# Robust Power Flow and Three-Phase Power Flow Analyses

arXiv: https://arxiv.org/abs/1803.01211 · HTML: https://mlsanity.com/paper/1803.01211/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2018.

## Built on by (most cited first, 3 of 3)

- [Adversarially Robust Learning for Security-Constrained Optimal Power Flow](https://mlsanity.com/paper/2111.06961/) (2021)
- [PowerChain: A Verifiable Agentic AI System for Automating Distribution Grid Analyses](https://mlsanity.com/paper/2508.17094/) (2025)
- [Towards Practical Physics-Informed ML Design and Evaluation for Power Grid](https://mlsanity.com/paper/2205.03673/) (2022)

## Abstract (arXiv)

Robust simulation is essential for reliable operation and planning of transmission and distribution power grids. At present, disparate methods exist for steady-state analysis of the transmission (power flow) and distribution power grid (three-phase power flow). Due to the non-linear nature of the problem, it is difficult for alternating current (AC) power flow and three-phase power flow analyses to ensure convergence to the correct physical solution, particularly from arbitrary initial conditions, or when evaluating a change (e.g. contingency) in the grid. In this paper, we describe our equivalent circuit formulation approach with current and voltage variables that models both the positive sequence network of the transmission grid and three-phase network of the distribution grid without loss of generality. The proposed circuit models and formalism enable the extension and application of circuit simulation techniques to solve for the steady-state solution with excellent robustness of convergence. Examples for positive sequence transmission and three-phase distribution systems, including actual 75k+ nodes Eastern Interconnection transmission test cases and 8k+ nodes taxonomy distribution test cases, are solved from arbitrary initial guesses to demonstrate the efficacy of our approach.