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

TL;DR

This paper investigates an hourly billing demand response model in smart grids, proving equilibrium uniqueness, analyzing efficiency, proposing algorithms for equilibrium computation, and demonstrating the benefits of online procedures under forecast uncertainties.

Contribution

It provides the first theoretical proof of equilibrium uniqueness and efficiency bounds for hourly billing demand response models, along with practical algorithms and simulations.

Findings

Unique consumption profile at Nash equilibrium

Bounded Price of Anarchy indicating efficiency

Online demand response reduces forecast errors

Abstract

An important part of the Smart Grid literature on residential Demand Response deals with game-theoretic consumption models. Among those papers, 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 the equilibrium profile by providing two algorithms: the cycling best response dynamics and a projected gradient descent method, and by giving an upper bound on their convergence rate to the equilibrium. Last, we simulate this demand response framework in a stochastic environment where the parameters depend on forecasts. We show numerically the relevance of an online demand response procedure, which reduces the impact of inaccurate forecasts.