Electrical Vehicles in the Smart Grid: A Mean Field Game Analysis

TL;DR

This paper models the competitive behavior of electric and hybrid vehicles in a smart grid using mean field game theory, analyzing how pricing strategies can reduce peak electricity demand.

Contribution

It introduces a novel mean field game framework for electric vehicle competition in the smart grid, providing differential equations for equilibrium analysis.

Findings

Pricing strategies can significantly reduce peak electricity demand

The model accurately predicts electricity price evolution

Simulations demonstrate the effectiveness of demand management

Abstract

In this article, we investigate the competitive interaction between electrical vehicles or hybrid oil-electricity vehicles in a Cournot market consisting of electricity transactions to or from an underlying electricity distribution network. We provide a mean field game formulation for this competition, and introduce the set of fundamental differential equations ruling the behavior of the vehicles at the feedback Nash equilibrium, referred here to as the mean field equilibrium. This framework allows for a consistent analysis of the evolution of the price of electricity as well as of the instantaneous electricity demand in the power grid. Simulations precisely quantify those parameters and suggest that significant reduction of the daily electricity peak demand can be achieved by appropriate electricity pricing.