Generic Construction and Efficient Evaluation of Flow Network DAEs and Their Derivatives in the Context of Gas Networks

We present a concept that provides an efficient description of differential-algebraic equations (DAEs) describing flow networks which provides the DAE function \(f\) and their Jacobians in an automatized way such that the sparsity pattern of the Jacobians is determined before their evaluation and previously determined values of \(f\) can be exploited. The user only has to provide the network topology and local function descriptions for each network element. The approach uses automatic differentiation (AD) and is adapted to switching element functions via the abs-normal-form (ANF).

This work was supported by the German Federal Ministry of Education and Research (BMBF) within the Research Campus MODAL (fund number 05M14ZAM) and by the Deutsche Forschungsgemeinschaft through the Collaborative Research Centre TRR154 Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks.

Authors and Affiliations

1. Department of Optimization, Zuse Institute Berlin, Berlin, Germany

   Tom Streubel & Philipp Trunschke

2. Department of Mathematics, Humboldt University of Berlin, Berlin, Germany

   Tom Streubel, Christian Strohm, Philipp Trunschke & Caren Tischendorf

Corresponding author

Correspondence to Tom Streubel .

Editors and Affiliations

1. Department of Information Systems, Freie Universität Berlin, Berlin, Germany

   Natalia Kliewer

2. Management Science Group, Otto-von-Guericke Universität Magdeburg, Magdeburg, Germany

   Jan Fabian Ehmke

3. Department of Mathematics, Freie Universität Berlin, Berlin, Germany

   Ralf Borndörfer

Reprints and permissions

© 2018 Springer International Publishing AG, part of Springer Nature

Policies and ethics