Practical, near-optimal design rule extraction for heat pumps in single-family buildings

To accelerate the market penetration of heat pump systems, their design must be both economically optimal and simple. Therefore, we investigate the extraction of practical design rules for heat pump systems from design optimizations. We minimize total costs using detailed, dynamic simulation-based surrogate optimizations. The simulation scenarios are selected through theory-guided optimal experimental design to enable the derivation of generalizable rules. Herein, we select practical features based on theoretical derivation and numerical cross-correlation analysis. To verify the convergence of the optimal scenario selection, we implement static, practical simulation models. For the optimally selected scenarios, we successfully extract a power law rule for the bivalence temperature, which leads to average optimality gaps of 0.2 %, compared to the optimal objective value. Practical features of this rule are price assumptions, weather data, total heat demand, and domestic hot water share; with a declining relevance to the rule. The prevailing practical rule, the monovalent design, leads to an average 10 % cost increase compared to the optimum. Analyzing the deviations between static and dynamic simulations reveals important considerations in simplified modeling. Regarding buffer tank sizing, the smallest size is the simple rule; however, the impact on total costs is less significant compared to heat pump sizing. Furthermore, demand-side management benefits from larger buffer tanks. Moreover, we show that considering the compressor speed dependency in heat pump modeling significantly impacts the design rule, highlighting the need for more detailed manufacturer data to enable an optimal and simple design. Finally, extrapolating the rule towards European climate scenarios and stochastic user behavior indicates an acceptable but slightly reduced performance, motivating future studies to further increase generalizability.