Calibration of wind turbine lifting line models from rotor loads

This paper is concerned with the calibration of lifting line models of wind turbine rotors. In fact, properly tuned lifting lines are key for the accurate simulation of wind energy systems, for example in the areas of performance, aeroelasticity and wake aerodynamics. The problem is formulated as the constrained optimization of a maximum likelihood cost function, driven by measurements of the rotor loads at the hub and possibly along the blades. Additive functions that correct the lift and drag characteristics of the blade airfoils are identified; such functions depend on the angle of attack and on the spanwise location along the blade, dependence that is approximated using suitable shape functions and their associated nodal parameters. The estimation problem expressed in terms of the physical nodal parameters is shown to be difficult and typically ill-posed, because of low observability and collinearity of the unknowns. To overcome this difficulty, a novel method is proposed that uses a singular value decomposition of the Fisher information matrix. By this decomposition, the problem is recast in terms of a new set of variables that are statistically independent; in turn, this is used for readily selecting only those parameters that are associated with a sufficiently high level of confidence. The mapping between the new statistically independent and the original physical parameters is expressed by eigenshape functions, whose inspection clarifies which parameters are observable in which ranges of the angle of attack and blade span domain. The paper is complemented by examples that illustrate the main features of the proposed method. At first, a scaled rotor model is tested in a wind tunnel, and hub measurements are used for the calibration of its lifting line model, whose nominal characteristics appear to be largely in error. Much improvement in the fidelity of the lifting line is observed after calibration by the procedure described here. Next, a simulation study is conducted that illustrates the effects of multiple blade load measurements in the ability to spanwise localize the contributions of different airfoils.