Non-linear dynamic behavior of a wind turbine under aerodynamic periodic loads

Abstract

Numerical simulations for studying the structural dynamics behavior of a three-bladed horizontal-axis wind turbine under aerodynamic loads are developed in this paper with the objective of studying the non- linear characteristics of such res ponse. The equations of motion are derived using Lagrange Equations and considering non-holonomic constraints which are inco rporated explicitly through the use of Lagrange Multipliers . The numerical model includes: ( i ) three blades, ( ii ) the nacelle; and ( iii ) the tower. The blades are considered as a set of multiple rigid bodies, perfectly a ttached to the hub, which connects them to the generator rotating shaft. The nacelle and the tower are modeled as bodies with concentr ated parameters, including rotational inertia. Aerodynamics loads acting on the blades are modeled as space-invariant distributed load with a time-varying magnitude. Changes on the aerodynamic load magnitude depend on the following factors: i ) rotor speed and ii ) wind speed variation with height, which de pends on the surface roughness. Besides, not only aerodynamic loads are considered in the model, but also electromagnetic damping and a control moment coming from the electrical generator. This moment is th e parameter normally used to control the rotor angular speed.