Fast-Slow Bursting Behaviors Of Multiple-Timescale Hydroelectric Governing System And Its Stability Analyses

Safe,efficient and stable operation is a necessary condition for constructions and maintenances of the hydropower industry.The hydroelectric governing system is the main part which plays an active role in ensuring the power generation,transmission,and regulation in the hydropower station.Characteristic stability studies are the key to ensure the stable operation.Fast-slow bursting oscillations are terrible manifestations affecting the safe and stable operation of the hydroelectric governing system.The terrible bursting might cause serious effects to the electromechanical system.The instability of the electromechanical system due to the severity of a fault or unexpected event from bursting occurrences can lead to the destruction of the whole power system of hydropower plants.The dynamic behaviors of the fast-slow bursting oscillations existing in hydroelectric governing system via periodic excitations are investigated.We integrate the nonelastic water column model of the hydro-turbine with the third-order nonlinear generator model.Further,we introduce the periodic functions of the hydraulic derivative coefficient and the electric field voltage.Based on the novel integrated nonlinear mathematical model of the hydroelectric governing system and the double periodic excitations claimed from the fast-slow analysis method,the fast-slow bursting behaviors of the system are found.The nonlinear dynamic behaviors of the system regarding the derivative gain,excitation frequency,and excitation amplitude are illustrated via bifurcation diagrams,time waveforms,phase trajectories,and power spectrums.The results show that the governing system sustains distinct kinds of nonlinear dynamic behaviors depending on the sensitive parameter values.The system can escape from the fast-slow bursting phenomenon when k_d grows larger.The increase ofΩleads the system to the stable state.However,the increase of B leads the system to the robust fast-slow bursting state.Finally,the analytical method and the results provide principal references for the sensitive parameter setting to guard the hydroelectric governing system from the fast-slow bursting behaviors caused by double periodic excitations and ensure the safe and stable operation of hydroelectric power stations.The dynamic behaviors of the fast-slow bursting oscillations existing in the multiple-timescale hydroelectric governing system are studied.We integrate the hydro-turbine elastic water hammer model together with the third-order nonlinear generator model.Then,we introduce the multiple timescale dynamics as well as the periodic excitation of the electric field voltage together to compose a novel mathematical model of the multi-timescale hydroelectric governing system.Based on the fast-slow analysis method,the nonlinear characteristics of the bursting oscillations with different timescale parameters are analyzed.Additionally,the influences of sensitive parameters(viz.the derivative gain of governor and the excitation amplitude)on the safe running of the governing system are discussed via the bifurcation diagrams,time waveforms,phase trajectories,and power spectrums.The results express that the multi-timescale system contains absolute fast-slow bursting dynamics or periodic fast-slow bursting dynamics depending upon the values of the timescale parameter.During the existing of the fast-slow bursting oscillations,the higher values of the derivative gain k_d are harmful to the operation of the hydroelectric station.Moreover,the lower values of the excitation amplitude B are secure for the operation of the hydroelectric station.Finally,the results provide the principal theoretical basis for comprehending and further researching the impacts of fast-slow bursting behaviors existing in the multi-timescale hydroelectric governing system.The stability and control of the electrical power system have become sensitive issues due to the numerous constructions of power generating stations.Synchronous machine instability occurrences and oscillations due to disturbances are harmful and can lead the system to power failure insecurity.Power system stability studies are conducted to identify power system behaviors and improve the synchronous machine stability by using the excitation control and power system stabilizer(PSS).The seventh-order mathematical model of the power system is established via the single machine infinite bus system model.Power system oscillatory behaviors under the influence of impedances are analyzed;meanwhile,the system stability performances affected by the excitation control system with and without the PSS active are discussed in detail.A single excitation control has a limited ability to dampen system oscillations,especially when the impedance increases.However,the excitation control system with the PSS active has a high ability to return the system from undergoing the disturbance to the stable state.PSS gain of 15 is the optimum value for activating the PSS.This investigation provides basic concepts for research engineers to conduct power system stability studies to ensure the reliable and efficient operations of the electrical power system.