The Fokker-Planck equation for a Stochastic Single Machine Infinite Bus (SMIB) System

Abstract

In power system, the single machine infinite bus system is formalized as second order ordinary differential equation and that equation called swing equation. After accounting the noise influence, the single machine infinite bus (SMIB) system assumes the structure of stochastic differential equations. This paper analyses a stochastically influenced SMIB system, using the Fokker-Planck equation. From the system theoretic view point, the single machine infinite bus system of the paper assumes the structure of a stochastic differential equation. The Fokker-Planck equation has a central importance in the theory of stochastic process has found its applications in stochastic stability, estimation and stochastic control as well.

More notably, The main contribution of this paper to develop the Fokker-Planck model and subsequently, accomplish the noise analysis of the stochastic single machine infinite bus system by deriving the conditional mean and variance evolutions. It is imperative to know the estimated states before designing a dynamic controller for the power system involving single machine infinite bus system.