Electrical vehicles in the smart grid: A mean field game analysis

Romain Couillet, Samir M. Perlaza, Hamidou Tembine, Mérouane Debbah

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number6194233
Pages (from-to)1086-1096
Number of pages11
JournalIEEE Journal on Selected Areas in Communications
Issue number6
StatePublished - 2012


  • Electrical Vehicles
  • Game Theory
  • Mean Field Equilibrium
  • Smart Grids
  • large populations

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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