Topological state estimation in water distribution systems: Mixed-integer quadratic programming approach

State estimation (SE) techniques can be applied to compute the most likely hydraulic state of a water distribution system from the available measurements at a given time. Different approaches exist in the technical literature to undertake such an analysis, but in all of them it is assumed that pump and valve statuses are known beforehand. Such consideration may lead to unrealistic results if real-time unnotified changes in the operation of the network take place, limiting the usefulness of the information provided by telemetry systems. This work eliminates the known-status assumption and presents the concept of topological state estimation (TSE), which not only computes the hydraulic state of the system, but also the current pump and valve status according to the existing measurements. More specifically, a novel methodology for TSE is set out in this paper. The proposed method is derived from the original mixed-integer non-linear programming formulation of the problem, which is transformed in an iterative mixed-integer quadratic programming problem by linearizing some hydraulic constraints. The potential of the methodology is presented by means of an illustrative example and a large case study, in which pumps, gate valves and check valves exist. Results show that TSE would successfully contribute to make the most of available telemetry systems, hence expanding the online monitoring possibilities of water distribution networks.

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