Dynamic modeling and analysis of gyroscopic effects in bottom-fixed wind turbines under normal and extreme wind conditions

This study develops an 11-degree-of-freedom nonlinear model for bottom-fixed wind turbine systems via Lagrangian mechanics, incorporating blade and tower bending, rotor and generator rotations, and—critical for gyroscopic analysis—tower torsion. The analytical gyroscopic matrix is derived through an optimal linearization method to fully characterize gyroscopic coupling within the system. On this basis, three gyroscopic models are constructed to comprehensively analyze gyroscopic effects on system responses and long-term load assessments under both normal and extreme wind conditions, with wind shear and yaw misalignments incorporated. The findings highlight that retaining the first- and second-order terms of the velocity field expressed in local coordinates, together with applying small-angle approximations, constitutes the most efficient linearization method for accurately deriving the system mass, gyroscopic, and stiffness matrices. Under both normal and extreme operating conditions, gyroscopic forces are negligible compared with inertial and elastic forces, exerting minimal influence on the structural responses. Nevertheless, improper incorporation of the gyroscopic matrix can lead to overestimation of the tower torsional fatigue and ultimate moments. Most importantly, under turbulent extreme winds with yaw misalignments beyond [−12∘, 14°], the idling bottom-fixed wind turbine exhibits substantial increases in both structural responses and dynamic sensitivity, making gyroscopic effects significant and profoundly altering system behavior.