A Distributed Online Pricing Strategy for Demand Response Programs

TL;DR

This paper proposes a distributed online pricing algorithm for demand response programs that learns consumer cost functions in real-time, minimizing utility costs under uncertainty with proven logarithmic regret.

Contribution

It introduces a joint online learning and pricing method that estimates consumer responses and adapts prices without multiple communication rounds, improving practical implementation.

Findings

Achieves logarithmic regret in the operating horizon.

Uses linear regression for consumer response estimation.

Simulation confirms rapid decay of performance gap.

Abstract

We study a demand response problem from utility (also referred to as operator)'s perspective with realistic settings, in which the utility faces uncertainty and limited communication. Specifically, the utility does not know the cost function of consumers and cannot have multiple rounds of information exchange with consumers. We formulate an optimization problem for the utility to minimize its operational cost considering time-varying demand response targets and responses of consumers. We develop a joint online learning and pricing algorithm. In each time slot, the utility sends out a price signal to all consumers and estimates the cost functions of consumers based on their noisy responses. We measure the performance of our algorithm using regret analysis and show that our online algorithm achieves logarithmic regret with respect to the operating horizon. In addition, our algorithm employs linear regression to estimate the aggregate response of consumers, making it easy to implement in practice. Simulation experiments validate the theoretic results and show that the performance gap between our algorithm and the offline optimality decays quickly.