Given the dual carbon goals, to promote renewable energy consumption, restrain carbon emission of the park and deal with the randomness of the renewable energy, this paper constructs a park-level hydrogen energy integrated energy system with reversible solid oxide cells (RSOC), and proposes a robust dispatching model considering both supply and demand responses, as well as a stepped carbon trading mechanism and taking into account the uncertainty of renewable energy. First, the RSOC and hydrogen storage tank are used to absorb the surplus output of renewable energy. Second, organic Rankine cycle (ORC) waste heat power generation and comprehensive demand response are introduced to form a double-side response to supply and demand to optimize thermoelectric operation. Then robust optimization theory is used to deal with the uncertainty of renewable energy. After that, a robust dispatching model is constructed with the goal of minimizing the sum of the system energy purchase carbon transaction, wind-solar penalty, and demand response costs, and is analyzed by CPLEX. Finally, the validity of the model is verified by the simulation results of an example.