Low-order state space models for borehole heat exchangers

Optimal model based control strategies for borefield thermal storage systems require a dynamic model of the borefield. This paper investigates to which extent a low-order state-space model is able to predict the thermal dynamics of a single borehole. Three approaches are analyzed: (i) first principle models, (ii) models obtained by model reduction techniques and (iii) models obtained by parameter estimation. The resulting models are compared to the DST-model implemented in Trnsys for different validation data sets. It is found that a 6th order model, obtained by model reduction of a first principle model, is able to predict the mean fluid temperature response to a given heat load with an accuracy of up to 2% for a time horizon of 10 years. If the model order is further decreased by means of model reduction, the faster dynamics are inaccurately described. However, by means of parameter estimation the model performance of such very-low-order models can be significantly improved. For a 4th order model, for instance, the relative model error is reduced up to a factor 4 after parameter estimation based on an identification data set covering a period of 3 months. This benefit is partially counterweighted by an inferior extrapolation capacity.