State Estimation in Water Networks: A Tutorial

~ ~ "'hi 6h, q .. = K C. D~·63CO.(h ·~h) I h ·-h '1'°.46 IJ 1I lJ IJ IJ I J 1 j First we must deal with the non-linearities inherent in water flow through pipes and other elements. The relationship between flow and pressure (or head) in a pipe can be represented using a number of alternative empirical formulae. An example is the Hazen-Williams equation: exact flows and pressures throughout the system from online SCADA data, in real time. This would allow the operator to see the effects of operational control and to respond accordingly. Although demand forecasting and, to some degree, pump scheduling packages are in regular use in the water industry, they suffer from the unreliability and stochasticity of input data. A state-estimator reduces the uncertainty in the available infonnation and would pennit the application of such techniques with greater confidence. This paper offers an explanation of the basic principles of state estimation using simple mathematics and a very simple model of a water network. It makes no claim to novelty as, in the simplistic fonn described here, the method is well known. Nevertheless, despite the fact that state-estimation is widely used in power distribution systems, the application to water networks is still a matter for ongoing research and development. Introduction