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Dimension-reduced Optimization of Multi-zone Thermostatically Controlled Loads

Xueyuan Cui, Yi Wang, Bolun Xu

TL;DR

This work tackles the challenge of optimizing multi-zone TCLs under high dimensionality by introducing latent-variable representations learned with a multi-task auto-encoder to capture time-coupled state, action, and disturbance dynamics. It develops two optimization pathways, OptIden (gradient-based in latent space) and OptSim (zeroth-order with a latent black-box model), enabling efficient and accurate scheduling across different deployment scenarios. Case studies on a 90-zone building (scalable to 1080 zones) show that latent-variable methods substantially reduce computational effort and improve cost performance compared with high-dimensional baselines, while providing robust performance under noise and model errors. The approach paves the way for scalable demand-response in large buildings and offers avenues for integration with end-to-end optimization and reinforcement learning.

Abstract

This study proposes a computationally efficient method for optimizing multi-zone thermostatically controlled loads (TCLs) by leveraging dimensionality reduction through an auto-encoder. We develop a multi-task learning framework to jointly represent latent variables and formulate a state-space model based on observed TCL operation data. This significantly reduces the dimensionality of TCL variables and states while preserving critical nonlinear interdependencies in TCL control. To address various application scenarios, we introduce optimization algorithms based on system identification (OptIden) and system simulation (OptSim) tailored to the latent variable representation. These approaches employ automatic differentiation and zeroth-order techniques, respectively, for efficient implementation. We evaluate the proposed method using a 90-zone apartment prototype, comparing its performance to traditional high-dimensional optimization. Results demonstrate that our approach effectively reduces control costs while achieving significantly higher computational efficiency.

Dimension-reduced Optimization of Multi-zone Thermostatically Controlled Loads

TL;DR

This work tackles the challenge of optimizing multi-zone TCLs under high dimensionality by introducing latent-variable representations learned with a multi-task auto-encoder to capture time-coupled state, action, and disturbance dynamics. It develops two optimization pathways, OptIden (gradient-based in latent space) and OptSim (zeroth-order with a latent black-box model), enabling efficient and accurate scheduling across different deployment scenarios. Case studies on a 90-zone building (scalable to 1080 zones) show that latent-variable methods substantially reduce computational effort and improve cost performance compared with high-dimensional baselines, while providing robust performance under noise and model errors. The approach paves the way for scalable demand-response in large buildings and offers avenues for integration with end-to-end optimization and reinforcement learning.

Abstract

This study proposes a computationally efficient method for optimizing multi-zone thermostatically controlled loads (TCLs) by leveraging dimensionality reduction through an auto-encoder. We develop a multi-task learning framework to jointly represent latent variables and formulate a state-space model based on observed TCL operation data. This significantly reduces the dimensionality of TCL variables and states while preserving critical nonlinear interdependencies in TCL control. To address various application scenarios, we introduce optimization algorithms based on system identification (OptIden) and system simulation (OptSim) tailored to the latent variable representation. These approaches employ automatic differentiation and zeroth-order techniques, respectively, for efficient implementation. We evaluate the proposed method using a 90-zone apartment prototype, comparing its performance to traditional high-dimensional optimization. Results demonstrate that our approach effectively reduces control costs while achieving significantly higher computational efficiency.
Paper Structure (29 sections, 2 theorems, 27 equations, 14 figures, 11 tables, 1 algorithm)

This paper contains 29 sections, 2 theorems, 27 equations, 14 figures, 11 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Problem Statement
  4. Methodology
  5. Multi-task based Representation of Latent Variables
  6. Variable transformation
  7. Training algorithm
  8. Dimension-reduced Optimization with Latent Variables
  9. OptIden algorithm
  10. OptSim algorithm
  11. Latent Error Analysis
  12. Errors of OptIden Algorithm
  13. Modeling of latent variables
  14. Optimization results
  15. Errors of OptSim Algorithm
  16. ...and 14 more sections

Key Result

Proposition 1

The model error ${e}^m$ depends on ${e}^s$ and is independent of ${e}^a$ and ${e}^\delta$.

Figures (14)

  • Figure 1: Workflow of the proposed methodology.
  • Figure 2: Proposed framework for the representation of latent variables.
  • Figure 3: Proposed OptIden algorithm with latent variables.
  • Figure 4: Proposed OptSim algorithm with latent variables.
  • Figure 5: Error analysis within the OptIden algorithm.
  • ...and 9 more figures

Theorems & Definitions (10)

  • Remark 1: Independent AEs for variable representation
  • Remark 2: Zeroth order optimization with latent variables
  • Definition 1
  • Proposition 1: Latent model error analysis
  • proof
  • Definition 2
  • Proposition 2: Latent optimization error analysis
  • proof
  • Remark 3: Mitigation of modeling and optimization errors
  • Remark 4: Error comparison