs. Equation (10) enforces the optimization to select the k-th charging technology out of a set of K charging technology
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types to be placed at charging location. Constraint (11) states the binary definition of the optimisation decision variable for the k-th charging technology type to be placed at i-th candidate location i.e. the binary definition of I candidate location points with K charging technology types.
3. Numerical Results For the representation of the gains in novelty of the presented paper, a methodological test transportation network is involved of I = 100 discrete points distributed in a plane 10 × 10, as shown in Figure 6a). It must be emphasized, that the proposed optimization methodology can be used for more complex and bigger transportation network, such as shown in [12] and [17]. For the transportation grid, the distance between two consecutive candidate locations is 1 p.u., and in this case study 1 p.u. equals 100 km. In addition to solving the optimization model in this paper, linear programming with the Matlab formulation of the optimization problem is used. This research paper is set to use deterministic approach for the data in the Input part of the optimization procedure, as shown on Figure 3. For instance, the components of the input data such as the charging and mobility behaviors, which will serve further to determine the optimal charging locations’ layout and charging technology to be placed at location for fulfilling the EV drivers’ needs, at this stage of the research are involved as per the deterministic approach. Hence, for the future research, it is planned to include stochastic approach for the data modelling in the input part, for example, using a previously involved procedure, [17], to find representative trajectories of the stochastic mobility behavior, constraint on stochastic Quality of Service, charging convenience, stochastic driving range for the purpose to derive the optimal results with its’ probability of occurrence, to the benefit of the stakeholders, as shown earlier in one of the SCI papers published [17] and based on which this research paper is established. Figure 6b) shows the aggregated spatial layout of the EV trajectories, where the discrete points as candidate locations are also part of the EV mobility trajectories. For this case-study, these trajectories are representative of the mobility behavior. The number of trajectories, Nv, is 3 and thus equals the number of EVs equally as in the case-study represented in [1]. As these points are part of a trajectory of the EVs, according to the charging reliability constraint of the optimization model, Subsection 2.1.3, there must be a location selected within the driving range of the EV. Above all, this constraint ensures that logistically and optimally from a CI planners perspective, there is at least one charging location selected to engage unlimited mobility for EVs. The optimization procedure is executed for the different values of the driving range, Rv equal to 200, 400 and 800 km in order to validate and confirm the importance of the constraints. It is fundamental assumption that when starting the EV is fully charged and the losses in range due to EV driver’s skills and road configuration are neglected. It must be stressed that these losses in distance are here included in Rv and any other influences in driving range distance are profoundly elaborated in research paper [12]. Above all, the proposed methodology can take any arbitrary value regarding the driving range, Rv. The overall number of charging technology types for this paper is K = 3, where the first charging technology, k=1, is a fast charge (FC) technology with charging time CT1 is 30 min, for k=2, the charging technology is medium charge (MC) technology, with charging time CT2 120 min and for k=3, slow charge (SC) technology with charging time CT3 is 300 min. To sum up for the Input data preparation part (Subsection 2.1) – a methodological discrete transportation network is introduced to show the advantages of the newly involved optimization constraint regarding the charging convenience. The i-th candidate location out of I = 100 candidate locations is subject to placing the k-th charging technology type out of K charging technology types with charging time CTk. The mobility behaviour of the EV users is involved with deterministic representative trajectories, which are arbitrary selected and stochastic modelling of mobility driving patterns as shown in [17], is not subject in this research. The charging behavior is represented with the Time of Convenience, that acts as charging convenience buffer for i-th candidate location in accordance with the needs of v-th EV driver. ToC reflects the preparedness of the EVUs to wait when arriving at charging location. Additionally, the CI planners are able to include the anticipation for the EVUs to participate in a charging strategy such as smart charging, for which longer charging times are required. Therefore, multiple values for ToC are considered in this case-study i.e. 30, 120, 450 min. For the case study to be more clear, it is simply assumed that all EV drivers require the same values for ToC when arriving at charging location; nonetheless, these values can be arbitrary changed. After execution of the optimization model, with regards to the Input data, Table 1, shows the optimal locations layout for the value of ToC, 30, 120 and 450 min and for the different values of the driving range 200, 400 and 800
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km. For the first value of ToC, 30 min and value of the driving range 200, 400 or 800 km, is the most severe case when the charging convenience buffer is shortest required for candidate location and equal to the value of the charging time of the fastest charging technology. Consequently, as shown in Table 1, for the value of 30 min, only FC technology is placed at optimal locations for all the values of the Rv. Above all, the model ensures that the EVUs complete their trajectories (charging reliability criterion). As the value of ToC increases to 120 and 450 min, the optimal layout changes and also the share in locations of FC and MC. For the value of 450 min, and for the values of the driving range 200, 400 and 800 km, it is shown that the mixture of charging technology types is different, since the constraint allows placing slower charging technology types at optimal locations. To deliver better understanding of the charging convenience buffer involved with the ToC constraint imposed by EVU, the optimization model is looped through the values starting from 30 min to 600 min with a 10 min step increasing the charging convenience buffer. Increasing the ToC would mean that when EVUs are at charging location, the waiting time is higher and thus the charging convenience is lower. It is the case, when EVUs is anticipated not to take part in any charging strategy, their charging behavior implies “charge-and-go”. It is expected that by imposing shorter ToC to push the optimization model in selection of faster charging technology types with shorter charging times, thus acting in relaxing the charging convenience buffer over the charging location. Results are shown in Table 2. Results show that the share of slower charging technology types, i.e. in this case MC and SC increase their part as the charging convenience buffer with ToC increases. This is the case, when it is anticipated that the EVUs are willing to take part in smart charging strategy, when longer charging times are required. This charging behavior, by the use of ToC can be included in the CI optimization to oversee the need for charging technology to be placed at charging location. Higher the charging convenience buffer over the charging location relaxes the constraint in the optimization and as optimal output a slower charging technology is selected. These results open the perspective of charging convenience which is provided through the involvement of ToC in this paper: The shorter the time in willingness to wait when arriving at charging location, the more would the EVU be convenient for charging at that location. Notice on the results: The model gives the optimal layout and the optimal charging technology to be placed for the value of the charging convenience limitation, ToC. It shows the optimal charging mix of technology types where are to be placed by also ensuring the charging reliability for unlimited mobility of EVs. As an added value of the contribution of this research is going one step further is increasing the value of the ToC to a significantly large number (2000 min) i.e. enormously long charging convenience buffer, and for the value of the driving range 200 km, to oversee the change in the overall optimal charging technology mix, as shown on Figure 7. Figure 7 shows that the optimal charging technology mix stays unchanged after the value of ToC reaches 450 min and the share of FC is 46.875 % MC is 25 % and SC is 28.125 %. This is due to the criterion of ensuring the charging reliability of the charging infrastructure for the minimal number of charging stations to cover the EVU trajectories in order to complete their trajectories.
4. Conclusions This paper offers an optimization procedure to develop and improve the charging infrastructure placement as a vital component of the transportation system. Using a set-covering principle and a linear programming approach, the optimal set of locations is identified and the optimal charging technology mix determined. The model is based on the engagement of the charging reliability of the charging infrastructure and the charging convenience as part of the charging behavior. As a point of discussion, the Time of Convenience is introduced, as a limitation over the charging location and acting as a charging convenience buffer to contribute in optimal charging technology selection for a charging location. Since the charging behavior can be related to wiliness to participate in smart-charging strategy where longer charging times are anticipated, the ToC is a user oriented input that involves the charging convenience of the user. If the user is willing to wait longer at charging location, slower charging technology is to be placed at that location, hence, not disrupting his charging convenience. Otherwise, when charging convenience requires placing faster charging technology, the ToC acts a shorter charging convenience buffer. The queue theory is used as fundamental methodology in regards to the waiting time to charge. The presented charging infrastructure planning optimization procedure is a generally applicable optimization solution. To show its advantages, a methodological discrete 10 × 10 road network is considered and electric vehicle trajectories included to find the optimal solution. For the shorter charging convenience buffer at location, the faster charging technology types with shorter charging times prevail and vice-versa. Additionally, the optimal charging infrastructure plan in shown, with regards to the charging behavior, mobility behavior and representative trajectories. Future research is to be made on incorporating more
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segments of queue theory in combination with set-covering theory to contribute more in the charging infrastructure planning. Stochastic approaches are expected to be applied for the tasks involved in the input data preparation part, nonetheless, the parameters regarding the accessibility, comfort and urban limitations. This paper represents the basis for the future work in the field of providing new concepts for the improvement of the transportation systems.
5. References [1] Deb, Sanchari, Kari Tammi, Karuna Kalita, and Pinakeswar Mahanta. "Review of recent trends in charging infrastructure planning for electric vehicles." Wiley Interdisciplinary Reviews: Energy and Environment 7, no. 6 (2018): e306. [2] Wang, Ying-Wei, and Chuan-Ren Wang. "Locating passenger vehicle refueling stations." Transportation Research Part E: Logistics and Transportation Review 46, no. 5 (2010): 791-801. [3] Ge, Shaoyun, Liang Feng, and Hong Liu. "The planning of electric vehicle charging station based on grid partition method." In 2011 International Conference on Electrical and Control Engineering, pp. 2726-2730. IEEE, 2011. [4] Wang, Ying-Wei, and Chuah-Chih Lin. "Locating multiple types of recharging stations for battery-powered electric vehicle transport." Transportation Research Part E: Logistics and Transportation Review 58 (2013): 7687. [5] Davidov, S., & Pantoš, M. (2016). Planning of electric vehicle infrastructure based on charging reliability and quality of service. Energy. [6] Xiong, Yanhai, Jiarui Gan, Bo An, Chunyan Miao, and Ana LC Bazzan. "Optimal electric vehicle fast charging station placement based on game theoretical framework." IEEE Transactions on Intelligent Transportation Systems 19, no. 8 (2018): 2493-2504. [7] Lam, Albert YS, Yiu-Wing Leung, and Xiaowen Chu. "Electric vehicle charging station placement: Formulation, complexity, and solutions." IEEE Transactions on Smart Grid 5, no. 6 (2014): 2846-2856. [8] Xiong, Yanhai, Jiarui Gan, Bo An, Chunyan Miao, and Ana LC Bazzan. "Optimal electric vehicle charging station placement." In Twenty-Fourth International Joint Conference on Artificial Intelligence. 2015. [9] Wang, Guibin, Zhao Xu, Fushuan Wen, and Kit Po Wong. "Traffic-constrained multiobjective planning of electric-vehicle charging stations." IEEE Transactions on Power Delivery 28, no. 4 (2013): 2363-2372. [10] Liu, Jin-peng, Teng-xi Zhang, Jiang Zhu, and Tian-nan Ma. "Allocation optimization of electric vehicle charging station (EVCS) considering with charging satisfaction and distributed renewables integration." Energy 164 (2018): 560-574. [11] Guo, Fang, Jun Yang, and Jianyi Lu. "The battery charging station location problem: Impact of users’ range anxiety and distance convenience." Transportation Research Part E: Logistics and Transportation Review 114 (2018): 1-18. [12] Davidov, Sreten, and Miloš Pantoš. "Impact of stochastic driving range on the optimal charging infrastructure expansion planning." Energy 141 (2017): 603-612. [13] Wang, Baocheng, Yafei Hu, and Fanfeng Zeng. "A user cost and convenience oriented EV charging and discharging scheduling algorithm in V2G based microgrid." In 2017 International Conference on Circuits, Devices and Systems (ICCDS), pp. 156-162. IEEE, 2017. [14] Chung, Hwei-Ming, Wen-Tai Li, Chau Yuen, Chao-Kai Wen, and Noel Crespi. "Electric vehicle charge scheduling mechanism to maximize cost efficiency and user convenience." IEEE Transactions on Smart Grid (2018). [15] Magome, Nozomu, and Shigeru Tamura. "A New Decentralized Control of EVs for Load Frequency Control Retaining EV users’ Convenience." In 2018 IEEE International Telecommunications Energy Conference (INTELEC), pp. 1-6. IEEE, 2018.
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[16] Technitis, Georgios, Walied Othman, Kamran Safi, and Robert Weibel. "From A to B, randomly: a point-to-point random trajectory generator for animal movement." International Journal of Geographical Information Science 29, no. 6 (2015): 912-934. [17] Davidov, Sreten, and Miloš Pantoš. "Stochastic expansion planning of the electric-drive vehicle charging infrastructure." Energy 141 (2017): 189-201. [18] Saaty, T. L. (1961). Elements of queueing theory: with applications (Vol. 34203). New York: McGraw-Hill. [19] Lopes, J. P., Almeida, P. M. R., Silva, A. M., & Soares, F. J. (2009). Smart charging strategies for electric vehicles: Enhancing grid performance and maximizing the use of variable renewable energy resources.
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Figure Captions Figure 1 Example of road network discretisation Figure 2 Example representation of the v-th EV user trajectory Figure 3 Principle scheme in the proposed optimal charging infrastructure planning Figure 4 An example trajectory with the charging reliability criterion presented to engage unlimited mobility of EVs Figure 5 ToC acting as charging convenience buffer to fulfil the charging time of the charging technology for the charging convenience of the charging infrastructure Figure 6 a) Discrete test road network and b) Spatial layout representation of all EVUs trajectories Figure 7 Increasing ToC to significantly large number (case of driving range 200 km)
Table Captions Table 1 Changing the optimal layout of locations due to the value of ToC for the value of range, Rv= 200 km, 400 km and 800 km....................................................................................................................................................................15 Table 2 Optimal charging technology mix as function of ToC for the different values of the driving range Rv= 200 km, 400 km and 800 km.......................................................................................................................................................18
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Figure 1 Example of road network discretisation
Figure 2 Example representation of the v-th EV user trajectory
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Figure 3 Principle scheme in the proposed optimal charging infrastructure planning
Figure 4 An example trajectory with the charging reliability criterion presented to engage unlimited mobility of EVs
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Figure 5 ToC acting as charging convenience buffer to fulfil the charging time of the charging technology for the charging convenience of the charging infrastructure
a) b) Figure 6 a) Discrete test road network and b) Spatial layout representation of all EVUs trajectories 100 FC MC SC
90
Charging technology share (%)
80 70 60 50 40 30 20 10 0
0
1000
Time of Convenience, ToC v (min)
Figure 7 Increasing ToC to significantly large number (case of driving range 200 km)
2000
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Table 1 Changing the optimal layout of locations due to the value of ToC for the value of range, Rv= 200 km, 400 km and 800 km
ToC=30 min
Rv= 200 km ToC=120 min
ToC=450 min
ToC=30 min
Rv= 400 km ToC=120 min
ToC=450
ToC=30 min
Rv= 800 km ToC=120 min
ToC=450
FC
MC
SC
FC
MC
SC
FC
MC
SC
FC
MC
SC
FC
MC
SC
FC
MC
SC
FC
MC
SC
FC
MC
SC
FC
MC
SC
1 3 6 7 9 12 14 18 20 23 26 32 34 38 40 45 46 52 54 58 60 65 72 74 78 80 83 87
/
/
1 3 7 9 12 14 16 18 20 23 32 34 36 38 40 45 52 54 56 58 60 65 72 74 80 83 87 92
78
/
1 3 12 14 32 34 45 46 52 72 74 79 88 94 95
8 10 23 30 48 50 68 97
6 26 28 54 65 70 77 83 92
4 8 20 23 26 34 48 50 52 74 78 92 96
/
/
4 9 12 34 38 40 52 70 74 92 96
26 78
/
12 34 40 52 68 74
80
4 9 26 28 92 96
30 34 78 92
/
/
10 78 92
34
/
30
34 92
78
92 94 96 98
94 96 98
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Table 2 Optimal charging technology mix as function of ToC for the different values of the driving range Rv= 200 km, 400 km and 800 km
Rv= 200 km
Rv=400 km
Rv=800 km
ToC (min)
FC (%)
MC (%)
SC (%)
FC (%)
MC (%)
SC (%)
FC (%)
MC (%)
SC (%)
100
0
0
100
0
0
100
0
0
30
100
0
0
100
0
0
100
0
0
40
100
0
0
100
0
0
100
0
0
50
100
0
0
100
0
0
100
0
0
60
100
0
0
100
0
0
100
0
0
70
100
0
0
100
0
0
100
0
0
80
100
0
0
100
0
0
100
0
0
90
100
0
0
100
0
0
100
0
0
100
100
0
0
100
0
0
100
0
0
110
96.875
3.125
0
84.615
15.385
0
75
25
0
120
96.875
3.125
0
84.615
15.385
0
75
25
0
130
96.875
3.125
0
84.615
15.385
0
75
25
0
140
96.875
3.125
0
84.615
15.385
0
75
25
0
150
96.875
3.125
0
84.615
15.385
0
75
25
0
160
96.875
3.125
0
84.615
15.385
0
75
25
0
170
96.875
3.125
0
84.615
15.385
0
75
25
0
180
96.875
3.125
0
84.615
15.385
0
75
25
0
190
96.875
3.125
0
84.615
15.385
0
75
25
0
200
96.875
3.125
0
84.615
15.385
0
75
25
0
210
96.875
3.125
0
84.615
15.385
0
75
25
0
220
96.875
3.125
0
84.615
15.385
0
75
25
0
230
96.875
3.125
0
84.615
15.385
0
75
25
0
240
96.875
3.125
0
84.615
15.385
0
75
25
0
250
96.875
3.125
0
84.615
15.385
0
75
25
0
260
96.875
3.125
0
84.615
15.385
0
75
25
0
270
96.875
3.125
0
84.615
15.385
0
75
25
0
280
96.875
3.125
0
84.615
15.385
0
75
25
0
290
81.25
18.75
0
69.231
30.769
0
75
25
0
300
81.25
18.75
0
69.231
30.769
0
75
25
0
310
81.25
18.75
0
69.231
30.769
0
75
25
0
320
81.25
18.75
0
69.231
30.769
0
75
25
0
330
81.25
18.75
0
69.231
30.769
0
75
25
0
340
81.25
18.75
0
69.231
30.769
0
75
25
0
350
81.25
18.75
0
69.231
30.769
0
75
25
0
360
81.25
18.75
0
69.231
30.769
0
75
25
0
370
81.25
18.75
0
69.231
30.769
0
75
25
0
380
81.25
18.75
0
69.231
30.769
0
75
25
0
390
81.25
18.75
0
69.231
30.769
0
75
25
0
400
81.25
18.75
0
69.231
30.769
0
75
25
0
410
81.25
18.75
0
69.231
30.769
0
75
25
0
420
Journal Pre-proof
81.25
18.75
0
69.231
30.769
0
75
25
0
430
81.25
18.75
0
69.231
30.769
0
75
25
0
440
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
450
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
460
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
470
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
480
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
490
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
500
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
510
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
520
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
530
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
540
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
550
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
560
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
570
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
580
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
590
46.875
25
28.125
46.154
7.692
46.154
25.000
50.000
25.000
600
Journal Pre-proof
Conflict of Interest and Authorship Conformation Form Please check the following as appropriate: o
All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version.
o
This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue.
o
The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript
o
The following authors have affiliations with organizations with direct or indirect financial interest in the subject matter discussed in the manuscript:
Author’s name Affiliation There are no other authors. It is my research work.
Journal Pre-proof Title: Optimal Charging Infrastructure Planning based on a Charging Convenience Buffer Author: Sreten Davidov, PhD Research highlights
Including the charging convenience in the charging infrastructure placement planning
Charging convenience as constraint of the charging behavior
Queue principle used for the waiting time as occurrence at optimal location
Charging reliability and behavior included in a set-covering locations selection model