Page 175 - Fluid Power Engineering

148 Chapter Eight

Extreme Wind Speed (EWS)
Chapter 7 focused on wind assessments from the point of view of
energy production. Other aspects of a wind assessment that are of
interest to turbine manufacturers are the dynamic loads on the tower,
blades, and other components of the turbine caused by extreme wind
conditions. In addition to distribution of wind speed and turbulence,
EWS is an important parameter. The estimated EWS is the maximum
windspeedthatislikelytooccurin50years.Thereareseveralintervals
of interest: 3-s, 10-s, and 10-min. For instance, v 3s is the 3-s average
50y
estimated EWS that is exceeded once every 50 years; v 10m is the 10-min
50y
average estimated EWS that is exceeded once every 50 years. These
quantities are estimated statistically because, in most cases, 50-year
time series of 3-s wind speeds are not available and, furthermore, any
single 50-year time series may not be representative. Gumbel distri-
bution is commonly used to model extreme values of time series data.
It is a two-parameter (a, b) distribution of the form: 1

F(v) = e −e −(v−b)/a (8-1)

This is the annual cumulative probability that wind speed v is ex-
ceeded. Mean and standard deviation of the distribution are:

μ = b + γ a (8-2)
πa
σ = √ (8-3)
6
where γ is the Euler’s constant and is equal to 0.5772. The process of
finding the parameters of the distribution are:

1. Choose a wind speed time series that spans 10 years or more.
This is recommended to obtain a higher degree of confidence
in the estimate of EWS. Smaller time series increase uncer-
tainty in the estimate of EWS. The granularity of the time
series will also determine the granularity of the EWS. For ex-
ample, if the time series is hourly average wind speed, then
EWS will be the extreme hourly average wind speed in, say,
50 years.
2. Specify a threshold for sampling extreme events. For example,
a threshold of 15 m/s may be used for identifying extreme
wind events.
3. Identify a collection of extreme points in a time series with
wind speeds above the threshold value. The collection must
contain at least 20 points for higher degree of confidence in