Method for determining the estimated waiting time of an electric vehicle in charging infrastructure

Abstract

The invention relates to a method for determining the estimated waiting time (W) of an electric vehicle at charging stations. a) Mobility requests are collected from a known number of trips between [locations]. b) Data relating to the locations of existing charging stations is collected. c) The energy requirements of electric vehicles are determined via a route planner (p) based on the data collected in steps a) and b). d) Waiting times (W) at stations for said mobility requests are determined from the data in steps a), b), and c) - by estimating the arrival rate (δ) of electric vehicles at the stations - by estimating the service rate (µ) of the stations from the charging times calculated by a route planner (p) - by integrating the arrival rate (δ) and the service rate (µ) into a queuing model. Figure 1 to be published

Description

Title of the invention: Method for determining the estimated waiting time of an electric vehicle in charging infrastructure. Technical field

[0001] The invention relates to the charging of electric vehicles, and more particularly, the optimization of charging times of electric vehicles according to the configuration and availability of charging stations in a geographical area.

[0002] Recent studies show that a small electric vehicle with a range of approximately 160 km could meet the energy needs of about 90% of driving days in various US cities. The needs of most single-car households would be met without requiring any behavioral changes for more than 5% of driving days. However, when considering electric vehicles for personal use, concerns about driving range are undoubtedly unavoidable.

[0003] While route optimization and charging strategy are important features for electric vehicle users, there are other levers to help users transition to electromobility and guide them in choosing the electric vehicle best suited to their needs.

[0004] In particular, the optimization of the placement of charging infrastructure for electric vehicles on the territory, as well as simulators allowing analysis of the trade-offs between travel time, battery capacity and number of charging represent tools to remove the barriers to the adoption of electromobility while guaranteeing a "fair" carbon footprint with regard to the life cycle of the electric vehicle purchased.

[0005] The optimal location of charging infrastructure is important to facilitate the widespread adoption of electric vehicles. However, this effort also faces a dilemma: drivers are hesitant to buy electric vehicles due to a lack of adequate charging facilities, while operators are reluctant to invest in such infrastructure without guaranteed demand to ensure profitability.

[0006] In recent years, the scientific literature has made a significant effort to provide effective solutions to guide decision-makers and operators in their role as planners of charging infrastructure locations. The problem of charging station location is indeed a well-established one with various possible approaches.

[0007] Unlike traditional facility location models that pinpoint customer charging demand to specific network nodes, a new branch of research has emerged to address the charging station location problem (known as CSLP) by focusing on flow-based demand. This approach recognizes that electric vehicle drivers undertaking long journeys, often exceeding their vehicle's range, require intermediate charging. Charging demand is therefore modeled as a series of origin-destination trips. In this model, fast charging stations must be strategically placed so that the distance between two consecutive stations does not exceed the vehicles' range.This branch of the problem is also known as the supply flow localization model (known by the acronym FRLM), and it is the category in which the present invention falls.

[0008] The optimized criteria for this type of problem often fall within the interests of the owners of the electrical network or the operators of the charging stations, thus aiming to reduce the costs of installation, maintenance and operation.

[0009] In addition to choosing a relevant optimization objective, the CSLP in question is based on three main elements: the model of travel and charging behaviors, the model of the impact of travel and charging demand on waiting times at access points, the solution algorithm to determine the optimal location of the charging infrastructure.

[0010] Regarding the first point, some studies propose estimating travel and charging behaviors from geolocation (GPS) trajectory data or inferring them from the occupancy and attractiveness of geographic areas. However, these data-driven approaches are subject to errors due to inherent uncertainty in the data used (e.g., bias in the user sample, lack of information on vehicle type, etc.). Furthermore, the reliance on data that is difficult to obtain hinders the reproducibility and generalizability of the approach.

[0011] Waiting time at charging points is generally estimated using a queuing model, the most common probably being the M / M / c model, which is based on the assumption that the arrival rate of vehicles at charging points follows a Poisson process, that the service rate of charging points follows an exponential distribution, with the number of charging points available in a given charging station.

[0012] Attempts to precisely parameterize the standard M / M / c have been made, relying mainly on the availability of real load data.

[0013] Finally, with regard to approaches to solving CSLP, it is known that this class of problems cannot be solved exactly for large-scale problem instances. Several works propose feasible solution strategies for city- or region-scale scenarios based on approximation methods, genetic algorithms, heuristics, or hierarchical decomposition methods.

[0014] However, none of these works manages to address, in a unified manner, an accurate estimation of the demand for electric vehicle charging and an accurate modeling of the queue without depending on data availability. Prior art

[0015] French patent FR 3145711 discloses a method for positioning charging stations for electric vehicles within a given predetermined area, including a road network for constructing charging stations within that predetermined area (a given physical territory corresponding to the predetermined area; for example, a country, a region, a department, etc.). By positioning and constructing charging stations in relevant locations, the charging service for electric vehicles can be improved, thereby reducing travel times for electric vehicles and enabling more possible journeys for electric vehicles.

[0016] The method in question thus consists of determining the locations of electric vehicle charging station infrastructure within a territory by using, for example, statistical data on the use and attractiveness of geographical areas. This method notably uses a route planner for electric vehicles that accurately estimates the energy consumption of the electric vehicle, the location of charging needs, and the required charging level.

[0017] This is therefore an interesting solution for developing the supply of charging stations in a given area. Indeed, some current journeys are difficult, or even impossible, in electric vehicles due to the location of current charging stations, for example.

[0018] However, it remains possible to improve this process, particularly to determine more accurately the time taken by the electric vehicle user to recharge their battery during a trip. Indeed, it is not only the charging time itself that must be taken into account, but also the waiting time for the charging station to become available again, depending on the size of the queue if the station is already in use by another user upon arrival.

[0019] The aim of the invention is therefore to determine, more precisely, the waiting time for charging an electric vehicle in an infrastructure comprising one or more charging stations, and, in particular, in the simplest way possible. Summary of the invention

[0020] The invention relates firstly to a method for determining the waiting time of an electric vehicle in charging infrastructures, each comprising one or more charging stations constituting a charging station system, in a given geographical area comprising a road network with road segments connected by intersections, said method comprising the following steps, at least one, in particular all, of which is implemented by electronic / computer means:

[0021] a) Mobility requests are collected from a known number of journeys between

[0022] an origin and a destination in the road network of said geographical area over a given period of time, in particular a daily period,

[0023] b) Data relating to the locations of existing charging stations in said geographical area are collected

[0024] c) the energy requirements of electric vehicles for said mobility demands are determined via an electric vehicle route planner based on the data collected in steps a) and b)

[0025] d) for said mobility requests, queue durations at charging stations are determined by modeling based on the mobility requests collected in step a), data relating to the locations of the charging stations collected in step b) and the energy requirements determined in step c)

[0026] - by estimating the arrival rate ô of electric vehicles at charging stations at based on said mobility requests

[0027] - by estimating the service rate p of the charging stations from the times of charging calculated by a route planner for electric vehicles, for said mobility requests

[0028] - by integrating the estimated arrival rate ô and the estimated service rate p as parameters in a queue duration model to deduce the estimated queue durations at charging stations.

[0029] Preferably, the queue duration model is the so-called M / M / c model. The M / M / c queuing model is a type of stochastic process that describes the behavior of a queuing system with c servers, where clients arrive randomly according to a Poisson process and are served with an exponential distribution of service time. The M / M / c model belongs to the family of Markovian queuing models, which means that the state of the system depends solely on the number of customers in the system at any given time, and not on their arrival or service history.

[0030] Preferably, mobility requests are collected according to step a) from a data platform, in particular open data, bringing together data on the flow of electric vehicles between an origin and a destination in a road network of the geographical area. This could, for example, be open data from an official government body, which is more easily accessible than data collected by private operators. For France, this data can be obtained via the platform https: / / www.data.gouv.fr.

[0031] This approach mitigates biases in real data (for example, depending on data collection methods, particularly from one region to another).

[0032] It remains possible to collect these mobility requests from real journeys that have been measured.

[0033] Preferably, data relating to the locations of existing charging stations (S) in said geographical area are collected according to step b) from a data platform, including open data, identifying and locating existing stations in said area. This allows the use of a collaborative platform, known for its comprehensive and accurate dataset. This could be the OpenChargeMap REST API.

[0034] Optionally, the data collected in steps a) and / or b) can be supplemented, or even replaced, by real data, possibly collected in real time.

[0035] Preferably, in step d), the arrival rate (π) of electric vehicles at charging stations and the service rate p of charging stations are estimated.

[0036] - by a substep d1) of initialization and calculation of the arrival rates ô and rates of service p, assuming zero waiting time at charging stations

[0037] - then a substep d2) of calculating the waiting times at the stations recharge, (here, the queue times are no longer zero, or no longer all zero)

[0038] - then a substep d3) of determining again the arrival rate ô and the rate service (p) from the queue times calculated in step d2),

[0039] - then a substep d4) of actual calculation of waiting times from the rate arrival time and service rate p are re-determined in sub-step c3).

[0040] Preferably, to implement the method according to the invention, an average battery capacity for the fleet of motor vehicles in the geographical area considered, for example on the scale of a country, can be considered.

[0041] Preferably, in the initialization substep dl), the initialization of the charging stations best suited to the needs of long-distance travel is optimized with waiting times, considering all possible routes for a given mobility demand called a journey, each journey corresponding to an origin-destination pair having been assigned to a specific movement flow, said sub-step dl) preferably having three phases:

[0042] - a phase dl.l, where the optimal route for electric vehicles is calculated (VE) using the initial set of a plurality of charging stations, the calculation producing an initial set of optimal charging stations, said initial set being accompanied by a set of charging times, with, for the stations in the solution set, the assignment of the associated charging times, and for all other stations, the assignment of a zero value, - a phase dl.2, where a set of possible combinations of the initial optimal stations is calculated, then, for each combination in the set, the optimal route and the optimal charging stations are recalculated, updating the system of available charging stations by removing the Eth combination from the set - a phase dl.3, where the optimal charging station solutions obtained in phase cl.2 are aggregated, to obtain the arrival rate ô and the service rate p.

[0043] Preferably, in substep d11), an hourly flow of electric vehicles is calculated, which differs according to a division of the time period considered, for example according to a division into daytime and nighttime hours for a daily period.

[0044] Preferably, in substep dl), the penetration rate parameter (k) of electric vehicles is used.

[0045] Penetration rate is understood to mean the percentage of electric vehicles in the vehicle fleet.

[0046] Preferably, the queuing calculation substep d2) uses the service rates p and arrival rates ô obtained in substep cl) as key parameters of the queuing model to determine the waiting times at each charging station.

[0047] The invention also relates to a method for using the estimated waiting times of an electric vehicle in charging infrastructures, each comprising one or more charging stations constituting a charging station system, in a given geographical area, said estimated waiting times (W) being obtained with the method described above, such that

[0048] el) said queue times are exploited by creating a tool for visualizing the estimated queue times at charging stations in the geographical area, in particular on the dashboard of the electric vehicle, in a mobile phone application or as a resource available on the internet.

[0049] It is thus possible to make available information on estimated waiting times for vehicle charging, in particular according to different traffic conditions (during peak travel periods for example).

[0050] The invention also relates to a method for using the estimated waiting times of an electric vehicle in charging infrastructures, each comprising one or more charging stations constituting a charging station system, in a given geographical area, said estimated waiting times being obtained with the method described above, such as

[0051] e2) we exploit said queue durations - by planning a route defined by a succession of road segments for one of said journeys in said geographical area, the planning carried out by a route planner, taking into account said queue durations to estimate the journey time including the charging time according to the possible route(s).

[0052] This allows us to improve route proposals, resulting in shorter travel times or at least more precise estimates of the different possible routes.

[0053] The invention also relates to a method for using the estimated waiting times of an electric vehicle in charging infrastructures, each comprising one or more charging stations constituting a charging station system, in a given geographical area, said estimated waiting times being obtained with the method described above, such as

[0054] e3) we exploit said queue durations by integrating the queue durations estimated waiting times in electric vehicle control strategies.

[0055] The estimation of queueing times can thus be taken into account by the vehicle's on-board computer.

[0056] The invention also relates to a method for using the estimated waiting times of an electric vehicle in charging infrastructures, each comprising one or more charging stations constituting a charging station system, in a given geographical area, said estimated waiting times being obtained with the method described above, such as

[0057] e4) these queue durations are exploited - by determining the location of new charging infrastructure - and / or by adjusting the number of charging stations in new charging infrastructures, in existing charging infrastructures, or in existing hydrocarbon energy distribution infrastructures,

[0058] in particular with a view to constructing new charging stations or relocating or removing existing charging stations.

[0059] This allows for better selection of new locations for charging infrastructure, better adjustment of the number of charging stations in the infrastructure, and implementation of the corresponding constructions / modifications resulting from the results of the queue time estimation method according to the invention.

[0060] The invention also relates to an electronic / computer system for determining the estimated waiting time of an electric vehicle in charging infrastructure, each comprising one or more charging stations constituting a charging station system, in a given geographical area comprising a road network with road segments connected by intersections, said system comprising

[0061] a) means for collecting mobility requests from a known number of journeys between an origin and a destination in the road network of said geographical area over a given period of time, in particular a daily period, and the corresponding data on the energy requirements of electric vehicles for these requests

[0062] b) means for collecting data relating to the locations of existing charging stations in said geographical area

[0063] c) means of determining said mobility requests via a route planner based on the data collected in steps a) and b) of the energy requirements of electric vehicles

[0064] d) means for determining said mobility demands by modeling queue durations at charging stations from data collected with means a) and b) and determined by means c)

[0065] - means for estimating the arrival rate (θ) of electric vehicles at stations recharging from said mobility requests

[0066] - means for estimating the service rate p of charging stations from the charging times calculated by an electric vehicle route planner for said mobility requests

[0067] - means for integrating the estimated arrival rate θ and the service rate (p) estimated as parameters in a queuing model to deduce the estimated queue times at charging stations.

[0068] The invention also relates to a computer program product downloadable from a communication network and / or stored on a computer-readable medium and / or executable by a processor or server, comprising program code instructions for implementing the method described above described, when said program is run on a computer, mobile phone, computer processing circuit, or computing device.

[0069] The invention as thus defined is therefore a method for determining the The invention addresses the likely queues that electric vehicles are likely to encounter at charging infrastructure: it improves route planning for electric vehicles by taking into account the additional waiting time for a charging station to become available before charging can begin. Consequently, the use of the invention can lead to different route planning strategies aimed, for example, at avoiding stations with the longest waiting times.

[0070] The method proposed by the invention for determining the queue at charging stations preferably does not use actual usage data from the charging points (although, of course, the invention can also use actual data if it is available / freely accessible). Surprisingly, this is rather an advantage, because the queue can be calculated according to the invention based on physical models that allow for the precise determination, in space and time, of the energy demand of electric vehicles moving within a given area. These physical models thus make it possible to parameterize the probabilistic queuing models, known in the literature, in a more realistic way and without relying on often private and inaccessible data.

[0071] This is therefore a more relevant solution than existing solutions, for example those proposed by route planners provided by car manufacturers, which are limited to simply advising the route and the charging sequence without considering the impact of queues on travel time.

[0072] Furthermore, the invention can make it possible to determine, on the one hand, the evolution of queues according to the growth of the number of electric vehicles in the territory concerned, and, on the other hand, to guide managers and installers of charging infrastructure in the choices of development and investment in order to, ultimately, build new infrastructure or add charging stations to existing infrastructure in an optimal way. List of figures

[0073] Other features and advantages of the process according to the invention will become apparent from the following description of non-limiting examples of embodiments, with reference to the figures attached and described below. [Fig 1]

[0074] Fig. 1 represents a block diagram of the method for determining waiting times at charging stations according to the invention. [Fig 2]

[0075] [Fig.2] details a step of the block diagram of the process according to the invention according to [Fig.1]. [Fig 3]

[0076] Fig. 3 represents the waiting times calculated with the method according to the invention at each of the identified charging stations, for the territory of France. [Fig 4]

[0077] Figure 4 shows a map of recommended locations for installing new charging stations in France, based on the results obtained with the queue time determination method according to the invention. Description of embodiments

[0078] For the purposes of the invention, "charging stations" (also referred to herein as "charging terminals") refer to charging stations for electric vehicles, more specifically for recharging the batteries of electric vehicles.

[0079] Several charging stations can be grouped together in a charging infrastructure, and the charging stations or terminals are each equipped with one or more charging servers, also called charging ports or charging points.

[0080] An electric vehicle is understood to be a vehicle comprising - or solely an electric motor powered by a battery. In other words, this vehicle does not have an internal combustion engine, such as a gasoline, diesel, or hydrogen engine.

[0081] - either an electric motor and an internal combustion engine, of the vehicle type plug-in hybrid.

[0082] By locations, we mean for example a point or a position, such as a geolocation coordinate (for example GPS from the English "Global Positioning System" meaning global navigation system, or "Galileo").

[0083] The terms "queue duration" and "waiting time" at charging stations have the same meaning.

[0084] The road network comprises road segments (also called road sections) connected by intersections (or crossroads). The intersections can thus correspond to points in the road network, and the road segments to arcs connecting the points in the road network. According to one embodiment of the invention, the road segments take into account the topography of the road network, in particular the slope of the road segment, the infrastructure and signage by means of a geographic information system, traffic data by means of a geolocation system or a geographic information system, and preferably meteorological data by means of an application programming interface system.

[0085] The route planner is used here assuming that each intersection includes a potential charging station. The route planner may include a GPS (Global Positioning System) or a mobile phone to determine the vehicle's location, and it may also include software capable of determining a possible route from an origin to a destination based on various parameters (travel time, energy consumption, vehicle type, road types, speed, etc.). In other words, it is assumed that a charging station can potentially be located at each intersection of the road network. Consequently, a route can be planned with the possibility of charging the battery at at least one intersection.

[0086] The route planner makes it possible to determine the travel time (or journey time) to travel the possible route (via the road segments of this route) by an electric vehicle and / or the energy consumption by the electric vehicle of each possible route (on the road segments of this route).

[0087] The route planner also makes it possible, for each possible route, to identify, among the potential charging stations (at each intersection of the road network), which ones are used by the electric vehicle to recharge its battery. It also makes it possible to determine the battery's target charge level. In other words, the route planner takes charging time into account based on the charge level: the battery is not systematically charged to 100% at every charging station. Indeed, battery charging time is not linear, and the planner seeks the best compromise between charge level and charging time.

[0088] Advantageously, the road sections of the road network in the geographical area under consideration can take into account the topography of the road network, in particular the slope of the road section, the infrastructure and the signage by means of a geographic information system (GIS), traffic data by means of a geolocation system, such as a GPS, or a geographic information system (GIS) and preferably meteorological data by means of an application programming interface system (an API is the English acronym for "Application Programming Interface", or application programming interface in French).

[0089] Taking the slope into account directly impacts energy consumption.

[0090] Taking road infrastructure and signage into account allows for consideration of traffic lights, "yield" or "stop" signs where a stop may be required, speed limits, or speed bumps, for example. All these elements can impact the average speed and speed profile on a section of road.

[0091] A speed profile refers to the variation in instantaneous speeds along a section of road. The speed profile can be represented by a curve of instantaneous speed as a function of distance along the road section. The speed profile thus takes into account the accelerations and decelerations that can occur along the road section, which is not possible with average speed alone. This speed profile can be established, in particular, from measurements of vehicles, electric or otherwise, traveling on the road network. For example, this speed profile can be established from data from the Geco air® application (IFP Energies nouvelles, France), which records the speeds of road users along road sections. Geco air® is an application designed to reduce travel-related pollution and, to this end, it collects position and instantaneous speed data.

[0092] Traffic data allows for the consideration of traffic density and its impact on average speed. Traffic data can, in particular, correspond to the average speed and / or travel time of vehicles on a section of the road network in time slots, for example, every ten minutes. For this purpose, one can, for example, measure the average speed throughout the day, preferably over several days. In this way, one can retrieve a history of traffic and its daily variation recorded throughout the day.

[0093] By applying traffic data, it is possible to evaluate more precisely the travel time and / or energy consumption according to the day and time considered and / or according to real-time traffic data.

[0094] Weather data, particularly temperature data, is also useful for determining energy consumption when the vehicle's heating or air conditioning is activated. This can be done using a REST weather API, such as the "Météo France™" API, to retrieve real-time weather conditions at the starting point and update them regularly along the route, for example, at fixed time (e.g., hourly) or space (e.g., every 60 km) intervals. Interpolation methods can then be used to obtain weather information for each road segment. The ambient temperature can be obtained for each road segment by interpolating the temperature forecasts obtained from the weather API.

[0095] Each road segment can also be classified according to its topology, notably with an associated "functional" class, ranging, for example, from 1 for main highways to 5 for secondary urban streets. Furthermore, each road segment can be defined by a unique identifier and by its geometry with three-dimensional coordinates (at least the coordinates of both ends of the road segment). The coordinates can preferably be expressed in latitude, longitude, and altitude above sea level. Finally, the type of intersection and / or signage at the downstream end of each section of road can also be recovered: in particular, one can take into account the types of road infrastructure and signage such as traffic lights, stop signs, yield signs, roundabouts and toll plazas.

[0096] According to an advantageous implementation of the invention, the route planner may include a travel time model, that is to say a model for estimating the time required to travel a portion of road.

[0097] In order to correctly estimate the charging time Tc, a simple model inspired by the CC-CV charging method (“constant-current constant-voltage” for constant current - constant voltage), with a pre-charge phase when the battery capacity is low, such as that described in the document “FAV Pinto, LHMK Costa, and MD de Amorim, “Modeling Spare Capacity Reuse in EV Charging Stations based on the Li-ion Battery Profile,” in International Conference on Connected Vehicles and Expo (ICCVE), 2014, pp. 92-98”, can be used.

[0098] Advantageously, the route planner can also include a driving model. In order to accurately estimate the energy consumption required for travel along an arc of the routing graph, the first step is to predict the driver's behavior on the road segment, in order to forecast the vehicle's traction power demand. For example, a model such as the "Intelligent Driver Model" (IDM) described in the document "M. Treiber, A. Hennecke, and D. Helbing, 'Congested Traffic States in Empirical Observations and Microscopie Simulations,' Physical Review E, vol. 62, pp. 1805-1824, 2000" can be used to generate synthetic expected speed profiles on each arc of the routing graph as a function of dynamic traffic data.This model is a car-following model that describes the dynamics of the position and speed of vehicles interacting with preceding vehicles.

[0099] The present invention proposes an integrated framework for solving the problem of charging station location (CSLP for brevity) on a national scale, France being an example in this case, comprising:

[0100] - an optimal trip planner for electric vehicles, for estimation specifics of the load request,

[0101] - and a queuing model based on the load demand produced by the travel planner.

[0102] In particular, for the configuration of the queuing model, in this case the model called M / M / c, the invention proposes a new algorithm for estimating:

[0103] - the arrival rate of vehicles at each charging station from demand travel

[0104] - and the service rate of the charging stations based on the calculated charging times by the optimal trip planner.

[0105] This allows the strategy of the invention to be less dependent on the availability of proprietary data (e.g., charging station usage statistics) and to be more generalizable. The CSLP is then formulated as a two-level optimization aimed at minimizing the total travel time for users subject to spatial constraints related to land use (e.g., the installation of charging stations only at existing service stations).

[0106] For practical reasons, a method is then proposed to decouple the two levels of optimization and to proceed with the planning of the location of the charging stations, and with the evaluation of the overall duration of the journeys undergone by users in a sequential manner.

[0107] The method proposed by the invention is finally used to evaluate the performance and resilience of the charging infrastructure in different scenarios (i.e. according to, in particular, the increase in the rate of vehicle penetration in the territory concerned and the unavailability of charging stations).

[0108] A charging station is considered unavailable in particular in the following cases: - if it is broken

[0109] - if the waiting time at the station exceeds a given waiting time threshold, for example more than 20 minutes

[0110] The method according to the invention is detailed below with the aid of the figures: The geographical area considered here by way of illustration is metropolitan France.

[0111] The invention proposes a structured method for managing queues at electric vehicle charging stations, taking into account not only mobility demand but also the energy requirements of journeys. The approach adopted aims to optimize the use of charging infrastructure, thereby minimizing waiting times for users and improving the overall energy efficiency of these stations. Figure 1 illustrates this process, broken down into several key blocks, which are explained in detail below:

[0112] Step a: An input matrix of journeys between an origin (O) and a destination (D) is constructed. To better reflect real-world scenarios, given that road use and traffic volumes can vary considerably from one journey to another, travel flows are integrated. This approach improves the accuracy of the traffic analysis, leading to improvements in the efficiency of charging infrastructure. The weighting process uses the most recent national origin-destination vehicle flow matrix from the official French government open data platform (https: / / www.data.gouv.fr / ), estimating the journey average daily traffic of vehicles between departments. This approach mitigates biases in real data (e.g., data collection methods or regional differences), providing a more accurate and realistic representation of travel flows.

[0113] Alternatively, this data matrix can be constructed by making other assumptions, by establishing prospective scenarios. Thus, it is possible to consider the national matrix multiplied n times, for example 2 or 3 times (by multiplying each element of the matrix n times by the same value, each element of the matrix representing the number of journeys over a given period, in particular daily journeys from an origin O to a destination D), in order to simulate the impacts of a "crossover" scenario on queues and / or the optimal placement of stations.

[0114] Possible routes may correspond, for example, to the most frequently used routes (generally speaking, taking into account all vehicles and not just electric vehicles), the most probable routes, or those connecting the largest cities. The "origin" and "destination" correspond to points on the road network. Each possible route thus corresponds to an Origin-Destination pair, and each of these possible routes is directional. For example, the Origin-Destination route, which concerns the route starting from Origin and arriving at Destination, is different from the Destination-Origin route, which starts from Destination and arrives at Origin.

[0115] Alternatively, these routes can be obtained by measuring actual Origin-Destination routes.

[0116] Step b: The location of infrastructure including one or more charging stations (known by the acronym EV Charging Infrastructure for Electric Vehicles) is identified / acquired. For this analysis, a REST application programming interface (API) from OpenChargeMap, a non-commercial and collaborative platform recognized for its comprehensive and accurate dataset, can be used. This API enabled the precise identification of the locations of existing charging stations.

[0117] Step c:

[0118] The route planner (“eco-charging” in English), also referred to in this text as route planner p, focuses on determining and minimizing the total travel time, T j, for each trip j identified in step a). This time includes components such as travel time, charging time and waiting time, which are significantly influenced by EV charging infrastructure.

[0119] This optimization problem can be formulated in the following general and compact way: 'Aavïks O'M »®S.'ïÆ 7s - -

[0120] under the constraints Wïï^s Qnwsx

[0121] where

[0122] rj indicates the travel route decision for the / -th journey

[0123] Qj refers to the amount of recharging required to complete the Jth journey,

[0124] Qmax and Qmin represent the physical limits of the battery capacity.

[0125] The total travel time for the Jth trip, denoted Tj, is a sum of travel, charging, and waiting times.

[0126] Ttravel.j(rj) calculates the travel time based on the chosen route rJ, T / \ * charge,j\Q denotes the time spent recharging, which depends on the amount of charge ÿj, and T / ç \ estimates the waiting time at charging stations, influenced by * waitjy^ ?j-> Q the chosen route rJ, the charging request Q j, and the overall system configuration S (the set of stations considered).

[0127] To solve this problem, we adopt a methodology which starts from that described in the aforementioned French patent FR 3145711, where the optimization problem, initially constrained, is reformulated in a more manageable way by integrating the constraints directly into the structure of the graph.

[0128] This integration is achieved by the lexicographic product of two distinct graphs:

[0129] - a routing graph, describing the possible travel paths, - and a completely disconnected graph, representing the allowed battery charge states.

[0130] This two-dimensional graph architecture allows for an explicit incorporation of constraints into the optimization process.

[0131] This transformed problem is then addressed using the Bellman-Ford algorithm to efficiently calculate the shortest paths. This method facilitates the identification of optimal routes and battery management strategies, thus ensuring the efficiency and feasibility of the solutions.

[0132] Determination of queue parameters: Since actual data on arrival and service rates at each station are difficult to obtain due to their private nature, it is chosen not to depend on this data, which can of course be integrated optionally if available.

[0133] We therefore derive these parameters (arrival and service rates at each station) using an optimal routing strategy which is more generalizable and does not rely on inaccessible data.

[0134] This step of determining the parameters of the queues, necessary for their integration into the studied model M / M / c, is divided into three sub-steps, which are schematically illustrated in [Fig.2]:

[0135] Substep 1.1: Initialization.

[0136] To optimize the initialization of the charging stations best suited to the needs of long-distance travel with waiting times, it is useful to analyze the different identified routes, numbered from j = 1... R (R represents the set of potential routes).

[0137] By examining all possible routes, a specific waiting time is assigned to each station, thus ensuring that each station maintains an appropriate customer (electric vehicle) arrival rate and an efficient service rate per server (charging port).

[0138] For this step, we adopt a queue-free route planning or "eco-charging" approach. In other words, in the objective function of the PO problem, the term representing the waiting time Twaitj is considered to be zero (denoted by W = 0 in [Fig.2]).

[0139] To do this, the OD matrix (from step a) was processed to convert interdepartmental vehicle flows into more detailed intercity flows for the selected cities.

[0140] Each origin-destination (OD) pair has been assigned to a specific displacement flow, designated by V j.

[0141] To take into account the significant reduction in traffic volume during nighttime hours, it is assumed that the flow of vehicles is concentrated during active hours (from 6 a.m. to 9 p.m.) and the hourly flow of vehicles has been calculated as follows:

[0142] In addition, to integrate the increasing prevalence of electric vehicles into the traffic analysis, the penetration rate k of electric vehicles was introduced.

[0143] The hourly volume of electric vehicles was therefore calculated using the following formula:

[0144] To explain the methodology according to the invention precisely, the three key phases of our algorithm are presented in detail.

[0145] This methodology processes each origin-destination pair OD and finally assigns the parameters p and X to each charging station.

[0146] Phase 1: Calculation of recharge times for the initial system So

[0147] Initially, during this first phase, the planner algorithm p calculates the optimal route of electric vehicles (EVs) using the initial system of charging stations, denoted by So and having a size of Ns-

[0148] This calculation produces an initial set of optimal charging locations, labeled , included in the initial system, accompanied by a set of charging times, designated Tq, also of size Ns. For stations in the solution set 5*, the associated charging times are assigned, and for all others, a value of zero is assigned.

[0149] Phase 2: Recharge time for alternative systems^

[0150] The second phase consists of calculating all possible combinations of the optimal charging locations contained in 5*. We denote the set of these combinations generated by C and we specify its size as Nc.

[0151] Subsequently, for each element i in the set C, the optimal route and optimal charging locations are recalculated.

[0152] This is achieved by updating the system of available charging stations, now designated by S; , by removing the *-th combination from C, as follows S:. — S» Phase 3#: Aggregation of solutions

[0153] This update forces the route planner to choose different charging locations, and generates a new set of optimal charging stations, labeled along with their respective charging times, indicated by T(.

[0154] Regarding the arrival rate for each combination, it can be calculated using the following formula:

[0155] After iterating over the Nc combinations, we obtain the set of optimal stations, designated which includes the union of all the solutions identified for the current origin-destination pair, expressed as follows:

[0156] Furthermore, since each station can be selected by the optimizer multiple times during the different combinations, we derive a set that records the selection frequency of each station during our process, denoted by Fj. For each origin-destination pair, the total recharge time for all stations is given by: TT .■ c

[0157] Then, for each station k = 1... Ns, the resulting average recharge time, adjusted according to the number of times a station was selected, is calculated as follows:

[0158] And the arrival rate, DJ, is given by:

[0159] Once the calculations for all origin-destination pairs (3660 in this example, but which could be any variable R indicating the number of pairs) are completed, the set of solution stations, denoted by S*, is calculated as the union of the

[0160] We can then proceed to calculate the final metrics for each station. The charging time is determined by taking the weighted average of the charging times for all OD pairs, where the weight corresponds to the hourly volume of electric vehicles. More precisely, the final average charging time T at each station k is given by the formula

[0161] where V is the total volume of electric vehicles (EVs) and is calculated as follows:

[0162] Furthermore, the service rate is defined as the inverse of the total service time T, calculated at each station f as follows: I --X...... if s < ' f T* SJ ■■ ? ! U oihèrwisÈ.

[0163] Furthermore, the arrival rate A. is the aggregation of the arrival rates of all R pairs OD, expressed as follows: mc) ». y'

[0164] Substep 1.2: Queue calculation.

[0165] The service and arrival rates obtained are used as key parameters in the queuing model to determine the waiting times at each station k.

[0166] This allows for the generation of a waiting time vector for each station. To do this, the M / M / c queuing model is applied, which is particularly well-suited to systems with multiple service facilities and random arrivals. In this model, each port or charging point at the station acts as a server, and electric vehicles waiting to charge are considered clients.

[0167] The arrival of electric vehicles is modeled by a Poisson process characterized by a rate X calculated during phase 3, indicating the average number of vehicles arriving per unit of time. This model was chosen because of the memoryless property of the Poisson process, which is ideal for representing the random and independent nature of the arrivals.

[0168] As for the service process, in this case the charging of electric vehicles, it follows an exponential distribution with a service rate q calculated during phase 3, which represents the average number of electric vehicles that can be fully charged per server and per unit of time.

[0169] The number of servers, denoted C, corresponds to the available reload ports. This number is important because it directly impacts the station's ability to efficiently handle incoming traffic. From this model, several key performance indicators are derived, calculated using formulas established in queuing theory. Traffic intensity is defined as p = (C / i) - The probability that the system is empty, Pq, is calculated using the formula

[0170] The waiting probability, Pw, is determined by

[0171] The average waiting time in the queue, Wq, is calculated as follows:

[0172] Substep 1.3: Determination of queue parameters.

[0173] After calculating this vector, designated by jy* in [Fig.2], the balancing phase of service rates and arrival times at stations begins. This phase includes restarting route planning with the planner (“eco-charging”), integrating the waiting time vector into the objective function P.

[0174] It is also possible to restart the route planning several times at this stage, to carry out several iterations, but it has been found that sufficiently convincing results were obtained with a single iteration.

[0175] Next, the final values ​​of the parameters of the M / M / c model are recalculated, following the three phases presented previously.

[0176] Step 2: Calculation of waiting time: in this step, we restart substep 1.2 using the M / M / c queue model already described with the new parameters obtained at the end of step 1.3. Applications - Examples

[0177] By adopting this method, the user can obtain an estimate of the likely waiting time at electric vehicle charging stations. This information is useful for the optimal route planner for electric vehicles, which takes queues into account, and it can be integrated into vehicle dashboards or into smartphone applications and websites.

[0178] Furthermore, this estimate can be used to develop an interactive dashboard that visualizes charging stations nationwide. This dashboard can then provide electric vehicle users with the estimated waiting time for charging based on various traffic conditions, such as peak travel periods.

[0179] A third application of this estimation is the optimal design and subsequent construction of charging infrastructure, intended for charging station installers. This approach makes it possible to efficiently size the installations according to anticipated needs.

[0180] The following is an example for several possible applications of the process according to the invention.

[0181] Using data from studies conducted by the National Institute of Statistics and Economic Studies (INSEE), 61 cities were selected based on specific criteria relating to population and attractiveness. From these cities, by calculating the partial permutations of pairs of cities, we derived R = 3660 origin-destination (or route) pairs for "eco-charging". This allows us to remain representative of typical travel behavior within France.

[0182] Example 1: Estimating waiting times at charging stations - Display screen on dashboard

[0183] For this example, we used the actual locations of fast charging stations (power greater than 50 kW), observed in January 2024, using the OpenChargeMap REST API, which lists 1569 stations. We applied the method explained previously, which allowed us to estimate the arrival rate, the service rate, and the waiting time for each station. We assumed an average battery capacity for the French vehicle fleet of 55 kWh in 2024.

[0184] A map of France showing the waiting times at each station obtained by the method according to the invention is shown in [Fig.3], the size of the points ranging from 0 to 60 minutes.

[0185] An interactive dashboard for visualizing charging stations nationwide has been created specifically for electric vehicle users. It displays estimated waiting times and provides useful information based on penetration rates to help plan trips effectively and optimize the use of charging stations, as shown in [Fig. 4].

[0186] Example 2: Route planning on an OD journey and over France

[0187] Route planning constitutes a second application of the present invention.

[0188] By integrating queue management, it allows the user to plan their journey optimally, thus guaranteeing a stress-free trip.

[0189] This point can be illustrated with the Paris-Marseille route, analyzed under different rates of electric vehicle penetration.

[0190] The optimal calculation algorithm according to the invention is applied by considering that a station becomes unavailable as soon as the waiting time there exceeds 20 minutes. This method efficiently targets the fastest routes, organizes the battery charging phases, and evaluates the total travel time, including charging, waiting, and travel times. The results of this analysis are presented in Table 1.

[0191] Table 1 below highlights the significant impact of electric vehicle penetration rates on travel time. A high rate can significantly increase waiting times, making some stations unavailable due to long queues. In cases such as a 10% penetration rate, illustrated in Table 1, this can even make the Paris-Marseille journey impossible.

[0192] [Tables 1] Penetration rate 2 5 10 Number of recharges 3 4 Fail Travel time [hours] 9.42 9.90 Fail

[0193] This study was also carried out on a national scale: the optimal calculator according to the invention was deployed on the 3660 origin-destination pairs analyzed, establishing the rule that a station is considered unavailable if the waiting time exceeds 20 minutes.

[0194] Table 2 illustrates the success rate of the journeys, thus revealing the feasibility of the journeys according to the penetration rate of electric vehicles and the average journey time.

[0195] The analysis clearly highlights the impact of penetration rate and queues on the feasibility and duration of journeys.

[0196] [Tables2] Penetration rate 2 5 10 Success rate [%] 97 95 59 Average travel time [hours] 2.5 2.6 3.4

[0197] The success rate is to be understood in contrast to the failures in the previous table: it is the % of journeys that could be completed completely with the existing charging stations available.

[0198] These results highlight the need to improve charging infrastructure in a strategic and targeted manner to better meet the growing demands of electric vehicle users. This optimization, based on waiting time data, represents the third successful implementation of the method according to the invention, demonstrating its effectiveness and relevance in the development of a truly adaptive and resilient charging network.

[0199] Example 3: Optimal placement of charging stations

[0200] In this example, we adopted the method proposed in the aforementioned patent, which is based on solving a two-level optimization problem.

[0201] This method has been enhanced by integrating waiting time into the calculation of the total travel time for the lower-level optimization problem, which corresponds to problem PO. Furthermore, a spatial constraint has been introduced into the higher-level optimization problem, thus modifying its initial formulation, which now appears as follows:

[0202] where:

[0203] R: The set of potential routes (in our example, R includes 3660 routes)

[0204] N ; Number of candidate sites for the installation of new charging stations.

[0205] g — The set of all candidate sites for placing stations charging stations, where each represents a specific geographical site

[0206] xk: Binary decision variable. For each location V in -5, xk is defined such that xk = 1 if a charging station is placed at and xk = 0 otherwise.

[0207] x: Vector that encapsulates decisions across all sites candidates

[0208] T^x): represents the travel time for each vehicle during journey j, depending on the configuration of the charging stations determined by x. This includes travel, charging and waiting times, which are determined as a solution to the lower-level problem taking into account the selected charging stops 5'.

[0209] Constraint (1b): Limits the total number of charging stations to K.

[0210] The constraint (the): Ensures that each decision variable xk is binary.

[0211] The constraint (Id): Models the system's dependencies and interactions among the selected charging stations, ensuring that their configuration does not exceed the specified limits B, which could represent spatial, electrical, or resource limitations. In our case, this constraint ensures that our proposed charging stations are strategically integrated with existing service stations.

[0212] Solving the two-level optimization problem (P0-P1) can be lengthy due to the interdependence between the two levels. The solution to the route planning problem ("eco-charging") (PO), which includes travel time TtmveiArj, charging time, and waiting time j, serves as input for the ■ "■ * load^Qjj * waîl,^p^ Q jj higher-level problem.

[0213] Above all, this time depends on the waiting time, which is computationally expensive given the large number of possible combinations for calculating the parameters of the M / M / c model.

[0214] For simplicity, this extended calculation is performed only once for a charging station system S and then serves as input for the two-level optimization problem. Consequently, the waiting time / c 1 no longer depends on either rJ or Qj. * watt, ftp ■> ?p ÿj]

[0215] In this context, the objective function of the PO problem is simplified as follows •G - + t

[0216] The proposed heuristic strategy is structured in two phases: - The initial phase consists of identifying a set of optimal candidate stations and potential location areas,

[0217] - The next phase then focuses on determining the locations optimal for station placement, which may involve selecting a subset from the previously identified candidates.

[0218] 1) Selection of potential locations for charging stations:

[0219] In the first phase, identifying the most suitable locations for fast charging stations for long journeys requires a comprehensive analysis of the roads linking different cities.

[0220] By evaluating all potential routes, the distribution of charging infrastructure can be optimized to effectively meet the needs of electric vehicle users traveling between cities. To do this, we adopted the same approach as that described in the aforementioned patent to identify all candidate charging stations.

[0221] The methodology begins by solving the lower-level optimization for the 61 selected French cities, resulting in 3660 origin-destination pairs. In this scenario, each node on the graph is treated as a virtual charging station without a queue. This approach yielded a substantial set of 1767 optimal candidate stations. This configuration serves as a basis for evaluating the infrastructure needed to optimally support electric vehicles.

[0222] Subsequently, using the OD matrix data, a vehicle flow is assigned to each candidate station. This step ensures that the distribution and capacity of the stations are aligned with actual vehicle movement patterns, thereby improving the efficiency of the proposed charging network.

[0223] The method according to the invention is applied to improve the existing infrastructure of charging stations. The aim is to determine which areas are already optimally served and which require improvements.

[0224] To effectively take into account existing stations and identify optimal areas for infrastructure improvement, a 10 km x 10 km grid overlay was implemented across the region encompassing France. Within For each cell in the grid, the density of optimal candidate stations and existing stations was calculated, taking into account the traffic volume. By overlaying these two datasets as heat maps, it is possible to locate intersections that highlight areas of high demand lacking sufficient infrastructure. This approach systematically evaluates and identifies potential areas for development and upgrades within the charging station network.

[0225] Figure 4 shows an example of the intersection between the heat map of candidate stations and the existing infrastructure, which comprised 1,424 stations in April 2023. This intersection creates a map of priority locations for future fast charging stations. For this analysis, we used the OpenChargeMap REST API, as mentioned earlier in the text.

[0226] The black squares on the map ([Fig.4]) represent the intersections of the two heat maps and are already optimally served, each having at least one existing station. The remaining areas are identified as candidate areas for infrastructure improvement.

[0227] In the aforementioned patent, the centers of non-intersecting squares serve as initial candidates for charging station locations, and a grouping method was used to refine and optimize the selection, thus ensuring strategic placement of these installations. In this work, additional spatial constraints as defined in equation (Id) are incorporated, and a new approach is proposed to improve the charging station network. 1. Strategic deployment of fast charging stations

[0228] In the second phase, the main objective is to address the higher-level problem as defined by equations (la) to (Id). More specifically, constraint (Id) ensures that the proposed charging stations are strategically integrated with existing service stations. However, given the significant computational challenges associated with this problem, a practical alternative solution based on a heuristic is proposed. To implement this, the intersections of areas lacking infrastructure (as detailed in the first step) with existing service stations are analyzed. Areas with service stations but lacking charging facilities will be prioritized according to increasing traffic volumes. This prioritization provides crucial information on which areas should be equipped first to optimally meet demand.

[0229] With regard to minimizing the collective travel time of all electric vehicles in the network, as detailed in equation (la), this metric is evaluated after the fact, after applying the heuristic choice to determine the optimal locations of the charging stations. It is also appropriate Note that with each evaluation of this metric for a given infrastructure configuration, waiting times must be recalculated. By assessing the time efficiency of charging station locations, the aim is to ensure that users benefit from reduced overall travel times, including travel, charging, and waiting times, as well as efficient access to charging facilities. This subsequent analysis can also help identify opportunities for improvement and necessary adjustments or the integration of additional constraints. Ultimately, this leads to better placement of charging stations that effectively meets spatial and temporal demands.

[0230] To test the method according to the invention, the locations of fast charging stations observed in the real world in April 2023 and January 2024 were taken into account, using the OpenChargeMap REST API. 145 newly installed stations were detected in France between these two periods. The method according to the invention was applied to improve the existing charging station infrastructure starting in April 2023, and the performance was compared with that observed in January 2024. To illustrate this, an example of a journey from Paris to Marseille, France, was analyzed.

[0231] In the first simulation experiment, an electric vehicle penetration rate of 2% is considered. Table 3 below presents the results in terms of optimal charging stops for the three configurations. With the current station configuration in April 2023, only 3 stops are suggested by the optimal EV routing. However, for the January 2024 system and our strategy, there are 4 stops, but at different locations. This is explained by the addition of stations since April 2023, where the optimization chose to make an additional stop in order to save on the total travel time, as can be seen in Table 3. Furthermore, it should be noted that by adding stations strategically, more time can be saved. With the strategy according to the invention, the travel time between Paris and Marseille for each electric vehicle traveling on this route has been successfully reduced.

[0232] Although the savings may seem modest, when multiplied by the flow of electric vehicles from the OD matrix, which totals 381 for this route, approximately 22 hours per day can be saved, compared to 6 hours per day for the January 2024 configuration.

[0233] Another point to emphasize is that this example of time saving on a single trip should be considered in the context of the more than one million daily trips recorded in the national OD matrix. This improvement is particularly noteworthy when addressing the challenge of long-distance route planning for electric vehicles.

[0234] [Tables3] Infrastructure configuration April 2023 January 2024 Strategy according to the invention Number of recharges 3 4 4 Travel time [hours] 10.26 10.23 10.19 Daily travel time savings [hours] -6.24 21.90

[0235] The second simulation experiment focuses on analyzing the effects of increasing electric vehicle penetration rates, particularly in response to current demand. This assessment highlights the resilience of the proposed strategy compared to the configuration used in April 2023.

[0236] Although both configurations have the same number of stations, their different arrangements offer crucial insights into their respective efficiencies. Table 4 below shows that the strategy according to the invention becomes more robust as the penetration rate increases. Indeed, with an electric vehicle penetration rate exceeding 10%, the journey from Paris to Marseille becomes impractical with existing charging stations in January 2024. However, our strategy can support up to an electric vehicle penetration rate of 30%, achieving shorter travel times than those observed with the existing infrastructure.

[0237] [Tables4] Penetration rate 2% 10% 30% 40% January 2024 10.23 hours 10.61 hours Failure Failure Invention 10.19 hours 10.34 hours 10.83 hours Failure

[0238] It should also be noted that the electronic / computer system according to the invention is understood as any system encompassing electronic components / devices, including any computer device of which a computer or calculator or controller or server, or a network comprising at least one of these devices.

[0239] According to a preferred embodiment, the various steps of the proposed process according to the invention are implemented by one or more software programs or computer programs, comprising software instructions intended to be executed by a data processor of a relay module according to the proposed technique and designed to control the execution of the various steps of the processes.

[0240] Consequently, the proposed method also relates to a program, capable of being executed by a computer or a data processor, this program comprising instructions for controlling the execution of the steps of a process as mentioned above. This program may use any programming language and be in the form of source code, object code, or code intermediate between source and object code, such as in a partially compiled form, or in any other desirable form. The proposed technique also relates to a data processor-readable information carrier comprising instructions for a program as mentioned above. The information carrier may be any entity or device capable of storing the program.For example, the medium may include a storage device, such as a ROM (e.g., a CD-ROM or a microelectronic circuit ROM), or a magnetic recording device, such as a hard drive. Furthermore, the information medium may be a transmissible medium, such as an electrical or optical signal, which can be transmitted via an electrical or optical cable, by radio, or by other means. The program, according to the proposed technique, may, in particular, be downloaded from a network such as the Internet.

[0241] Alternatively, the information carrier may be an integrated circuit in which the program is incorporated, the circuit being adapted to execute or to be used in the execution of the process in question. According to one embodiment, the proposed technique is implemented by means of software and / or hardware components. In this context, the term "module" may refer in this document to a software component, a hardware component, or a set of hardware and software components. A software component corresponds to one or more computer programs, one or more subroutines of a program, or more generally to any element of a program or software capable of implementing a function or a set of functions, as described below for the module concerned. Such a software component is executed by a data processor of a physical entity (terminal, server, gateway, router, etc.).) and is likely to access the hardware resources of this physical entity (memories, recording media, communication buses, electronic input / output cards, user interfaces, etc.).

[0242] Similarly, a hardware component corresponds to any element of a hardware assembly capable of implementing a function or set of functions, as described below for the module concerned. It may be a programmable hardware component or one with an integrated processor for executing software, for example, an integrated circuit, a smart card, a memory card, an electronic board for executing firmware, etc. Each The component of the system described above naturally implements its own software modules. The various embodiments mentioned above can be combined to implement the proposed technique.

Claims

1. Demands Method for determining the waiting time (W) of an electric vehicle (EV) in charging infrastructure (I) each comprising one or more charging stations (S) constituting a system (SO) of charging stations, in a given geographical area comprising a road network having road segments (PR) connected to each other by intersections, said method comprising the following steps, at least one, in particular all, of which is implemented by electronic / computer means: a) Mobility requests are collected from a known number of journeys (J) between an origin and a destination within the road network of said geographical area over a given period of time, including a daily period, b) data relating to the locations of existing charging stations (S) in said geographical area are collected; c) the energy requirements of electric vehicles (EVs) for said mobility demands are determined via an electric vehicle route planner (p) based on the data collected in steps a) and b) d) for said mobility demands, the waiting times (W) at charging stations (S) are determined by modeling, based on the mobility demands collected in step a), data relating to the locations of the charging stations (S) collected in step b) and the energy requirements determined in step c) - by estimating the arrival rate (δ) of electric vehicles (EVs) at charging stations (S) based on said mobility demands - by estimating the service rate (p) of charging stations (S) based on charging times calculated by an electric vehicle route planner (p) for said mobility demands - by integrating the estimated arrival rate (ô) and the estimated service rate (p) as parameters in a queuing model to deduce the estimated queuing times at the charging stations (S).

2. Method for determining the estimated waiting time of an electric vehicle (EV) according to the preceding claim, characterized in that mobility requests are collected according to step a) from a data platform, in particular open data, bringing together data on the flow of electric vehicles (EVs) between an origin (0) and a destination (D) in a road network of the geographical area.

3. A method for determining the estimated waiting time of an electric vehicle (EV) according to any one of the preceding claims, characterized in that data relating to the locations of existing charging stations (S) in said geographical area are collected according to step b) from a data platform, including open data, identifying and locating existing stations (S) in said area.

4. A method for determining the estimated waiting time of an electric vehicle according to one of the preceding claims, characterized in that the data collected in steps a) and / or b) are supplemented or replaced by actual data, possibly collected in real time.

5. A method for determining the estimated waiting time of an electric vehicle according to any one of the preceding claims, characterized in that, in step d), the arrival rate (τ) of electric vehicles at charging stations (S) and the service rate (p) of charging stations (S) are estimated – by a substep d1) of initializing and calculating the arrival rates (τ) and service rate (p), considering the waiting time (τ) at charging stations (S) to be zero – then a substep d2) of calculating the waiting times (W) at charging stations (S), – then a substep d3) of again determining the arrival rate (τ) and the service rate (p) from the waiting times (W) calculated in step d2), – then a substep d4) of actually calculating the waiting times (W) from the arrival rate (τ) and the service rate (p) redetermined in substep d3).

6. A method for determining the estimated waiting time of an electric vehicle according to the preceding claim, characterized in that in the initialization substep d1), optimization is the initialization of the charging stations (S) best suited to the needs of long-distance travel with waiting times, considering all possible routes for a given mobility demand called journey, each journey corresponding to an origin-destination pair (0-D) having been assigned to a specific travel flow, said substep dl) preferably having three phases: - a phase dl.l, where the optimal route of electric vehicles (EVs) is calculated using the initial set (SO) of a plurality (Ns) of charging stations (S), the calculation producing an initial set (S*0) of optimal charging stations (S), said initial set being accompanied by a set (Ns) of charging times (TO), with, for the stations (S) in the set (S*0) of solutions, the assignment of the associated charging times (Tr), and for all other stations, the assignment of a zero value, - a phase dl.2, where we calculate a set (c) of size (Ne) of the (i) possible combinations of the initial optimal stations (S*0), then, for each combination (i) in the set (c), we recalculate the optimal route and the optimal charging stations (S), updating the system of available charging stations (Si) by removing the i-th combination from the set (c) - a phase dl.3, where we aggregate the optimal charging station (S) solutions obtained in phase cl.2, to obtain the arrival rate (ô) and the service rate (p).

7. A method for determining the estimated waiting time of an electric vehicle (EV) according to one of claims 5 or 6, characterized in that, in substep d11), an hourly flow of electric vehicles is calculated, which differs according to a division of the time period considered, for example according to a division into daytime and nighttime hours for a daily period.

8. Method for determining the estimated queueing time of an electric vehicle according to claim 5 to 7, characterized in that, in substep d1), the penetration rate parameter (k) of electric vehicles (EV) is used.

9. A method for determining the estimated waiting time of an electric vehicle according to claims 5 to 8, characterized in that substep d2) of queue calculation uses the service rates (p) and arrival rates (ô) obtained in substep d1) as parameters queuing model keys to determine the waiting times (k) at each charging station (S)

10. . Method of exploiting the estimated queue times (W) of an electric vehicle (EV) in charging infrastructure (I) each comprising one or more charging stations (S) constituting a system (S0) of charging stations, in a given geographical area, said estimated queue times (W) being obtained with the method according to any one of the preceding claims, characterized in that e) said queue times (W) are exploited by creating a tool for visualizing the estimated queue times at the charging stations (S) in the geographical area, in particular on the dashboard of the electric vehicle (EV), in a mobile phone application or as a resource available on the internet.

11. . Method of exploiting the estimated queuing times of an electric vehicle (EV) in charging infrastructures (I) each comprising one or more charging stations (S) constituting a system (S0) of charging stations, in a given geographical area, said estimated queuing times (W) being obtained with the method according to any one of claims 1 to 9, characterized in that e2) said queuing times are exploited - by planning a route defined by a succession of road segments for one of said journeys in said geographical area, the planning carried out by a route planner, taking into account said queuing times to estimate the travel time including the charging time according to Ic / lcs possible route(s).

12. . Method of exploiting the estimated queuing times of an electric vehicle (EV) in charging infrastructures (I) each comprising one or more charging stations (S) constituting a system (S0) of charging stations, in a given geographical area, said estimated queuing times being obtained with the method according to any one of claims 1 to 9, characterized in that e3) said queuing times are exploited by integrating the estimated queuing times into the control strategies of electric vehicles.

13. . Method for exploiting the estimated waiting times of a electric vehicle (EV) in charging infrastructure (I) each comprising one or more charging stations (S) constituting a system (SO) of charging stations, in a given geographical area, said estimated queue times being obtained with the method according to any one of claims 1 to 9, characterized in that e4) said queue times are exploited - by determining the location of new charging infrastructure (!') - and / or by adjusting the number of charging stations (S') in new charging infrastructures or in existing charging infrastructures (I) or in existing hydrocarbon energy distribution infrastructures, in particular with a view to constructing new charging stations (S') or moving or removing existing charging stations (S).

14. Electronic / computer system for determining the estimated waiting time of an electric vehicle (EV) in charging infrastructure (I) each comprising one or more charging stations (S) constituting a system (SO) of charging stations, in a given geographical area comprising a road network having road segments (PR) connected to each other by intersections, said system comprising a) means for collecting mobility requests from a known number of journeys (J) between an origin and a destination in the road network of said geographical area over a given period of time, in particular a daily period,and the corresponding data on the energy requirements of electric vehicles (EVs) for these requests; b) means for collecting data relating to the locations of existing charging stations (S) in said geographical area; c) means for determining said mobility requests via a route planner (p) from the data collected with the means of collecting a) and b) the energy requirements of electric vehicles, d) means for determining said mobility demands by modeling the queue times at charging stations (S) from the mobility demands collected with the means of collection a), data relating to the locations of the charging stations collected with the means of collection b) and the energy needs determined with the means of determination c) - means for estimating the arrival rate (ô) of electric vehicles at charging stations (S) from said mobility demands - means for estimating the service rate (p) of charging stations (S) from the charging times calculated by a route planner (p) for electric vehicles for said mobility demands - means for integrating the estimated arrival rate (ô) and the estimated service rate (p) as parameters in a queueing model to deduce the estimated queue times (W) at charging stations (S).

15. Product computer program downloadable from a communication network and / or stored on a computer-readable medium and / or executable by a processor or server, comprising program code instructions for carrying out the method according to any one of claims 1 to 13, when said program is executed on a computer, mobile phone, computer processing circuit or computing device.

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