Fluid temperature predictions of geothermal borefields using load estimations via state observers

Fluid temperature predictions of geothermal borefields usually involve temporal superposition of its characteristic g-function, using load aggregation schemes to reduce computational times. Assuming that the ground has linear properties, it can be modelled as a linear state-space system where the states are the aggregated loads. However, the application and accuracy of these models is compromised when the borefield is already operating and its load history is not registered or there are gaps in the data. This paper assesses the performance of state observers to estimate the borefield load history to obtain accurate fluid predictions. Results show that both Time-Varying Kalman Filter (TVKF) and Moving Horizon Estimator (MHE) provide predictions with average and maximum errors below 0.1∘C and 1∘C, respectively. MHE outperforms TVKF in terms of n-step ahead output predictions and load history profile estimates at the expense of about five times more computational time.