On the Stochastic Filtering Theory of a Power System Dynamics

Abstract

This paper revisits the Markovian state vector of a Single Machine Infinite Bus (SMIB) system in non-linear filtering framework. In power system dynamics, the non-linear stochastic swing equation was the subject of investigations in the Fokker-Planck setting. The Fokker-Planck setting accounts for the process noise correction term and ignores the observation noise correction term to analyse stochastic systems. In contrast to the Fokker-Planck setting, this paper introduces the notion of the 'Kushner-Stratonovich setting', which accounts for the process noise as well as observation noise correction terms in the conditional moment evolution equation. The Kushner-Stratonovich setting is the cornerstone formalism of non-linear filtering problems of stochastic control systems.

Classification Study of New Power System Stability Considering Stochastic Disturbance Factors

“…Dbifurcation mainly studies the bifurcation of new invariant measures from a set of reference measures, which can be obtained by determining the sign of the maximum Lyapunov exponent. P-bifurcation is related to the qualitative change in the stationary probability density of the system response and is generally studied by finding the extreme value of the stationary probability density [100]. Research on nonlinear stochastic dynamics of Hamiltonian systems [85,101] provided a theoretical basis for the study of stochastic bifurcation.…”