Pump scheduling in drinking water distribution systems through convex relaxation and time step duration adjustment
Résumé
The pump scheduling problem in drinking water distribution systems aims to minimize the electrical costs due to pumping while ensuring the supply of water to end-consumers. Recently, new interests concerning this problem have been observed because drinking water networks seem well-suited for taking advantage of new electricity markets such as spot markets and secondary electricity grid regulation, because of their water storage ability and the flexibility in the pumping operation. However, the optimal control of a drinking water distribution system remains complex because it relies both on discrete decision such as switching pump on and off, and nonlinear constraints for the description of pressure-related physical laws. By arguing that the non-convex constraints tend to be fulfilled because of the shape of the objective function, even if we don’t take them into account, we propose to approximate the non-convex constraints by their convex hull. Then, a feasible solution is recovered by adjusting the time steps duration. Applications to two networks previously studied and comparison with proposed methods are presented in order to highlight the relevance of our solution.