通过复固定点的存在性和唯一性解决功率流方程的可解性
Solvability of Power Flow Equations Through Existence and Uniqueness of Complex Fixed Point
AI总结：
本文提出了一种新的分析方法，利用复域中固定点的收缩性质，为功率流方程的解的存在性和唯一性提供了更强的充分条件，并通过大量计算实验验证了其有效性。
摘要：
负荷水平的变化和系统拓扑性质的变化可能导致电力系统运行点逐渐接近其传输能力的边缘，从而导致电压崩溃等灾难性后果。从建模的角度来看，电压崩溃与功率流方程的可解性密切相关。确定功率流方程解的存在性和唯一性条件是电力系统中的一个基本问题，具有重要的理论和实际意义。本文在状态（电压）空间的一个子集内，提供了保证功率流解存在性和唯一性的强充分条件。新的分析方法大量利用了复域中固定点形式的收缩性质，从而得到了比以往主要基于实域分析的条件更严格的分析条件。进行了大量的计算实验，验证了所提出条件的正确性和有效性。
英文摘要：
Variations of loading level and changes in system topological property may cause the operating point of an electric power systems to move gradually towards the verge of its transmission capability, which can lead to catastrophic outcomes such as voltage collapse blackout. From a modeling perspective, voltage collapse is closely related to the solvability of power flow equations. Determining conditions for existence and uniqueness of solution to power flow equations is one of the fundamental problems in power systems that has great theoretical and practical significance. In this paper, we provide strong sufficient condition certifying the existence and uniqueness of power flow solutions in a subset of state (voltage) space. The novel analytical approach heavily exploits the contractive properties of the fixed-point form in complex domain, which leads to much sharper analytical conditions than previous ones based primarily on analysis in the real domain. Extensive computational experiments are performed which validate the correctness and demonstrate the effectiveness of the proposed condition.
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