A Comparison of Multi-Blade Coordinate Transformation and Direct Periodic Techniques for Wind Turbine Control Design

Abstract

The inherent periodic behavior of an operating wind turbine is not well accommodated by common time-invariant analysis and control techniques. A multi-blade coordinate transformation (MBC) helps to overcome this issue for rotors with three or more blades by mapping the dynamic state variables into a non-rotating reference frame. A number of researchers have applied MBC for modal analyses and individual blade pitch controller designs. They do so by assuming the transformed system model from MBC is time-invariant, which is not often the case. The paper explores the validity of the time-invariant assumption by comparison to direct periodic techniques, which retain all periodic system information. In a modal analysis study, eigenvalues of a system after MBC are compared to direct Floquet modes. In an individual blade pitch control design study, a linear quadratic regulation (LQR) design after MBC is compared to direct periodic LQR. A 5-MW three-bladed wind turbine model is used to quantify performance differences. Normal operating conditions are considered as well as conditions selected to increase the harmonics that are unfiltered by MBC. It is found that the direct periodic methods produce almost identical results to timeinvariant methods after MBC under all conditions studied. MBC is recommended for threebladed turbines, which can be followed by Floquet analysis or periodic control design methods if necessary.