Simplification of water distribution networks using non-linear Thevenin theorem and its application for maximum power transfer

Abstract

Abstract The boundaries of existing cities are expanding rapidly due to the exponential growth in urban population. Therefore, the existing water distribution networks (WDNs) need to be expanded up to the newly developed areas to meet the additional water demand. The optimal design of a sub-network planned for network expansion requires multiple simulations under various constraints. Simulating the additional sub-network along with the existing network takes a lot of CPU time. In this study, a methodology is proposed to replace an existing large pipe network with its equivalent network consisting of a single source and a single pipe by applying the non-linear Thevenin theorem being used for electrical circuits. The equivalent network model parameters are extracted by fitting the driving-node head-loss characteristics at the connecting node. Unlike all other available methods except the traditionally used reservoir–pump model, the equivalent network presented in this study reduces to only two elements. The theoretical aspect of the reservoir–pump model can be explained by the proposed Thevenin reduction method. The advantage of the proposed method is put forward by deriving an analytical expression for the condition of maximum power transfer from the equivalent main network to the sub-network. The economic diameter value of the connecting pipe is subsequently determined. The proposed network reduction method is demonstrated on different WDNs for various demand patterns. The reduced networks yield accurate results and simulate faster when compared with those of the original networks. The proposed methodology is beneficial for a focused analysis of a sub-network and to transfer maximum power to the sub-network connected to a large existing hydraulic network.