Modeling Control Valves in Water Distribution Systems Using a Continuous State Formulation
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 11
Abstract
Control valves are commonly used for the operation of water distribution systems. Modeling these devices typically requires that their operating states are known, or that a computationally expensive search is undertaken over all possible operating states. This paper presents a novel method of modeling control valves (including flow control, pressure sustaining, pressure reducing and check valves) in extended-period simulations of water distribution systems. Instead of the normal discrete control problem formulation, it is approached with the Karush-Kuhn-Tucker equations for an optimization problem with constraints. The proposed method does not prerequire the operating state (open, closed, active) of each valve to be determined, as this is done implicitly. Pipe and valve flow rates and nodal heads are determined by: (1) minimizing deviations from targets at control valves, and (2) satisfy the state equations (conservation of mass and energy) by solving a constrained least-squares problem. Sensitivity equations with respect to the control variables (valve settings) are derived from the state equations, and the control variables are updated using Levenberg-Marquardt iterations. The results of simple problems and case studies are presented to demonstrate the effectiveness of the approach.
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Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 11 • November 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 1, 2013
Accepted: May 20, 2014
Published online: Jul 8, 2014
Published in print: Nov 1, 2014
Discussion open until: Dec 8, 2014
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