Optimal capacity configuration of a solar–air source heat pump system coupled with dual thermal storage under different heating scenarios in northern rural China

Solar-assisted heating systems with integrated thermal storage are increasingly recognized as an effective solution for reducing carbon emissions in rural buildings. However, conventional capacity design approaches for solar-air source heat pump (SAASHP) systems with dual thermal storage often neglect terminal storage effects and dynamic heating demand, leading to unclear capacity demand relationships and potential system overdesign. To address this issue, this study develops a multi-objective optimization framework for a SAASHP system coupled with a sand-based thermal storage floor (SBTSF). The framework systematically evaluates the impacts of terminal configuration, indoor temperature demand characteristics, and regional heating load on system capacity allocation and identifies the capacity-demand relationship under dual-storage conditions. The results show that, under identical heating load conditions, the optimized configurations significantly reduce system capacity across all terminal types while maintaining comparable or slightly improved performance. The SBTSF achieves the largest reductions in solar collector area, heat pump capacity, and storage tank volume (up to 43.5%, 26.2%, and 68.7%, respectively), reflecting its enhanced load regulation capability. Dynamic indoor temperature demand has a limited impact on installed capacity but improves economic and energy performance by reshaping the temporal distribution of heating demand. Regression analysis further establishes quantitative relationships between heating load and key system capacities (R 2 ≈ 0.73), providing practical configuration ranges for dual-storage systems. These findings suggest that capacity design should move beyond conventional load-based approaches toward a demand-storage-terminal coupled framework, offering a quantitative basis for the optimal design of SAASHP systems with dual thermal storage.