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基于Lyapunov指数的电力系统随机分岔分析

发表时间:2019-08-30  浏览量:180  下载量:11
全部作者: 张彦,魏军强,卢占会
作者单位: 华北电力大学数理学院
摘 要: 在稳定性理论发展的早期,大多数经典的方法都是基于确定性系统,最大Lyapunov指数是作为随机稳定性的重要指标之一。考虑引入乘性噪声的单机无穷大(single machine infinite bus,SMIB)系统,当不断变换噪声强度时,描述该系统的随机模型的稳定性将发生变化,引起随机分岔现象。基于Lyapunov指数的正负可以判断该模型的稳定性。由于乘性噪声的特殊性,先用极坐标变换然后用Fourier配置法,计算得出最大Lyapunov指数,进而分析随机分岔现象。分析结果表明,随机SMIB系统存在着随机分岔现象。在不同的阻尼系数下,对应的平稳概率密度函数没有明显变化,但是引起分岔的噪声强度是不同的。
关 键 词: 应用数学;随机单机无穷大系统;白噪声过程;最大Lyapunov指数;Fourier配置法
Title: Stochastic bifurcation analysis of power system based on Lyapunov exponent
Author: ZHANG Yan, WEI Junqiang, LU Zhanhui
Organization: School of Mathematics and Physics, North China Electric Power University
Abstract: In the early days of stability theory, most classical methods were based on deterministic systems. The top Lyapunov exponent is one of the important indexes of stochastic stability. Considering the single machine infinite bus (SMIB) system with multiplicative noise, when the noise intensity continuously changes, the stability of the stochastic model describing the system will change, causing stochastic bifurcation. The stability of the model can be judged based on the positive and negative of Lyapunov exponent. Due to the particularity of multiplicative noise, the top Lyapunov exponent is calculated by using polar coordinate transformation and then Fourier configuration method, and the phenomenon of stochastic bifurcation is analyzed. The analysis results show that stochastic bifurcation exists in stochastic SMIB systems. Under different damping coefficients, the corresponding stationary probability density function does not change significantly, but the noise intensity that causes bifurcation is different.
Key words: applied mathematics; stochastic single machine infinite bus system; white noise process; top Lyapunov exponent; Fourier configuration method
发表期数: 2019年8月第4期
引用格式: 张彦,魏军强,卢占会. 基于Lyapunov指数的电力系统随机分岔分析[J]. 中国科技论文在线精品论文,2019,12(4):561-568.
 
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