Optimal Mechanisms for Demand Response: An Indifference Set Approach
Mohammad Mehrabi, Omer Karaduman, Stefan Wager
TL;DR
This paper addresses demand response when consumers employ HEMS constrained by indifference sets $\mathbf{R}_i$ to meet needs while responding to price signals. It develops a mean-field analysis showing that price-based demand response is asymptotically optimal as $n\to\infty$, with the mean-field objective $H(z)=\mathbb{E}[h(z; \mathbf{R})]$ and optimal price $p^*=\lambda z^*$ for $z^*\in \arg\max_{z\in\mathcal{P}} \{H(z)-z\cdot q_0\}$. A practical learning algorithm estimates $\nabla H$ via $\nabla \widehat{H}_n(z)=\frac{1}{n}\sum_i q_i(z)$ and updates prices accordingly, enabling gradient-based optimization using only market data. A Phoenix OpenDSS case demonstrates that dynamic pricing can flatten the net-demand duck curve while preserving grid stability, with measurable cost reductions across different risk functions $\sigma_s$. The framework offers a scalable, privacy-preserving path to demand response in large markets and suggests future work on endogeneity of preferences and general-equilibrium implications.
Abstract
The time at which renewable (e.g., solar or wind) energy resources produce electricity cannot generally be controlled. In many settings, however, consumers have some flexibility in their energy consumption needs, and there is growing interest in demand-response programs that leverage this flexibility to shift energy consumption to better match renewable production -- thus enabling more efficient utilization of these resources. We study optimal demand response in a setting where consumers use home energy management systems (HEMS) to autonomously adjust their electricity consumption. Our core assumption is that HEMS operationalize flexibility by querying the consumer for their preferences and computing the ``indifference set'' of all energy consumption profiles that can be used to satisfy these preferences. Then, given an indifference set, HEMS can respond to grid signals while guaranteeing user-defined comfort and functionality; e.g., if a consumer sets a temperature range, a HEMS can precool and preheat to align with peak renewable production, thus improving efficiency without sacrificing comfort. We show that while price-based mechanisms are not generally optimal for demand response, they become asymptotically optimal in large markets under a mean-field limit. Furthermore, we show that optimal dynamic prices can be efficiently computed in large markets by only querying HEMS about their planned consumption under different price signals. Using an OpenDSS-powered grid simulation for Phoenix, Arizona, we demonstrate that our approach enables meaningful demand response without creating grid instability.