Integrated optimal control and borefield sizing for (small) hybrid heating and cooling systems

Hybrid heating and cooling systems integrate various heat and cold sources into a one system. This allows a control algorithm to activate the most efficient heat source at every moment, thereby having the potential to significantly reduce energy use, operational costs, and carbon emissions. A promising candidate to control these systems is Model Predictive Control (MPC), as it can automatically exploit the high inherent flexibility of these systems.

However, hybrid heating and cooling systems—particularly those incorporating a borefield, which is the focus of this paper—can have high investment costs, as drilling boreholes and installing piping can be expensive. To keep these investment costs acceptable, it is crucial to avoid oversizing components, especially the borefield. A potential solution is to integrate the (optimal) control strategy directly into the sizing process using an integrated optimal control and sizing (IOCS) methodology. This approach simultaneously minimizes both investment (CAPEX) and operational (OPEX) costs.

In the literature, most studies on borefield sizing, both for purely ground-source and hybrid systems, employ predefined, inflexible building demand profiles, typically generated using building simulation software [1]. As a result, the interdependence between borefield sizing and (optimal) control is often overlooked, resulting in an oversized borefield.

The main goal of this paper is therefore to integrate a non-linear program-based (NLP), physics-based MPC formulation in an optimal borefield sizing strategy such that the overall operational cost of the system and the borefield investment cost are minimized simultaneously.

To this end, this paper develops and compares, in terms of accuracy and computational speed, two methods by applying them to two use cases: a residential building and an office building. These cases were selected to represent both heating-dominated (residential) and cooling-dominated (office) buildings. High-fidelity, physics-based, non-linear controller models of these use cases are developed using Modelica, an object-oriented, equation-based, acausal, multi-domain modeling language. Subsequently, TACO (Toolchain for Automated Control and Optimization), an in-house developed Modelica-based toolchain for non-linear white-box MPC, is used to translate these models into NLP-based optimal control problems and efficiently solve them.