Graph Partitioning in the Analysis of Pressure Dependent Water Distribution Systems
Partition de graphe de réseaux pour l'analyse conduite par la pression des réseaux de distribution d'eau
Elhay, S. ; Deuerlein, J. ; Piller, O. ; Simpson, A.R.
Type de document
Article de revue scientifique à comité de lecture
Affiliation de l'auteur
UNIVERSITY OF ADELAIDE SCHOOL OF COMPUTER SCIENCE ADELAIDE AUS ; 3S CONSULT GMBH KARLSRUHE DEU ; IRSTEA BORDEAUX UR ETBX FRA ; UNIVERSITY OF ADELAIDE SCHOOL OF CIVIL ADELAIDE AUS
Résumé / Abstract
The forest core partitioning algorithm (FCPA) and the fast graph matrix partitioning algorithm (GMPA) have been used to improve efficiency in the determination of the steady-state heads and flows of water distribution systems that have large, complex network graphs. In this paper, a single framework for the FCPA and the GMPA is used to extend their application from demand dependent models to pressure dependent models (PDMs). The PDM topological minor (TM) is characterized, important properties of its key matrices are identified, and efficient evaluation schemes for the key matrices are presented. The TM captures the network's most important characteristics: It has exactly the same number of loops as the full network, and the flows and heads of those elements not in the TM depend linearly on those of the TM. The inverse of the TM's Schur complement is shown to be the top, left block of the inverse of the full system Jacobian's Schur complement, thereby providing information about the system's essential behavior more economically than is otherwise possible. The new results are applicable to other nonlinear network problems, such as in gas, district heating, and electrical distribution.
Journal of Water Resources Planning and Management, vol. 144, num. 4, p. 04018011-1 - 04018011-13