A simple but robust convergence trajectory controlled method for pressure driven analysis in water distribution system.

This paper presents a novel convergence trajectory controlled method to perform pressure driven analysis (PDA) in water distribution systems (WDSs). The proposed method makes forcibly the convergence error decrease continuously, which is fundamentally different from the traditional uncontrolled convergence process, thereby ensuring a robust convergence behavior for hydraulic analysis with PDA in WDS. In addition, two Relaxation Factor section strategies are developed to control the convergence trajectory towards the desired downtrends. The novel methodology is implemented based on EPANET3.0 by modifying the source code which is available in GitHub (https://github.com/OpenWaterAnalytics/epanet-dev). Firstly, the improved code was validated extensively with a benchmark WDS under rigorous boundary conditions. Subsequently, four challenging different size WDSs are also tested in terms of the effectiveness and efficiency. The results illustrate that the proposed method is able to enable the convergence of PDA to be more stable and more robust, even under some extreme abnormal boundary conditions.