The behavior of the aerodynamic pendulum with vertical axis of rotation
Parametric analysis of the behavior of an aerodynamic pendulum is carried out, motivated by the study of a small wind power generator with a vertical axis. A mathematical model for the free rotation of this pendulum is constructed, leading to a system of nonlinear ODEs and transcendental algebraic equations. A qualitative analysis of the phase portrait is carried out: all equilibrium solutions are found, their stability is studied, characteristics of a stable rotational regime are determined; and domains of attraction for equilibrium solutions and for the rotational regime are also found. The mathematical model is used to study the operational regimes of the system “wind turbine + generator”. Estimations of the trapped power as a function of the external load in the circuit are obtained; optimal values for the power and the load are found. A pitch angle control mechanism is proposed in order to increase this power.