Dynamic Optimization Approach for Solving an Optimal Scheduling Problem in Water Distribution Systems

A new dynamic optimization (DO) approach to solve large scale optimal scheduling problems for water distribution networks is presented. The main motivation of this research is to formulate an algorithm which is significantly faster than existing approaches. Optimal scheduling is a complex task as it includes the extended period hydraulic model represented by differential algebraic equations and mixed-integer decision variables. Obtaining a strictly optimal solution involves excessive computational effort; however, a near optimal solution can be found at significantly reduced effort using a simple heuristic assumption. The proposed method progresses in two stages—initially a relaxed continuous problem is solved and in the second stage, a mixed-integer solution is found which tracks the optimal reservoir trajectories by time decomposition and application of a local branch and bound method. This paper describes the first stage of the method. The state and algebraic variables are numerically resolved using a hydraulic simulator and the reduced gradients are calculated using adjoint equations. A comparative analysis is made of the results obtained from the DO formulation and also from a traditional nonlinear programming method on a benchmark water supply scheme, thus showing the numerical efficiency of the new approach.