Iterative Hydraulic Interval State Estimation for Water Distribution Networks

Abstract

State estimation of hydraulics (i.e., pressure and flows) in water distribution networks is an important tool for efficient and resilient operation. However, hydraulic state estimation is a challenging task in practice due to the scarcity of measurements and the presence of several modeling uncertainties. Standard state estimation techniques may produce unreliable estimates with no information of the estimation error magnitude, especially when historical data are used in place of missing measurements. This paper proposes a comprehensive methodology for generating hydraulic state bounding estimates by considering both measurement and parametric uncertainties. The methodology is based on solving the nonlinear interval hydraulic equations using bounding linearization, a technique that restricts the nonlinearities within a convex set, thus converting the problem to a form which is solvable using linear optimization. An iterative procedure improves the bounding linearization, converging to the tightest possible bounds. Simulation results demonstrate that the proposed methodology produces tight state bounds that can replace Monte Carlo simulations.