Abstract
The stochastic dynamic programming (SDP) method faces computational difficulties when used to determine the optimal operation of multiple storages. A new approach, a combined SDP-statistical disaggregation approach is introduced to determine releases for a special situation relating to multiple reservoir systems, that is, for a system of multiple storages where operational data are available. The approach consists of defining an equivalent single reservoir which represents the system of multiple reservoirs. The optimal releases from the equivalent single reservoir are derived by the use of SDP. Disaggregation of the optimal releases from the equivalent single reservoir, to produce the releases from the individual storages is based on historical operational data. The Melbourne (Australia) water supply system is considered as the example. The releases derived from the combined SDP-statistical disaggregation approach are tested by operating a simulation model, and the conclusion is made that the approach produces satisfactory releases for a system of multiple reservoirs where operational data are available. The method cannot be applied to existing systems where insufficient or no operational data are available, or to proposed systems where operational data are not available. The method uses a small amount of computer time.
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References
Amir, R., 1967, Optimum operation of a multi-reservoir water supply system, Thesis (PhD), Stanford University, Stanford, California, U.S.A.
Anderson, T. W., 1958, An Introduction to Multivariate Statistical Analysis, John Wiley, New York.
Arvanitidis, N. V. and Rosing, J., 1970, Composite representation of a multi-reservoir hydroelectric power system, IEEE Trans. on Power Apparatus and Systems, Vol. Pas-89, No. 2, pp. 319–326.
Butcher, W. S. and Fordham, J. W., 1970, Optimum operation using stochastic dynamic programming, Pub. No. 9, Center for Water Resour. Res., University of Nevada, Reno, Nevada, U.S.A.
Healy, M. J. R., 1968, Algorithm AS 6; triangular decomposition of a symmetric matrix, J. Royal Stat. Soc. Series C (Appl. Stat.) 17, 195–197.
Kuiper, J. and Ortolano, L., 1973, A dynamic programming-simulation strategy for the capacity expansion of hydroelectric power systems, Water Resour. Res. 9, 1497–1510.
Little, J. D. C., 1955, The use of storage water in a hydroelectric system, Operations Res. 3, 187–197.
Mejia, J. M. and Rousselle, J., 1976, Disaggregation models in hydrology revisited, Water Resour. Res. 12, 185–186.
Perera, B. J. C., 1985, Stochastic dynamic programming applied to multiple reservoir systems, Thesis (PhD), Monash University, Australia.
Smith, R. A., 1981, Aggregation-disaggregation techniques for the operation of multi-reservoir systems, Thesis (PhD), Colorado State University, Fort Collins, Colorado, U.S.A.
Su, S. Y. and Deininger, R. A., 1974, Modelling the regulation of Lake Superior under uncertainty of future water supplies, Water Resour. Res. 10, 11–25.
Torabi, M. and Mobasheri, F., 1973, A stochastic dynamic programming model for the optimum operation of a multi-purpose reservoir, Water Resour. Bull. 9, 1089–1099.
Turgeon, A., 1980, Optimal operation of multi-reservoir power systems with stochastic inflows, Water Resour. Res. 16, 275–283.
Turgeon, A., 1981, A decomposition method for the long-term scheduling of reservoirs in series, Water Resour. Res. 17, 1565–1570.
Valencia, R. D. and Schaake, J. C. Jr., Disaggregation processes in stochastic hydrology, Water Resour. Res. 9, 580–585.
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Perera, B.J.C., Codner, G.P. A combined stochastic dynamic programming-statistical disaggregation approach applied to multiple reservoir systems. Water Resour Manage 2, 153–171 (1988). https://doi.org/10.1007/BF00429898
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DOI: https://doi.org/10.1007/BF00429898
Key words
- Stochastic dynamic programming
- statistical disaggregation
- optimal operation
- equivalent single reservoir
- aggregation
- water supply systems
- multiple reservoirs