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.

Error Bounds for Radial Network Topology Learning from Quantized Measurements
 Samuel Talkington, Aditya Rangarajan, Pedro A. de Alcântara, Line Roald, Daniel K. Molzahn, and Daniel R. Fuhrmann
 IEEE Transactions on Power Systems (to appear) / arXiv / bibTeX
Efficient Network Reconfiguration by Randomized Switching
 Samuel Talkington, Dmitrii M. Ostrovskii, and Daniel K. Molzahn
 arXiv / code / bibTeX
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
 arXiv / bibTeX
Differentiating Through Power Flow Solutions for Admittance and Topology Control
 Samuel Talkington, Daniel Turizo, Sergio A. Dorado-Rojas, Rahul K. Gupta, and Daniel K. Molzahn
 arXiv / bibTeX
Strategic Electric Distribution Network Sensing via Spectral Bandits
 Samuel Talkington, Rahul Gupta, Richard Asiamah, Paprapee Buason, and Daniel K. Molzahn
 63rd IEEE Conference on Decision and Control (CDC) / arXiv / slides / bibTeX
Localized Structure in Secondary Distribution System Voltage Sensitivity Matrices
 Samuel Talkington, Santiago Grijalva, Matthew J. Reno, Joseph A. Azzolini, and Jouni Peppanen
 Electric Power Systems Research / bibTeX
Phase Retrieval via Model-Free Power Flow Jacobian Recovery
 Samuel Talkington, Santiago Grijalva
 14th ACM International Conference on Future Energy Systems (e-Energy) / arXiv / code / slides / bibTeX
Conditions for Estimation of Sensitivities of Voltage Magnitudes to Complex Power Injections
 Samuel Talkington, Daniel Turizo, Santiago Grijalva, Jorge Fernandez, Daniel K. Molzahn
 IEEE Transactions on Power Systems / arXiv / code / bibTeX
Sparse Time Series Sampling for Recovery of Behind-the-Meter Inverter Control Models
 Samuel Talkington, Santiago Grijalva, and Matthew J. Reno
 IEEE PES Innovative Smart Grid Technologies Conference (ISGT) / bibTeX