Abstract
Stationary network problems are considered, unifying linear Kirchhoff equations and non-linear element equations, possessing a proper signature of the derivatives. The global non-degeneracy of the Jacobi matrix is proven, providing the applicability of globally convergent tracing algorithms for such systems. It is shown that stationary problems in gas transport networks can be written in the form necessary for the global convergence. Two stabilized algorithms for the solution of these problems are implemented. The algorithms outperform a standard Newtonian solver for a number of realistic networks. The algorithms do not depend on the starting point, are stable, converge for all scenarios and, additionally, provide feasibility indicator for the problem statement.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Clees, T., et al.: A globally convergent method for generalized resistive systems and its application to stationary problems in gas transport networks. In: Proceedings of SIMULTECH 2016, pp. 64–70. SCITEPRESS (2016)
Armijo, L.: Minimization of functions having Lipschitz continuous first partial derivatives. Pac. J. Math. 16(1), 1–3 (1966)
Katzenelson, J.: An algorithm for solving nonlinear resistor networks. Bell Syst. Tech. J. 44(8), 1605–1620 (1965)
Chien, M.J., Kuh, E.S.: Solving piecewise-linear equations for resistive networks. Int. J. Circ. Theory Appl. 4(1), 1–24 (1976)
Griewank, A., et al.: Solving piecewise linear systems in abs-normal form. Linear Algebra Appl. 471, 500–530 (2015)
Kelley, C.T.: Iterative Methods for Linear and Nonlinear Equations. SIAM, Philadelphia (1995)
Allgower, E.L., Georg, K.: Introduction to Numerical Continuation Methods. SIAM, Philadelphia (2003)
Press, W.H., et al.: Numerical Recipes in C. Cambridge University Press, New York (1992)
Wächter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25–57 (2006)
Clees, T., et al.: MYNTS: multi-physics network simulator. In: Proceedings of SIMULTECH 2016, pp. 179–186. SCITEPRESS (2016)
Mischner, J., et al.: Systemplanerische Grundlagen der Gasversorgung. Oldenbourg Industrieverlag GmbH, München (2011)
Schmidt, M., et al.: High detail stationary optimization models for gas networks. Optim. Eng. 16(1), 131–164 (2015)
DIN EN ISO 12213-2: Natural Gas – Calculation of compression factor, European Committee for Standartization (2010)
Acknowledgements
We are grateful to the participants of SIMULTECH 2016 conference for fruitful discussions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Clees, T., Nikitin, I., Nikitina, L. (2018). Making Network Solvers Globally Convergent. In: Obaidat, M., Ören, T., Merkuryev, Y. (eds) Simulation and Modeling Methodologies, Technologies and Applications. SIMULTECH 2016. Advances in Intelligent Systems and Computing, vol 676. Springer, Cham. https://doi.org/10.1007/978-3-319-69832-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-69832-8_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-69831-1
Online ISBN: 978-3-319-69832-8
eBook Packages: EngineeringEngineering (R0)