In this paper, we quantify voltage and current phasor-based measurement requirements for the unique estimation of the electric grid topology and admittance parameters. Our approach is underpinned by the concept of a rigidity matrix that has been extensively studied in graph rigidity theory. Specifically, we show that the rank of the rigidity matrix is the same as that of a voltage coefficient matrix in a corresponding electric power system. Accordingly, we show that there is a minimum number of measurements required to uniquely estimate the admittance matrix and corresponding grid topology. By means of a numerical example on the IEEE 4-node radial network, we demonstrate that our approach is suitable for applications in electric power grids.
@article{arxiv.2410.17553,
title = {Electric Grid Topology and Admittance Estimation: Quantifying Phasor-based Measurement Requirements},
author = {Norak Rin and Iman Shames and Ian R. Petersen and Elizabeth L. Ratnam},
journal= {arXiv preprint arXiv:2410.17553},
year = {2025}
}