Optimal Deterministic Reservoir Operations in Continuous Time
Publication: Journal of Water Resources Planning and Management
Volume 125, Issue 3
Abstract
In 1946, Massé discussed the optimal operation of a single reservoir for hydroelectric energy production. He obtained his results by both economic reasoning and rigorous mathematical derivations using a generalized form of the calculus of variations. In this article, the procedure of Massé is generalized to cases where: (1) the benefits from release are not related directly to the release but rather to the discharge at a downstream point; (2) there may be several points downstream where an objective is to be achieved; and (3) there are several reservoirs. Massé and Varlet found that the optimal strategy is the one that maintains the marginal value of the release constant in time whenever the reservoir is neither full nor empty. It is shown rigorously here that, in the general case, for a strategy to be optimal, the “memory-integrated future marginal value” of the release must be constant. This result is generalized to a system of several reservoirs and illustrated on a simplified description of the Seine river basin upstream of Paris, France.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bellman, R. E. ( 1957). Dynamic programming. Princeton University Press, Princeton, N.J.
2.
Bryson, A. E., and Ho, Y.-C. ( 1969). Applied optimal control. Blaisdell Publishing, Waltham, Mass.
3.
Klemes, V. ( 1979). “Storage mass curve analysis in a systems-analytic perspective.” Water Resour. Res., 15(2), 359–370.
4.
Laufer, F., and Morel-Seytoux, H. J. ( 1979). “Optimal weekly releases from a seasonal reservoir. I: Deterministic future.” Water Resour. Res., 15(2), 383–398.
5.
Massé, P. ( 1946). Les réserves et la régulation de l'avenir dans la vie économique. I: Avenir déterminé. Hermann & Cie, Publishers, Paris (in French).
6.
Morel-Seytoux, H. J. ( 1976). “Chapter 9: Optimization and uncertainty.” Stochastic approaches to water resources, H. W. Shen, ed., Vol. 1, Fort Collins, Colorado, 1–37.
7.
Morel-Seytoux, H. J. ( 1997). “Gestion optimale conjointe de plusieurs réservoirs en avenir déterminé.” HYDROWAR Rep. No. 97.3, Hydrology Days Publications, Atherton, Calif. (in French).
8.
Morel-Seytoux, H. J. ( 1998a). “Extension de la théorie du reservoir linéaire avec variation de la constante en fonction des débits, retard fractionnaire et débordement.” HYDROWAR Rep. No. 98.3, Hydrology Days Publications, Atherton, Calif. (in French).
9.
Morel-Seytoux, H. J. ( 1998b). “Optimal reservoir operations in a deterministic and continuous time framework.” HYDROWAR Rep. No. 98.4, Hydrology Days Publications, Atherton, Calif.
10.
Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., and Mishcenko, E. F. ( 1964). The mathematical theory of optimal processes, D. E. Brown, translator, The Macmillan Co., New York.
11.
Varlet, H. ( 1923). “Étude graphique des conditions d'exploitation d'un réservoir de régularisation.” Ann. Ponts et Chaussées, Mém. Doc., PartieTech., Paris, 93, 61–79.
Information & Authors
Information
Published In
History
Published online: May 1, 1999
Published in print: May 1999
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.