Servo-Elastic Dynamics of a Hydraulic Actuator Pitching a Blade with Large Deflections

Abstract

Abstract. This paper deals with the servo-elastic dynamics of a hydraulic pitch actuator acting on a largely bend wind turbine blade. The compressibility of the oil and flexibility of the hoses introduce a dynamic mode in the pitch bearing degree of freedom. This mode may obtain negative damping if the proportional gain on the actuator position error is defined too large relative to the viscous forces in the hydraulic system and the total rotational inertia of the pitch bearing degree of freedom. A simple expression for the stability limit of this proportional gain is derived for tuning the gain based on the Ziegler-Nichols method. Computed transfer functions from reference to actual pitch angles indicate that the actuator can be approximated as a low-pass filter with some appropriate limitations on pitching speed and acceleration. The structural blade model includes the geometrical coupling of edgewise bending and torsion for large flapwise deflections. This coupling is shown to introduce edgewise bending response for pitch reference oscillations around the natural frequency of the edgewise bending mode, in which frequency range the transfer function from reference to actual pitch angle cannot be modeled as a simple low-pass filter. The pitch bearing is assumed to be frictionless as a first approximation. IntroductionThis paper deals with the modeling and analysis of the servo-elastic dynamics of a hydraulic pitch actuator acting on the blade of the 5 MW Reference Wind Turbine (RWT) by NREL [1]. This work has two objectives: A dynamic characterization of hydraulic pitch actuators and an identification of bending-torsion coupling effects for largely bend blades with pitch actuation.The authors have not found any previous work on detailed modeling and analysis of hydraulic pitch actuators acting on wind turbine blades. Caselitz et al. [2] have presented a numericalexperimental analysis of a pitch controller using electrical pitch actuators, where the dynamics of these electrical actuators are included in the analysis as hardware-in-the-loop.Nonlinear effects of large flapwise blade deflections on the power production and loads of MWsized wind turbines have been studied from nonlinear aeroelastic simulations [3,4]. These studies showed two main effects: A reduction in power production by up to 5 % due to reduced effective rotor area when the blade bend downwind and inward under the loading, and an increased pitch torque by up to 50 % at the blade root due to the increased distance from the pitch axis to the point of action of the inplane forces on the blade. The reduced power production is compensated by the controller through the blade pitch angle settings [3], which causes the blade loads and tower thrust loads to increase above rated wind speeds. The effect of the increased pitch torque on the pitch actuator and its control has not been considered.

Dynamic response analysis of wind turbines under blade pitch system fault, grid loss, and shutdown events

“…Because of the nonlinear relationship between the cylinder and the pitch motion, the Pr may vary during one complete stroke. It is shown in the works of Hansen and Kallesoe and Froyd that the Pr reaches its peak at zero pitch angle and drops slightly as the pitch angle increases. To simplify, this study assumes a constant Pr during the entire shutdown process.…”

Load response of a two‐rotor floating wind turbine undergoing blade‐pitch system faults

“…During normal operating conditions, blade‐pitch dynamics is taken into account by means of a second‐order transfer function from reference to actual blade‐pitch angle (natural frequency Hz and damping ratio 50,51 ). Blade‐pitch fault cases are introduced in the fully coupled simulation at a particular user‐specified time.…”

Robust fault detection of linear systems using a computationally efficient set-membership method

“…The proportional valve is controlled by a proportional feedback of the piston position error. The closed loop dynamic of the pitch system can be approximated by a second order system as : where β r is the pitch reference, see [15]. The nominal values of ξ and ω n are given in Table I.…”