On the Averaging in the Multi-Blade Coordinate Transformations for Wind Turbines: An H∞Model Matching Approach

The blade dynamics of a wind turbine are periodic with the angular position of the rotor. For analysis of these dynamics it is common practice to use the so-called Multi-Blade Coordinate (MBC) transformation in combination with a system matrix averaging technique to obtain a linear time-invariant model. The MBC transformation eliminates the periodicity over a rotation of the rotor, while retaining important blade dynamics. However, in the averaging step the inevitable residual periodic dynamics can result in an inaccurate linear representation. This paper shows the inaccuracy of the state-of-the-art averaging technique using a high fidelity two-bladed wind turbine model. The state-of-the-art technique is compared to two novel averaging methods. Results show a close resemblance of the computed models from the proposed methods to the frequency response average, whereas the conventional method shows erroneous results.