  We present a new stochastic approach to describe and remodel the conversion
process of a wind farm at a sampling frequency of 1Hz. When conditioning on
various wind direction sectors, the dynamics of the conversion process appear
as a fluctuating trajectory around an average IEC-like power curve, see section
II. Our approach is to consider the wind farm as a dynamical system that can be
described as a stochastic drift/diffusion model, where a drift coefficient
describes the attraction towards the power curve and a diffusion coefficient
quantifies additional turbulent fluctuations. These stochastic coefficients are
inserted into a Langevin equation that, once properly adapted to our particular
system, models a synthetic signal of power output for any given wind
speed/direction signals, see section III. When combined with a pre-model for
turbulent wind fluctuations, the stochastic approach models the power output of
the wind farm at a sampling frequency of 1Hz using only ten-minute average
values of wind speed and directions. The stochastic signals generated are
compared to the measured signal, and show a good statistical agreement,
including a proper reproduction of the intermittent, gusty features measured.
In parallel, a second application for performance monitoring is introduced in
section IV. The drift coefficient can be used as a sensitive measure of the
global wind farm performance. When monitoring the wind farm as a whole, the
drift coefficient registers some significant deviation from normal operation if
one of twelve wind turbines is shut down during less than 4% of the time. Also,
intermittent anomalies can be detected more rapidly than when using ten-minute
averaging methods. Finally, a probabilistic description of the conversion
process is proposed and modeled in appendix A, that can in turn be used to
further improve the estimation of the stochastic coefficients.
