The low-carbon construction of integrated energy systems is a crucial path to achieving dual carbon goals, with the power-generation side having the greatest potential for emissions reduction and the most direct means of reduction, which is a current research focus. However, existing studies lack the precise modeling of carbon capture devices and the cascaded utilization of hydrogen energy. Therefore, this paper establishes a carbon capture power plant model based on a comprehensive, flexible operational mode and a coupled model of a two-stage P2G (Power-to-Gas) device, exploring the “energy time-shift” characteristics of the coupled system. IGDT (Information Gap Decision Theory) is used to discuss the impact of uncertainties on the power generation side system. The results show that by promoting the consumption of clean energy and utilizing the high energy efficiency of hydrogen while reducing reliance on fossil fuels, the proposed system not only meets current energy demands but also achieves a more efficient emission reduction, laying a solid foundation for a sustainable future. By considering the impact of uncertainties, the system ensures resilience and adaptability under fluctuating renewable energy supply conditions, making a significant contribution to the field of sustainable energy transition.