A globally convergent method for generalized resistive systems and its application to stationary problems in gas transport networks

We consider generalized resistive systems, comprising linear Kirchhoff equations and non-linear element equations, depending on the flow through the element and on two adjacent nodal variables. The derivatives of the element equation should possess a special signature. For such systems we prove the...

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Bibliographic Details
Published in2016 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH) pp. 1 - 7
Main Authors Clees, Tanja, Hornung, Nils, Nikitin, Igor, Nikitina, Lialia
Format Conference Proceeding
LanguageEnglish
Published SCITEPRESS 01.07.2016
Subjects
Convergence
Gas Transport Networks
Globally Convergent Methods
Jacobian matrices
Linear systems
Mathematical model
Non-linear Systems
Pins
Regulators
Symmetric matrices
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Summary:We consider generalized resistive systems, comprising linear Kirchhoff equations and non-linear element equations, depending on the flow through the element and on two adjacent nodal variables. The derivatives of the element equation should possess a special signature. For such systems we prove the global non-degeneracy of the Jacobi matrix and the applicability of globally convergent solution tracing algorithms. We show that the stationary problems in gas transport networks belong to this generalized resistive type. We apply the tracing algorithm to several realistic networks and compare its performance with a generic Newton solver.