中文摘要：

利用Carleman线性化原理研究电力系统非线性振荡稳定性问题,通过分析得到了二阶及二阶以上电力系统动态方程解析解的表达式。通过Carleman线性化分析方法得到了系统的非线性高阶模态,可以用于研究电力系统的非线性动态特性及大干扰下系统的稳定性,揭示了非线性模态相关性对系统动态特性的影响。同时将线性模态参与因子的概念扩展到非线性模态中,定量地衡量各振荡模式之间的非线性相关作用。通过36节点系统的仿真计算与Prony分析结果进行了对比。通过Carleman线性化方法分析电力系统非线性模式之间的相互作用,可以在小干扰稳定和传统的线性化分析基础上更加深入地理解非线性系统的动态特性,为分析大干扰和强非线性情况下系统的稳定性和动态特性提供了一种新的手段。

英文摘要：

The stability of power system with nonlinear oscillations is analyzed by using Carleman linearization theory.The explicit second order and high order solutions of the power system dynamics are obtained.The nonlinear high order modes of the system are calculated by Carleman linearization,which can be used to analyze the stability of the power system with large disturbances,as well as the nonlinear dynamical characteristics.Influences of the nonlinear mode correlations on the dynamical characteristics are studied.The concept of participation factor is extended from linear mode to nonlinear mode,and the interactions between different oscillation modes are evaluated.Epri-36 simulation results,compared with that of the Prony analysis,show the efficiency of the proposed method.By analyzing the interaction between nonlinear modes of power system through Carleman linearization theory,the dynamic characteristic of nonlinear system could be more clearly understood than small signal stability method and conventional linearized analysis.Carleman linearization theory provides a new method for studying the stability and the dynamic behavior under large disturbance and nonlinear condition.