Topological Index Criteria in DAE for Water Networks ZIB-Report 05-49 (December 2005) TOPOLOGICAL INDEX CRITERIA IN DAE FOR WATER NETWORKS

The dynamics of pressurized water networks are naturally modeled by differential-algebraic equations (DAE). This article investigates fundamental structural properties of such a DAE model under weak regularity assumptions. The usual algebraic index-1 condition is shown to be necessary and sufficient with respect to several index concepts, as well as sufficient for solvability in a strong sense. Using the physical properties of nonlinear network elements and the inherent saddle point structure of network hydraulics, we then derive purely topological index criteria in terms of the network graph and the choice of control variables. Several examples illustrate the theoretical results and explore different non-index-1 situations. A brief discussion of the implications for operative planning based on discrete time DAE boundary value problems concludes the paper.