摘要：AbstractWe present an extension of the method of eigenmode decomposition of Gramians proposed earlier for the small-signal stability analysis of dynamical systems. In this paper we derive the spectral decomposition for finite Gramians on any time interval and with arbitrary initial conditions. These expansions allow both a stability analysis of non-stationary systems and a monitoring of instability development in unstable systems. Eigen components in the expansion of Gramians on a finite interval of time we called finite sub-Gramians. Because each sub-Gramian is associated with a particular eigenvector, the sources of instability can be easily localized and tracked in real time. We perform a simulation experiment in which finite sub-Gramians are used to analyze the development of instability arising in an actual power grid on Russky Island when it is disconnected from the mainland network.
关键词：Keywordspower systemsLyapunov direct methodtransient stability analysisfinite Gramiansub-Gramian approachsimulation experiment
