Chemical, Biological and Environmental Engineering Introduction to Solar Power.
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Transcript of Chemical, Biological and Environmental Engineering Introduction to Solar Power.
Chemical, Biological and Environmental Engineering
Introduction to Solar Power
Advanced Materials and Sustainable Energy LabCBEE
The Solar ResourceBefore we can talk about solar power, we need to talk
about the sun
• How much sunlight is available?– Relates to what is the resource at a site?
• Where the sun is at any time?– Relates to chosing effective locations and panel tilts of
solar panels
Advanced Materials and Sustainable Energy LabCBEE
The Sun and Blackbody RadiationThe sun
– 1.4 million km in diameter– 3.8 x 1020 MW of radiated electromagnetic energy
Blackbodies– Both a perfect emitter and a perfect absorber– Perfect emitter – radiates more energy per unit of surface
area than a real object of the same temperature– Perfect absorber – absorbs all radiation, none is reflected
(Clearly, no such thing exists but is a good approximation)
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Plank’s Law• Plank’s law – energy at a given wavelength emitted
by a blackbody depends on temperature
8
5
3.74 10
14400exp 1
E
T
• λ = wavelength (μm) • Eλ = emissive power per unit area of blackbody (W/m2-μm)• T = absolute temperature (K)
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Electromagnetic Spectrum
Source: en.wikipedia.org/wiki/Electromagnetic_radiation
Visible light has a wavelength of between 0.4 and 0.7 μm, ultraviolet values immediately shorter, infrared longer
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Stefan-Boltzmann Law• Total radiant power emitted is given by the
Stefan–Boltzman law of radiation
4 E A T
• E = total blackbody emission rate (W) • σ = Stefan-Boltzmann constant = 5.67x10-8 W/m2-K4
• T = absolute temperature (K)• A = surface area of blackbody (m2)
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Wien’s Displacement Rule• The wavelength at which the emissive power
per unit area reaches its maximum point
max
2898
T
T = absolute temperature (K)λmax = wavelength for maximal emissive power (μm)
For the sun , T = 5800 K; λmax =0.5 μm For earth (as a blackbody), T = 288 K; λmax = 10.1 μm
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288 K Blackbody Spectrum
The earth as a blackbody
Area under curve is the total radiant power emitted
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Extraterrestrial Solar Spectrum
Integrate over all wavelengths to get solar constant
SC = 1.377 kW/m2
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Air Mass Ratio
h1 = path length through atmosphere with sun directly overhead h2 = path length through atmosphere to spot on surfaceβ = altitude angle of the sun
As sunlight passes through the atmosphere, less energy arrives at the earth’s surface
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Air Mass Ratio
“AM1” (Air mass ratio of 1) means sun is directly overhead
AM0 means no atmosphere
AM1.5 is assumed average at the earth’s surface
2
1
1air mass ratio =
sin
hm
h
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Solar Spectrum on Surface
As sun appears lower in sky air mass (m in figure) increases.
Notice large loss towards blue end for higher m(which is why sun appears reddish at sunrise and sunset)
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The Earth’s OrbitOne revolution every 365.24 days
Distance of the earth from the sun
n = day number (Jan. 1 is day 1)
d (km) varies from 147x106 km on Jan. 2 to 152x106 km on July 3 (closer in winter, further in summer!)
(I’ll be doing angles in degrees throughout)
8 360( 93)1.5 10 1 0.017sin km
365
nd
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The Earth’s OrbitIn one day, the earth rotates 360.99˚
The earth sweeps out what is called the ecliptic plane– Earth’s spin axis currently makes angle of 23.45˚ with
ecliptic– Equinox – equal day and night (approx 3/21 and 9/21)– Winter solstice – North Pole is tilted furthest from the sun– Summer solstice – North Pole is tilted closest to the sun
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The Earth’s Orbit
For solar energy applications, we’ll consider the characteristics of the earth’s orbit to be unchanging
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Direct beam radiation IBC – passes in a straight line through the atmosphere to the receiver
Diffuse radiation IDC – scattered by molecules and particulates in the atmosphere
Clear Sky Direct-Beam Radiation
Reflected radiation IRC – bounced off a surface near the
reflector
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Extraterrestrial Solar Insolation I0
Starting point for clear sky radiation calculations
I0 passes perpendicularly through an imaginary surface outside of the earth’s atmosphere
I0 depends on distance between earth and sun and on intensity of the sun which is fairly predictable
Ignoring sunspots, I0 can be written as
SC = solar constant = 1.377 kW/m2
n = day number
20
360SC 1 0.034cos (W/m )
365
nI
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Extraterrestrial Solar Insolation I0
In one year, less than half of I0 reaches earth’s surface as a direct beam
On a sunny, clear day, beam radiation may exceed 70% of I0
Figure 7.19
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Attenuation of Incoming RadiationTreat attenuation as an exponential decay function
kmBI Ae
IB = beam portion of the radiation that reaches the earth’s surface A = apparent extraterrestrial fluxk = optical depth m = air mass ratio
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Attenuation of Incoming Radiation
kmBI Ae
A and k can be approximated as
23601160 75sin 275 (W/m )
365A n
3600.174 0.035sin 100
365k n
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Solar Insolation on a Collecting Surface
Direct-beam radiation is a function of the angle between the sun and the collecting surface
In order to optimize this we need to know where the sun is in the sky…
Diffuse radiation comes from all directions; typically between 6% and 14% of the direct value
Reflected radiation comes from nearby surfaces, – Depends on surface reflectance– 0.8 for clean snow to 0.1 for asphalt shingle roof
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Solar Insolation on a Collecting Surface
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Other essential data for your siteYou need to know:• Average cloud cover for site
– You can get this from the “National Solar Radiation Data Base” (NSRDB)
– Maps for solar resource as affected by weather available– Database available at
http://rredc.nrel.gov/solar/old_data/nsrdb/1991-2005/
• Whether there are obstacles in path of sun– We need to figure out the path of the sun in the sky…
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US Annual Insolation
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Worldwide Annual Insolation
In 2007 worldwide PV peak was about 7800 MW, with almost half (3860 MW) in Germany, 1919 MW in Japan, 830 in USA and 655 in Spain
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The Sun’s Position in the SkyPredicts where the sun will be in the sky at any time
Allows you to pick the best tilt angles for (PV) panels Rule of thumb for the Northern Hemisphere - a south facing
collector tilted at an angle equal to the local latitude
Solar declination
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Solar DeclinationSolar declination δ – the angle formed between the
plane of the equator and the line from the center of the sun to the center of the earth
δ varies between +/- 23.45˚
Assuming a sinusoidal relationship, a 365 day year, and n=81 is the spring equinox, the approximation of δ for any day n can be found from
36023.45sin 81
365n
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Altitude Angle and Azimuth Angle
Azimuth Angle
Altitude Angle
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Solar Position at Any Time of DayDescribed in terms of altitude angle β and azimuth
angle of the sun ϕS
– β and ϕS depend on latitude, day number, and time of day
Azimuth angle (ϕS ) convention – positive in the morning when sun is in the east– negative in the evening when sun is in the west – reference in the Northern Hemisphere (for us) is true
south
Hours are referenced to solar noon
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Solar Noon and Collector TiltSolar noon – sun is directly over the local line of
longitude
Optimal tilt angle for a collector is when the sun is perpendicular to that surface (therefore = L)
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Altitude Angle βN at Solar NoonAltitude angle at solar noon βN – angle between the
sun and the local horizon
Zenith – perpendicular axis at a site
90N L
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Altitude Angle and Azimuth AngleHour angle H- the number of degrees the earth must
rotate before sun will be over your line of longitude
The earth rotates at 15˚/hr, then
At 11 AM solar time, H = +15˚ (the earth needs to rotate 1 more hour to get to solar noon…)
At 2 PM solar time, H = -30˚
15hour angle hours before solar noon
hourH
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Altitude Angle and Azimuth Angle
sin cos cos cos sin sinL H L
cos sinsin
cosS
H
H = hour angleL = latitude (degrees)
Test to determine if the angle magnitude is less than or greater than 90˚ with respect to true south-
tanif cos , then 90 , else 90
tan S SHL
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Solar Time vs. Clock TimeSolar equations work in solar time (ST)
Solar time is measured relative to solar noon
Adjustments –– For a longitudinal adjustment related to time zones– For the uneven movement of the earth around the sun
(usually ignored)
Clock time has 24 1-hour time zones, each spanning 15˚ of longitude– Solar time differs 4 minutes for 1˚ of longitude
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World Time Zone Map
Source: http://aa.usno.navy.mil/graphics/TimeZoneMap0802.pdf
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US Local Time Meridians
Time Zone Local Time Meridian
Eastern 75˚Central 90˚
Mountain 105˚Pacific 120˚
Eastern Alaska 135˚Alaska and Hawaii 150˚
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Solar Time vs. Clock TimeThe earth’s elliptical orbit causes the length of a solar
day to vary throughout the year
Difference between a 24-h day and a solar day is given by the Equation of Time E
(n is the day number again)
9.87sin 2 7.53 1.5sin minutes E B B B
360-81 (degrees)
364B n
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Solar Time vs. Clock TimeCombining longitude correction and the Equation of
Time we get the following:
CT – clock time
ST – solar time
LT Meridian – Local Time Meridian
During Daylight Savings, add one hour to the local time
Solar Time (ST) Clock Time (CT) +
4 min+ LT Meridian Local Longitude + (min)
degreeE
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Monthly and Annual InsolationTotal annual output of fixed system insensitive to tilt angle
Significant variation of month when most energy is generated
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Tracking SystemsMost residential solar systems have a fixed mount
Sometimes tracking systems are cost effective
Tracking systems are either: – single axis (usually with a rotating polar mount [parallel to
earth’s axis of rotation)– two axis (horizontal [altitude, up-down] and vertical
[azimuth, east-west]
Approximate benefits are 20% gain for single axis, 25% to 30% gain for two axis
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Sun Path Diagrams for Shading Analysis
We now know how to locate the sun in the sky at any time– This can also help determine what sites will be in the
shade at any time
Use Sun Path diagram for your location (latitude)– Sketch the azimuth and altitude angles of trees, buildings,
and other obstructions– Sections of the sun path diagram that are covered
indicate times when the site will be in the shade
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Sun Path Diagram for Shading Analysis
Trees to the southeast, small building to the southwest
Estimate the amount of energy lost to shading
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Here’s a Sun Path Diagram for CVO
You can create one for your site at http://solardat.uoregon.edu/SunChartProgram.html
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California Solar Shade Control ActThe shading of solar collectors has been an area of legal and
legislative concern (e.g., a neighbor’s tree is blocking a solar panel)
California has the Solar Shade Control Act (1979) to address this issue– No new trees and shrubs can be placed on neighboring property that
would cast a shadow greater than 10 percent of a collector absorption area between the hours of 10 am and 2 pm.
– Exceptions are made if the tree is on designated timberland, or the tree provides passive cooling with net energy savings exceeding that of the shaded collector
– First people were convicted in 2008 because of their redwoods
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The Guilty Trees were Subject to Court Ordered Pruning
Details:– Trees planted in 1997– Complainant moved in 1993– Installed PV in 2001– No shade from trees in 2001…
Source: NYTimes, 4/7/08