The power flow equations are at the core of most of the computations for designing and
operating electric grids. This system of multivariate nonlinear equations relate the power …

The solution to an optimal power flow (OPF) problem provides a minimum cost operating
point for an electric power system. The performance of OPF solution techniques strongly …

Active research activity in power systems areas has focused on developing computational
methods to solve load flow equations where a key question is the maximum number of …

The power flow equations, which relate power injections and voltage phasors, are at the
heart of many electric power system computations. While Newton-based methods typically …

Abstract The Holomorphic Embedding Load-Flow Method (HELM) was recently introduced
as a novel technique to constructively solve the power flow equations in power networks …

Computing mixed volume of convex polytopes is an important problem in computational
algebraic geometry. This paper establishes sufficient conditions under which the mixed …

We begin with formulating the station-ary equations of the Kuramoto model as a system of
polynomial equations in a novel way. Then, based on an algebraic geometric root count, we …

The power flow equations model the steady-state relationship between the power injections
and voltage phasors in an electric power system. By separating the real and imaginary …

In this article, we study the monitoring and control of long-term voltage stability considering
load tap changer (LTC) dynamics. We show that under generic conditions, the LTC …

We compare three formulations of stationary equations of the Kuramoto model as systems of
polynomial equations. In the comparison, we present bounds on the numbers of real …