Multi-Resolution Large Population Stochastic Differential Games and Their Application to Demand Response Management in the Smart Grid

Quanyan Zhu, Tamer Başar

Research output: Contribution to journalArticle

Abstract

Dynamic demand response (DR) management is becoming an integral part of power system and market operational practice. Motivated by the smart grid DR management problem, we propose a multi-resolution stochastic differential game-theoretic framework to model the players' intra-group and inter-group interactions in a large population regime. We study the game in both risk-neutral and risk-sensitive settings, and provide closed-form solutions for symmetric mean-field responses in the case of homogeneous group populations, and characterize the symmetric mean-field Nash equilibrium using the Hamilton-Jacobi-Bellman (HJB) equation together with the Fokker-Planck-Kolmogorov (FPK) equation. Finally, we apply the framework to the smart grid DR management problem and illustrate with a numerical example.

Original languageEnglish (US)
Pages (from-to)68-88
Number of pages21
JournalDynamic Games and Applications
Volume3
Issue number1
DOIs
StatePublished - Feb 28 2013

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Keywords

  • Demand response
  • Large-population games
  • Mean-field Nash equilibrium
  • Multi-resolution games
  • Power grid
  • Smart grid
  • Stochastic differential games

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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