A Fixed-Point Algorithm for the AC Power Flow Problem

John W. Simpson-Porco; Liangjie Chen

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A Fixed-Point Algorithm for the AC Power Flow Problem

Liangjie Chen, John W. Simpson-Porco

Systems and Control · Submitted 4 Oct 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,202 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.72 · human participants 0.01 · controlled comparison 0.72 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.96 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This paper presents an algorithm that solves the AC power flow problem for balanced, three-phase transmission systems at steady state.	contribution 0.98	0.88	0.18	asserted 1.00
s1	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.	contribution 0.98	0.83	0.10	asserted 1.00
s2	The algorithm is derived by vectorizing the component-wise AC power flow equations and manipulating them into a novel equivalent fixed-point form.	method 0.97	0.95	0.07	asserted 1.00
s3	Preliminary theoretical results guaranteeing convergence are reported for the case of a two-bus power system.	result 0.85	0.91	0.09	asserted 0.94
s4	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.	method 0.54	0.96	0.24	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original 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.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites as background 1 paper

In recent years, there have been many fixed-point or contraction-based studies on the power flow problem and its solvability in various contexts (see, e.g., [ref] ).

Solvability of Power Flow Equations Through Existence and Uniqueness of Complex Fixed Point · Introduction · 0.97

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