Stochastic modelling of a wind turbine’s power output with special respect to turbulent dynamics

A frequent challenge for wind energy applications is to grasp the impacts of turbulent wind fields properly. The wind turbine power performance curve, usually determined applying the IEC standard 61400-12, provides a functional relation between the measured wind speed u and the corresponding power output P of the turbine. But it is not sufficient to describe the actual dynamics of the power output on small time scales. Recently, we introduced an alternative method to estimate the power curve of a wind turbine based on high-frequency data. The crucial point of this method is that we first reconstruct the wind turbine’s entire response dynamics that, then, yields the power curve by a fixed-point analysis. To reconstruct the power conversion dynamics of the wind turbine, we apply a dynamical systems approach, assuming that the variable P (t) follows a diffusion process. Its evolution in time is given by a Langevin equation consisting of a deterministic relaxation term and a stochastic noise term. The coefficients defininig these terms can directly be extracted from the given data sets. On the basis of simulated data, we verified the method and showed that it is more accurate than the standard method. For measured data we reconstructed the deterministic dynamics of a representative wind turbine and estimated the corresponding power characteristics to demonstrate the application of the method. The split of the dynamics into a deterministic and a stochastic part allows to distinguish the actual behaviour of the wind turbine, i.e. relaxation and control effects, from the turbulent effects of the wind. We gain an understanding of something like the turbulent dynamics of wind energy conversion and obtain a method to describe the actual fluctuations in power output.