Analysis of bifurcation and stable region for water turbine generator shaft torsional vibrations

Using Lagrange equations, a set of differential equations are established, to research the local stability and bifurcation at the equilibrium point of water turbine generators for shaft torsional vibrations. It is proved that there isn't Hopf bifurcation for normal parameters in the parameter space. The water tubine generator's stable region is estimated by the Lyapnuov function, and the stable bifurcations are testi-fied by Sanxia water turbine generator's simulation.