Observability Analysis of Water Distribution Systems Under Parametric and Measurement Uncertainty

A state estimator is an algorithm that computes the current state of a system from on-line measurements. It is a widely held belief that since state estimators are used in the power industry they are appropriate for water networks. However, one of the key differences is the observability of the respective systems. Power systems have sufficient measurements to give high redundancy values whereas water networks are not typically as well metered. Furthermore, there is a much greater level of uncertainty present in water network models (parametric uncertainty) and in the measurements. The measurement uncertainty is largely due to the predominance of pseudo-demand measurements necessary to make up for the lack of real transducers. Before state estimation can be used, it is essential to know how observable the water distribution network is. A poorly observable system will produce misleading state estimates. This paper will present a new method, using a linear fractional transformation (LFT), which separates the parametric uncertainty in the network parameters from the nominal system. This will be compared numerically with results from a Monte Carlo simulation, applied to a thirty-four-node test network. Finally, using an algorithm based on eigenfunction analysis, the paper will demonstrate how additional measurements can be chosen in order to make the system more strongly observable.