EML4450L7

EML4450L7 - Sustainable Energy Science and Engineering...

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S ustainable E nergy S cience and E ngineering C enter Direction of Beam Radiation: The geometric relationships between a plane of any particular orientation relative to the earth at any time and the incoming beam solar radiation can be described in terms of several angles (Latitude( φ ), Declination( δ ), Slope( β ), Surface azimuth angle( γ ), Hour angle( ω ), Angle of incidence( θ ), Zenith angle( θ z ), Solar altitude angle ( α s ) and solar azimuth angle ( γ s )). Observer-Sun Angles θ z = 90 o α s
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S ustainable E nergy S cience and E ngineering C enter ψ ψ ψ α sin Sun’s Position α= sin δ sin φ+ cos cos ω cos ψ= sin α sin φ− sin cos cos Zenith
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S ustainable E nergy S cience and E ngineering C enter Source: Photovoltaic systems Engineering by Messenger & Ventre, CRC 2000. Observer-Sun Angles
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S ustainable E nergy S cience and E ngineering C enter Collector Angle There is a set of useful relationships among these angles. Equations relating the angle of incidence of beam radiation on a surface, θ , to the other angles are: δ= 23.45sin 360 284 + n 365 cos θ= sin δ sin φ cos β sin cos sin cos γ + cos cos cos cos ω + cos sin sin cos cos + cos sin sin sin and cos cos θ z cos β+ sin z sin cos( s −γ ) cos z = cos cos cos ω+ sin sin For horizontal surfaces. The angle of incidence is the zenith angle of the sun θ z ( 0 o or 90 o when the sun is above the horizon). For this situation β =0 equator β 90 o β θ normal Beam radiation
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S ustainable E nergy S cience and E ngineering C enter The optimum tilt angle for a south facing photovoltaic module in Tallahassee (latitude, φ = 30.438 N) at solar noon on March 1. March 1 - sixtieth day of the year Solar declination δ = = = -8.3 o Tilt angle: φ − δ = 38.738 o 23.45sin 360 284 + n Tilt Angle of a PV Module ( ) 365 23.45sin 360 365 284 + 60) ()
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S ustainable E nergy S cience and E ngineering C enter Tracking Surface Angles For a plane rotated about a horizontal east-west axis with single daily adjustment of beam radiation being normal to the surface at noon each day: The slope of the surface is fixed for each day: If ( φ - δ ) >0, γ = 0 o ; ( φ - δ ) < 0, γ = 180 o cos θ= sin 2 δ+ cos 2 δ cos ω β=φ−δ At solar noon φ z = φ - δ
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S ustainable E nergy S cience and E ngineering C enter Sunset Hour Angle The sunset hour angle ω s , when θ z = 90 ° is given by δφ δ φ ω tan tan cos cos sin sin cos = = s Number of daylight hours: If latitude and declination are known, the day length can be calculated from the formula: () tan tan cos 15 2 1 = N ω= 12 T 24 × 360 o Where T is the time of day expressed with respect to solar midnight on a 24 hr clock.
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S ustainable E nergy S cience and E ngineering C enter Nomogram Information on latitude ( φ ) and declination ( δ ) leads directly to times of sunset and day length for either hemisphere. These parameters can be conveniently determined from the nomogram (shown on the side) as devised by Whillier (1965b).
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S ustainable E nergy S cience and E ngineering C enter Sunshine Days
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This note was uploaded on 10/22/2011 for the course EML 4450 taught by Professor Greska during the Fall '06 term at FSU.

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EML4450L7 - Sustainable Energy Science and Engineering...

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