Improved Inflow Modeling in Stochastic Dual Dynamic Programming
Publication: Journal of Water Resources Planning and Management
Volume 142, Issue 12
Abstract
Stochastic dual dynamic programming (SDDP) is a widely used technique for operation optimization of large-scale hydropower systems in which reservoir inflow uncertainty is modeled with discrete scenarios produced by statistical time series models, such as the family of periodic auto-regressive (PAR) models. It is a common practice in statistical modeling of hydrologic time series to fit a well-known probability distribution (usually normal distribution) to the data by applying proper transformation. Box-Cox transformation is a commonly used transformation in the case of normal distribution fitting. The convexity requirement of SDDP means that nonlinearly transformed time series cannot be used for statistical inflow model calibration. In this paper, a linear approximation is proposed to estimate the expected value of the next stage inflow. In the proposed approach, next-stage inflows are estimated by a model that uses transformed time series. Furthermore, using the proposed linear approximation, it is shown that it is possible to utilize the time series transformed by Box-Cox transformation for scenario generation in SDDP. The Karoon multireservoir system in Iran has been used as a case study in order to show the effectiveness of the proposed method. Some concluding remarks have also been provided by comparing the results of the two SDDP models, with and without the proposed linear approximation.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors gratefully acknowledge the financial support provided by the Iran Water and Power Resources Development Company (grant #923566). The authors thank the reviewers, the Associate Editor, and the Editor for their constructive comments.
References
Bellman, R. (1961). Adaptive control processes: A guided tour, Princeton University Press, Princeton, NJ.
Box, G., and Cox, D. (1964). “An analysis of transformations.” J. R. Stat. Soc. B, 26(2), 211–252.
Casteletti, C., de Rigo, D., Rizzoli, A., Soncini-Sessa, R., and Weber, E. (2007). “Neuro-dynamic programming for designing water reservoir network management policies.” Control Eng. Pract., 15(8), 1031–1038.
de Matos, V. L., and Finardi, E. C. (2012). “A computational study of a stochastic optimization model for long term hydrothermal scheduling.” Electr. Power Energy Syst., 43(1), 1443–1452.
de Matos, V. L., Philpott, A. B., and Finardi, E. C. (2015). “Improving the performance of stochastic dual dynamic programming.” J. Comput. Appl. Math., 290, 196–208.
Gjelsvik, A., Mo, B., and Haugstad, A. (2010). “Long- and medium-term operations planning and stochastic modeling in hydro-dominated power systems based on stochastic dynamic programming.” Handbook of power systems. I: Energy systems, Springer, Berlin, 33–55.
Goor, Q., Kelman, R., and Tilmant, A. (2011). “Optimal multipurpose-multireservoir operation model with variable productivity of hydropower plants.” J. Water Resour. Plann. Manage., 258–267.
Hipel, K. W., and McLeod, A. I. (1994). Time series modelling of water resources and environmental systems, Elsevier, Amsterdam, Netherlands.
Homem-de-Mello, T., de Matos, V. L., and Finardi, E. C. (2011). “Sampling strategies and stopping criteria for stochastic dual dynamic programming: A case study in long-term hydrothermal scheduling.” Energy Syst., 2(1), 1–31.
Infanger, G., and Morton, D. P. (1996). “Cut sharing for multistage stochastic linear programs with interstage dependency.” Math. Program., 75(2), 241–256.
Johnson, S., Stedinger, J., Shoemaker, J., Li, C., and Tejada-Guibert, A. (1993). “Numerical solution of continuous-state dynamic programs using linear and spline interpolation.” Oper. Res., 41(3), 484–500.
Karamouz, M., Szidarovszky, F., and Zahraie, B. (2003). Water resources systems analysis, CRC Press, Boca Raton, FL, 608.
Maceira, M. E. P., and Damazio, J. M. (2004). “The use of PAR (p) model in the stochastic dual dynamic programming optimization scheme used in the operation planning of the Brazilian hydropower system.” 8th Int. Conf. on Probabilistic Methods Applied to Power Systems, Iowa State Univ., Ames, IA.
Maceira, M. E. P., Marzano, L. G. B., Penna, D. D. J., Diniz, A. L., and Justino, T. C. (2015). “Application of CVaR risk aversion approach in the expansion and operation planning and for setting the spot price in the Brazilian hydrothermal interconnected system.” Electr. Power Energy Syst., 72, 126–135.
Pereira, M. V. F., and Pinto, L. M. V. G. (1985). “Stochastic optimization of a multireservoir hydroelectric system—A decomposition approach.” Water Resour. Res., 21(6), 779–792.
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 De Matos, V. L. (2012). “Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion.” Eur. J. Oper. Res., 218(2), 470–483.
Rebennack, S., Flach, B., Pereira, M. V., and Pardalos, P. M. (2012). “Stochastic hydro-thermal scheduling under emissions constraints.” IEEE Trans. Power Syst., 27(1), 58–68.
Saad, M., Turgeon, A., Bigras, P., and Duquette, R. (1994). “Learning disaggregation technique for the operation of long-term hydroelectric power systems.” Water Resour. Res., 30(11), 3195–3202.
Shapiro, A. (2011). “Analysis of stochastic dual dynamic programming method.” Eur. J. Oper. Res., 209(1), 63–72.
Tavanir Holding Company. (2012). Electric power industry in Iran, Tehran, Iran.
Tilmant, A., and Kelman, R. (2007). “A stochastic approach to analyze trade-offs and risks associated with large-scale water resources systems.” Water Resour. Res., 43(6), W06425.
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.
Wang, W. C., Chau, K. W., Cheng, C. T., and Qui, L. (2009). “A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series.” J. Hydrol., 374(3–4), 294–306.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 142 • Issue 12 • December 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Oct 29, 2015
Accepted: Jun 29, 2016
Published online: Aug 30, 2016
Published in print: Dec 1, 2016
Discussion open until: Jan 30, 2017
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.