Model-independent periodic stability analysis of wind turbines

In this work, a new method is proposed for the stability analysis of wind turbines. The method uses input-output time histories obtained by conducting virtual excitation experiments with a suitable wind turbine simulation model. Next, a single-input/single-output periodic reduced model is identified from the recorded response and used for a stability analysis conducted according to the Floquet theory. Since only input-output sequences are used, the approach is model independent in the sense that it is applicable to wind turbine simulation models of arbitrary complexity. The use of the Floquet theory reveals a much richer picture than the one obtained by widespread classical approaches based on the use of the multi-blade coordinate transformation of Coleman. In fact, it is shown here that, for each principal mode computed by the classical approach, there are in reality infinite super-harmonics of varying strength fanning out from the principal one at multiples of the rotor speed. The relative strength of each harmonic in a fan provides for a way of measuring how periodically one specific fan of modes behaves. The notion of super-harmonics allows one to justify the presence of peaks in the response spectra, peaks that cannot be explained by the classical time-invariant analysis. The Campbell diagram, i.e., the plot of system frequencies vs. rotor speed, is in this work enriched by the presence of the super-harmonics, revealing a much more complex pattern of possible resonant conditions with the per-rev excitations than normally assumed.