Steady states of alternating-current (AC) circuits have been studied in considerable detail. In 1982, Baillieul and Byrnes derived an upper bound on the number of steady states in a loss-less AC circuit [IEEE TCAS, 29(11): 724--737] and conjectured that this bound holds for AC circuits in general. We prove this is indeed the case, among other results, by studying a certain multi-homogeneous structure in an algebraisation.
@article{arxiv.1412.8054,
title = {Power Flow as an Algebraic System},
author = {Jakub Marecek and Timothy McCoy and Martin Mevissen},
journal= {arXiv preprint arXiv:1412.8054},
year = {2016}
}