Ellipsoid method for quantifying the uncertainty in water system state estimation

For a water distribution system simulation the three main causes of uncertainty are: an inaccurate network model; inaccurate predictions of consumptions; and errors associated with measurements (random and systematic). A smaller contribution to simulation uncertainty comes from the inaccuracy of the mathematical solution techniques and from the precision limits of the computers used. The input uncertainty, from all these sources, is transferred, through the state estimation process, and results in estimates of the operating states that are also uncertain. The precise way in which the input uncertainty affects the accuracies of calculated states is rather complicated, many interrelated factors are involved. The distribution of meters throughout the network, the network´s topology and the operating state of the network all play an important role. Confidence limit analysis-the process of quantifying this uncertainty on state estimates-has implications in many areas of water system operations from distribution system design, through telemetry system design and implementation to real-time control and decision support. This paper reports our experiences with the ellipsoid algorithm that has been adapted to provide confidence limits on state estimates in the nonlinear water system state estimation proces