We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic forc...We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell- Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.展开更多
Wind energy sources have different structures and functions from conventional power plants in the power system.These resources can affect the exchange of active and reactive power of the network.Therefore,power system...Wind energy sources have different structures and functions from conventional power plants in the power system.These resources can affect the exchange of active and reactive power of the network.Therefore,power system stability will be affected by the performance of wind power plants,especially in the event of a fault.In this paper,the improvement of the dynamic stability in power system equipped by wind farm is examined through the supplementary controller design in the high voltage direct current(HVDC)based on voltage source converter(VSC)transmission system.In this regard,impacts of the VSC HVDC system and wind farm on the improvement of system stability are considered.Also,an algorithm based on controllability(observability)concept is proposed to select most appropriate and effective coupling between inputs-outputs(IO)signals of system in different work conditions.The selected coupling is used to apply damping controller signal.Finally,a fractional order PID controller(FO-PID)based on exchange market algorithm(EMA)is designed as damping controller.The analysis of the results shows that the wind farm does not directly contribute to the improvement of the dynamic stability of power system.However,it can increase the controllability of the oscillatory mode and improve the performance of the supplementary controller.展开更多
In this paper,the asymptotic stability with probability one of multi-degree-of-freedom(MDOF)nonlinear oscillators with fractional derivative damping parametrically excited by Gaussian white noises is investigated.A st...In this paper,the asymptotic stability with probability one of multi-degree-of-freedom(MDOF)nonlinear oscillators with fractional derivative damping parametrically excited by Gaussian white noises is investigated.A stochastic averaging method and the Khasminskii’s procedure are employed to evaluate the largest Lyapunov exponent,whose sign determines the stability of the system.As an example,two coupled nonlinear oscillators with fractional derivative damping is worked out to demonstrate the proposed procedure and to examine the effect of fractional order on the stochastic stability of system.In particular,the case of factional order more than 1 is studied for the first time.展开更多
The stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative of Caputo's definition is analyzed.First,the system state is approximately descr...The stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative of Caputo's definition is analyzed.First,the system state is approximately described by It equations through the stochastic averaging method based on the generalized harmonic function.Then,the associated expression for the largest Lyapunov exponent of the linearized averaged It is derived,and the necessary and sufficient condition for the asymptotic stability with probability one of the trivial solution of the original system is obtained approximately by letting the largest Lyapunov exponent be negative.The effects of fractional orders and random excitation intensities on the asymptotic stability with probability one determined by the largest Lyapunov exponent are shown graphically.展开更多
Anomalous diffusion is a widespread physical phenomenon,and numerical methods of fractional diffusion models are of important scientific significance and engineering application value.For time fractional diffusion-wav...Anomalous diffusion is a widespread physical phenomenon,and numerical methods of fractional diffusion models are of important scientific significance and engineering application value.For time fractional diffusion-wave equation with damping,a difference(ASC-N,alternating segment Crank-Nicolson)scheme with intrinsic parallelism is proposed.Based on alternating technology,the ASC-N scheme is constructed with four kinds of Saul’yev asymmetric schemes and Crank-Nicolson(C-N)scheme.The unconditional stability and convergence are rigorously analyzed.The theoretical analysis and numerical experiments show that the ASC-N scheme is effective for solving time fractional diffusion-wave equation.展开更多
文摘We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell- Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.
文摘Wind energy sources have different structures and functions from conventional power plants in the power system.These resources can affect the exchange of active and reactive power of the network.Therefore,power system stability will be affected by the performance of wind power plants,especially in the event of a fault.In this paper,the improvement of the dynamic stability in power system equipped by wind farm is examined through the supplementary controller design in the high voltage direct current(HVDC)based on voltage source converter(VSC)transmission system.In this regard,impacts of the VSC HVDC system and wind farm on the improvement of system stability are considered.Also,an algorithm based on controllability(observability)concept is proposed to select most appropriate and effective coupling between inputs-outputs(IO)signals of system in different work conditions.The selected coupling is used to apply damping controller signal.Finally,a fractional order PID controller(FO-PID)based on exchange market algorithm(EMA)is designed as damping controller.The analysis of the results shows that the wind farm does not directly contribute to the improvement of the dynamic stability of power system.However,it can increase the controllability of the oscillatory mode and improve the performance of the supplementary controller.
基金supported by the National Natural Science Foundation of China(Grant Nos.10932009,11072212,11272279 and 11002059)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20103501120003)+1 种基金Fujian Province Natural Science Foundation of China(Grant No.2010J05006)Fundamental Research Funds for Huaqiao University(Grant No.JB-SJ1010)
文摘In this paper,the asymptotic stability with probability one of multi-degree-of-freedom(MDOF)nonlinear oscillators with fractional derivative damping parametrically excited by Gaussian white noises is investigated.A stochastic averaging method and the Khasminskii’s procedure are employed to evaluate the largest Lyapunov exponent,whose sign determines the stability of the system.As an example,two coupled nonlinear oscillators with fractional derivative damping is worked out to demonstrate the proposed procedure and to examine the effect of fractional order on the stochastic stability of system.In particular,the case of factional order more than 1 is studied for the first time.
基金supported by the National Natural Science Foundation of China(Grant Nos.10932009,11072212 and 11002059)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20103501120003)+2 种基金the Natural Science Foundation of Fujian Province (Grant No.2010J05006)the Fundamental Research Funds for Huaqiao University(Grant No.JB-SJ1010)the Research & Development Start Funds of Huaqiao University(Grant No.09BS622)
文摘The stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative of Caputo's definition is analyzed.First,the system state is approximately described by It equations through the stochastic averaging method based on the generalized harmonic function.Then,the associated expression for the largest Lyapunov exponent of the linearized averaged It is derived,and the necessary and sufficient condition for the asymptotic stability with probability one of the trivial solution of the original system is obtained approximately by letting the largest Lyapunov exponent be negative.The effects of fractional orders and random excitation intensities on the asymptotic stability with probability one determined by the largest Lyapunov exponent are shown graphically.
基金by the Subproject of Major Science and Technology Program of China(No.2017ZX07101001-01)the Fundamental Research Funds for the Central Universities(Nos.2018MS168 and 2020MS043).
文摘Anomalous diffusion is a widespread physical phenomenon,and numerical methods of fractional diffusion models are of important scientific significance and engineering application value.For time fractional diffusion-wave equation with damping,a difference(ASC-N,alternating segment Crank-Nicolson)scheme with intrinsic parallelism is proposed.Based on alternating technology,the ASC-N scheme is constructed with four kinds of Saul’yev asymmetric schemes and Crank-Nicolson(C-N)scheme.The unconditional stability and convergence are rigorously analyzed.The theoretical analysis and numerical experiments show that the ASC-N scheme is effective for solving time fractional diffusion-wave equation.
