The new power system with a high proportion of renewable energy grid integration serves as a pivotal platform for achieving the "dual carbon" goals. However, the uncertainty in renewable energy output inevitably poses challenges such as difficulty in peak load regulation and insufficient flexibility to the power system. To effectively balance the economy and security of the system, several measures are taken. Firstly, the improved worst case conditional value at risk (WCVaR) is introduced to assess the risks posed by the uncertainty of renewable energy output to the power system. Secondly, price-based demand response and low-carbon flexibility retrofits for thermal power units are introduced to enhance the level of renewable energy absorption while mitigating excessive carbon emissions caused by deep peak load regulation of thermal power units. Thirdly, a low-carbon economic optimization scheduling model for the power system is established, with the objective function of minimizing the total system operation cost and operation risk value. Finally, the effectiveness of the model is verified through practical examples.