Extending the Global-Gradient Algorithm to Solve Pressure-Control Valves

This work introduces two novel methods to the solution of water distribution networks equipped with pressure-control valves based on the global-gradient algorithm (GGA). One method, which can be viewed as an extension of that used to estimate the variable speed coefficient of variable speed pumps, leads to a nonsymmetric system to be solved at each iteration by introducing a new unknown (the head loss at the valve) and imposing the head at the controlled node. The second method maintains the symmetry of the system to be solved by imposing the head at the controlled node, removing the pipe equipped with the valve, and adjusting the mass-balance equation in the other node of the removed pipe. The performances of the proposed methods were analyzed on four case studies, and the results were also compared to those of EPANET 2 in terms of hydraulic accuracy and efficiency.