Markovian power curves for wind turbines

This paper shows a novel method to characterize wind turbine power performance directly from high-frequency fluctuating measurements. In particular, we show how to evaluate the dynamic response of the wind turbine system on fluctuating wind speed in the range of seconds. The method is based on the stochastic differential equations known as the Langevin equations of diffusive Markov processes. Thus, the fluctuating wind turbine power output is decomposed into two functions: (i) the relaxation, which describes the deterministic dynamic response of the wind turbine to its desired operation state, and (ii) the stochastic force (noise), which is an intrinsic feature of the system of wind power conversion. As a main result, we show that independently of the turbulence intensity of the wind, the characteristic of the wind turbine power performance is properly reconstructed. This characteristic is given by their fixed points (steady states) from the deterministic dynamic relaxation conditioned for given wind speed values. The method to estimate these coefficients directly from the data is presented and applied to numerical model data, as well as to real-world measured power output data. The method is universal and is not only more accurate than the current standard procedure of ensemble averaging (IEC-61400-12) but it also allows a faster and robust estimation of wind turbines' power curves. Copyright (C) 2007 John Wiley & Sons, Ltd.