Generalized Normalized Cut and Spanning Trees for Water Distribution Network Partitioning

Abstract

This study present an efficient graph-theoretical method for automatic design of district metered areas (DMAs) in water distribution networks (WDNs). The proposed method consists of two main parts, WDN partitioning and DMA connection, and is tested on a real-life WDN for which three spectral partitioning methods, multiple weight cases, and two clustering criteria are compared. The efficiency of the proposed DMA connection algorithm with respect to the traditional combinatorial approach is shown for different numbers of established DMAs. The final solution is selected according to a multicriteria evaluation model, which was developed in order to reduce the subjective influence in the selection process and considers hydraulic, cost, and topological criteria. The results show that all three tested spectral partitioning methods, i.e., the ratio cut, normalized cut, and newly proposed generalized normalized cut, are suitable for WDN partitioning and that the quality of the obtained solutions can be further improved by considering appropriate topological and cost-based WDN information in the partitioning process.