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

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.