Driven by the "dual carbon" goal, in order to further improve the role of load-side fixed, variable frequency air conditioning load and basic flexible load in demand response and analyze their carbon reduction capabilities, this paper proposes an optimal operation strategy of power system considering fixed, variable frequency air conditioning load and flexible load participating in demand response of carbon trading. Firstly, the single model of fixed and variable frequency air conditioners is established and its power aggregation model is derived; on this basis, the maximum load reduction capacity of fixed and variable frequency air conditioners is calculated by combining a variety of main factors that affect the participation of air conditioner users in demand response; in addition, the consideration of fixed and variable frequency air conditioning loads is added in the traditional demand response scheduling model, and a carbon trading mechanism is introduced. On this basis, a power system optimal operation strategy aiming at minimizing the comprehensive operation cost such as unit generation cost, carbon emission cost, and load dispatching cost is constructed. Finally, a certain distribution network system is verified and analyzed, and the effectiveness of the proposed strategy in terms of economic optimization and energy saving and emission reduction is verified by setting a variety of operating scenarios to compare.