Optimal pump scheduling and water flow in water distribution networks

This paper focuses on the optimal operation of water distribution networks. We model water distribution networks using physical and hydraulic constraints, and formulate a joint pump scheduling and water flow problem using the hydraulic characteristics of variable speed pumps. The optimal pump scheduling and water flow problem is a mixed integer nonlinear program. This problem is generally non-convex, and hence NP-hard. We propose a second-order cone relaxation for this problem, and analytically show that the proposed relaxation is exact for a wide class of water network topologies. The proposed problem is a mixed integer nonlinear program with a linear objective function and quadratic constraints. This problem can be solved with a commercial solver such as CPLEX. Finally, we consider a real-world water network, and demonstrate the effectiveness of the proposed relaxation in computing the optimal pump schedules and water flows.