Towards a comprehensive framework for V2G optimal operation in presence of uncertainty

As the global fleet of Electric Vehicles keeps increasing in number, the Vehicle To Grid (V2G) paradigm is gaining more and more attention. From the grid point of view an aggregate of electric vehicles can act as a flexible load, thus able to provide balancing services. The problem of computing the optimal day-ahead charging schedule for all vehicles in the fleet is a challenging one, especially because it is affected by many sources of uncertainty. In this paper we consider the uncertainty deriving from arrival and departure times, arrival energy and services market outcomes. We propose a general optimization framework to deal with the day ahead planning that encompasses different kind of use-cases. We adopt a robust paradigm to enforce the constraints and an expectation paradigm for the cost function. For all constraints and cost terms we propose an exact formulation or a very tight approximation, even in the case of piece-wise linear battery dynamics. Numerical results corroborates the theoretical findings.