An adaptive modeling method with optimal order selection for thermostatically controlled loads

Song, Xiao-Rui, Bao, Yu-Qing, Yao, Shuai ORCID: https://orcid.org/0000-0002-7202-7961 and Hu, Wen-Yan 2026. An adaptive modeling method with optimal order selection for thermostatically controlled loads. Applied Energy 423 , 128349. 10.1016/j.apenergy.2026.128349

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Abstract

With the increasing penetration of renewable power generation and growing need for load-side regulation, demand-side resources represented by thermostatically controlled loads (TCLs), including air-conditioners, refrigerators, and heat pumps, are becoming increasingly important for enhancing power system flexibility. Accurate modeling of TCLs is a critical prerequisite to achieve their optimal control. However, existing modeling approaches rely heavily on detailed physical structural information, with model order selection largely based on engineering experience, which complicates the assurance of model accuracy. To address these limitations, this paper proposes a generic modeling framework that is independent of physical structural information and features adaptive model order selection. Firstly, the thermodynamic behavior of TCLs is represented using a unified Nonlinear Autoregressive with Exogenous Inputs (NARX) model to capture input-output characteristics. This formulation does not require explicit knowledge of the system's spatial or physical structure. Secondly, a candidate set of model orders is constructed, and an adaptive forgetting-factor recursive least squares algorithm is employed to identify parameters for all order combinations in the set, yielding a set of order-parameter candidates. Finally, the optimal model order and corresponding parameters are determined based on Pareto optimization by balancing prediction accuracy, computational efficiency, and model complexity. Case study results demonstrate that the proposed modeling method effectively overcomes the limitations associated with reliance on physical structural information and fixed model order selection. Compared with several existing physical and data-driven models, i.e., Autoregressive with Exogenous Inputs (ARX), the Second-Order Equivalent Thermal Parameter model (2R2C), and Support Vector Regression (SVR), the proposed approach achieves the highest prediction accuracy while maintaining moderate computation cost.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Engineering
Additional Information:	RRS applied.
Publisher:	Elsevier
ISSN:	0306-2619
Date of First Compliant Deposit:	14 July 2026
Date of Acceptance:	30 June 2026
Last Modified:	14 Jul 2026 15:51
URI:	https://orca.cardiff.ac.uk/id/eprint/188183

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