To address the new challenge of wind power installed capacity growth on the peak shaving capability of thermal power units under carbon peak and carbon neutrality targets, a robust optimization capacity configuration and economic dispatch model for thermal power units and energy storage is proposed. This model considers the wind power output volatility and carbon tax, and optimizes the energy storage system capacity and charging and discharging strategies for thermal power units by establishing a discrete set of uncertain scenarios in the annual time scale of wind power. Using the Column and constraint generation (C&CG) algorithm, the model is transformed into a main problem for optimizing energy storage capacity and a sub problem for optimizing scheduling strategies, and is solved through alternating iterations. Based on the optimization results of different wind power proportions and robustness levels, the simulation is conducted using historical wind power data throughout the year to analyse the costs and benefits. It is recommended that thermal power plants should be equipped with energy storage systems equivalent to 19% of their thermal power unit capacity. The configuration can achieve up to 85.5% conventional peak shaving capability and promote low-carbon economic operation of thermal power units, while ensuring the economic viability of the energy storage investment.