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Sequencing paths of optimal control adjustments determined by the optimal reactive dispatch via Lagrange multiplier sensitivity analysis

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  • Martins Barros, Rafael
  • Guimarães Lage, Guilherme
  • de Andrade Lira Rabêlo, Ricardo

Abstract

Optimal power flows play a key role in power system operation planning. While most papers in the literature focus on attaining optima, sequencing paths of optimal control adjustments that lead the system from an initial operating point towards the optimum remain scarcely accounted for. Thus, this work proposes a practical framework based upon power system steady-state analysis for sequencing strictly feasible paths of optimal control adjustments determined by the Optimal Reactive Dispatch (ORD) via Lagrange multiplier sensitivity analysis. The proposed framework is methodologically founded on the reformulation of the ORD in terms of optimal control adjustments rather than optimal control values, successive Newton’s power flow calculations to assure a strictly feasible path from the initial operating point towards the optimum, and successive resolutions of the reformulated ORD’s associated dual problem to determine Lagrange multipliers along such sequence path. Thus, pondering optimal control adjustments by their respective Lagrange multipliers indicates which control action must be realised. Numerical results for IEEE test-systems with up to 300 buses with an increased number of controllable variables are obtained to validate and illustrate the efficiency and robustness of the proposed framework.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:301:y:2022:i:1:p:373-385
    DOI: 10.1016/j.ejor.2021.11.001
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    References listed on IDEAS

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    1. Zohrizadeh, Fariba & Josz, Cedric & Jin, Ming & Madani, Ramtin & Lavaei, Javad & Sojoudi, Somayeh, 2020. "A survey on conic relaxations of optimal power flow problem," European Journal of Operational Research, Elsevier, vol. 287(2), pages 391-409.
    2. Krebs, Vanessa & Schewe, Lars & Schmidt, Martin, 2018. "Uniqueness and multiplicity of market equilibria on DC power flow networks," European Journal of Operational Research, Elsevier, vol. 271(1), pages 165-178.
    3. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, December.
    4. 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.
    5. 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.
    6. Chen, J.J. & Wu, Q.H. & Zhang, L.L. & Wu, P.Z., 2017. "Multi-objective mean–variance–skewness model for nonconvex and stochastic optimal power flow considering wind power and load uncertainties," European Journal of Operational Research, Elsevier, vol. 263(2), pages 719-732.
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