This paper proposes a decentralized robust two-stage dispatch framework for multi-area integrated electric-gas systems (M-IEGSs)

with the consideration of Weymouth and linepack equations of tie-pipelines. The overall methodology includes the equivalent conversion for the robust two-stage program and the decentralized optimization for the equivalent form. To obtain a tractable and equivalent counterpart for the robust two-stage program

a quadruple-loop procedure based on the column-and-constraint generation (C&CG) and the penalty convex-concave procedure (P-CCP) algorithms is derived

resulting in a series of mixed integer second-order cone programs (MISOCPs). Then

an improved I-ADMM is proposed to realize the decentralized optimization for MISOCPs. Moreover

three acceleration methods are devised to reduce the computation burden. Simulation results validate the effectiveness of the proposed methodology and corresponding acceleration measures.