An Efficient Mixed Integer Nonlinear Program Model for Optimal Positions of Pressure Reducing Valves in Water Distribution Systems

Abstract

Water loss happens in all water distribution systems (WDSs). To deal with such the problems, pressure management strategy should be applied to lessen the water leakage flow. The optimal pressure management is formulated to minimize the total of excessive pressures in all demand supplying nodes. In mathematical formulation, it is a mixed-integer nonlinear program (MINLP). The existing MINLP model having been used until now for optimizing PRV locations is proven to be hard for MINLP algorithms based gradient methods and therefore is only suitable for small-scale WDSs with a limited number of demand patterns. In this paper, an efficient non-smooth constraints are proposed to model whether PRVs are installed on links for the optimal PRV localization problem. Since these constraints can be approximated by relaxed forms of complementarity inequalities, high quality MINLP solution can be achieved in a reasonable computation time. To demonstrate the efficacy of our new modeling approach, comparison of the performance of the newly formulated MINLP with the existing one for solving optimal PRV locating problems for a real WDS are taken. The results have shown that with our new MINLP model, better MINLP solution can be attained even for WDSs with multiple demand patterns.