CHAPTER 11 (draft text)
MEASURING THE WIND SPEED
1.2.1 Evaluation of Wind Intensity
The energy captured by the rotor of a wind turbine is proportional to the cubic power of the wind
speed. Therefore, it is very important to evaluate the historical wind power intensity (W/m2) to
access the economical feasibility of a site, taking in account seasonal as well as year-to-year
variations in the local climate [3–5]. To estimate the wind power mechanical capacity, P,
Bernoulli’s equation (defined in Chapter 3) is used with respect to the mass flow derivative of its
kinetic energy,
Ke:
Also, there is a difference in the kinetic energy (usually expressed in kg _ m/s ¼ 9.81 W) in the
wind speed just reaching and just leaving the turbine. A net wind mechanical power of the
turbine is imposed by this kinetic energy difference, which may estimated by equation (4.1) as
Meteorological Mapping There are meteorological maps showing curves connecting the same
intensity of average wind speed. Although such maps may yield valuable information, they are
not sufficient for a complete analysis because the meteorological data acquisition stations do not
look only for a determination of the wind potential for power energy use. Therefore, a final
decision on the site will be made only after a convenient local selection procedure and thorough
data acquisition [2,3].
Local wind power is directly proportional to the distribution of speed, so that different places that
have the same annual average speed can present very distinct values of wind power. Figure 4.2
displays a typical wind speed distribution curve for a given site. That distribution can be made
monthly or annually. It is determined through bars of occurrence numbers, or percentile of
occurrence, for each range of wind speed over a long period of time. It is usually observed as a
variation of wind
linked with climate changes in the area. It is typical in temperate climates to have summer
characterized as a season of little wind and winter as a season of stronger winds.
When the wind speed is lower than 3 m/s (referred to as a calm period), the power becomes very
limited for the extraction of energy and the system should be stopped. Therefore, for power
plants, calm periods will determine the time required for energy storage. As discussed next,
power distribution varies according to the intensity of the wind and with the power coefficient of
the turbine. A typical distribution curve of power assumes the form shown in Figure 4.3. Sites
with high average wind speeds do not have calm periods, and there is not much need of storage.
However, high wind speed may cause structural problems in a system or in a turbine.
The worldwide wind pattern is caused by differences in temperature around the globe as well as
by Earth’s rotation. The temperature difference causes a huge convection effect above the ground
surface, which makes the airflow move upward on the equator and go downward at about 30_
north and south latitudes. This air
convection is distorted by the tangent speed differences of Earth’s spin such that the wind tends
to move east to west. Horizontal wind speed near the equator is very low because winds move
more upward. The most pronounced intensities of wind go from west to east between latitudes
30_ and 60_ north and south of the equator, forming two natural wind tunnels by a motion
caused by the circulation of east to west winds below the 30_ latitudes (see Figure 4.4). Usually,
west wind speeds are higher than east wind speeds. This general tendency is affected strongly by
the ground formation (mostly by valleys and mountains). As a result, it is very useful to represent
wind variation by a probabilistic vector of determined intensity and direction.
Weibull Probability Distribution To establish a probability distribution, it is important to
establish the duration curve of the wind speed for every hour of the day, every day of the year, a
total of 8760 pieces of data. Figure 4.5 shows a curve
formed by points marked in several speed ranges, in accordance with the number of hours
accumulated for a particular wind intensity and above that range [4–7].
Wind movement around the Earth is a random phenomenon. Therefore, a large sample of wind
data taken over many years should be gathered, to increase confidence in the data available. This
is not always possible, so shorter periods are often used. The data are often averaged over the
calendar months and can be described by the Weibull probability function, given as [4]
The Weibull function expresses the fraction of time the wind speed is between v and v þ _v for a
given _v. In practice, most sites around the world present a wind distribution for k (shape factor)
within the range 1.5 to 2.5. For most of them, k ¼ 2, a typical wind distribution found in most
sites, is known as the Rayleigh distribution, given by
Factor c, known as the scale factor, is related to the number of days with high wind speeds. The
higher c is, the higher the number of windy days. This parameter is enough to represent the wind
speed for most practical cases.
Weather repeats in seasons from one year to the next. For the purpose of wind variation studies,
this period is usually taken as divided into the total number of hours (8760 hours/year). The unit
of h in equation (4.6) may be stated as a percentage of hours per year per meter per second.
Equation (4.7) can be plotted for various parameters c as shown in Figure 4.6. The values of h
are the number of hours in a year that the wind speed is within the interval from v to v þ _v
divided by the speed interval _v. This plot provides a useful and realistic view of the average
speed.
There is a predominant wind speed throughout a year. The predominant speed can be considered
in at least three different ways, with very distinct implications. One could be defined as a single
speed at which the wind blows most of the time. It is a simplistic method that does not take into
account secondary predominant speeds, which may contain a lot of energy. A second way of
defining wind speed is by the average speed experienced by h throughout the year, given by
In this case, if c = Vav, the Rayleigh distribution given by equation (4.7) becomes
A third and more appropriate definition is to use the concept of root mean cube speed, Vrmc,
analogous to the root mean square (effective value). This definition is based on the idea that
yearly average power varies with the cube of the wind speed experienced by h; that is,
Table 4.1 lists some popular formulas for the calculation of wind speed, root mean cubic power,
and energy density over the number n of speed samples during the year, usually with
ρi = 1:225 kg/m3 at t = 150 C.
If we assume that the power coefficient Cp in equation (4.5), is no higher than 0.5 for high wind
speeds and two-blade turbines, we can conveniently take this value as the maximum practical
rotor efficiency. Therefore, the maximum output power for the root mean cubic of the wind
speed is
The total annual energy at the site can be obtained from equation (4.11) by multiplying it by
8760 hours. So the energy density per year and per swept area of the blades is given by
the wind speed, there is a significant increase and shift in the power density along the speed
axis. Such changes would not be noticed much if only the yearly maximum or average speeds
were used for those estimations, because they retain almost the same value in the two
distributions represented.
Based on these curves and on the load to be fed, it is possible to establish the turbine–generator
power that would have the best utilization factor for a given wind condition. It is evident that the
longer the wind behavior in an area is observed, the more appropriate will be the design of a
small power plant. Variable-speed control is recommended for a good wind energy system, due
to the cubic relation of the yearly energy to the wind speed.
Analysis of Wind Speed by Visualization If a site being evaluated is not close to meteorological
stations, a good practical suggestion is to observe the existing trees. Their deformation level will
serve as a good indicator of the wind speeds in the area. The intensity of the wind increases with
height; therefore, trees of larger span are reached by more intense winds, which can harm their
growth. The following levels of tree deformation are recognized:
_ Brush. When branches are on the lee side (the side exposed to wind), especially in the absence
of leaves the winds are weak.
_ Flag. Branches are the lee barriers (the static trunks in their original position, free to
windward), in other words, the side from which the wind blows.
_ Lie down. The wind is strong enough to produce permanent deformations in trunks and
branches.
_ Shear. The wind is always strong, to the point of breaking branches, giving the impression that
they were cut uniformly.
_ Rug of trees. The wind energy is so strong that it limits the growth of trees to some inches of
the soil, giving the impression that the trees form a rug.
For small wind power installations, a visual assessment of the wind intensity is described in
Table 4.2, which is an adaptation of the Beaufort table [3]. The International Committee of
Meteorology adopted such a table in 1874; wind measurement using anemometers did not begin
until 1939.
Technique of the Balloon Another very simple method to measure wind speed is by
measurement of the speed of a balloon allowed to move freely in the air [3,4]. Two points of a
known reasonable distance on the ground are selected. The time required for the balloon to pass
between the two points in a horizontal line is recorded, and the wind speed is inferred from that.