Vehicle-to-Grid Coordination via Mean Field Game

Abstract

The electrification of the transportation sector is urgently needed to combat global warming. However, the rapidly increasing number of electric vehicles (EVs) on the road is threatening the reliable operation of the power grid. Specifically, the simultaneous charging of many EVs often creates a sudden increase in demand, which needs to be handled by scarce flexibility in the system. Despite this, EVs can become part of the scarce flexibility through vehicle-to-grid (V2G) services if well-coordinated. This letter casts the EV coordination problem in the game-theoretic framework to study the equilibrium charging strategy. Specifically, we assume each EV aims to minimize the charging cost yet maximize the benefit of charging. Both terms couple the EVs’ decisions, yielding the EV coordination game (EVCG). Note that the detailed charging behaviors of a large population of EVs can be rather hard to analyze accurately. We resort to the notion of the mean field game (MFG). By introducing the mean field term, we can analyze the MFG corresponding to EVCG. Specifically, we prove that the MFG admits a Nash equilibrium, which is the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> -Nash equilibrium of EVCG. Besides showing the existence of the equilibrium, we propose an efficient algorithm to enable the distributed control based on the equilibrium strategy.