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Data-driven online control for real-time optimal economic dispatch and temperature regulation in district heating systems

Xinyi Yi, Ioannis Lestas

Abstract

District heating systems (DHSs) require coordinated economic dispatch and temperature regulation under uncertain operating conditions. Existing DHS operation strategies often rely on disturbance forecasts and nominal models, so their economic and thermal performance may degrade when predictive information or model knowledge is inaccurate. This paper develops a data-driven online control framework for DHS operation by embedding steady-state economic optimality conditions into the temperature dynamics, so that the closed-loop system converges to the economically optimal operating point without relying on disturbance forecasts. Based on this formulation, we develop a Data-Enabled Policy Optimization (DeePO)-based online learning controller and incorporate Adaptive Moment Estimation (ADAM) to improve closed-loop performance. We further establish convergence and performance guarantees for the resulting closed-loop system. Simulations on an industrial-park DHS in Northern China show that the proposed method achieves stable near-optimal operation and strong empirical robustness to both static and time-varying model mismatch under practical disturbance conditions.

Data-driven online control for real-time optimal economic dispatch and temperature regulation in district heating systems

Abstract

District heating systems (DHSs) require coordinated economic dispatch and temperature regulation under uncertain operating conditions. Existing DHS operation strategies often rely on disturbance forecasts and nominal models, so their economic and thermal performance may degrade when predictive information or model knowledge is inaccurate. This paper develops a data-driven online control framework for DHS operation by embedding steady-state economic optimality conditions into the temperature dynamics, so that the closed-loop system converges to the economically optimal operating point without relying on disturbance forecasts. Based on this formulation, we develop a Data-Enabled Policy Optimization (DeePO)-based online learning controller and incorporate Adaptive Moment Estimation (ADAM) to improve closed-loop performance. We further establish convergence and performance guarantees for the resulting closed-loop system. Simulations on an industrial-park DHS in Northern China show that the proposed method achieves stable near-optimal operation and strong empirical robustness to both static and time-varying model mismatch under practical disturbance conditions.
Paper Structure (37 sections, 7 theorems, 34 equations, 7 figures, 4 tables, 2 algorithms)

This paper contains 37 sections, 7 theorems, 34 equations, 7 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Forecast-reliant and model-based DHS operation
  3. Data-driven enhancements within MPC-based DHS operation
  4. Online data-driven control opportunities for real-time economic dispatch and temperature regulation in DHSs
  5. Contributions and paper organization
  6. District heating system (DHS) model
  7. Temperature dynamics of DHSs
  8. Steady-state optimization of DHSs
  9. LQR problem formulation
  10. Discrete-time temperature dynamics
  11. Output and error definition
  12. Augmented dynamics
  13. Model-based LQR temperature regulator
  14. Stationary distribution of $\boldsymbol{x_k}$
  15. Cost function
  16. ...and 22 more sections

Key Result

Theorem 1

If the DHS (origindy) achieves an equilibrium at $\boldsymbol{{T^\star}}$ and $\boldsymbol{h^G}^\star$, and satisfies $\boldsymbol{F^M {h^G}^\star} = \boldsymbol{0}$ and $\boldsymbol{1^\top F^D {T^\star}} = 0$, where $\boldsymbol{F^M}\in\mathbb{R}^{(|\mathcal{G}|-1)\times |\mathcal{G}|}$ is defined Then it uniquely solves the optimization problems E1 and E2.

Figures (7)

  • Figure 1: Effect of disturbance-covariance estimation on DeePO convergence.
  • Figure 2: Comparison of convergence behavior and sample efficiency between DeePO and ZO-PO.
  • Figure 3: Temperature evolution under ADAM-DeePO.
  • Figure 4: Optimality error evolution under ADAM-DeePO.
  • Figure 5: Heat generation under ADAM-DeePO.
  • ...and 2 more figures

Theorems & Definitions (10)

  • Theorem 1
  • Definition 1
  • Proposition 1
  • remark 1: Role of estimating $\boldsymbol{U}_\epsilon$
  • Theorem 2
  • remark 2
  • Lemma 1
  • Lemma 2
  • Theorem 3
  • Theorem 4