A Unified (P)DAE Modeling Approach for Flow Networks

  • Lennart Jansen
  • Caren Tischendorf
Conference paper
Part of the Differential-Algebraic Equations Forum book series (DAEF)


We present a unified modeling approach for different types of flow networks, for instance electric circuits, water and gas supplying networks. In all cases the flow network is described by the pressures at the nodes of the network and the flows through the branches of the network. It is shown that the mass balance equations at each node are independent of the type of flow medium and can be described by the use of incidence matrices reflecting the network topology. Additionally, various types of net element models are presented. Finally, all network describing equations are summarized for some prototype networks which differ by the various net element models. They yield in pure linear/nonlinear equation systems, differential-algebraic systems or partial differential equation systems. All of them may have serious rank changes in the model functions if switching elements belong to the network. The model descriptions presented here keep all the network structure information and can be exploited for the analysis, numerical simulation and optimization of such networks.


Modeling Flow network Partial differential algebraic equation Circuit Water network Gas network 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Humboldt-Univerität zu BerlinBerlinGermany

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