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Decomposable Formulation of Transmission Constraints for Decentralized Power Systems Optimization

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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