Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedding AC Power Flow in the Complex Plane Part I: Modelling and
  Mathematical Foundation   Part I of this paper embeds the AC power flow problem with voltage control
and exponential load model 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. The paper
presents two distinct approaches to modelling the voltage control of generator
nodes. Exponential (or voltage-dependent) load models are crucial for accurate
power flow studies under stressed conditions. This new framework for power flow
studies exploits the theory of analytic continuation, especially the monodromy
theorem for resolving issues that have plagued conventional numerical methods
for decades. Here the focus is on the indispensable role of Pade approximants
for analytic continuation of complex functions, expressed as power series,
beyond the boundary of convergence of the series. The zero-pole distribution of
these rational approximants serves as a proximity index to voltage collapse.
Finally the mathematical underpinnings of this framework, namely the Stahl's
theory and the rate of convergence of Pade approximants are explained.

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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex