Short-term modeling of hybrid geothermal systems for Model Predictive Control

Abstract

Model Predictive Control (MPC) has shown significant energy savings potential in the operation of building energy systems, yet it needs accurate and simple models for optimization. In hybrid geothermal systems the source-side temperatures affect the system efficiency and its operational feasibility. Since the ground dynamics are rather slow, simplifications such as considering a constant coefficient of performance (COP) are made. We evaluate the added value of including a short-term dynamic borefield model to the controller. Simulations are performed in a heating-dominated building equipped with a hybrid geothermal system for two winter weeks. We consider 4 different modeling strategies where the formulation of the COP and the return fluid temperature from the borefield is varied in complexity. Results show that using a constant COP results in a bang-bang behavior of the heat pump, while with an accurate prediction of the COP the operation is smoother, saving 0.46%, 1.86% and 2.71% for low, average and high electricity-to-gas price ratios respectively. Including a short-term borefield model avoids shutting down the heat pump due to safety constraints which saves up to 8.12% more money while the use of the groundsource is quintupled. Despite reducing the optimization iteration number by almost 18%, simulation time is increased.

Sustainability of Shallow Geothermal Energy for Building Air-Conditioning

“…Figueroa et al [64] apply a model predictive controller methodology to a GSHP system. They model the COP by non-linear equations, including the inlet and outlet temperatures of the ground and variable mass flow rates of the heat transfer fluid.…”

A low-order semi-physical borefield model for optimal control applications

“…The thermal resistances R ST,i and capacities C ST,i of the short-term nodes can be computed from the ground and borehole physical information using radial heat transfer relations, whereas the thermal resistances R LT,i and capacities C LT,i of the long-term nodes are estimated using data from the analytical gfunction. The model structure focuses on the ground dynamics given by the T b − T s relation in Equation 1, but the borehole wall node T b could be extended to include the borehole dynamics connecting it to existing borehole controller models such as the ones from Witte et al (2018) or Cupeiro Figueroa et al (2019).…”

“…In hybrid geothermal systems, the incorporation of a borefield model that predicts the working fluid temperatures is an excellent asset. In the short-term time scales, it can guarantee the ground source heat pump (GSHP) reliability (Cupeiro Figueroa et al, 2019) whereas incorporating the long-term time scales leads to a more sustainable use of the borefield, achieving substantial savings (Cupeiro .…”

A Methodology for Long-Term Model Predictive Control of Hybrid Geothermal Systems: The Shadow-Cost Formulation

“…where T f is the average fluid temperature and Qbor is the heat flow being injected/extracted into/from the ground. Using a similar approach to model the ground, Cupeiro Figueroa et al [23] included the advection component and applied the model into a non-linear MPC approach to prove the added value of a variable COP and of the borefield model. An analysis of the RC ground diffusion network was made, proving that the predictions of the fluid temperature are accurate within the week range.…”

“…However, this maximum capacity may vary depending on the GSHP operation conditions. Starting from the correlation defined by Cupeiro Figueroa et al [23], we encountered some issues during the optimization as the fitted COP tended to very high values at low modulation levels. Therefore, the condenser Qcon and evaporator Qeva capacities were chosen as the preferred variables to be fitted, while calculating the compressor power Ẇcom and the COP starting from these.…”