Economics of Electric Vehicle Charging: A Game Theoretic Approach

TLDR

The study investigates grid‑to‑vehicle energy exchange between a smart grid and plug‑in electric vehicle groups using a noncooperative Stackelberg game and proposes a distributed algorithm to achieve equilibrium. The authors model the interaction as a noncooperative Stackelberg game where the smart grid sets a price to maximize revenue while ensuring participation, and PEVGs choose charging strategies to balance benefit and cost, with a distributed algorithm and a time‑varying extension. The game admits a socially optimal Stackelberg equilibrium, and simulations show that the distributed algorithm successfully drives the smart grid and PEVGs to this equilibrium.

Abstract

In this paper, the problem of grid-to-vehicle energy exchange between a smart grid and plug-in electric vehicle groups (PEVGs) is studied using a noncooperative Stackelberg game. In this game, on the one hand, the smart grid, which acts as a leader, needs to decide on its price so as to optimize its revenue while ensuring the PEVGs' participation. On the other hand, the PEVGs, which act as followers, need to decide on their charging strategies so as to optimize a tradeoff between the benefit from battery charging and the associated cost. Using variational inequalities, it is shown that the proposed game possesses a socially optimal Stackelberg equilibrium in which the grid optimizes its price while the PEVGs choose their equilibrium strategies. A distributed algorithm that enables the PEVGs and the smart grid to reach this equilibrium is proposed and assessed by extensive simulations. Further, the model is extended to a time-varying case that can incorporate and handle slowly varying environments.