Wind Energy

21
Extreme Events Under Low-Frequency Wind
Speed Variability and Wind Energy Generation
Alin A. Cârsteanu and Jorge J. Castro
Summary. Low-frequency wind speed variability represents an important challenge
to statistical estimation for atmospheric turbulence and its impact on wind energy
generation, given that it does not allow for the usual stationarity assumption in
time series analysis. This work presents a framework for the parameterization of
the cascade representation of turbulent processes, where stationarity of the cascade
generator is assessed from the breakdown coefficients of time series.
21.1 Introduction
The effect of low-frequency (or climatic-scale) variability in wind velocities
amounts to nonstationarity in the time series at scales comparable to the
series length. When this is the case, the probabilities of future events cannot be
inferred statistically from the past. In particular, the estimated probabilities
of extreme events, which are by definition scarce and therefore difficult to
estimate from statistics in the absence of phenomenologically based models
even under stationary conditions, are the most sensitive to nonstationarities.
On the other hand, empirical observations have recently triggered an
alarm concerning more frequent atmospheric extreme events, associated with
climatic-scale variations (in lay terms, climate change), be they of human or
natural origin. This raises the problem of being able to quantify a variation in
the parameters of the underlying probability distribution functions of those
extreme events, without using directly the statistics of extreme events, which
are unable to offer reasonable confidence levels due to their scarcity. We propose
here a scaling stationarity criterion, based on the multifractal nature of
energy cascading in the terrestrial atmosphere.
Atmospheric extreme events are typically associated with the occurrence
of extreme velocity departures of turbulent fluctuations over contiguous spacetime
domains, a phenomenon called “coherence.” These coherent structures
are clustering effects typical of the multifractal energy cascade which governs
turbulent velocity scaling. The scaling law of velocity fluctuations,