Existence Of Hidden Attractors Of Pumped Storage Power Station Under Typical Working Conditions And Its Stability Analysis

Pumped storage power station,as a flexible adjustable power source for power grid dispatching,new energy power consumption and network source coordination,its stable operation is very important for power security and energy security.With the high proportion of wind and solar intermittent energy entering the power grid,the fluctuation of the power grid is aggravated.Due to the complex switching conditions and hydro electromechanical coupling behavior,pumped storage will show rich dynamic behavior,even more complex chaotic characteristics,which affects the dynamic stability of the system.As a special chaotic state,the existence of hidden attractor will cause sudden changes in the speed of the system due to the unexpected disturbance of the attractor,which makes the system vibration difficult to predict.It is an internal inducing factor that affects the stable and safe operation of the power station.In this paper,the influence of hidden attractors on the dynamic stability of pumped storage power station is studied under the typical working conditions(turbine,pump,pump power failure)(1)According to the operation condition of hydraulic turbine,combined with various nonlinear analysis tools(bifurcation diagram,time domain diagram,phase diagram,Lyapunov exponent spectrum diagram,and basin of attraction diagram,etc.),the influence of integer order to fractional order on the bifurcation characteristics and stability of the governing system is studied by taking the governing parameter k_p and fractional order as controllable parameters.Through numerical simulation,it is found that the equilibrium point is stable when the system adjusts the parameter k_p=5.3,and the basin of attraction of the chaotic attractor generated by the system does not intersect with the neighborhood of the equilibrium point,which indicates the existence of the hidden attractor.Secondly,the fractional order model is extended to the fractional order model with memory and history dependence,and the chaotic mode of the system under different orders is analyzed.By observing the drawn basin,it can be concluded that the stability of the hydraulic turbine governing system will change with different initial opening values,which makes the system prone to different dynamic behaviors due to the existence of hidden attractors.(2)Taking the pump turbine governing system as the research object,by studying the relationship between the equilibrium point and the hidden attractor of the pump turbine governing system,combined with the Lyapunov exponent spectrum,bifurcation diagram,time domain diagram and basin of attraction diagram and other nonlinear dynamic analysis tools,multi angle analysis of the system under different conditions of steady-state and pump power-off transient with the regulation parameter k_d and different guide vanes is carried out.Based on the bifurcation and stability characteristics of the opening y,the stability evolution law of the system depending on the regulation parameter k_d and the initial value of the guide vane opening is studied.The results show that,with the change of governor parameter k_d,there is no equilibrium point in the system,but the dynamic behaviors such as asymptotic stability,limit cycle and chaos appear in the system.It is found that there are hidden attractors in the system.Combined with bifurcation diagram,the hidden dynamic behaviors in the system are discussed.At the same time,considering the nonlinear characteristics of governor,the stability of the system is obviously affected.The smaller and slower change of guide vane opening y can improve the stability performance of the system in the transition process.(3)The basin of attraction is a tool to study the attractor and stability of the system.By studying the variation law of the suction basin with different initial values such as guide vane opening,the rich dynamics of the system under different working conditions are comprehensively observed,including chaos,etc.Secondly,it reflects that the topological shape of the suction basin can be changed under different operating conditions,and the water flow is stable.The topology of suction basin is more complex in turbine condition than in pump condition.Due to the existence of hidden attractor,the system may have chaotic oscillation phenomenon such as speed regulation out of control due to small change of initial value,which is worthy of attention in the actual operation process of power station.