@misc{talkington2025differentiatingpowerflowsolutions,
title={{Differentiating Through Power Flow Solutions for Admittance and Topology Control}},
author={Samuel Talkington and Daniel Turizo and Sergio A. Dorado-Rojas and Rahul K. Gupta and Daniel K. Molzahn},
year={2025},
eprint={2510.17071},
archivePrefix={arXiv},
primaryClass={eess.SY},
url={https://arxiv.org/abs/2510.17071},
}The power flow equations relate bus voltage phasors to power injections via the network admittance matrix. These equations are central to the key operational and protection functions of power systems (e.g., optimal power flow scheduling and control, state estimation, protection, and fault location, among others). As control, optimization, and estimation of network admittance parameters are central to multiple avenues of research in electric power systems, we propose a linearization of power flow solutions obtained by implicitly differentiating them with respect to the network admittance parameters. This is achieved by utilizing the implicit function theorem, in which we show that such a differentiation is guaranteed to exist under mild conditions and is applicable to generic power systems (radial or meshed). The proposed theory is applied to derive sensitivities of complex voltages, line currents, and power flows. The developed theory of linearizing the power flow equations around changes in the complex network admittance parameters has numerous applications. We demonstrate several of these applications, such as predicting the nodal voltages when the network topology changes without solving the power flow equations. We showcase the application for continuous admittance control, which is used to increase the hosting capacity of a given distribution network.
Coauthor Websites:
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
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
arXiv / bibTeX
Strategic Electric Distribution Network Sensing via Spectral Bandits
Samuel Talkington, Rahul Gupta, Richard Asiamah, Paprapee Buason, and Daniel K. Molzahn
IEEE CDC 2024 / arXiv / slides / bibTeX
A data-driven sensor placement approach for detecting voltage violations in distribution systems
Paprapee Buason, Sidhant Misra, Samuel Talkington, and Daniel K. Molzahn
Electric Power Systems Research / arXiv / 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
ACM 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