简化单机水电系统负阻尼时频率振荡的类Hopf非光滑分岔分析

Hopf-like Non-smooth Bifurcation Analysis of Frequency Oscillation in Simplified Single Hydropower Generator System With Negative Damping

该文从切换型振荡角度,分析负阻尼情形下死区或限幅参与的频率振荡,说明负阻尼下超低频频率振荡(ultra-low frequency oscillation,ULFO)的机理之一是切换型振荡,并揭示了含死区和限幅的单机水电系统在突变负荷扰动下的超低频频率振荡可对应分段光滑连续系统的单次穿越型类Hopf非光滑分岔。首先,介绍分段光滑连续系统边界平衡点分岔(boundary equilibrium bifurcation,BEB)、类Hopf分岔和单次穿越型类Hopf分岔;其次,给出单水电机组电力系统的非光滑动力系统模型;然后,对比分析有/无死区和限幅(切换边界)时,单机系统负阻尼时频率振荡的差异,初步说明稳定的持续振荡与限幅和死区切换边界相关,无法单纯使用负阻尼或传统Hopf分岔来解释;进一步,借助广义Jacobi矩阵,说明有死区或限幅边界作用的切换型振荡对应的是发生单次穿越型类Hopf分岔;最后,分析突变负荷扰动下单机系统的平衡点、扰动后轨迹的非光滑分岔特性,说明单次穿越型类Hopf分岔是伴随着稳定结点穿越边界变为不稳定焦点的类Hopf分岔。

Considering the single-hydropower-generator power system(SHG-PS) with dead zone and limit in the case of negative damping,this paper analyzed the ultra-low frequency oscillation(ULFO),with respect to the sudden load disturbance and the non-smooth bifurcation theory of the piecewise-smooth continuous system(PSCS).It can be revealed that one of the mechanisms of ULFO is the switchingtype oscillation,which is corresponding to the single crossing Hopf-like non-smooth bifurcation.In detail,first,the boundary equilibrium bifurcation(BEB),the Hopf-like bifurcation and the single crossing Hopf-like bifurcation of the PSCS were introduced.Secondly,the non-smooth dynamic model for the SHG-PS was presented.Then,the difference of frequency oscillation with/without switching boundary of dead zone and limit for the SHG-PS engaged with negative damping was analyzed and compared.It shows that the stable continuous oscillation is related to the switching boundary,which cannot be simply explained by the negative damping theory or the traditional Hopf bifurcation.Furthermore,the analysis of the generalized Jacobi matrix shows that the switching-type oscillation induced by switching boundary of dead zone or limit,corresponds to the single crossing Hopf-like bifurcation.Finally,the non-smooth bifurcation characteristics of the equilibrium point and the trajectory after disturbance were analyzed with different sudden load disturbance.It shows that the single crossing Hopf-like bifurcation is a kind of Hopf-like bifurcation with a stable node crossing the boundary and becoming an unstable focus.