Abstract: Integrated gasification fuel cell (IGFC) is an efficient, clean, and stable green coal-fired power technology highly compatible with carbon capture system (CCS). It is expected to overcome the high cost and high energy consumption of low-concentration CO₂ under the traditional CCS. In this paper, a wind-thermal-energy storage power system with IGFC-CCS is constructed; the operation mechanism of IGFC-CCS is studied; the mathematical model of each link in IGFC is established; and the operation conditions of the combustion utilization rate and cathode air utilization rate are analyzed. The electricity-carbon characteristics of IGFC-CCS are analyzed. To consider the uncertainty of wind power, a two-stage distributionally robust optimization is proposed for economic dispatch. The k-adaptability theory is introduced, and a solution based on the orthant support subset strategy is proposed to obtain a robust counterpart. Finally, case studies are carried out in the modified IEEE-30 node system. The results show that the IGFC-CCS can use anode carbon enrichment to achieve low-carbon economic dispatch, verifying that the proposed optimization method can improve the interpretability of the feasible solution.