Rafael Huang Cestari

Sebastien Ducos
email: s.ducos@maisadour.com

Ernesto Exposito
email: ernesto.exposito@univ-pau.fr

iPaaS in Agriculture 4.0: An Industrial Case

Keywords: agriculture, iPaaS, integration, automation, interoperability

Current automation approaches in the Industry 4.0 have generated increased interest in the utilization of Integration Platforms as a Service (iPaaS) cloud architectures in order to unify and synchronize several systems, applications, and services in order to build smart solutions for automated and adaptive industrial process management. Existing iPaaS solutions present several out-of-the-box connectors and automation engines for easier integration of customers' projects, but show issues regarding overall adaptation outside their scope, brand locking, and occasionally high prices. Moreover, existing platforms fail to respond adequately to the needs of deploying multiple decision models capable of offering automated or semi-automated management of processes, thanks to the integration of the large diversity of data and event sources as well as the different physical or logical action entities. With the popularization of open-source software and applications such as BPM Engines, Machine Learning libraries, and Integration suites and libraries, it is possible to develop a fully customizable and adaptable, open-source iPaaS that can be used both in and outside industrial applications. In this paper, we propose a generic iPaaS architecture implemented on the basis of several open source solutions boasting integration, interoperability, and automated decision-making capabilities in the domain of Agriculture 4.0.

A proof-of-concept based on these solutions is presented, as well as a case study on MAÏSADOUR's grain storage process with a comparison with the currently human-operated tasks.

I. I NTRODUCTION ( H EADING 1 )

The needs for automation of agricultural activities has been an urgent necessity in the context of the new Industry 4.0 revolution. In order to keep up with the ever-growing global population and market demands, new technologies, methods, and techniques are constantly developed in order to maximize production efficiency. Various devices and systems, such as automated harvesters, environment monitors, and humidity and temperature controllers are utilized in several agricultural applications to great effect, assuring efficient cultivation, gathering and storage of products. However, when considering the expansion of these applications and the amount of data generated, the cohesion and cooperation between these systems can be improved and expanded, allowing for a greater scope of automation and logistics management. A promising solution is represented by the Integration Platform as a Service (iPaaS), which is a suite of cloud services that enables managing and integration flows by connecting a wide range of applications or data sources without manually installing or managing any hardware or middleware [START_REF] Ebert | Integration Platform as a Service[END_REF]. This allows for the creation of scalable, efficient, and cohesive systems designed for automated activities, data evaluation, and decision-making, which includes not only contextual devices, but also the resulting products and the involved human participants as well, following the principles of the Internet of Everything (IoE) concept [START_REF]The Internet of Everything[END_REF]. It also guarantees the interoperability of present and future systems by guaranteeing smooth context adaptation and system evolution.

Beyond the scope of integration and automation, there is also the possibility of increasing process efficiency with the use of Machine Learning (ML) modules and methods, taking in and analyzing data in order to improve its decision-making capabilities, making it faster, more precise, cheaper, or more reliable, as it can reduce the amount of human interaction needed within the loop.

In this paper, we present our findings in the framework of an industrial project aimed at designing and prototyping an iPaaS solution well-suited for grain storage and processing capable of integrating heterogeneous actors such as data collectors, temperature and humidity controllers, in-site grain transport systems, transport personnel tracking, business process engines, databases, among others. The main goal of this solution is to reduce energy consumption, as well as reduce the need of interaction by human experts in the process. This solution has been designed in order to facilitate the integration of additional systems, making it possible for it to be used in applications other than those focused on agricultural activities, while also retaining the ease of intercommunication between systems and the ability to provide automated decision-making with Business Process Management (BPM) engines and Machine Learning (ML) modules. This paper is organized as follows: In Section II, the state of the art is laid out, as well as the needs and goals of the expected IPaaS solution. In Section III, the proposed solution is characterized and defined. In Section IV, the implementation of the solution is explained and detailed. Finally, in Section V, results are presented and in Section VI, final conclusions and perspectives are made.

II. I NTEGRATION P LATFORM AS A S ERVICE

An iPaaS is a cloud-based solution for integration of different applications, services, private and public clouds, and systems without having to invest time and resources into installing, developing and maintaining integration software, middleware and hardware [START_REF]The Maïsadour Cooperative Group in a nutshell[END_REF]. The iPaaS facilitates development of business systems, leveraging of data (especially large amounts), reducing time-to-value and installation costs, and requires less specialized skills to be deployed.

This paper focuses on an Industrial Case belonging to MAÏSADOUR, an international food cooperative that deals in agricultural, pork, fish, and poultry products, among others [START_REF]Integration Platform as a Service (iPaas)[END_REF]. The case in question is the process of drying and storing grains that have been recently harvested.

It is required for the iPaaS solution to possess integration and interoperability features, such as connectors and messaging patterns, for the unison of the different actors in the process, a business process engine or management features for automated coordination of the process, and a decision engine or ML functionalities for automated decisions and improvement of the process, also reducing the need for human interaction. Additionally, the solution should, have a low or reasonable cost, allow for full control of its functions, and provide ease of usage and implementation. Several companies offer iPaaS solutions and services that include these features. A brief analysis of the most used and reviewed services was made utilizing information from Gartner provided from their Peer Review [START_REF] Inc | iPaaS Integration Platform Software Reviews[END_REF] website and "Magic Quadrant" 2019 report [START_REF] Inc | Gartner Reprint 'Magic Quadrant[END_REF].

Microsoft Azure Integration Services is composed of several Azure services such as Azure Logic Apps, Azure API Management, and Azure Service Bus. Data integration and workflow automation are also offered separately. These services can make use of Enterprise Integration Patterns (EIP) [START_REF]Azure -Enterprise Data Integration Patterns with Azure Service Bus[END_REF] and several messaging patterns [START_REF]Messaging patterns -Cloud Design Patterns[END_REF]. There are more than 360 different connectors available between these services [START_REF]Connector reference overview[END_REF]. It has innate integration with other solutions provided by Microsoft for these use cases, but has brand locking problems.

The Dell Boomi platform includes several functionalities, such as core application/data integration, API and Business-to-Business management, and workflow automation and application development. Different offerings are available, geared towards specific use cases and with a set amount of endpoints. Boomi has over 1500 unique connectors available [START_REF]Integrations & Supported Applications[END_REF] as well as different integration patterns [START_REF] Boomi | eBooks -eBook -Exploring Data Integration Patterns[END_REF]. Customer support is considered lacking, and there are missing features such as data virtualization and event stream analytics. IBM Cloud Integration is composed of several services such as IBM API Connect, App Connect, MQ, Event Streams, IBM Aspera, Secure Gateway Service, IBM BPM and others. It boasts standard messaging functions [START_REF]IBM MQ[END_REF] and over a hundred built-in connectors with the possibility of the customer developing custom ones [START_REF]Connectors for App Connect | IBM[END_REF]. It has a large scope of applications, being adaptable for various use cases when paired with other solutions provided by IBM. It also provides both free and paid versions. Implementation of this platform is considered difficult, and support provided has been criticized by customers.

Informatica Intelligent Cloud Services (IICS) is a microservices-based

iPaaS that provides several fundamental functionalities, such as Business-to-Business integration, API management, and data integration. Several messaging patterns [START_REF]Message Exchange Patterns[END_REF] and over 400 pre-built connectors are available as well as several custom ones [START_REF]All Cloud Connectors: Demos & Documentation | Informatica[END_REF]. It is considered to be more expensive than its competitors, and lacks certain features such as event processing.

As it can be observed from the information in the analysis and in Tables I, most of the solutions fulfill the criteria established for our case. They are widely accepted by several customers and provide automation and customer support, albeit said support is considered lacking. Integration with third-parties is also difficult. The use case-specific nature of some offerings also hampers adaptability. Finally, most of these solutions are entirely dependent on the development on the provider's side, reducing the level of control that the customer has. Based on this study, it appears that the needs for a generic, open and extensible iPaaS platform have not yet been met. Such generic solution should allow users to have full access to all of the platform's functionalities, allowing its specialization based on new connectors, features and systems well-adapted to a large diversity of industrial contexts. Moreover, this also means that some of the ease-of-use advantages of proprietary solutions are also lost, which results in a steeper learning curve or higher entry-level knowledge, as well as longer development time required to fully cope with specific needs for industrial process management.

III. P ROPOSED S OLUTION

As stated previously, there are real needs to design and implement an open, generic and extensible iPaaS platform, based on the integration or development of a large diversity of software and services. In order for this proposition to be viable, it needs to address three key capabilities: Integration, allowing systems to communicate with each other, Planning and Execution, enabling automation in decision making and following a general business process model, and Monitoring and Analysis, evaluating received data and outcomes and proposing or implementing solutions to control the managed process automatically.

In order to design such an iPaaS solution, the ARCADIA approach was followed, which is a system engineering method based on the use of models, with a focus on the collaborative definition, evaluation and exploitation of its architecture [START_REF]Capella MBSE Tool -Arcadia[END_REF]. Due to space limitations, the initial operational and system analysis phases will not be presented in this article. These phases have allowed us to identify the functionalities and the generic internal architecture of the IPaaS platform that is illustrated by the Logical Architecture diagram presented in Figure 1.

The iPaaS is composed of three main logical components: the integration module, the process manager, and the prediction module. Logical actors relevant to the architecture are the data collector, which can be also seen as the workspace or environment, the data storage, the boiler and sensors, and the grains. The integration module receives and sends information between the various components and actors involved in the process, guaranteeing that messages and data are formatted and relayed accordingly. The process manager controls the flow and decisions of the process, coordinating it. Finally, the prediction module, as the name implies, is responsible for the prediction of relevant parameters from data acquired from by the data collectors. Once the logical architecture phase was achieved, the identification of concrete components and subsystems able to satisfy the expected functional and structural requirements of the platforms was carried out. During the Physical architecture phase a set of components were identified as satisfying the expected requirements, in particular: the Java-based Camel framework (v2.25.0) for building system integrations [START_REF] Cranton | Apache Camel Developer's Cookbook[END_REF], Camunda BPM (v7.13), which is a Business Process Management Notation (BPMN) Engine and editor capable of automation [START_REF]Workflow and Decision Automation Platform[END_REF], and Apache Kafka (v2.12 -2.4.1), which is a distributed streaming platform facilitating real-time data sources integration [START_REF]Apache Kafka[END_REF]. The Physical Architecture can be seen on Figure 2. Camel fulfills the role of integration, allowing for easier communication between different applications and services, and guarantees interoperability by having several different components (connectors) that allow for easy communication between systems, and constant updates and additions to said components in order to comply with newer standards. Camunda is responsible for automating the process through BPMN diagrams, as well as laying out the whole process with a comprehensive diagram, which is interchangeable with other BPMN diagram editors and engines. Finally, Kafka deals with any additional communication that has to be done and cannot be easily solved with a Camel application. Comparisons were made between the chosen components and possible alternatives as to prove that these choices were better suited for the project. However, due to this paper's limits, these comparisons will be left out.

For automated data processing and decision-making, a ML module was written in Python utilizing Tensorflow (v1. 15.2), an open-source machine-learning platform [START_REF]TensorFlow[END_REF], implementing Adaptive-Network-Based Fuzzy Inference System (ANFIS) [START_REF] Jang | ANFIS: adaptive-network-based fuzzy inference system[END_REF]. In addition to these components of the iPaaS, a CouchDB database was also utilized for the storage of necessary data, which will be discussed later on.

In regard to the scalability of the iPaaS, it was decided, after a review of diverse cloud technologies, which is not discussed here due to this article's limits, to use Docker and Kubernetes as the main components to manage scalability and elasticity requirements. In the next section, a proof-of-concept focused on the integration, interoperability, and decision management and learning capabilities will be presented.

IV. I MPLEMENTATION

One iPaaS prototype implementation has been built in order to manage agriculture processes while minimizing energy consumption. This prototype uses Camel as its main integrator solution. Java components are built using the Camel library in order to make communication between existing and future components easier. The prototype is based on the integration of CouchDB, Camunda BPM, Apache Kafka, and information from Openweather's API through appropriate connectors (such as ones dedicated to CouchDB and Kafka) or through HTTP REST API calls (which is the case for Camunda and the weather API).

A generic agriculture process, managed by Camunda from within a WildFly server, that represents the grain storage case has been implemented. As it can be seen in Figure 3, the process diagram consists of several tasks and gateways that must be completed and satisfied in order for the process to move forward. The first tasks are the data collection tasks that gather the weather, human and IoT data relevant to the drying and storage process. These must be completed in parallel to each other. Following that, the data is saved in CouchDB and then run by the ML module to acquire the parameters and setpoints necessary for the drying process (temperature, extraction time, humidity level, humidity goal) while minimizing energy consumption. This communication is done with Apache Kafka topics as intermediaries between the Camel application and the ML module. Once the predicted parameters and outcomes are acquired by the Camel application, they are then returned to the Camunda engine, which then decides whether or not it is an acceptable outcome. If it is acceptable, then the values are sent to the boiler, otherwise the data is sent back to the ML module for another prediction. Throughout this process, the data and outcomes are saved in order to use it as training data for the ML module. The ML module itself uses historical data from previous operations in order to train its model for predictions based on desired output humidity, detected input humidity, and extraction weight. The dataset utilized contains the parameters from 153 individual drying cycles, with inputs from human experts in order to reduce overall energy consumption. The model is created after 5000 iterations and will define 16 rules, by default (adjustable), automatically according to the input data in addition to the rules that can be defined by an expert, utilizing 70% of the historical data as training data and the remaining 30% as test data to verify its prediction accuracy. The predicted values are the extraction time, and the temperature settings for the dryer, which are also used in another step for the prediction of gas and energy consumption for the operation. The gas consumption value is the determining factor whether the predicted parameters are acceptable or not, as the main goals are not only to reduce the necessity of human interaction in the process, but also to guarantee that the overall energy consumption is acceptable or even reduced to optimal values. Due to time constraints, only the prediction of the extraction time was done by the proof-of-concept, using the value from the historical data as a comparison for the accuracy of the predicted value as well as the determining factor for the completion of a process cycle.

V. E VALUATION AND RESULTS

In this context, we will focus on the data science dimension, more precisely, on the processing and knowledge resulting from the data. First, we will see an ANFIS based approach to predict the dryers setting parameters for the cereal drying process. Then, this prediction will be made using an ML model. Finally, the results will be presented with a comparison of the different approaches, according to key criteria for the company, demonstrating the advantages and disadvantages of each according to their needs and points of view.

A. ANFIS Solution

The Adaptive Neuro Fuzzy Inference System approach was chosen allowing great flexibility with good results as well as a good understanding of predictions. In order to measure the loss, the Huber loss regression function is used because it is less sensitive to outliers in data than the squared error loss. It's also differentiable at 0. Huber loss approaches MSE when 𝛿 ~0 and MAE when 𝛿 ~∞ (large numbers) [START_REF] Grover | 5 Regression Loss Functions All Machine Learners Should Know[END_REF]. Regarding optimization, the Adam algorithm is used, which is an adaptive learning rate optimization algorithm that's been designed specifically for training deep neural networks. Adam can be seen as a combination of RMSprop and Stochastic Gradient Descent (SGD) with momentum. It uses squared gradients to scale the learning rate like RMSprop and it takes advantage of momentum by using moving average of the gradient instead of gradient itself like SGD with momentum. Today, Adam is definitely one of the best optimization algorithms for deep learning and its popularity is growing very fast [START_REF] Bushaev | Adam -latest trends in deep learning optimization[END_REF].

This approach was implemented in Python and more precisely with the Tensorflow framework because it's an open-source framework which is complete and efficient. Figure 4 shows the predicted data compared to the actual data concerning the optimal settings to be defined in order to have good productivity while reducing energy consumption. As we can see, the model achieves good results with a small training sample. Figure 5 shows the evolution of the relevance of the model for each generation after being optimized using the Adam algorithm. We can see that after 100 epochs, the model has practically reached its optimization limits. Here, we have defined 5000 epochs in order to be a little more precise. With a learning rate defined at 0.01, we can observe that the training and validation loss are close to 0 which represents a good result. In addition, the training time is rather fast since it amounts to only 12.7s.

B. ML Approach

Regarding this approach, the exponential GPR model was chosen thanks to a study on several models. In order to implement it, the MATLAB tool was used, allowing a quick and complete analysis. The data used are obviously the same as for the previous approach in order to have a relevant comparison.

C. Approaches Comparison

Both solutions have been used to meet an existential need to apply decisions based on real-time observations and reduce human intervention. Several performance and also industrial-oriented criteria were selected in order to compare these two approaches. According to the above table based on previous experiences, we can say that both solutions are viable and have various advantages. The ML approach has a better performance and is faster to develop, however it provides little or no explicability and needs very clean data upstream. It's a really good approach to predict consumptions, for example, if you have a lot of reliable data. The ANFIS approach will therefore be more relevant if there is a need for auditability but also if there are specific rules to be considered where an expert can easily integrate them into the system. The latter is also much more flexible and can respond to a wider range of needs like the grain drying process where there are a lot of conditions and too much imprecise data.

D. Proof of concept

The platform performed without issues, managing to automatically retrieve the necessary data, store it, and then send it for the prediction of the extraction time values. No stability issues were experienced during testing. Installation and adaptation required time and effort in order to understand the particularities of intercommunication between each component. While the solutions deployed have their intercommunication methods resolved in this prototype, adding new systems or components could take a few hours before being fully incorporated into the automated system.

VI. C ONCLUSIONS AND PERSPECTIVES

In this article, we have proposed a generic and open iPaaS architecture that is well-suited to satisfy integrability, interoperability and extensibility requirements as well as to allow the management of industry 4.0 real-time processes including well-adapted decision models.

We have illustrated how several decision models can be easily integrated and adapted in order to satisfy multiple applications and needs. For example, the fuzzy logic method would be perfect for monitoring or recommending industrial installations where many rules are already defined and known and where system interpretability is mandatory. On the other hand, the ML method is also very interesting for processes requiring high precision thanks to its very efficient models. In recent years, many applications have used fuzzy logic, optimization algorithms or neural networks in various fields. However, in most cases, a single decision model is not enough. If we take fuzzy logic, it can be said to provide the rough reasoning and constraint management which makes it flexible but has a low learning capacity, whereas on the other hand neural networks have this high learning capacity but have the incomprehensible "black box" syndrome. This is why we offer this architecture which allows smooth integration of the two models illustrated above but also offers the possibility of hosting several decision models, in parallel, which can be evaluated, adjusted and used simultaneously in order to help decision making. The interoperability of these models offers the possibility of capitalizing on their strengths while compensating for their weaknesses, which represents a major advantage for CPS who need high adaptability. The logical and physical architectures that were designed and implemented achieved a good foundation for an iPaaS, being robust and adaptable enough for reliable use in varied scenarios. In the future, the platform will be further developed in order to evaluate scalability and elasticity properties in multi-tenant scenarios.

Fig. 1 .

 1 Fig. 1. Logical Architecture of the solution

Fig. 2 .

 2 Fig. 2. Physical Architecture of the solution

Fig. 3 .

 3 Fig. 3. BPM Diagram of the process

Fig. 4 .

 4 Fig. 4. Predicted (orange) vs Actual (Blue) Data

Fig 5 .

 5 Fig 5. Training & Validation loss

Fig. 6 .

 6 Fig. 6. Predicted (yellow) vs Actual (blue) Data

Figure 6

 6 Figure 6 shows the predictions made in relation to the actual data, in particular : RMSE: 0.018865, R-Squared: 0.87, MSE: 0.0003559, MAE: 0.013531, Training time: 0.53s. The model presents very good results with a R-Squared amounting to 0.87 and RMSE, MSE and MAE close to 0, knowing that several optimizations are still possible, such as data filtering/cleaning, as well as increasing the number of individuals to be trained. In addition, the training time is really very fast with only 0.53s.

TABLE I .

 I S OLUTION C OMPARISON (F UNCTIONAL F EATURES )

	Solution	Overview	Process &
			Decision Engine
	Microsoft	Pub/Sub, Request-Reply, Queues, Point-to-Point,	Yes/Yes
		API/WebServices(WS) , Over 360 connectors, Paid, Includes
		Support, limited control
	Dell	Point-to-Point, Pub/Sub, API/WS, Over 1500 connectors, Paid,	Yes/No
		Includes Support, limited control
	IBM	Pub/Sub, Sync & Async, Over 100 connectors + custom , Paid &	Yes/Yes
		Free, Includes support, limited control
	Informatica	Request-Reply, Pub/Sub, Queuing, One way, WS. Over 400	Yes/Yes
		connectors + custom, Paid, Includes support, limited control

TABLE II .

 II C OMPARISON TABLE

	Criteria	ANFIS Solution	ML Solution
	Model Performance	Satisfactory performance	Very satisfactory performance
	Explainability	Auditable	Complex
	Model build speed	Fast	Very Fast
	Model build complexity	Simple	Simple
	Input data	Not very sensitive to outliers	Very sensitive to outliers
	Flexibility	Very flexible	Situational

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE

A CKNOWLEDGMENT

We thank MAÏSADOUR and UPPA for their financial and institutional support of the underlying research of this article.

R EFERENCES


Abood Mourad
email: abood.mourad@centralesupelec.fr

Martin Hennebel
email: martin.hennebel@centralesupelec.fr

Ahmed Amrani
email: ahmed.amrani@irt-systemx.fr

Amira Ben Hamida
email: amira.benhamida@irt-systemx.fr

Deploying Fast-charging Stations for Electric Vehicles Based on Mobility Flows and Local Photovoltaic Production

Keywords: electric vehicles, recharging, optimization, mobility, photovoltaic

The need for deploying fast-charging stations for electric vehicles (EVs) is becoming essential in recent years. This need is justified by the increasing recharging demand, and supported by new recharging technologies making EV chargers more efficient. For this purpose, we introduce an optimization model for finding the optimal deployment of EV fast-charging stations through a network of highways, while taking into account their recharging demands and the restrictions imposed by the electric grid. We also consider the availability of local photovoltaic (PV) power station and integrate its energy to the proposed recharging network. In addition, we present a case study on Paris-Saclay area where the actual mobility flows and electric network specifications are considered. We thus provide the optimal locations for EV charging stations at the studied area, and we indicate the number of chargers to be deployed at each station. Finally, we study the potential benefits of integrating local PV energy and analyze its different prices and production costs.

I. INTRODUCTION

Electric Vehicles (EVs) represent a promising opportunity that can lead to fundamental shifts in people transportation. With their batteries and charging times being considerably enhanced in recent years, EVs can provide a sustainable transportation solution [START_REF] Mourad | A survey of models and algorithms for optimizing shared mobility[END_REF]. The deployment of fast-charging stations is thus essential especially on highways where EVs need to be recharged at very short periods of time. For this purpose, chargers with high powers need to be installed in order to fulfil the increasing charging demand for EVs. In addition, the availability of locally-produced green energy (e.g. wind or solar sources) can also help in providing the energy needed to supply these chargers. However, green energy sources still suffer from uncertainty in their production and their relatively high production costs [START_REF] Robertson | Renewable integration for remote communities: Comparative allowable cost analyses for hydro, solar and wave energy[END_REF].

In this paper, we introduce an optimization model to find the optimal locations for deploying EV fast-charging stations through a network of highways. The model takes into account EV charging demands as well as the capacity provided by the electric grid. In addition, we consider the availability of local photovoltaic (PV) power station and we study the use of its produced energy for supplying EV chargers. We thus present a mathematical formulation for the problem where the aim is to maximize charging demand coverage while respecting budget limits, parking slot limitations, and the available capacities of the electric grid and PV production. Then, we present a case study on Paris-Saclay area where the optimal locations for EV charging stations at the studied area are provided as well as the number of fast-chargers at each location. Finally, we study the potential benefits of integrating locally-produced PV energy and analyze its different prices and production costs using different investment indices.

II. RELATED WORK

Research on deploying EV fast-charging stations on highspeed roads is swiftly increasing in recent years. These fast chargers, also referred to as level-3 chargers, are characterized by their high charging capacity (400-500V/50A) and relatively short charging times (e.g. a Tesla Roadster can be fully recharged in less than 20 minutes) [START_REF] Shareef | A review of the stageof-the-art charging technologies, placement methodologies, and impacts of electric vehicles[END_REF]. For example, in [START_REF] He | A Optimal locations of U.S. fast charging stations for long-distance trip completion by battery electric vehicles[END_REF], the problem of selecting locations for fast-charging stations through a highway network for long-distance trips in the US was considered. Through a mixed integer programming model, authors efficiently selected the number and locations of EV charging stations and highlighted the importance of this selection in planning such a charging service. Another fast-charging location model was introduced in [START_REF] Sun | Locating charging stations for electric vehicles[END_REF], where the selection of charging locations was based on passenger travel behaviors as well as the specifications of the electric grid. Through a case study on Dalian-China, the authors concluded that travel distances and located charging capacities are key factors in successfully deploying fast-charging services.

Many recent studies are focusing on using green energy sources for supplying EV charging networks. In [START_REF] Khan | Review of solar photovoltaic and wind hybrid energy systems for sizing strategies optimization techniques and cost analysis methodologies[END_REF], a review of photovoltaic energy systems along with their sizing strategies, optimization techniques, and cost evaluation methodologies was provided. In addition, the main indices for analyzing 978-1-7281-6919-4/20/$31.00 ©2020 IEEE energy costs and pricing schemes has been presented. A relevant application of these indices can be found in [START_REF] Ozcan | Project and cost-based evaluation of solar energy performance in three different geographical regions of Turkey: Investment analysis application[END_REF] where the investment of a photovoltaic energy system was evaluated through a case study in three different cities in Turkey. In order to model production uncertainty in photovoltaic energy systems, a scenario-based approach to evaluate the potential use of solar energy for charging EVs was introduced in [START_REF] Good | Scenario-based modelling of the potential for solar energy charging of electric vehicles in two Scandinavian cities[END_REF]. Results of testing the proposed approach on two Scandinavian cities demonstrated that PV energy yield can cover EV demands in most of the considered scenarios. The necessity of stochastic approaches to deal with uncertainty in PV production was also confirmed in [START_REF] Thomas | Optimal operation of an energy management system for a grid-connected smart building considering photovoltaics' uncertainty and stochastic electric vehicles' driving schedule[END_REF]. This was done by evaluating a set of case studies using a linear programming framework that takes into account PV uncertainty and stochastic EV driving schedules.

III. PROBLEM DESCRIPTION

In this problem, we consider two types of fast chargers, one for charging small electric vehicles, and the other for charging heavy electric In addition, We consider a set of potential charging locations S = I ∪ V, where I includes locations that are powered by the distribution network, and V includes those that are powered by a local PV station. Every charging location s ∈ S is defined by a cost (c s ) indicating required investment to use this location as a charging station, and has a maximum electric capacity and a max/min number of fast chargers that can be installed for small vehicles as well as heavy trucks (max a s , min a s , max b s and min b s respectively). The investment cost (c s ) includes land cost and cabling expenses. For charging locations that are powered by the distribution network, the maximum electric capacity is fixed and depends on the distribution network itself. We refer to this fixed capacity as q s (∀ s ∈ I). On the other hand, this capacity can not be fixed for charging locations that are powered by PV energy as it highly depends on PV energy production which is stochastic (i.e. it depends on cloudiness index, season, and solar irradiation). We thus refer to this varying electric capacity as λ s (∀ s ∈ V). In order to build mobility paths, we consider a set of coupling nodes N representing different highway intersections. As such, we consider a set of paths P that link sequences of coupling nodes. Every path p ∈ P is defined by its charging demands d a p , d b p , representing the number of electric vehicles and trucks, respectively, to be recharged per day. The set of charging locations that are associated with each path p is denoted as S p . The numbers of electric vehicles and trucks that can be recharged using a fast charger per day are defined as β a and β b respectively. Similarly, the amounts of electric power needed to recharge an electric vehicle or an electric truck using a fast charger are defined as q a and q b respectively. Moreover, installing a fast charger for electric vehicles or trucks implies extra costs (i.e. charger costs). These costs are defined as c a and c b respectively. For the sake of simplicity, we assume all electric vehicles to be homogeneous, and thus, their recharging time and energy are the same. We consider the same assumption for electric trucks.

Hence, the choice of deploying a charging station at location s ∈ S and the number of fast chargers to be installed is based on the recharging demand through the path where s is located. However, the number of chargers to be installed is limited by the available electric capacity and by the availability of places and parking slots at location s. As such, we build a model to optimize this deployment by maximizing the satisfied demand while respecting the different constraints.

IV. MATHEMATICAL MODELING

In order to model the problem, we introduce a binary variable x s which is equal to 1 if a charging station is deployed at location s ∈ S, and 0 otherwise. In addition, we introduce a continuous variable y p ∈ [0, 1] representing the demand coverage rate on path p, and two integer variables, z a s and z b s , representing the number of fast chargers to be installed at charging location s ∈ S for electric vehicles and trucks respectively. The optimization model is thus formulated as follows:

M ax Z = p∈P ( d a p + d b p ) y p (1)
s.t. s∈S c s x s + c a z a s + c b z b s ≤ C (2) p∈P ( d a p + d b p ) y p ≥ Q (3) s∈Sp β a z a s ≥ d a p ∀ p ∈ P (4) s∈Sp β b z b s ≥ d b p ∀ p ∈ P ( 5
)
min a s ≤ z a s ≤ max a s ∀ s ∈ S (6)
min b s ≤ z b s ≤ max b s ∀ s ∈ S (7)
q a z a s + q b z b s ≤ q s ∀ s ∈ I (8)
q a z a s + q b z b s ≤ λ s ∀ s ∈ V (9) if y p = 0 =⇒ z a s + z b s = 0 ∀ s ∈ S p , ∀ p ∈ P (10) if z a s + z b s > 0 =⇒ x s = 1 ∀ s ∈ S (11) x s ∈ {0, 1}, y p ∈ [0, 1] ∀ s ∈ S, ∀ p ∈ P (12) z a s , z b s , q s , λ s , ∈ N ∀ s ∈ S (13) d a p , d b p , β a , β b , q a , q b ∈ N ∀ p ∈ P (14) min a s , max a s , min b s , max b s ∈ N ∀ s ∈ S (15) c s , c a , c b ∈ R ∀ s ∈ S (16)
The objective function (1) aims at maximizing the total covered demand for charging both vehicles and trucks. Regarding model constraints, constraint (2) ensures that the sum of location costs and chargers installation costs does not exceed total budget limit. Constraint (3) states that a minimum coverage of the overall charging demand must be ensured. Constraints (4 and 5) ensure that charging demands, for vehicles and trucks respectively, are covered at each mobility path. Constraints ( 6) and ( 7) state that the number of fast chargers to be installed must respect the specified limits at each charging location. Constraints (8) ensure that the electric power required to operate the installed chargers at a specific charging location does not exceed the available electric capacity provided by the distribution network at that location. Similarly, constraints (9) ensure that the electric power needed at charging locations, where a PV station is located nearby, must not exceed the actual PV energy production provided by that station. Constraints [START_REF] Funke | How much charging infrastructure do electric vehicles need? A review of the evidence and international comparison[END_REF] and (11) are used to link the different variables of the model. Finally, constraints (12) to (16) define domains for model variables and parameters.

V. RESULTS AND DISCUSSION

In this section, we introduce our case study for Paris-Saclay area and describe how its different parameters and PV production scenarios are generated (section V-A). We then test the proposed model using Cplex solver and present the obtained results (section V-B). Finally, we study the different energy prices and production costs and analyze their impact on the profitability of the project (section V-C).

A. Paris-Saclay case study

Paris-Saclay is an agglomeration community located at the south of Paris. As it is geographically close to the capital and to main economical activities, Paris-Saclay is traversed by many major mobility axes (e.g. A6, A10, N20 in Fig. 1). These axes are used by personal vehicles and heavy trucks for short-distance trips (e.g. commuting) as well as international transit flows. In addition, a large photo-voltaic (PV) farm is to be installed at Marcoussis district (next to the intersection of "A10" and "N104" highways, Fig. 1) with 76500 solar panels and up to 24 GWh annual power production. This farm has the potential of increasing charging power at nearby EV charging stations while reducing their reliance on the existing distribution network. In this study, we consider the intersections of major axes to be the set of coupling nodes. Mobility paths are then constructed using sequences of these nodes. For example, path "N20" is defined by the sequence of nodes (1, 16, 18, 15) (Fig. 2). As such, we define 9 different paths based on the actual mobility flows at Paris-Saclay area (Fig. 2). Each path is associated with vehicle and truck flows and their charging demands. The actual charging demand (i.e. the number of EVs to be recharged) is then calculated by considering 5% of the overall daily flow on each one of the defined paths1 (i.e. an average of 2980 vehicle/h on each path). This percentage is fixed based on EV sales share of the French automobile market in 2020 [START_REF] Funke | How much charging infrastructure do electric vehicles need? A review of the evidence and international comparison[END_REF]. In addition, we consider the actual charging stations (currently operational or projected) and the actual service stations as the set of potential charging locations at Paris-Saclay area. Costs, electric grid specifications, and the maximum number of fast chargers that can be installed at each location are fixed based on their real data 2 . Charging locations are then associated to paths so that the model can decide which locations to use and how many chargers to install at each location. Regarding chargers power, we assume that a fast charger requires 50 kW (≈20 minutes) for recharging an electric vehicle, and 250 kW (≈30 minutes) for recharging an electric truck. The costs of installing a fast charger for vehicles and trucks are estimated at 12k C and 15k C, respectively. Test parameters are summarized in Table I. Regarding PV production, the generated power of a PV farm at instant t can be calculated as follows:

P (t) = ( 1 -µ(t) ) × I(t) × δ × η (17)
Where µ(t) is the cloudiness index at instant t (%), I(t) is the irradiation at instant t (W/m 2 ), δ is the surface of solar panels (m 2 ), and η is the efficiency that corresponds to the electric quantity produced as a percentage of the received solar power. We assume that this power is used for charging EVs. This generated power highly depends on irradiation and cloudiness index as they differ during seasons and day hours. For example, PV production is maximal in a sunny day during Summer at noon. The actual values of irradiation at different seasons and day hours are fixed, and thus, known in advance 3 . Based on real irradiation values, we estimate the amount of PV energy that can be produced by the considered PV farm during a sunny day at each month of the year (see Fig. 4 in appendix). We observe that up to 90 MWh/day can be generated during summer months when irradiation is at its highest, while this production drops to approximately 30 MWh/day during winter. However, these values can be seen as the maximal daily production (i.e. calculated in fully-sunny days), and thus, will be reduced due to cloudiness effects. In addition, PV farms rely on their annual energy production more than power peaks and profiles throughout a day or a season. A high power consumption (charging) combined with a high PV energy production can thus create flow fluctuations to the grid unless they are well synchronized. Unlike the irradiation, the cloudiness index (µ(t)) can not be fixed in advance as it depends on weather conditions (i.e. µ(t) is stochastic). We thus need to model this uncertainty using a set of scenarios and calculate their probability distribution. We consider 4 different day profiles: (1) Fully-Sunny, where µ(t) is between 0% & 25%, (2) Partially-Cloudy, where µ(t) is between 25% & 50%, (3) Mostly-Cloudy, where µ(t) is between 50% & 75%, and (4) Fully-Cloudy, where µ(t) is between 75% & 100%. In addition, we divide the day into 8 time periods (i.e. (12AM,3AM), (3AM,6AM), .. , (9PM,12AM)). These day periods help in capturing different mobility patterns (e.g. period (6AM-9AM) is a peak period when people commute, etc.). We also consider the four seasons (e.g. the probability of having a fully-sunny day is higher in Summer than in winter, Table II). As a result, we build our set of scenarios, where every scenario is defined by a day-profile, a day-period, and a season. In order to calculate their probabilities, we use weather measurements of the last 10 years and we cluster them according to day profiles, periods, and seasons using K-Means approach 4 . The resulting probability distribution represents an input to our model.

B. Deploying EV fast-chargers

We test the proposed model using Paris-Saclay data in order to obtain the optimal deployment of EV charging stations in the area. Results indicate the number of chargers to be installed at each selected location ((z a s , z b s ) in Fig. 3). It can be observed that the number of vehicle chargers is relatively higher than that for trucks at all selected locations. This can be explained by the higher number of vehicles to be recharged at different paths. Another important observation is that the proposed deployment can cover up to 33.1% of the overall EV charging demand. More precisely, some paths are fullycovered (e.g. "A126" with 100%), some are partially-covered (e.g. "A10" and "N118" with 38% and 64% respectively), and some others are poorly-covered (e.g. "A6" and "N104" with only 3.8% and 8.3% respectively). Low coverage rates at some paths are due to the small number of charging locations and the limited electric capacity at these locations. As introduced earlier, the considered PV farm is located at the intersection of "A10" and "N104" which are poorlycovered paths. Thus, integrating its produced energy has the potential of enhancing the coverage rates at these paths as more chargers can be installed. To analyze this potential benefit, we quantify the amount of energy that can be produced at different scenarios and we calculate the demand coverage rate at each case. We then compare the obtained rates to the case where no PV production is considered (Table III). By averaging 10 different runs of the model, we observe that coverage rates can increase from 3.8% and 8.3% to 47.1% and 74.2% respectively during Summer where PV production is maximal. This positive impact can also be witnessed on the overall coverage rate with approximately 7% to 11% increase in Spring and Summer scenarios. As a result, locally-produced PV energy can help in enhancing the quality of EV charging service especially along paths where the demand is high and electric grid is limited.

C. Analyzing energy prices and production costs

We study three different investment indices to evaluate the profitability of integrating PV energy. First, Levelized Cost of Energy (LCOE) which represents the average net cost of electricity generation for the planned PV farm over its lifetime [START_REF] Khan | Review of solar photovoltaic and wind hybrid energy systems for sizing strategies optimization techniques and cost analysis methodologies[END_REF]. It can be calculated as the ratio between lifetime costs and energy production, as follows:

LCOE = n t=1 I t + M t + F t (1 + r) t n t=1 E t (1 + r) t (18)
Where I t , M t , and F t are the investment, maintenance, and fuel costs in year t, E t is the electricity generation in year t, and r is the discount rate. Second, Return on Investment (ROI) which is used to evaluate the efficiency of an investment by measuring its amount of return [START_REF] Ozcan | Project and cost-based evaluation of solar energy performance in three different geographical regions of Turkey: Investment analysis application[END_REF]. It is calculated by dividing project net income to its total cost, as follows:

ROI = P roject return (income -cost) P roject cost × 100 (19)
Third, Payback Period (PP) which represents the amount of time needed to recover the cost of an investment. It can be calculated by dividing overall project investment to its annual profit, as follows:

P P = Investment amount Annual prof it (20)
The project of installing solar panels at Paris-Saclay area requires an investment of 20MC. The investment costs (I t ) appear only in the first year as they represent the cost of installing solar panels and EV fast-chargers (estimated at 870KC based on the number of chargers proposed by the model). Maintenance costs (M t ) of a PV farm appear every 3 years and are estimated to 10% of the annual profit 5 . Fuel costs (F t ) are ignored in this case and the annual electricity generation (E t ) is estimated at 24 GWh (i.e. we assume that all generated PV energy is used for charging EVs). Discount rate (r) is fixed at 5%. In addition, project income is the difference between PV production cost (i.e. the calculated LCOE) and the price of selling this energy for charging EVs. In France, the price of charging an EV using a Tesla super-charger is 0.2 C/kWh. Thus, the cost of generating a kilowatt at the PV station must be less than 0.2C in order to have a positive income. PV farms are often evaluated over 20 years lifetime [START_REF] Ozcan | Project and cost-based evaluation of solar energy performance in three different geographical regions of Turkey: Investment analysis application[END_REF]. However, we calculate the introduced indices on 10, 15, and 20 years lifetime (Table IV). Results show that net cost of the generated PV energy (LCOE) is estimated at 0.11, 0.08, and 0.07 C/kWh over different lifetime intervals. These values can be seen as the minimum cost required for selling electricity at break-even prices so that project expenses can be recovered during its lifetime. Relatively, the planned investment brings a positive return of 260% over a 20 years lifetime. This means that every 100C of investment in the considered PV farm will be returned as 260C at the end of its lifetime. These positive ROI values justify the benefits of using the locallyproduced PV energy for supplying EV chargers. Regarding the refund time of investment (PP), results indicate the considered investment will be able to pay itself back in approximately 7 years, which is less than half of the project lifetime.

VI. CONCLUSION

In this paper, an optimization model for the deployment of EV fast-charging stations through a network of highways has been introduced. The model has been tested using a Cplex solver and a case study on Paris-Saclay area has been performed. After selecting optimal locations for charging stations, the results highlighted the benefits of integrating PV energy production on improving demand coverage rates. In addition, the economical benefits of this integration has been quantified (ROI = 260% over 20 years lifetime). We believe that this study helps in a better understanding of the potential use of green energy sources for satisfying the increasing charging demand for electric vehicles.

Fig. 1 :

 1 Fig. 1: Paris-Saclay -Major axes and recharging points

Fig. 3 :

 3 Fig. 3: Number of chargers per station

TABLE I :

 I Test parameters

	Parameter	Value	Parameter	Value
	c a	12kC	c b	15kC
	β a	36 vehicles	β b	24 trucks
	q a	50 kW	q b	250 kW

TABLE II :

 II Cloudiness index -Paris Orly (2010-2020)

		Winter	Spring	Summer	Autumn
	Fully-Sunny	16.9 %	27.2 %	35.6 %	22.9 %
	Partially-Cloudy	6.7 %	9.1 %	15.6 %	9.1 %
	Mostly-Cloudy	11.4 %	17.6 %	21.5 %	11.6 %
	Fully-Cloudy	65.1 %	46.1 %	27.3 %	56.2 %

TABLE III :

 III Demand coverage with PV production per season

		No PV	PV-Wint.	PV-Spr.	PV-Sum.	PV-Aut.
	Overall	33.1%	37.3%	40.9%	44.4%	39.1%
	A10	3.8%	19.9%	33.5%	47.1%	27.1%
	N104	8.3%	29.9%	53.3%	74.2%	39.8%

TABLE IV :

 IV PV energy -Cost analysis

		10 years	15 years	20 years
	Levelized Cost of Energy (LCOE)	0.11	0.08	0.07
	Return on Investment (ROI)	148%	224%	260%
	Payback Period (PP)	9.66	7.39	6.65

Mobility flows at Paris-Saclay area are provided by DiRIF (Road Direction in Ile-de-France region) indicating number of vehicles per hour on each path.

Data of charging stations and electric network specifications are provided by Paris-Saclay Agglomeration Community (CPS)

We use data provided by the Photo-voltaic Geographical Information System (PVGIS) to build the irradiation matrix for Paris-Saclay area

Weather data for Paris-Orly airport, including cloudiness index, are provided by Météo France

National Center of Photovoltaic Resources (CRPV)

ACKNOWLEDGMENT This research work is carried out within the PGMO research project at GeePs laboratory, CentraleSupélec. The work is in collaboration with the Institute of Research and Technology SystemX and the Agglomeration Community of Paris-Saclay.


Abood Mourad
email: abood.mourad@centralesupelec.fr

Martin Hennebel
email: martin.hennebel@centralesupelec.fr

The Optimal Deployment of Recharging Stations for Electric Vehicles Based on Mobility Flows and Electric Grid Specifications 1

Keywords: electric vehicles, recharging, optimization, mobility, electric grid

With the increasing interest in using electric vehicles (EVs) in future transportation systems, the need for deploying fast charging infrastructures becomes essential. In order to fulfil this need, it is important to anticipate EV future charging demands and requirements, and optimize their deployment. In this paper, we develop an optimization model to solve the problem of positioning fast-charging stations for EVs. The proposed model takes into account the different mobility flows and recharging demands as well as the constraints imposed by the available electric grid. In addition, the model considers the availability of alternative energy sources (i.e. photo-voltaic). For this purpose, we provide a mathematical formulation for the considered problem aiming at maximizing the covered recharging demand while respecting investment budget limits and the available capacities provided by the electric grid. Through a case study on Paris-Saclay area, we obtain the optimal locations for deploying EV charging stations as well as the number of chargers that need to be installed at each charging station. Results also highlight the benefits of integrating locally-produced photo-voltaic energy on EV recharging service.

I. INTRODUCTION

Electric vehicles (EVs) have witnessed a considerable development in recent years. By improving their battery capacities and recharging technologies, EVs can circulate for long distances and be recharged in short periods of time (e.g. a Tesla Roadster can travel up to 340 km while recharging its battery takes no more than 20 minutes using fast-charging technology [START_REF] Shareef | A review of the stageof-the-art charging technologies, placement methodologies, and impacts of electric vehicles[END_REF]). The need for deploying fast-charging infrastructures, especially on highways and high-speed roads, becomes essential. In order to fulfil this need and determine its required investments, it is important to anticipate EV future charging demands and requirements, and optimize their facility location taking into account the different mobility flows (i.e. small vehicles, lorry, etc.) and the existing electric grid [START_REF] Sun | Locating charging stations for electric vehicles[END_REF].

In this paper, after reviewing the related literature (section II), we develop an optimization model to solve the problem of deploying recharging stations for EVs on a highway network This research work is carried out as part of the PGMO research project at GeePs laboratory within CentraleSupélec engineering school.

(section III). The proposed model takes into account the different mobility flows and recharging demands as well as the constraints imposed by the available electric grid. In addition, the model considers the availability of a local solar farm and integrates its produced energy to the system. More precisely, the deployment of EV charging stations and the number of fast-chargers is based on the charging demand in the first place. This deployment also respects the restrictions of the electric grid as well as the availability of parking places at charging stations. For this purpose, we provide a mathematical formulation for the problem aiming at maximizing the covered recharging demand while respecting investment budget limits and the available capacities provided by the electric grid (section IV). The relying optimization problem corresponds to the well-known facility location problem where our facilities are the recharging stations [START_REF] Deb | Review of recent trends in charging infrastructure planning for electric vehicles[END_REF]. By solving this problem, we obtain the optimal locations for deploying EV charging stations as well as the number of chargers to be installed at each charging station (section V). Finally, in section VI, the key findings are highlighted and research perspectives are suggested.

II. BACKGROUND

Research on locating EV charging stations can be classified into three main categories; transportation, electric, and multidisciplinary approaches. Transportation approaches focus only on the transportation perspective (i.e. mobility flows and passengers demand) when designing EV charging networks [START_REF] Capar | An arc cover-path-cover formulation and strategic analysis of alternative-fuel station locations[END_REF]. On the other hand, electric approaches aim to locate EV charging stations in power systems such that their capacity and security requirements are satisfied and the investment costs needed to upgrade them are minimized [START_REF] Guo | Infrastructure planning for fast charging stations in a competitive market[END_REF]. As both transportation and electric perspectives are important, multidisciplinary approaches consider both types of constraints are considered [START_REF] He | A Optimal locations of U.S. fast charging stations for long-distance trip completion by battery electric vehicles[END_REF]. In addition, different types of chargers have been considered in the literature. These are: level-1 chargers (referred to as slow charging, 110V/15A), level-2 chargers (220V/15-30A), and level-3 chargers (referred to as fast-charging, 400-500V/50A). These chargers have different features and requirements, such as; power capacities, charging times, cabling and outlets, etc. Some studies considered only one type of chargers while other studies integrated different types of chargers. For example, in [START_REF] Csiszár | Urban public charging station locating method for electric vehicles based on land use approach[END_REF], the distribution of level-2 charging stations among territory segments is considered, based on the potential use of EVs and the different parking behaviors. In [START_REF] He | A Optimal locations of U.S. fast charging stations for long-distance trip completion by battery electric vehicles[END_REF], the focus is on selecting locations for fast recharging stations (level-3) through a highway network for long-distance trips in the US. In [START_REF] Sun | Locating charging stations for electric vehicles[END_REF], the deployment of both level-2 and level-3 chargers is considered to fulfil EV charging needs while respecting the specifications of the electric grid.

Regarding decision models, some studies suggested to use a Facility Location Model (FLM) [START_REF] Csiszár | Urban public charging station locating method for electric vehicles based on land use approach[END_REF], while others introduced a Flow Refueling Location Model (FRLM) as it provides a better coverage of mobility flows [START_REF] Capar | An arc cover-path-cover formulation and strategic analysis of alternative-fuel station locations[END_REF]. In addition, different objectives are assigned to these models, such as: minimizing investment costs [START_REF] Yi | Data-driven optimal charging decision making for connected and automated electric vehicles: A personal usage scenario[END_REF], maximizing covered mobility flows or the number recharged EVs [START_REF] Sun | Locating charging stations for electric vehicles[END_REF], or minimizing CO 2 emissions [START_REF] Liu | Data-driven intelligent location of public charging stations for electric vehicles[END_REF]. Once the decision model is built along with its objectives and constraints, most studies suggest solving it using a mathematical solver (e.g. Cplex, Gurobi, etc.) so that the optimal deployment of EV charging stations is obtained. However, some studies developed other methods for solving these models, such as: Branch-and-Bound (B&B) and Dynamic Programming (DA) approaches (see [START_REF] Zhang | PEV Fast-Charging Station Siting and Sizing on Coupled Transportation and Power Networks[END_REF] and [START_REF] Yi | Data-driven optimal charging decision making for connected and automated electric vehicles: A personal usage scenario[END_REF] respectively). In this paper, we consider a multidisciplinary approach for locating EV fast charging stations. We also consider two types of fast chargers: for small vehicles and heavy trucks. In addition, we introduce a facility location model that aims at maximizing the covered charging demand. We then solve the proposed model using Cplex mathematical solver and analyze the obtained results through a case study on Paris-Saclay area.

III. PROBLEM DESCRIPTION

We focus in this problem on finding the optimal deployment of EV recharging stations and the number of fast chargers to be installed through a network of highways (mobility axes). In this problem, we consider two types of fast chargers, one for charging small electric vehicles, and the other for charging heavy electric trucks. In addition, We consider a set of potential charging locations S ( nodes s0, s1, .. , s4 in Fig. 1). Every charging location s ∈ S is defined by a cost (c s ) indicating required investment to use this location as a charging station, and has a maximum electric capacity q s and a max/min number of fast chargers that can be installed for small vehicles as well as heavy trucks (max a s , min a s , max b s and min b s respectively). The investment cost (c s ) includes land cost and cabling expenses. In addition, we consider a set of coupling nodes N , where these nodes are used to build our mobility paths (nodes n0, n1, .. , n5 in Fig. 1). As such, we consider a set of paths P that link sequences of coupling nodes [START_REF] Yu | A Path Planning and Navigation Control System Design for Driverless Electric Bus[END_REF]. Every path p ∈ P is defined by its charging demands d a p , d b p , representing the number of EVs (i.e. vehicles and trucks respectively) to be recharged per day. The numbers of electric vehicles and trucks that can be recharged using a fast charger per day are defined as β a and β b respectively. Similarly, the amounts of electric power needed to recharge an electric vehicle or an electric truck using a fast charger are defined as q a and q b respectively. Moreover, installing a fast charger for electric vehicles or trucks requires additional costs (i.e. charger costs), these costs are defined as c a and c b respectively. Finally, we assume all electric vehicles to be identical, and thus, their recharging requirements to be the same (i.e. recharging any vehicle requires the same amount of time and energy). We consider the same assumption for electric trucks.

Hence, the choice of locating a recharging station at s and the number of fast chargers to be installed must be based on the recharging demand through the path where s is located. However, we can not install more chargers at a station than what the grid can accommodate. In addition, The number of chargers to be installed is also limited by the availability of places and parking slots at each recharging stations. As such, the aim is to build a model to optimize this deployment while the satisfied demand is maximized.

IV. MATHEMATICAL MODEL

In order to model the problem, we introduce on binary variable:

x s =
1 if a charging station is deployed at node s ∈ S 0 otherwise

In addition, we introduce a continuous variable y p ∈ [0, 1] representing the demand coverage rate on path p, and two integer variables, z a s and z b s , representing the number of fast chargers to be installed at charging location s ∈ S for electric vehicles and trucks respectively. The optimization model is thus formulated as follows:

M ax Z = p∈P ( d a p + d b p ) y p (1)
s.t.

s∈S c s x s + c a z a s + c b z b s ≤ C (2) p∈P ( d a p + d b p ) y p ≥ Q (3) s∈Sp β a z a s ≥ d a p ∀ p ∈ P (4) s∈Sp β b z b s ≥ d b p ∀ p ∈ P (5) min a s ≤ z a s ≤ max a s ∀ s ∈ S ( 6
)
min b s ≤ z b s ≤ max b s ∀ s ∈ S ( 7
)
q a z a s + q b z b s ≤ q s ∀ s ∈ S ( 8
)
if y p = 0 =⇒ z a s + z b s = 0 ∀ s ∈ S p , ∀ p ∈ P (9) if z a s + z b s > 0 =⇒ x s = 1 ∀ s ∈ S (10)
x s , y p ∈ {0, 1} ∀ s ∈ S, ∀ p ∈ P (11)

z a s , z b s ∈ N ∀ s ∈ S ( 12
)
d a p , d b p , β a , β b , q s , q a , q b ∈ N ∀ s ∈ S, ∀ p ∈ P (13) min a s , max a s , min b s , max b s ∈ N ∀ s ∈ S (14) c s , c a , c b ∈ R ∀ s ∈ S (15)
The objective function (1) maximizes the total covered charging demand based on the covered paths. Regarding model constraints, constraint (2) ensures that the sum of location costs and chargers installation costs does not exceed total budget limit. Constraint (3) states that a minimum of the overall charging demand must be satisfied. Constraints (4 and 5) ensure the satisfaction of charging demands for vehicles and trucks at each path. Constraints ( 6) and [START_REF] Csiszár | Urban public charging station locating method for electric vehicles based on land use approach[END_REF] state that the number of fast chargers (for vehicles and trucks) to be installed must be within the specified limits at each charging location. Constraints (8) ensure that the electric power required to operate the installed chargers does not exceed the available electric capacity at the charging locations. Constraints ( 9) and ( 10) are used to link the variables introduced earlier in the model. Finally, constraints [START_REF] Yu | A Path Planning and Navigation Control System Design for Driverless Electric Bus[END_REF] to (15) define domains for the different elements of the model.

V. COMPUTATIONAL RESULTS

We present some results obtained by testing the proposed model using Cplex solver on a case study for Paris-Saclay area (section V-A). We also consider the availability of a photo-voltaic farm and highlight the benefits of integrating its generated power on EV recharging rates (section V-B).

A. Paris-Saclay case study

The interest in Paris-Saclay area is that it contains residential and business zones besides many transit axes that pass through it (e.g. A10, A6, N20 in Fig. 2). Many of these axes are not just used by personal and small vehicles, but also by heavy trucks carrying goods to nearby areas. Thus, these flows include local trips within the area (short-distance) as well as inter-city and international transit flows (long-distance). As introduced earlier, we need to define a set of coupling nodes, a set of potential charging locations, and a set of mobility paths. Coupling nodes are defined by taking the intersections of major mobility axes in the area. Paths are then defined by sequences of these nodes. For example, in Fig. 3, the path "N118" is defined by the sequence of nodes (2, 3, 13, 4, 10). We thus define 9 different paths representing EV flows and their recharging demands (Fig. 3). The actual number of electric vehicles and trucks to be recharged is then defined by taking 5% of the overall number of vehicles circulating through each path per day 1 . This percentage represents EV sales share of the overall vehicle market in France in 2020 [START_REF] Funke | How much charging infrastructure do electric vehicles need? A review of the evidence and international comparison[END_REF]. Regarding charging locations, we consider the actual and projected charging stations, along with the actual service stations at Paris-Saclay area. Costs, electric capacities, and the maximum number of chargers that can be installed at each potential location are fixed based on their real data 2 . Charging points are then associated to paths so that the model can decide which points to use and how many chargers to install based on their recharging demands (e.g. charging points: s 13 , s 28 and s 62 are associated to path "N118"). We also assume that a fast charger requires 50 kW (20 minutes) to recharge an electric vehicle. In addition, fast chargers require 250 kW (30 minutes) to recharge an electric truck. We thus assume electric vehicles to be homogeneous in terms of battery and recharging time (same assumption for electric trucks). Finally, the costs of installing a fast charger for vehicles and trucks are estimated at 12k and 15k euros, respectively. Test parameters are summarized in Table I. Results of testing the proposed model on Paris-Saclay data are presented in Fig. 4. The number of fast chargers to be installed at each selected charging point is given in parenthesis (vehicle chargers, truck chargers). For example, the model suggests installing 6 vehicle chargers and 2 truck chargers at charging point s 13 . We observe that the number of vehicle chargers is higher than that for trucks at all selected charging points. This is because the number of vehicles to be recharged is relatively higher at all defined paths, and thus requires more chargers. Results also indicate that the proposed solution can cover up to 33.1% of the overall charging demand. In the details, some paths are fully-covered (e.g. "A126" with 100% demand coverage), some are partially-covered (e.g. "A10" with 38% demand coverage), and others are poorly-covered (e.g. "A6" and "N104" with only 3.8% and 8.3% respectively). Low coverage rates can be explained by the small number of charging points that are associated to these paths and by the limited electric capacity at these points. Furthermore, we test the proposed model with different charging powers. We thus increase the charging power of chargers with up to 1.5, 2, and 4 times and we analyze its impact on covered charging demand. We observe that as chargers become more powerful, the demand coverage percentage increases (up to 40.9%, 52.5%, and 71.1% respectively, Fig. 5). This highlights the importance of increasing the capacity of these chargers and thus integrating new sources of energy (e.g. photo-voltaic power) to accommodate this increase. Integrating green-energy sources can potentially increase electric network capacity while reducing its reliance on other polluting sources. For this purpose, a large photo-voltaic (PV) farm is to be installed at Paris-Saclay area (at point s 97 , next to the intersection of "A10" and "N104" highways, Fig. 2) with 76500 solar panels and up to 24 GWh annual power production. This farm can allow installing more EV chargers and increasing their recharging capacities. The generated power of a photo-voltaic farm at instant t can be calculated as follows:

P (t) = ( 1 -µ(t) ) × I(t) × δ × η (16)
Where µ(t) is the cloudiness index at instant t (%), I(t) is the irradiation at instant t (W/m 2 ), δ is the surface of solar panels (m 2 ), and η is the efficiency that corresponds to the electric quantity produced as a percentage of the received solar power. This generated power highly depends on irradiation and cloudiness index as they differ during seasons and day hours (e.g. PV production is maximal in a sunny day during Summer at noon). The actual values of irradiation at different seasons and day hours are fixed, and thus, known in advance 3 .

Unlike the irradiation, the cloudiness index (µ(t)) can not be fixed in advance as it highly depends on weather conditions (i.e. µ(t) is stochastic). We thus need to model this uncertainty using a set of scenarios and calculate their probability distribution. To overcome this difficulty, we consider 4 different day profiles: (1) Fully-Sunny, where µ(t) is between 0% & 25%, (2) Partially-Cloudy, where µ(t) is between 25% & 50%, (3) Mostly-Cloudy, where µ(t) is between 50% & 75%, and (4) Fully-Cloudy, where µ(t) is between 75% & 100%. In addition, we divide the day into 8 time periods (i.e. (12AM,3AM), (3AM,6AM), .. , (9PM,12AM)). These day periods help in capturing different mobility patterns (e.g. period (6AM-9AM) is a peak period when people commute, etc.). We also consider the four seasons (e.g. the probability of having a fully-sunny day is higher in Summer than in winter, Table II). As a result, we build our set of scenarios, where every scenario is defined by a day-profile, a day-period, and a season. In order to calculate their probabilities, we use weather measurements of the last 10 years and we cluster them according to day profiles, periods, and seasons using K-Means approach 4 . The resulting probability distribution represents an input to our model. In order to integrate PV production, an additional set of constraints need to be added to the mathematical model:

q a z a v + q b z b v ≤ P v ∀ v ∈ V (17)
Constraints (17) state that the energy required to operate the additional EV chargers must not exceed the amount of PV energy produced at PV farm v.

Fig. 6: PV production impact on demand coverage per season

To analyze the benefits of integrating PV energy, we quantify the amount of energy produced at different seasons and calculate the percentage of charging demand covered at each case. We then compare these rates to the original one where no PV production was considered. We consider two different demand flows: at 9AM (when vehicle and truck flows are maximal), and at 12AM (when solar irradiation and PV production are maximal) (Fig. 6). For both flows, and by averaging 10 different runs of the model, results indicate a positive effect of PV production on the overall demand coverage. This effect is most remarkable in Spring and Summer with approximately 7% to 10% increase on demand coverage. As the considered PV farm is located at the intersection of "A10" and "N104" highways, the demand coverage increases from 3.8% and 8.3% to 28.9% and 42.6% at the morning peak (9AM) when PV production is included. Locally-produced PV energy can thus help in enhancing the quality of EV charging service while respecting the environmental aspects.

VI. CONCLUSIONS

In this paper, an optimization model for deploying EV recharging stations through a network of highways has been introduced. The model has been tested using a Cplex solver and a case study on Paris-Saclay area has been performed. The obtained results has indicated the selected locations for EV recharging stations and highlighted the importance of improving chargers capacities and integrating PV production. One interesting perspective of this research is to consider the different energy production costs as they can change energy flows in the smart grid. We thus believe that this study helps in a better understanding of the potential deployment of EV recharging stations in real-life applications, and promoting more research towards studying this rising trend.

Fig. 1 :

 1 Fig. 1: Graph example -nodes and paths

Fig. 2 :Fig. 3 :

 23 Fig. 2: Paris-Saclay -Major axes and recharging points

Fig. 4 :

 4 Fig. 4: Number of chargers per stations

Fig. 5 :

 5 Fig. 5: Demand coverage with different charging powers

TABLE I :

 I Test parameters

	Parameter	Value	Parameter	Value
	c a	12k euros	c b	15k euros
	β a	36 vehicles	β b	24 trucks
	q a	50kW	q b	250kW

TABLE II :

 II Cloudiness index -Paris Orly (2010-2020)

		Winter	Spring	Summer	Autumn
	Fully-Sunny	16.9 %	27.2 %	35.6 %	22.9 %
	Partially-Cloudy	6.7 %	9.1 %	15.6 %	9.1 %
	Mostly-Cloudy	11.4 %	17.6 %	21.5 %	11.6 %
	Fully-Cloudy	65.1 %	46.1 %	27.3 %	56.2 %

Traffic data at Paris-Saclay area are provided by DiRIF (Road Direction in Ile-de-France region)

Data of recharging stations and electric network specifications are provided by Paris-Saclay Agglomeration Community (CAPS)

We use data provided by the Photo-voltaic Geographical Information System (PVGIS) to build the irradiation matrix for Paris-Saclay area

Weather data for Paris-Orly airport, including cloudiness index, are provided by Météo France

ACKNOWLEDGMENT This research work is carried out within the PGMO research project at GeePs laboratory, CentraleSupélec. The work is in collaboration with the Institute of Research and Technology SystemX and the Agglomeration Community of Paris-Saclay.