Advertisement

Long-Term Operation of Reservoirs in Series

  • G. S. Christensen
  • S. A. Soliman
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 38)

Abstract

In this chapter we discuss the optimal long-term operation of multireservoir power systems connected in series on a river for maximum total benefits from the system. This chapter begins with the problem formulation, where the problem is posed as a mathematical problem. The second section, Section 3.3.1, is concerned with the applications of dynamic programming with the decomposition approach to solve the problem. For a large-scale power system, the use of full stochastic dynamic programming to solve the problem is computationally infeasible for a system greater than three or four reservoirs. In Section 3.3.2, we develop a method to solve the problem using the minimum norm formulation in the framework of functional analysis optimization technique. We compare, for the same system, the results obtained using dynamic programming with the decomposition approach with those obtained using the minimum norm formulation approach (Refs. 3.7–3.10).

Keywords

Power System Decomposition Approach Water Resource Research Stochastic Dynamic Programming Hydropower System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 3.1.
    Arvanitidies, N. V., and Rosing, J., “Composite Representation of a Multireservoir Hydroelectric Power System,” IEEE Transactions on Power Apparatus and Systems PAS-89(2), 319–326 (1970).CrossRefGoogle Scholar
  2. 3.2.
    Arvanitidies, N. V., and Rosing, J., “Optimal Operation of Multireservoir Systems Using a Composite Representation,” IEEE Transactions on Power Apparatus and Systems PAS-89(2), 327–335 (1970).CrossRefGoogle Scholar
  3. 3.3.
    Duran, H., et al., “Optimal Operation of Multireservoir Systems Using an Aggregation-Decomposition Approach,” IEEE Transactions on Power Apparatus and Systems, PAS-104(8), 2086–2092 (1985).CrossRefGoogle Scholar
  4. 3.4.
    Turgeon, A., “A Decomposition/Projection Method for the Multireservoir Operating Problem,” Paper presented at the Joint National TIMS/ORSA Meeting, Los Angeles, California November, 1978.Google Scholar
  5. 3.5.
    Turgeon, A., “Optimal Operation of Multireservoir Power System with Stochastic Inflows,” Water Resources Research 16(6), 275–283 (1980).CrossRefGoogle Scholar
  6. 3.6.
    Turgeon, A., “A Decomposition Method for the Long-Term Scheduling of Reservoirs in Series,” Water Resources Research 17(6), 1565–1570 (1981).CrossRefGoogle Scholar
  7. 3.7.
    Olcer, S., et al., “Application of Linear and Dynamic Programming to the Optimization of the Production of Hydroelectric Power,” Optimal Control Application and Methods 6, 43–56 (1985).CrossRefGoogle Scholar
  8. 3.8.
    Grygier, J. C., and Stedinger, J. R., “Algorithms for Optimizing Hydropower System Operation,” Water Resources Research 21(1), 1–10 (1985).CrossRefGoogle Scholar
  9. 3.9.
    Halliburton, T. S., and Sirisena, H. R., “Development of a Stochastic Optimization for Multireservoir Scheduling,” IEEE Transactions on Automatic Control AC-29, 82–84 (1984).CrossRefGoogle Scholar
  10. 3.10.
    Marino, M. A., and Loaiciga, H. A., “Quadratic Model for Reservoir Management: Applications to the Central Valley Project,” Water Resources Research 21(5), 631–641 (1985).CrossRefGoogle Scholar
  11. 3.11.
    Sage, A. P., Optimal Systems Control, Prentice-Hall, Englewood Cliffs, New Jersey, 1968.Google Scholar
  12. 3.12.
    El-Hawary, M. A., and Christensen, G. S., Optimal Economic Operation of Electric Power System, Academic Press, New York, 1979.Google Scholar
  13. 3.13.
    Shamaly, A., Christensen, G. S., and El-Hawary, M. A., “A Transformation for Necessary Optimality Conditions for Systems with Polynomial Nonlinearities,” IEEE Transactions on Automatic Control AC-24(6), 983–985 (1979).MathSciNetCrossRefGoogle Scholar
  14. 3.14.
    Shamaly, A., Christensen, G. S., and El-Hawary, M. A., “Optimal Control of Large Turboalternator,” Journal of Optimization Theory and Applications 34(1), 83–97 (1981).MathSciNetMATHCrossRefGoogle Scholar
  15. 3.15.
    Soliman, S. A., and Christensen, G. S., “Discrete Stochastic Optimal Long-Term Scheduling of Series Reservoir,” 14th IASTED International Conference, Vancouver, June 4–6, 1986.Google Scholar
  16. 3.16.
    Soliman, S. A., Christensen, G. S., and Abdel-Halim, M. A., “Optimal Operation of Multireservoir Power System Using Functional Analysis,” Journal of Optimization Theory and Applications 49(3), 449–461 (1986).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • G. S. Christensen
    • 1
  • S. A. Soliman
    • 2
  1. 1.University of AlbertaEdmontonCanada
  2. 2.Ain Shams UniversityCairoEgypt

Personalised recommendations