Economic Predictive Control with Periodic Horizon for Water Distribution Networks

This paper deals with the control of pumps in large-scale water distribution networks with the aim of minimizing economic costs while satisfying operational constraints. Finding a control algorithm in combination with a model that can be applied in real-time is a challenging problem due to the nonlinearities presented by the pipes and the network sizes. We propose a predictive control algorithm with a periodic horizon. The method provides a way for the economic operation of large water networks with a small linear model. Economic Predictive control with a periodic horizon and a terminal state constraint is constructed to keep the state trajectories close to an optimal periodic trajectory. Barrier terms are also included in the cost function to prevent constraint violations. The proposed method is tested on the EPANET implementation of the water network of a medium size Danish town (Randers) and shown to perform as intended under varying conditions.