将AC功率流嵌入复平面 第一部分：建模与数学基础
Embedding AC Power Flow in the Complex Plane Part I: Modelling and Mathematical Foundation
AI总结：
本文第一部分将AC功率流问题与电压控制及指数负载模型嵌入复平面，提出两种电压控制建模方法，利用解析延拓理论解决传统数值方法难题，探讨Pade近似在复函数解析延拓中的作用及电压崩溃的判据。
摘要：
本文第一部分将AC功率流问题与电压控制及指数负载模型嵌入复平面。在复平面中建模网络控制器调节电压相量幅度的行为是一项挑战，因为必须保持全纯性的框架以获得具有固定幅度的复变量。本文提出了两种不同的发电机节点电压控制建模方法。指数（或电压依赖）负载模型对于在应力条件下进行准确的功率流研究至关重要。该新的功率流研究框架利用了解析延拓理论，特别是单值定理，以解决困扰传统数值方法数十年的问题。这里关注Pade近似在复函数解析延拓中的不可或缺作用，这些复函数以幂级数形式表达，并超越级数收敛边界。这些有理近似的零极点分布作为电压崩溃的判据。最后解释了该框架的数学基础，即Stahl理论以及Pade近似的收敛速度。
英文摘要：
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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