Optimal Sizing Procedure for Electric Vehicle Supply Infrastructure Based on DC Microgrid with Station Commitment

: The di ﬀ usion of electric vehicles (EVs) can be sustained by the presence of integrated solutions o ﬀ ering parking and clean power supply. The recourse to DC systems allows better integration of EV bidirectional energy exchange, photovoltaic panels, and energy storage. In this paper, a methodology for optimal techno-economic sizing of a DC-microgrid for covering EV mobility needs is carried out. It is based on the deﬁnition of di ﬀ erent scenarios of operation, according to typical EV usage outlooks and environmental conditions. In each scenario, optimal operation is carried out by means of a speciﬁc approach for EV commitment on di ﬀ erent stations. The sizing procedure is able to handle the modular structure of microgrid devices. The proposed approach is applied to a case study of an envisaged EV service ﬂeet for the Bari port authority.


Introduction
The spreading of electric vehicles (EVs) can represent a powerful means to cope with mobility needs and realize a diversification of transport energy use with a lower carbon footprint [1]. In order to bolster the diffusion of EVs among end-users (e.g., residential, commuters, company fleets), along with selling price reduction, the presence of charging stations represents the most remarkable aspect [2]. However, to avoid demand peaks given by the presence of several EVs at the same time (e.g., at work arrival, or at homecoming), the charge process should be planned, supervised, and controlled through a smart charging strategy, as described in [3,4]. The exploitation of vehicle-to-grid (V2G) is useful to cope with this necessity, where the EVs can act as a mobile energy storage device and even feed one another, implementing vehicle-to-vehicle exchanges as envisaged by [5].
Photovoltaic (PV) technology is particularly suitable for integration with EV charging stations, as reviewed in [6]. A specific realization is obtained by canopies able to host PV panels and provide for shaded vehicle parking, as proposed by [7], whereas, in [8] an analysis on different utilization cases of this system in urban contexts is reported. The integration of PV and EV charging station has been proposed in several works, e.g., charge/discharge models of EVs in the presence of PV are analysed in [9], and in [10] economic models are developed for EV and parking owner perspectives under parking fee policies. Effects on regional basis are analysed in [11]. In order to reduce the EV impact on the network, the integration of energy storage systems (ESS) in EV charging stations can be useful [12], with the aim of shifting power exchange according to price signals, smoothing out time variations [13]. Moreover, smart EV charging points, even integrated in microgrids, can contribute to -A mixed-integer procedure for EV-based microgrid optimal sizing and operation is provided, to cope with the modularity of microgrid components; - The individuation of utilization scenarios, according to weather conditions and envisaged EV uses, is adopted, and discounted investment and operation costs are included; -A specific EV commitment is developed, in order to plan the station to which each EV should be connected; -In order to draw the influence of DC microgrid layout, an accurate configuration is analysed on a realistic test case.
The paper is organized as follows. In Section 2, the proposed DC microgrid configurations are illustrated, and the formulation of the proposed methodology for DC microgrid optimal sizing and operation is described. In Section 3, the input data for the test case are presented. Simulation results are illustrated and discussed in Section 4. Conclusions are reported in Section 5.

DC Microgrid Optimal Sizing Methodology
For the complete list of symbols and their meaning, please refer to the Nomenclature at the end of the paper.

DC Microgrid Configurations
In order to carry out the sizing procedure, the proposed configurations for the DC microgrid of the EVSI are considered. The configuration, briefly discussed in [17], is depicted in Figure 1. It involves a bidirectional AC/DC converter for grid connection at Point of Common Coupling (PCC), monodirectional DC/DC converter with MPPT functionality for the integration of the PV system, a bidirectional DC/DC converter for the ESS, and different bidirectional DC/DC converters for the EV charging stations, in order to enable V2G performances. All the converters, including relevant protection devices, are connected to a common DC busbar at a proper voltage level. Moreover, suitable internal collection systems for the input of PV panel strings to the converter and for the ESS modules are provided.

Modeling of EVSI Components
The EVSI can include Np PV technologies and Ni ESS technologies, and is able to exchange power with Nj EVs through Nk stations, where a set of Nr standards can be chosen. The behavior of each component is described by proper models for each t-th time step in the s-th scenario. In order to assess the operation of the microgrid in the presence of different frameworks for vehicle use and generation availability, a scenario-based procedure is considered, analogously to analysis carried out in different contexts of renewable-storage coupling in [30] and in photovoltaicbased nanogrid reliability analysis in [31]. Since solar power production depends on weather conditions and seasons, and storage devices and EVs can show different use in weekdays as well as in subperiods of the year, a certain number Ns of scenarios, i.e., typical days, are defined in advance, considering that each s-th scenario can be observed for a given number of times s D during the year. Moreover, due to the limited dimensions of the microgrids, the sizing procedure accounts for power and energy aspects, leaving voltage control to the implementation stage close to real time, even if operation under different scenarios is accounted for.

PV Systems
The power output of the p-th PV system depends on the available solar radiation

Modeling of EVSI Components
The EVSI can include Np PV technologies and Ni ESS technologies, and is able to exchange power with N j EVs through Nk stations, where a set of Nr standards can be chosen. The behavior of each component is described by proper models for each t-th time step in the s-th scenario.
In order to assess the operation of the microgrid in the presence of different frameworks for vehicle use and generation availability, a scenario-based procedure is considered, analogously to analysis carried out in different contexts of renewable-storage coupling in [30] and in photovoltaic-based nanogrid reliability analysis in [31]. Since solar power production depends on weather conditions and seasons, and storage devices and EVs can show different use in weekdays as well as in subperiods of the year, a certain number Ns of scenarios, i.e., typical days, are defined in advance, considering that each s-th scenario can be observed for a given number of times D s during the year. Moreover, due to the limited dimensions of the microgrids, the sizing procedure accounts for power and energy aspects, leaving voltage control to the implementation stage close to real time, even if operation under different scenarios is accounted for.

PV Systems
The power output of the p-th PV system depends on the available solar radiation G p,s,t , installed PV power R p and technological features, by means of the following expression: In (1), the efficiency of the p-th PV system, η p,s,t , is related to the forecasted weather conditions of the specific time step (i.e., solar radiation and ambient temperature ϑ s,t ) as follows [18]: where η std p is the efficiency level at standard conditions (incident radiation 1 kW/m 2 , temperature ϑ std p = 25 • C) and a p is the power coefficient p-th PV system. Moreover, the temperature variation from nominal operating conditions (with reference temperature ϑ NOCT p = 20 • C and reference radiation G NOCT p = 0.8 kW/m 2 ) is related to the normal operating temperature of the PV cell ϑ p . These data can be easily taken from PV panel datasheets.
Since the relation (1) linearly links power output with the installed power R p according to solar radiation G p,s,t , P p,s,t is not included in state variables. The incident solar radiation G p,s,t is estimated with a proper model based on the determination of direct, diffuse, and reflected radiation according to the day, the time of the day, and the PV panel orientation, starting from total radiation forecast on horizontal plane [32].
The PV installation R p is limited by available surface of parking roofs S tot and should ensure shadowing for all the parking places next to EV charging stations, each requiring an area S k : Moreover, since the PV system is made up by discrete modules, the installed power of the p-th PV technology to the number n p of PV modules, according to the unit power of the module M p , by the following equality constraint: Finally, the size of PV converter should be not less than the installed power of the PV system, and only one converter per each PV technology has to be installed. Converter sizes W m are determined in order to comply with voltage range variation of PV panel strings under temperature variations.

Energy Storage Systems
The behavior of ESSs is characterized by the energy amount present in the storage device in each time step. However, a high degree of correspondence is observed between energy amount and state-of-charge (SOC), given by the levels of current [33]. The assumption of discarding voltage variations in this procedure further leads to the exploitation of SOC in each time step E i,s,t to define ESS availability in the operation planning [25].
SOC variation over the time step duration ∆t is due to charging/discharging process, with power levels P c i,s,t or P d i,s,t , by proper charge and discharge efficiencies, η c i and η d i . The following relation holds for the t-th time step: where E i,s,t−1 represents the SOC of the i-th ESS in the previous time step of the s-th scenario. For t = 1, E i,s,0 represents the imposed SOC initial condition. The last term in (7) refers to self-discharge, as a quota z i of installed amount R i . Moreover, the SOC at t = Nt is imposed equal to the initial condition, allowing replication of the behavior for consecutive days: Technical limits of the i-th ESS are accounted by means of constraints on charge power, discharge power, and SOC, depending on installed amount R i by means of energy-to-power ratios in charge and discharge, ϕ c i and ϕ d i , and maximum/minimum SOC levels, e i and e i : The total installation of ESSs is limited by available volume V tot for hosting the devices: Analogously to PV system, the following equality constraints link the installed size of the i-th ESS to the number n i of modules, according to the unit size of the chosen battery M i , and to the size of the converter:

Electric Vehicles and Stations
EVs are dealt with as storage devices, as long as they are connected to a station. The relation for SOC update is valid for the t-th time step between τ A j,s + 1 and τ L j,s : where, at t = τ A j,s + 1, E j,s,t−1 = E A j,s , as the initial SOC condition at EV arrival, whereas at t = τ L j,s , E j,s,t = E L j,s , the final desired SOC level at EV leaving. It should be remarked that this formulation is based on the assumption that each EV is parked for one interval per day. In the case the daily EV usage pattern includes two (or more) parking intervals, it is dealt with as two (or more) virtual EVs with a single parking interval.
Technical limits of the j-th EV, valid during parking interval, involve constraints on power levels, capped by charge and discharge limits P c j and P d j , and on SOC and power levels: As regards technologies for charging stations, the following relations (20)-(21) link maximum charge/discharge power of the k-th station, P c k and P d k respectively, to the power exchange levels admitted by the r-th technology, Ψ c r and Ψ d r , whereas the association of the r-th technology to the k-th station is ensured by (22). It should be noted that the case where the r-th EV station standard would not provide for V2G is modelled by Ψ d r = 0:

Electric Vehicles Station Commitment
The electric vehicle commitment is aimed at scheduling the station at which each EV should be connected, creating a link between their features.
In the planning stage, the number of stations Nk to be included in the EVSI is evaluated. For each time step of each scenario, the number of parked vehicles J s,t is determined starting from information on τ A j,s and τ L j,s . Therefore, for each scenario, the maximum number of EVs parked at the same time is obtained, and the relevant time interval is individuated: The number of EV stations is eventually set to the minimum necessary to cover the maximum amount of EVs parked at the same time in any scenario: Moreover, EV exploitation is characterized by evaluating, for each EV in each scenario, the average power needed to reach the final state π j,s : Once Nk is determined, for each scenario, the EV commitment starts from the time step τ s . The J s EVs parked in this time step are associated to the charging stations according to a list sorted according to the index π j,s : the EV with the highest index is connected to the first station, k = 1, and so on.
After that, the remaining N j − J s EVs are ordered according to the power index π j,s . For each EV in this ranking, starting from the first one, the procedure tries the connection to the first available station, avoiding time superposition with the EVs previously selected.
This procedure can leave in idle state the last stations. In this way, the binary parameter β j,k,s is determined for all EVs, stations, and scenarios.
For purpose of exemplification, an application of the EV station commitment procedure is reported in Appendix A.
Therefore, the amount of charge and discharge power that the j-th EV can exchange depends not only on the EV features, but also on the k-th station it is connected to in the s-th scenario, as follows:

Microgrid Balance and Power Exchanges
The overall behaviour of the microgrid is governed by power balance relation, where the generation is represented by net PV production, ESS discharge, possible EV discharge, and grid withdrawal, whereas the load includes ESS and EV charge and grid power delivery. Due to limited dimensions, microgrid balance is expressed as a single-bus power balance, considering net power contributions at the DC bus by means of converter efficiency for each device (reducing generation and increasing the load), as reported in (29): The power exchange across the interfacing converter should withstand specific constraints related to the installed converter size R F , as reported in relations (30)-(31): The power exchange of the DC microgrid with the AC distribution network, in injection P g s,t or in absorption P w s,t , is limited by the following relations, avoiding contemporaneous withdrawal and injection by means of the binary variable b g s,t : where P g is a conveniently high value. Moreover, grid exchange levels are bounded by installed converter size R F , therefore the following relations hold:

Objective and Procedure Formulation
The goal of DC microgrid optimal design under the EV exploitation conditions and space limitations is achieved by minimizing the total lifetime cost C T of the EVSI: The lifetime operation cost C O is determined by actualizing the yearly operation cost of the EVSI C Y O , determined by considering the occurrence of the s-th scenario for D s times over one year, as follows: where the terms in square brackets include total cost for electricity purchase from AC network at unit cost q w s,t , total income from power delivery to AC network at unit revenue γ g s,t , total degradation cost for EV charge at rate q j,s,t , and for EV discharge at rate γ j,s,t .
Assuming that the analyzed year replicates along all the lifetime, C O is determined by discounting C Y O by the annuity factor: The building cost C B is determined as the sum of purchasing and installation costs associated to PVs C P B , ESSs C I B , EV stations C K B , and grid connections C G B , as follows: The single contributions are determined by the following (40)-(43), respectively, exploiting unit costs for PV panels c p and ESS modules c i related to total size, whereas costs of PV converters c m , ESS converters c h , EV station technologies c r , grid converter c f , and AC grid connection c g are linked to the values of binary variables for size selection.
Microgrid optimal design problem can be synthesized in the following Mixed Integer Linear Programming formulation: where equalities g(x) = 0, inequalities h(x) ≤ 0, and state variable limits x ≤ x ≤ x include the relations reported in Section 2.2.

Test System
The investigation is based on the expected installation of the proposed system in the area of the Bari Port Authority, Italy, where a fleet of service EV is aimed to serve utility needs. In particular, five EVs, with nominal sizes of 24 kWh and exploitable SOC range of 0.2÷0.9 p.u., are supposed to replace current fuel-based service cars. Their uses are depicted in Figures 2 and 3, in terms of average daily route length and average vehicle parking time, respectively. Each EV leaves the station with a SOC of 0.8 p.u. According to these data, five charging stations are considered in the EVSI since all the EVs are parked at night. It can be noted that EV5 has two parking intervals, therefore they are dealt with separately in the procedure, just as there were six EVs.  Meteorological data are taken from a one-year measurement of a weather station, on an hourly basis [34]. In accordance with data sources, the analysis is carried out with a time step duration t  = 1 h. The collected data on vehicle usage and weather conditions for the reference year are divided in Ns = 9 scenarios, according to seasons and weather conditions, as detailed in Table 1 where the numeration and occurrence times s D are reported. Within each scenario, a proper ratio of working days and holidays is applied. Two kinds of PV panels and three battery typologies are exploitable, and their features are synthesized in Tables 2 and 3 Table 4, where efficiency values and installation costs are shown as well. The latter are estimated by proper linear cost functions according to converter size, obtained from an ad hoc market investigation.   Meteorological data are taken from a one-year measurement of a weather station, on an hourly basis [34]. In accordance with data sources, the analysis is carried out with a time step duration t  = 1 h. The collected data on vehicle usage and weather conditions for the reference year are divided in Ns = 9 scenarios, according to seasons and weather conditions, as detailed in Table 1 where the numeration and occurrence times s D are reported. Within each scenario, a proper ratio of working days and holidays is applied. Two kinds of PV panels and three battery typologies are exploitable, and their features are synthesized in Tables 2 and 3, respectively. Available room for their installation is limited by k S = 15 m 2 , tot S = 120 m 2 , tot V = 2 m 3 . Moreover, different converter sizes are considered, as reported in Table 4, where efficiency values and installation costs are shown as well. The latter are estimated by proper linear cost functions according to converter size, obtained from an ad hoc market investigation.  Meteorological data are taken from a one-year measurement of a weather station, on an hourly basis [34]. In accordance with data sources, the analysis is carried out with a time step duration ∆t = 1 h.
The collected data on vehicle usage and weather conditions for the reference year are divided in Ns = 9 scenarios, according to seasons and weather conditions, as detailed in Table 1 where the numeration and occurrence times D s are reported. Within each scenario, a proper ratio of working days and holidays is applied. Two kinds of PV panels and three battery typologies are exploitable, and their features are synthesized in Tables 2 and 3, respectively. Available room for their installation is limited by S k = 15 m 2 , S tot = 120 m 2 , V tot = 2 m 3 . Moreover, different converter sizes are considered, as reported in Table 4, where efficiency values and installation costs are shown as well. The latter are estimated by proper linear cost functions according to converter size, obtained from an ad hoc market investigation.  The AC grid connection cost c g is fixed at 125 €/kWh. The cost of electricity withdrawal from the grid q w s,t varies for hours and scenarios, in the range 0.14÷0.19 €/kWh, whereas unit revenue for electric energy delivery γ g s,t is in the range 0.025÷0.055 €/kWh [37]. EV charging cost q j,s,t is fixed at 0.05 €/kWh according to values for wearing cost [38], whereas EV discharge is not priced (γ j,s,t = 0). EVSI lifetime Ny is assumed equal to 20 years, with discount rate α equal to 0.05.

Results and Discussion
The procedure is implemented in MatLAB2015b ® framework, and solved by means of intlinprog function. In particular, a first solution of the linear relaxed problem (without integer constraints on variables) is obtained by interior-point, therefore a cut generation to restrict the linear solution is performed and finally the branch-and-bound technique is applied, generating two subproblems by proper heuristics and evaluating the most suitable solution according to best projection on improving lower or upper bounds [39]. Simulations are carried out on a workstation HP Z440 equipped with Intel Xeon 3.50 GHz processor with 16 GB RAM.
In Table 5, the values of average power π j,s are synthesized. It can be noted that the values are quite low, seldom exceeding 1 kW, therefore the choice of the minimum size for station is expected. As regards EV-station commitment, the results are illustrated in Figure 4. It can be seen that the 5 EVs are associated to stations according to the order of π j,s , since they are contemporaneously parked during the night. Moreover, since EV4 always has the maximum power demand, it is always associated with the first station. The mid-day parking interval of EV5 is associated with the first available station.
Energies 2019, 12, x FOR PEER REVIEW 11 of 21 associated with the first station. The mid-day parking interval of EV5 is associated with the first available station. A synthesis of the obtained results is reported in Table 6 for installations, where unexploited technologies among the available ones described in Section 2 are not reported for purpose of brevity. It can be seen that the goal of minimum economic effort is reached by exploiting the lower size of EV stations, polycrystalline PV modules and, where deemed necessary, LiPo batteries. No ESS installation is provided, due to the high installation cost of the converter and to the possibility of exploiting EVs for storage tasks thanks to V2G stations. Yearly energy exchange levels are reported in Figure 5, where it can be seen that, out of the total value of 19.86 MWh, PV covers 76.1% of production, leaving 16.6% to EV discharge and 7.3% to grid withdrawal. Whereas, total consumption is composed by EV charge for 58.1% grid injection for 35.9% and losses represent 6.0%. Moreover, the ratio of grid withdrawal on grid injection is 0.203, whereas the ratio of EV discharge on EV charge is 0.285, showing a preference to EV as power storage, when present.
Economic results are synthesized in Table 7. It can be noted that the building cost represents almost 93% of the objective function. Operation costs are very limited, reaching 518.5 € yearly. A synthesis of the obtained results is reported in Table 6 for installations, where unexploited technologies among the available ones described in Section 2 are not reported for purpose of brevity. It can be seen that the goal of minimum economic effort is reached by exploiting the lower size of EV stations, polycrystalline PV modules and, where deemed necessary, LiPo batteries. No ESS installation is provided, due to the high installation cost of the converter and to the possibility of exploiting EVs for storage tasks thanks to V2G stations. Yearly energy exchange levels are reported in Figure 5, where it can be seen that, out of the total value of 19.86 MWh, PV covers 76.1% of production, leaving 16.6% to EV discharge and 7.3% to grid withdrawal. Whereas, total consumption is composed by EV charge for 58.1% grid injection for 35.9% and losses represent 6.0%. Moreover, the ratio of grid withdrawal on grid injection is 0.203, whereas the ratio of EV discharge on EV charge is 0.285, showing a preference to EV as power storage, when present.
Economic results are synthesized in Table 7. It can be noted that the building cost represents almost 93% of the objective function. Operation costs are very limited, reaching 518.5 € yearly.  For sake of exemplification, trends in all the analyzed scenarios of electric power balance, of EV power exchange levels and of state of charge (SOC) of EVs are reported in Figures 6-8, respectively. It can be seen that an amount of grid power delivery is observed in all scenarios except rainy days of Scenario 3 and Scenario 6, where the limited PV production is fully exploited to charge EVs. Whereas, grid power withdrawal is registered only in five scenarios, and is not present in summer. A limited amount of EV discharge is observed in all scenarios, mostly related to EV 3 and EV 1 due to their parking time in intervals with higher PV production, allowing SOC increase beyond the final value or a decrease towards the minimum. However, EV discharge is present only to exchange power with other EVs.
As regards computational performances, the whole procedure took 40.0 s to reach the solution.  For sake of exemplification, trends in all the analyzed scenarios of electric power balance, of EV power exchange levels and of state of charge (SOC) of EVs are reported in Figures 6-8, respectively. It can be seen that an amount of grid power delivery is observed in all scenarios except rainy days of Scenario 3 and Scenario 6, where the limited PV production is fully exploited to charge EVs. Whereas, grid power withdrawal is registered only in five scenarios, and is not present in summer. A limited amount of EV discharge is observed in all scenarios, mostly related to EV 3 and EV 1 due to their parking time in intervals with higher PV production, allowing SOC increase beyond the final value or a decrease towards the minimum. However, EV discharge is present only to exchange power with other EVs.  For sake of exemplification, trends in all the analyzed scenarios of electric power balance, of EV power exchange levels and of state of charge (SOC) of EVs are reported in Figures 6-8, respectively. It can be seen that an amount of grid power delivery is observed in all scenarios except rainy days of Scenario 3 and Scenario 6, where the limited PV production is fully exploited to charge EVs. Whereas, grid power withdrawal is registered only in five scenarios, and is not present in summer. A limited amount of EV discharge is observed in all scenarios, mostly related to EV 3 and EV 1 due to their parking time in intervals with higher PV production, allowing SOC increase beyond the final value or a decrease towards the minimum. However, EV discharge is present only to exchange power with other EVs.
As regards computational performances, the whole procedure took 40.0 s to reach the solution.

Conclusions
In this paper, a mixed-integer linear optimization methodology has been carried out for technoeconomic sizing of a DC-microgrid including PV canopy, EV charging stations with V2G features, and battery-based ESS with the connection to AC distribution network. The procedure is based on the definition of operating scenarios according to weather conditions and EV uses, and involves a

Conclusions
In this paper, a mixed-integer linear optimization methodology has been carried out for technoeconomic sizing of a DC-microgrid including PV canopy, EV charging stations with V2G features, and battery-based ESS with the connection to AC distribution network. The procedure is based on the definition of operating scenarios according to weather conditions and EV uses, and involves a As regards computational performances, the whole procedure took 40.0 s to reach the solution.

Conclusions
In this paper, a mixed-integer linear optimization methodology has been carried out for techno-economic sizing of a DC-microgrid including PV canopy, EV charging stations with V2G features, and battery-based ESS with the connection to AC distribution network. The procedure is based on the definition of operating scenarios according to weather conditions and EV uses, and involves a specific model for the commitment of EV connection to charging station according to EV planned mobility needs. The proposed approach has been applied to a case study of envisaged EV service fleet for Bari Port Authority. Results have shown that the presence of ESS can be hindered by the higher cost due to dedicated converters. The effectiveness of the EV-station commitment strategy has been verified. Future work will deal with the investigation of further DC microgrid configurations, as well as the influence of reliability figures on the selection of the technical solutions. Funding: This document has been created in the context of the CONNECT project. The CONNECT project has received funding from the ECSEL Joint Undertaking under Grant Agreement n • 737434-2 and from the national programmes/funding authorities of Germany, Italy, Slovakia, Spain, and The Netherlands. The ECSEL JU has no liability in respect of this document, which is merely representing the authors' view.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.    Variable to select power withdrawal or injection from the AC grid at the t-th time step in the s-th scenario b i,s,t Variable to select either charge or discharge for the i-th ESS at the t-th time step in the s-th scenario b j,s,t Variable to select either charge or discharge for the j-th EV at the t-th time step in the s-th scenario b r,k

Nomenclature
Variable linking the k-th station to the r-th standard for charging/V2G it is equipped with Binary variable to select the installation of the f -th two-port AC/DC grid converter

Appendix A. An Example of EV and Station Commitment Procedure
Let us suppose that a group of 15 EVs should be managed by a microgrid including Nk= 7 stations, according to a scenario of utilization. In Figure A1, they are numbered according to the power index π j,s and their parking times are represented. It can be seen that, in this case, a maximum of J s = 6 EVs are contemporaneously parked at τ s = 17, namely, EVs 2, 3, 7, 9, 11, 15. These EVs are associated to the first six stations in this order. Therefore, the remaining EVs are committed, according to the numbering order. In particular, EV 1 finds station 1 free at its parking time, and is settled there. Whereas, EV 4 cannot be connected to station 1, busy due to the presence of EV 1, nor to station 2, where EV 2 is connected, but it finds station 3 free. Proceeding in this way, the final EV-station commitment is obtained, as reported in Table A1, where bold numbers report EVs parked at hour 17. It can be noted that station 7 is unexploited.  Therefore, the remaining EVs are committed, according to the numbering order. In particular, EV 1 finds station 1 free at its parking time, and is settled there. Whereas, EV 4 cannot be connected to station 1, busy due to the presence of EV 1, nor to station 2, where EV 2 is connected, but it finds station