This work studies the stability and hidden dynamics of the nonlinear hydro-turbine governing system with an output limiting link,and propose a new six-dimensional system,which exhibits some hidden attractors.The param...This work studies the stability and hidden dynamics of the nonlinear hydro-turbine governing system with an output limiting link,and propose a new six-dimensional system,which exhibits some hidden attractors.The parameter switching algorithm is used to numerically study the dynamic behaviors of the system.Moreover,it is investigated that for some parameters the system with a stable equilibrium point can generate strange hidden attractors.A self-excited attractor with the change of its parameters is also recognized.In addition,numerical simulations are carried out to analyze the dynamic behaviors of the proposed system by using the Lyapunov exponent spectra,Lyapunov dimensions,bifurcation diagrams,phase space orbits,and basins of attraction.Consequently,the findings in this work show that the basins of hidden attractors are tiny for which the standard computational procedure for localization is unavailable.These simulation results are conducive to better understanding of hidden chaotic attractors in higher-dimensional dynamical systems,and are also of great significance in revealing chaotic oscillations such as uncontrolled speed adjustment in the operation of hydropower station due to small changes of initial values.展开更多
A fast-slow coupled model of the hydro-turbine governing system （HTGS） is established by introducing frequency disturbance in this paper. Based on the proposed model, the performances of two time scales for bursting...A fast-slow coupled model of the hydro-turbine governing system （HTGS） is established by introducing frequency disturbance in this paper. Based on the proposed model, the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams, time waveforms and phase portraits. We find that stability and operational characteristics of the HTGS change with the value of system parameter kd. Furthermore, the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out. Meanwhile, we obtain that the relative deviation of the mechanical torque mt rises with the increase of a. These methods and results of the study, combined with the performance of two time scales and the fast-slow coupled engineering model, provide some theoretical bases for investigating interesting physical phenomena of the engineering system.展开更多
This paper investigates the stability of the Francis hydro-turbine governing system with complex penstocks in the grid-connected mode. Firstly, a novel fractional-order nonlinear mathematical model of a Francis hydro-...This paper investigates the stability of the Francis hydro-turbine governing system with complex penstocks in the grid-connected mode. Firstly, a novel fractional-order nonlinear mathematical model of a Francis hydro-turbine governing system with complex penstocks is built from an engineering application perspective. This model is described by state-space equations and is composed of the Francis hydro-turbine model, the fractional-order complex penstocks model, the third-order generator model, and the hydraulic speed governing system model. Based on stability theory for a fractional-order nonlinear system, this study discovers a basic law of the bifurcation points of the above system with a change in the fractional-order a. Secondly, the stable region of the governing system is investigated in detail,and nonlinear dynamical behaviors of the system are identified and studied exhaustively via bifurcation diagrams, time waveforms, phase orbits, Poincare maps, power spectrums and spectrograms. Results of these numerical experiments provide a theoretical reference for further studies of the stability of hydropower stations.展开更多
Hydro-turbine governing system is a time-varying complex system with strong non-linearity,and its dynamic characteristics are jointly affected by hydraulic,mechanical,electrical,and other factors.Aiming at the stabili...Hydro-turbine governing system is a time-varying complex system with strong non-linearity,and its dynamic characteristics are jointly affected by hydraulic,mechanical,electrical,and other factors.Aiming at the stability of the hydroturbine governing system,this paper first builds a dynamic model of the hydro-turbine governing system through mechanism modeling,and introduces the transfer coefficient characteristics under different load conditions to obtain the stability category of the system.BP neural network is used to perform the machine study and the predictive analysis of the stability of the system under different working conditions is carried out by using the additional momentum method to optimize the algorithm.The test set results show that the method can accurately distinguish the stability category of the hydro-turbine governing system(HTGS),and the research results can provide a theoretical reference for the operation and management of smart hydropower stations in the future.展开更多
基金the Fundamental Research Funds for the Northwest A&F University(Grant No./Z1090220172)the Scientific Research Foundation of the Natural Science Foundation of Shaanxi Province,China(Grant No.2019JLP-24)+1 种基金the Shaanxi Province Innovation Talent Promotion PlanScience and Technology Innovation Team,China(Grant No.2020TD-025)the Water Conservancy Science and Technology Program of Shaanxi Province,China(Grant No.2018slkj-9)。
文摘This work studies the stability and hidden dynamics of the nonlinear hydro-turbine governing system with an output limiting link,and propose a new six-dimensional system,which exhibits some hidden attractors.The parameter switching algorithm is used to numerically study the dynamic behaviors of the system.Moreover,it is investigated that for some parameters the system with a stable equilibrium point can generate strange hidden attractors.A self-excited attractor with the change of its parameters is also recognized.In addition,numerical simulations are carried out to analyze the dynamic behaviors of the proposed system by using the Lyapunov exponent spectra,Lyapunov dimensions,bifurcation diagrams,phase space orbits,and basins of attraction.Consequently,the findings in this work show that the basins of hidden attractors are tiny for which the standard computational procedure for localization is unavailable.These simulation results are conducive to better understanding of hidden chaotic attractors in higher-dimensional dynamical systems,and are also of great significance in revealing chaotic oscillations such as uncontrolled speed adjustment in the operation of hydropower station due to small changes of initial values.
基金Project supported by the Scientific Research Foundation of the National Natural Science Foundation of China–Outstanding Youth Foundation(Grant No.51622906)the National Natural Science Foundation of China(Grant No.51479173)+3 种基金the Fundamental Research Funds for the Central Universities,China(Grant No.201304030577)the Scientific Research Funds of Northwest A&F University,China(Grant No.2013BSJJ095)the Science Fund for Excellent Young Scholars from Northwest A&F University(Grant No.Z109021515)the Shaanxi Provincial Nova Program,China(Grant No.2016KJXX-55)
文摘A fast-slow coupled model of the hydro-turbine governing system （HTGS） is established by introducing frequency disturbance in this paper. Based on the proposed model, the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams, time waveforms and phase portraits. We find that stability and operational characteristics of the HTGS change with the value of system parameter kd. Furthermore, the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out. Meanwhile, we obtain that the relative deviation of the mechanical torque mt rises with the increase of a. These methods and results of the study, combined with the performance of two time scales and the fast-slow coupled engineering model, provide some theoretical bases for investigating interesting physical phenomena of the engineering system.
基金supported by the Scientific Research Foundation of the National Natural Science Foundation-Outstanding Youth Foundation(No.51622906)National Natural Science Foundation of China (No.51479173)+4 种基金Fundamental Research Funds for the Central Universities (201304030577)Scientific Research Funds of Northwest A&F University (2013BSJJ095)the Scientific Research Foundation for Water Engineering in Shaanxi Province (2013slkj-12)the Science Fund for Excellent Young Scholars from Northwest A&F University (Z109021515)the Shaanxi Nova Program (2016KJXX-55)
文摘This paper investigates the stability of the Francis hydro-turbine governing system with complex penstocks in the grid-connected mode. Firstly, a novel fractional-order nonlinear mathematical model of a Francis hydro-turbine governing system with complex penstocks is built from an engineering application perspective. This model is described by state-space equations and is composed of the Francis hydro-turbine model, the fractional-order complex penstocks model, the third-order generator model, and the hydraulic speed governing system model. Based on stability theory for a fractional-order nonlinear system, this study discovers a basic law of the bifurcation points of the above system with a change in the fractional-order a. Secondly, the stable region of the governing system is investigated in detail,and nonlinear dynamical behaviors of the system are identified and studied exhaustively via bifurcation diagrams, time waveforms, phase orbits, Poincare maps, power spectrums and spectrograms. Results of these numerical experiments provide a theoretical reference for further studies of the stability of hydropower stations.
文摘Hydro-turbine governing system is a time-varying complex system with strong non-linearity,and its dynamic characteristics are jointly affected by hydraulic,mechanical,electrical,and other factors.Aiming at the stability of the hydroturbine governing system,this paper first builds a dynamic model of the hydro-turbine governing system through mechanism modeling,and introduces the transfer coefficient characteristics under different load conditions to obtain the stability category of the system.BP neural network is used to perform the machine study and the predictive analysis of the stability of the system under different working conditions is carried out by using the additional momentum method to optimize the algorithm.The test set results show that the method can accurately distinguish the stability category of the hydro-turbine governing system(HTGS),and the research results can provide a theoretical reference for the operation and management of smart hydropower stations in the future.
