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A Nonlinear Network Flow Algorithm for Maximization of Benefits in a Hydroelectric Power System

Author

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  • Richard E. Rosenthal

    (The University of Tennessee, Knoxville, Tennessee)

Abstract

A nonlinear network flow algorithm for maximization of benefits in a multireservoir hydroelectric power system is presented. The problem was posed by Tennessee Valley Authority (TVA) as an optimization model with a nonseparable nonlinear objective function and with linear network flow constraints. The proposed algorithm is based on reduced gradient methodology (with somewhat nonstandard modifications) and on primal linear network flows (with simplifications resulting from the special structure of the problem network). An unusual feature of the algorithm is an integer programming subproblem whose exact solution determines the superbasic set and the search directions. The algorithm is coded by means of an efficient basis-tree labeling system which consists of a single node-length array and which is specifically designed for the physical context of the problem. Test problems on a 6-reservoir TVA subsystem were solved with computer costs well within the “affordable” range.

Suggested Citation

  • Richard E. Rosenthal, 1981. "A Nonlinear Network Flow Algorithm for Maximization of Benefits in a Hydroelectric Power System," Operations Research, INFORMS, vol. 29(4), pages 763-786, August.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:4:p:763-786
    DOI: 10.1287/opre.29.4.763
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    Citations

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    Cited by:

    1. Antoine Gautier & Frieda Granot, 1996. "Ripples, complements, and substitutes in generalized networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(1), pages 1-21, February.
    2. Mehrdad Taghian & Iman Ahmadianfar, 2018. "Maximizing the Firm Energy Yield Preserving Total Energy Generation Via an Optimal Reservoir Operation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(1), pages 141-154, January.
    3. Habib Akbari-Alashti & Omid Bozorg Haddad & Miguel Mariño, 2015. "Application of Fixed Length Gene Genetic Programming (FLGGP) in Hydropower Reservoir Operation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(9), pages 3357-3370, July.
    4. Philpott, A. B. & Craddock, M. & Waterer, H., 2000. "Hydro-electric unit commitment subject to uncertain demand," European Journal of Operational Research, Elsevier, vol. 125(2), pages 410-424, September.
    5. Frederic H. Murphy & Zhong Xian Wang, 1993. "A network reformulation of an electric utility expansion planning model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(4), pages 451-457, June.
    6. Anibal Azevedo & Aurelio Oliveira & Secundino Soares, 2009. "Interior point method for long-term generation scheduling of large-scale hydrothermal systems," Annals of Operations Research, Springer, vol. 169(1), pages 55-80, July.

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