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基于Lyapunov指數的電力系統隨機分岔分析

發表時間:2019-08-30? 瀏覽量:396? 下載量:36
全部作者: 張彥,魏軍強,盧占會
作者單位: 華北電力大學數理學院
摘 要: 在穩定性理論發展的早期,大多數經典的方法都是基于確定性系統,最大Lyapunov指數是作為隨機穩定性的重要指標之一??紤]引入乘性噪聲的單機無窮大(single machine infinite bus,SMIB)系統,當不斷變換噪聲強度時,描述該系統的隨機模型的穩定性將發生變化,引起隨機分岔現象?;贚yapunov指數的正負可以判斷該模型的穩定性。由于乘性噪聲的特殊性,先用極坐標變換然后用Fourier配置法,計算得出最大Lyapunov指數,進而分析隨機分岔現象。分析結果表明,隨機SMIB系統存在著隨機分岔現象。在不同的阻尼系數下,對應的平穩概率密度函數沒有明顯變化,但是引起分岔的噪聲強度是不同的。
關 鍵 詞: 應用數學;隨機單機無窮大系統;白噪聲過程;最大Lyapunov指數;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
發表期數: 2019年8月第4期
引用格式: 張彥,魏軍強,盧占會. 基于Lyapunov指數的電力系統隨機分岔分析[J]. 中國科技論文在線精品論文,2019,12(4):561-568.
 
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