基于轨迹的非线性转子系统参数稳定裕度的计算

对高维非线性非自治转子系统进行数值积分后，将各自由度的运动方程中除该自由度外的所有状态变量用积分结果代换，得到n个互相解耦且含有多个时变参数的单自由度子方程。引和在电力系统中得到广泛应用的轨迹保稳降维概念，将已有的R^n轨线映射为一系列的R^1映象轨线。在R^1观察空间的外力一位移扩展相平面上利用动态中心点的动能差序列研究转子系统中常见的周期运动、倍周期运动、概周期运动和失稳运动的特点。给出对应上述几种典型运动形式的轨线稳定裕度的定量评估指标。根据轨线稳定裕度求取参数稳定裕度，以指导工程设计和控制。

ESTIMATION OF STABILITY MARGIN OF PARAMETER OF NONLINEAR ROTOR SYSTEM BASED ON TRAJECTORY

Through numerical integration, a high dimensional nonlinear nonautonomous rotor system can be uncoupled into n subsystems with only one degree of freedom Each subsystem has only one state variable and contains time varying parameters to present all other state variables Then the concept of stability preserving reduction of trajectory, which has found wide application on power system stability, is introduced to nonlinear rotor systems and n dimensional trajectory is mapped into a series of one dimensional observing trajectory Characteristics of typical motion in rotor systems, namely periodic motion, double periodic motion, quasi periodic motion and unstable motion, are studied on extended phase plane and kinetic energy series in one dimensional observing space, and the corresponding stability margins of trajectory are evaluated quantitatively By means of stability margin of trajectory, stability margin of parameter can be calculated easily, which is used to conduct design and control of engineering