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A primal-dual integrated nonlinear rescaling approach applied to the optimal reactive dispatch problem

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  • Pinheiro, Ricardo B.N.M.
  • Lage, Guilherme G.
  • da Costa, Geraldo R.M.

Abstract

The objective of this paper is to propose a novel augmented Lagrangian approach for solving the Optimal Reactive Dispatch (ORD) problem in electric power systems, which consists in a large nonconvex Nonlinear Programming (NLP) problem. Given an NLP problem, its associated dual problem is solved by a proximal point method, whose distance between two points is calculated by means of a convex combination involving Bregman’s distance and Csiszar’s entropic φ-divergence distance pondered by a weighting factor, namely Integrated Distance Measure (IDM). Such dual proximal point method with the IDM leads to an equivalent augmented Lagrangian method with a new family of nonquadratic penalty functions for the primal problem, namely Integrated Nonlinear Rescaling (INLR) method. The concepts of integrated logarithmic modified barrier and integrated exponential functions, which are elements of the new family of penalty functions, are defined. A Primal-Dual Integrated Nonlinear Rescaling (PDINLR) method is proposed to solve convex and nonconvex NLPs. A small convex NLP problem is used to depict how such algorithm attains optima, and a small nonconvex NLP problem is used to show how the proposed approach outperforms other known methods in the area when a suitable value for the weighting factor is chosen. The effectiveness, efficiency and the robustness of the proposed PDINLR method with the integrated logarithmic modified barrier function are shown by the resolution of the ORD problem for the IEEE 30 and 300-bus test-systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:276:y:2019:i:3:p:1137-1153
    DOI: 10.1016/j.ejor.2019.01.060
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    References listed on IDEAS

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    1. Gouveia, Eduardo M. & Matos, Manuel A., 2009. "Symmetric AC fuzzy power flow model," European Journal of Operational Research, Elsevier, vol. 197(3), pages 1012-1018, September.
    2. R. Polyak & I. Griva, 2004. "Primal-Dual Nonlinear Rescaling Method for Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 111-156, July.
    3. Alfredo N. Iusem & B. F. Svaiter & Marc Teboulle, 1994. "Entropy-Like Proximal Methods in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 790-814, November.
    4. Shargh, S. & Khorshid ghazani, B. & Mohammadi-ivatloo, B. & Seyedi, H. & Abapour, M., 2016. "Probabilistic multi-objective optimal power flow considering correlated wind power and load uncertainties," Renewable Energy, Elsevier, vol. 94(C), pages 10-21.
    5. 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.
    6. Marc Teboulle, 1992. "Entropic Proximal Mappings with Applications to Nonlinear Programming," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 670-690, August.
    7. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
    8. Schulze, Tim & Grothey, Andreas & McKinnon, Ken, 2017. "A stabilised scenario decomposition algorithm applied to stochastic unit commitment problems," European Journal of Operational Research, Elsevier, vol. 261(1), pages 247-259.
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    Cited by:

    1. 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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