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VB-NET: A physics-constrained gray-box deep learning framework for modeling air conditioning systems as virtual batteries

Yuchen Qi, Ye Guo, Yinliang Xu

TL;DR

This paper proposes VB-NET, a physics-constrained gray-box deep learning framework that transforms complex AC thermodynamics into a standardized Virtual Battery (VB) model, and mathematically proves the isomorphic equivalence between the AC and VB models.

Abstract

The increasing penetration of renewable energy necessitates unlocking demand-side flexibility. While air conditioning (AC) systems offer significant thermal inertia, existing physical and data-driven models struggle with parameter acquisition, interpretability, and data scarcity. This paper proposes VB-NET, a physics-constrained gray-box deep learning framework that transforms complex AC thermodynamics into a standardized Virtual Battery (VB) model. We first mathematically prove the isomorphic equivalence between the AC and VB models. Subsequently, VB-NET is designed to strictly enforces physical laws by decoupling shared meteorological drivers from private building thermal fingerprints and embedding a differentiable physics layer. Experimental results demonstrate that VB-NET significantly outperforms conventional black-box models in state of charge tracking while successfully recovering underlying thermodynamic laws to yield physically consistent parameters. Furthermore, utilizing multi-task learning and terminal sensitivity modulation, VB-NET overcomes the cold-start dilemma, achieving high-precision modeling for new AC units using only 2% to 6% of historical data. Ultimately, this study provides an interpretable and data-efficient pathway for aggregating decentralized AC resources for grid regulation.

VB-NET: A physics-constrained gray-box deep learning framework for modeling air conditioning systems as virtual batteries

TL;DR

This paper proposes VB-NET, a physics-constrained gray-box deep learning framework that transforms complex AC thermodynamics into a standardized Virtual Battery (VB) model, and mathematically proves the isomorphic equivalence between the AC and VB models.

Abstract

The increasing penetration of renewable energy necessitates unlocking demand-side flexibility. While air conditioning (AC) systems offer significant thermal inertia, existing physical and data-driven models struggle with parameter acquisition, interpretability, and data scarcity. This paper proposes VB-NET, a physics-constrained gray-box deep learning framework that transforms complex AC thermodynamics into a standardized Virtual Battery (VB) model. We first mathematically prove the isomorphic equivalence between the AC and VB models. Subsequently, VB-NET is designed to strictly enforces physical laws by decoupling shared meteorological drivers from private building thermal fingerprints and embedding a differentiable physics layer. Experimental results demonstrate that VB-NET significantly outperforms conventional black-box models in state of charge tracking while successfully recovering underlying thermodynamic laws to yield physically consistent parameters. Furthermore, utilizing multi-task learning and terminal sensitivity modulation, VB-NET overcomes the cold-start dilemma, achieving high-precision modeling for new AC units using only 2% to 6% of historical data. Ultimately, this study provides an interpretable and data-efficient pathway for aggregating decentralized AC resources for grid regulation.
Paper Structure (12 sections, 17 equations, 7 figures, 2 tables)

This paper contains 12 sections, 17 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Modeling
  3. Theoretical Analysis
  4. VB-NET Design
  5. Disentangled Feature Encoding Mechanism
  6. Physics-Informed Parameter Identification
  7. Differentiable Physics Evolution Layer
  8. Case Study
  9. Experiment Setup
  10. Case A: Feasibility of VB-NET
  11. Case B: Cold-Start Experiment
  12. Conclusion

Figures (7)

  • Figure 1: The mapping from the indoor temperature of AC system to the SOC of VB in summer cooling case.
  • Figure 2: The structure of VB-NET.
  • Figure 3: Comparison of SOC tracking performance between VB-NET and conventional deep learning models (MLP, CNN, LSTM).
  • Figure 4: The linear relationship between the identified power loss ($P_{loss}$) and the indoor-outdoor temperature difference across different AC units.
  • Figure 5: Comparison of the identified virtual capacity ($C_f$) under different temperature deadband settings.
  • ...and 2 more figures