On the machine swing dynamics: a perspective

A formal approach to rephrase nonlinear filtering of stochastic differential equations is the Kushner setting in applied mathematics and dynamical systems. Thanks to the ability of the Carleman linearization, the ‘nonlinear’ stochastic differential equation can be equivalently expressed as a finite system of ‘bilinear’ stochastic differential equations with the augmented state under the finite closure. Interestingly, the novelty of this paper is to embed the Carleman linearization into a stochastic evolution of the Markov process. To illustrate the Carleman linearization of the Markov process, this paper embeds the Carleman linearization into a nonlinear swing stochastic differential equation. Furthermore, we achieve the nonlinear swing equation filtering in the Carleman setting. Filtering in the Carleman setting has simplified algorithmic procedure. The concerning augmented state accounts for the nonlinearity as well as stochasticity. We show that filtering of the nonlinear stochastic swing equation in the Carleman framework is more refined as well as sharper in contrast to benchmark nonlinear EKF. This paper suggests the usefulness of the Carleman embedding into the stochastic differential equation to filter the concerning nonlinear stochastic differential system. This paper will be of interest to nonlinear stochastic dynamists exploring and unfolding linearization embedding techniques to their research.

Applied the Software of MATLAB to Calculate the Critical Clearing Time in Power System

Aims: to avoid improper critical clearing time values due to clerical errors during the artificial calculation process, so that takes advantage of MATLAB application software to compile with those equations such as power angle, swing equation, equal area criterions, etc. to calculate of critical clearing time. Study Design: This article starts introduction with what the way of the calculation such as power angle, swing equation, equal area criterions, etc in literature, and referred lots of the latest literature to develop. Place and Duration of Study: The setting of the critical clearing time plays an important role in the power system. The start-up time of any protection relay must be shorter than the critical clearing time; otherwise the fault will expand and cause serious damage when the system fails. Therefore, it is an important question the set time of the protection relay needed to caution in planning design. Methodology: To use MATLAB application software links with above equations to compile the program the calculation of critical clearing time. Results: The program has been proved very effective and accurate for calculating the reasonable setting value of proportion relay, the same time it would shortened of assignment time by design planners. Conclusion: Computerized operating procedures can be used to avoid improper critical clearing time values due to clerical errors during the artificial calculation process.