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

Model Predictive Control (MPC) predictive's nature makes it attractive for controlling high-capacity structures such as thermally activated building systems (TABS). Using weather predictions in the order of days, the system is able to react in advance to changes in the building heating and cooling needs. However, this prediction horizon window may be sub-optimal when hybrid geothermal systems are used, since the ground dynamics are in the order of months and even years. This paper proposes a methodology that includes a shadow-cost in the objective function to take into account the long-term effects that appear in the borefield. The shadow-cost is computed for a given long-term horizon that is discretized over time using predictions of the building heating and cooling needs. The methodology is applied to a case with only heating and active regeneration of the ground thermal balance. Results show that the formulation with the shadow cost is able to optimally use the active regeneration, reducing the overall operational costs at the expenses of an increased computational time. The effects of the shadow cost long-term horizon and the predictions accuracy are also investigated.