Open Access Open Access  Restricted Access Subscription Access

Reservoirs optimization with dynamic programming

Phan Thi Thu Phuong, Dao Thi Ngoc Han, Hoang Van Lai, Bui Minh Tri


Differential Evolution (DE) and Dynamic Programming (DP) are important optimal methods in reservoir regulation. In the previous work [1], we presented the outline of DE, and applied it into Pleikrong reservoir, a big one in the Highland of Vietnam for dry season of 2010 year. Continuing from that, in this work, we present the outline of DP and then again, apply it to Pleikrong reservoir; and also apply it to Ialy, the biggest reservoir in Sesan cascade in the Highland of Vietnam; to reach optimal regulation for the maximum power production in the dry season of two years: 2010 and 2012. The results getting from DP are compared to the results by using DE. The results by these two methods have the same trend of releases which is storing the water at the beginning and significantly releasing at the end of the calculation time.


dynamic programming; reservoirs; cascade; Sesan; optimization


P. T. T. Phuong, H. V. Lai, and B. D. Tri. Reservoir optimization with differential evolution. Vietnam Journal of Mechanics, 38, (1), (2016), pp. 39–48. doi:10.15625/0866-7136/38/1/6490.

V. Chandramouli and H. Raman. Multireservoir modeling with dynamic programming and neural networks. Journal of Water Resources Planning and Management, 127, (2), (2001), pp. 89–98. doi:10.1061/(asce)0733-9496(2001)127:2(89).

N. L. C. Dias, M. V. F. Pereira, and J. Kelman. Optimization of flood control and power generation requirements in a multi-purpose reservoir. IFAC Proceedings Volumes, 18, (7), (1985), pp. 101–104. doi:10.1016/s1474-6670(17)60421-x.

D. P. Loucks, E. Van Beek, J. R. Stedinger, J. P. M. Dijkman, and M. T. Villars. Water resources systems planning and management: an introduction to methods, models and applications. UNESCO, Hydraulics, (2005).

K. D. W. Nandalal. Reservoir management under consideration of stratification and hydraulic phenomena. PhD thesis, Department of Water Resources, Wageningen Agricultural University, Netherlands, (1995).

W. W.-G. Yeh. Reservoir management and operations models: A state-of-the-art review. Water Resources Research, 21, (12), (1985), pp. 1797–1818. doi:10.1029/WR021i012p01797.

V. T. Chow. Methodology for water resources planning: DDDP and MLOM. Water Resourses Research, University of Illinois, (1971).

R. E. Larson. State increment dynamic programming. Elsevier, New York, (1968).

S. E. Dreyfus and A. M. Law. Art and theory of dynamic programming. Academic Press, Inc., (1977).

M. Heidari, V. T. Chow, P. V. Kokotovic, and D. D. Meredith. Discrete differential dynamic programing approach to water resources systems optimization. Water Resources Research, 7, (2), (1971), pp. 273–282. doi:10.1029/wr007i002p00273.

H. V. Khoi and L. B. Trung. Applying of 2-D dynamic programming to find the optimal hydropower reservoir system operation. Journal of Water resources and Environmental Engineering, 1, (2003), pp. 37–43. (in Vietnamese).

L. Hung. Multi-objective reservoirs optimization. PhD thesis, Da Nang University, (2012).

R. Bellman. Dynamic programming. Princeton University Press, (1957).

J. W. Labadie. Generalized dynamic programming package: CSUDP - Documentation and user guide. Colorado State University, (2003).

J. W. Labadie. Optimal operation of multireservoir systems: State-of-the-art review. Journal of Water Resources Planning and Management, 130, (2), (2004), pp. 93–111. doi:10.1061/(ASCE)0733-9496(2004)130:2(93).

K. D. W. Nandalal and J. J. Bogardi. Dynamic programming based operation of reservoirs: Applicability and limits. Cambridge University Press, (2007). doi:10.1017/cbo9780511535710.

P. Nopmongcol and A. J. Askew. Multilevel incremental dynamic programing. Water Resources Research, 12, (6), (1976), pp. 1291–1297. doi:10.1029/wr012i006p01291.

Real-time optimization, dynamic programming. Technical report, Lecture 19-20, 1.731 Water Resource Systems, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, (2006).

Operation procedure of the inter-reservoir on Sesan river basin. No 1182/QD-TTg, (2014). (in Vietnamese).

Full Text: PDF


  • There are currently no refbacks.