###### Abstract
Previous works have fixated on the coordination of natural gas and electricity networks at synergistic scheduling level. Electricity network flow rules are summarized in [22] to solve the gas flow problem. Reference [23] presented a methodology for considering the combination of the natural gas network. Coordination with stochastic scheduling were studied in [24]. Scheduling problems, including electricity demand response, were presented in [25,26]. Natural gas prices impacting on the system were examined in [27,28,29]. Several investigations have fixated on solving steady-state natural gas flow. The challenges are contributed from the non-linear and non-convex Weymouth equation, that is, the natural gas flow is a nonlinear programming (NLP) problem. References [22,23] employed a nonlinear solution or commercial solvers to determine gas flow, including interior point method or Newton-Raphson methods. Approximate piecewise linearization methods were presented in [30] and [31] by transforming to a mixed-integer linear programming (MILP) problem. To eliminate non-convexity, researchers in [10] and [32] employed the special form of the Weymouth equation by transforming the NLP problem to MISOCP via convex relaxation. Natural gas and electricity networks are owned by various operators and stakeholders. However, both networks are often seen as an integrated system to achieve coordinated operation or establish a third-party coordinator with a lot of information interaction. The main contributions of this work are as follows:  
* Proposed a novel CO framework and this changes the traditional decision sequence. With this framework, it is possible to avoid frequent information interaction and without a third coordinator. * A model is constructed to generate NGFUs' gas consumption constraints. A CR indicator and an update method are introduced, to generate reasonable gas consumption constraints information deliver from gas network operator (GNO) to electricity network operator (ENO). * Impact of considering classic demand response program [33] and congestion is discussed in a decentralized and coordinated operation. For GNO optimization subproblem, an improve SCP method based SOC with reasonable initial expansion value is used to determine the steady-state gas flow in a natural gas network. * Simulations under different scenarios, considering the NG and electricity networks operation, based on a benchmark 6-bus electricity system and 6-node natural gas system were used to verify the proposed framework, considering solution convergence and benefits obtained. * The impact of the coordinated operation is studied with congestions and demand response. The present method can give a better convergence when compared to a very popular method such as ADMM. Section 2 presents the formulations of the framework for coordination operation for one IEGS. Section 3 provides a mathematical model for the two sub-optimization problems, namely, GNO optimization and ENO optimization. Section 4 gives the solution methodology for solving the optimization of the two networks based on Weymouth function. Case studies and discussions are given in Section 5. Conclusion and future work are provided in Section 6.