Modal Analysis of Rotating Wind Turbine using Multiblade Coordinate Transformation and Harmonic Power Spectrum

Understanding and characterization of wind turbine dynamics, especially when operating, is an important though challenging task. The main problem is that an operating wind turbine cannot be truly modeled as a time invariant system, which limits the applicability of conventional well-established modal analysis methods. This paper compares two experimental techniques that characterize the dynamic behavior of an operating horizontal axis wind turbine (Vestas V27, 225kW, rotor diameter 27m, 12 accelerometers on each blade). The first method uses a multiblade coordinate transformation to convert the time periodic system into a time invariant one, assuming that the system is perfectly isotropic. Conventional operational modal analysis then can be applied to identify the modal parameters of the time invariant model. The second method processes the periodic response directly based on an extension of modal analysis to linear time periodic systems. It utilizes the harmonic power spectrum, which is analogous to the power spectrum for a time invariant system, to identify a periodic model for the turbine. This work demonstrates both of these methods on measurements from the operating turbine and discusses the challenges that are encountered. The procedure is demonstrated by using it to extract the time-periodic mode shapes of the first edge-wise modes, revealing that this turbine apparently has non-negligible blade-to-blade variations and hence the dynamics of these modes are considerably different than one would expect for an anisotropic turbine.