具周期时滞系统的移动均值及其在电力系统中的应用

Moving averages for periodic time-delay differential system and application to the power system

基于 2 0世纪 60年代Halanay和Hale关于微分系统平均性的思想 ,利用移动均值方法 ,研究了一类非线性具周期时滞系统的移动均值 ,利用移动均值方法和分区间分析方法证明了该类系统的平均化定理 ,得到了该类系统及其平均化系统解的渐近性行为 .本文的分区间分析方法及定理与以往研究的不同之处在于考虑了平均化系统中的时滞项 .最后将结论应用到一个具有周期激励的时滞系统模型———非同期合闸产生的过电压模型 ,研究了该类系统在周期扰动和反馈控制下的稳定性问题 。

This paper is partly based on the idea of averaging of differential systems proposed by Halanay and Hale in the 1960 s. The moving averages for periodic time-delay differential system is presented and its averaging theorems are proved by the method of moving averages and district-analysis. The asymptotic behavior of the solutions to the system and its averaged system are obtained. The district-analysis and the theorem differ from previous work in taking into account the time-delay terms existing in the averaged system. A model of over-voltage with time-delay and with periodic excitation, caused by asynchronous closing of switches in power systems, is given. Study on the system stabilization under periodic disturbances and feedback time-delay verifies the above results.