This letter devises a Reachable Eigenanalysis (ReachEigen) theory as a formal method to analyze uncertain eigenvalues in power systems. ReachEigen computes the set of the possible spectra, taking into account the changes of both the system operating points and the characteristic equations caused by uncertainties. The innovation of ReachEigen lies in: 1) a Newton-iteration-based eigensolver which tractably tackles the “random walk” of steady-state operating points and delineates the propagation of uncertainty effects in the system eigenvalues; and 2) a reachability method established on the Netwon's eigensolver, which bounds the set of uncertain eigenvalues through a single calculation and thus is immune to the combinatorial explosion issue under a large number of uncertain factors. Case studies on a networked microgrid verifies the efficiency of ReachEigen and its superiority over existing methods. The efficacy of ReachEigen of providing early warning information for small-signal stability under uncertainties is also illustrated.

中文翻译：

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可达特征分析

这封信设计了可达特征分析 (ReachEigen) 理论作为分析电力系统中不确定特征值的正式方法。ReachEigen 计算可能的谱集，同时考虑到系统工作点和由不确定性引起的特征方程的变化。ReachEigen 的创新之处在于：1）一种基于牛顿迭代的特征求解器，它可以轻松解决稳态工作点的“随机游动”问题，并描绘了系统特征值中不确定性效应的传播；2）建立在Netwon的特征求解器上的可达性方法，通过一次计算就对不确定特征值集进行了界定，从而不受大量不确定因素下的组合爆炸问题的影响。网络化微电网的案例研究验证了 ReachEigen 的效率及其优于现有方法的优势。还说明了 ReachEigen 为不确定性下的小信号稳定性提供预警信息的功效。