Application of Thevenin Theorem for Model Reduction and Analysis of Large Water Distribution Networks

Due to rapid urbanization, the existing water distribution networks need to be expanded by adding sub-networks for the newly developed areas. The stochastic nature of demands requires several simulations of the full network for optimum design and cost minimization. The size of the simulation problem thus becomes complex and computationally expensive. The reduced models can be handy for designing and optimizing such networks. This paper describes the usage of equivalent electrical circuit theory to reduce a large water distribution network for focussed analysis of a sub-network. Two methodologies are proposed to obtain the equivalent network using linear and nonlinear forms of the Thevenin theorem. Unlike other network reduction methods, the reduced equivalent networks derived from these methodologies have only two elements, such as a reservoir and an equivalent pipe for the existing network. In the first method, the nonlinear pipe network is replaced and implemented with its analogous linear electrical network in a circuit simulator for finding open circuit voltage and short circuit current at the desired node and branch. The equivalent pipe network parameters are estimated using these values. In the second method, the equivalent network parameters are extracted by ffitting the driving point headloss characteristics at the desired node with a suitable headloss formula. Applicability and comparison of the proposed network reduction methodologies are demonstrated on a realistic water distribution network connected with a sub-network. The simulated results of the reduced networks are compared with the solutions of the original nonlinear network. The reduced network obtained from the second method is found to yield more accurate results than the first method when the driving point headloss characteristic curve is fitted accurately. The reduced networks can be solved in much less computation cost than the original network. Therefore, the proposed network reduction methodologies are beneficial for analyzing a focused part, i.e. sub-network, of a large pipe network with stochastic demands in much less computational effort.