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Derivation and generation of path-based valid inequalities for transmission expansion planning

Author

Listed:
  • J. Kyle Skolfield

    (Arizona State University)

  • Laura M. Escobar

    (São Paulo State University (UNESP))

  • Adolfo R. Escobedo

    (Arizona State University)

Abstract

This paper seeks to solve the long-term transmission expansion planning problem in power systems more effectively by reducing the solution search space and the computational effort. The proposed methodology finds and adds cutting planes based on structural insights about bus angle differences along paths. Two lemmas and a theorem are proposed which formally establish the validity of these cutting planes onto the underlying mathematical formulations. These path-based bus angle difference constraints, which tighten the relaxed feasible region, are used in combination with branch-and-bound to find lower bounds on the optimal investment of the transmission expansion planning problem. This work also creates an algorithm that automates the process of finding and applying the most effective valid inequalities, resulting in significantly reduced testing and computational time. The algorithm is implemented in Python, using Gurobi to add constraints and solve the exact DCOPF-based transmission expansion problem. This paper uses two different-sized systems to illustrate the effectiveness of the proposed framework: the GOC 500-bus system and a modified Polish 2383-bus system.

Suggested Citation

  • J. Kyle Skolfield & Laura M. Escobar & Adolfo R. Escobedo, 2022. "Derivation and generation of path-based valid inequalities for transmission expansion planning," Annals of Operations Research, Springer, vol. 312(2), pages 1031-1049, May.
    • Handle: RePEc:spr:annopr:v:312:y:2022:i:2:d:10.1007_s10479-022-04643-1
    DOI: 10.1007/s10479-022-04643-1
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    References listed on IDEAS

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    1. M. Jenabi & S. Fatemi Ghomi & S. Torabi & S. Hosseinian, 2015. "Acceleration strategies of Benders decomposition for the security constraints power system expansion planning," Annals of Operations Research, Springer, vol. 235(1), pages 337-369, December.
    2. Burak Kocuk & Hyemin Jeon & Santanu S. Dey & Jeff Linderoth & James Luedtke & Xu Andy Sun, 2016. "A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching," Operations Research, INFORMS, vol. 64(4), pages 922-938, August.
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