The integrated electricity-gas system (IEGS) is the foundation of the Energy Internet. As inevitable risk factors

the widespread blackout and large-scale energy supply disruptions represent serious threats to the IEGS. Improving the load restoration ability of IEGS is an important measure to mitigate the harm caused by blackouts. However

the increasing penetration of wind power has posed some difficulties to IEGS load restoration. In view of this

based on distributionally robust optimization (DRO)

a two-stage IEGS restoration model is developed in this paper. Through a detailed mathematical model of an electric power system (EPS) with multiple generating resources and a natural gas system (NGS) with dynamic characteristics

the supporting role of the NGS operation flexibility for IEGS restoration is fully explored and quantitatively analyzed. Through the construction of a Wasserstein metric-based ambiguity set of wind power forecast deviation

the proposed two-stage IEGS restoration model can incorporate operational risks when the uncertainty of wind power output is encountered and also take into account the flexible reserve capacity (FRC) allocation and deployment constraints. The proposed model can realize the reasonable scheduling of wind power

automatically determine the allocation of the required FRC

and optimize the load restoration schemes. Moreover

the proposed model can be converted into a mixed integer linear programming problem which can be directly solved. In the case study

the advantages of the proposed model are compared with three conventional restoration models based on two test systems

and sensitivity analysis is conducted.