Model And Nonlinear Dynamic Analysis Of Francis Turbine Governing System

Turbine governing system dynamic quality directly affects the security, reliability ofhydropower plant operation and reliability, supply quality of power system; therefore itbecomes very important to establish an appropriate mathmatical model and to analyze itsdymnamic characteristics. Hydraulic turbine regulating system is a complex nonlinear controlsystem, which has non-minimum-phase characteristic and time varying parameter.Hydrodynamics and mechano-electric dynamics are all involved in such a nonlinear dynamicsystem. And its working state includes runing, shutdown, connecting in power network, underunload, etc. It thus compliacte and difficult for the theory and method involved in establishingmathmatical model and analyzing dynamic characteristics.Based on the principle of turbine governing system, this paper divided the hydro-turbinegoverning system into conduit system, hydro-turbine, generator, governor by the modularmodeling method. The model of evey subsystem is deduced and established, and itsadvantages, disadvantages and applicable condition are analyzed. It can be discibed as follows:linear model only is an approximation of system, nonlinear model can more accurately reflectthe system charaterristics; linearized model is only applicable to study the motioncharacteristcs under small fluctuations, while nonlinear model can be used in any disturbance;the analysis theory of linear model is more mature, and its results can reflect some basicfeatures of dynamic process; the description and analysis results of nonlinear model are moreaccurate, and its analysis and simulation becomes more mature and convenience. Soestablishing sutabile mathematical model should be depended on specific purpose andrequirments.On the basis of subsystem mathematiacal model, the integrating methords andprecautions are put forward in this paper. And two commonly used nonlinear models, singlemachine single tube simple model and nonlinear model with a surge tank and long tailrace,which suit for large fluctuations, are established.In this paper, stability theory, bifurcation theory and numerical calculating methods ofmomvement characteristics are simply introduced. And algorithm criterion for Hopfbifurcation of four and high dimentional system and the simple calculating methodes ofpower spectrum and Lyapunov exponents are described in detail. This paper analysis the nonlinear dynamic characteristics of the model, base on thenonlinear dynamics theory. Mainly includes: the bifurcation characteristics while systemparameter changes, the stability of system and movement characteristics while select thesystem parameters.Through research and analysis to get these following conclusion:Hopf bifurcation theory of nonlinear system is applicable to the analysis of hydro-turbinegoverning system. It can be applied to solute the stability domain of the system parameters.These results provide a new way for select the parameter of hydro turbine governing system.Low-frequency oscillation amplitude may exist, if the governor parameters are notproper, when the system is subject to external disturbance or not. Parameters of the system arethe critical bifurcation point. This phenomenon provides a possible explanation for the lowfrequency oscillation phenomena of hydropower station.The system motion is periodic motion, whether the system is divergent, convergent orthe oscillation amplitude, when adjustment parameter values in a certain range. Thisphenomenon also provides that the more difference between the adjustment parameter and thebifurcation critical value, the better dynamic stability performance the system has.The influence of different system parameters on the stability domain is not identical.Larger unit inertia time constant, larger water diversion pipeline friction coefficient, largerdamping coefficient of the velocity deviation can increase system stability domain, while, thelarger water inertia time constant and the larger response time to servomotor parameters canreduce system stability domain.