DHV water pumping optimization

Abstract

his contribution investigates the possibilities for optimizing a drinking water network over a horizon of 48 hours, given variable water demands, energy prices and constraints on the pumping strategy and water levels in the reservoirs. Both the dynamic model and goal function are non-linear in the control inputs, the pump flow rates. Since each pump can be switched on or off every 15 minutes and since there are 15 pumps in the system, for a horizon of 48 hours there are 2(4×48×15) switching possibilities. Obviously, this problem is too big to solve it in real-time by enumeration. Hence, a decomposition of the problem is needed. Relaxing the constraints and assuming a continuous-time flow rate, allows a (semi)-analytical solution using Lagrangian theory. Furthermore, a numerical solution of the constrained optimization problem is found by using the TomLab PROMPT toolbox. The conversion from a continuous-time pump flow rate to a strategy with on/off switching is also investigated, as well as the possibility of linear feedback control. The resulting trajectories of the pump flow rates and water levels in the reservoirs are realistic and can be physically interpreted.