Power Flow as an Algebraic System

Abstract

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.

References in corpus (1)

• On the Network Topology Dependent Solution Count of the Algebraic Load Flow Equations

Cited by in corpus (4)

• Unmixing the mixed volume computation
• Investigating the Maximum Number of Real Solutions to the Power Flow Equations: Analysis of Lossless Four-Bus Systems
• Locating Power Flow Solution Space Boundaries: A Numerical Polynomial Homotopy Approach
• Three Formulations of the Kuramoto Model as a System of Polynomial Equations