The integration of wind power is vital for enabling a low-carbon energy transition and fostering a sustainable society. However, its intermittent nature and the power system's limited transmission capacity challenge system stability. This study develops a low-carbon optimal scheduling model incorporating post-combustion carbon capture technology, energy storage, and an improved genetic algorithm (GA) to solve the optimization problem efficiently. The model evaluates the impact of carbon capture prices on energy storage allocation and unit power supply costs under high wind power penetration. Results demonstrate that increasing wind power capacity reduces the unit cost of electricity supply from 0.202 CNY/kWh to 0.164 CNY/kWh while improving system stability through energy storage deployment. Additionally, increasing the carbon capture price raises generation costs, peaking at 3.584 million CNY, but significantly reduces carbon emissions. For instance, at a carbon capture price of 100 CNY per ton, energy storage capacity reaches 127.6 MWh with a power output of 74.9 MW, achieving a unit cost of 0.152 CNY/kWh. These findings highlight the effectiveness of the proposed model and the improved GA in balancing economic, environmental, and system stability goals, offering a robust strategy for sustainable power system operation.