# A Holomorphic Embedding Based Continuation Method for Identifying Multiple Power Flow Solutions

## TL;DR

This paper introduces a novel holomorphic embedding continuation method that efficiently finds multiple power flow solutions by combining large step sizes with strategic switching around singularities, validated on IEEE test cases.

## Contribution

The paper presents a new holomorphic embedding-based continuation method that improves efficiency in locating multiple power flow solutions by integrating large step sizes and singularity handling.

## Key findings

- Method reduces computational steps compared to traditional routines.
- Effective in traversing non-singular and singular solution curve segments.
- Validated on standard IEEE test cases with favorable results.

## Abstract

In this paper, we propose an efficient continuation method for locating multiple power flow solutions. We adopt the holomorphic embedding technique to represent solution curves as holomorphic functions in the complex plane. The holomorphicity, which provides global information of the curve at any regular point, enables large step sizes in the path-following procedure such that non-singular curve segments can be traversed with very few steps. When approaching singular points, we switch to the traditional predictor-corrector routine to pass through them and switch back afterward to the holomorphic embedding routine. We also propose a warm starter when switching to the predictor-corrector routine, i.e. a large initial step size based on the poles of the Pad\'{e} approximation of the derived holomorphic function, since these poles reveal the locations of singularities on the curve. Numerical analysis and experiments on many standard IEEE test cases are presented, along with the comparison to the full predictor-corrector routine, confirming the efficiency of the method.