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A Novel Lagrangian Multiplier Update Algorithm for Short-Term Hydro-Thermal Coordination

Author

Listed:
  • P. M. R. Bento

    (IT—Instituto de Telecomunicações, University of Beira Interior, 6201-001 Covilhã, Portugal)

  • S. J. P. S. Mariano

    (IT—Instituto de Telecomunicações, University of Beira Interior, 6201-001 Covilhã, Portugal)

  • M. R. A. Calado

    (IT—Instituto de Telecomunicações, University of Beira Interior, 6201-001 Covilhã, Portugal)

  • L. A. F. M. Ferreira

    (Instituto Superior Técnico and INESC-ID, University of Lisbon, 1049-001 Lisbon, Portugal)

Abstract

The backbone of a conventional electrical power generation system relies on hydro-thermal coordination. Due to its intrinsic complex, large-scale and constrained nature, the feasibility of a direct approach is reduced. With this limitation in mind, decomposition methods, particularly Lagrangian relaxation, constitutes a consolidated choice to “simplify” the problem. Thus, translating a relaxed problem approach indirectly leads to solutions of the primal problem. In turn, the dual problem is solved iteratively, and Lagrange multipliers are updated between each iteration using subgradient methods. However, this class of methods presents a set of sensitive aspects that often require time-consuming tuning tasks or to rely on the dispatchers’ own expertise and experience. Hence, to tackle these shortcomings, a novel Lagrangian multiplier update adaptative algorithm is proposed, with the aim of automatically adjust the step-size used to update Lagrange multipliers, therefore avoiding the need to pre-select a set of parameters. A results comparison is made against two traditionally employed step-size update heuristics, using a real hydrothermal scenario derived from the Portuguese power system. The proposed adaptive algorithm managed to obtain improved performances in terms of the dual problem, thereby reducing the duality gap with the optimal primal problem.

Suggested Citation

  • P. M. R. Bento & S. J. P. S. Mariano & M. R. A. Calado & L. A. F. M. Ferreira, 2020. "A Novel Lagrangian Multiplier Update Algorithm for Short-Term Hydro-Thermal Coordination," Energies, MDPI, vol. 13(24), pages 1-19, December.
  • Handle: RePEc:gam:jeners:v:13:y:2020:i:24:p:6621-:d:462552
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    References listed on IDEAS

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    1. Smarajit Ghosh & Manvir Kaur & Suman Bhullar & Vinod Karar, 2019. "Hybrid ABC-BAT for Solving Short-Term Hydrothermal Scheduling Problems," Energies, MDPI, vol. 12(3), pages 1-15, February.
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    4. Jian, Jinbao & Pan, Shanshan & Yang, Linfeng, 2019. "Solution for short-term hydrothermal scheduling with a logarithmic size mixed-integer linear programming formulation," Energy, Elsevier, vol. 171(C), pages 770-784.
    5. Ping Che & Zhenhao Tang & Hua Gong & Xiaoli Zhao, 2018. "An Improved Lagrangian Relaxation Algorithm for the Robust Generation Self-Scheduling Problem," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-12, July.
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    7. Omid Hoseynpour & Behnam Mohammadi-ivatloo & Morteza Nazari-Heris & Somayeh Asadi, 2017. "Application of Dynamic Non-Linear Programming Technique to Non-Convex Short-Term Hydrothermal Scheduling Problem," Energies, MDPI, vol. 10(9), pages 1-17, September.
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    Cited by:

    1. Ali Ahmad & Syed Abdul Rahman Kashif & Arslan Ashraf & Muhammad Majid Gulzar & Mohammed Alqahtani & Muhammad Khalid, 2023. "Coordinated Economic Operation of Hydrothermal Units with HVDC Link Based on Lagrange Multipliers," Mathematics, MDPI, vol. 11(7), pages 1-19, March.
    2. Carolina Gil Marcelino & Carlos Camacho-Gómez & Silvia Jiménez-Fernández & Sancho Salcedo-Sanz, 2021. "Optimal Generation Scheduling in Hydro-Power Plants with the Coral Reefs Optimization Algorithm," Energies, MDPI, vol. 14(9), pages 1-24, April.

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