Liu, LeiJu, PingWu, Feng2022-09-262022-09-262017-11-30Liu, L., Ju, P., & Wu, F. (2017). Dynamical analysis of one machine to infinite bus power systems under Gauss type random excitation. <i>Electronic Journal of Differential Equations, 2017</i>(298), pp. 1-15.1072-6691https://hdl.handle.net/10877/16170We 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.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalPower systemsRandom excitationStochastic fluctuationStationary distributionAsymptotic pathwise estimationAsymptotic moment estimationArticle