High-Order Global Algorithm for the Pressure-Driven Modeling of Water Distribution Networks

This paper presents a novel algorithm with improved convergence and robustness for the pressure-driven modeling of water distribution networks (WDNs), to be implemented as hydraulic engine in the fourth release of the SWANP version 4.0 software. The innovative approach is based on increasing the order of convergence, which is quadratic for algorithms obtained from the Newton Raphson linearization of the equations for WDN resolution. As an example, the cubic order of convergence is obtained by evaluating system matrices at the generic iteration in a more refined way to account for the curvature of the hyperplane associated with the system in the direction of the Newton Raphson step. To show the benefits of the methodology, a third-order algorithm is constructed and compared with a traditional second-order. Both algorithms are based on the direct pressure-driven formulation expressing outflows as a function of service pressure and are equipped with the dampening of the Newton Raphson step. Applications on two case studies of different size, in which challenging pressure-driven conditions are created through demand amplification and segment isolation scenarios, prove that the methodology always reduces the total number of iterations required for convergence and the application of the step dampening. Overall, the results also show that the more stable convergence behavior is accompanied by an appreciable reduction in computation times. Further analyses proved that the third-order algorithm has similar convergence properties to algorithms based on the inverse pressure-driven formulation recently proposed in the scientific literature and can therefore be considered as a valid alternative to these algorithms.