Technical Papers
Jan 30, 2017

Effective Streamflow Process Modeling for Optimal Reservoir Operation Using Stochastic Dual Dynamic Programming

Publication: Journal of Water Resources Planning and Management
Volume 143, Issue 4

Abstract

This article presents an innovative streamflow process model for use in reservoir operational rule design in stochastic dual dynamic programming (SDDP). Model features, which can be applied independently, are (1) a multiplicative process model for the forward phase and its linearized version for the backward phase; and (2) a nonuniform time-step length that is inversely proportional to seasonal variability. The advantages are (1) guaranteeing positive streamflow values still maintaining problem linearity, and (2) making system adaptation faster during high variable periods. Model identification is straightforward, as with the additive periodic autoregressive model generally used in SDDP. The proposed model is applied on the Senegal River system for the optimal operation of Manantali Reservoir and evaluated against the streamflow process model currently used in the water management literature.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

Luciano Raso’s research was funded by the AXA Research Fund.

References

Albergel, J., Bader, J.-C., and Lamagat, J.-P. (1997). “Flood and drought: Application to the Senegal River management.” IAHS Publ. Ser. Proc. Rep.-Int. Assoc. Hydrol. Sci., 240, 509–518.
Arjoon, D., Mohamed, Y., Goor, Q., and Tilmant, A. (2014). “Hydro-economic risk assessment in the eastern Nile River basin.” Water Resour. Econ., 8, 16–31.
Bader, J.-C., Lamagat, J.-P., and Guiguen, N. (2003). “Gestion du barrage de manantali sur le fleuve sénégal: Analyse quantitative d’un conflit d’objectifs.” Hydrol. Sci. J., 48(4), 525–538.
Bartolini, P., and Salas, J. D. (1993). “Modeling of streamflow processes at different time scales.” Water Resour. Res., 29(8), 2573–2587.
Bartolini, P., Salas, J. D., and Obeysekera, J. (1988). “Multivariate periodic ARMA(1, 1) processes.” Water Resour. Res., 24(8), 1237–1246.
Bellman, R. E., and Dreyfus, S. E. (1966). Applied dynamic programming, Princeton University Press, Princeton, NJ.
Bertsekas, D. P., and Tsitsiklis, J. N. (1995). “Neuro-dynamic programming: An overview.” Proc., 34th IEEE Conf. on Decision and Control, Vol. 1, IEEE, New York, 560–564.
Bezerra, B., Veiga, Á., Barroso, L. A., and Pereira, M. (2012). “Assessment of parameter uncertainty in autoregressive streamflow models for stochastic long-term hydrothermal scheduling.” Proc., Power and Energy Society General Meeting 2012, IEEE, New York, 1–8.
Birge, J. R., and Louveaux, F. (1997). Introduction to stochastic programming, Springer, Berlin.
Box, G., Jenkins, G., and Reinsel, G. (1970). Time series analysis, Holden-Day, San Francisco.
Camacho, F., McLeod, A., and Hipel, K. (1987). “Multivariate contemporaneous ARMA model with hydrological applications.” Stochastic Hydrol. Hydraul., 1(2), 141–154.
Castelletti, A., Pianosi, F., and Soncini-Sessa, R. (2008). “Water reservoir control under economic, social and environmental constraints.” Automatica, 44(6), 1595–1607.
Dekking, M. (2005). A modern introduction to probability and statistics: Understanding why and how, Springer, Berlin.
Fraval, P., Bader, J., Mané, L., David-Benz, H., Lamagat, J., and Diagne, O. D. (2002). “The quest for integrated and sustainable water management in the senegal river valley.” Proc., 5th Inter-Regional Conf. on Environment and Water (ENVIROWATER), Ouagadougou, Burkina Faso, 5–8.
Gjelsvik, A., Mo, B., and Haugstad, A. (2010). “Long-and medium-term operations planning and stochastic modelling in hydro-dominated power systems based on stochastic dual dynamic programming.” Handbook of power systems I, 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.
Karamouz, M., Szidarovszky, F., and Zahraie, B. (2003). Water resources systems analysis, CRC Press, Boca Raton, FL.
Koutsoyiannis, D. (2009). “A random walk on water.” Hydrology Earth Syst. Sci. Discuss., 6(5), 6611–6658.
Linowsky, K., and Philpott, A. B. (2005). “On the convergence of sampling-based decomposition algorithms for multistage stochastic programs.” J. Optim. Theory Appl., 125(2), 349–366.
Loucks, D. P. (1992). “Water resource systems models: Their role in planning.” J. Water Resour. Plann. Manage., 214–223.
Marques, G. F., and Tilmant, A. (2013). “The economic value of coordination in large-scale multireservoir systems: The Parana River case.” Water Resour. Res., 49(11), 7546–7557.
Mayne, D. Q., Rawlings, J. B., Rao, C. V., and Scokaert, P. O. M. (2000). “Constrained model predictive control: Stability and optimality.” Automatica, 36(6), 789–814.
Nicklow, J., et al. (2010). “State of the art for genetic algorithms and beyond in water resources planning and management.” J. Water Resour. Plann. Manage., 412–432.
Pereira, M., Oliveira, G., Costa, C., and Kelman, J. (1984). “Stochastic streamflow models for hydroelectric systems.” Water Resour. Res., 20(3), 379–390.
Pereira, M., and Pinto, L. M. (1991). “Multi-stage stochastic optimization applied to energy planning.” Math. Program., 52(1), 359–375.
Philpott, A. B., and Guan, Z. (2008). “On the convergence of stochastic dual dynamic programming and related methods.” Oper. Res. Lett., 36(4), 450–455.
Rabiner, L. R., and Juang, B.-H. (1986). “An introduction to hidden Markov models.” IEEE ASSP Mag., 3(1), 4–16.
Raso, L., and Malaterre, P. O. (2016). “Combining short-term and long-term reservoir operation using infinite horizon model predictive control.” J. Irrig. Drain. Eng., .
Raso, L., Schwanenberg, D., van de Giesen, N. C., and van Overloop, P. J. (2014). “Short-term optimal operation of water systems using ensemble forecasts.” Adv. Water Resour., 71, 200–208.
Reed, P. M., Hadka, D., Herman, J. D., Kasprzyk, J. R., and Kollat, J. B. (2013). “Evolutionary multiobjective optimization in water resources: The past, present, and future.” Adv. Water Resour., 51, 438–456.
Salas, J. D. (1980). Applied modeling of hydrologic time series, Water Resources, Littleton, CO.
Salas, J. D., Tabios, G. Q., and Bartolini, P. (1985). “Approaches to multivariate modeling of water resources time series.” J. Am. Water Resour. Assoc., 21(4), 683–708.
Seifi, A., and Hipel, K. W. (2001). “Interior-point method for reservoir operation with stochastic inflows.” J. Water Resour. Plann. Manage., 48–57.
Shapiro, A. (2011). “Analysis of stochastic dual dynamic programming method.” Eur. J. Oper. Res., 209(1), 63–72.
Shapiro, A., and Andrzej, P. R. (2003). Stochastic programming, Elsevier, Amsterdam, Netherlands.
Soncini-Sessa, R., Castelletti, A., and Weber, E. (2007). Integrated and participatory water resources management, Elsevier, Amsterdam, Netherlands.
Stedinger, J. R., Sule, B. F., and Loucks, D. P. (1984). “Stochastic dynamic programming models for reservoir operation optimization.” Water Resour. Res., 20(11), 1499–1505.
Stedinger, J. R., and Taylor, M. R. (1982). “Synthetic streamflow generation: 1. Model verification and validation.” Water Resour. Res., 18(4), 909–918.
Tilmant, A., Arjoon, D., and Marques, G. F. (2014). “Economic value of storage in multireservoir systems.” J. Water Resour. Plann. Manage., 375–383.
Tilmant, A., Beevers, L., and Muyunda, B. (2010). “Restoring a flow regime through the coordinated operation of a multireservoir system: The case of the Zambezi River basin.” Water Resour. Res., 46(7), W07533.
Tilmant, A., Goor, Q., and Pinte, D. (2009). “Agricultural-to-hydropower water transfers: Sharing water and benefits in hydropower-irrigation systems.” Hydrol. Earth Syst. Sci., 13(7), 1091–1101.
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., and Kinzelbach, W. (2012). “The cost of noncooperation in international river basins.” Water Resour. Res., 48(1), W01503.
Tilmant, A., Kinzelbach, W., Juizo, D., Beevers, L., Senn, D., and Casarotto, C. (2012). “Economic valuation of benefits and costs associated with the coordinated development and management of the Zambezi River basin.” Water Policy, 14(3), 490.
Tilmant, A., Lettany, J., and Kelman, R. (2007). “Hydrological risk assessment in the Euphrates-Tigris River basin: A stochastic dual dynamic programming approach.” Water Int., 32(2), 294–309.
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.
Trezos, T., and Yeh, W. W.-G. (1987). “Use of stochastic dynamic programming for reservoir management.” Water Resour. Res., 23(6), 983–996.
Tsitsiklis, J. N., and Van Roy, B. (1996). “Feature-based methods for large scale dynamic programming.” Mach. Learn., 22(1–3), 59–94.
Turgeon, A. (1980). “Optimal operation of multireservoir power systems with stochastic inflows.” Water Resour. Res., 16(2), 275–283.
Van Overloop, P. J., Weijs, S., and Dijkstra, S. (2008). “Multiple model predictive control on a drainage canal system.” Control Eng. Pract., 16(5), 531–540.
Vecchia, A. (1985). “Periodic autoregressive-moving average (parma) modeling with applications to water resources.” J. Am. Water Resour. Assoc., 21(5), 721–730.
Weijs, S. V. (2011). “Information theory for risk-based water system operation.” Ph.D. thesis, Delft Univ. of Technology, Delft, Netherlands.

Information & Authors

Information

Published In

Go to Journal of Water Resources Planning and Management
Journal of Water Resources Planning and Management
Volume 143Issue 4April 2017

History

Received: Apr 12, 2016
Accepted: Oct 5, 2016
Published online: Jan 30, 2017
Published in print: Apr 1, 2017
Discussion open until: Jun 30, 2017

Permissions

Request permissions for this article.

Authors

Affiliations

Luciano Raso [email protected]
Delft Univ. of Technology, Jaffalaan 5, 2628 BX Delft, Netherlands (corresponding author). E-mail: [email protected]
Pierre-Olivier Malaterre
IRSTEA, 361 Rue Jean François Breton, 34196 Montpellier, France.
Jean-Claude Bader
IRD, 361 Rue Jean François Breton, 34196 Montpellier, France.

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share