全纯嵌入负荷流方法的基础
Fundamentals of the Holomorphic Embedding Load-Flow Method
AI总结：
本文基于全纯嵌入负荷流方法的理论基础，通过全纯性保持嵌入将负荷流问题转化为代数曲线研究，并利用幂级数技术进行实际计算，最终通过Stahl定理确保方法的完整性。
摘要：
全纯嵌入负荷流方法（HELM）最近被引入作为一种构造性地求解电力网络中功率流方程的新技术，基于先进的复分析。本文详细建立了该方法的理论基础。从功率流方程的基本射影不变性出发，展示了如何设计保持全纯性的嵌入，最终将功率流问题本质上转化为代数曲线的研究。补充这一代数-几何观点，即该方法的基础，展示了如何应用标准分析技术（幂级数）进行实际计算。Stahl定理关于Padé近似子提供的解析延拓的最大性，则确保了该方法的完整性。另一方面，展示了如何将该方法扩展以适应平滑控制，如普遍存在的发电机控制的PV节点。
英文摘要：
The Holomorphic Embedding Load-Flow Method (HELM) was recently introduced as a novel technique to constructively solve the power-flow equations in power grids, based on advanced complex analysis. In this paper, the theoretical foundations of the method are established in detail. Starting from a fundamental projective invariance of the power-flow equations, it is shown how to devise holomorphicity-preserving embeddings that ultimately allow regarding the power-flow problem as essentially a study in algebraic curves. Complementing this algebraic-geometric viewpoint, which lays the foundation of the method, it is shown how to apply standard analytic techniques (power series) for practical computation. Stahl's theorem on the maximality of the analytic continuation provided by Padé approximants then ensures the completeness of the method. On the other hand, it is shown how to extend the method to accommodate smooth controls, such as the ubiquitous generator-controlled PV bus.
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