Discrete Pump Scheduling and Leakage Control Using Linear Programming for Optimal Operation of Water Distribution Systems

Pump station scheduling is a major issue in optimal water system operation. Pump operation may be of an on/off form or of a fluctuating form using a variable-frequency drive (VFD). This research proposes an iterative linear discrete pump-scheduling algorithm using linear programming (LP). The examined problem includes nonlinear convex headloss, leakage, and varying total-head pump energy consumption constraints. A discrete pump operation index is proposed to select time steps on which to enforce a discrete pump operation constraint. After each iteration step, the index is recalculated based on the previous iteration steps’ results and the discrete operation constraint is added or removed from the time steps accordingly. The iterative process stops when all time steps have been discretely evaluated. The algorithm is first demonstrated on a small illustrative example application and compared to the global minimal results found by enumeration. Next, the algorithm is demonstrated on two complex example applications using several test cases. The resulting optimization model may be used to provide applicable operational schemes, including hydraulic water head constraints, leakage, varying pump energy consumption, and sequential discrete pump operation, minimizing operational cost. As linear programming is used, the proposed algorithm has short solution times with assurances of solution convergence to the global minimum. Different from commonly used approaches, including mixed integer programming (MIP), or evolutionary methods, a new approach is presented for discrete pump scheduling using linear programming, applicable to general discrete decision problems.