In response to pressing environmental challenges, the power system is gradually developing towards a more efficient, clean, and sustainable direction. Carbon capture power plants (CCPPs) and wind power generation will play a significant role in this eco-friendly transformation. However, the high energy consumption of CCPPs and the anti-peak regulation characteristics of wind power lead to contradictions in their coordinated operation during peak shaving, restricting the system's low-carbon economic development. Aiming at the above challenges, an interval optimization method is proposed to coordinate wind power and CCPPs. Firstly, a flexible operation model of CCPPs is established, and the coordinated scheduling mechanism of wind power joint carbon capture operation and load-side demand response is introduced to optimize the system carbon emission through low carbon scheduling on both sides of the source and load. Secondly, interval numbers are used to manage the uncertainty of wind power output, and the interval-optimized scheduling model of wind power combined CCPPs is established. To solve the proposed model, the improved interval possibility method is adopted to transform the uncertain model into a deterministic one, which is solved by the CPLEX solver. Finally, the simulation outcomes using the IEEE 30-bus system framework reveal that the proposed approach significantly enhances the coordination between CCPPs and wind power. Notably, when compared to scenarios that solely focus on CCPPs, the proposed method achieves a substantial reduction in total costs by 16.67 % and decreases carbon emissions by 26.53 %. This sets a significant reference for low-carbon economic dispatch within power systems, providing key insights and foundational guidelines for future implementations, as well as novel strategies and technological support for the sustainable transformation of the power system towards lower carbon emissions.