Optimal Pressure Regulation in Water Distribution Systems Based on an Extended Model for Pressure Reducing Valves

Optimal pressure regulation to reduce water losses in water distribution systems (WDSs) becomes an important concern due to the increasing water demand and the threat of drought in many areas of the world. The leakage amount in a WDS depends heavily on its operating pressure and thus can be minimized by implementing optimal pressure strategies through pressure reducing valves (PRVs). To achieve this, a model-based optimization is necessary, where an accurate model of the PRVs is required. The PRV models having been used until now for pressure regulations are two-mode models which cannot circumstantiate many situations occurring in WDSs. In this paper, we extend the existing model by a three-mode one for PRVs which is able to describe the required circumstances of pressure regulations in WDSs. The non-smoothness of this model is smoothed by an approximation approach, thus allowing the formulation and solution of a continuous nonlinear optimization problem for optimal pressure regulation. Two benchmark WDSs are used to verify our approach and it can be shown from the results that our PRV model outperforms the existing models in terms of the quality and accuracy of the optimal solutions.