Low-Carbon Dispatch of Integrated Electricity–Gas Systems Considering Flexible Resources and Uncertainties

High renewable energy penetration and surging electrical demand challenge the operation of integrated electricity–gas systems (IEGS) due to source and load uncertainties. This paper proposes a multi-objective optimal scheduling framework that harnesses flexible resources within the IEGS to balance economic, environmental, and energy efficiency goals. First, a liquid storage tank is introduced to reform the traditional carbon capture, utilization, and storage system. Additionally, a hydrogen energy multi-utilization structure—integrating two-stage power-to-gas, hydrogen fuel cells, and hydrogen storage—is developed to improve operational flexibility under renewable fluctuations and carbon constraints. Second, electric vehicles (EVs) schedulability is quantitatively evaluated across different charging scenarios, defining carbon quotas and profit calculation methods to incentivize EV participation. To address source-load uncertainties, a two-stage robust optimization model utilizing a box uncertainty set and budget constraints is constructed to secure the optimal scheduling solution under worst-case scenarios. Finally, by introducing penalty factors for carbon emissions and energy loss, the multi-objective function is transformed into a single-objective problem to minimize operation costs, emissions, and energy wastage. The results show that the coupled CCUS–HEMU configuration reduces the total and environmental costs by 15.50% and 77.13%. Under the worst-case source–load scenario, bidirectional EV charging further reduces the total cost by 22.10%, increases renewable-energy utilization from 87.34% to 94.34%, and decreases load fluctuation and the maximum peak–valley difference by 68.95% and 14.85%, respectively, thereby enhancing the system’s low-carbon flexibility and robustness against operational uncertainties.