Stability analysis of pitch-regulated, variable-speed wind turbines in closed loop operation using a linear eigenvalue approach



A multi-body aeroelastic design code based on the implementation of the combined aeroelastic beam element is extended to cover closed loop operation conditions of wind turbines. The equations of a controller for variable generator speed and pitch-controlled operation in high wind speeds are combined with the aeroelastic equations of motion for the complete wind turbine, in order to provide a compound aeroservoelastic system of equations. The control equations comprise linear differential equations for the pitch and generator torque actuators, the control feedback elements (proportional–integral control) and the various filters acting on the feedback signals. In its non-linear form, the dynamic equations are integrated in time to provide the reference state, while upon linearization of the system and transformation in the non-rotating frame, the linear stability equations are derived. Stability results for a multi-MW wind turbine show that the coupling of the controller dynamics with the aeroelastic dynamics of the machine is important and must be taken into account in view of defining the controller parameters. Copyright © 2008 John Wiley & Sons, Ltd.