A Graph Theory Modelling Approach for the Optimal Operation of Water Distribution Systems under Water Quality Constraints

Optimal water system operation, including hydraulic and water quality constraints are complex problems to solve due to the nonlinear relationship of head-loss to flow and disinfectant-loss to time. A common approach used today is evolutionary algorithms (EA) such as genetic algorithms or others. For large problems with a large number of decision variables, ether over extended period or having several pumping units, the extended solution time of the EA approach may render the approach not relevant. The proposed method utilized the operation graph optimization (OGO) algorithm proposed previously by the authors, demonstrating high speed discrete minimal cost, optimization with hydraulic constraints. A minimal cost algorithm is proposed, including hydraulic and water quality constraints. The suggested algorithm raises the concentration of the residual chlorine in the network by optimally decreasing the operational volume of the water tanks, and by such increasing the pump switching frequency. The algorithm is demonstrated and compared to enumeration on a single pressure zone example network (1 water tank, 1 pumping unit), on a large example network (C-Town, 7 water tanks, 11 pumping units). The resulting pump schedule is not a global minimum when compared to the best enumeration result on a single pressure zone. However, the algorithm may serve, especially in large water systems, as a quick and feasible answer to system operators, regarding the water volume to maintain in the different tanks to provide minimal chlorine service concentration at near minimal cost.