Demand Response Under Stochastic, Price-Dependent User Behavior

TL;DR

This paper develops a stochastic, feedback-based pricing strategy for residential demand response that accounts for customer response uncertainty, demonstrating its stability and near-optimality through theoretical analysis and simulations.

Contribution

It introduces a novel stochastic framework for demand response with decision-dependent customer response models and proposes feedback-based pricing strategies to handle uncertainty.

Findings

Proves stability and near-optimality of the proposed strategies.

Validates effectiveness through numerical simulations.

Extends demand response models to stochastic, decision-dependent settings.

Abstract

This paper focuses on price-based residential demand response implemented through dynamic adjustments of electricity prices during DR events. It extends existing DR models to a stochastic framework in which customer response is represented by price-dependent random variables, leveraging models and tools from the theory of stochastic optimization with decision-dependent distributions. The inherent epistemic uncertainty in the customers' responses renders open-loop, model-based DR strategies impractical. To address this challenge, the paper proposes to employ stochastic, feedback-based pricing strategies to compensate for estimation errors and uncertainty in customer response. The paper then establishes theoretical results demonstrating the stability and near-optimality of the proposed approach and validates its effectiveness through numerical simulations.