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Chance-constrained model predictive control for drinking water networks
Grosso Pérez, Juan Manuel; Ocampo-Martínez, Carlos; Puig Cayuela, Vicenç; Joseph Duran, Bernat
Universitat Politècnica de Catalunya. Departament d'Enginyeria de Sistemes, Automàtica i Informàtica Industrial; Universitat Politècnica de Catalunya. Institut de Robòtica i Informàtica Industrial; Universitat Politècnica de Catalunya. SAC - Sistemes Avançats de Control
This paper addresses a chance-constrained model predictive control (CC-MPC) strategy for the management of drinking water networks (DWNs) based on a finite horizon stochastic optimisation problem with joint probabilistic (chance) constraints. In this approach, water demands are considered additive stochastic disturbances with non-stationary uncertainty description, unbounded support and known (or approximated) quasi-concave probabilistic distribution. A deterministic equivalent of the stochastic problem is formulated using Boole's inequality to decompose joint chance constraints into single chance constraints and by considering a uniform allocation of risk to bound these later constraints. The resultant deterministic-equivalent optimisation problem is suitable to be solved with tractable quadratic programming (QP) or second order cone programming (SOCP) algorithms. The reformulation allows to explicitly and easily propagate uncertainty over the prediction horizon, and leads to a cost-efficient management of risk that consists in a dynamic back-off to avoid frequent violation of constraints. Results of applying the proposed approach to a real case study - the Barcelona DWN (Spain) - have shown that the network performance (in terms of operational costs) and the necessary back-off (to cope with stochastic disturbances) are optimised simultaneously within a single problem, keeping tractability of the solution, even in large-scale networks. The general formulation of the approach and the automatic computation of proper back-off within the MPC framework replace the need of experience-based heuristics or bi-level optimisation schemes that might compromise the trade-off between profits, reliability and computational burden. © 2014 Elsevier Ltd.
Peer Reviewed
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
Water-supply -- Management -- Mathematical models
Chance constraints
Drinking water networks
Aigua -- Abastament -- Control
Article - Draft

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