Determination of the Response Amplitude Operator of a tidal turbine as a spectral transfer function

Abstract

A transfer function determination method is proposed in this study to predict the unsteady fluctuations of the performance of a tidal turbine model. This method is derived from the Response Amplitude Operator (RAO) applied in the offshore industry to predict linear wave-induced loads on large structures. It is based on a spectral approach and requires the acquisition of a turbine parameter (e.g. torque, thrust, power or root-blade force) in synchronization with an upstream flow velocity measurement. On the frequency range where the causality between these two signals is proven, the transfer function is established using the ratio between the cross-spectral density and the spectral density of the incoming velocity.
The linearity is verified using the coherence function, which shows validity for the turbine power in the lowest frequencies only. This transfer function is then used to reconstruct the power fluctuations which is compared to the recorded one for a particular flow condition with bathymetry generated turbulence. The result shows the dependence on the accurate location of the velocity measurement point used for the reconstruction. This point must exactly correspond to the expected turbine location, i.e. where the turbine response needs to be processed. Bearing in mind its limits, the method can be used to predict the loadings of extreme events on the turbine structure and the performance variations corresponding to the unsteady characteristics of a turbulent flow, for a better grid integration.