Modal Response of 3-Bladed Wind Turbines

A set of linear equations describing the motion of an operating 3-bladed HAWT are obtained from the dynamic characteristics of the stationary turbine by adding rotating frame effects. The approach makes use of the Coleman multi-blade transformation to present all results relative to the fixed frame. The formulation is in terms of a selected number of stationary, real, mode shapes. The formulation is applied to the expression of both the aerodynamic loading and the displacement response in terms of the operating mode shapes. This technique is applied to the conditions of vertical wind shear and off-yaw operation of a hypothetical 46-m wind turbine. The principal objective of the paper is to enable the characteristic of the inflow to be related to the nature of the response. A second objective is to illustrate a method of extracting linearized models from general aeroelastic codes such as ADAMS™.