计及时变系统完整非线性的振荡模式分析

Oscillation Mode Analysis Considering Full Nonlinearity of Time-varying Systems

提出评估非自治非线性因素对振荡行为影响程度的指标。其绝对值在定常的线性模型下严格为0,并随着时变性或非线性影响的增强而增加。据此,可量化地比较不同因素的影响。受扰轨迹完整地反映了时滞环节及离散控制等本质非线性因素和时变因素对系统动态行为的影响。采用小波脊方法估算受扰轨迹在适当宽度的时间窗口内的振荡模式,并随着窗口的滑动得到振荡模式的时间序列。用该序列可以量化非自治非线性振荡的特性,并指导对大振幅低频振荡的分析与控制。仿真发现,即使是3机9节点的小系统,其动态行为也可能不同于平衡点特征根的描述,而平衡点特征根甚至可能丢掉最危险的非线性模式。

An index to evaluate the influence on oscillation behavior of both nonlinearity and time-variance is proposed. The absolute value of the index is zero for a steady linear model, and increases with the nonlinearity and time variation factors of the model. Therefore, effects of the different factors can be compared quantitatively. Since the disturbed trajectories fully reflect the effects on dynamic behaviors of these factors including time-delay and discrete actions, the wavelet ridge algorithm is used to analyze oscillation modes within a proper time window along the trajectories. Then a time series of oscillation modes are obtained with sliding the window. This can be used to quantitatively assess time-varying nonlinear oscillations and restrain strong oscillations. Simulations on a 3-machine 9-node system show that the dynamic behaviors may be fully different from eigenvalue results at the equilibrium point, and the latter may even miss the most critical nonlinear modes.