Abstract： A nonlinear model was established for a hydroturbine speed governing system with complex penstocks to study nonlinear behaviors of the system. A response curve with critical points of Hopf Bifurcation was obtained through a theoretical analysis. It was shown that the system is stable on one side of the curve but unstable on the other side. The stability of the system was analyzed on both sides of the Hopf bifurcation curve by means of numerical simulations. These simulations not only justified the theoretical analysis but also determined a proper range of PID parameters for a stable governor. The nonlinear dynamic behaviors of the governing system were clarified by using bifurcation diagram, Poincare map, power spectrum diagram, time domain diagram, phase orbits diagram and a spectrum diagram. These analysis methods and results will be useful for allowing a hydropower station in safe operations.
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