Optimal Pump Scheduling in Water Distribution Systems Using Graph Theory under Hydraulic and Chlorine Constraints
Publication: Journal of Water Resources Planning and Management
Volume 142, Issue 10
Abstract
Finding the optimal pump operation in water distribution systems, taking into account hydraulic and water quality constraints, is a complex problem due to the nonlinear relationship between dynamic head loss and flow rate and between chlorine decay and water age, and due to the size of the problem. The proposed algorithm, for minimum cost pump scheduling, utilizes the operational graph algorithm applied to hydraulic and quality constraints. The proposed algorithm utilizes a graph algorithm that considers hydraulic and water quality constraints to find the pump scheduling that minimizes pump operational costs. The algorithm has short solution times and therefore is suitable for real-time water system control or, if used offline, for giving a recommendation on the pump operation taking into account hydraulic and water quality constraints. The algorithm results were compared with the best results found by enumeration to show that the operational graph algorithm returns a global minimal solution and, when combined with quality constraints, returns near-optimal results. The proposed algorithm was successfully demonstrated on a 24-h example application with a single pumping unit and, on the C-Town example application, with 11 pumping units and 168 time steps.
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Acknowledgments
We would like to thank Reviewers 1 and 3 for their thorough review and detailed comments, which greatly contributed to the paper. This study was supported by the Technion Grand Water Research Institute, by the joint Israeli Office of the Chief Scientist (OCS) Ministry of Science, Technology and Space (MOST), and by the German Federal Ministry of Education and Research (BMBF) under Project No. 02WA1298.
References
Alperovits, E., and Shamir, U. (1977). “Design of optimal water distribution systems.” Water Resour. Res., 13(6), 885–900.
Berardi, L., and Giustolisi, O. (2016). “Special issue on the battle of background leakage assessment for water networks.” J. Water Resour. Plann. Manage., C2016001.
Broad, D. R., Dandy, G. C., and Maier, H. R. (2005). “Water distribution system optimization using metamodels.” J. Water Resour. Plann. Manage. Div., 172–180.
Broad, D. R., Maier, H. R., and Dandy, G. C. (2010). “Optimal operation of complex water distribution systems using metamodels.” J. Water Resour. Plann. Manage. Div., 433–443.
Cohen, D. (1992). “Optimal operation of multi-quality networks.” D.Sc. thesis, Faculty of Agricultural Engineering, Technion–Israel Institute of Technology (in Hebrew).
Cohen, D., Shamir, U., and Sinai, G. (2000). “Optimal operation of multi-quality networks—III: The Q-C-H model.” Eng. Optim., 33, 1–35.
Cohen, D., Shamir, U., and Sinai, G. (2004). “Sensitivity analysis of optimal operation of irrigation supply systems with water quality considerations.” Irrig. Drain. Syst., 18(3), 227–253.
Dandy, G. C., and Engelhardt, M. O. (2006). “Multi-objective trade-offs between cost and reliability in the replacement of water mains.” J. Water Resour. Plann. Manage. Div., 79–88.
Dijkstra, E. W. (1959). “A note on two problems in connexion with graphs.” Numerische Mathematik, 1, 269–271.
EPANET 2.0 [Computer software]. U.S. EPA, Washington, DC.
Giustolisi, O., et al. (2014). “Battle of background leakage assessment for water networks (BBLAWN) at WDSA conference 2014.” Proc., Engineering, 16th Water Distribution System Analysis Conf., WDSA2014—Urban Water Hydroinformatics and Strategic Planning, Vol. 89, 4–12.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning, Addison-Wesley, New York.
Goldman, E. F. (1998). “The application of simulated annealing for optimal operation of water distribution systems.” Ph.D. dissertation, Arizona State Univ., Tempe, AZ.
Holland, J. H. (1975). Adaptation in natural and artificial systems, University of Michigan Press, Ann Arbor, MI.
Nicklow, J., et al. (2010). “State of the art for genetic algorithms and beyond in water resources planning and management.” J. Water Resour. Plann. Manage., 412–432.
Ostfeld, A. (2005) “A review of modeling water quality in distribution systems.” Urban Water J., 2(2), 107–114.
Ostfeld, A., and, and Shamir, U. (1993). “Optimal operation of multiquality distribution systems: Steady state conditions.” J. Water Resour. Plann. Manage., 119(6), 645–662.
Ostfeld, A., Kogan, D., and Shamir, U. (2002). “Reliability simulation of water distribution systems—Single and multiquality.” Urban Water Elsevier. Sci., 4(1), 53–61.
Ostfeld, A., Oliker, N., and Salomons, E. (2014). “Multiobjective optimization for least cost design and resiliency of water distribution systems.” J. Water Resour. Plann. Manage., 04014037.
Ostfeld, A., and Salomons, E. (2004). “Optimal operation of multiquality water distribution systems: Unsteady conditions.” Eng. Optim., 36(3), 337–359.
Ostfeld, A., and Shamir, U. (1996). “Design of optimal reliable multiquality water supply systems.” J. Water Resour. Plann. Manage. Div., 322–333.
Price, E., and Ostfeld, A. (2015). “Graph theory modeling approach for optimal operation of water distribution systems.” J. Hydraul. Eng., 04015061.
Rossman, L., Clark, R., and Grayman, W. (1994). “Modeling chlorine residuals in drinking-water distribution systems.” J. Environ. Eng., 803–820.
Rossman, L., Uber, J., and Grayman, W. (1995). “Modeling disinfectant residuals in drinking-water storage tanks.” J. Environ. Eng., 752–755.
Sakarya, B. A., and Mays, L. W. (2000). “Optimal operation of water distribution pumps considering water quality.” J. Water Res. Plann. Manage. Div., 210–220.
Savic, D., and Walters, G. (1997). “Genetic algorithms for least cost design of water distribution networks.” J. Water Resour. Plann. Manage. Div., 67–77.
Simpson, A. R., Dandy, G. C., and Murphy, L. J. (1994). “Genetic algorithms compared to other techniques for pipe optimization.” J. Water Resour. Plann. Manage. Div., 423–443.
Vamvakeridou-Lyroudia, L. S., Walters, G. A., and Savic, D. A. (2005). “Fuzzy multi-objective optimization of water distribution networks.” J. Water Resour. Plann. Manage. Div., 467–476.
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© 2016 American Society of Civil Engineers.
History
Received: Nov 24, 2015
Accepted: Mar 14, 2016
Published online: Jun 7, 2016
Published in print: Oct 1, 2016
Discussion open until: Nov 7, 2016
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