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MPC using mixed-integer programming for aquifer thermal energy storages

Johannes van Randenborgh, Moritz Schulze Darup

TL;DR

The paper tackles sustainable ATES operation by developing a nonlinear PDE-based ATES model that captures ground temperature dynamics and HX coupling, and embedding it in a tailored model predictive control framework that results in a mixed-integer quadratic program. A three-mode piecewise affine (PWA) representation enables MPC to decide heating, storing, or cooling actions while respecting boundary conditions and environmental constraints. An unscented Kalman filter provides nonlinear state estimation from borehole measurements, and a move-blocking MI OCP is solved on real Belgian data, achieving energy balance improvements and demonstrating practical viability. The work advances ATES control by enabling balanced energy delivery, reduced unbalance, and sustainable subsurface operation, with clear pathways for speed-ups and broader UTES applicability.

Abstract

Aquifer thermal energy storages (ATES) are used to temporally store thermal energy in groundwater saturated aquifers. Typically, two storages are combined, one for heat and one for cold, to support heating and cooling of buildings. This way, the use of classical fossil fuel-based heating, ventilation, and air conditioning can be significantly reduced. Exploiting the benefits of ATES beyond "seasonal" heating in winter and cooling in summer as well as meeting legislative restrictions requires sophisticated control. We propose a tailored model predictive control (MPC) scheme for the sustainable operation of ATES systems, which mainly builds on a novel model and objective function. The new approach leads to a mixed-integer quadratic program. Its performance is evaluated on real data from an ATES system in Belgium.

MPC using mixed-integer programming for aquifer thermal energy storages

TL;DR

The paper tackles sustainable ATES operation by developing a nonlinear PDE-based ATES model that captures ground temperature dynamics and HX coupling, and embedding it in a tailored model predictive control framework that results in a mixed-integer quadratic program. A three-mode piecewise affine (PWA) representation enables MPC to decide heating, storing, or cooling actions while respecting boundary conditions and environmental constraints. An unscented Kalman filter provides nonlinear state estimation from borehole measurements, and a move-blocking MI OCP is solved on real Belgian data, achieving energy balance improvements and demonstrating practical viability. The work advances ATES control by enabling balanced energy delivery, reduced unbalance, and sustainable subsurface operation, with clear pathways for speed-ups and broader UTES applicability.

Abstract

Aquifer thermal energy storages (ATES) are used to temporally store thermal energy in groundwater saturated aquifers. Typically, two storages are combined, one for heat and one for cold, to support heating and cooling of buildings. This way, the use of classical fossil fuel-based heating, ventilation, and air conditioning can be significantly reduced. Exploiting the benefits of ATES beyond "seasonal" heating in winter and cooling in summer as well as meeting legislative restrictions requires sophisticated control. We propose a tailored model predictive control (MPC) scheme for the sustainable operation of ATES systems, which mainly builds on a novel model and objective function. The new approach leads to a mixed-integer quadratic program. Its performance is evaluated on real data from an ATES system in Belgium.
Paper Structure (18 sections, 26 equations, 4 figures)

This paper contains 18 sections, 26 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Principles of ATES operation
  3. Control approaches for ATES
  4. Challenges and contributions
  5. Organization
  6. A novel model for ATES systems
  7. Temperature profiles in ATES
  8. Heat exchanger
  9. Combined model for ATES system
  10. A tailored MPC scheme
  11. Objective function
  12. Nonlinear sate observer
  13. Numerical study
  14. Parameters of the prediction model
  15. Simulation of real-world system
  16. ...and 3 more sections

Figures (4)

  • Figure 1: Schematic illustration of the ATES system in cooling mode (i.e., $u(t_k)<0$).
  • Figure 2: Illustration of boundary conditions for and discretization of the PDE \ref{['eq:T_PDE_simplified']} for the warm and cold aquifer depending on the different operation modes of the ATES system. Arrows indicate flow directions.
  • Figure 3: Energy demand (gray) of the building compared with the delivered energy by the ATES system in 2005 over time in comparison with the controller given by Desmedt.2007 (light red) and the tailored MPC scheme (light blue).
  • Figure 4: Comparison of the mean of the absolute error of the UKF for the aquifers over the spatial domain. The light red and blue triangles indicate the absolute maximum error for the warm and cold aquifer, respectively.