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A nonlinear mathematical model for hydro turbine governing system with saturation nonlinearity in small perturbation has been proposed with all the essential components,i.e. turbine,PID type governor with saturation part and generator included in the model. Existence,stability and direction of Hopf bifurcation of an example HTGS are investigated in detail and presented in forms of bifurcation diagrams and time waveforms. The analysis show that a supercritical Hopf bifurcation may exist in hydraulic turbine systems in some certain conditions. Moreover,the dynamic behavior of system with different parameters such as Tw,Tab,Tyand K are studied extensively. An example with numerical simulations is presented to illustrate the theoretical results. The researches provide a reasonable explanation for the Hopf phenomenon happened in operation of hydroelectric generating unit.
A nonlinear mathematical model for hydro turbine governing system with saturation nonlinearity in small perturbation has been proposed with all the essential components, ie turbine, PID type governor with saturation part and generator included in the model. Existence, stability and direction of Hopf bifurcation of an example HTGS are investigated in detail and presented in forms of bifurcation diagrams and time waveforms. The analysis show that a supercritical Hopf bifurcation may exist in hydraulic turbine systems in some certain conditions. Furthermore, the dynamic behavior of system with different parameters such as Tw, Tab. Tyand K are studied extensively. The example of numerical simulations is presented to illustrate the theoretical results. The researches provide a reasonable explanation for the Hopf phenomenon happened in operation of hydroelectric generating unit.