Power Flow as an Algebraic System

Understand

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.