Incentive compatible online pricing of customer directrix load-based demand response for load aggregators

Zhang, Yi, Fan, Shuai, Meng, Yan, Huang, Renke, Li, Zuyi, Wu, Jianzhong ORCID: https://orcid.org/0000-0001-7928-3602 and He, Guangyu 2026. Incentive compatible online pricing of customer directrix load-based demand response for load aggregators. IEEE Transactions on Smart Grid 10.1109/tsg.2026.3703143

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Abstract

In demand response (DR) programs, load aggregators (LAs) coordinate DR customers to provide flexibility support for the smart grid. However, existing pricing mechanisms often struggle to simultaneously achieve incentive compatibility and operational controllability in retail-side DR. To address this challenge, this paper proposes an incentive compatible online pricing strategy for customer directrix load (CDL)-based DR of LAs. Unlike traditional price-based DR schemes, the proposed approach leverages CDL, which inherently enhances controllability by serving as both the guiding signal and the performance evaluation metric. Within the CDL framework, a DR customer response model and an LA centralized optimization model are established. Under a general discomfort function setting, the centralized response is characterized by a one-dimensional fixed-point equation, based on which a customized incentive compatible pricing strategy is derived to align individual customer responses with the LA’s desired response curve. Furthermore, the widely used quadratic discomfort model is studied as an analytically tractable special case, leading to closed-form response and pricing expressions. An online learning algorithm is then proposed to enable LAs to learn the unobservable discomfort parameters of DR customers from observable response decisions, thereby reducing information exposure and enhancing practical implementation performance. The proposed algorithm is theoretically shown to achieve logarithmic regret with respect to the operating cycle, and a problem-level regret lower bound is further established to show that the minimax cumulative regret of the underlying CDL-based online pricing problem is also logarithmic. Simulation results based on real-world data demonstrate the validity and effectiveness of the proposed method.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Schools > Engineering
Additional Information:	License information from Publisher: LICENSE 1: URL: https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html, Start Date: 2026-01-01
Publisher:	Institute of Electrical and Electronics Engineers
ISSN:	1949-3053
Last Modified:	03 Jul 2026 10:45
URI:	https://orca.cardiff.ac.uk/id/eprint/187895

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