Conformable分数阶单机无穷大电力系统分岔与混沌研究

严波,贺少波

系统科学与数学 ›› 2020, Vol. 40 ›› Issue (6) : 954-968.

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PDF(4933 KB)
系统科学与数学 ›› 2020, Vol. 40 ›› Issue (6) : 954-968. DOI: 10.12341/jssms13903
论文

Conformable分数阶单机无穷大电力系统分岔与混沌研究

    严波1,贺少波2
作者信息 +

The Bifurcation and Chaos Analysis of Conformable Fractional Order Unipolar Infinite Power System

    YAN Bo1 ,HE Shaobo2
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摘要

基于Conformable分数阶微分定义和Adomian分解 算法, 设计了Conformable分数阶非线性系统半解析解算法 和Lyapunov指数谱算法. 采用Lyapunov 指数谱、分岔图和吸引子相图分析了Conformable分数阶单机无穷大电力系统中的分岔与混沌现象, 揭示了系统状态随参数和微分阶数变化时的规律以及系统走向混沌的道路. Matlab仿真数值模拟结果 表明: Conformable分数阶单机无穷大电力系统的动力学特征丰 富, 系统产生混沌的最小阶数为0.41, 系统初值的改变直接影 响系统状态, 并发现了多涡卷混沌吸引子和共存吸引子, 功角失稳是产生多涡卷吸引子的根本原因. 研究结果表明了求解算法的有效性与Conformable 分数阶单机无穷大电力系统动力学特性 的丰富性.

Abstract

Based on the definition of conformable fractional-order differential and its properties, and the Adomain decomposition algorithm, a semi-analytical solution and a Lyapunov index spectral algorithm of conformable fractional order nonlinear systems are developed. The bifurcation and chaos phenomenon of the unipolar infinite power system of conformable fractional order is analysized by using Lyapunov exponent spectrum and bifurcation diagram, and the change rule of the system state with the parameters and the differential order and the road of the system toward chaos is revealed. Matlab numerical simulation results show that the dynamics behaviors of the unipolar infinite power system of conformable fractional order is rich, and the condition of generating chaos of which is that the minimum differential order number is 0.41, and the system state is directly affected by the initial values, and multi-scroll chaotic attractor and the attractor coexistence phenomenon is found, angle instability is the fundamental reason for the generation of multi-scroll chaotic attractor. Overall, the research results prove the Adomian decomposition method's effectiveness and the dynamics behaviors' richness of the conformable fractional order unipolar infinite power systems.

关键词

Conformable分数阶系统 / Adomian分解算法 / 单机无穷大电力系统 / 功角失稳 / 混沌.

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严波 , 贺少波. Conformable分数阶单机无穷大电力系统分岔与混沌研究. 系统科学与数学, 2020, 40(6): 954-968. https://doi.org/10.12341/jssms13903
YAN Bo , HE Shaobo. The Bifurcation and Chaos Analysis of Conformable Fractional Order Unipolar Infinite Power System. Journal of Systems Science and Mathematical Sciences, 2020, 40(6): 954-968 https://doi.org/10.12341/jssms13903
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