Optimal Reorganization and Extension of an Existing Water Distribution Network using the Thevenin Equivalent Network

A water distribution network (WDN) costs more than 60% of the total cost of a water supply system. It is indeed crucial to optimize a WDN for its economical design. Due to rapid urbanization and population growth, a particular portion of the existing network must be reorganized or extended to new zones. For the purpose of optimal reorganization, the new zone or the portion of the existing network can be identified as the sub-network. The optimal design of the sub-network demands high computational effort as the entire network needs to be simulated multiple times. To improve computational efficiency, the sub-network is separated from the large network, and the remaining network is replaced with its equivalent network with a minimum number of elements using the Thevenin theorem. The theorem can replace an extensive network with its equivalent, having a single reservoir connected in series with an equivalent pipe. The optimal design of the sub-network uses the derived Thevenin equivalent network connected with the sub-network. As the overall network size becomes considerably small, the computational effort also reduces exponentially. The probability of getting the most optimal solution is also improved as the search space is reduced. The proposed methodology is demonstrated with the help of a realistic WDN and computational efficiency is investigated for various sets of pipe diameters. The network reduction method is found to be enormously helpful for hydraulic engineers in designing and optimizing a sub-network for reorganization and extension.