An Electric Vehicle Load Management Application of the Mixed Strategist Dynamics and the Maximum Entropy Principle

An application of an evolutionary game dynamics called mixed strategist dynamics (MSD), for the decentralized load scheduling of plug-in electric vehicles (PEVs), is proposed in this paper. Following an analogy with the maximum entropy principle (MEP) for tuning parameters of discrete probability distributions, entropy of the total load distribution and the local load distributions are considered as objectives of the scheduling approach, and a tradeoff among them is defined by the electric vehicle owners' convenience. While entropy maximization for the local load distributions contributes to preserve the batteries' states of health, entropy maximization for the total load distribution reduces the undesirable peak effects over the transformer loading. The problem is formulated such that final states of charge are assured depending on time constraints defined by the owners. Furthermore, mixed strategies in the MSD are defined such that they represent the vertices of the convex set of feasible load profiles which results from the constraints imposed by owners and chargers. The synergy of several PEVs is modeled as an application of the MSD in a multipopulation scenario, where the interaction among populations follows another evolutionary game dynamics called best reply (BR) dynamics. The performance of the proposed approach is tested on real data measured on a distribution transformer from the SOREA utility grid company in the region of Savoie, France.