轨迹特征根的解析估算及其误差分析

Analytical Calculation of Power System Trajectory Eigenvalues and Its Error Analysis

在一系列滑动的时间窗口内,用信号处理技术提取振荡模式的方法并不适用于时变太快或非线性太强的场合。为克服此缺点,沿实际受扰轨迹,在每个积分步的始点将非线性系统的数学模型逐段线性化,并求解该分段线性系统特征根的时间序列。进一步将上述分段线性化动态方程映射为一系列时变的单机系统,用扩展等面积准则(EEAC)辨识每个积分步长内的振荡模式,并推导出轨迹断面特征根的解析估算公式。以多机轨迹断面特征根为标准,审视解析估算公式的精度,并评估平衡点特征根对非线性的不适应性。

Requiring quite wide sliding windows, signal processing techniques for extracting oscillation-mode information are applicable for neither fast time-varying systems nor strong nonlinear systems. To overcome the shortcomings, a method to calculate time-varying eigenvalues series is proposed based on the piecewise-linearized system models along the disturbed trajectories. Eigenvalue calculation is performed at the beginning of every time step for numerical integration. Furthermore, the piecewise-linearized dynamic equations are mapped into a series of time-varying one machine infinite bus （OMIB） systems and the oscillation mode within each integration-step can be identified with analytical formulas of extended equal-area criterion （EEAC）. This makes the estimation of trajectory eigenvalues not only quickly but also accurately. The method is applied to a 3 machine 9-node test system and the effects of nonlinear non-autonomous factors on the eigenvalues are investigated.