IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v36y2024i6p1562-1578.html
   My bibliography  Save this article

Decomposable Formulation of Transmission Constraints for Decentralized Power Systems Optimization

Author

Listed:
  • Álinson Santos Xavier

    (Energy Systems and Infrastructure Analysis Division, Argonne National Laboratory, Lemont, Illinois 60439)

  • Santanu Subhas Dey

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Feng Qiu

    (Energy Systems and Infrastructure Analysis Division, Argonne National Laboratory, Lemont, Illinois 60439)

Abstract

One of the most complicating factors in decentralized solution methods for a broad range of power system optimization problems is the modeling of power flow equations. Existing formulations for direct current power flows either have limited scalability or are very dense and unstructured, making them unsuitable for large-scale decentralized studies. In this work, we present a novel sparsified variant of the injection shift factors formulation, which has a decomposable block-diagonal structure and scales well for large systems. We also propose a decentralized solution method, based on the alternating direction multiplier method, that efficiently handles transmission line outages in N-1 security requirements. Benchmarks on multizonal security-constrained unit commitment problems show that the proposed formulation and algorithm can reliably and efficiently solve interconnection-level test systems with up to 6,515 buses with no convergence or numerical issues.

Suggested Citation

  • Álinson Santos Xavier & Santanu Subhas Dey & Feng Qiu, 2024. "Decomposable Formulation of Transmission Constraints for Decentralized Power Systems Optimization," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1562-1578, December.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:6:p:1562-1578
    DOI: 10.1287/ijoc.2022.0326
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2022.0326
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2022.0326?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
    ---><---

    References listed on IDEAS

    as
    1. Matthias Walter, 2014. "Sparsity of Lift-and-Project Cutting Planes," Operations Research Proceedings, in: Stefan Helber & Michael Breitner & Daniel Rösch & Cornelia Schön & Johann-Matthias Graf von der Schu (ed.), Operations Research Proceedings 2012, edition 127, pages 9-14, Springer.
    2. Santanu S. Dey & Marco Molinaro & Qianyi Wang, 2018. "Analysis of Sparse Cutting Planes for Sparse MILPs with Applications to Stochastic MILPs," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 304-332, February.
    3. Robert E. Bixby, 2002. "Solving Real-World Linear Programs: A Decade and More of Progress," Operations Research, INFORMS, vol. 50(1), pages 3-15, February.
    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. Bach, Lukas & Hasle, Geir & Schulz, Christian, 2019. "Adaptive Large Neighborhood Search on the Graphics Processing Unit," European Journal of Operational Research, Elsevier, vol. 275(1), pages 53-66.
    2. Xiaoyi Gu & Santanu S. Dey & Jean-Philippe P. Richard, 2024. "Solving Sparse Separable Bilinear Programs Using Lifted Bilinear Cover Inequalities," INFORMS Journal on Computing, INFORMS, vol. 36(3), pages 884-899, May.
    3. Duque, Daniel & Lozano, Leonardo & Medaglia, Andrés L., 2015. "An exact method for the biobjective shortest path problem for large-scale road networks," European Journal of Operational Research, Elsevier, vol. 242(3), pages 788-797.
    4. Castro, Jordi, 2006. "Minimum-distance controlled perturbation methods for large-scale tabular data protection," European Journal of Operational Research, Elsevier, vol. 171(1), pages 39-52, May.
    5. Defeng Liu & Andrea Lodi & Mathieu Tanneau, 2021. "Learning chordal extensions," Journal of Global Optimization, Springer, vol. 81(1), pages 3-22, September.
    6. Andrey M. Lizyayev, 2009. "Stochastic Dominance: Convexity and Some Efficiency Tests," Tinbergen Institute Discussion Papers 09-112/2, Tinbergen Institute, revised 05 Jan 2010.
    7. Timo Berthold & Jakob Witzig, 2021. "Conflict Analysis for MINLP," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 421-435, May.
    8. Leonardo Lozano & Daniel Duque & Andrés L. Medaglia, 2016. "An Exact Algorithm for the Elementary Shortest Path Problem with Resource Constraints," Transportation Science, INFORMS, vol. 50(1), pages 348-357, February.
    9. Juan Carlos Duque & Raúl Ramos & Jordi Suriñach, 2007. "Supervised Regionalization Methods: A Survey," International Regional Science Review, , vol. 30(3), pages 195-220, July.
    10. Harrod, Steven & Schlechte, Thomas, 2013. "A direct comparison of physical block occupancy versus timed block occupancy in train timetabling formulations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 54(C), pages 50-66.
    11. A Corominas & R Pastor, 2011. "Designing greedy algorithms for the flow-shop problem by means of Empirically Adjusted Greedy Heuristics (EAGH)," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1704-1710, September.
    12. Im, Haesol & Wolkowicz, Henry, 2023. "Revisiting degeneracy, strict feasibility, stability, in linear programming," European Journal of Operational Research, Elsevier, vol. 310(2), pages 495-510.
    13. Ambros M. Gleixner & Timo Berthold & Benjamin Müller & Stefan Weltge, 2017. "Three enhancements for optimization-based bound tightening," Journal of Global Optimization, Springer, vol. 67(4), pages 731-757, April.
    14. Semih Atakan & Suvrajeet Sen, 2018. "A Progressive Hedging based branch-and-bound algorithm for mixed-integer stochastic programs," Computational Management Science, Springer, vol. 15(3), pages 501-540, October.
    15. Jordi Castro, 2007. "A Shortest-Paths Heuristic for Statistical Data Protection in Positive Tables," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 520-533, November.
    16. Daniel Espinoza & Eduardo Moreno, 2014. "A primal-dual aggregation algorithm for minimizing conditional value-at-risk in linear programs," Computational Optimization and Applications, Springer, vol. 59(3), pages 617-638, December.
    17. Parreño-Torres, Consuelo & Alvarez-Valdes, Ramon & Ruiz, Rubén, 2019. "Integer programming models for the pre-marshalling problem," European Journal of Operational Research, Elsevier, vol. 274(1), pages 142-154.
    18. John Alasdair Warwicker & Steffen Rebennack, 2022. "A Comparison of Two Mixed-Integer Linear Programs for Piecewise Linear Function Fitting," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1042-1047, March.
    19. Thorsten Koch & Ted Ralphs & Yuji Shinano, 2012. "Could we use a million cores to solve an integer program?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(1), pages 67-93, August.
    20. Kroon, L.G. & Zuidwijk, R.A., 2003. "Mathematical models for planning support," ERIM Report Series Research in Management ERS-2003-032-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

    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:inm:orijoc:v:36:y:2024:i:6:p:1562-1578. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.