IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v165y2015i3d10.1007_s10957-014-0610-y.html
   My bibliography  Save this article

Local Minima of Quadratic Functionals and Control of Hydro-electric Power Stations

Author

Listed:
  • M. M. A. Ferreira

    (FEUP, ISR, University of Porto)

  • A. F. Ribeiro

    (University of Porto)

  • G. V. Smirnov

    (University of Minho)

Abstract

We consider a control problem for a cascade of hydro-electric power stations, where some of the stations have reversible turbines. Our aim was to optimize the profit of power production satisfying restrictions on the water level in the reservoirs. From the mathematical point of view, this consists in minimizing an infinite-dimensional quadratic functional subject to cone constraints. Sufficient conditions of optimality for the abstract problem are derived and are then specialized for our problem. Noteworthy, the restrictions imposed on the power stations problem are in the form of control constraints and pure state constraints. The particular case of one power station is analyzed in detail, showing that reversible turbines always improve the profit.

Suggested Citation

  • M. M. A. Ferreira & A. F. Ribeiro & G. V. Smirnov, 2015. "Local Minima of Quadratic Functionals and Control of Hydro-electric Power Stations," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 985-1005, June.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:3:d:10.1007_s10957-014-0610-y
    DOI: 10.1007/s10957-014-0610-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-014-0610-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-014-0610-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. K. Malanowski & H. Maurer & S. Pickenhain, 2004. "Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 595-617, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Zizhao & Li, Yang & Wu, Feng & Wu, Jiawei & Shi, Linjun & Lin, Keman, 2024. "Multi-objective day-ahead scheduling of cascade hydropower-photovoltaic complementary system with pumping installation," Energy, Elsevier, vol. 290(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. M. Gerdts, 2006. "Local Minimum Principle for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 443-462, September.
    2. Gerardo Sánchez Licea, 2021. "Weak Measurable Optimal Controls for the Problems of Bolza," Mathematics, MDPI, vol. 9(2), pages 1-17, January.
    3. Leonardo Mazzini, 2023. "Neighboring Optimal Guidance in Bang Bang Control with Target," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 310-336, October.
    4. Enes Kacapor & Teodor M. Atanackovic & Cemal Dolicanin, 2020. "Optimal Shape and First Integrals for Inverted Compressed Column," Mathematics, MDPI, vol. 8(3), pages 1-14, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:165:y:2015:i:3:d:10.1007_s10957-014-0610-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.