IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v301y2022i1p373-385.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221721009310
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2021.11.001?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. 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, September.
    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.
    Full references (including those not matched with items on IDEAS)

    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. Skolfield, J. Kyle & Escobedo, Adolfo R., 2022. "Operations research in optimal power flow: A guide to recent and emerging methodologies and applications," European Journal of Operational Research, Elsevier, vol. 300(2), pages 387-404.
    2. Aigner, Kevin-Martin & Clarner, Jan-Patrick & Liers, Frauke & Martin, Alexander, 2022. "Robust approximation of chance constrained DC optimal power flow under decision-dependent uncertainty," European Journal of Operational Research, Elsevier, vol. 301(1), pages 318-333.
    3. Shahmohammadi, Ali & Sioshansi, Ramteen & Conejo, Antonio J. & Afsharnia, Saeed, 2018. "Market equilibria and interactions between strategic generation, wind, and storage," Applied Energy, Elsevier, vol. 220(C), pages 876-892.
    4. Alp Atakan & Mehmet Ekmekci & Ludovic Renou, 2021. "Cross-verification and Persuasive Cheap Talk," Papers 2102.13562, arXiv.org, revised Apr 2021.
    5. Arthur Medeiros & Thales Ramos & José Tavares de Oliveira & Manoel F. Medeiros Júnior, 2020. "Direct Voltage Control of a Doubly Fed Induction Generator by Means of Optimal Strategy," Energies, MDPI, vol. 13(3), pages 1-28, February.
    6. Ivorra, Benjamin & Mohammadi, Bijan & Manuel Ramos, Angel, 2015. "A multi-layer line search method to improve the initialization of optimization algorithms," European Journal of Operational Research, Elsevier, vol. 247(3), pages 711-720.
    7. Tanaka, Ken'ichiro & Toda, Alexis Akira, 2015. "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis," University of California at San Diego, Economics Working Paper Series qt7g23r5kh, Department of Economics, UC San Diego.
    8. Ashrafi, M. & Khanjani, M.J. & Fadaei-Kermani, E. & Barani, G.A., 2015. "Farm drainage channel network optimization by improved modified minimal spanning tree," Agricultural Water Management, Elsevier, vol. 161(C), pages 1-8.
    9. Sergey Badikov & Antoine Jacquier & Daphne Qing Liu & Patrick Roome, 2016. "No-arbitrage bounds for the forward smile given marginals," Papers 1603.06389, arXiv.org, revised Oct 2016.
    10. Szidarovszky, Ferenc & Luo, Yi, 2014. "Incorporating risk seeking attitude into defense strategy," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 104-109.
    11. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.
    12. Morshed, Mohammad Javad & Hmida, Jalel Ben & Fekih, Afef, 2018. "A probabilistic multi-objective approach for power flow optimization in hybrid wind-PV-PEV systems," Applied Energy, Elsevier, vol. 211(C), pages 1136-1149.
    13. Martin Bichler & Johannes Knörr & Felipe Maldonado, 2023. "Pricing in Nonconvex Markets: How to Price Electricity in the Presence of Demand Response," Information Systems Research, INFORMS, vol. 34(2), pages 652-675, June.
    14. Csaba I. Fábián, 2021. "Gaining traction: on the convergence of an inner approximation scheme for probability maximization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 491-519, June.
    15. Bouslah, B. & Gharbi, A. & Pellerin, R., 2016. "Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint," Omega, Elsevier, vol. 61(C), pages 110-126.
    16. Rafał Wiśniowski & Krzysztof Skrzypaszek & Tomasz Małachowski, 2020. "Selection of a Suitable Rheological Model for Drilling Fluid Using Applied Numerical Methods," Energies, MDPI, vol. 13(12), pages 1-17, June.
    17. Egerer, Jonas & Grimm, Veronika & Grübel, Julia & Zöttl, Gregor, 2022. "Long-run market equilibria in coupled energy sectors: A study of uniqueness," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1335-1354.
    18. Yuichi Takano & Renata Sotirov, 2012. "A polynomial optimization approach to constant rebalanced portfolio selection," Computational Optimization and Applications, Springer, vol. 52(3), pages 645-666, July.
    19. Enrique I. Acuña & Ian S. Lowndes, 2014. "A Review of Primary Mine Ventilation System Optimization," Interfaces, INFORMS, vol. 44(2), pages 163-175, April.
    20. Nadia Demarteau & Thomas Breuer & Baudouin Standaert, 2012. "Selecting a Mix of Prevention Strategies against Cervical Cancer for Maximum Efficiency with an Optimization Program," PharmacoEconomics, Springer, vol. 30(4), pages 337-353, April.

    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:eee:ejores:v:301:y:2022:i:1:p:373-385. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.