A binary expansion approach for the water pump scheduling problem in large and high-altitude water supply systems

first_pageDownload PDFsettingsOrder Article Reprints Open AccessArticle A Binary Expansion Approach for the Water Pump Scheduling Problem in Large and High-Altitude Water Supply Systems by Denise Cariaga 1,2,*ORCID,Álvaro Lorca 1,3,†ORCID andMiguel F. Anjos 2,4,† 1 Department of Industrial and Systems Engineering, Pontificia Universidad Católica de Chile, Santiago 7820436, Chile 2 School of Mathematics, The University of Edinburgh, Edinburgh EH9 3FD, UK 3 Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago 7820436, Chile 4 GERAD, HEC Montreal, Montreal, QC H3T 1N8, Canada * Author to whom correspondence should be addressed. † These authors contributed equally to this work. Energies 2024, 17(16), 4107; https://doi.org/10.3390/en17164107 Submission received: 17 July 2024 / Revised: 14 August 2024 / Accepted: 15 August 2024 / Published: 18 August 2024 (This article belongs to the Section A3: Wind, Wave and Tidal Energy) Downloadkeyboard_arrow_down Browse Figures Versions Notes Abstract The water pump scheduling problem is an optimisation model that determines which water pumps will be turned on or off at each time period over a given time horizon for a given water supply system. This problem has received considerable attention in mining and desalination due to the high power consumption of water pumps and desalination plants and the complicated dynamics of water flows and the power market. Motivated by this, in this paper we solve the optimal operation of a desalinated water supply system consisting of interconnected tanks and pumps that transport water to high-altitude reservoirs. The optimisation of this process encounters several difficulties arising from (i) the nonlinearities of the equations for the frictional losses along the pipes and pumps, which makes the problem a nonlinear mixed-integer model, and (ii) many possible combinations of pressure head and flow rates, which quickly leads to high computational costs. These limitations prevent the problem from being solved in a reasonable computational time in high-altitude water supply systems with more than six pumps and reservoirs, as in many networks worldwide. Therefore, in this work we develop new exact methods for the optimal pump scheduling problem that use a binary expansion approach to efficiently account for the existing nonlinearities by reducing the computational difficulties of the original problem while keeping an excellent representation of the physical phenomena involved. We also extensively tested the proposed approach in different network topologies and a case study for a real-world copper mine water network, and we conclude that the binary expansion approach significantly reduces the computational time for solving the problem with high precision, which can be very relevant for the practical daily operation of real-world water supply systems.

Mots clés

• discrete optimisation
• water supply systems
• water pump scheduling problem
• nonlinear optimisation