With the integration of renewable power and electric vehicle,the power system stability is of increasing concern because the active power generated by the renewable energy and absorbed by the electric vehicle vary ran...With the integration of renewable power and electric vehicle,the power system stability is of increasing concern because the active power generated by the renewable energy and absorbed by the electric vehicle vary randomly.Based on the deterministic differential equation model,the nonlinear and linear stochastic differential equation models of power system under Gauss type random excitation are proposed in this paper.The angle curves under different random excitations were simulated using Euler-Maruyama(EM) numerical method.The numerical stability of EM method was proved.The mean stability and mean square stability of the power system under Gauss type of random small excitation were verified theoretically and illustrated with simulation sample.展开更多
This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment sta...This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment stability property of the viscoelastic system,we use the stochastic averaging method,Girsanov theorem and Feynmann-Kac formula to derive the approximate analytic expansion of the moment Lyapunov exponent.Furthermore,the Monte Carlo simulation results for the original system are given to check the accuracy of the approximate analytic results.At the end of this paper,results are presented to show some quantitative pictures of the effects of the system parameters,noise parameters and viscoelastic parameters on the stability of the viscoelastic plate.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 51137002,51190102)the Fundamental Research Funds for the Central Universities (Grant No. BZX/09B101-32)
文摘With the integration of renewable power and electric vehicle,the power system stability is of increasing concern because the active power generated by the renewable energy and absorbed by the electric vehicle vary randomly.Based on the deterministic differential equation model,the nonlinear and linear stochastic differential equation models of power system under Gauss type random excitation are proposed in this paper.The angle curves under different random excitations were simulated using Euler-Maruyama(EM) numerical method.The numerical stability of EM method was proved.The mean stability and mean square stability of the power system under Gauss type of random small excitation were verified theoretically and illustrated with simulation sample.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072107 and 91016022)the Specialized Research Fund for the Doctoral Program of Higher Education of China (GrantNo.20093218110003)
文摘This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment stability property of the viscoelastic system,we use the stochastic averaging method,Girsanov theorem and Feynmann-Kac formula to derive the approximate analytic expansion of the moment Lyapunov exponent.Furthermore,the Monte Carlo simulation results for the original system are given to check the accuracy of the approximate analytic results.At the end of this paper,results are presented to show some quantitative pictures of the effects of the system parameters,noise parameters and viscoelastic parameters on the stability of the viscoelastic plate.
