Abstract
Dynamic Programming (DP) is considered as a good technique for optimal reservoir operation due to the sequential decision making and ease in handling non-linear objective functions and constraints. But the application of DP to multireservoir system is not that encouraging due to the problem `curse of dimensionality'. Incremental DP, discrete differential DP, DP with successive approximation, incremental DP with successive approximation are some of the algorithms evolved to tackle this curse of dimensionality for DP. But in all these cases, it is difficult to choose an initial trial trajectory, to get at an optimal solution and there is no control over the number of iterations required for convergence. In this paper, a new algorithm, Folded DP, is proposed, which overcomes these difficulties. Though it is also an iterative process, no initial trial trajectory is required to start with. So, the number of iterations is independent of any initial condition. The developed algorithm is applied to a hypothetical reservoir system, solved by earlier researchers.Operating policy obtained using the present algorithm has compared well with that of the earlier algorithm.
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References
Baliarsingh, F.: 2000, 'Long-term and Short-term Optimal Reservoir Operation for Flood Control', Doctoral Thesis, Indian Institute of Technology, Kharagpur, India.
Bellman, R.: 1957, Dynamic Programming, Princeton University Press, Princeton, N.J.
Giles, J. E. and Wunderlich, W. O.: 1981, 'Weekly multipurpose planning model for TVA reservoir system'J. Water Resour. Plng. Mgmt. ASCE 107(WR2), 495-511.
Hall, W. A., Tauxe, G. W. and Yeh, W. W.-G.: 1969, 'An alternate procedure for the optimization of operations for planning with multiple river, multiple purpose systems', Water Resour. Res. 5(6), 1367-1372.
Heidari, M., Chow, V. T., Kokotovic, P. V. and Meredith, D. D. 1971, 'Discrete differential dynamic programming approach to water resources systems optimization', Water Resour. Res. 7(2), 273-282.
Larson, R. E.: 1968, State Increment Dynamic Programming, Elsevier, New York, U.S.A.
Larson, R. E. and Korsak, A. J.: 1970, 'A dynamic programming successive approximations technique with convergence proofs'Automatica 6, 245-252.
Nopmongcol, P. and Askew, A. J.: 1976, 'Multilevel incremental dynamic programming', Water Resour. Res. 12(6), 1291-1297.
Ozden, M.: 1984, 'A Binary State DP algorithm for operation problems of multireservoir systems', Water Resour. Res. 20(1), 9-14.
Perera, B. J. C. and Codner, G. P.: 1998, 'Computational improvement for stochastic dynamic programming models of urban water supply reservoirs', J. Amer. Water Resour. Assoc. 34(2), 267-278.
Turgeon, A.: 1981, 'Optimal short-term hydro scheduling from the principle of progressive optimality', Water Resour. Res. 17(3), 481-486.
Yakowitz, S.: 1982, 'Dynamic programming applications in water resources', Water Resour. Res. 18(4), 673-696.
Yeh, W.W.-G.: 1985, 'Reservoir management and operations models a state-of-the-art review', Water Resour. Res. 21(12), 1797-1818.
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Kumar, D.N., Baliarsingh, F. Folded Dynamic Programming for Optimal Operation of Multireservoir System. Water Resources Management 17, 337–353 (2003). https://doi.org/10.1023/A:1025894500491
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DOI: https://doi.org/10.1023/A:1025894500491