To address the challenges of complex multi-agent interest interactions under the green certificate and carbon trading mechanism and the low-carbon scheduling of integrated energy systems(IES)

this paper proposes a bi-level optimized model for hydrogen-containing IES based on a Stackelberg game. Firstly

a Stackelberg game framework is constructed between the operator and the user aggregators. The upper-level operator aims to maximize the revenue by coordinating multi- energy equipment and green certificate-carbon trading through dynamic electricity/heat pricing strategies. The lower-level user aggregators respond to price signals by optimizing shiftable electrical loads and curtailable thermal loads. Secondly

a user- side bidirectional electric-thermal conversion mechanism and a dual-compensation demand response mechanism guided by carbon quotas are introduced. The former enhances the energy flexibility by electric thermal price differences to drive flexible energy supply

and the latter combines load compensation price with carbon quota incentives to overcome the challenge of insufficient user participation enthusiasm. Then

for model solving

the nonlinear bi-level programming problem is transformed into a mixed-integer linear programming(MILP) problem using Karush Kuhn Tucker(KKT) conditions and the Big-M method

and then efficiently solved using CPLEX. The simulation results demonstrate that the proposed strategy significantly reduces system carbon emissions

increases user profits

promotes operator revenue growth

and improves load curve smoothness through electric-thermal conversion equipment

which verifies the synergistic enhancement of multi-energy collaboration

providing theoretical and technical support for low-carbon energy scheduling involving multi-agent coordination.