轨迹断面特征根对受扰轨迹最远点及动态鞍点的诠释

Annotation for FEP and DSP in Terms of Trajectory Section Eigenvalues

对于任何复杂模型,通过仿真得到特定扰动下的受扰轨迹后,就可沿轨迹将系统模型等值为分段定常的线性系统。轨迹断面特征根法采用的假设与欧拉积分法完全相同,即系统在且仅在单个仿真步长内被定常线性化。因此,在每个积分步内,不但可用静态扩展等面积准则(EEAC)法分析该轨迹断面上的能量稳定裕度(轨迹断面能量),也可用平衡点特征根技术分析该轨迹断面上的振荡阻尼与瞬时频率,而将断面处的不平衡功率与动能视为初始扰动。完整的受扰轨迹成为大、小扰动稳定分析的共同基础,断面特征根可反映复杂因素对振荡特性的影响,而EEAC可反映复杂因素影响同步稳定性的本质。引入"轨迹断面虚拟平衡点特征根序列"的概念,以计入断面处动能对滑步失稳的影响,并将滑步失稳与振荡失稳两者的机理相关联。据此考证最远点(FEP)和动态鞍点(DSP)处的振荡阻尼与瞬时频率,揭示大、小扰动失稳的内在联系。

For any complex model, an equivalent model of a complex system can be found by using piecewise time-invariant linear system models derived along disturbed trajectories resulting from simulation studies. The method of trajectory section eigenvalues has the same assumptions used for numerical integration, namely that the system is time-invariant linearized in and only in a single simulation step. Therefore, in each integration step, not only the energy margin of the trajectory section can be analyzed by using a static extended equal-area criterion （EEAC） method, but also the oscillation damping and instantaneous frequency of the trajectories section can be observed with the analysis of equilibrium point eigenvalues, regarding the unbalanced power and kinetic energy in the section as the initial disturbance. The complete disturbed trajectory forms a uniform basis for large and small disturbance stability analysis. Section eigenvalues can reflect the effect of complex factors of the oscillation characteristics, and EEAC can reflect the essence of the complicated influence on synchronous stability. Introducing the concept of ＂sequences of trajectory section eigenvalues at the virtual equilibrium point＂, the influence of section kinetic energy on the pole-slip instability can be taken into account, in association with the two mechanisms of pole-slip instability and oscillatory instability. The oscillation damping and instantaneous frequency of far end point （FEP） and dynamic saddle point （DSP） are analyzed and the essential relations of large disturbance instability and small disturbance instability are revealed.