Electron. J. Differential Equations, Vol. 2017 (2017), No. 298, pp. 1-15.

Dynamical analysis of one machine to infinite bus power systems under Gauss type random excitation

Lei Liu, Ping Ju, Feng Wu

Abstract:
We discuss the asymptotic behavior of the stochastic one machine to infinite bus power systems. Using the exponential martingale inequality and the Borel-Cantelli Lemma, we obtain asymptotic moment estimation and asymptotic pathwise estimation of the stochastic one machine to infinite bus systems. Using the ergodic properties, we give a good explanation of the fluctuation phenomena. By means of the property of periodicity, Hormander's theorem and a detailed balance method, the existence and probability density function of the stationary distribution on the cylindrical are illustrated.

Submitted October 8, 2016. Published November 30, 2017.
Math Subject Classifications: 34F05, 60H10, 93E03.
Key Words: Power systems; Random excitation; stochastic fluctuation; stationary distribution; asymptotic pathwise estimation; asymptotic moment estimation.

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Lei Liu
College of Science
Hohai University
Nanjing, 210098, China
email: liulei_hust@163.com
Ping Ju
College of Energy and Electrical Engineering
Hohai University
Nanjing, 210098, China
email: pju@hhu.edu.cn
Feng Wu
College of Energy and Electrical Engineering
Hohai University
Nanjing, 210098, China
email: wufeng@hhu.edu.cn

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