Dynamic characteristics for a hydro-turbine governing system with viscoelastic materials described by fractional calculus

This paper brings attention to the dynamic characteristics of a hydro-turbine governing system with viscoelastic materials. Fractional calculus is introduced to established a diversified nonlinear mathematical model of a hydro-turbine governing system, considering the memory characteristic of the viscoelastic materials of the hydraulic servo system. Furthermore, the effect of different fractional orders on the generator speed is studied by analysis of fractional bifurcation diagrams, time waveforms, phase orbits, Poincare maps, power spectrums and spectrograms. Fortunately, some motion laws of the bifurcation points and chaotic regions with the increase of fractional order α are obtained, and the safe range of kd with different fraction order is presented. All of the above results provide a sound theoretical basis for designing and running of the hydro-turbine governing system.