摘要
研究了电力系统在周期和准周期扰动下的次谐和混沌轨道。首先假定扰动具有正弦形式 ,采用梅尼科夫方法对其中存在的次谐轨道和混沌吸引子进行了系统的分析 ,指出了由连续的次谐分叉进入混沌状态的途径。对周期非正弦扰动情况的分析表明 ,该状态下的系统动力学性质与正弦周期扰动情况下类似 ,但轨道空间形式更为复杂。对于准周期扰动情况 ,首先给出了不变环面的存在条件 ,然后预见了弱扰动下混沌轨道附近的混沌环面及强扰动下环面破裂所产生的混沌现象 。
This paper investigates the orbits of sub-harmonic and chaos in power system under periodic and quasi-periodic perturbation. At first, with the hypothesis that the periodic perturbation has the sine wave form and by Melnikov method, the systemic analysis of sub-harmonic orbits and chaos attractor in such system is given, and the route to chaos by a series of sub-harmonic bifurcation is pointed out. The analysis to the case of periodic but not sine perturbation implies that the dynamic is similar to the case of sine perturbation, but the spatial property of those orbits is more complex. To the case of quasi-periodic perturbation, the condition for existence of invariant tori is given out firstly. Then, with weak perturbation, the chaotic tori near the chaos orbit is prefigured, while the chaos introduced by the break of tories is prefigured too with relative strong perturbation. Numerical simulations prove these conclusions.
出处
《电力系统自动化》
EI
CSCD
北大核心
2002年第15期9-14,44,共7页
Automation of Electric Power Systems
基金
国家重点基础研究专项经费资助项目 (G19980 2 0 30 8)
关键词
微扰电力系统
混沌轨道
次谐轨道
周期扰动
准周期扰动
Chaos theory
Computer simulation
Harmonic analysis
Mathematical models
Perturbation techniques
