Presentation of Wind Data Presentation of Wind Data

The wind energy that is available at a specific The wind energy that is available at a specific site is usually presented on an annual basis.site is usually presented on an annual basis.

There are several methods by which this data There are several methods by which this data can be presented.can be presented.– Some of these methods carry the identical Some of these methods carry the identical

information, presented from slightly different information, presented from slightly different viewpoints.viewpoints.

The goal is to evaluate the energy that can be The goal is to evaluate the energy that can be produced from the wind at a site.produced from the wind at a site.

Presentation of Wind DataPresentation of Wind Data

Wind data is usually summarized by annual averages Wind data is usually summarized by annual averages and totals.and totals.– This can be a bit misleading, since seasonal variations are This can be a bit misleading, since seasonal variations are

significant.significant. In some cases, monthly averages are also presented.In some cases, monthly averages are also presented.

– For non-grid-connected turbines, the annual peak winds may For non-grid-connected turbines, the annual peak winds may not correspond to the peak electrical energy demands.not correspond to the peak electrical energy demands.

Typical plots that describe annual wind data are shown Typical plots that describe annual wind data are shown on the next several slides.on the next several slides.

Wind Speed Frequency Distribution PlotsWind Speed Frequency Distribution Plots One method of presenting wind speed data is to produce a One method of presenting wind speed data is to produce a

histogram of the number of hours each year that the wind speed histogram of the number of hours each year that the wind speed is within a certain band.is within a certain band.

An example is shown below:An example is shown below:

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Wind Speed (m/sec)

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nu

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Normalized Wind Speed Frequency DiagramsNormalized Wind Speed Frequency Diagrams Rather than report the total time the wind is within a certain Rather than report the total time the wind is within a certain

band, sometimes the data is normalized by dividing by the total band, sometimes the data is normalized by dividing by the total number of hours.number of hours.

The result is a probability vs. wind speed histogram.The result is a probability vs. wind speed histogram.

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Wind Speed (m/sec)

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bab

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(%

)

The Weibull DistributionThe Weibull Distribution

Most wind data is modeled analytically by assuming it follows a Most wind data is modeled analytically by assuming it follows a WeibullWeibull probability distribution function.probability distribution function.– If P(V) is the probability of the wind being at speed V, then the Weibull If P(V) is the probability of the wind being at speed V, then the Weibull

distribution is given by:distribution is given by:

– The parameters k and C are called the scale and shape parameters, respectively, The parameters k and C are called the scale and shape parameters, respectively, and are chosen to fit the data.and are chosen to fit the data.

– C has dimensions of velocity, and k is dimensionless.C has dimensions of velocity, and k is dimensionless.

It is convenient to work with an equation rather than discrete data.It is convenient to work with an equation rather than discrete data.

k

Vk 1Ck V

P V eC C

The Weibull Distribution ContinuedThe Weibull Distribution Continued

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Wind Speed (m/sec)

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k

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The Cumulative Wiebull DistributionThe Cumulative Wiebull Distribution

The cumulative distribution PThe cumulative distribution Pcc(V) gives the probability (V) gives the probability

of the wind speed exceeding a certain value:of the wind speed exceeding a certain value:

Pc V( ) = P %V( )0

V

∫ d%V

=kC

%VC

⎡

⎣⎢

⎤

⎦⎥

k−1

e−

%VC

⎛

⎝⎜⎞

⎠⎟

k

0

V

∫ d%V

Integrate by substitution:

u=VC

⎛⎝⎜

⎞⎠⎟

k

du=kVC

⎛⎝⎜

⎞⎠⎟

k−1 1C

⎛⎝⎜

⎞⎠⎟dV =

kC

VC

⎛⎝⎜

⎞⎠⎟

k−1

dV

Pc V( ) = e−u

0

VC

⎛⎝⎜

⎞⎠⎟

k

∫ du=−e−u

0

VC

⎛⎝⎜

⎞⎠⎟

k

=1−e−

VC

⎛⎝⎜

⎞⎠⎟

k

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Wind Speed, V (m/sec)

% t

ime

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d sp

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exce

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V

Plot of the Cumulative Weibull Plot of the Cumulative Weibull DistributionDistribution

k

V

CcP V e

Development of a Weibull Estimate Development of a Weibull Estimate from Wind Datafrom Wind Data

The Wind RoseThe Wind Rose

Wind speed frequency diagrams do not provide Wind speed frequency diagrams do not provide information on the direction that the wind is blowing.information on the direction that the wind is blowing.

This is often done by a graph called a “wind rose.”This is often done by a graph called a “wind rose.” A wind rose is a polar plot giving the direction, A wind rose is a polar plot giving the direction,

magnitude, and cube of the magnitude of the wind.magnitude, and cube of the magnitude of the wind.– The data is usually averaged over a year.The data is usually averaged over a year.

– In some cases, shorter time periods, such as months, may be In some cases, shorter time periods, such as months, may be appropriate.appropriate.

Description of the Wind Rose PlotDescription of the Wind Rose Plot

The polar plot is usually broken up into 12 30° sectors, and average The polar plot is usually broken up into 12 30° sectors, and average data is presented over each sector.data is presented over each sector.

The first rose “petal” in a given direction is the fraction of the time, The first rose “petal” in a given direction is the fraction of the time, normalized to 100%, that the wind is blowing from that direction.normalized to 100%, that the wind is blowing from that direction.

The second petal is the fraction of time wind blows from a The second petal is the fraction of time wind blows from a particular direction multiplied by the average wind speed in that particular direction multiplied by the average wind speed in that direction, and normalized to 100%.direction, and normalized to 100%.

The second petal is the fraction of time wind blows from a The second petal is the fraction of time wind blows from a particular direction multiplied by the average cube of the wind particular direction multiplied by the average cube of the wind speed from that direction, and normalized to 100%.speed from that direction, and normalized to 100%.

The last two petals give information about how “useful” the wind The last two petals give information about how “useful” the wind is from a given direction.is from a given direction.– For example, if the wind usually blows from a particular direction, but not For example, if the wind usually blows from a particular direction, but not

very hard.very hard.

Wind Rose ExamplesWind Rose ExamplesDirectionSpeedEnergy

Use of the Wind RoseUse of the Wind Rose

The wind rose gives a graphical interpretation of much The wind rose gives a graphical interpretation of much of the data that is considered when evaluating a wind of the data that is considered when evaluating a wind power site.power site.

The second plot (previous slide) shows the wind and The second plot (previous slide) shows the wind and most of the wind energy comes from a prevailing most of the wind energy comes from a prevailing direction.direction.– In this case, the site can be designed with this in mind, and In this case, the site can be designed with this in mind, and

turbine technology with limited ability to rotate into the wind turbine technology with limited ability to rotate into the wind can be considered.can be considered.

Link to Wind Rose Applet:Link to Wind Rose Applet:– www.windpower.org/en/tour/wres/roseplot.htm

Wind Speed Power Curves for Specific TurbinesWind Speed Power Curves for Specific Turbines

A wind turbine power curve shows the rated power as a A wind turbine power curve shows the rated power as a function of wind speed, as follows:function of wind speed, as follows:

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Wind Speed (m/sec)

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Cut in speedRated speed

Rated Power

Shut Down speed

Wind Speed Power CurvesWind Speed Power Curves

Wind speed power curves, when considered with Wind speed power curves, when considered with wind speed frequency diagrams, allow the wind speed frequency diagrams, allow the calculation of the total power that can be calculation of the total power that can be produced at a site.produced at a site.

This allows the designer to choose turbine This allows the designer to choose turbine technology appropriate for a given situation.technology appropriate for a given situation.

In addition, the wind rose illustrates the In addition, the wind rose illustrates the requirements for swiveling, etc. requirements for swiveling, etc.