Stability analysis of electric power systems using finite Gramians**This work was supported by research project No.14-08-01098-a of the Russian Foundation for Basic Research (RFBR).

Abstract

We present an extension of the method of eigenmode decomposition of Gramians proposed earlier for the 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 subGramians 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.

The sub-Gramian method as a tool for the automotive suspension tuning

“…Potentially it may allow its application to timevariant and certain types of non-linear systems. However, its results appear to be difficult to interpret and use [2]. This created a need to find a relatively simple, yet highly variable and containing multiple feedbacks technical system in order to study practical features of the finite sub-Gramian method.…”