Stability And Hopf Bifurcation Study On A Class Of Nonlinear Dynamics Hydro-turbine Governing Systems Model

The hydro-turbine governing system is constituted by hydropower,electricity and machine module,considered as a classical nonlinear dynamic system with abundant dynamic characteristics.Furthermore the structure and the control process of the system are relatively complicated.The stability of the hydro-turbine governing system is a key part to the security and stability of the whole hydropower.In recent years,guarantying the power system frequency stability and improving the stability of the hydropower system is research focus by optimization algorithm,the application of new materials and new technology,which has great realistic significance.Based on different actual demand,three different models of turbine governing system are established.We applied the basic theory of nonlinear dynamics and scientific analysis method,such as Hopf bifurcation theory,the center manifold theorem,Routh Routh-Hurwitz criterion and numerical simulation.The parameters that determine the stability and Hopf bifurcation of the system is mainly analyzed Main content of this paper are as follows:1.The paper introduces development process and domestic and overseas research status of the hydro-turbine governing system.Research purposes and significance are proposed.Meanwhile,stability theory,high-dimensional Hopf bifurcation,center manifold theorem and numerical simulation method are given.2.The slot supply hydropower station is analyzed.We ignore the resilience of the piping system,and assume that the diversion pipeline is shorter.Using the rigid model,a six-dimension hydro-turbine governing state equation with a straight-tube surge tank is established by analyzing hydropower station.Utilizing theory and numerical method,the nonlinear dynamic behavior of the system is researched.3.Since the diversion pipeline has viscosity,the hydro-turbine governing system has a memory in time and space,and non-locality.A single machine single tube simple hydro-turbine governing model with four-dimension is researched by fractional calculus theory.Based on definition and numerical solution method of the fractional order system,we obtain a positive definite Lyapunov function.Using the group theorem of Galois,we analyze the stability of the system.4.Firstly,a PI hydro-turbine governing system with saturation module is established,which exists control delays in the terms of the speed and the position of the servomotor.Second,we investigate the stability of equilibrium points and HopfBifurcation for PI hydro-turbine governing system under the four different delay cases.The direction and stability of the Hopf Bifurcation is determined by three parameters.Finally,some time sequence diagram,phase trajectory and numerical simulation illustrate the dynamic behavior of the system.