Characteristics of the Wind - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 499

the scale of the rotor, the larger the amplitude, the longer the duration, and the lower the
frequency of occurrence of the planar gust fronts that envelop it.
The ultimate strength design of a wind turbine and the design of shutdown and safety
controls are typically driven by extreme, somewhat isolated, gusts which are embedded in
the turbulent winds. For analysis of extreme values, one generally resorts to a probability
of maximum value or external gust model [Coleman and Meyers 1982]. Discrete gust
models are used routinely in aircraft design [ e.g. , Bisplinghoff and Ashley 1957, Babister
1980].

Models Non-Uniform in Space and Unsteady in Time

The actual inflow to a turbine is both unsteady and nonuniform, so this type of model
is the most realistic and, of course, the most complex. It considers a nonuniform flow
front, that is perhaps two-dimensional, which varies with time. The need for this level of
complexity will differ for different rotor sizes. For example, both spatially and temporally
varying inflow models may be required for large-scale rotors, whereas temporal variations
alone may suffice for small rotors.

Stochastic Models

The final turbulence model type is stochastic (sometimes called probabilistic ) . The
three types of inflow models described previously contain deterministic descriptions of the
wind fluctuations. Stochastic models, on the other hand, are based on the concept that
turbulence is made up of sinusoidal waves or eddies with many periods and random ampli-
tudes. The spectrum of the turbulence, like that shown in Figure 8-4, is typically used to
describe the frequency of occurrence of fluctuations with different periods, and is given as
a graph of the average kinetic energy associated with eddies or disturbances which have a
common period but time-random amplitudes. Stochastic models may also use probability
distribution or other statistical parameters.
Stoddard and Potter [1986] point out that stochastic analysis can be invaluable in deve-
loping models of the wind inflow from measurements of the response of an operating wind
turbine, because it facilitates the following critical tasks:

-- representation of many data points taken in field tests;

-- rapid evaluation of fatigue loads;

-- comparison of model predictions with historical field data.

The method of bins [Akins 1978] is a simple application of stochastic methods to power
performance testing of wind turbines. Another application of a stochastic approach is to
represent the timewise variation of a wind “front” with probabilistic formulations. This
might be the probability of experiencing a given shape and magnitude of non-uniformity
in the inflow. In this case the spatial variation is still deterministic. The number of times
the wind speed exceeds a prescribed value ( i.e., exceedance statistics ) is another example
of a stochastic model. Such a model is applicable to fatigue analysis. There are many
other applications of stochastic modeling in wind engineering.

Dimensions of Turbulence Models

Turbulence models of all types can be classified as one-, two-, or three-dimensional,
depending on the number of spatial coordinates ( i.e. , x, y , and z ) needed to describe the
wind velocity field. One-dimensional or large-scale turbulence models assume that the