A new low‐order mathematical model is introduced to analyse blade dynamics and blade load‐reducing control strategies for wind turbines. The model consists of a typical wing section model combined with a rotor speed model, leading to four structural degrees of freedom (flapwise, edgewise and torsional blade oscillations and rotor speed). The aerodynamics is described by an unsteady aerodynamic model. The equations of motion are derived in non‐linear and linear form. The linear equations of motion are used for stability analysis and control design. The non‐linear equations of motion are used for time simulations to evaluate control performance. The stability analysis shows that the model is capable of predicting classical flutter and stall‐induced vibrations. The results from the stability analysis are compared with known results, showing good agreement. The model is used to compare the performance of one proportional–integral–derivative controller and two full‐state feedback controllers. Copyright © 2006 John Wiley & Sons, Ltd.

This paper extends Hodges–Dowell's partial differential equations of blade motion, by including the effects from gravity, pitch action and varying rotor speed. New equations describing the pitch action and rotor speeds are also derived. The physical interpretation of the individual terms in the equations is discussed. The partial differential equations of motion are approximated by ordinary differential equations of motion using an assumed mode method. The ordinary differential equations are used to simulate a sudden pitch change of a rotating blade. This work is a part of a project on pitch blade interaction, and the model will be extended to include an aerodynamic model and be used for analysis of basic properties of pitch blade interaction. Copyright © 2007 John Wiley & Sons, Ltd.

This paper deals with effects of geometric non-linearities on the aeroelastic stability of a steady-state defl ected blade. Today, wind turbine blades are long and slender structures that can have a considerable steady-state defl ection which affects the dynamic behaviour of the blade. The fl apwise blade defl ection causes the edgewise blade motion to couple to torsional blade motion and thereby to the aerodynamics through the angle of attack. The analysis shows that in the worst case for this particular blade, the edgewise damping can be decreased by half.

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