Unified Framework for Deriving Simultaneous Equation Algorithms for Water Distribution Networks

The known formulations for steady-state hydraulics within looped water distribution networks are rederived in terms of linear and nonlinear transformations of the original set of partly linear and partly nonlinear equations that express conservation of mass and energy. All of these formulations lead to a system of nonlinear equations that can be linearized as a function of the chosen unknowns using either the Newton-Raphson (NR) or the linear theory (LT) approaches. This produces a number of different algorithms, some of which are already known in the literature, whereas others have been originally developed within this work. For the sake of clarity, all the different algorithms were rederived using the same analytical approach and a unified notation. They were all applied to the same test case network with randomly perturbed demands to compare their convergence characteristics. The results show that all of the linearly transformed formulations have exactly the same convergence rate, whose value depends on whether a NR or LT algorithm was used, and that they converge faster than the nonlinearly transformed formulations do. A number of computational factors suggest that the global algorithm, in either its NR or LT form, is the most attractive of the various formulations to implement.