Complex Behavior of a Wind Turbine Induced by Nonlinear Aerodynamics

Rotational speed increases as wind speed is ideal for a small wind turbine because the turbine outputs maximum power under the specific speed. Different average rotational speeds of a windmill were recorded at a low mean wind speed in field tests. The low rotational speeds would give rise to passive optimal control of the wind turbines failure. Furthermore, the varied rotation speeds would be relative to a hysteresis induced by saddle-node bifurcations for the small wind turbine in variant electric loads. Meanwhile, the variety of the rotational speeds fades away as moderate or fresh breeze constantly blowing. This study investigated the mechanism of the disappearance of the varied rotational speeds. Bifurcation lines of saddle-node bifurcation points were observed at variant electric loads and different wind speeds via a nonlinear mathematical model for the wind turbine. The bifurcation diagram demonstrates that the bifurcation lines close each other at a narrow variation of low electric loads as increasing wind speed. The movement of the bifurcation lines expresses why the varied rotational speeds were observed only at low wind speeds. The dynamics are important to the design of optimal control algorithms for small wind turbines.