Embedding AC Power Flow with Voltage Control in the Complex Plane : The Case of Analytic Continuation via Pad\'e Approximants

TL;DR

This paper advances the Holomorphic Embedding Load Flow Method by embedding AC power flow with voltage control in the complex plane, utilizing Padé approximants for analytic continuation, and demonstrating improved robustness over traditional methods.

Contribution

It introduces a novel embedding approach for AC power flow with voltage regulation in the complex plane, leveraging Padé approximants for analytic continuation, enhancing solution stability.

Findings

Proposes a new embedding method for AC power flow with voltage control.

Demonstrates the method's superiority over Newton-Raphson and relaxation techniques.

Shows improved convergence and robustness in power flow solutions.

Abstract

This paper proposes a method to embed the AC power flow problem with voltage magnitude constraints in the complex plane. Modeling the action of network controllers that regulate the magnitude of voltage phasors is a challenging task in the complex plane as it has to preserve the framework of holomorphicity for obtention of these complex variables with fixed magnitude. Hence this paper presents a significant step in the development of the idea of Holomorphic Embedding Load Flow Method (HELM), introduced in 2012, that exploits the theory of analytic continuation, especially the monodromy theorem for resolving issues that have plagued conventional numerical methods for decades. This paper also illustrates the indispensable role of Pad\'e approximants for analytic continuation of complex functions, expressed as power series, beyond the boundary of convergence of the series. Later the paper demonstrates the superiority of the proposed method over the well-established Newton-Raphson as well as the recently developed semidefinite and moment relaxation of power flow problems.