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


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)


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)


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

http://upload.wikimedia.org/wikipedia/commons/f/f1/EM_spectrum.svg


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)


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


288 K Blackbody Spectrum

The earth as a blackbody

Area under curve is the total radiant power emitted


Extraterrestrial Solar Spectrum

Integrate over all wavelengths to get solar constant

SC = 1.377 kW/m2


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


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


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)


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


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


The Earth’s Orbit

For solar energy applications, we’ll consider the characteristics of the earth’s orbit to be unchanging


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


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


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


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


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


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


Solar Insolation on a Collecting Surface


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…

http://rredc.nrel.gov/solar/old_data/nsrdb/1991-2005/


US Annual Insolation


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


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


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


Altitude Angle and Azimuth Angle

Azimuth Angle

Altitude Angle


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


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)


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


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


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


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


World Time Zone Map

Source: http://aa.usno.navy.mil/graphics/TimeZoneMap0802.pdf


US Local Time Meridians

Time Zone Local Time Meridian

Eastern 75˚Central 90˚

Mountain 105˚Pacific 120˚

Eastern Alaska 135˚Alaska and Hawaii 150˚


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


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


Monthly and Annual InsolationTotal annual output of fixed system insensitive to tilt angle

Significant variation of month when most energy is generated


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


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


Sun Path Diagram for Shading Analysis

Trees to the southeast, small building to the southwest

Estimate the amount of energy lost to shading


Here’s a Sun Path Diagram for CVO

You can create one for your site at http://solardat.uoregon.edu/SunChartProgram.html

http://solardat.uoregon.edu/SunChartProgram.html


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


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

chemical, biological and environmental engineering introduction to solar power

Documents

advanced materials

solar power slide

earths surface slide

sunset slide

blackbody area

surface area of blackbody

blackbody spectrum

blackbody radiation