Applications of the single-port linear Thevenin theorem for focused and efficient analysis of a sub-network connected with a large existing pipe network

An existing water distribution network (WDN) may need to be expanded by adding a sub-network for the newly developed areas. The size of the problem becomes larger when the stochastic nature of domestic demands, optimal design and layouts, control, and operation of various hydraulic components are considered. In this study, the single-port Thevenin theorem used in electrical circuits is applied to reduce a large WDN with its equivalent network consisting of a single source and a single pipe. The equivalent network is then attached to a sub-network for focused analysis. The accuracy and robustness of the proposed network reduction procedure are investigated on realistic WDNs for various sub-network demands using steady and extended period simulations. A simplified approach is also presented to achieve the same objective but constrained by the level of accuracy. Hydraulic engineers can use the proposed methodology as an efficient network reduction tool.