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A modified Primal–Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

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  • Soler, Edilaine Martins
  • de Sousa, Vanusa Alves
  • da Costa, Geraldo R.M.

Abstract

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal–Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient.

Suggested Citation

  • Soler, Edilaine Martins & de Sousa, Vanusa Alves & da Costa, Geraldo R.M., 2012. "A modified Primal–Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables," European Journal of Operational Research, Elsevier, vol. 222(3), pages 616-622.
    • Handle: RePEc:eee:ejores:v:222:y:2012:i:3:p:616-622
    DOI: 10.1016/j.ejor.2012.05.021
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    References listed on IDEAS

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    1. Poojari, C.A. & Beasley, J.E., 2009. "Improving benders decomposition using a genetic algorithm," European Journal of Operational Research, Elsevier, vol. 199(1), pages 89-97, November.
    2. Rosehart, William & Roman, Codruta & Behjat, Laleh, 2006. "Interior point models for power system stability problems," European Journal of Operational Research, Elsevier, vol. 171(3), pages 1127-1138, June.
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    Cited by:

    1. Alencar, Marina Valença & da Silva, Diego Nunes & Nepomuceno, Leonardo & Martins, André Christóvão Pio & Balbo, Antonio Roberto & Soler, Edilaine Martins, 2024. "Discrete optimal power flow with prohibited zones, multiple-fuel options, and practical operational rules for control devices," Applied Energy, Elsevier, vol. 358(C).
    2. Esmaili, Masoud & Shayanfar, Heidar Ali & Moslemi, Ramin, 2014. "Locating series FACTS devices for multi-objective congestion management improving voltage and transient stability," European Journal of Operational Research, Elsevier, vol. 236(2), pages 763-773.
    3. Pinheiro, Ricardo B.N.M. & Lage, Guilherme G. & da Costa, Geraldo R.M., 2019. "A primal-dual integrated nonlinear rescaling approach applied to the optimal reactive dispatch problem," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1137-1153.
    4. Martins Barros, Rafael & Guimarães Lage, Guilherme & de Andrade Lira Rabêlo, Ricardo, 2022. "Sequencing paths of optimal control adjustments determined by the optimal reactive dispatch via Lagrange multiplier sensitivity analysis," European Journal of Operational Research, Elsevier, vol. 301(1), pages 373-385.

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