Water loss according to water leakages in water distribution systems (WDSs) is a challenging problem worldwide. An inappropriate operation of the WDS leads to unnecessarily high pressure distribution in the WDS and thus a large amount of water leakage exists. For this reason, optimal pressure management in WDSs through regulating operations of pressure reducing valves (PRVs) is priority for water utilities. The pressure management can be accomplished in a hierarchical control scheme with high level and low level controllers. While the high level controller is responsible for calculating pressure set points for critical nodes, the task of a low level controller is to regulate the pressures at the critical nodes to the set points. The optimal pressure management in the high level controller can be casted into a nonlinear programing problem (NLP) where PRV models are crucial and determine proper operation of the WDS and quality of overall pressure control. PRV models having been used until now either describe two operating modes (active and open modes) or three operating modes (active, open and check valve modes) with parameter dependence. Such models make the formulated NLP unsuitable for the case PRVs work in check valve modes or resulted in inaccurate NLP solution with unexpected operation modes of PRVs, respectively. Therefore, this paper proposes an accurate PRV model based on complementarity constraints. The new PRV model is parameter-less dependence and is capable of describing complete operation modes of PRVs in practice. As a result, the formulated NLP is general and provides accurate NLP solution. The efficiency of our new PRV model is demonstrated on numerous case studies for optimal pressure management of WDSs.
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