Comparison of Newton-Raphson Global and Loop Algorithms for Water Distribution Network Resolution

Abstract

This paper presents the comparison of two algorithms for water distribution network resolution in terms of computational efficiency: the Newton-Raphson Global (NR-GA) and the Newton-Raphson Loop Flows (NR-LF). Both algorithms use the hydraulic equations linearized by the Newton-Raphson method; however, whereas NR-GA solves the equations projected onto network nodes and pipes, the NR-LF solves the equations projected onto network loops and then requires the loop matrix to be determined prior to its application. In particular, the computational efficiency of the latter algorithm turns out to be maximized when reference to the sparsest possible loop matrix is made. In a bid to apply efficiently the NR-LF to high complexity case studies, a new automatic procedure for the identification of the basis of minimum loops from the topological viewpoint (i.e., of the basis of independent loops made up of the lowest number of pipes) is presented. The comparison between the NR-GA and NR-LF points out the slight superiority of the latter, which offers shorter computation times above all for case studies of low-intermediate topological complexity. However, an increase in network topology complexity affects the performance of the NR-LF more than that of the NR-GA, thus leading to an almost identical performance in case studies of very complex topology.