Lecture 2:Fundamental Renewable Energy Supply

Lecturers:

Syafaruddin & Takashi Hiyama

syafa@st.eecs.kumamoto-u.ac.jp

hiyama@cs.kumamoto-u.ac.jp

Time and Venue:

Wednesdays: 10:20 – 11:50, Room No.: 208

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http://www.cs.kumamoto-u.ac.jp/epslab/APSF/

Contents:1.1. Energy Balance of the EarthEnergy Balance of the Earth

• Renewable Energy sources (Solar Energy)

• Atmosphere

• Balance of Energy Flow

2.2. Solar RadiationSolar Radiation

• Principles

• Supply Characteristics

3.3. Wind EnergyWind Energy

• Principles

• Supply Characteristics

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Energy Balance of the EarthEnergy Balance of the Earth

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Introduction: Solar energy has a share of more than 99.9 % of all the energy converted on earthThe solar radiation incident on the earth is weakened within the atmosphere and partially converted into other energy forms (e.g. wind, hydro power)

Solar Energy

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Some facts about the Sun:Some facts about the Sun:•The sun is the central body of our planetary system; it is the star closest to the earth•The nucleus has temperatures of approximately 15 Mio. K (~15.7×106 K)•Energy is released by nuclear fusion where hydrogen is melted to helium•Approximately 650 Mio. t/s of hydrogen are converted into approximately 646 Mio. t/s of helium•The difference of approximately 4 Mio. t/s is converted into energy•The resulting mass loss is converted into energy (E). •According to Einstein, it can be calculated multiplying mass m and the square of the speed of light vc

E = mvc2

•The energy released within the nucleus of the sun is initially transported by radiation to approximately 0.7 times the solar radius•Further transport to the surface of the sun takes place through convection. •Afterwards, the energy is released into space

Solar Energy…cont.

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Schematic structure and main parameters of the sun:

Solar Energy…cont.

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The energy stream released by the sun:− The radiation of matter consists of protons and electrons released by the sun at a speed of approximately 500 km/s. However, only a few of these electrically charged particles reach the earth’s surface, as most of them are deflected by the terrestrial magnetic field. This is of particular importance for life on earth, as this harsh matter radiation would not allow organic life in its current form.− Electromagnetic radiation mainly released by the photosphere coversthe entire frequency from short-wave to long-wave radiation. This type of solar radiation is approximately equivalent to that of a black body.

The radiant flux density of the sun Ms can be derived from the temperature within the photosphere (approximately 5,785 K);the degree of emission and the Stefan-Boltzmann-constant; it is approximately 63.5 106 W/m2.

The radiant flux density at the outer rim of the earth atmosphere Esc can be calculated:

Solar Energy…cont.

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•If the diameter of the sun ds is assumed up to the photosphere (approximately 1.39 x109 m) ;•a mean distance between the sun and the earth (LES) of approximately 1.5 x1011 m is taken into consideration,• a radiant flux density of approximately 1,370 1,370 W/mW/m22 at the top rim of the earth atmosphere •This mean value is called the solar constant•Over several years it varies less than 0.1 % due to a fluctuation in solar activity.

Solar Energy…cont.

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Elliptical orbit of the earth around the sun Solar constant in the course of one year

The solar radiation incident on the atmospheric rim throughout the course ofthe year is nevertheless characterized by seasonal variations. They are caused bythe elliptical orbit, where the earth moves around the sun during the course of oneyear

The solar constant reaches its maximum in January at almost 1,420 W/m2, due to reaching the shortest distance between the sun and the earth (Perihelion) on January, 2nd. The opposite takes place on July, 2nd, when it reaches its minimum with approximately 1,330 W/m2 (Aphelion).

Atmosphere

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•The atmosphere of the atmosphere of the earth earth is defined as the gaseous atmosphere held by the gravitational force of the earth. •It is divided into different "layers”.•Only the lower layers are of particular interest for the use of renewable energies on the surface of the earth. For the use of wind power, the atmosphere up to an altitude of, at most, several 100 m is significant.

Atmosphere…cont.

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Troposphere (the lower section):Troposphere (the lower section):It is the atmospheric layer that influences the weather and where formation of clouds and precipitation mainly takes place. In a timely and spatial average, it is characterized by a temperature decrease with increasing altitude. The extent of this temperature change depends on location and time. The temperature gradient can fluctuate within relatively large boundaries around a mean value of 0.65 K/100 m. Under certain meteorological circumstances, vertically sharply defined layers occur where the temperature does not decrease with increasing altitude, but increases instead. Such inversions occur particularly often at altitudes between 1,000 and 2,000 m at the planetary boundary layer as well as immediately above the surface of the earth ("soil inversions") and at the tropopause.

Atmosphere…cont.

Tropopause:The boundary of the troposphere and connected to the

stratosphere.Stratosphere:a temperature maximum is reached at an altitude of 40 to

50 km. Mesosphere:it reaches the next temperature extreme, a minimum at

an altitude of approximately 80 km. Above it, demarcated by the mesopause, is located the

thermosphere

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Atmosphere…cont.• Up to an altitude of around 100 km, the atmosphere consists of a mixture of

different gasesgases

The proportion of its ingredients is as defined as a chemical compound.

• This gaseous mix is – especially in the troposphere – mixed water vapour and interspersed with aerosol suspensions. However, this is subject to strong fluctuations depending on time and location.

• The basic mass, dry, pure air, consists of a mix of gases that cannot enter into the liquid or solid phase under atmospheric conditions (i.e. permanent gases).

• Their condensation or solidification temperatures are far below the temperatures occurring within the atmosphere.

Main components: nitrogen (N2) and and oxygen (O2),

Others: argon (Ar) and carbon dioxide (CO2), neon (Ne), helium (He), krypton (Kr) and xenon (Xe) as well as small amounts of ozone (O3) ,and hydrogen (H2) in the atmosphere.

Particularly the proportions of ozone (O3) and hydrogen (H2) gases vary depending on time and location

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Atmosphere…cont.

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Balance of Energy Flow

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Energy from the three primary renewable energy sources sun, geothermal heat, and planetary gravitation and motion, occurs on the earth in very different forms (e.g. heat, fossil energy carriers or biomass) or causes very different effects (e.g. waves, evaporation and precipitation)

Examples of energy derivations:•Wind energy, for example, is a result of air movements within the caused by solar radiation and influenced by the rotation of the earth. •The heat on the crust of the earth that is accessible to human beings consists of solar energy and geothermal heat.

Balance of Energy Flow…cont.

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Balance of Energy Flow…cont.

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the Earth is almost in an energetic balance, the added energy has to be balanced by a corresponding withdrawal.

Energy sources:•The very largest part of the energy converted on the earth every year thus originates from the sun (over 99.9 %). •Planetary gravitation and motion as well as geothermal energy additionally only account for approximately 0.022 % of the energy balance.

Energy Usages:The global use of primary energy from fossil biogenous and fossil mineral energy reserves and resources adds a further 0.006 % or approximately 413 EJ (2005) per year

Energy balance of Earth

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Optical windows: The atmosphere is to a large extent impermeable for solar radiation.

• Only within the optical spectral range (0.3 to 5.0 μm; window Iwindow I) and

• within the low-frequency range (10-2 to 102 m, window window IIII) radiation can pass the atmosphere (so-called optical windows of the atmosphere).

• Due to energetic reasons only window I window I is relevant for the technical use of solar energy. The most important part of the optical window I covers the range of visible light between 0.38 and 0.78 μm.

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Solar RadiationSolar RadiationPrinciples

Principles…cont.

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Optical windows of the atmosphere

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Solar RadiationSolar RadiationWeakening of radiation extinction process

DiffusionDiffusion: diversion of radiation from its original radiation anglewithout energy transfer and thus without a loss of energy. Such diffusion takes place i.e. in air molecules, water drops, ice crystals, and aerosol particles.Rayleigh diffusionRayleigh diffusion: diffusion at particles with a radius significantly smaller than the wavelength of the incident light (e.g. air molecules). Mie diffusionMie diffusion: takes place at particles with a radius within the wavelength of the incident light and larger (e.g. aerosol particles). The larger the particles at which the sunlight is diffused, the more they diffuse into a forward direction. Mie diffusion then turns into diffraction.

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Absorption: the conversion of solar radiation into other energy forms.

In general, solar radiation is converted into heat during this process.Such absorption can take place in aerosol, cloud and precipitation particles.

Additionally, a selective absorption is possible; here selected spectral andwave-length ranges of solar radiation are absorbed by some gases existingwithin the atmosphere.

This is especially the case for ozone (O3) and water vapour (H2O). Ozone, for example, almost completely absorbs the spectral range between 0.22 and 0.31 μm. Carbon dioxide (CO2), in comparison, only minimally absorbs solar radiation.

Solar RadiationSolar RadiationWeakening of radiation extinction process

Solar RadiationSolar RadiationWeakening of radiation extinction process

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This weakening is described by the so-called transmission factor τG ; it covers all weakening effects affecting solar global radiation incident on the outer atmospheric layer passing through the atmosphere. Gg is the global radiation and ESC the solar constant.

The transmission factor consists of the Rayleigh diffusion τRD, the Mie diffusion τMD and the absorption within gases τGA as well as the absorption within particles τPA :

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Solar RadiationSolar RadiationSpectral Range

Due to the weakening of the radiation within the atmosphere of the earth, the energy distribution spectrum of sunlight is changed

The spectrum of the solar radiation before & after passing through the earth’s atmosphere:

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Solar RadiationSolar RadiationSpectral Range…cont.

Due to the described radiation weakening processes within the atmosphere of the earth, the energy distribution of solar radiation reaching the earth shows the following characteristics:− The energy maximum is within the visible spectral range between 0.5 and0.6 μm (green to yellow light).− With a decreasing wave length (i.e. in the ultraviolet spectrum) the radiated power decreases rapidly.− With an increasing spectral range (i.e. in the infrared spectrum) the radiation decreases more slowly.− Some specific wave lengths show deep cuts in the energy distribution curve ("dark ranges"). They are caused by selective absorption of the sunlight by selected elements within the atmosphere.

Solar Radiation Solar Radiation Direct, diffuse and global radiation

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The diffusion mechanisms within the atmosphere cause diffuse and direct radiation to incident on the surface of the earth.Direct Direct radiation:radiation: the radiation incident on a particular spot, having travelled astraight path from the sun. Diffuse radiation:Diffuse radiation: the radiation emerged by diffusion in the atmosphere and thus indirectly reaching a particular spot on the earth’s surface.

The sum of direct (beam) radiation Gb and diffuse radiation Gd,

always related to the horizontal receiving surface, is called global radiation global radiation Gg

The diffuse radiation Gd consists of the radiation diffused in the atmosphereatmosphere, the atmospheric counteratmospheric counter--radiationradiation, and the radiation reflected by the neighborhoodreflected by the neighborhood.

Solar Radiation Solar Radiation Direct radiation on tilted, aligned surfaces

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The direct radiation incident on a tilted surface is determined by its incident angle ψ. This angle in turn is dependent on the alignment and the location of the receiving surface and the position of the sun

Geometric interrelationships of radiation incident on tilted surfaces

α : the slope or tilt angle of the surface (horizontal 0), β : the surface azimuthangle (i.e. diversion from the South alignment, south 0, west positive), φ : the latitude (north positive), δ : the solar declination and wh: the hourly angle of the sun;this angle is at 0°when the sun is at its highest position and is negative in the morning and positive in the afternoon.

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Conversion of the direct solar radiation on a tilted, aligned surface Gb,t,a (i.e. oriented towards a particular direction) can be calculated from the direct radiation Gb on the horizontal surface, using the angle of radiation incidence ψ, the inclination of the surface with respect to the horizontal level α, the solar azimuth angle β, and the collector azimuth angle (alignment of the surface normal according to the direction) γ :

Solar Radiation Solar Radiation Direct radiation on tilted, aligned surfaces…cont

Solar Radiation Solar Radiation Diffuse radiation on tilted, aligned surfaces

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The conversion of the diffuse proportion of the solar radiation on the tilted and aligned surface Gd,t,a depends on a number of influencing factors and cannot be described entirely analytically. If it is assumed, as a simplification, that diffuse radiation is evenly distributed withinspace, the same proportion incidents from all directions on a particular point ofthe surface of the earth (isotropic model). Under these simplified boundary conditions, the diffuse radiation incident on tilted, aligned surfaces is calculated with the diffuse radiation incident on the horizontal surface Gd and the angle of inclination of the receiving surface against the horizontal α

Assuming an isotropic distribution of radiation only describes the given circumstances to a limited extent. If the atmosphere is solely filled with diffuse radiation due to a heavy and homogenous cloud cover, the area around the positionof the sun is nevertheless generally brighter than the rest of the sky circumsolar circumsolar shareshare

Solar Radiation Solar Radiation Reflection radiation on tilted, aligned surfaces

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A certain proportion of the global radiation incident in the neighborhood of a defined surface is reflected onto the receiving tilted, aligned surface Gr,t,a

This reflected radiation can be calculated using the albedo AG (i.e. the ratio of reflected to the incident global radiation), the global radiation incident on the horizontal receiving surface Gg, and the inclination angle towards the horizontal α

The albedo depends on site-specific conditions:Snow: 0.7 - 0.9 Sand: 0.25 - 0.35 Farmland / Forest: 0.1 - 0.2

Solar Radiation Solar Radiation Global radiation on tilted, aligned surfaces

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The global radiation incident on an tilted and aligned surface, for example the surface of a photovoltaic module, consistsof the incident direct (Gb,t,a)and diffuse radiation (Gd,t,a) as well as the radiation reflected by the neighborhood on this receiving surface (Gr,t,a).

Supply Supply characteristicscharacteristicsMeasuring radiation

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If radiation energy has to be measured in absolute terms, the incident solar energy has to be converted into a measurable parameter first. Most of these radiation measurement instruments thus absorb the radiation energy on a blackened surface which converts it into heat. Due to this process the temperature of the surface increases. Correspondingly, an amount of heat per time unit is released by heat transfer in the instrument or into the air by thermal radiation. In this case, the resulting temperature increase is a measure for the radiation energy. Types of such absolute instruments :•Moll-Gorcynsky pyranometer•the compensation-pyrheliometer named after Angström.

A relative instrument can be used to calibrate such an absolute instrument. One example of a relative instrument is the Michelson-Marten Actinometer.

Supply Supply characteristicscharacteristicsMeasuring radiation…cont.

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In order to measure direct solar radiation (i.e. the proportion of direct radiation related to the global radiation) the pyrheliometerpyrheliometer is used. One of two equal, blackened thin Manganin surfaces is exposed to direct solar radiation which, in turn, heats it up. The other surface, without incident solar radiation, is heated with electrical energy to the same temperature as the exposed surface. The production of heat is proportional to the square of the electric current. Thus the electric current is equivalent to the absorbed radiation energy.

Pyrheliometers are normally adjusted to the incident radiation, and are built in a way that enables only direct radiation to incident on the receiving surface, for example by positioning the plane surface within a tube.

Supply Supply characteristicscharacteristicsMeasuring radiation…cont.

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In order to measure global radiationmeasure global radiation, pyranometers are used (e.g. the Moll-Gorcynsky pyranometer). This instrument has a radiation thermopile as receivingsurface. Its counter junctions are thermally connected with the casing. The temperaturedifference caused by heating of the receiving surface due to the solarradiation generates pressure, which serves as a measure for global radiation.

In order to avoid atmospheric influences on the measuring processto avoid atmospheric influences on the measuring process, the receivingsurface is protected with spherical calotte made of different materials, in accordancewith the spectral range to be measured.

In order to measure for example shortshort--wave wave radiation fluxesradiation fluxes, hemispheres made of silica glass are used. To measure long long and shortand short--wave radiation fluxeswave radiation fluxes, spherical caps made of polyethylene, and for long-wave radiation fluxes silicon hemispheres are used.

Pyranometers are mainly aligned horizontally. If the direct radiation proportion of the global radiation is cut out, cut out, e.g. by shielding from direct solar radiation by a circular disk or a fixed shade ring (shadow band), these instruments can also be used to measure diffuse radiation.

Supply characteristics Supply characteristics Distribution of radiation

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Worldwide, global radiation is measured at numerous sites. If these measured radiation values available as hourly, daily or monthly mean values are added up over one year and the long-term mean values are calculated, the average expected radiation for this particular site is obtained

Distribution of annual mean values of total global radiation world wide

Supply characteristics Supply characteristics Time variations

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The solar radiation supply in one location is subject to significant time fluctuations. Some of these fluctuations are of deterministic, some of them of stochastic nature.

Annual, daily and hourly curves of measured global radiated power based on an exemplary site in North Germany

Supply characteristics Supply characteristics Time variations…cont.

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Deterministic and stochastic part of solar radiation

Wind Energy

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Solar radiation also maintains the movement of the air masses within the atmosphere of the earth. Of the total solar radiation incident on the outer layer of the atmosphere, approximately 2.5 % or 1.4 1020 J/a are utilized for the atmospheric movement. This leads to a theoretical overall wind power of approximately 4.3 1015 W.

The energy contained in the moving air masses, which for example can be converted into mechanical and electrical energy by wind mills, is a secondary

form of solar energy.

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Wind EnergyWind EnergyPrinciples Mechanism

Wind is generated as equalizing currents, essentially as a result ofvarying temperature levels on the surface of the earth differences in air pressure. The air masses then flow from higher pressure areasto lower pressure areas.

Gradient force caused by the pressure gradient between such ahigh and a low-pressure zone impacts on an air particle.

Coriolis force impacts on each particle within a rotating reference system and is always vertical to the direction of movement and to the rotational axis.

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Wind EnergyWind EnergyPrinciples Mechanism

Origin of geostrophic wind

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If there is a large pressure difference at great altitudes, an air particle exposed to this pressure difference starts moving from a point of higher air pressure to a point of lower air pressure. It thus wants to migrate from an isobar with the pressure p1 towards an isobar with the pressure p2 Through the movement from p1 towards the lower pressure level p2, the gradient gradient forceforce accelerates the particle at constantly increasing speed. At the same time, the influence of the CoriolisCoriolis force force increases. This force is defined as the result of the product of particle mass, angular velocity of the rotating system, and the particle velocity relative to the rotating reference system.As it impacts always vertically to the direction of the movement, it constantly causes a change of the direction of the velocity vector. The resulting change of the directional movement lasts as long as the magnitude of the Coriolis force is equal to the gradient force. The particle is then not any longer subject to a resultant force; it is in equilibrium. Its speed and the Coriolis force hence remain unchanged, it is moving in parallel to the isobars.The consequent wind category, where air moves alongside the isobars, is called the geostrophicgeostrophic windwind

……continuecontinue

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The larger the pressure gradient, the closer the isobars are together and the higher is the gradient force. Therefore the air particles are accelerated more, and the speed of the particle moving from isobar with the pressure p1 to the isobar with the pressure p2 increases. The amount of the Coriolis force, however, increases proportionally to the speed of the particle the force impacts on.

Therefore for isobars located in parallel the equilibrium of forces between Coriolis force and gradient force, and thus the straight movement of the particle along the isobars always occur, independently of the difference in pressure or the gradient force. The speed of the geostrophic wind itself depends solely on the size of the pressure differences.

……continuecontinue

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Wind EnergyWind EnergyPrinciples Mechanism…cont

In areas with a low or a high-pressure core the isobars:two forces already mentioned, a third force, the centrifugal forcethe centrifugal force, also acts on the air particle. It points radially outwards .The resulting wind is called the gradient wind. In the northern hemisphere, it blows anti-clockwise, and clockwise in the southern hemisphere, around low pressure areas. For a high pressure area, the situation is reversed. As the centrifugal force reinforces the gradient force in a high pressure zone and weakens it in a low pressure zone, the gradient wind velocity in the high pressure area is greater than in the low pressure area

Geostrophic and gradient wind

Wind Energy Wind Energy Principles --- Global air circulation systems

43Planetary air flow at high altitudes

Due to these complex interdependencies, influenced additionally to a large extent by sea and land, as well as seasonal and other effects, a global air circulation system is created. It is responsible for the global exchange of air. For energetic utilization, these air movements are only of minor importance, as it is currently almost impossible to use the energy of the moved atmosphere at great altitudes, where these air circulation systems are active.

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On a global scale, the surface of the earth heats up most where the sun is in the zenith (i.e. in the area around the equator). This causes a low pressure zone close to the equator, where air streams in from the North and the South.

The subtropical high pressure belt is characterized by weak winds and clear weather. On the polar side follows a zone where the Western winds of the medium latitudes are predominant. E.g: Central Europe is located within this zone of influence. Wind direction and wind velocity change significantly depending on the wandering cyclones and anticyclones in this area. This West wind area is limited by a low pressure trough towards each of the poles. In the polar areas the wind conditions show strong fluctuations.

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Wind EnergyWind EnergyPrinciples --- Local air circulation systems

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The forces responsible for wind generation are active everywhere within the atmosphere. The resulting vertical mean wind velocity profile for selected surface conditionsThe vertical course of the wind, and thus the altitude of the planetary boundary layer depend on the weather conditions, the roughness of the soil and the character of the topography. Dependence of wind velocity vWi on altitude h

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The roughness of the soil is determined by vegetation and land development.Above surfaces with a low level of roughness (e.g. water surfaces): the wind velocity increases very quickly with increasing altitude in the lower 10 % of the planetary boundary layer. In contrast, above areas with a high level of roughness (e.g. settlements) the wind velocity of the free atmosphere is reached at higher altitudes; the vertical increase of the wind velocity above ground is slower. The roughness of the ground is a measure for the rate of increase of the wind velocity in the vertical direction above ground. It is generally described by the term roughness length.

Wind EnergyWind EnergyPrinciples --- Local air circulation systems

Exemplary roughness lengths of different surfaces

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Wind EnergyWind EnergyPrinciples---Local air circulation systems

Besides the roughness length, the thermal stratifithe thermal stratification also has an impact on the vertical change in wind velocity in the planetary boundary layer.If, for example, the vertical temperature decrease is in the range of 0.98 K/100 m, ((dry-)adiabatic temperature gradient). The atmosphere is then layered neutrally. In this case the thermal stratification of the atmosphere has no influence on the vertical wind profile. If, however, the vertical temperature gradient is smaller than the adiabatic gradient, stratification is stable. The wind velocity increases more quickly with increasing altitude above ground under these conditions. In the case of unstable stratification (i.e. a larger vertical temperature gradient compared to the adiabatic case) the wind velocity increase is smaller with increasing altitudes.

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The Hellmann approach (the so-called Hellmann altitude formula) is arelatively simple approximationvWi,h is the mean wind velocity at an altitude h vWi,ref is the wind speed at a reference altitude href (mostly 10 m). αHell is the altitude wind exponent (Hellmann-Exponent, the roughness exponent) and a function of the roughness length as wellas the thermal stability in the planetary boundary layer.

Wind EnergyWind EnergyPrinciples --- Local air circulation systems

Approximation values for the Hellmann-Exponent (αHell)dependent on location in coastal regions and stratification stability

Wind Energy Wind Energy Principles --- Influence of topography

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the effect of the change in velocity caused by orographyorography..e.g. above the crest of escarpments, hills or ridges, is often named in relative terms and defined as Speed-Up-Ratio. vWi is the mean wind velocity and Δh the corresponding altitude above ground. The index x defines the cross-section through the elevation and the index a a point on the upwind side of the hill, where the current is not influenced by it.

the Speed-Up-Ratio Δs or in short, the Speed-Up

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For flat two-dimensional chains of hills the approximation Δs = 2 hH / l1/2Δs = 1.6 hH / l1/2 can be used. hH : the height of the hill above the surroundingsl1/2 : half-value length and thus the horizontal distance between the peak and the half-value height (i.e. half the peak height of the hill). E.g: a maximum speed increase of around 60 % or more can result for typical values (hH = 100 m; l1/2 = 250 m), which then has a significant influence on, for example, the energy yield of a wind mill.

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‘The altitude of the maximal increase in wind speed above the peak for most hills is between 2.5 and 5.0 m’

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Wind Energy Wind Energy Principles --- Wind power

The kinetic energy EWi of moving air masses depends on the air mass mWi and the square value of the wind velocity vWi

The air mass flow entering through a particular surface mWi is defined by thesurface S it flows through, the density of the air ρWi and the wind velocity vWi

The wind power is proportionalto the cube of the wind velocity; furthermore it depends on the density of the airρWi and the cross-sectional area S of the wind flow

Wind Energy Wind Energy Supply characteristics- - - Measuring wind direction and wind speed

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Instruments that measure the wind speed (anemometers) are distinguished as either measuring the instantaneous or the mean value

Instruments that measure the instantaneous value:− Plate-anemometers, where the wind pressure directs a pendulous plate aligned vertically to the wind direction;− Dynamic air speed indicators, where either the pitot pressure (i.e. the pressure at the front stagnation point of a body flowing against (Pitot-tube)) or the dynamic pressure (i.e. the difference between the Pitot-pressure and the static surrounding pressure (Prandtl’s Pitot tube)) are measured;− Thermal anemometers, where the temperature of e.g. heating wires changes as a result of the air masses flowing past. This change can easily be measured.

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Instruments to measure the mean value:− Cup anemometers, anemometers which either measure the mean wind velocity over a few seconds (approximately 10 to 30 s) or the wind path, i.e. the product of the mean wind velocity and the time. Cup anemometers are currently the most widely used measuring instruments for 10-minute mean values as well as the 2-second-gust);− Impeller anemometers, offering principally the same features as the cup anemometers.

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Distribution of yearly annual mean values of the wind speed for 10 m aboveground worldwide

Wind Energy Wind Energy Supply characteristics- - - Wind distribution

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Wind Energy Wind Energy Supply characteristics- - - Time variations

Annual, daily and hourly courses of wind velocities for the example of a site inNorth Germany

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In spite of the diurnal and the annual course observed onaverage, measured wind velocities can vary significantly at different times, in different locations, and at different heights above ground. This is why it is very difficult very difficult to compare measured time series. Therefore time series of measured wind velocity, with varying time dissipation, are characterized by their distribution functionsdistribution functions.

Wind Energy Wind Energy Supply characteristics- - - Frequency Distribution

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Wind Energy Wind Energy Supply characteristics- - - Frequency

Distribution

Frequency distribution of wind velocity time series for different sites (left) and a corresponding mathematical approximation for site B (right)

Today, mainly the Weibull Distributionis used being the more generally defined distribution function