Linear quadratic dynamic programming for water reservoir management. (English) Zbl 0892.90059

Özelkan, Ertunga C.; Galambosi, Ágnes; Fernández-Gaucherand, Emmanuel; Duckstein, Lucien

Appl. Math. Modelling 21, No. 9, 591-598 (1997).

Summary: Dynamic programming (DP) is applied in order to determine the optimal management policy for a water reservoir by modeling the physical problem via a linear quadratic (LQ) structure. A simplified solution to the LQ tracking problem is provided under mild assumptions. The model presents an aggregated multicriteria decision making problem where flood control, hydroelectric power, and water demand have to be satisfied: Simultaneously, the energy production is to be maximized, the mismatch of water demand minimized, and the water release should not cause flooding. The system constraints are basically the conservation of mass within the reservoir system, and the minimum and the maximum allowable limits for the water release and the reservoir level. The stochastic variables consist of the water inflow from the reservoir drainage basin, precipitation, and evaporation. The Tenkiller Ferry dam on the Illinois River basin in Oklahoma is analyzed as a case study.

MSC:

90B05	Inventory, storage, reservoirs
90C15	Stochastic programming
90C90	Applications of mathematical programming
90B90	Case-oriented studies in operations research
90C39	Dynamic programming

Keywords:

stochastic dynamic programming; linear quadratic tracking; optimal management policy; water reservoir; flood control; hydroelectric power; water demand

References:

[1]	Yakowitz, S., Dynamic programming applications in water resources, Water Resources Res., 18, 4, 673-696 (1982)
[2]	Yeh, W. W.-G., Reservoir management and operation models: A state-of-the-art review, Water Resources Res., 21, 12, 1797-1818 (1985)
[3]	Esogbue, A. O., A taxonomic treatment of dynamic programming models of water resources systems, (Esogbue, A. O., Dynamic Programming for Optimal Water Resources Systems Analysis (1989), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ), 27-71
[4]	Pindyck, R. S., An application of the linear quadratic tracking problem to economic stabilization policy, IEEE Trans. Automatic Control, AC-17, 3, 287-300 (1972)
[5]	Chan, Y. T.; Maille, J. P., Extensions of a linear quadratic tracking algorithm to include control constraints, IEEE Trans. Automatic Control, AC-20, 6, 801-803 (1975)
[6]	Jacobson, D. H., Extensions of Linear-Quadratic Control, Optimization and Matrix Theory, ((1977), Academic Press: Academic Press New York), 217 · Zbl 0331.49026
[7]	Jacobson, D. H.; Martin, D. H.; Pachter, M.; Geveci, T., Extensions of Linear-Quadratic Control Theory, ((1980), Springer-Verlag: Springer-Verlag Berlin), 288 · Zbl 0435.93001
[8]	Wasimi, S. A.; Kitanidis, P. K., Real-time forecasting and daily operation of a multireservoir system during floods by linear quadratic Gaussian control, Water Resources Res., 19, 6, 1511-1522 (1983)
[9]	Loaiciga, H. A.; Marino, M. A., An approach to parameter estimation and stochastic control in water resources with an application to reservoir operation, Water Resources Res., 21, 11, 1575-1584 (1985)
[10]	Georgakakos, A. P.; Marks, D. H., A new method for the real-time operation of reservoir systems, Water Resources Res., 23, 7, 1376-1390 (1987)
[11]	Georgakakos, A. P., Extended linear quadratic Gaussian control: Further extensions, Water Resources Res., 25, 2, 191-201 (1989)
[12]	McLaughlin, D.; Velasco, H. L., Real-time control of a system of large hydropower reservoirs, Water Resources Res., 26, 4, 623-635 (1990)
[13]	Kirk, D. E., Optimal Control Theory: An Introduction, ((1970), PrenticeHall: PrenticeHall Englewood Cliffs, NJ), 53-95
[14]	Athans, M., The discrete time linear-quadratic-Gaussian stochastic control problem, Ann. Econ. Soc. Meas., 1, 4, 449-491 (1972)
[15]	Bertsekas, D. P., Dynamic Programming: Deterministic and Stochastic Models, ((1987), PrenticeHall: PrenticeHall Englewood Cliffs, NJ), 55-64
[16]	Athans, M., The role and use of the stochastic linear-quadratic-Gaussian problem in control system design, IEEE Trans. Automatic Control, AC-16, 6, 529-552 (1971)
[17]	Georgakakos, A. P., Operational trade-offs in reservoir control, Water Resources Res., 29, 11, 3801-3819 (1993)
[18]	US Army Corps of Engineers, Southwestern Division, Tulsa District, Restudy of Tenkiller Ferry Lake Illinois River, Oklahoma, Draft Survey Report and Environmental Impact Statement (1982)