Dynamic analysis and modeling of a novel fractional-order hydro-turbine-generator unit

In order to study the stability of a hydro-turbine-generator unit in further depth, we establish a novel nonlinear fractional-order mathematical model considering a fractional-order damping force, a fractional-order oil-film force, an asymmetric magnetic pull and a hydraulic-asymmetric force. Furthermore, the nonlinear dynamics of the above fractional-order hydro-turbine-generator unit system with six typical fractional orders are studied in detail. Based on these, we analyze the effect of the fractional-order α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} on bifurcation points, the orbit of centroid of the rotor, the power and the frequency of the rotor. Fortunately, some variable laws are found from numerical simulation results. Finally, all of these results have enriched the dynamical behaviors of a hydro-turbine-generator system.