Explicit Expressions for State Estimation Sensitivity Analysis in Water Systems

Abstract

The implementation of state estimation techniques to water systems enables the hydraulic state of a given network to be computed at any time. However, errors in both measurements and model parameters can severely affect the quality of the state estimate, thus sensitivity analysis is crucial to assess its performance. The aim of this paper is to provide general explicit expressions for the sensitivities of the objective function and the primal variables of the state estimation problem with respect to both measurements and roughness parameters based on the perturbation of the Karush-Kuhn-Tucker (KKT) conditions. Additionally, among all the possible applications of sensitivity analysis, two specific forms of such analysis for water systems are presented: identifiability of roughness parameters, and linear state estimate approximation. The merit of these applications is illustrated by means of a case study, which highlights the usefulness of compact sensitivity formulae to further understanding of state estimation solutions.