Stability And Bifurcation Analysis Of Hydraulic Power Generation System Excited By Stochastic Noise

At present,with the development of China’s economy and science and technology,the hydropower industry is also rising rapidly.Due to the factors of domestic environmental protection,energy conservation and emission reduction and power supply and demand,the scale of hydropower stations is getting larger and larger,and the demand is also getting larger and larger.As the core part of the hydropower station,the subsystem of the hydroelectric generator system presents complex nonlinear characteristics.In the actual working condition of water motor system,its stability will be affected by various forms.For example,the damage problem of water pipe in the case of continuous impact of water hammer and the internal structure of the whole turbine unit in the operation process leads to the phenomenon of self-excited vibration of the system.The emergence of these problems will reduce the power generation efficiency of the hydropower station system and reduce the safety and stability of the unit,and may also appear the rejection situation when the power system is grid-connected.In this paper,considering the influence of random factors on the regulating system of hydraulic turbine with surge chamber,the multiplicative noise excitation is added to the system model to make it more close to the real working conditions.Then it is explored in detail through stochastic stability and stochastic bifurcation theory,such as stochastic bifurcation theory,stochastic average method,Lyapunov exponential method,numerical simulation and so on.Research contents of this paper:1.This paper describes in detail the research history and present situation of the regulating system of water turbine at home and abroad,and puts forward the purpose and significance of choosing this topic.Then the stability analysis of stochastic dynamics and the theoretical knowledge of bifurcation,the definition of random noise,the numerical method of stochastic numerical simulation and the principle of color noise in the application of the system are introduced.2.The stability and random Hopf bifurcation of the hydraulic turbine regulation system under white noise excitation are studied.The Turbine regulating system with gaussian white noise is transformed into two dimensional stochastic differential equation by the stochastic order reduction method and center manifold.The stochastic stability of the trivial solution of the modulus equation is analyzed by the maximal Lyapunov exponent and the singular boundary theory,and the corresponding local and global stability conditions of the turbine system are obtained.Then,the bifurcation and bifurcation behavior of the hydraulic turbine system are analyzed.The results of numerical simulation show that the Monte Carlo simulation is in good agreement with the analytical solution,which shows the effectiveness of the proposed method.After,numerical simulation,it is found that the hydraulic turbine system will become unstable with the decrease of parameterμ₄ under the influence of white noise.3.The stability and Hopf bifurcation of the regulating system of hydraulic turbine under color noise excitation are studied.In this paper,the uniform color noise approximation principle and equivalent nonlinearization method are used to transform the system into a simple nonlinear white noise system model.By using the theory of stochastic nonlinear dynamics of the stochastic averaging method and center manifold,reduced the system with white noise into two-dimensional differential equation,using the theory of maximum Lyapunov index and singular boundary respectively discusses the local and global stability of the sufficient conditions of the line,and through the analysis of the qualitative change and degradation of invariant measure FPK equations function change of shape,explores the system D bifurcation and P bifurcation scenario.It is found by numerical simulation that as the noise intensity decreases,the system in the unstable state will approach to the stable state.