Simulation-Optimization Model to Derive Operation Rules of Multiple Cascaded Reservoirs for Nash Equilibrium
Publication: Journal of Water Resources Planning and Management
Volume 145, Issue 5
Abstract
Operation rules are commonly used to make decisions for cascaded hydropower reservoirs for profit maximization, given the energy price of current and future periods. For large-scale cascaded hydropower reservoirs whose decisions can affect market price, the operation optimization models are transformed into game models to get Nash equilibriums. For market competition of multiple cascaded hydropower reservoirs, a multiplayer game model is established in which the actions are storage energy based operation rules and the payoff function values are simulated profits of cascades using the rules. The game model is solved using a successive low dimensional search method in which only one parameter of the rules is optimized at each step. The proposed method is tested using data of three cascaded reservoirs in Southwestern China in a hypothetical pure hydropower market. Results show the effect of different kind of models on rule curves and the potential impact of market reformation to the operation of the cascaded hydropower reservoirs. For the studied cascaded reservoirs, the profit increasing percentages can be 2.6%–3.9% with 0.5%–2.0% energy losing, comparing the game model to the energy maximization model.
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Data Availability Statement
The following data, models, or code generated or used during the study are available from the corresponding author by request. (Part of the JAVA code of the proposed method.)
Acknowledgments
The research work described in this paper is supported by the National Nature Science Foundation of China (51679027, 91647113, and 91547201).
References
Aboutalebi, M., O. Bozorg Haddad, and H. A. Loáiciga. 2015. “Optimal monthly reservoir operation rules for hydropower generation derived with SVR-NSGAII.” J. Water Resour. Plann. Manage. 141 (11): 04015029. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000553.
Ahmadi Najl, A., A. Haghighi, and H. M. Vali Samani. 2016. “Simultaneous optimization of operating rules and rule curves for multireservoir systems using a self-adaptive simulation-GA model.” J. Water Resour. Plann. Manage. 142 (10): 04016041. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000688.
Chang, L. C., F. J. Chang, K. W. Wang, and S. Y. Dai. 2010. “Constrained genetic algorithms for optimizing multi-use reservoir operation.” J. Hydrol. 390 (1): 66–74. https://doi.org/10.1016/j.jhydrol.2010.06.031.
Cheng, C., L. Yan, A. Mirchi, and K. Madani. 2016. “China’s booming hydropower: Systems modeling challenges and opportunities.” J. Water Resour. Plann. Manage. 143 (1): 02516002. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000723.
Feng, M., P. Liu, S. Guo, Z. Gui, X. Zhang, W. Zhang, and L. Xiong. 2017. “Identifying changing patterns of reservoir operating rules under various inflow alteration scenarios.” Adv. Water Resour. 104: 23–36. https://doi.org/10.1016/j.advwatres.2017.03.003.
Flach, B. C., L. A. Barroso, and M. V. F. Pereira. 2010. “Long-term optimal allocation of hydro generation for a price-maker company in a competitive market: Latest developments and a stochastic dual dynamic programming approach.” IET Gener. Transm. Distrib. 4 (2): 299–314. https://doi.org/10.1049/iet-gtd.2009.0107.
Giuliani, M., and A. Castelletti. 2013. “Assessing the value of cooperation and information exchange in large water resources systems by agent-based optimization.” Water Resour. Res. 49 (7): 3912–3926. https://doi.org/10.1002/wrcr.20287.
Giuliani, M., A. Castelletti, F. Pianosi, E. Mason, and P. M. Reed. 2015. “Curses, tradeoffs, and scalable management: Advancing evolutionary multiobjective direct policy search to improve water reservoir operations.” J. Water Resour. Plann. Manage. 142 (2): 04015050. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000570.
Guo, X., T. Hu, X. Zeng, and X. Li. 2012. “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.
Hu, T., J. Mao, M. Tian, H. Dai, and G. Rong. 2017. “New constraint-handling technique for evolutionary optimization of reservoir operation.” J. Water Resour. Plann. Manage. 144 (3): 04017097. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000891.
Hui, R., J. R. Lund, and K. Madani. 2016. “Game theory and risk-based leveed river system planning with noncooperation.” Water Resour. Res. 52 (1): 119–134. https://doi.org/10.1002/2015WR017707.
Kelman, J., J. R. Stedinger, L. A. Cooper, E. Hsu, and S. Q. Yuan. 1990. “Sampling stochastic dynamic programming applied to reservoir operation.” Water Resour. Res. 26 (3): 447–454. https://doi.org/10.1029/WR026i003p00447.
Kelman, R., L. A. N. Barroso, and M. V. F. Pereira. 2001. “Market power assessment and mitigation in hydrothermal systems.” IEEE Trans. Power Syst. 16 (3): 354–359. https://doi.org/10.1109/59.932268.
Koutsoyiannis, D., and A. Economou. 2003. “Evaluation of the parameterization- simulation-optimization approach for the control of reservoir systems.” Water Resour. Res. 39 (6): 1170. https://doi.org/10.1029/2003WR002148.
Liu, P., X. Cai, and S. Guo. 2011a. “Deriving multiple near-optimal solutions to deterministic reservoir operation problems.” Water Resour. Res. 47 (8): W08506. https://doi.org/10.1029/2011WR010998.
Liu, P., S. Guo, L. Xiong, W. Li, and H. Zhang. 2006. “Deriving reservoir refill operating rules by using the proposed DPNS model.” Water Resour. Manage. 20 (3): 337–357. https://doi.org/10.1007/s11269-006-0322-7.
Liu, P., S. Guo, X. Xu, and J. Chen. 2011b. “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.
Lund, J. R. 2000. “Derived power production and energy drawdown rules for reservoirs.” J. Water Resour. Plan. Manage. 126 (2): 108–111. https://doi.org/10.1061/(ASCE)0733-9496(2000)126:2(108).
Lund, J. R., and I. Ferreira. 1996. “Operating rule optimization for Missouri River reservoir system.” J. Water Resour. Plan. Manage. 122 (4): 287–295. https://doi.org/10.1061/(ASCE)0733-9496(1996)122:4(287.
Madani, K. 2010. “Game theory and water resources.” J. Hydrol. 381 (3): 225–238. https://doi.org/10.1016/j.jhydrol.2009.11.045.
Madani, K., and M. Hooshyar. 2014. “A game theory–reinforcement learning (GT–RL) method to develop optimal operation policies for multi-operator reservoir systems.” J. Hydrol. 519: 732–742. https://doi.org/10.1016/j.jhydrol.2014.07.061.
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.
Nash, J. 1953. “Two-person cooperative games.” Econometrica 21 (1): 128–140. https://doi.org/10.2307/1906951.
Pereira, M. V. F., and L. M. V. G. Pinto. 1985. “Stochastic optimization of a multireservoir hydroelectric system: A decomposition approach.” Water Resour. Res. 21 (6): 779–792. https://doi.org/10.1029/WR021i006p00779.
Schardong, A., and S. P. Simonovic. 2015. “Coupled self-adaptive multiobjective differential evolution and network flow algorithm approach for optimal reservoir operation.” J. Water Resour. Plann. Manage. 141 (10): 04015015. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000525.
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.
Tilmant, A., and W. Kinzelbach. 2012. “The cost of noncooperation in international river basins.” Water Resour. Res. 48 (1): W01503. https://doi.org/10.1029/2011WR011034.
Turgeon, A., and R. Charbonneau. 1998. “An aggregation-disaggregation approach to long-term reservoir management.” Water Resour. Res. 34 (12): 3585–3594. https://doi.org/10.1029/98WR02608.
Wan, W., J. Zhao, J. R. Lund, T. Zhao, X. Lei, and H. Wang. 2016. “Optimal hedging rule for reservoir refill.” J. Water Resour. Plan. Manage. 142 (11): 04016051. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000692.
Wang, K. W., L. C. Chang, and F. J. Chang. 2011. “Multi-tier interactive genetic algorithms for the optimization of long-term reservoir operation.” Adv. Water Resour. 34 (10): 1343–1351. https://doi.org/10.1016/j.advwatres.2011.07.004.
Wu, X., C. Cheng, J. R. Lund, W. Niu, and S. Miao. 2018. “Stochastic dynamic programming for hydropower reservoir operations with multiple local optima.” J. Hydrol. 564: 712–722. https://doi.org/10.1016/j.jhydrol.2018.07.026.
Wu, X., C. Cheng, Y. Zeng, and J. R. Lund. 2016. “Centralized versus distributed cooperative operating rules for multiple cascaded hydropower reservoirs.” J. Water Resour. Plan. Manage. 142 (11): 05016008. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000685.
Xu, W., J. Zhao, T. Zhao, and Z. Wang. 2014. “Adaptive reservoir operation model incorporating nonstationary inflow prediction.” J. Water Resour. Plan. Manage. 141 (8): 04014099. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000502.
Yang, G., S. Guo, P. Liu, L. Li, and C. Xu. 2017. “Multiobjective reservoir operating rules based on cascade reservoir input variable selection method.” Water Resour. Res. 53 (4): 3446–3463. https://doi.org/10.1002/2016WR020301.
Yang, Y.-C. E., X. Cai, and D. M. Stipanović. 2009. “A decentralized optimization algorithm for multiagent system-based watershed management.” Water Resour. Res. 45 (8): W08430. https://doi.org/10.1029/2008WR007634.
Zeng, M., L. Peng, Q. Fan, and Y. Zhang. 2016a. “Trans-regional electricity transmission in China: Status, issues and strategies.” Renew. Sustain. Energy Rev. 66: 572–583. https://doi.org/10.1016/j.rser.2016.08.023.
Zeng, M., Y. Yang, L. Wang, and J. Sun. 2016b. “The power industry reform in China 2015: Policies, evaluations and solutions.” Renew. Sustain. Energy Rev. 57: 94–110. https://doi.org/10.1016/j.rser.2015.12.203.
Zeng, Y., X. Wu, C. Cheng, and Y. Wang. 2014. “Chance-constrained optimal hedging rules for cascaded hydropower reservoirs.” J. Water Resour. Plann. 140 (7): 04014010. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000427.
Zhao, T., J. Zhao, J. R. Lund, and D. Yang. 2014. “Optimal hedging rules for reservoir flood operation from forecast uncertainties.” J. Water Resour. Plan. Manage. 140 (12): 04014041. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000432.
Zhao, T., J. Zhao, D. Yang, and H. Wang. 2013. “Generalized martingale model of the uncertainty evolution of streamflow forecasts.” Adv. Water Resour. 57: 41–51. https://doi.org/10.1016/j.advwatres.2013.03.008.
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Published In
Journal of Water Resources Planning and Management
Volume 145 • Issue 5 • May 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Jan 25, 2018
Accepted: Oct 10, 2018
Published online: Feb 26, 2019
Published in print: May 1, 2019
Discussion open until: Jul 26, 2019
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