Optimal Operation Rules for Parallel Reservoir Systems with Distributed Water Demands
Publication: Journal of Water Resources Planning and Management
Volume 148, Issue 6
Abstract
This paper addresses the doubts regarding the spatial characteristics of the commonly used rules for parallel reservoir system operation. The rules based on aggregation-decomposition determine the system total release first and then assign this release to individual reservoirs, without considering the water demand distribution in the river network. In this paper, a conceptual model for parallel reservoir systems with distributed water demands is proposed. Three specific optimality conditions are derived for determining the optimal analytical solution. A rigorous proof shows that the aggregation-decomposition-based rules are a special case of the derived rules. An efficient algorithm is then developed based on the optimality conditions and shortage allocation index (SAI), in which a larger SAI indicates taking a higher percentage of the system water shortage, as release or storage. Unlike traditional algorithms that modify the violated variables empirically, we propose a criterion in terms of relative deviation indicators to determine the crucial priority of variable modification. This criterion can effectively address constraint violations. The optimal rules along with the solution algorithm are then demonstrated by the operation of a parallel reservoir system in the Shiyang River Basin, China. The results show that the proposed rules and algorithm are more efficient and effective than traditional algorithms and aggregation-decomposition-based rules, especially in dry seasons with more binding constraints.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. The list items include (1) the inflows and algorithmic parameters of the hypothetical three-reservoir system in Subsection 1 of Case study which are shown in Fig. 6 and Table 3; (2) the monthly step inflow data from 1970 to 2000 in the Shiyang River Basin; and (3) the codes of the HRAP-D and ADBR in the Shiyang River Basin.
Acknowledgments
The authors are grateful to the two anonymous reviewers and the editors for their insightful comments and encouragement that contributed to significant improvements of the manuscript. This study was supported by the National Natural Science Foundation of China (Grant Nos. 92047302, 91747208, and 51861125102) and the State Key Laboratory of Hydroscience and Engineering-Tsinghua (Grant No. 2019-KY-01).
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.
Balinski, M. L., and W. J. Baumol. 1968. “The dual in nonlinear programming and its economic interpretation.” Rev. Econ. Stud. 35 (3): 237–256. https://doi.org/10.2307/2296660.
Bazaraa, M. S., H. D. Sherali, and C. M. Shetty. 2006. Nonlinear programming: Theory and algorithms. Chichester, UK: Wiley.
Bower, B. T., M. M. Hufschmidt, and W. W. Reedy. 1962. “Operating procedures: Their role in the design of water-resource systems by simulation analyses.” In Design of water resource systems, 443–458. Cambridge, MA: Harvard University Press.
Burness, H. S., and J. P. Quirk. 1981. The theory of the dam: An application to the Colorado River, 107–130. Lafayette, IN: Purdue University Press.
Chang, L. C., and F. J. Chang. 2009. “Multi-objective evolutionary algorithm for operating parallel reservoir system.” J. Hydrol. 377 (1–2): 12–20. https://doi.org/10.1016/j.jhydrol.2009.07.061.
Clark, E. J. 1956. “Impounding reservoirs.” J. Am. Water Works Assn. 48 (4): 349–354.
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).
Eheart, J. W., and R. M. Lyon. 1983. “Alternative structures for water rights markets.” Water Resour. Res. 19 (4): 887–894. https://doi.org/10.1029/WR019i004p00887.
Guo, X., T. Hu, X. Zeng, and X. Li. 2013. “Extension of parametric rule with the hedging rule for managing multireservoir system during droughts.” J. Water Resour. Plann. Manage. 139 (2): 139–148. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000241.
Hashimoto, T., J. R. Stedinger, and D. P. Loucks. 1982. “Reliability, resiliency, and vulnerability criteria.” Water Resour. Res. 18 (1): 14–20. https://doi.org/10.1029/WR018i001p00014.
Hui, R., and J. R. Lund. 2015. “Flood storage allocation rules for parallel reservoirs.” J. Water Resour. Plann. Manage. 141 (5): 04014075. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000469.
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).
Li, L., P. Liu, D. E. Rheinheimer, C. Deng, and Y. Zhou. 2014. “Identifying explicit formulation of operating rules for multi-reservoir systems using genetic programming.” Water Resour. Manage. 28 (6): 1545–1565. https://doi.org/10.1007/s11269-014-0563-9.
Liu, P., S. Guo, X. Xu, and J. Chen. 2011. “Derivation of aggregation-based joint operating rule curves for cascade hydropower reservoirs.” Water Resour. Manage. 25 (13): 3177–3200. https://doi.org/10.1007/s11269-011-9851-9.
Loucks, D. P., J. R. Stedinger, and D. A. Haith. 1981. Water resource systems planning and analysis. Englewood Cliffs, NJ: Prentice-Hall.
Maass, A., M. Hufschmidt, R. Dorfman, H. A. Thomas, S. A. Marglin, and G. M. Fair. 1962. Design of water-resource systems. Cambridge, MA: Harvard University Press.
Masse, P. 1946. Les réserves et la régulation de l’avenir dans la vie économique. Paris: Hermann.
Ming, B., P. Liu, S. Liu, X. Zhang, M. Feng, and X. Wang. 2017. “Optimizing utility-scale photovoltaic power generation for integration into a hydropower reservoir by incorporating long-and short-term operational decisions.” Appl. Energy 204 (Oct): 432–445. https://doi.org/10.1016/j.apenergy.2017.07.046.
Nalbantis, I., and D. Koutsoyiannis. 1997. “A parametric rule for planning and management of multiple-reservoir systems.” Water Resour. Res. 33 (9): 2165–2177. https://doi.org/10.1029/97WR01034.
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, Y., J. Chu, A. Peng, and H. Zhou. 2015. “Optimization operation model coupled with improving water-transfer rules and hedging rules for inter-basin water transfer-supply systems.” Water Resour. Manage. 29 (10): 3787–3806. https://doi.org/10.1007/s11269-015-1029-4.
Rani, D., and M. M. Moreira. 2009. “Simulation-optimization modeling: A survey and potential application in reservoir systems operation.” Water Resour. Manage. 24 (6): 1107–1138. https://doi.org/10.1007/s11269-009-9488-0.
Sand, G. M. 1984. “An analytical investigation of operating policies for water-supply reservoirs in parallel.” Ph.D. dissertation, Faculty of the Graduate School, Cornell Univ.
Shiau, J.-T. 2011. “Analytical optimal hedging with explicit incorporation of reservoir release and carryover storage targets.” Water Resour. Res. 47 (1): 30–47. https://doi.org/10.1029/2010WR009166.
Shih, J. S., and C. ReVelle. 1994. “Water-supply operations during drought: Continuous hedging rule.” J. Water Resour. Plann. Manage. 120 (5): 613–629. https://doi.org/10.1061/(ASCE)0733-9496(1994)120:5(613).
Shih, J. S., and C. ReVelle. 1995. “Water supply operations during drought: A discrete hedging rule.” Eur. J. Oper. Res. 82 (1): 163–175. https://doi.org/10.1016/0377-2217(93)E0237-R.
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.
Tang, Z., J. Ma, H. Peng, S. Peng, and J. Wei. 2017. “Spatiotemporal changes of vegetation and their responses to temperature and precipitation in upper Shiyang river basin.” Adv. Space Res. 60 (5): 969–979. https://doi.org/10.1016/j.asr.2017.05.033.
Tu, M. Y., N. S. Hsu, F. T. Tsai, and W. W. Yeh. 2008. “Optimization of hedging rules for reservoir operations.” J. Water Resour. Plann. Manage. 134 (1): 3–13. https://doi.org/10.1061/(ASCE)0733-9496(2008)134:1(3).
Wang, Y., B. Liu, S. Peng, S. Cai, and D. Zhang. 2018. “Review and prospect about water resources operation research.” In Proc., MATEC Web Conf., 246. Les Ulis, France: EDP Sciences. https://doi.org/10.1051/matecconf/201824601023.
Wang, Z., H. Zheng, and X. Wang. 2009. “A harmonious water rights allocation model for Shiyang River Basin, Gansu Province, China.” Int. J. Water Resour. Dev. 25 (2): 355–371. https://doi.org/10.1080/07900620902868836.
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. 2008. “Hedging rule for reservoir operations: 1. A theoretical analysis.” Water Resour. Res. 44 (1): 1–9. https://doi.org/10.1029/2006WR005481.
Zeng, X., T. Hu, L. Xiong, Z. Cao, and C. Xu. 2015. “Derivation of operation rules for reservoirs in parallel with joint water demand.” J. Am. Water Resour. Assn. 5 (3): 2. https://doi.org/10.1002/2015WR017250.
Zhang, C., G. Wang, Y. Peng, G. Tang, and G. Liang. 2012. “A negotiation-based multi-objective, multi-party decision-making model for inter-basin water transfer scheme optimization.” Water Resour. Manage. 26 (14): 4029–4038. https://doi.org/10.1007/s11269-012-0127-9.
Zhang, X., P. Liu, C.-Y. Xu, B. Ming, A. Xie, and M. Feng. 2018. “Conditional value-at-risk for nonstationary streamflow and its application for derivation of the adaptive reservoir flood limited water level.” J. Water Resour. Plann. Manage. 144 (3): 04018005. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000906.
Zhao, J., X. Cai, and Z. Wang. 2011. “Optimality conditions for a two-stage reservoir operation problem.” Water Resour. Res. 47 (8): 1–16. https://doi.org/10.1029/2010WR009971.
Zhu, X., C. Zhang, J. Yin, H. Zhou, and Y. Jiang. 2014. “Optimization of water diversion based on reservoir operating rules: Analysis of the Biliu River Reservoir, China.” J. Hydrol. Eng. 19 (2): 411–421. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000805.
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Received: Apr 21, 2021
Accepted: Dec 10, 2021
Published online: Mar 16, 2022
Published in print: Jun 1, 2022
Discussion open until: Aug 16, 2022
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