2015/03/28 by Sina Sadeghi Baghsorkhi, Baghsorkhi, Sina S., Sergey Pavlovich Suetin +1
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Complex Variables (math.CV) #Electromagnetic Scattering and Analysis #FOS: Electrical engineering #FOS: Mathematics #Lightning and Electromagnetic Phenomena #Numerical Analysis (math.NA) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1504.03249
openalex publication_date 2015/03/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
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 Padé 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.