  In the last few years, the dynamical characterization of the power output of
a wind turbine by means of a Langevin equation has been well established. For
this approach, temporally highly resolved measurements of wind speed and power
output are used to obtain the drift and diffusion coefficients of the energy
conversion process. These coefficients fully determine a Langevin stochastic
differential equation with Gaussian white noise. The drift term specifies the
deterministic behavior of the system whereas the diffusion term describes the
stochastic behavior of the system. A precise estimation of these coefficients
is essential to understand the dynamics of the power conversion process of the
wind turbine. We show that the dynamics of the power output of a wind turbine
have a hidden dependency on turbine's different operational states. Here, we
use an approach based on clustering Pearson correlation matrices for different
observables on a moving time window to identify different operational states.
We have identified five operational states in total, for example the state of
rated power. Those different operational states distinguish non-stationary
behavior in the mutual dependencies and represent different turbine control
settings. As a next step, we condition our Langevin analysis on these different
states to reveal distinctly different behaviors of the power conversion process
for each operational state. Moreover, in our new representation hysteresis
effects which have typically appeared in the Langevin dynamics of wind turbines
seem to be resolved. We assign these typically observed hysteresis effects
clearly to the change of the wind energy system between our estimated different
operational states. In this contribution, we discuss further consequences for
the meaning of hysteric switching and detection of malbehaviors in wind
turbines.

Data Analysis, Statistics and Probability