Characteristics of the Wind - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 481

Characteristics of the Steady Wind

Throughout this topic, time-varying wind speed is considered to be made up of a steady
value plus a fluctuation about this steady value, as expressed in Equations 8-3. Moreover,
the steady value is assumed to be quasi-static , so that its time variation is negligible for the
purpose at hand. It is generally the steady wind which is referred to when discussing wind
energy resources and wind turbine siting. The fluctuating component of the wind is referred
to when discussing turbulence effects on the turbine structure and controls. Obviously, the
characteristics of both the steady and fluctuating components of the wind will depend on
the time and space scales selected for averaging.
Two parameters commonly used to characterize the steady wind at a given elevation
are frequency distribution of wind speed on an annual basis and persistence. “Frequency”
indicates the cumulative time the wind blows at a prescribed value as distinct from
“persistence” which provides statistics on the continuous time the wind maintains that speed.
For example, a frequency distribution might indicate that the summer wind is below the
turbine cut-in speed 25 percent of the time, while persistence analysis will indicate how this
“downtime” is distributed in terms of periods of different lengths.
Frequency distribution and persistence are important factors in both the design and
siting of a wind turbine generator. The energy input to a wind turbine can be calculated
from the frequency distribution of the wind. Turbulence usually increases directly with
steady wind speed, so frequency distribution is also a significant factor in the structural
fatigue life of turbine components. The persistence of wind is important in the assessment
of wind energy potential, since dependability of generated power, required storage levels,
capacity credits from the user, and the design of hybrid systems depend on this information.
The higher the persistence, the more uniform and dependable is the wind energy production.

Wind Speed Frequency Distribution

Equation (8-2) for the annual average wind power density can be re-written in terms of
a wind speed frequency distribution function as follows:

¥

w a = 0.5 r
8,760 year

U 3 dt = 0.5 r
8,760

ò

U 3 f U dU

ò

(8-4a)

0

dt
dU

d
dU [ F ( U 1 ³ U )]

f U = = (8-4b)

year

where

f U = frequency distribution function of the steady wind speed [(h/y)/(m/s)]

F ( ) = annual time that ( ); cumulative frequency distribution function (h/y)

U 1 = arbitrary value of U (m/s)

The frequency distribution function, f U , is expressed as a function of the steady wind speed.
It must start at zero for a wind speed of zero, rise to at least one maximum value, and then
decrease to zero as the wind speed becomes large. Several non-Gaussian distributions
have been suggested as appropriate models for f U . These distributions include the gamma
distribution [Putnam 1948 and Sherlock 1951], the lognormal distribution [Luna and Church
1974], the inverse Gaussian distribution [Bardsley 1980], the squared normal distribution
[Carlin and Haslett 1982], and the Weibull distribution [ e.g. , Davenport 1965, Justus et al.
1976a and 1978]. Of these distributions the Weibull has received the most use in wind