Charging Strategies of EV Aggregator Under Renewable Generation and Congestion: A Normalized Nash Equilibrium Approach

This paper proposes a two-stage charging scheme for the electric vehicle aggregator to minimize the charging cost of each individual participator, while taking uncertain renewable generation and aggregator's capacity into account. The charging problem is formulated as a generalized Nash game with shared global constraints, where the congestion constraint and renewable energy utility constraint that couple all participators' strategies serve as the global constraints and should be satisfied for all possible outcomes of uncertainty. The normalized Nash equilibrium (NNE) is used to characterize a fair charging decision among the participants. It is shown that when the commission fee charged by the aggregator is a convex function and proportionally shared by the consumers, the NNE can be efficiently computed from a particular convex optimization problem, and is noninferior if the commission fee function is separable in players. An adaptive scenario generation algorithm is developed to solve the proposed model in a tractable manner. A dynamic real-time bidding scheme is suggested for practical implementations in a receding horizon fashion, accounting for tackling various kinds of uncertainties. Numerical results are presented to corroborate the proposed technique.