A Game Theoretic Approach for EV Recharge Pricing Under Competition: Analysis and Simulation

Electric Vehicles (EV) are a key element of future smart cities, providing a clean transportation technology and potential benefits for the grid. Nevertheless, limited vehicle autonomy and lack of charging stations are preventing EVs to be broadly accepted. To address this challenge, French GreenFeed project is working to develop an interoperable and universal architecture to allow EV recharge across multiple cities and countries. In this work, we consider such architecture and focus on price setting by its main actors. We show how a Stackelberg game models the market, and we study the outcomes when users choose a recharge station according to objective and subjective parameters. Simulation shows the different actors' revenues, and the social and user welfare for different scenarios. I. INTRODUCTION Electric Vehicles (EV) and Hybrid Electric Vehicles are expected to dominate the automobile industry in the near future [12]. They present the great advantage of being environmentally friendly, dramatically reducing greenhouse gases emissions with respect to fossil-fuel vehicles [8], while almost eliminating noise pollution. Moreover, EVs are nowadays part of a whole evolutionary energy context. Energy transition is taking place in several countries in order to introduce distributed and renewable energy resources into the grid. Electricity market is also changing into a deregulated market, where time-variant tariffs are introduced, making demand side management solutions possible. In this context, EVs become also attractive because of the ancillary services they can offer to the grid. They can provide flexibility, by the possibility to shift the battery recharge. They can also provide the grid with the energy stored in their batteries through Vehicle to Grid (V2G) technologies, when energy production is lower than demand, and can store energy when supply exceeds demand. In spite of the aforementioned advantages, EVs are facing some barriers to their large adoption, such as the so-called range anxiety. This term refers to the fear that the vehicle will not have enough range to reach the destination. With state-of-the-art batteries, vehicle's autonomy is on the average 50 km and it can reach up to 160 km with large batteries [10]. However, these figures may dramatically vary according to driving manner and particular circumstances (e.g. temperature, weight, etc.). In this context, it is of paramount importance to have ubiquitous, easy and fast means to get the recharge service and to pay for it, regardless the EV model, without problems of interoperability or users' contract. In this sense, industry and research institutions, and standardisation bodies are carrying out efforts to develop electromobility and charging solutions, such as GreenFeed [3], green eMotion [2], standard ISO 15118 [5], the French initiative for EV roaming Gireve [1], or the platform Hubject [4]. Ongoing French project GreenFeed, aims to develop interoperable recharge solutions to foster EVs penetration. The project has defined an architecture, following the standard ISO 15118, that has the following main actors: EV Users (EVU), e-Mobility Provider (EMO), Charging Point Operator (CPO) and e-Mobility Operator Clearing House (EMOCH), as shown in Fig. 1a. Such architecture structures a supply chain market for EV recharge. This work is part of the outcome of GreenFeed project, and focuses on the problem of setting EV recharge price at the different levels of the supply chain-one of the questions raised by the project. We assume variable recharge costs faced by the mobility providers (EMOs), but a fixed recharge price paid by the final client (EVU). Fixed prices are attractive from the point of view of the EVU, who is then shielded from electricity price volatility. We model the situation as a Stackelberg game, where CPOs play first, setting a price to be paid by the EMO, and where the EMO follows, setting a price for the recharge, which is paid by the final client. In addition, we take into account clients decision about where to get their EV recharged, considering subjective and objective parameters about the CPOs. Our results show interesting insights which could help CPOs and EMOs to set prices, and regulators to evaluate the market structure induced by GreenFeed's architecture. Simulation allow us to show in several scenarios the existence of a Nash equilibrium. The reminder of this paper is organised as follows. Section II reviews related work. In Section III we introduce the GreenFeed architecture, formally explain the market structure and the problem under study. We then formalise the problem as a Stackelberg