Low-order state space models for borehole heat exchangers

The development of optimal model based control strategies for borefield thermal energy storage systems requires a low-order dynamic model of the borefield. This article investigates two approaches to obtain a low-order state space description of a borehole heat exchanger(BHE): (1) model reduction (MR) of a one-dimensional finite-difference model (1D-FDM) and (2) parameter estimation (PE). The resulting models are compared to the duct storage model (DST-model) implemented in TRNSYS. It is found that a sixth-order model, obtained by MR of a 1D-FDM, is able to predict the mean fluid temperature for a typical annual load profile with an accuracy of up to 2%. Further decreasing the model order by means of MR yields a bad description of the faster dynamics excited by the load profile. The performance of such very low-order models is significantly improved by PE. The maximum temperature error for a fourth-order model obtained by PE using identification data covering a period of three months, for instance, is a factor 4 lower than for a fourth-order model obtained by MR. This benefit is partially counterweighted by an inferior extrapolation capacity. Sensitivity analysis is performed to investigate the impact of non-idealities, namely (1) the impact of estimation errors on the physical parameters used to set up the 1D-FDM and (2) the impact of measurement noise on the models found by PE. It is shown that the ground thermal conductivity is the parameter that mostly affects the accuracy of the 1D-FDM and, thus, of the reduced-order models derived. The main impact of measurement noise is the reduction of the maximum model order for parameter estitmation to six or lower, depending on the identification dataset used and the magnitude of the measurement error.