Distributed operation of integrated electricity and gas systems (IEGS) receives much attention since it respects data security and privacy between different agencies. This paper proposes an extended convex hull (ECH) based method to address the distributed optimal energy flow (OEF) problem in the IEGS. First, a multi-block IEGS model is obtained by dividing it into N blocks according to physical and regional differences. This multi-block model is then convexified by replacing the nonconvex gas transmission equation with its ECH-based constraints. The Jacobi-Proximal alternating direction method of multipliers (J-ADMM) algorithm is adopted to solve the convexified model and minimize its operation cost. Finally, the feasibility of the optimal solution for the convexified problem is checked, and a sufficient condition is developed. The optimal solution for the original nonconvex problem is recovered from that for the convexified problem if the sufficient condition is satisfied. Test results reveal that this method is tractable and effective in obtaining the feasible optimal solution for radial gas networks.
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