Preprocessing of water distribution systems to assess connectivity and solvability in the presence of flow control devices

Abstract

Although mathematical modeling of the hydraulics and water quality of drinking water distribution networks is widely used in network planning and management existing solvers sometimes deliver no results or even wrong results if the connectivity of the system is not correctly maintained. In this paper two major causes for deficient network connectivity are considered. In the first case, the network graph consists of several maximal connected components where some of them have no node with a fixed head source. Those deficient networks can result from errors in the reference data system (GIS) or during data transfer. In the second case, all the links and nodes of the network graph are connected. However, some links representing control devices have upper and/or lower bounds for the flows. Similar problems as in the first case can be observed if the topology of the network is reduced by removing links with active flow control devices from the graph resulting in a disconnected system. The problem is that the identification of control devices that are active (when an inequality constraint is fulfilled be equality) at a certain time step is not straight forward and depends on the actual hydraulic state of the distribution system. In this paper two preprocessing steps of the hydraulic steady-state or extended period simulations are proposed to check the solvability of the mathematical problem with respect to the flow constraints. In the first step, the connectivity of the system is analyzed and network parts without a fixed head source are identified. In the second step, a Linear Program (LP) is formulated that includes the nodal continuity conditions plus additional inequality constraints that refer to the operation of the flow controlling devices. The optimal objective value of the LP indicates if for the original problem either a) a solution exists, b) does not exist or c) exists but has redundant control constraints.