论文标题
Frenet框架作为公园变换的概括
The Frenet Frame as a Generalization of the Park Transform
论文作者
论文摘要
本文提出了基于FRENET框架的公园变换的概括，该框架是在空间曲线中定义的一组特殊的坐标。首先，针对三个维度讨论了所提出的几何变换，这对应于常见的三相电路。然后，讨论了所提出的转换的时间导数的表达，并引入了Frenet-Serret公式和Darboux载体。还描述了基于Cartan的移动框架和态度矩阵的参考框架及其分化的变化。最后，提出了三个以上阶段的电路的扩展。 FRENET框架的特征通过各种示例进行了说明，包括基于IEEE 39-BUS系统的案例研究。
The paper proposes a generalization of the Park transform based on the Frenet frame, which is a special set of coordinates defined in differential geometry for space curves. The proposed geometric transform is first discussed for three dimensions, which correspond to the common three-phase circuits. Then, the expression of the time derivative of the proposed transform is discussed and the Frenet-Serret formulas and the Darboux vector are introduced. The change of reference frame and its differentiation based on Cartan's moving frames and attitude matrices are also described. Finally, the extension to circuits with more than three phases is presented. The features of the Frenet frame are illustrated through a variety of examples, including a case study based on the IEEE 39-bus system.
