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

Game theory has proven to be a valuable tool to study strategic electricity consumers enrolled in a demand response (DR) program. Among the different billing mechanisms proposed, the hourly billing model is of special interest as an intuitive and fair mechanism. We focus on this model and answer to several theoretical and practical questions. First, we prove the uniqueness of the consumption profile corresponding to the Nash equilibrium and we analyze its efficiency by providing a bound on the price of anarchy. Next, we address the computational issue of this equilibrium profile by providing results on the convergence rates of two decentralized algorithms to compute the equilibrium: the cycling best response dynamics and a projected gradient descent method. Last, we simulate this DR framework in a stochastic environment where the parameters depend on forecasts. Numerically, we show the relevance of an online DR procedure which reduces the impact of inaccurate forecasts in comparison to a standard offline procedure.