Technical Papers
Mar 5, 2020

Algorithm Design Based on Derived Operation Rules for a System of Reservoirs in Parallel

Publication: Journal of Water Resources Planning and Management
Volume 146, Issue 5

Abstract

It is challenging to obtain optimal operation rules for a system of reservoirs in parallel. This study derives generic optimal operation rules from a multistage nonlinear programming (NLP) model established for a system of reservoirs in parallel with a single demand. The optimal operation depends on the system’s capability in coordinating individual reservoir storages to regulate inflows to those reservoirs and it is interfered by the full-empty cycles of reservoirs due to the variability of the inflows and/or the limitation of storage capacities. In general, small reservoirs are often made empty to leave space for future inflow or full to reserve water for the future, while large reservoirs are operated within their capacities. Based on the derived optimality conditions, a computationally efficient algorithm is developed for the NLP solution, which determines the system level releases and identifies all full and empty states and stages with no release for individual reservoirs in the system. The algorithm is demonstrated through a case study, in which the solution accuracy and computation time are compared with dynamic programming. This paper and subsequent studies on developing algorithms for optimal reservoir operation can potentially relieve the stress on water supply when new emerging sectors such as biomass and biofuel production increase water use.

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Data Availability Statement

All data, models, or code generated or used during the study are available from the corresponding author by request.

Acknowledgments

This work was funded by the DOE Center for Advanced Bioenergy and Bioproducts Innovation (US Department of Energy, Office of Science, Office of Biological and Environmental Research under Award Number DE-SC0018420). Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the US Department of Energy.

References

Ahmad, A., A. El-Shafie, S. F. M. Razali, and Z. S. Mohamad. 2014. “Reservoir optimization in water resources: A review.” Water Resour. Manage. 28 (11): 3391–3405. https://doi.org/10.1007/s11269-014-0700-5.
Bazaraa, M. S., H. D. Sherali, and C. M. Shetty. 2013. Nonlinear programming: Theory and algorithms. Hoboken, NJ: Wiley.
Castelletti, A., S. Galelli, M. Restelli, and R. Soncini-Sessa. 2010. “Tree-based reinforcement learning for optimal water reservoir operation.” Water Resour. Res. 46 (9): W09507. https://doi.org/10.1029/2009WR008898.
Chang, L. C., and F. J. Chang. 2009. “Multi-objective evolutionary algorithm for operating parallel reservoir system.” J. Hydrol. 377 (1): 12–20. https://doi.org/10.1016/j.jhydrol.2009.07.061.
Chen, D., A. S. Leon, N. L. Gibson, and P. Hosseini. 2016. “Dimension reduction of decision variables for multireservoir operation: A spectral optimization model.” Water Resour. Res. 52 (1): 36–51. https://doi.org/10.1002/2015WR017756.
Clark, E. J. 1950. “New York control curves.” J. (Am. Water Works Assn.) 42 (9): 823–827.
Ding, W., C. Zhang, X. Cai, Y. Li, and H. Zhou. 2017. “Multiobjective hedging rules for flood water conservation.” Water Resour. Res. 53 (3): 1963–1981. https://doi.org/10.1002/2016WR019452.
Ding, W., C. Zhang, Y. Peng, R. Zeng, H. Zhou, and X. Cai. 2015. “An analytical framework for flood water conservation considering forecast uncertainty and acceptable risk.” Water Resour. Res. 51 (6): 4702–4726. https://doi.org/10.1002/2015WR017127.
Draper, A. J., and J. R. Lund. 2004. “Optimal hedging and carryover storage value.” J. Water Resour. Plann. Manage. 130 (1): 83–87. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:1(83).
Hochbaum, D. S. 2007. “Complexity and algorithms for nonlinear optimization problems.” Ann. Oper. Res. 153 (1): 257–296. https://doi.org/10.1007/s10479-007-0172-6.
Hui, R., J. Lund, J. Zhao, and T. Zhao. 2016. “ Optimal pre-storm flood hedging releases for a single reservoir.” Water Resour. Manage. 30 (1): 5113–5129. https://doi.org/10.1007/s11269-016-1472-x.
Jairaj, P. G., and S. Vedula. 2003. “Modeling reservoir irrigation in uncertain hydrologic environment.” J. Irrig. Drain. Eng. 129 (3): 164–172. https://doi.org/10.1061/(ASCE)0733-9437(2003)129:3(164).
Jalali, M. R., A. Afshar, and M. A. Marino. 2007. “Multi-colony ant algorithm for continuous multi-reservoir operation optimization problem.” Water Resour. Manage. 21 (9): 1429–1447. https://doi.org/10.1007/s11269-006-9092-5.
Johnson, S. A., J. R. Stedinger, and K. Staschus. 1991. “Heuristic operating policies for reservoir system simulation.” Water Resour. Res. 27 (5): 673–685. https://doi.org/10.1029/91WR00320.
Labadie, J. W. 2004. “Optimal operation of multireservoir systems: State-of-the-art review.” J. Water Resour. Plann. Manage. 130 (2): 93–111. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:2(93).
Leyffer, S., and A. Mahajan. 2010. Nonlinear constrained optimization: Methods and software. Argonne, IL: Argonee National Laboratory.
Lund, J., et al. 2017. “Reservoir operation design.” Chap. 130 in Handbook of applied hydrology, edited by V. Singh. New York: McGraw Hill Education.
Lund, J. R., and J. Guzman. 1999. “Derived operating rules for reservoirs in series or in parallel.” J. Water Resour. Plann. Manage. 125 (3): 143–153. https://doi.org/10.1061/(ASCE)0733-9496(1999)125:3(143).
Nagesh Kumar, D., and M. Janga Reddy. 2007. “Multipurpose reservoir operation using particle swarm optimization.” J. Water Resour. Plann. Manage. 133 (3): 192–201. https://doi.org/10.1061/(ASCE)0733-9496(2007)133:3(192).
Oliveira, R., and D. P. Loucks. 1997. “Operating rules for multireservoir systems.” Water Resour. Res. 33 (4): 839–852. https://doi.org/10.1029/96WR03745.
Peng, A., Y. Peng, H. Zhou, and C. Zhang. 2015. “Multi-reservoir joint operating rule in inter-basin water transfer-supply project.” Sci. China Technol. Sci. 58 (1): 123–137. https://doi.org/10.1007/s11431-014-5641-y.
Rheinboldt, W. C. 1998. Vol. 70 of Methods for solving systems of nonlinear equations. Philadelphia, PA: Society for Industrial and Applied Mathematics.
Shiau, J. T. 2011. “Analytical optimal hedging with explicit incorporation of reservoir release and carryover storage targets.” Water Resour. Res. 47 (1): W01515. https://doi.org/10.1029/2010WR009166.
Stedinger, J. R., B. F. Sule, and D. P. Loucks. 1984. “Stochastic dynamic programming models for reservoir operation optimization.” Water Resour. Res. 20 (11): 1499–1505. https://doi.org/10.1029/WR020i011p01499.
Wan, W., J. Zhao, J. R. Lund, T. Zhao, X. Lei, and H. Wang. 2016. “Optimal hedging rule for reservoir refill.” J. Water Resour. Plann. Manage. 142 (11): 04016051. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000692.
Wardlaw, R., and M. Sharif. 1999. “Evaluation of genetic algorithms for optimal reservoir system operation.” J. Water Resour. Plann. Manage. 125 (1): 25–33. https://doi.org/10.1061/(ASCE)0733-9496(1999)125:1(25).
Wurbs, R. A. 1993. “Reservoir-system simulation and optimization models.” J. Water Resour. Plann. Manage. 119 (4): 455–472. https://doi.org/10.1061/(ASCE)0733-9496(1993)119:4(455).
Xu, W., J. Zhao, T. Zhao, and Z. Wang. 2014. “Adaptive reservoir operation model incorporating nonstationary inflow prediction.” J. Water Resour. Plann. Manage. 141 (8): 04014099. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000502.
Yeh, W. W. G. 1985. “Reservoir management and operations models: A state-of-the-art review.” Water Resour. Res. 21 (12): 1797–1818. https://doi.org/10.1029/WR021i012p01797.
You, J. Y., and X. Cai. 2008a. “Hedging rule for reservoir operations: 1. A theoretical analysis.” Water Resour. Res. 44 (1): W01415. https://doi.org/10.1029/2006WR005481.
You, J. Y., and X. Cai. 2008b. “Hedging rule for reservoir operations: 2. A numerical model.” Water Resour. Res. 44 (1): W01416. https://doi.org/10.1029/2006WR005482.
Zeng, X., T. Hu, L. Xiong, Z. Cao, and C. Xu. 2015. “Derivation of operation rules for reservoirs in parallel with joint water demand.” Water Resour. Res. 51 (12): 9539–9563. https://doi.org/10.1002/2015WR017250.
Zhao, J., X. Cai, and Z. Wang. 2011. “Optimality conditions for a two-stage reservoir operation problem.” Water Resour. Res. 47 (8): W08503. https://doi.org/10.1029/2010WR009971.
Zhao, T., J. Zhao, J. R. Lund, and D. Yang. 2014. “Optimal hedging rules for reservoir flood operation from forecast uncertainties.” J. Water Resour. Plann. Manage. 140 (12): 04014041. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000432.

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Go to Journal of Water Resources Planning and Management
Journal of Water Resources Planning and Management
Volume 146Issue 5May 2020

History

Received: Mar 2, 2019
Accepted: Nov 6, 2019
Published online: Mar 5, 2020
Published in print: May 1, 2020
Discussion open until: Aug 5, 2020

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Authors

Affiliations

Qiankun Zhao, S.M.ASCE
Graduate Student, Ven Te Chow Hydrosystems Laboratory, Dept. of Civil and Environmental Engineering, DOE Center for Advanced Bioenergy and Bioproducts Innovation, Univ. of Illinois at Urbana-Champaign, Urbana, IL 61801.
Ximing Cai, Ph.D., M.ASCE [email protected]
Professor, Ven Te Chow Hydrosystems Laboratory, Dept. of Civil and Environmental Engineering, DOE Center for Advanced Bioenergy and Bioproducts Innovation, Univ. of Illinois at Urbana-Champaign, Urbana, IL 61801 (corresponding author). Email: [email protected]; [email protected]
Yu Li, Ph.D.
Lecturer, School of Hydraulic Engineering, Dalian Univ. of Technology, Dalian 116024, China.

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