2015 Volume 2015 Pages 142-148
This paper discusses the stochastic evolutions of the state trajectories of a stochastic Single Machine Infinite Bus (SMIB) system. The dynamical equation of the SMIB system assumes the structure of a second-order non-linear differential equation. That is described as a power swing equation. After accounting for the stochasticity in the machine swing equation as well as accomplishing the phase space formulation, we are led to a vector stochastic differential equation. Importantly, the Itô stochasticity as well as the Stratonovich stochasticity coincide for the stochastic swing equation, since the Wang-Zakai correction term of the stochastic integral will vanish for the special case. Despite universality of the second-order non-linear machine swing equation in theoretical studies, e.g. power system dynamics, circuits and systems literature, the stochasticity of the machine swing equation is not analysed in a greater detail yet. In this paper, we analyse the stochasticity of the swing equation after utilizing the notion of the stochastic evolution of a scalar function of vector stochastic processes in combination with conditional expectation. Note that the stochastic state vector of the machine swing equation of this paper is a Markov process.
