A stochastic optimization approach to the aggregation of electric vehicles for the provision of ancillary services

We address the problem of the optimal management of an aggregate of electric vehicles (EVs) for the provision of ancillary services to the grid, by means of a bidirectional vehicle-to-grid (V2G) infrastructure. We consider the case of a charging point operator that acts as an aggregator and has to optimally choose the charge/discharge power profile of each vehicle so as to maximize its profits, while satisfying technical constraints and final user constraints (the latter expressed as a minimum desired charge for motion). In this setting the aggregator can operate on both an energy market and an ancillary services market: in the latter, the deployed power depends on a signal received by the aggregator after the market closing time; this signal can be discrete or continuous. We formulate the problem via stochastic programming, under the assumptions of optimal bidding strategy and known vehicle arrivals and departures. We obtain, via mixed-integer linear programming, an exact robust counterpart of the constraints and an expected value cost function, which is exact if the signal is discrete. If the signal is continuous, the cost function varies depending on the probability distribution of the signal and could require an approximation to obtain a computationally tractable formulation. We then show that, in the case of uniform probability, an efficient formulation can be obtained by introducing a negligible approximation of the cost function; a numerical example shows the validity of the approach. Copyright (C) 2020 The Authors.