为了反映风电系统参数连续变化对其电压稳定性的影响和揭示风电系统电压稳定机制,针对目前的分岔理论研究了风电系统电压稳定性的局限性,对风电系统进行了两参数鞍结分岔边界的计算与研究。借助常规电力系统计算二维参数分岔边界的方法...为了反映风电系统参数连续变化对其电压稳定性的影响和揭示风电系统电压稳定机制,针对目前的分岔理论研究了风电系统电压稳定性的局限性,对风电系统进行了两参数鞍结分岔边界的计算与研究。借助常规电力系统计算二维参数分岔边界的方法和思路,以风电注入有功功率Pinject、静止无功补偿(static var compensation,SVC)参数Bmax、放大倍数Kr为分岔控制参数,计算得到风电系统节点电压鞍结二维分岔边界。在此基础上深入分析,最后得出风电场注入有功和SVC参数共同作用下影响风电系统电压稳定性的规律:在SVC参数Bmax(或Kr)和风电注入有功功率Pinject的共同作用下,风电场机端(即补偿点)电压稳定性得以提高;增大SVC参数Bmax和Kr,都能有效扩展鞍结分岔边界,并且Bmax的作用更明显。展开更多
基于混沌分岔理论,研究了开关频率对单相正弦脉宽调制(SPWM)逆变器的影响。以基本H桥逆变器为研究对象,采用一阶离散模型分析系统的混沌行为。应用频闪映射图、分岔图和频谱图,从时域到频域详细分析了开关频率对逆变器动态性能的影响。...基于混沌分岔理论,研究了开关频率对单相正弦脉宽调制(SPWM)逆变器的影响。以基本H桥逆变器为研究对象,采用一阶离散模型分析系统的混沌行为。应用频闪映射图、分岔图和频谱图,从时域到频域详细分析了开关频率对逆变器动态性能的影响。通过时滞反馈控制改善了系统在中低频段的混沌状态,并结合二阶时滞模型的雅可比矩阵特征值给出了系统稳定运行的参数域。通过仿真与实验,观察了电流在不同开关频率(3 k Hz和2 k Hz)下的分岔和混沌行为。结果表明,时滞反馈控制能有效抑制低开关频率造成的混沌,当时滞系数取0.22时,控制器抑制混沌的效果最好。展开更多
Using a combination of analytical and numerical methods, the paper studies bifurcations and chaotic motions of a two-dimensional airfoil with cubic nonlinearity in incompressible flow. One type of critical points (cha...Using a combination of analytical and numerical methods, the paper studies bifurcations and chaotic motions of a two-dimensional airfoil with cubic nonlinearity in incompressible flow. One type of critical points (characterized by a negative eigenvalue, a simple zero eigenvalue and a pair of purely imaginary eigenvalues) for the bifurcation response equations is considered. With the aid of the normal form theory, the explicit expressions of the critical bifurcation lines leading to incipient and secondary bifurcations are obtained. The stability of the bifurcation solutions is also investigated. By using the undetermined coefficient method, the homoclinic orbit is found, and the uniform convergence of the homoclinic orbit series expansion is proved. It analytically demonstrates that there exists a homoclinic orbit joining the initial equilibrium point to itself, therefore Smale horseshoe chaos occurs for this system via Si'lnikov criterion. The system evolves into chaotic motion through period-doubling bifurcation, and is periodic again as the dimensionless airflow speed increases. Numerical simulations are also given, which confirm the analytical results.展开更多
In this paper, the dynamic behaviors of a discrete epidemic model with a nonlinear incidence rate obtained by Euler method are discussed, which can exhibit the periodic motions and chaotic behaviors under the suitable...In this paper, the dynamic behaviors of a discrete epidemic model with a nonlinear incidence rate obtained by Euler method are discussed, which can exhibit the periodic motions and chaotic behaviors under the suitable system parameter conditions. Codimension-two bifurcations of the discrete epidemic model, associated with 1：1 strong resonance, 1：2 strong resonance, 1：3 strong resonance and 1：4 strong resonance, are analyzed by using the bifurcation theorem and the normal form method of maps. Moreover, in order to eliminate the chaotic behavior of the discrete epidemic model, a tracking controller is designed such that the disease disappears gradually. Finally, numerical simulations are obtained by the phase portraits, the maximum Lyapunov exponents diagrams for two different varying parameters in 3-dimension space, the bifurcation diagrams, the computations of Lyapunov exponents and the dynamic response. They not only illustrate the validity of the proposed results, but also display the interesting and complex dynamical behaviors.展开更多
文摘为了反映风电系统参数连续变化对其电压稳定性的影响和揭示风电系统电压稳定机制,针对目前的分岔理论研究了风电系统电压稳定性的局限性,对风电系统进行了两参数鞍结分岔边界的计算与研究。借助常规电力系统计算二维参数分岔边界的方法和思路,以风电注入有功功率Pinject、静止无功补偿(static var compensation,SVC)参数Bmax、放大倍数Kr为分岔控制参数,计算得到风电系统节点电压鞍结二维分岔边界。在此基础上深入分析,最后得出风电场注入有功和SVC参数共同作用下影响风电系统电压稳定性的规律:在SVC参数Bmax(或Kr)和风电注入有功功率Pinject的共同作用下,风电场机端(即补偿点)电压稳定性得以提高;增大SVC参数Bmax和Kr,都能有效扩展鞍结分岔边界,并且Bmax的作用更明显。
文摘基于混沌分岔理论,研究了开关频率对单相正弦脉宽调制(SPWM)逆变器的影响。以基本H桥逆变器为研究对象,采用一阶离散模型分析系统的混沌行为。应用频闪映射图、分岔图和频谱图,从时域到频域详细分析了开关频率对逆变器动态性能的影响。通过时滞反馈控制改善了系统在中低频段的混沌状态,并结合二阶时滞模型的雅可比矩阵特征值给出了系统稳定运行的参数域。通过仿真与实验,观察了电流在不同开关频率(3 k Hz和2 k Hz)下的分岔和混沌行为。结果表明,时滞反馈控制能有效抑制低开关频率造成的混沌,当时滞系数取0.22时,控制器抑制混沌的效果最好。
基金supported by the National Natural Science Foundation of China (Grant Nos. 10972099, 10632040)China Postdoctoral Science Foundation (Grant No. 20090450765)the Natural Science Foundation of Tianjin, China (Grant No. 09JCZDJC26800)
文摘Using a combination of analytical and numerical methods, the paper studies bifurcations and chaotic motions of a two-dimensional airfoil with cubic nonlinearity in incompressible flow. One type of critical points (characterized by a negative eigenvalue, a simple zero eigenvalue and a pair of purely imaginary eigenvalues) for the bifurcation response equations is considered. With the aid of the normal form theory, the explicit expressions of the critical bifurcation lines leading to incipient and secondary bifurcations are obtained. The stability of the bifurcation solutions is also investigated. By using the undetermined coefficient method, the homoclinic orbit is found, and the uniform convergence of the homoclinic orbit series expansion is proved. It analytically demonstrates that there exists a homoclinic orbit joining the initial equilibrium point to itself, therefore Smale horseshoe chaos occurs for this system via Si'lnikov criterion. The system evolves into chaotic motion through period-doubling bifurcation, and is periodic again as the dimensionless airflow speed increases. Numerical simulations are also given, which confirm the analytical results.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 60974004 and 71001074, and the Science Research Foundation of Department of Education of Liaoning Province of China under Grant No. W2010302.
文摘In this paper, the dynamic behaviors of a discrete epidemic model with a nonlinear incidence rate obtained by Euler method are discussed, which can exhibit the periodic motions and chaotic behaviors under the suitable system parameter conditions. Codimension-two bifurcations of the discrete epidemic model, associated with 1：1 strong resonance, 1：2 strong resonance, 1：3 strong resonance and 1：4 strong resonance, are analyzed by using the bifurcation theorem and the normal form method of maps. Moreover, in order to eliminate the chaotic behavior of the discrete epidemic model, a tracking controller is designed such that the disease disappears gradually. Finally, numerical simulations are obtained by the phase portraits, the maximum Lyapunov exponents diagrams for two different varying parameters in 3-dimension space, the bifurcation diagrams, the computations of Lyapunov exponents and the dynamic response. They not only illustrate the validity of the proposed results, but also display the interesting and complex dynamical behaviors.
