A stochastic approximation method for price-based assignment of Electric Vehicles to Charging Stations

This paper considers a setting where a number of users want to drive their Electric Vehicles (EVs) to a certain geographical area, park them in a Charging Station (CS), and receive them fully charged upon departure. Each CS faces a number of constraints related to the power that it can provide. In order to serve its EVs, each CS solves an optimization problem to derive the charging schedule, so that no constraints are violated and the energy needs of the parked EVs are met. The motivating problem is that centrally located CSs become congested and users that arrive later can no longer be served. In order to tackle this problem we propose a method for the stochastic estimation of Charging Stations' shadow prices based on a dual decomposition method applied to offline simulations. Prices are determined so as to serve as many EVs as possible and minimize the social cost while satisfying their constraints and energy needs. The algorithm's performance was evaluated under a number of possible online scenarios and compared to a benchmark solution in terms of competitive ratio and number of EVs served.