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Further development on globally convergent algorithms for solution of stationary network problems is presented. The algorithms make use of global non-degeneracy of Jacobi matrix of the system, composed of Kirchhoff's flow conservation conditions and transport element equations. This property is achieved under certain monotonicity conditions on element equations and guarantees an existence of a unique solution of the problem as well as convergence to this solution from an arbitrary starting point. In application to gas transport networks, these algorithms are supported by a proper modeling of gas compressors, based on individually calibrated physical characteristics. This paper extends the modeling of compressors by hierarchical methods of topological reduction, combining the working diagrams for parallel and sequential connections of compressors. Estimations are also made for application of topological reduction methods beyond the compressor stations in generic network problems. Efficiency of the methods is tested by numerical experiments on realistic networks.
The paper presents the topological reduction method applied to gas transport networks, using contraction of series, parallel and tree-like subgraphs. The contraction operations are implemented for pipe elements, described by quadratic friction law. This allows significant reduction of the graphs and acceleration of solution procedure for stationary network problems. The algorithm has been tested on several realistic network examples. The possible extensions of the method to different friction laws and other elements are discussed.