Abstract
A new formulation is presented for the analysis of reservoir systems synthesizing concepts from the traditional stochastic theory of reservoir storage, moments analysis and reliability programming. The analysis is based on the development of the first and second moments for the stochastic storage state variable. These expressions include terms for the failure probabilities (probabilities of spill or deficit) and consider the storage bounds explicitly. Using this analysis, expected values of the storage state, variances of storage, optimal release policies and failure probabilities — useful information in the context of reservoir operations and design, can be obtained from a nonlinear programming solution. The solutions developed from studies of single reservoir operations on both an annual and monthly basis, compare favorably with those obtained from simulation. The presentation herein is directed to both traditional reservoir storage theorists who are interested in the design of a reservoir and modern reservoir analysts who are interested in the long term operation of reservoirs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adams, B.J.; Ponnambalam, K. 1994: An algorithm for determining closed-loop operations policies for multi-reservoir systems, Stochastic and Statistical Methods in Hydrology and Environ. Engg., Kluwer Publ., Dordrecht, 389–395
Georgakakos, A.P.; Marks, D.H. 1987: A new method for the real-time operation of reservoir systems, Water Resour. Res. 23(7), 1376–1390
Georgakakos, A.P. 1989: Extended linear quadratic Gaussian control: Further extensions, Water Resour. Res. 25(2), 191–201
Kendall, D.G. 1957: Some problems in the theory of dams, J.R. Statist. Soc. 1319, 207–212 [cited in Phatarfod, 1989]
Klemes, V. 1981: Applied stochastic theory of storage in evolution, Advances in Hydroscience 12, 79–141
Klemes, V. 1987: One hundred years of applied storage reservoir theory, Water Resour. Mgt. 1, 159–175
Loucks, D.P. et al. 1981: Water Resource Systems Planning and Analysis, Prentice-Hall International, Inc., Englewoods Cliffs, N.J.
Moran, P.A.P. 1954: Probability theory of dams and storage systems, Australian Journal of Applied Science 5, 116–124
Moran, P.A.P. 1955: A probability theory of dams and storage systems: Modifications of the release rules, Australian Journal of Applied Science 6, 117–130
Phatarfod, R.M. 1979: The bottomless dam, Journal of Hydrology 40, 337–363
Phatarfod, R.M. 1986: The effect of serial correlation on reservoir size, Water Resour. Res. 22(6), 927–934
Phatarfod, R.M. 1989: Riverflow and reservoir storage models, Math. Comput. Modelling 12, 1057–1077
Phatarfod, R.M. 1994: Seasonality of flows and its effect on reservoir size, In Time Series Analysis in Hydrology and Environ. Engg., (Eds.) Hipel, McLeod, Panu and Singh, Kluwer Publ, Dordrecht, 395–407
Savarenskiy, A.D. 1940: A method for streamflow computation (in Russian). Gidrotekhn. Stroit. 2, 24–28 [cited in Klemes 1981]
Simonovic, P.S.; Marino, M.A. 1980: Reliability programming in reservoir management 1, Water Resour. Res. 16(5), 844–848
Turgeon, A. 1981: A decomposition method for the long-term scheduling of reservoirs in series, Water Resour. Res. 17(6), 1565–1570
Wasimi, A.S.; Kitandis, P.K. 1983: Real-time forecasting and daily operation of a multireservoir system during floods by linear quadratic Gaussian control, Water Resour. Res. 19(6), 1511–1522
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fletcher, S.G., Ponnambalam, K. A new formulation for the stochastic control of systems with bounded state variables: An application to a single reservoir system. Stochastic Hydrol Hydraul 10, 167–186 (1996). https://doi.org/10.1007/BF01581462
Issue Date:
DOI: https://doi.org/10.1007/BF01581462