Stability And Bifurcation Theories Of Dynamical Systems And Its Applications

In this paper, we study the application of qualitatively, stability and bifurcation theories of dynamics systems in power systems. We discover that parameters play an important role in stability and feasibility region of the power systems. The results provide methods to decide stability and domain of parameters.The paper consists of two chapters. The first chapter introduces some fundamental definitions and theorems of dynamics systems such as bifurcation and stability theory. In the second chapter, we study the complex nonlinear phenomena in a fundamental power system provided by paper , especially the effects of parameters on bifurcation and stability. We apply different ways from article [6] to analyze local stability and bifurcation of balance position in the dynamics systems. When and with control There are two sorts of fixed points, One is stable, While the other is always unstable. is saddle-node bifurcation value, corresponding to breakdown of the power system. As , There is not any fixed point. We also apply Lyapunov function to evaluate the attraction region of stable fixed point which corresponds to running region of the power system, We give the boundary of stability region by means of article [8], Finally, the numerical simulate results verify the theoretical analysis.