Dynamic Behavior Analysis,Control And Synchronization Of Chaotic System

In the process of power system operation,the system will produce low-frequency oscillation due to the changes of system parameters or external disturbances,which will lead to chaotic motion,periodic motion and other behaviors that are not conducive to the stability of the system.Therefore,it is of great significance to study the dynamic behavior of the power system for the stable operation of the power system.In this thesis,the dynamic behaviors and controlled problems in the third-order model of power system are mainly discussed.In the first part,the dynamical behaviors,controlled and synchronization problems are investigated in the third-order model of the integer order power system.The bifurcation diagram,Lyapunov exponential diagram and phase diagram of the corresponding differential equations are obtained by numerical simulation using the existing third-order mathematical model of power system.Furthermore,the influences of system parameters change on the dynamic behavior of the system are analyzed,and the Hopf bifurcation and chaos phenomena occur with the change of system parameters under certain conditions.By calculating the divergence of a vector field of the system,the dissipation of the system is obtained,and the fractal dimension of the system is calculated.When chaos appears,two controlled schemes of adaptive control and nonlinear feedback control are presented,respectively,to verify the proposed controlled schemes by using Lyapunov stability theory.In addition,the controller design scheme is discussed when some parameters are unknown.By constructing Lyapunov function,it is proved theoretically that three schemes can make the system asymptotically stable.Then,the synchronization of drive and response is considered when all parameters of the system are unknown.Finally,three controlled schemes are simulated numerically.In the second part,the dynamical behaviors and controlled problems are discussed in the third-order model of the fraction order power system.Firstly,the stability of the system is discussed.The system parameters are unchanged,only the order of the system is changed.By means of the fractional bifurcation diagram and the maximum Lyapunov exponential diagram,the approximate order of chaos in the same order fractional system and the different order fractional system is calculated and verified by simulation.Then,the controlled problems of fractional order system are discussed.By analogy with the integer order controlled design schemes,two chaotic controlled schemes of fractional order with known parameters are proposed,namely adaptive control and nonlinear feedback control,and then a controller design scheme with unknown parameters is proposed.Finally,all the schemes are numerically verified.