Seamless pressure-deficient water distribution system model

Pressure-deficient conditions are a common occurrence in water distribution systems. These situations require accurate modelling for timely decision making. However, the conventional demand-driven analysis approach to network modelling is unsuitable for operating conditions with insufficient pressure. Increasing emphasis is being placed on the need for water companies to satisfy stringent performance standards for the continuous supply of water to consumers and it is those pressure-deficient operating conditions which are critical in determining whether or not adequate supplies can be provided. It is therefore very unfortunate that the demand-driven analysis method becomes invalid for use in precisely those critical conditions. The aim of this paper is to present a new pressure-dependent demand function to help improve the simulation of pressure-deficient conditions. The proposed function has better computational properties than those in the literature and has been incorporated successfully in the governing equations for water distribution networks. In particular, the proposed function and its derivative do not have the discontinuities that often cause convergence difficulties in the solution of the constitutive equations. A robust Newton–Raphson algorithm was developed to model water distribution systems under both normal and pressure-deficient conditions in a seamless way. Examples which demonstrate the methodology are included.