Using SDDP to Develop Water-Value Functions for a Multireservoir System with International Treaties
Publication: Journal of Water Resources Planning and Management
Volume 144, Issue 2
Abstract
This paper presents the implementation of stochastic dual dynamic programming (SDDP) to generate water-value functions for operations planning of the British Columbia (BC) Hydro system. An inflow model is developed to generate stochastic seasonal volumes forecasts and monthly inflows for the Peace River and upper Columbia River in Canada. A model is developed to model storage spaces for flood control and storage account operations to comply with the Columbia River Treaty (CRT) and subsequent agreements between Canada and the United States. Two novel algorithms are developed. The first uses SDDP and an updating process to generate the end of planning horizon water-value function, and the second uses SDDP to generate monthly water-value functions with a new stopping criterion for SDDP. Analysis results of the water-value functions illustrate the importance of globally optimizing reservoirs and storage accounts and modeling stochastic inflows. Results of simulation studies show significant benefits of using water-value functions over currently used methods and the need for modeling inflow uncertainties and storage account operations.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The research project was fully funded by BC Hydro and by a CRD NSERC Grant (CRDPJ 385615-09 and CRDPJ 476296-14) to the second author. The authors would like to acknowledge the help of Wun Kin Cheng, Joel Evans, Adam Gobena, Jian Li, Herbert Louie, Thomas Siu, Camila Tang-Miya, Charles Wong, and many others at BC Hydro in data access, modeling, IT support, and administration. The authors would also like to acknowledge the review of SDDP development by Dr. Andy Philpott, the Department of Engineering Science, University of Auckland, New Zealand. The authors are also grateful for the very detailed suggestions from the Editor, Associate Editor, and three anonymous reviewers, which helped improve the quality of this paper significantly.
References
Abdalla, A. E. (2007). “A reinforcement learning algorithm for operations planning of a hydroelectric power multireservoir system.” Ph.D. thesis, Univ. of British Columbia, Vancouver, Canada.
Barto, A., and Sutton, R. (1998). Reinforcement learning: An introduction, MIT Press, Boston.
Bellman, R. (1957). Dynamic programming, Princeton University Press, Princeton, NJ.
Birge, J. R., and Louveaux, F. (1997). Introduction to stochastic programming, Springer, New York.
Charnes, A., Cooper, W. W., and Ferguson, R. O. (1955). “Optimal estimation of executive compensation by linear programming.” Manage. Sci., 1(2), 138–151.
Druce, D. L. (1990). “Incorporating daily flood control objectives into a monthly stochastic dynamic programing model for a hydroelectric complex.” Water Resour. Res., 26(1), 5–11.
Fane, L. (2003). “Generalized optimization in the British Columbia hydroelectric system.” Master’s thesis, Univ. of British Columbia, Vancouver, Canada.
Goor, Q., Kelman, R., and Tilmant, A. (2011). “Optimal multipurpose-multireservoir operation model with variable productivity of hydropower plants.” J. Water Resour. Plan. Manage., 258–267.
Guan, Z., and Philpott, A. B. (2011). “A multistage stochastic programming model for the New Zealand dairy industry.” Int. J. Prod. Econ., 134(2), 289–299.
Guan, Z., Shawwash, Z., Abdalla, A., Ayad, A., and Evans, J. (2013). “Assessing how uncertainty affects reservoir operations.” Hydro Rev., 32(3), 76–81.
Hyde, J. M. (2010). “Columbia River Treaty past and future.” ⟨https://www.crt2014-2024review.gov/files/10aug_hyde_treatypastfuture_finalrev.pdf⟩ (May 28, 2016).
Jacobs, J., et al. (1995). “SOCRATES: A system for scheduling hydroelectric generation under uncertainty.” Ann. Oper. Res., 59(1), 99–133.
Kaut, M., and Wallace, S. W. (2003). Evaluation of scenario-generation methods for stochastic programming, Humboldt-Universitätzu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik, Berlin.
Kelman, J., Stedinger, J. R., Cooper, L. A., Hsu, E., and Yuan, S.-Q. (1990). “Sampling stochastic dynamic programming applied to reservoir operation.” Water Resour. Res., 26(3), 447–454.
Koutsoyiannis, D. (2000). “A generalized mathematical framework for stochastic simulation and forecast of hydrologic time series.” Water Resour. Res., 36(6), 1519–1533.
Labadie, J. (2004). “Optimal operation of multireservoir systems: State-of-the-art review.” J. Water Resour. Plan. Manage., 93–111.
Maceira, M. E. P., Duarte, V. S., Penna, D. D. J., Moraes, L. A. M., and Melo, A. C. G. (2008). “Ten years of application of stochastic dual dynamic programming in official and agent studies in Brazil—Description of the NEWAVE program.” ⟨http://www.pscc-central.org/uploads/tx_ethpublications/pscc2008_704.pdf⟩ (May 28, 2016).
Mamun, A., Shawwash, Z., Abdalla, A., Li, J., and Siu, T. (2015). “Application of a goal programming algorithm to incorporate environmental requirements in a multi-objective Columbia River Treaty Reservoir optimization model.” Can. Water Resour. J., 40(1), 111–125.
Pereira, M. V. F., and Pinto, L. M. V. G. (1991). “Multi-stage stochastic optimization applied to energy planning.” Math. Program., 52(1–3), 359–375.
Philpott, A. B., and Guan, Z. (2008). “On the convergence of stochastic dual dynamic programming and other methods.” Oper. Res. Lett., 36(4), 450–455.
Poorsepahy-Samian, H., Espanmanesh, V., and Zahraie, B. (2016). “Improved inflow modeling in stochastic dual dynamic programming.” J. Water Resour. Plan. Manage., 04016065.
Shabani, N. (2009). “Optimization of the river hydroelectric system with a reinforcement learning approach.” Master’s thesis, Univ. of British Columbia, Vancouver, Canada.
Shawwash, Z. K., Siu, T. K., and Russell, S. O. R. (2000). “The BC Hydro short term hydro scheduling optimization model.” IEEE Trans. Power Syst., 15(3), 1125–1131.
Tilmant, A., Pinte, D., and Goor, Q. (2008). “Assessing marginal water values in multipurpose multireservoir systems via stochastic programming.” Water Resour. Res., 44(12), W12431.
U.S. Army Corps of Engineers. (2003). “Columbia River Treaty flood control operating plan.” ⟨https://www.crt2014-2024review.gov/Files/FCOP2003.pdf⟩ (May 28, 2016).
U.S. Army Corps of Engineers. (2013). “Columbia River Treaty assured operating plan and determination of downstream power benefits for operating year 2017–18.” ⟨http://www.nwd-wc.usace.army.mil/PB/PEB_08/docs/aop/18AOPddpb.pdf⟩ (May 28, 2016).
Wolfgang, O., Haugstad, A., Mo, B., Gjelsvik, A., Wangensteen, I., and Doorman, G. (2009). “Hydro reservoir handling in Norway before and after deregulation.” Energy, 34(10), 1642–1651.
Information & Authors
Information
Published In
Copyright
©2017 American Society of Civil Engineers.
History
Received: Sep 1, 2016
Accepted: Jul 7, 2017
Published online: Nov 28, 2017
Published in print: Feb 1, 2018
Discussion open until: Apr 28, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.