Assessing mixed-integer-based heat pump modeling approaches for model predictive control applications in buildings

Model predictive control can reduce heating systems’ operating costs and energy consumption. This especially applies to heat pumps, whose operation efficiency highly depends on the heating system’s source and sink temperatures. In literature, process models for heat pumps mostly introduce the coefficient of performance as a parameter thus assuming constant supply temperatures. However, supply temperature adjustment is crucial to overcharge buffer storages and hence shift energy to more favorable times, which is the basis of model predictive control concepts. We close this gap by developing two different air-source heat pump modeling approaches using the supply temperature as control variable: a piecewise linear model based on simulation results and a quadratic modeling approach. Both methods are benchmarked with a simplified linear model representing the state of research. The simplified linear model underestimates the cost of storage charging as it neglects the supply temperature’s influence on the coefficient of performance and results in 8.7% higher operating costs and 12.1% higher energy demand than the piecewise linear approach. However, the simplified linear model yields the lowest average computation time compared to the piecewise and quadratic approaches. The quadratic approach results in both lower operating costs (-1.9%) and energy demand (-1.8%), as well as lower computation times than the piecewise approach, consequently representing the best trade-off between performance and computational effort. We recommend future work to apply the method to a ground- or water-source heat pump and to a coupled building energy system to investigate the transferability of our findings.