Optimizing Aquifer Thermal Energy Storage Systems through Mixed-Integer Programming-Based Model Predictive Control

Core Concepts

A tailored model predictive control scheme is proposed to optimize the sustainable operation of aquifer thermal energy storage systems by minimizing operational costs, tracking building energy demand, and maintaining energy balance.

Abstract

The paper presents a novel model and a tailored model predictive control (MPC) scheme for the sustainable operation of aquifer thermal energy storage (ATES) systems.
The key highlights are:

Model Derivation:

The model is based on discretized partial differential equations describing the temperature profiles in the warm and cold aquifers.
A simplified heat exchanger model is used to capture the coupling between the aquifers and the building.
The combined model results in a piecewise affine system, which is suitable for mixed-integer optimization.

MPC Scheme:

The objective function of the MPC scheme aims to minimize operational costs, track the building's energy demand, and maintain energy balance in the ATES system.
A nonlinear state observer based on an unscented Kalman filter is designed to estimate the temperature profiles in the aquifers.

Numerical Study:

The performance of the tailored MPC scheme is evaluated using real-world data from an ATES system in Belgium.
The results show that the proposed MPC scheme can achieve energy balance, unlike a previously deployed controller, while reducing the overall energy contribution to the building.
The state estimation by the unscented Kalman filter is found to be accurate, with a maximum mean absolute error of around 0.86 K.

The paper demonstrates that the proposed MPC scheme can effectively optimize the sustainable operation of ATES systems, addressing the challenges of unbalanced energy demand and maintaining the viability of the subsurface.

Stats

The building demands about 1400 MWh more heat than cold during the heating season (October to April).
The building demanded 402 MWh more heat than cold at the end of the year.
The deployed controller failed to achieve energy balance, with the ATES system delivering 277 MWh more heat than cold.
The tailored MPC scheme lowered the overall energy contribution to the building's energy demand to 54.5%, compared to 69% for the deployed controller.

Quotes

"Dealing with the unbalanced energy demand, deployed controller [6] failed to achieve energy balance and the ATES system delivering 277 MWh more heat than cold."
"The proposed tailored MPC scheme, however, was able to reach energy balance. In fact, the ATES system delivered in total only 27 MWh more heat to the building than demanded."

Key Insights Distilled From

MPC using mixed-integer programming for aquifer thermal energy storages

by Johannes van... at arxiv.org 04-16-2024

https://arxiv.org/pdf/2404.09786.pdf

Deeper Inquiries

How can the bespoke matrix structures of the model be exploited to further improve the computational efficiency of the optimization?

The bespoke matrix structures of the model, particularly the piecewise affine (PWA) system model derived in the context, can be leveraged to enhance computational efficiency in several ways:

Sparse Matrix Representation: By exploiting the sparsity pattern inherent in the PWA model, sparse matrix techniques can be utilized. Sparse matrices store only non-zero elements, reducing memory requirements and speeding up matrix operations such as multiplication and inversion.

Structure Exploitation: The specific structure of the matrices in the model, such as block-diagonal or banded structures, can be exploited to optimize computational routines. Algorithms tailored to exploit these structures can lead to faster computations.

Parallel Processing: The matrix operations in the optimization problem can be parallelized to take advantage of multi-core processors or distributed computing systems. Parallel processing can significantly reduce the overall computation time.

Reduced Complexity: Simplifying the model further based on the matrix structures can lead to reduced computational complexity. This may involve reducing the number of decision variables or constraints while maintaining the model's accuracy.

Algorithmic Optimization: Tailoring optimization algorithms to the specific matrix structures can improve efficiency. For example, using specialized solvers designed for PWA models or mixed-integer quadratic programs can lead to faster convergence.

Precomputation and Caching: Precomputing certain matrix operations or storing intermediate results in a cache can eliminate redundant calculations and speed up subsequent iterations of the optimization problem.

By strategically utilizing the bespoke matrix structures of the model and implementing these optimization strategies, the computational efficiency of the optimization process can be significantly enhanced.

How can the potential challenges and considerations in extending the presented modeling approach to other types of underground thermal energy storage systems be addressed?

Extending the presented modeling approach to other types of underground thermal energy storage (UTES) systems may pose several challenges and considerations, which can be addressed through the following strategies:

Geological Variability: Different UTES systems may operate in geologically diverse environments, leading to variations in thermal properties and behavior. Conducting thorough site-specific geological assessments and adapting the model parameters accordingly can help account for these variations.

System Configuration: Various UTES systems, such as borehole heat exchangers or cavern storages, have unique configurations and operational characteristics. Customizing the model equations and boundary conditions to align with the specific system type is essential for accurate representation.

Energy Transfer Mechanisms: Different UTES systems may involve distinct energy transfer mechanisms, such as direct heat exchange or indirect circulation. Modifying the model equations to accommodate these variations and incorporating relevant physical principles is crucial.

Legislative and Environmental Factors: Legislative restrictions and environmental considerations specific to each UTES system type must be integrated into the model. Adhering to regulations, such as energy balance requirements or environmental impact assessments, is essential for sustainable operation.

Data Availability and Validation: Access to reliable data for calibration and validation of the model is vital when extending it to other UTES systems. Conducting field studies, collecting operational data, and validating the model against real-world performance are key steps in ensuring accuracy.

Model Flexibility and Adaptability: Designing the model with flexibility and adaptability in mind allows for easy customization to different UTES configurations. Parameterizing the model in a modular fashion and incorporating adjustable components can facilitate its extension to diverse systems.

By addressing these challenges and considerations through tailored adjustments, thorough validation, and a comprehensive understanding of the specific UTES system characteristics, the presented modeling approach can be successfully extended to a broader range of underground thermal energy storage systems.

How can the MPC scheme be integrated with a sophisticated building model to better account for the building's energy demands and return temperatures?

Integrating the Model Predictive Control (MPC) scheme with a sophisticated building model can enhance the accuracy and efficiency of energy management in the following ways:

Dynamic Building Simulation: Incorporating a detailed building energy simulation model allows for real-time prediction of energy demand based on building occupancy, weather conditions, and internal loads. This information can be fed into the MPC controller for proactive energy management.

Thermal Comfort Considerations: A sophisticated building model can account for occupant comfort preferences, indoor air quality, and thermal comfort requirements. By integrating these factors into the MPC scheme, optimal control strategies can be devised to maintain comfort while minimizing energy consumption.

HVAC System Integration: Linking the MPC controller with the building's HVAC system enables coordinated control of heating, ventilation, and air conditioning based on predicted energy demands. This integration ensures that the HVAC system operates efficiently to meet the building's needs.

Return Temperature Optimization: By considering the return temperatures from the building side of the heat exchanger, the MPC scheme can adjust the operation of the ATES system to optimize energy transfer and minimize losses. Balancing supply and return temperatures improves system efficiency.

Fault Detection and Diagnostics: A sophisticated building model can facilitate fault detection and diagnostics in the HVAC system. By integrating this capability with the MPC controller, proactive measures can be taken to address system inefficiencies or malfunctions.

Multi-Objective Optimization: The integrated MPC scheme can optimize energy consumption, cost savings, and environmental impact simultaneously. By considering multiple objectives and constraints, the controller can make informed decisions to achieve overall system efficiency.

Adaptive Control Strategies: Continuous feedback from the building model allows the MPC scheme to adapt its control strategies in response to changing conditions. This adaptive approach ensures optimal performance under varying operational scenarios.

By integrating the MPC scheme with a sophisticated building model, a holistic and intelligent energy management system can be established, leading to improved energy efficiency, occupant comfort, and overall sustainability of the building's operations.