Embedding AC Power Flow with Voltage Control in the Complex Plane : The Case of Analytic Continuation via Padé Approximants

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 holo- morphicity for obtention of these complex variables with fix ed magnitude. Hence this paper presents a significant step in th e development of the idea of Holomorphic Embedding Load Flow Method (HELM) (1), introduced in 2012, that exploits the theory of analytic continuation, especially the monodromy theorem (2) for resolving issues that have plagued conventional numerical methods for decades. This paper also illustrates the indispensable role of Padapproximants 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 semidefini te and moment relaxation of power flow problems.