Symmetry Considerations When Using Proper Orthogonal Decomposition for Predicting Wind Turbine Yaw Loads

In an earlier study, the authors discussed the efficiency of low-dimensional representations of inflow turbulence random fields in predicting statistics of wind turbine loads that included blade and tower bending moments. Both root-mean-square and $10-min$ extreme statistics for these loads were approximated very well when time-domain simulations were carried out on a $600kW$ two-bladed turbine and only a limited number of inflow “modes” were employed using proper orthogonal decomposition (POD). Here, turbine yaw loads are considered and the conventional ordering of POD modes is seen to be not as efficient in predicting full-field load statistics for the same turbine. Based on symmetry arguments, reasons for a different treatment of yaw loads are presented and reasons for observed deviation from the expected monotonic convergence to full-field load statistics with increasing POD mode number are illustrated.