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To improve the coordination and complementarity of multiple energy sources, balancing the interests of different participants in a multi-energy system is of great importance. However, traditional centralized optimization can hardly reflect the game relationship between supply side and demand sides. A trading model based on the Stackelberg game model is proposed in this paper to balance the interests of the supply side and demand side and reduce the carbon emissions. First of all, the process of trading between the supply side and demand side based on smart contracts is described. A contractual consensus is obtained through an internal game, and the transaction is completed automatically. Secondly, a bilevel optimization model is established to coordinate the benefits of both parties based on the Stackelberg game model. The energy operator acts as a leader, and considers the two objectives, i.e., maximizing net income and minimizing carbon emissions, and uses the linear weighting method to convert the dual objectives into single objective. Users act as followers and aim to increase the comprehensive benefits, including energy cost and comfort. Then, Karush–Kuhn–Tucker optimality condition is used to transform the bilevel optimization model into an equivalent single-level model. Finally, simulation results show that the proposed method can coordinate the economic interests of both sides of supply and demand and effectively reduce the carbon emissions of the energy operator. [ABSTRACT FROM AUTHOR]