  This paper presents an algorithm that solves the AC power flow problem for
balanced, three-phase transmission systems at steady state. The algorithm
extends the "fixed-point power flow" algorithm in the literature to include
transmission losses, phase-shifting transformers, and a distributed slack bus
model. The algorithm is derived by vectorizing the component-wise AC power flow
equations and manipulating them into a novel equivalent fixed-point form.
Preliminary theoretical results guaranteeing convergence are reported for the
case of a two-bus power system. We validate the algorithm through extensive
simulations on test systems of various sizes under different loading levels,
and compare its convergence behavior against those of classic power flow
algorithms.
