Capital-Cost Minimization of Hydraulic Network

Water distribution systems involve considerable capital costs. One basic analysis is to minimize the cost for a deterministic load pattern. This study presents a method to determine the global minimum of the capital costs for continuous diameters. Using fundamental graph theory the original nonconvex problem is decomposed into independent sets of convex functions subject to linear constraints. Standard algorithms are available to solve the transformed version. The nonconvex capital cost function of a hydraulic network has been transformed to subsets of nonlinear convex functions by a decomposition principle from graph theory. The variables are the flows and head losses in each pipe and the constraints linear expressions of the head losses. The global minimum cost solution follows using a standard nonlinear programming algorithm.