CONTROL METHODOLOGIES FOR HORIZONTAL AXIS WIND TURBINE LOADS ALLEVIATION

Abstract

A nonlinear differential model for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications is presented. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and succes sively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flow, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal com ponents of relative velocity between flow and airfoil, their derivatives, and section angular velocity. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R = 61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266 rad/sec. The first analysis per formed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically pe riodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller.The performance of the spatial repetitive controller is compared with an in dustrial PI controller also in presence of an external disturbance. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both exter nal disturbances and periodic trend in the model dynamics and reaching the nominal angular velocity value at the same time. Moreover unsteady aerodynamics effects (wind shear and tower shadow) produce vibratory loads which, in turn, may induce fatigue problems, but also affect the qual ity of power generated by the wind turbine (potentially causing problems to the electric grid) and increases noise generation. The most effective and multipurpose way to control horizontal axis wind turbine is changing blade pitch in order to guarantee suited aerodynamic incidence. Acting on blade pitch allows to reduce vibratory loads and regulate generated torque at the same time. In this work an original Multi Harmonics Individual blade Control to alleviate the effects of this kind of loads, while tracking the nominal angular velocity, is presented. The proposed control acts in such way that, once a specific undesired frequency acts on the system, the controller is capable to reject it by minimizing the error between the desired operating condition and the current one.