Control-oriented modeling of geothermal borefield thermal dynamics through Hammerstein-Wiener models

Geothermal energy is considered a clean and sustainable form of renewable energy, that can be exploited directly or indirectly by means of specific devices. Ground-coupled heat pumps are widely used systems to obtain this energy. Control of ground-coupled heat pump systems, where thermal energy is extracted or injected from and to a geothermal borefield, is important for optimal geothermal energy use in the building sector and smart grids. Model-based control of such systems is potentially an optimal solution but this requires control-oriented models for the borefield thermal dynamics, which is quite complicated due to thermal interactions between the boreholes, large-scale nonlinear system dynamics, transient surface boundary conditions, etc. In this paper, we propose and demonstrate the successful identification of these complex dynamics through simple and well-structured nonlinear Hammerstein-Wiener models, which can be used in some advanced convex model-based control algorithms. The results are validated for different borefield configurations and parameters with reference to a detailed finite-element borefield thermal model. Finally, a set of advanced convex model-based control methods are shortly described where Hammerstein-Wiener models can be used as control models.