Admittance Matrix Concentration Inequalities for Understanding Uncertain Power Networks

Samuel Talkington; Cameron Khanpour; Rahul K. Gupta; Sergio A. Dorado-Rojas; Daniel Turizo; Hyeongon Park; Dmitrii M. Ostrovskii; Daniel K. Molzahn

Admittance Matrix Concentration Inequalities for Understanding Uncertain Power Networks

Samuel Talkington, Cameron Khanpour, Rahul K. Gupta, Sergio A. Dorado-Rojas, Daniel Turizo, Hyeongon Park, Dmitrii M. Ostrovskii, and Daniel K. Molzahn

1st PowerUp Conference (to appear)

September 2026

BibTeX

@inproceedings{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={2026},
      booktitle={Proceedings of the 1st PowerUp Conference},
      eprint={2510.17798},
      archivePrefix={arXiv},
      primaryClass={eess.SY},
      url={https://arxiv.org/abs/2510.17798},
}

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.