Aiming at the "Dual-Carbon" emission reduction target and the peak shaving problem of power system brought by the large-scale grid connection of new energy sources, a cascade hydro-thermal-wind-photovoltaic-storage multi-energy joint optimal scheduling model considering the stepped carbon trading is proposed. Firstly, hierarchical optimal scheduling is adopted, and the minimum load fluctuation is taken as the objective function in the upper model, using a modified sand cat swarm optimization(MSCSO)algorithm that considers Circle mapping strategy, triangular migration strategy, Levy flight migration strategy and elite reverse learning strategy to optimize the output of cascade hydropower. Thus, the equivalent load curve after smoothing is obtained. In the lower model, the minimum comprehensive cost is taken as the objective function to solve its piecewise linearization. Finally, a multi-scenario simulation is carried out in the modified IEEE 30 nodes, and the results show that the proposed model can effectively reduce carbon emissions, give full play to the deep peak shaving capacity of thermal power units, effectively improve the new energy consumption capacity and the low-carbon and economic operation of the system, which verifies the validity of the model.