Nonlinear Behaviors of a Small Wind Turbine Induced by Aerodynamics and Electromagnetic Field

Abstract

Modern small wind turbines output maximum electricity with the use of optimal controllers such as maximum power point tracking. A windmill would rotate at a speed around an optimal value for a specific wind speed under the control algorithms. Some of the average rotational speeds far beyond the optimal value were remarked at light wind in some field tests, and the variety of the speed dissolves as moderate or fresh breeze blowing repeatedly. The phenomenon could bring about passive optimal control failure. Furthermore, some investigations observed a hysteresis consisted of a couple of saddle-node bifurcations which are induced by nonlinear aerodynamics of the small windmill at different electricity output. This paper analyzed the behaviors of a small wind turbine through considering the coupling of the aerodynamics of the windmill and the electromagnetic field of a permanent magnet synchronize generator via a nonlinear mathematic model. More than two saddle-node bifurcations exist in the wind turbine system. Two sets of the saddle-node bifurcations separate the equilibrium points of the system into three leading branches. Moreover, two Hopf bifurcations were observed as well. The bifurcations induce the whirling speeds of the turbine spread over the lower leading branch of the equilibrium points. Meanwhile, a jump phenomenon from the saddle-node bifurcation clears up the variation at blowing fresh breeze. The bifurcation diagram demonstrates the reason that the variant whirling speeds were detected only at light breeze. The observed phenomena would inspire different optimum control design of small wind turbines.