### A Stochastic Single Machine-Infinite Bus System in Non-linear Filtering Contexts

#### Abstract

In power systems, the single machine-infinite bus system is formalized as a second-order non-linear differential equation and the equation is called a machine swing equation. After accounting for the noise influence, the Single Machine-Infinite Bus (SMIB) system assumes the structure of a Stochastic Differential Equation (SDE). This paper revisits the noisy state vector of the stochastic SMIB system from non-linear filtering perspectives. In the Fokker-Planck setting, we consider process noise and ignore observation noise. On the other hand, the non-linear filtering perspective accounts for the process noise as well as observation noise correction terms. Since the single machine-infinite bus system accounts for greater order of non-linearities, we wish to estimates the states of the SMIB system using higher-order filter. Subsequently, we compare the filtered state trajectories with celebrated extended Kalman filtering. The filter efficacy is examined by numerical experimentations with two sets of data. This paper fills a niche between non-linear filtering and power system dynamics. This paper reveals a connection between non-linear ordinary differential equation, stochastic differential equations and stochastic partial differential equations as well.

#### Keywords

Non-linear filtering equations, Single Machine-Infinite Bus (SMIB) system, Itô stochastic differential equation, stochastic partial differential equations