Admittance Matrix Concentration Inequalities for Understanding Uncertain Power Networks

BibTeX

@misc{talkington_concentration_2025,
      title={{Admittance Matrix Concentration Inequalities for Understanding Uncertain Power Networks}}, 
      author={Samuel Talkington and Cameron Khanpour and Rahul K. Gupta and Sergio A. Dorado-Rojas and Daniel Turizo and Hyeongon Park and Dmitrii M. Ostrovskii and Daniel K. Molzahn},
      year={2025},
      eprint={2510.17798},
      archivePrefix={arXiv},
      primaryClass={eess.SY},
      url={https://arxiv.org/abs/2510.17798}, 
}

Abstract

This paper presents probabilistic bounds for the spectrum of the admittance matrix and classical linear power flow models under uncertain network parameters; for example, probabilistic line contingencies. Our proposed approach imports tools from probability theory, such as concentration inequalities for random matrices with independent entries. It yields error bounds for common approximations of the AC power flow equations under parameter uncertainty, including the DC and LinDistFlow approximations.

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