Within the context of carbon peaking and neutrality,carbon capture plants can effectively reduce carbon emissions in power systems. Yet,the regular integration of these units for peak shaving in grids harnessing renewable energy tends to hamper system efficiency. Thus,acknowledging the operation and carbon trading mechanism of adaptable carbon capture plants,firstly,the incorporation of pumped storage plants is suggested to aid peak shaving,thereby facilitating wind power utilization,optimizing carbon capture plants for carbon sequestration,and reducing overall system carbon emissions. Then,given the uncertainty following grid-integrated wind power,fuzzy theory is employed to model system power constraints as fuzzy parameters,representing wind power and load. The constraint is transformed into a credibility-based fuzzy chance constraint. This fuzzy chance constraint is clarified by the clear equivalence classes. Prioritizing maximum system net income as the objective function,elements such as unit online revenue, extraction income, carbon trading profits,operational costs,and system security constraints are considered. The carbon capture-pumped storage joint operation model is developed. Finally,the model is solved using CPLEX. Simulation results validate that the integration of pumped storage plant enhances the system's net income by 7.62% and reduces carbon emissions by 7.01%,reflecting a balanced consideration of both economic and environmental aspects.