To improve the low-carbon and economic operation performance of park-level integrated energy systems (PIES), a low-carbon economic dispatch method considering flexible equipment operation and energy storage configuration is proposed. Firstly, the traditional combined heat and power (CHP) system is retrofitted with the Kalina cycle and electric boiler technologies. Turbine waste heat is recovered to decouple inherent heat-power coupling constraints, significantly enhancing the output flexibility of CHP units. Secondly, additional energy storage is configured in the park to boost wind power accommodation and improve system reliability and operational flexibility. Furthermore, a tiered carbon trading mechanism is introduced for coordinated optimal scheduling with flexible-output CHP and energy storage devices. The total operational cost is categorized into energy procurement cost, equipment operation & maintenance cost and energy sales revenue, and a low-carbon economic dispatch model is constructed with the objective of minimizing total system cost. Case study results verify that the proposed model effectively improves equipment operational flexibility and system stability, cuts carbon emissions and overall operating costs, and provides theoretical references for the sustainable development of park-level integrated energy systems.