Optimal design of PVT heat pump soil cross-seasonal energy storage systems: A multi-objective approach integrating RSM and NSGA-II across climate zones

The design of photovoltaic-thermal (PVT) heat pump soil cross-seasonal energy storage systems involves complex trade-offs among system efficiency, economic viability, and environmental impact. Conventional soil thermal balance-based methods ensure annual thermal equilibrium but fail to simultaneously optimize performance, payback period, and carbon emissions. This study proposes a multi-objective optimization framework integrating response surface methodology (RSM) with the non-dominated sorting genetic algorithm II (NSGA-II) to optimize three design variables (PVT area, borehole spacing, and borehole depth)with respect to three objectives: system comprehensive performance (COPcom-SYS), investment payback period (PSYS), and CO2 emissions (Cex). The framework is validated against real operational data from a commercial project in Dalian, China, and subsequently extended to three additional climate zones (Hohhot, Shenyang, and Wuwei). For the Dalian case, the optimal configuration (PVT area: 266.9 m2, borehole spacing: 2.2 m, and borehole depth: 73.6 m) improves COPcom-SYS by 0.6%, reduces PSYS by 17.3%, and decreases Cex by 20.0% relative to the soil thermal balance baseline. Cross-climate results consistently identify Pareto-optimal solutions outperforming baseline designs, demonstrating the framework's generalizability. The significance of design variables and their interactions is found to be climate-dependent, providing actionable guidance for region-specific system design.