Limitations of Deterministic Optimization Applied to Reservoir Operations
Publication: Journal of Water Resources Planning and Management
Volume 125, Issue 3
Abstract
Deterministic optimization can produce suboptimal reservoir-control policies by failing to incorporate adequately the impact of low-probability events. Resulting operating policies may not efficiently balance the costs of rationing, minor flooding, or other short-term impacts with the severe impacts of extreme flood or drought. This occurs when deterministic optimization is applied to systems that are not “certainty equivalent.” This paper demonstrates this by contrasting control policies developed using deterministic optimization of inflow forecasts with control policies using stochastic optimization of probabilistic inflows. For a range of hypothetical reservoir-control problems, it is observed that deterministic optimization results in costs that are greater on average and that are much greater for extreme events, particularly for reservoir systems with limited storage capacity and for objectives described by nonquadratic functions. This is true even when forecasts are relatively accurate, such as when streamflows are highly autocorrelated.
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References
1.
Bar-Shalom, Y. ( 1981). “Stochastic dynamic programming: Caution and probing.” IEEE Trans. on Automatic Control, AC-26(5), 1184–1195.
2.
Bar-Shalom, Y., and Tse, E. ( 1976). “Concepts and methods in stochastic control.” Control and dynamic systems, C. T. Leondes, ed., Academic, New York, 99–172.
3.
Bellman, R. E., and Dreyfus, S. E. ( 1962). Applied dynamic programming. Princeton University Press, Princeton, N.J.
4.
Bhaskar, N. R., and Whitlatch, E. E., Jr. ( 1980). “Derivation of monthly reservoir release policies.” Water Resour. Res., 16(6), 987–993.
5.
Bhaskar, N. R., and Whitlatch, E. E. ( 1987). “Comparison of reservoir linear operation rules using linear and dynamic programming.” Water Resour. Bull., 23(6), 1027–1036.
6.
Bryson, A., and Ho, Y. ( 1975). Applied optimal control. Ginn/Braisdell Press, Waltham, Mass.
7.
“Central Valley project operations criteria and plans (CVP-OCAP).” (1992). U.S. Department of the Interior, Bureau of Reclamation, Mid-Pacific Region, Sacramento, Calif.
8.
Chow, V. T., Maidment, D. R., and Tauxe, G. W. ( 1975). “Computer time and memory requirements for DP and DDDP in water resource systems analysis.” Water Resour. Res., 11(5), 621–628.
9.
Dandy, G. ( 1992). “Assessing the economic cost of restrictions on outdoor water use.” Water Resour. Res., 28(7), 1759–1766.
10.
Fiering, M. B., and Jackson, B. B. ( 1971). “Synthetic streamflows.” Water Resour. Monograph 1, American Geophysical Union, Washington, D.C.
11.
Foufoula-Georgiou, E., and Kitanidis, P. K. ( 1988). “Gradient dynamic programming for stochastic optimal control of multidimensional water resources systems.” Water Resour. Res., 24(8), 1345–1359.
12.
Georgakakos, A. P. ( 1989a). “Extended linear quadratic Gaussian control for the real time operation of reservoir systems.” Dynamic programming for optimal water resources systems analysis, A. O. Esogbue, ed., Prentice-Hall, Englewood Cliffs, N.J., 329–360.
13.
Georgakakos, A. P. ( 1989b). “Extended linear quadratic Gaussian control: Further extensions.” Water Resour. Res., 25(2), 191–201.
14.
Georgakakos, A. P., and Marks, D. H. ( 1987). “New method for the real-time operation of reservoir systems.” Water Resour. Res., 23(7), 1376–1390.
15.
Gill, P. E., Murray, W., Saunders, M. A., and Wright, M. H. ( 1986). “User's guide for NPSOL (version 4.0): A Fortran package for nonlinear programming.” Tech. Rep. No. SOL 86-2, Dept. of Operations Res., Stanford University, Stanford, Calif.
16.
Heidari, M., Te Chow, V. E. N., 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.
17.
Jain, S. K., Goel, M. K., and Agarwal, P. K. (1998). “Reservoir operation studies of Sabarmati system, India.”J. Water Resour Plng. and Mgmt., ASCE, 124(1), 31–38.
18.
Johnson, S. A., Stedinger, J. R., Shoemaker, C. A., Li, Y., and Tejada-Guibert, J. A. ( 1993). “Numerical solution of continuous-state dynamic programs using linear and spline interpolation.” Operations Res., 41(3), 484–500.
19.
Karamouz, M., and Vasiliadis, H. V. ( 1992). “Bayesian stochastic optimization of reservoir operation using uncertain forecasts.” Water Resour. Res., 28(5), 1221–1232.
20.
Kelman, J., Stedinger, J. R., Cooper, L. A., Hsu, E., and Yuan, S. Q. ( 1990). “Sampling stochastic dynamic programming applied to reservoir operation.” Water Resour. Res., 26(3), 447–454.
21.
Kitanidis, P. K. ( 1983). “Real-time forecasting of river flows and stochastic optimal control of multireservoir systems.” IIHR Report No. 258, ISWRRI Completion Rep. No. 133, Iowa Inst. of Hydr. Res., University of Iowa, Iowa City, Iowa.
22.
Kitanidis, P. K. ( 1987). “A first-order approximation to stochastic optimal control of reservoirs.” Stochastic Hydro. and Hydr., 1(3), 169–184.
23.
Kitanidis, P. K., and Andricevic, R. ( 1989). “Accuracy of the first-order approximation to the stochastic optimal control of reservoirs.” Dynamic programming for optimal water resources systems analysis, A. O. Esogbue, ed., Prentice-Hall, Englewood Cliffs, N.J., 373–385.
24.
Kitanidis, P. K., and Foufoula-Georgiou, E. ( 1987). “Error analysis of conventional discrete and gradient dynamic programming.” Water Resour. Res., 23(5), 845–858.
25.
Lamond, B. F., and Boukhtouta, A. ( 1995). “Optimizing future hydro-power production using Markov decision processes.” Document of Work 95-44, Laval University, Quebec.
26.
Larson, R. E. ( 1968). State increment dynamic programming. Elsevier Science, New York.
27.
Marino, M. A., and Loaiciga, H. A. ( 1985a). “Dynamic model for multireservoir operation.” Water Resour. Res., 21(5), 619–630.
28.
Marino, M. A., and Loaiciga, H. A. ( 1985b). “Quadratic model for reservoir management: Application to the Central Valley project.” Water Resour. Res., 21(5), 631–641.
29.
Marino, M. A., and Mahammadi, B. ( 1983). “Reservoir management: A reliability programming approach.” Water Resour. Res., 19(3), 613–620.
30.
Marino, M. A., and Simonovic, S. P. ( 1981). “Single multipurpose reservoir design: A modified optimal control problem by chance-constrained programming.” Advances in Water Resour., 4(1), 43–48.
31.
Martin, W. E., and Thomas, J. F. ( 1986). “Policy relevance in studies of urban residential water demand.” Water Resour. Res., 22(13), 1735–1741.
32.
Mercer, L. J., and Morgan, W. D. ( 1989). “Welfare effects of alternative water rationing schemes: A case study.” Water Resour. Bull., 25(1), 203–210.
33.
Murray, D., and Yakowitz, S. ( 1979). “Constrained differential dynamic programming and its application to multireservoir control.” Water Resour. Res., 15(5), 1017–1027.
34.
Ozden, M. ( 1984). “A binary state DP algorithm for operation problems of multireservoir systems.” Water Resour. Res., 20(1), 9–14.
35.
Pereira, M. V. F., and Pinto, L. M. V. G. ( 1985). “Stochastic optimization of a multireservoir hydroelectric system: A decomposition approach.” Water Resour. Res., 21(6), 779–792.
36.
Pereira, M. V. F., and Pinto, L. M. V. G. ( 1991). “Multi-stage stochastic optimization applied to energy planning.” Math. Programming, 52(2), 359–375.
37.
Philbrick, C. R. ( 1997). “Optimal real-time control of stochastic multipurpose multireservoir systems.” PhD thesis, Stanford University, Stanford, Calif.
38.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. ( 1992). Numerical recipes in FORTRAN: The art of scientific computing. Press Syndicate of the University of Cambridge, Cambridge, England.
39.
Provencher, B., and Burt, O. ( 1994). “Approximating the optimal groundwater pumping policy in a multiaquifer stochastic conjunctive use setting.” Water Resour. Res., 30(3), 833–844.
40.
Raman, H., and Chandramouli, V. (1996). “Deriving a general operating policy for reservoirs using neural network.”J. Water Resour. Plng. and Mgmt., ASCE, 122(5), 342–347.
41.
ReVelle, C., Joeres, E., and Kirby, W. ( 1969). “The linear decision rule in reservoir management and design. I. Development of the stochastic models.” Water Resour. Res., 5(4), 767–777.
42.
Rhenals, A. E., and Bras, R. L. ( 1981). “The irrigation scheduling problem and evapotranspiration uncertainty.” Water Resour. Res., 17(5), 1328–1338.
43.
Saad, M., Bigras, P., Turgeon, A. and Duquette, R. ( 1996). “Fuzzy learning decomposition for the scheduling of hydroelectric power systems.” Water Resour. Res., 32(1), 179–186.
44.
Saad, M., Turgeon, A., and Stedinger, J. R. ( 1992). “Censored-data correlation and principal component dynamic programming.” Water Resour. Res., 28(8), 2135–2140.
45.
Simonovic, S. ( 1979). “Two-step algorithm for design-stage long-term control of a multipurpose reservoir.” Advances in Water Resour., 2(1), 47–49.
46.
Sobel, M. J. ( 1989). “A multi-reservoir model with a myopic optimum.” Dynamic programming for optimal water resources systems analysis, A. O. Esogbue, ed., Prentice-Hall, Englewood Cliffs, N.J., 309–315.
47.
Stengel, R. F. ( 1994). Optimal control and estimation. Dover, New York.
48.
Tejada-Guibert, J. A., Johnson, S. A., and Stedinger, J. R. ( 1995). “The value of hydrologic information in stochastic dynamic programming models of a multireservoir system.” Water Resour. Res., 31(10), 2571–2579.
49.
Trezos, T., and Yeh, W. W. G. ( 1987). “Use of stochastic dynamic programming for reservoir management.” Water Resour. Res., 23(6), 983–996.
50.
U.S. Army Corps of Engineers. ( 1987). “Management of water control systems.” Rep. No. EM 1110-2-3600, Washington, D.C.
51.
U.S. Army Corps of Engineers. ( 1997). “Hydrologic engineering requirements for reservoirs.” Rep. No. EM 1110-2-1420, Washington, D.C.
52.
Wasimi, S. A., and Kitanidis, 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.
53.
Yakowitz, S. ( 1982). “Dynamic programming applications in water resources.” Water Resour. Res., 18(4), 673–696.
Information & Authors
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Published In
Journal of Water Resources Planning and Management
Volume 125 • Issue 3 • May 1999
Pages: 135 - 142
History
Published online: May 1, 1999
Published in print: May 1999
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