摘要
基于奇异摄动理论和非线性系统稳定域边界二次近似方法,推导出非线性多时间尺度系统忽略快动态降阶时,降阶前后系统稳定性的一般规律。通过将原系统稳定裕度指标在奇异摄动参数处进行高阶泰勒级数展开,给出定量预测降阶系统稳定裕度指标的表达式。在此基础上,提出一种非线性多时间尺度系统模型降阶方法,该降阶方法能保证降阶前后系统的稳定性一致。运用该降阶方法,对某交直流电力系统的数学模型进行了忽略快动态降阶研究。降阶前后系统的时域仿真结果证明所提出降阶方法是有效的,能为交直流电力系统的动态特性分析提供简化模型。
Based on singular perturbation theory and quadratic approximation method of the stability region boundary of nonlinear system, a stability law was derived for nonlinear multi-time scale system, whose order was reduced by neglecting fast dynamics. Then, the quantitative prediction expression of stability margin index of reduced system was presented using the high-order Taylor series expansion of stability margin index of the original system. Subsequently, a model order reduction method for nonlinear multi-scale systems was proposed, which can ensure stability consistency between original and reduced systems. Finally, according to the proposed reduction method, the model order of an AC/DC power system was reduced by neglecting fast dynamics. Time-domain simulation results demonstrate the proposed model reduction method is effective and applicable to provide simplified model for dynamic characteristic analysis of the AC/DC power system.
出处
《中国电机工程学报》
EI
CSCD
北大核心
2013年第16期162-170,5,共9页
Proceedings of the CSEE
基金
国家自然科学基金项目(50977090
51077130)
国家重点基础研究发展计划项目(973项目)(2012CB215103)~~
关键词
非线性多时间尺度系统
模型降阶
奇异摄动理论
稳定域边界
二次近似
nonlinear multi-time scale systems
model order reduction
singular perturbation theory
stability region boundary
quadratic approximation
