根据量测轨迹计算轨迹灵敏度的卷积法

轨迹灵敏度刻画系统中某一参数、初始条件发生微小变化时系统动态轨迹的变化程度。轨迹灵敏度已应用于参数辨识、动态安全分析等电力系统研究领域。直接由定义计算轨迹灵敏度通常依赖于数值积分的方法，不仅计算费时，模型和参数的误差会影响轨迹灵敏度的计算结果，而且不能充分揭示轨迹灵敏度的物理本质。文中提出一种基于量测轨迹的轨迹灵敏度计算方法，可以克服上述缺点。将时域响应轨迹变换到复频域后，根据轨迹在复频域上的分析性质，证明了轨迹灵敏度可以表示为系统的阶跃响应轨迹与脉冲响应轨迹的卷积或它们的线性组合。电力系统算例表明所提出的方法简捷、有效、可行。

A Convolution Method for Calculating the Trajectory Sensitivity Based on Measured Trajectory

Trajectory sensitivities provide a way for quantifying the variation of trajectory resulting from (small) changes of parameters and/or initial conditions. The trajectory sensitivity has been applied in power systems, such as for parameter identification, dynamic performance analysis and so on. The calculation of trajectory sensitivity based on the definition itself is usually time-consuming. It relies on the numerical integration, is liable to errors of model and parameters, and cannot provide the physical understanding about the sensitivity. A convolution method for calculating trajectory sensitivity is proposed in this paper, by use of typical system dynamic trajectories, which can be obtained by measurement. Based on the analytical characteristics of the measured trajectory in frequency domain, it is demonstrated that the trajectory sensitivity can be expressed as the linear composition or convolution of the step response and the impulse response. Power system example shows that the proposed method is simple, effective and feasible.