Addressing climate change and facilitating the large-scale integration of renewable energy sources(RESs)have driven the development of hydrogen-coupled integrated energy systems (HIES)

which enhance energy sustainability through coordinated electricity

thermal

natural gas

and hydrogen utilization.This study proposes a two-stage distributionally robust optimization (DRO)-based scheduling method to improve the economic efficiency and reduce carbon emissions of HIES.The framework incorporates a ladder-type carbon trading mechanism to regulate emissions and implements a demand response(DR)program to adjust flexible multi-energy loads

thereby prioritizing RES consumption.Uncertainties from RES generation and load demand are addressed through an ambiguity set

enabling robust decision-making.The column-and-constraint generation (CCG) algorithm efficiently solves the two-stage DRO model.Case studies demonstrate that the proposed method reduces operational costs by 3.56%

increases photovoltaic consumption rates by 5.44%

and significantly lowers carbon emissions compared to conventional approaches.Furthermore

the DRO framework achieves a superior balance between conservativeness and robustness over conventional stochastic and robust optimization methods

highlighting its potential to advance cost-effective

low-carbon energy systems while ensuring grid stability under uncertainty.