非线性模态构造方法与机电耦合系统Hopf分岔

Method of Constructing Nonlinear Normal Modes and Hopf Bifurcation in an ElectromechanicCoupled System

大型汽轮发电机组轴系与电网耦合次同步谐振（ＳＳＲ）现象是在某种参数条件下机电耦合系统产生Ｈｏｐｆ分岔的结果。在文献［１］中，作者提出了分析这种系统Ｈｏｐｆ分岔的非线性模态方法，得出了在固定参数下分岔解的结果。本文针对高维非线性动力系统（包括奇数维），提出新的非线性模态构造方法。

The subsynchronous resonance (SSR) phenomenon that may occur due to the coupling between the shaft systems of turbinegenerator sets and the electricnetworks, comes out of Hopf bifurcation in the electromechaniccoupled system under the condition of a certain parameter. In the reference, the author proposed the nonlinear normal mode method of analysing Hopf bifurcation in the system, and obtained the bifurcation solution under constant parameters. In this paper, a new method of constructing nonlinear normal modes is developed for high dimensional nonlinear dynamic systems (including odd dimensions), and the varying patterns of the bifurcation solution are given for the electromechaniccoupled subsynchronous oscillating system under variable auxiliary parameters.