Abstract: This paper proposes a data-driven robust optimization method for zero-carbon heating through synergy among photovoltaic (PV), energy storage, and electric heating film systems. First, a data-driven power cloud model is constructed based on historical operational data to characterize the uncertainty of PV-storage system output power. The model is then refined via convex hull fitting to generate robust uncertainty set boundaries, providing explicit constraints for robust optimization decisions. Second, a coupling coordination degree analysis is adopted to quantify the multi-energy complementary characteristics among PV generation, energy storage, and electric heating film heating. Subsequently, the coupling coordination analysis results are integrated with the robust uncertainty set constraints to establish a data-driven robust optimization model, which is efficiently solved using an improved column-and-constraint generation (C&CG) algorithm to achieve robust decision-making and optimal management of multi-energy synergistic operation. Finally, simulation results verify the accuracy and effectiveness of the proposed method.