ECE 499 Wind & Solar Power Systems

Part 2: Energy in the wind, wind resource characteristics, and wind measurement

Instructor: Dr. Ha LeDepartment of Electrical and Computer Engineering

California State Polytechnic University, Pomona

Fall 2015

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What will be presented?1. Energy in the wind

� Kinetic energy of wind. � Relation between power, rotor radius and wind speed.� Conservation of mass, energy, momentum. � Betz limit: Maximum power that may be extracted.

2. Wind resource characteristics � Wind creation and wind speed patterns.� Wind shear; Wind data analysis. � Power density; Power curve.� Estimation of wind turbine energy.� Wind resource assessment: wind classes and wind map.

3. Wind measurement

Reading: Wind textbook, Chapter 2, 3, 5. ���� Attention: Notation may be different because of different books use for the course lectu re notes.

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Kinetic energy of wind (1)

FIGURE 2-1 Cylinder r of air in front of HAWT rotor.

� The mass m from which energy is extracted is the mass contained in the volume of air that will flow through the rotor.

� For a horizontal axis wind turbine (HAWT), the volume of air is cylindrical , as shown in Fig. 2-1.

The kinetic energy contained in wind is:

where m is mass (kg) and v is wind speed (m/s); units of energy are kgm2/s2 = Joule.

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Kinetic energy of wind (2) The mass per second �� may be calculated as

where v is flow velocity, ρ is air density and A is the cross-section area.

The power P is

Unit of energy is Watt-seconds (=1J) � Unit of power is J /s=W

� The power P produced by a wind turbine is directly proportional to the cube of wind speed .

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Relation between power & rotor radius (1)

Power P

The impact of change in radius by a small amount ∆r , while everything else is constant, may be expressed as

� Meaning: If the radius is increased/decreased by 1%, power will increase/decrease by 2%.

���� Question: For larger changes in radius, the above formula does not apply. For instance, a 10% increase in radius will lead to increase by 21% in power. A 20% increase in radius will lead to 44% increase in power. Why?

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Relation between power & rotor radius (2)

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Relation between power & wind speed (1)

If wind speed is changed by a small amount and everything else is constant, then

� This means that if the speed is increased/decreased by 1%, energy will increase/decrease by 3%.

� However, if the wind speed is increased by 20%, the power will increase by 72.8% i.e.

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Relation between power & wind speed (2)

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Important basic laws for wind power

To understand wind power system design and operation, one needs to remember three laws :

1) Conservation of mass

2) Conservation of energy (for flowing fluid)

3) Conservation of momentum

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Conservation of mass (1)

Assumptions:

� All air that enters at A0 leaves from A2. Fluid flow is streamlined and so there is no loss of mass from the surface of the control volume.

� Fluid is incompressible i.e. there is no change in density.

Fig. 2-4 A control volume that follows streamlines that pass through the rotor. v0, vr , v2 are upstream, rotor, and downstream wind speeds. A0, Ar , A2 are upstream, rotor, and downstream cross-sectional areas.

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Conservation of mass (2)

The conservation of mass is: Mass flow through a control volume

where v2 is the average wind speed, taken over cross-sectional A2; vr is assumed to be uniform over Ar , the area of the rotor.

Since the rotor of turbine is extracting energy from air, the kinetic energy of air will reduce i.e. v0 > vr > v2

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Conservation of energy (1)Assumptions:

1) Fluid is incompressible i.e. the density does not change . Note that pressure can change.

2) Fluid flow is not viscid i.e. the equation applies to fluid flow outside a boundary layer . The boundary layer is where the friction between a surface and fluid causes slower fluid flow.

3) All the flow is along streamlines.

4) There is no work done by shear forces .

5) There is no heat exchange .

6) There is no mass transfer .

7) Relative position of fluid with respect to the earth’s surface does not change, that is, the potential energy remains constant.

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Conservation of energy (2)

� The kinetic energy results from the directed motion of the fluid;

� Pressure energy results from the random motion of particles in the fluid;

� Potential energy results from relative position of the fluid (e.g. gravitational potential energy of an object depends on its vertical position).

A simplified conservation of energy equation for fluids is

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Conservation of energy (3)

Bernoulli’s equation (Conservation of energy principle for flowing fluids)

�Bernoulli’s equation states that along a streamline when speed increases , then pressure decreases and when speed decreases, then pressure increases. The magnitude of change in pressure is governed by the quadratic relationship .

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Conservation of energy (4)Bernoulli’s equation applied to the control volume of Fig. 2-4

� Bernoulli’s law can be applied from A0 to the left of the rotor; and from right of the rotor to A2

� Bernoulli’s law cannot be applied across the rotor that extracts energy as the constant in the above equation will be different for the two regions.

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Conservation of momentum (1)

Assumptions:� There are no shear forces in the x-direction.� The pressure forces on edges A0 and A2 are equal.� There is no momentum loss or gain other than from A0

and A2.

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Conservation of momentum (2)� As the wind rotor extracts kinetic energy from wind, the wind

speed is reduced.

� Momentum is mass multiplied by speed � there is a change in momentum.

� Based on Newton’s second law, the rate of change of momentum in a control volume is equal to the sum of all the forces acting .

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Conservation of momentum (3)

Two opposite forces acting on the rotor:

� Rotor provides the external force that causes the change in momentum.

� The wind provides an equal, but opposite, force that acts on the rotor. (Newton’s third law).

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Conservation of momentum (4)Wind speed and pressure before and after the rotor

� Since the rotor hinders the flow of air , the pressure at the front of the rotor p0r ) is higher than the free-stream pressure (p0);

� The pressure at the back surface of rotor (p2r ) is below the free-stream pressure.

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Conservation of momentum (5)

� As the pressure is higher at the front of the rotor, the wind speed decreases from the free-stream wind speed (v0) as it approaches the front of the rotor.

� Since vr < v0, conservation of mass mandates that A0 < Ar .

� The pressure increases to the free-stream pressure as air moves toward A2, the wind speed decreases ���� A2 > Ar

� The volume to the right of the rotor is called the wake .

v0 > vr > v2

A0 < Ar < A2

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Betz limit (1)How much kinetic power canbe extracted from wind by an ideal energy converter device?Applying conservation of mass in control volume A0, Ar , and A2 with constant air density leads to

The force exerted on rotor by wind is

Applying Bernoulli’s law to two volumes: (a) Flow along streamlines from A0 to the front face of the rotor; and (b) flow from the back surface of rotor to A2 gives ����

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Betz limit (2)

Solving the above equations gives

� The wind speed at the rotor is average of the free-stream wind speed and the wind speed in the wake.

(2.19)

(2.20)

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Betz limit (3)The power delivered to the idealized rotor by the wind is:

����

The maximum power that the rotor can extract from wind is

From (2.19)

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Betz limit (4)The ratio between power available in the wind and the maximum extracted power is called the Betz limit :

� The Betz limit states that the maximum power which an ideal rotor can extract from wind is 59.3% of the power available in the wind.

� Cp is called the power coefficient of the wind turbine. Maximum C p = 0.593.

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Power coefficient of a wind rotor

Fig. 2-8 Power coefficient of a wind rotor (P/Pideal) as a function of ratio of wind speed at the wake to input wind speed.

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WT rating check using Betz limit

Example: Consider a turbine with rotor diameter = 2 m and power rating of 2 kW at 12 m/s.

Question: Is this wind turbine rating realistic?

Power available in the wind:

Maximum power that can be extracted:

���� Conclusion: This wind turbine rating is unrealistic. It can not produce 2 kW of power at 12 m/s.

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Factors affecting power coefficientThe Betz limit is a theoretical maximum power coefficient . In practice, three effects lead to a decrease in the maximum achievable power coefficient:

� Rotation of the wake behind the rotor.

� Finite number of blades and associated tip losses.

� Non-zero aerodynamic drag.

The overall turbine efficiency , ηoverall, is a function of both Cpand mechanical & electrical efficiency of the WT.

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Wind resource characteristics

Knowledge of the wind characteristics at a site is important for:

� Systems design: Requires knowledge of representative average wind conditions, the turbulent nature of the wind and extreme wind events. This information is used in the design and selection of a wind turbine intended for a particular site.

� Performance evaluation: Determining the expected energy productivity and cost effectiveness of a particular wind energy system based on the wind resource.

� Siting: The assessment or prediction of the relative desirability of candidate sites for one or more wind turbines.

� Operations: Need for wind resource information that can be used for load management, operational procedures (such as start-up and shutdown), and the prediction of maintenance or system life.

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Creation of wind – Global pattern (1)� The original source of the

energy contained in the earth’s wind resource is the sun .

� Global winds are caused by pressure differences across the earth’s surface due to the uneven heating of the earth by solar radiation.

� A larger amount of solar radiation is received at the tropics compared to the poles, which causes hot air to rise at the tropics and flow toward the poles .

� This flow occurs 10 to 15 km above the earth’s surface

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Creation of wind – Global pattern (2)� Coriolis force causes the

flow of hot air in the upper atmosphere to turn right. This flow does not continue beyond 300

latitude.

� The vertical motion of hot air causes low pressure at the tropics. Cold air from the higher latitudes flows toward the tropics , resulting in “surface” winds or trade winds .

Fig. 3-1 Atmospheric circulation of air. The arrows between the latitude lines indicate the direction of surface winds . The closed circulation or convection shown on the right indicates the vertical flow of air .

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Creation of wind – Global pattern (3)

� Fig. 3-1 shows worldwide wind circulation involves large-scale wind patterns which cover the entire planet. These affect prevailing near surface winds.

� The model is a simplified model because it does not reflect the effect that land masses have on the wind distribution.

Fig. 3-1 Atmospheric circulation of air

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Notes of global winds� The spatial variations in heat transfer to the earth’s

atmosphere create variations in the atmospheric pressure field that cause air to move from high to low pressure .

� The winds blow predominantly in the horizontal plane , responding to horizontal pressure gradients.

� There are forces that strive to mix the different temperature and pressure air masses distributed across the earth’s surface.

� In addition to the pressure gradient and gravitational forces, inertia of the air, the earth’s rotation, and frict ion with the earth’s surface (resulting in turbulence), affect the atmospheric winds . The influence of each of these forces differs depending on the scale of motion considered.

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Mechanics of wind motion (1)

In one of the simplest models for the mechanics of the atmosphere’s wind motion, four atmospheric forces can be considered. They are:

� Pressure forces

� The Coriolis force caused by the rotation of the earth

� Inertial forces due to large-scale circular motion

� Frictional forces at the earth’s surface.

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Mechanics of wind motion (2)Creation of geostrophic wind: Considering two forces

Fp is the pressure force on the air (per unit mass). Fc is Coriolis force whose magnitude depends on wind speed and latitude. The resultant of these two forces is the geostrophic wind , which tends to be parallel to isobars.

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Other atmospheric circulation patterns� The general circulation flow pattern described previously best

represents a model for a smooth spherical surface. In reality, the earth’s surface varies considerably , with large ocean and land masses. These different surfaces can affect the flow of air .

� The oceans act as a large sink for energy. Therefore, the movement of air is often affected by the ocean circulation .

� All these effects lead to differential pressures which affect the global winds and many of the persistent regional winds , such as those occurring during monsoons.

� Local heating or cooling may cause persistent local winds to occur on a seasonal or daily basis. These include sea breezes and mountain winds.

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Smaller scale atmospheric circulation� Can be divided into secondary and tertiary circulation .

Secondary circulation occurs if the centers of high or low pressure are caused by heating or cooling of the lower atmosphere. It includes the following:

� Hurricanes;

� Monsoon circulation;

� Extratropical cyclones.

Tertiary circulations are small-scale, local circulations characterized by local winds:

� Land and sea breezes; Valley and mountain winds;

� Monsoon-like flow (e.g. flow in California passes);

� Foehn winds (dry, high-temperature winds on the downwind side of mountain ranges);

� Thunderstorms; Tornadoes.

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Time & space scales of atmospheric motion

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Example of tertiary circulation

Diurnal valley and mountain winds

� During the day , the warmer air of the mountain slope rises and replaces the heavier cool air above it.

� The direction reverses at night , as cold air drains down the slopes and stagnates in the valley floor.

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Wind variations in time

Variations in wind speed in time can be divided into the following categories:

� Inter-annual : Variation from one year to the next

� Annual: Variation from one season to another

� Diurnal: Speed difference between day and night

� Short-term (gusts and turbulence): Fluctuation in minute- or second-time scale.

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Inter-annual variations

Inter-annual variations in wind speed occur over time scales greater than one year . They can have a large effect on long-term wind turbine production . Researchers are still looking for reliable prediction models for long-term mean wind speed.

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Annual variations (1)Annual variations in seasonal or monthly averaged wind speeds are common.

� For example, for the eastern one-third of the United States , maximum wind speeds occur during the winter and early spring .

� Spring maxima occur over the Great Plains, the North Central States, the Texas Coast, in the basins and valleys of the West, and the coastal areas of Central and Southern California.

� Winter maxima occur over all US mountainous regions , except for some areas in the lower Southwest, where spring maxima occur.

� Spring and summer maxima occur in the wind corridors of Oregon, Washington, and California.

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Annual variations (2)

Seasonal variation in available wind power per unit area for Amarillo, Texas

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Diurnal variationsOne example of diurnal variation is the previously-presented valley and mountain winds. Another example is the land-sea breezes below.

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Short-term wind speed variations (1)� Short-term variations usually mean variations over time

intervals of ten minutes or less .

� Ten-minute averages are typically determined using a sampling rate of about 1 second.

� It is generally accepted that variations in wind speed with periods from less than a second to ten minutes and that have a stochastic character are considered to represent turbulence .

� Turbulent fluctuations in the flow need to be quantified for turbine design and operation: e.g. maximum load and fatigue prediction, structural excitations, control, system operation, and power quality.

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Short-term wind speed variations (2)

Typical output from an anemometer

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Short-term wind speed variations (3)

Illustration of a discrete gust event:a=amplitude; b=rise time; c=maximum gust variation; d=lapse time.

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Wind shear� Wind shear is wind speed variation with height . Wind

shear influences both the assessment of wind resources and the design of wind turbines.

� Assessment of wind resources over a wide geographical area might require that the anemometer data from a number of sources be corrected to a common elevation.

� Design aspect: Rotor blade fatigue life will be influenced by the cyclic loads resulting from rotation through a wind field that varies in the vertical direction.

� Therefore, a model of the wind speed variation with height is required in wind energy applications.

� Details are in the following sections…

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Analysis of wind speed data

Wind shear:

Two mathematical models for analyzing the wind speed variation with height are:

1) Log law

2) Power law

� Method 1, log law , is based on a combination of theoretical and empirical research.

� Method 2, power law , is used by many wind energy researchers.

� Both methods are subject to uncertainty caused by the variable, complex nature of turbulent flows.

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Method 1: Logarithmic profile (log law) (1)

The log law is often used to extrapolate wind speed from a reference height zr to another level z using the following relationship:

� U(z) is the wind speed at height z

� U(zr) is the reference wind speed at height zr

� z0 is an approximate value of surface roughness length for various types of terrain.

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Method 1: Logarithmic profile (log law) (2)z0 is an approximate value of surface roughness length for various types of terrain. It can be calculated based on experimental data. The following table provides values of z0 for some terrains.

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Method 2: Power law (1)The power law represents a simple model for the vertical wind speed profile. Its basic form is:

� U(z) is the wind speed at height z

� U(zr) is the reference wind speed at height zr

� α is the power law exponent

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Method 2: Power law (2)

� The exponent αααα is a highly variable quantity .

� It varies with elevation, time of day, season, nature of the terrain, wind speed, temperature, and various thermal and mechanical mixing parameters.

� One value of αααα is 1/7, indicating a correspondence between wind profiles and flow over flat plates.

� Many researchers accept the empirical nature of the power law and choose certain empirical values of αααα that best fit available wind data

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Method 2: Power law (3)Some popular empirical methods for determining representativepower law exponents αααα are as follows.

Where reference wind speed Uref is given in m/s and reference surface roughness length zref in m.

for 0.001m < z0 < 10 m, where z0 represents the surface roughness in m (see previous table for sample values)

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Method 2: Power law (4)

Analysts should be very careful when selecting αααα as it can impact the calculation of wind power density (i.e. power/area, details later) significantly, as shown in the example below.

Problem: If U0=5 m/s at 10-m elevation, what are U and P/A at 30 m? Note that at 10 m, P/A=75.6 W/m2.

Effect of αααα on estimates of wind power density at higher elevations

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Wind power density

Power density=������� ����

����=(�

�)����

�=(1/2)���

Wind power density is defined as

where U is wind speed. The unit of power density is W / m2.

Attention:

� Since wind speed varies all the time, the variations must be taken into account to compute the power density correctly.

� Later sections will explain how to account for the variations (e.g. using probability density functions to characterize the variations).

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Power output curve for wind turbineThe power output curve, or power curve , is one of the most important properties of a wind turbine . It shows how much power the wind turbine produces for a range of wind speed.

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Wind data analysis, power density & wind turbine productivity

We consider 4 methods for characterizing wind speed data and determination of wind turbine power production, as follows:

1) Direct use of data averaged over a short time interval;

2) Method of bins ;

3) Development of velocity and power duration curves from data;

4) Statistical analysis using probability functions .

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Method 1: Direct use of data (1)If we have measured data which is a series of N wind speed observations, Ui, each averaged over the time interval ∆t. These data can be used to calculate the following useful parameters:

(1) The long-term average wind speed , ��, over the total period of data collection

(2) The standard deviation of the individual wind speed averages

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Method 1: Direct use of data (2)(3) The average wind power density

(4) The wind turbine average power

where Pw(Ui) is the power output defined by a WT power curve .

(5) The energy from a wind machine, Ew

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Method 2: Method of bins (1)� The method of bins provides a way to summarize wind

data and to determine expected turbine productivity .

� The data must first be separated into the wind speed intervals or bins in which they occur. It is most convenient to use the same size bins.

� Assume that the data are separated into NB bins of width w j, with midpoints m j, and frequency f j (the number of occurrences in each bin), such that:

N is the number of wind speed observations

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Method 2: Method of bins (2)The figure below illustrates a typical histogram .

This histogram was derived from one year of hourly data, for which the mean was 5.91 m/s and the standard deviation was 2.95 m/s.

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Method 2: Method of bins (3)Average wind speed, standard deviation, power densi ty, WT average power, and energy , can be determined as follows:

NB = number of bins; w j = width; m j = midpoints, f j = frequency = number of occurrences in each bin.

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Method 3: Velocity & Power Duration Curves (1)

Velocity and power duration curves can be useful when comparing the energy potential of candidate wind sites.

The velocity duration curve is a graph where

y axis: wind speed

x axis: number of hours in the year for which the speed equals or exceeds each particular value on the x axis.

Velocity duration curves

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Method 3: Velocity & Power Duration Curves (2)

Interpretation of velocity duration curves:

� The total area under the curve is a measure of the average wind speed.

� The flatter the curve, the more constant are the wind speeds.

� The steeper the curve, the more variable is the wind regime.

Velocity duration curves

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Method 3: Velocity & Power Duration Curves (3)

� A velocity duration curve can be converted to a power duration curve by cubing the ordinates (i.e. wind speed) , which are then proportional to the available wind power for a given rotor swept area.

� A power duration curve for a particular wind turbine at a given site may be constructed using the power duration curve in conjunction with a power curve for the wind turbine.

Power duration curves

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Method 3: Velocity & Power Duration Curves (4)

� The difference between the energy potential of different sites is visually apparent , because the areas under the curves are proportional to the annual energy available from the wind.

Power duration curves for a wind turbine

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Method 3: Velocity & Power Duration Curves (5)

How to construct velocity and power duration curves from wind speed data?

1) Arrange the data in bins;

2) Find the number of hours that a given velocity (or power per unit area) is exceeded;

3) Plot the resulting curves.

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Method 4: Statistical analysis� Statistical analysis can be used to determine the wind energy

potential of a given site and to estimate the energy outputfrom a wind turbine installed there.

� If time series measured data are available at the desired location and height, there may be little need for a data analysis in terms of probability distributions and statistical techniques. The previously described techniques may be used .

� If projection of measured data from one location to another is required, or when only summary data are available, then it is advantageous to use statistical analysis with probability distributions.

� A probability distribution is a term that describes the likelihood that certain values of a random variable (such as wind speed) will occur.

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Probability density function (1)

The frequency of occurrence of wind speeds may be described by the probability density function (pdf), p(U), of wind speed. The probability of a wind speed occurring between Ua and Ub is:

The total area under the probability density curve is given by:

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Probability density function (2)

If p(U) is known, it is possible to calculate mean wind speed , standard deviation of wind speed, mean wind power density as follows.

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Cumulative distribution functionThe cumulative distribution function (cdf) F(U) represents the time fraction or probability that the wind speed is smaller than or equal to a given wind speed, U. That means

F(U)=Probability (U’ ≤ U), U’ is a dummy variable

The derivative of the cdf is equal to the probability densityfunction

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Commonly used probability distributions for wind data analysis

Two probability distributions are commonly used for wind data analysis:

(1) Rayleigh: The Rayleigh distribution uses one parameter which is the mean wind speed .

(2) Weibull: The Weibull distribution is based on two parameters and, thus, can better represent a wider variety of wind regimes.

Both the Rayleigh and Weibull distributions are called ‘skew’ distributions in that they are defined only for values greater than 0 .

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Rayleigh distribution (1)The Rayleigh probability density function and the cumulative distribution function are given by:

is the mean wind speed

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Rayleigh distribution (2)

Example of Rayleigh probability density function

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Weibull distribution (1)Use of the Weibull pdf requires knowledge of two parameters: k, a shape factor, and c, a scale factor. Both of these parameters are functions of and .

The Weibull probability density function and the cumulative distribution function are given by:

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Weibull distribution (2)The relation between the average wind speed , standard deviation , and the Weibull distribution parameters are as follows.

The gamma function can be approximated as

It is not a straightforward process to get c and k in terms of U and . However, we can use approximations .

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Weibull parameters calculation (1)

Analytical-Empirical method:

For 1≤ k ≤ 10, a good approximation for k is:

k can then be used to solve for c

This method still requires use of the gamma function.

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Weibull parameters calculation (2)

Empirical method:

We first calculate k as in the previous analytical-empirical method i.e. for 1≤ k ≤ 10, k is:

Then c may be found based on

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Example of Weibull pdf

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Wind turbine energy production estimates using statistical techniques

For a given wind regime probability density function, p(U), and a known turbine power curve, Pw(U), the average wind turbine power is given by:

where η is the drive train efficiency (detail later) and Cp is the rotor power coefficient.

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Example of estimatingwind turbine energy production

The previous equation for the average wind turbine power may be simplified to obtain a more convenient equation (details in Manwell, p.64)

where D is the rotor diameter.

�

Example: Calculate the average annual production of an 18 meter diameter idealized ‘Rayleigh–Betz’ wind turbine at sea level in a 6 m/s average annual wind velocity regime.

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Capacity factorCapacity factor is an important parameter of a wind turbine.

It is defined as the ratio of the energy actually produced by the turbine to the energy that could have been produced if the machine ran at its rated power over a given time period

� CF is a measure of the energy productivity or performance of the generation system.

� CF can be evaluated on monthly or annual bases.

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Meaning of capacity factor

� The capacity factor ranges from 0 to 1 : CF = 0 indicates the generation system produce no energy, while CF=1 suggests that the generation system produces energy continuously at the full-rated power during the period of observation.

� Energy production of a wind plant (i.e. wind farm) follows climatic cycle of a 12-month period.

� A capacity factor computed on monthly basis for the entire year can provide the overall trend of the wind plant performance from the energy production for a given year .

� The capacity factors for wind plants are typically in the range of 25% to 30% , which is far lower than the conventional generation systems (60% to 70%).

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Example of capacity factor

Capacity factors for Storm Lake and Lake Benton wind plants (1/1/2002 through 12/31/2002

The capacity factors for 2002 for Storm Lake and Lake Benton are 31.05% and 33.44%, respectively

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Wind resource assessment (1)One of the first steps required for a wind energy feasibility study is an estimate of the available wind resource . Some of the methods are:

(1) Measurements only.

(2) Measure–correlate–predict.

(3) Global databases.

(4) Wind atlas methodology.

(5) Site data based modeling etc.

� We will not discuss these methods in details. Instead, we will consider two important methods for estimating wind resources , namely, wind classes and wind map of the US.

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Wind map and wind classes (1)� Wind resource assessment of the United States was carried out

since 1970s .

� The resulted wind energy atlases depicted the annual and seasonal wind resource on a state and regional leve l. They also included the wind resource’s certainty rating and an estimate for the percentage of land suitable for wind energy development based on variations in land-surface form.

� The wind energy atlases have been updated over time. Anintensive resource assessment program was carried out by the Pacific Northwest Laboratory in 1986.

� Under the program the conterminous United States was divided into grid cells 1/4 degree of latitude by 1/3 degree of longitude (around 120-km2 cell). Each grid cell was assigned a wind power class ranging from 1 to 7, with 7 being the w indiest.

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Wind map and wind classes (2)� The wind resource analysis is based on measured data

(where available) collected at heights of 20 to 60m (65 to 200ft) above ground at exposed sites.

� In most areas only near-surface data, 3 to 15m above ground, were available . Measured data at heights of about 50m and above from over 300 locations were included in 2010 to develop 80-m height map estimates.

� Vertical extrapolation to 10, 50, 80m etc. is based primarily on the 1/7 power law using data from exposed sites.

� Data available from many locations with measurements from more than one level indicate that, in spite of anomalies caused by terrain complexities, the 1/7 power law is generally appropriate .

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DOE wind power density classes

Note: Vertical extrapolation of wind speed based on the 1/7 power law. Mean wind speed is based on Rayleigh speed distribution of equivalent mean wind power density.

Areas designated as class 4 or greater are generally considered to be suitable for most wind turbine applications .

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US wind map at height of 50m

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Current wind maps of US� U.S. Annual Average Wind Speed at 30m Map: This map shows

national 30m wind speed potential for the United States. State maps are available at the WINDExchange website. This map is useful for siting residential wind turbines.

� U.S. 50m Wind Resource Map: This map shows national 50m wind resource potential which may be useful for both residential and utility WT siting.

� U.S. 80m Wind Resource Maps: National 80m land-based and offshore annual wind resource potential.

� U.S. 90m Offshore Wind Resource Map: 90m-height offshore wind resource potential.

� U.S. 100m Wind Speed Map: This map shows the land-based and offshore annual average wind speed at height of 100m.

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Wind measurementDefining wind speed is not trivial in reality. Here are some reasons.

� Wind velocity in the horizontal plane: For most turbines, energy is derived from the wind velocity vector in the horizontal plane.

� Wind velocity in the vertical direction: The vertical component of wind velocity is caused by convection, topography of land, or other factors.

� Wind velocity at a point versus a volume: Because of the stochastic nature of airflow, wind velocity vector at the particle level has a significant random component. Therefore, the wind velocity vector is spatially averaged.

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Types of anemometer (1)

Main three types of wind speed meters are: cup anemometers, propeller anemometers, sonic anemometers .

Cup anemometer:

� It is the most widely used. Most modern anemometers contain three cups with a vertical axis of rotation.

� The rotation speed of the cups is proportional to the wind speed . The output signal of an anemometer is a low-level AC sine wave; the frequency of the sine wave is proportional to the wind speed.

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Types of anemometer (2)Propeller anemometer:

� A propeller is used to measure wind speed. The axis of rotation of propeller anemometer is horizontal.

� In order to align the axis of rotation with the direction of wind , this type of anemometer also contains a wind vane . This instrument serves two purposes: Wind speed and wind direction measurement.

� For an anemometer used to measure the vertical component of wind speed, the axis of rotation is fixed to be vertical .

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Types of anemometer (3)Sonic anemometer:

� Ultrasound waves are used to measure wind speed and direction.

� Sonic anemometers operate by measuring the time taken for a pulse of sound to travel between a pair of transducers.

� This time depends on the distance between the transducers, the speed of sound and the air speed along the axis of the transducers

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Classification of anemometers

� Anemometers are classified according to IEC 61400-12-11 standard based on two parameters: Accuracy of measurement and terrain of measurement.

� The accuracy of anemometer is indicated with a class index, k, where k takes on values between 0 and 3. Class 0 is the highest accuracy and Class 3 is a lower accuracy anemometer.

� The terrain of measurement is indicated with a letter A, B, or S.

� Examples: Class 0.5B, Class 1A, Class 2B, etc.

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Instruments for wind applicationsWind energy applications use the following types of meteorological sensors:

� Anemometers to measure wind velocity;

� Wind vanes to measure wind direction;

� Thermometers to measure the ambient air temperature;

� Barometers to measure the air pressure.

Other required instruments:

Instrumentation towers (Met-towers): Towers that can reach 20m to over 150 m to mount meters. They are designed specifically for wind measurements, are lightweight and can be moved easily.

Data logger and communication device: To display, record, and analyze the data obtained from the sensors and transducers, and to transmit data.

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Example of Met-tower configuration

Turbulence characterization system of Pacific Northwest Laboratories

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Data processingTo perform statistical analysis of the measured data and to visualize the data , a variety of data processing methods are used. A simplified approach is as follows.

1) The data is first organized into bins . The two dimensions for the bins are wind speed and direction .

2) For wind direction, it is normal to use 16 bins with bin size of 22.5◦. Some programs use 12 bins with bin size of 30◦. The wind direction bins are called sectors.

3) Each wind speed bin contains the number of occurrences of speed .

4) Weibull parameters are then computed from the frequency data for each sector.

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Bins with wind speed and direction data

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Weibull parameters calculation

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Frequency plot for the NNW direction

Fig. 6-14 The Weibull parameters are derived by WindPRO. The jagged lines are the actual frequencies. The smooth curve is the computed Weibull distribution with A = 10.4 m/s and k = 2.24.

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Data management