次同步谐振中的分歧分析

应用Lyapunov-Schmidt方法对高维非线性向量场进行了约化,采用Hopf分歧理论分析了次同步谐振中出现的分歧现象.利用数值微分法求出了曲率系数对分歧参数的灵敏度,从而可预见分歧轨道稳定性态的变化.研究表明:不同的串联补偿度、不同的参数可能导致不同类型的分歧.在某一串联补偿度上,出现的次同步谐振可能被轨道稳定的极限环所取代.随着串联补偿度的升高,次同步谐振可能出现于虚轴左侧邻域.换句话说,在另一较高的串联补偿度上,轨道不稳定的极限环将从原来渐近稳定平衡点上分岔出来,系统的稳定性态将被改变.

BIFURCATION ANALYSIS IN SUB-SYNCHRONOUS RESONANCE

On the basis of the Hopf bifurcation theory, the bifurcation phenomenon occurring in sub-synchronous resonance is analyzed in the paper in terms of Lyapunov-Schmidt algorithm by which the high dimension nonlinear vector fields are reduced. The sensitivity of the bifurcation parameter to the curvature coefficient has also been investigated by using the numerical differential algorithm, which give a way to predict the dynamic characteristic variation of the bifurcation orbit. The investigation results show that different series capacitor compensation level or different system parameters may lead to different kind of bifurcations. At a given series compensation level, the original sub-synchronous resonance may change into stable limit cycle. With increase of the series compensation level, the sub-synchronous resonance may occur at the left side neighborhood of the imaginary axe. In other words, the unstable limit cycle will be bifurcated from the original asymptotical stable equilibrium point at another higher series compensation level, and the system dynamics will change.