Hydrogen–energy–carbon coupled pricing for integrated energy systems: Stackelberg game and robust demand response under renewable uncertainty

Driven by the global pursuit of carbon neutrality, the integration of hydrogen into multi-energy systems has become a key enabler for deep decarbonization. This paper proposes a robust optimization-based scheduling method for integrated energy systems, coupling multi-energy complementarity with a coordinated hydrogen-energy-carbon pricing strategy. First, a comprehensive energy architecture is established, integrating hydrogen, electricity, heat, and gas supplies, where the energy service provider leverages wind and other renewables to build a complementary energy supply system. A robust optimization model is formulated at the upper level, embedding a hydrogen-energy-carbon pricing mechanism. Second, a lower-level demand response model grounded in price elasticity theory is developed to characterize the dynamic interaction between user consumption behaviors and energy prices. A Stackelberg game framework, with the ESP as the leader and user groups as followers, is constructed to capture the bidirectional influence between pricing strategies and user-side responses. Regarding solution methodology, a refined column-and-constraint generation algorithm is designed to address renewable generation uncertainty, ensuring robust decision-making under worst-case scenarios. Case studies demonstrate that the proposed method maintains system stability under 20% renewable penetration and achieves a 21.95% reduction in carbon emissions through energy-carbon coordination, validating both the environmental benefits and practical feasibility of the approach.