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An important part of the Smart Grid literature on residential Demand Responsedeals with game-theoretic consumption models. Among those papers, the hourlybilling model is of special interest as an intuitive and fair mechanism. Wefocus on this model and answer to several theoretical and practical questions.First, we prove the uniqueness of the consumption profile corresponding to theNash equilibrium, and we analyze its efficiency by providing a bound on thePrice of Anarchy. Next, we address the computational issue of the equilibriumprofile by providing two algorithms: the cycling best response dynamics and aprojected gradient descent method, and by giving an upper bound on theirconvergence rate to the equilibrium. Last, we simulate this demand responseframework in a stochastic environment where the parameters depend on forecasts.We show numerically the relevance of an online demand response procedure, whichreduces the impact of inaccurate forecasts.

Analysis and Implementation of a Hourly Billing Mechanism for Demand Response Management