A Fixed-Point Algorithm for the AC Power Flow Problem

TL;DR

This paper introduces an extended fixed-point algorithm for solving the AC power flow problem in transmission systems, incorporating losses, transformers, and distributed slack, with proven convergence for simple cases and extensive validation.

Contribution

It extends the fixed-point power flow method to include additional system features and provides convergence guarantees and validation for practical power systems.

Findings

Algorithm successfully solves AC power flow with losses and transformers.

Convergence guarantees are established for simple two-bus systems.

Extensive simulations show competitive convergence behavior.

Abstract

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.