论文标题
使用微分几何形状重新审视瞬时频率的悖论
Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency
论文作者
论文摘要
本文提出了一个通用框架，以解释三相系统中瞬时频率（if）的概念。该论文首先基于傅立叶变换以及基于分析信号的概念的定义回忆起传统的频域分析。还显示了AC功率系统的三相电压的分析信号与CLARKE变换之间的联系。然后陈述了著名的五个悖论。在本文的第二部分中，提出了基于频率几何解释的方法。如果悖论，这种方法可以重新审视这五个，并通过共同的框架解释。案例研究说明了基于各种示例和IEEE 39-BUS系统的详细模型的提议框架的特征。
This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the definition of IF which is based on the concept of analytic signals. The link between analytic signals and Clarke transform of three-phase voltages of an ac power system is also shown. Then the well-known five paradoxes of the IF are stated. In the second part of the paper, an approach based on a geometric interpretation of the frequency is proposed. This approach serves to revisit the five IF paradoxes and explain them through a common framework. The case study illustrates the features of the proposed framework based on a variety of examples and on a detailed model of the IEEE 39-bus system.
