基于降维Carleman嵌入技术的电力系统高阶变量交互作用分析研究

Analysis of power system higher-order variables and interaction based on reduced Carleman embedding technology

引入Carleman嵌入式分析技术,导出降维Carleman线性化模型。利用线性化理论得到非线性模式、单状态变量的时域解及相应非线性参与因子,导出了高阶状态变量的解析解,并进一步将参与因子的概念拓展到高阶变量非线性参与因子。研究结果可用于研究电力系统的非线性动态特性,揭示和评估量化各模式以及各状态变量之间的非线性交互作用。最后,利用该方法分析了一个电力系统仿真算例,并与Prony分析进行了对比。通过分析各阶状态变量时域响应和相应的参与因子,对比研究系统工况发生变化时特征模式空间的变化,验证了所研究方法的有效性。

The reduced Carleman linearization model is provided after introducing the Carleman embedding technology. The nonlinear modes and the time response of single state variables and corresponding nonlinear participation factors are given. The higher-order state variables are deduced and the concept of participation factors is developed to nonlinear participation factors of higher-order state variables. These results can be used to study the nonlinear dynamic performances and evaluate the interactions between each mode and variable. Finally, the proposed method is used to study a power system simulation case and compared with Prony analysis. Through analyzing time domain solutions of every order variable and corresponding participation factors, and comparing the changes of eigenvalues space when system＇s operating condition changes, it verifies the validity of the method.