Mathematical Program with Vanishing Constraints for Optimal Pressure Control in Water Distribution Systems

Abstract

Optimizing pressure management to reduce water leakage in water distribution systems (WDSs) is one of the major tasks for water utilities. By regulating the operation of pressure reducing valves (PRVs) installed in WDSs, the pressure in WDSs can be kept under control and thus the water leakage amount can be decreased. Mathematically, the problem of pressure management to water leakage reduction can be formulated as a nonlinear optimization program. To make the optimization model proper for practice, the model of PRVs should be accurate and can describe all its operation modes in practice: active, fully opened, and check valve modes. In the literature, the model can be represented either by a non-smooth equation with low accuracy or by several complicated constraints. This research developed a highly accurate PRV model based on vanishing constraints. The idea comes from the fact that the model equation representing operations of PRVs in active mode will be vanished as PRVs operate in the check valve mode. The formulated mathematical program with vanishing constraints (MPVCs) can be solved efficiently by using the regularization approach. Several WDSs have evaluated the new PRV model which shows that accurate solutions are obtained with less computation time.