This paper addresses the energy management problem for multiple distribution-level integrated electric-gas prosumers (IEGPs) considering peer-to-peer (P2P) trading. The IEGPs are self-interested and interconnected, and they are also connected to transmission-level energy systems. Considering the equal decision-making structure and coupling constraints, the overall problem boils down to a generalized Nash game, whose equilibrium reflects the energy trading results. Due to the presence of Weymouth equations in the gas network, the decision-making problem of each IEGP becomes non-convex, which hinders direct application of the generalized Nash equilibrium (GNE) seeking algorithms. The non-convex Weymouth equation is convexified using the penalty convex-concave procedure. Then, a GNE can be offered by the proximal decompose algorithm with a convergence guarantee. The effectiveness of the proposed model and algorithm is verified by simulation results.

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.