Implications of Stahl's Theorems to Holomorphic Embedding Pt 1: Theoretical Convergence
Implications of Stahl's Theorems to Holomorphic Embedding Pt 1: Theoretical Convergence
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斯塔尔定理对全纯嵌入的含义第 1 部分：理论收敛
DOI：
10.17775/cseejpes.2020.01910
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Zhiwei Wang
中科院分区：
文献类型：
--
作者：
Songyan Li;D. Tylavsky;Di Shi;Zhiwei Wang
在电力工程界，斯塔尔定理被用来证明全纯嵌入法(HEM)应用于潮流问题时的收敛保证。在这篇由两部分组成的论文中，我们更详细地研究了斯塔尔定理对于现在应用这些定理的更广泛的问题的理论和数值收敛的含义。在铂。1，我们使用必要的数学表述来介绍该定理，然后翻译该语言以显示其对一般的非线性问题和具体的PF问题的收敛的影响。我们证明了在其他可能性中，嵌入特定的Chebotarev点的存在可能是收敛的理论障碍。文中还讨论了收敛的数值障碍。
What has become known as Stahl's Theorem in power engineering circles has been used to justify a convergence guarantee of the Holormorphic Embedding Method (HEM) as it applies to the power flow (PF) problem. In this two-part paper, we examine in more detail the implications of Stahl's theorems to both theoretcial and numerical convergence for a wider range of problems to which these theorems are now being applied. In Pt. 1, we introduce the theorem using the necessary mathematical parlance and then translate the language to show its implications to convergence of nonlinear problems in general and the PF problem specifically. We show that among other possibilities the existence of the Chebotarev points, which are embedding specific, are a possible theoretical impediment to convergence. Numerical impediments to convergences are discussed in the companion paper.