Energy optimization of water supply system scheduling: Novel MINLP model and efficient global optimization algorithm

Abstract

This article is concerned with global optimization of water supply system scheduling with pump operations to minimize total energy cost. The scheduling problem is first formulated as a non-convex mixed-integer nonlinear programming (MINLP) problem, accounting for flow rates in pipes, operation profiles of pumps, water levels of tanks, and customer demand. Binary variables denote on-off switch operations for pumps and flow directions in pipes, and nonlinear terms originate from characteristic functions for pumps and hydraulic functions for pipes. The proposed MINLP model is verified with EPANET, which is a leading software package for water distribution system modeling. We further develop a novel global optimization algorithm for solving the non-convex MINLP problem. To demonstrate the applicability of the proposed model and the efficiency of the tailored global optimization algorithm, we present results of two case studies with up to 4 tanks, 5 pumps, 5 check valves, and 21 pipes.

Pump scheduling in drinking water distribution networks with an LP/NLP-based branch and bound

“…This full enumeration scheme was successfully applied to a small DWDN of class BS but it probably does not scale well. Shi and You [49] consider a similar decomposition but they develop an exact method and use a tight master MILP where the hydraulic constraints are only partially relaxed: non-convex outer approximations defined by piecewise-linear segments are automatically generated and refined during the search. Contrarily to the previous works, this approach directly applies to DWDNs of class MS, although only experiments on two small DWDNs of class BS with a limited number of time steps are presented.…”

“…In this paper, we generalize the convex relaxation of [4] to DWDNs with loops, both in classes BS and MS, and devise an exact method based on a similar decomposition to [37] and [49]. The key differences with these approaches are that: (1) our MILP master relaxation is tighter than [37] and smaller than [49], and (2) the solutions are searched and evaluated within one single tree search.…”

“…In this paper, we generalize the convex relaxation of [4] to DWDNs with loops, both in classes BS and MS, and devise an exact method based on a similar decomposition to [37] and [49]. The key differences with these approaches are that: (1) our MILP master relaxation is tighter than [37] and smaller than [49], and (2) the solutions are searched and evaluated within one single tree search. Our approach bears similarities with the LP/NLP branch-and-bound framework developed by Quesada and Grossmann [42] for general convex MINLPs but we progressively tighten the MILP relaxation with combinatorial cuts, as in [37], instead of OA cuts.…”

“…For this paper, we built a benchmark set of 75 instances by applying the 5 electricity tariff profiles of [20] to a variety of networks with different characteristics coming from [35,44,20,56]. While it was not an option to reimplement the complex methods of the literature, we propose to perform an empiric comparison with the computational results reported in four recent papers [20,37,10,49].…”

“…Finally, we experimented our approach on various benchmark sets (Simple FSD/VSD [35], AT(M) [44,10], Poormond [20,37,49] and DWG [56]), and drove an empirical comparison with recently reported results [10,20,37,49] and with the reference global optimization solver BARON [46]. The computational results demonstrate the applicability of our generic solution method and also its efficiency regarding the results of the dedicated algorithms on given instances, although solving the non-convex NLP subproblems remains a bottleneck for the largest instances of class MS.…”