presentation on Green Electric Energy

Lecture 22Sun as Resource, PV

Professor Tom OverbyeDepartment of Electrical and

Computer Engineering

ECE 333 Green Electric Energy

Announcements

• Start reading Chapter 7• Homework 9 is 6.12, 6.14, 6.15. It doesn’t need to be turned in but should

be completed before the test. Kate will post solutions by next Tuesday. • Exam 2 is Thursday November 19 in class. You can bring in your old note

sheet and one new notes sheet. Kate is posting exam 2 from last semester. Test covers up through all of wind, but not solar.

The Sun’s Position in the Sky

• Predict where the sun will be in the sky at any time• Pick the best tilt angles for photovoltaic (PV) panels

Figure 7.6

• Another perspective-

Solar declination

Solar Noon and Collector Tilt

• Solar noon – sun is directly over the local line of longitude

• Rule of thumb for the Northern Hemisphere - a south facing collector tilted at an angle equal to the local latitude

• During solar noon, the sun’s rays are perpendicular to the collector face

Figure 7.8

Altitude Angle βN at Solar Noon

• Altitude angle at solar noon βN – angle between the sun and the local horizon

• Zenith – perpendicular axis at a site

90 (7.7)N L

Figure 7.9

Example 7.2 – Tilt of a PV Module

• Find the optimum tilt angle for a south-facing PV module located at in Tucson (latitude 32.1˚) at solar noon on March 1

• From Table 7.1, March 1 is day n = 60

Example 7.2 – Tilt of a PV Module

• The solar declination δ is

• The altitude angle is

• To make the sun’s rays perpendicular to the panel, we need to tilt the panel by

360 36023.45sin 81 = 23.45sin 60 81 = -8.3 365 365

n

90 = 90 32.1 8.3 49.6 N L

90 = 40.4Ntilt

Solar Position at Any Time of Day

• Described 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

Altitude Angle and Azimuth Angle

Figure 7.10

Azimuth Angle

Altitude Angle

Altitude Angle and Azimuth Angle

• Hour angle H- the number of degrees the earth must rotate before sun will be over your line of longitude

• If we consider the earth to rotate at 15˚/hr, then

• At 11 AM solar time, H = +15˚ (the earth needs to rotate 1 more hour)

• At 2 PM solar time, H = -30˚

15hour angle hours before solar noon (7.10) hour

H

Altitude Angle and Azimuth Angle

sin cos cos cos sin sin (7.8) L H L cos sinsin (7.9)

cosSH

• H = hour angle• L = 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 (7.11) tan S SH

L

Example 7.3 – Where is the Sun?

• Find altitude angle β and azimuth angle ϕS at 3 PM solar time in Boulder, CO (L = 40˚) on the summer solstice

• At the solstice, we know the solar declination δ ˚ = 23.45• Hour angle H is found from (7.10)

• The altitude angle is found from (7.8)

15 -3 h 45h

H

sin cos 40cos 23.45cos 45 sin 40sin 23.45 0.7527

1sin 0.7527 48.8

Example 7.3 – Where is the Sun?

• The sin of the azimuth angle is found from (7.9)

• Two possible azimuth angles exist

• Apply the test (7.11)

cos 23.45 sin 45sin = -0.9848

cos 48.8S

1 = sin -0.9848 80S

1 = 180 -sin -0.9848 260 or 100S

cos cos 45 0.707H tan tan 23.45 0.517tan tan 40L

= 80 (80 west of south)S

Sun Path Diagrams for Shading Analysis

• Now we 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

• 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

• Can estimate the amount of energy lost to shading

Figure 7.15

California Solar Shade Control Act

• The 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

Source: NYTimes, 4/7/08

Solar Time vs. Clock Time

• Most solar work deals only in solar time (ST)• Solar time is measured relative to solar noon• Two adjustments –

– For a longitudinal adjustment related to time zones– For the uneven movement of the earth around the sun

• Problem with solar time –two places can only have the same solar time is if they are directly north-south of each other

• Solar time differs 4 minutes for 1˚ of longitude• Clock time has 24 1-hour time zones, each spanning 15˚ of longitude

World Time Zone Map

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

US Local Time Meridians (Table 7.4)

Time Zone Local Time MeridianEastern 75˚Central 90˚

Mountain 105˚Pacific 120˚

Eastern Alaska 135˚Alaska and

Hawaii150˚

Solar Time vs. Clock Time

• The 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

9.87sin 2 7.53 1.5sin minutes (7.12)E B B B

360 -81 (degrees) (7.13)364

B n

Solar Time vs. Clock Time

• Combining 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) degree

E

(7.14)

Example 7.5 – Solar Time vs. Local Time

• Find Eastern Daylight Time for solar noon in Boston (longitude 71.1˚ W) on July 1

• July 1 corresponds to n = 182• From the Equation of Time (7.12) and (7.13) we

obtain 360 360 = ( 81) (182 81) 99.89364 364

B n

= 9.87sin 2 7.53cos 1.5sin = 3.5 minE B B B

Example 7.5 – Solar Time vs. Local Time

• The local time meridian for Boston is 75˚, so the difference is 75 ˚-71.7 ˚, and we know that each degree corresponds to 4 minutes

• Using (7.14)

• But we need to adjust it for Daylight Savings, so add 1 hour

= 4 min/ 75 71.1 ( 3.5min)CT ST = 12 : 00 12.1min 11: 49.9 AM ESTCT

= 12 : 49.9 AM EDTCT

Sunrise and Sunset

• Can approximate the sunrise and sunset times• Solve (7.8) for where the altitude angle is zero

• + sign on HSR indicates sunrise, - indicates sunset

sin cos cos cos sin sin (7.8) L H L sin cos cos cos sin sin 0 (7.15) L H L

sin sincos = tan tan (7.16) cos cos

LH LL

1cos ( tan tan ) (7.17) SRH L Hour angle of sunrise

Sunrise (geometric) 12 : 00 (7.18) 15 /

SRHh

Sunrise and Sunset

• Weather service definition is the time at which the upper limb (top) of the sun crosses the horizon, but the geometric sunrise is based on the center

• There is also atmospheric refraction• Adjustment factor Q

• Subtract this from the geometric sunrise

3.467Q (min) (7.19) cos cos sin SRL H

Clear Sky Direct-Beam Radiation

• Direct beam radiation IBC – passes in a straight line through the atmosphere to the receiver

• Diffuse radiation IDC – scattered by molecules in the atmosphere

• Reflected radiation IRC

– bounced off a surface near the reflector

Figure 7.18

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 number2

0360SC 1 0.034cos (W/m ) (7.20) 365

nI These changes are due to the variation in earth’s distance from the sun

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 Radiation

• Can treat attenuation as an exponential decay function

(7.21) kmBI Ae

• IB = beam portion of the radiation that reaches the earth’s surface

• A = apparent extraterrestrial flux• k = optical depth • m = air mass ratio from (7.4)

Attenuation of Incoming Radiation

(7.21) kmBI Ae

From curve fits of the table data, A and k are approximately

23601160 75sin 275 (W/m ) (7.22) 365

A n

3600.174 0.035sin 100 (7.23) 365

k n

Solar Insolation on a Collecting Surface

• Direct-beam radiation is just a function of the angle between the sun and the collecting surface (i.e., the incident angle

• Diffuse radiation is assumed to be coming from essentially all directions to the angle doesn’t matter; it is typically between 6% and 14% of the direct value.

• Reflected radiation comes from a nearby surface, and depends on the surface reflectance, ranging down from 0.8 for clean snow to 0.1 for a shingle roof.

cosBC BI I

Solar Insolation on a Collecting Surface, cont.

1 cos2RC BH DHI I I

Tracking Systems

• Most residential solar systems have a fixed mount, but 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), or two axis (horizontal [altitude, up-down] and vertical [azimuth, east-west]

• Ballpark figures for tracking system benefits are about 20% more for a single axis, and 25 to 30% more for a two axis

Monthly and Annual Insolation

• For a fixed system the total annual output is somewhat insensitive to the tilt angle, but there is a substantial variation in when the most energy is generated

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

Photovoltaics (PV)

Photovoltaic definition- a material or device that is capable of converting the energy contained in photons of light into an electrical voltage and current

Rooftop PV modules on a village health center in West Bengal, India

http://www1.eere.energy.gov/solar/pv_use.html

"Sojourner" exploring Mars, 1997

University of Illinois 2009 Solar Decathalon House – 2nd place overall

http://www.solardecathlon.uiuc.edu/gallery.html#

PV History

• Edmund Becquerel (1839)• Adams and Day (1876)• Albert Einstein (1904)• Czochralski (1940s)• Vanguard I satellite (1958)

• Today…

http://www.nrel.gov/pv/pv_manufacturing/cost_capacity.html

Cost/Capacity Analysis(Wp is peak Watt)

PV System Overview (slides from Prof. Angus Rockett)

Shadows

• Solar cell is a diode• Photopower coverted to DC• Shadows & defects convert

generating areas to loads• DC is converted to AC by an

inverter• Loads are unpredictable• Storage helps match

generation to load

Pat Chapman Solar Example

• When Prof. Chapman built a new house in Urbana in 2007 he added some solar PV.

• His system has 14 moduleswith 205 W each, for atotal of 2870W. He hasa 3300 W inverter.

• Total cost was about $27,000,but tax credits reduced itto $16,900.

• He should be getting about 3700 kWh per year

Source: www.patrickchapman.com/solar.htm

Solar Intensity: Atmospheric Effects

Sun photosphere

“AM” means “air mass”

Inte

nsity

Extraterestrial sunlight (AM0)

Sunlight at sea level at 40° N Lattitude at noon (AM1.5)

Some General Issues in PV

• The device• Efficiency, cost, manufacturability automation, testing

• Encapsulation• Cost, weight, strength, yellowing, etc.

• Accelerated lifetime testing• 30 year outdoor test is difficult• Damp heat, light soak, etc.

• Inverter & system design• Micro-inverters, blocking diodes, reliability

What are Solar Cells?

Cur

rent

Voltage

Open-circuit voltage

Short-circuit current

Maximum Power Point

n-ty

pe

p-ty

pe

-+

Load

• Solar cells are diodes• Light (photons) generate free

carriers (electrons and holes) which are collected by the electric field of the diode junction

• The output current is a fraction of this photocurrent

• The output voltage is a fraction of the diode built-in voltage

Standard Equivalent Circuit Model

Pho

tocu

rren

t so

urce Dio

de

Shu

nt

resi

stan

ce

Load

Series resistance

Where does the power go?

(minimize)

(max

imiz

e)

Energy-band Diagrams

• Electrons in solids fill states until you run out of them• Conduction band – top band, here electrons contribute to

current flow, empty at absolute zero for semiconductors• Valence band – highest energy band where electrons are

normally present at absolute zero• An electron must acquire the band gap energy to jump across

to the conduction band, measured in electron-volts eV• Silicon band gap energy is 1.12 eV

Energy-band Diagrams

http://upload.wikimedia.org/wikipedia/commons/c/c7/Isolator-metal.svg

• The probability of finding an electron in a state is the Fermi distribution

• The Fermi energy is the energy at which the probability of finding an electron is 0.5

Electrons and Holes

• Electrons create holes when they jump to the conduction band

• Electrons can move in the conduction band• Can talk about holes moving also (the way electrical

engineers are used to thinking – like how current moves from + to -)

• Photons with enough energy create hole-electron pairs in a semiconductor

Photons

• Photons are characterized by their wavelength (frequency) and their energy

(8.1)c v

(8.2)hcE hvv

Quantity Si GaAs CdTe InPBand gap (eV) 1.12 1.42 1.5 1.35

Cut-off wavelength (μm) 1.11 0.87 0.83 0.92

Table 8.2 Band Gap and Cut-off Wavelength Above Which Electron Excitation Doesn’t Occur

Silicon Solar Cell Max Efficiency

• Upper bound on the efficiency of a silicon solar cell:• Band gap: 1.12 eV, Wavelength: 1.11 μm

• This means that photons with wavelengths longer than 1.11 μm cannot send an electron to the conduction band.

• Photons with a shorter wavelength but more energy than 1.12 eV dissipate the extra energy as heat

Silicon Solar Cell Max Efficiency

• For an Air Mass Ratio of 1.5, 49.6% is the maximum possible fraction of the sun’s energy that can be collected with a silicon solar cell

Inte

nsity

(mW

/m2 -m

)

Photons used

Maximum energy collected = Egap

Usable power 24%

Unused Photons 19%

31% Loss for Energy above Egap

Voc < Egap 16%

Fill Factor 5%Other Losses 5%

Limitations to Solar Cell Performance

Other losses:AbsorptionCollectionReflectionSeries RShunts

Analysis for a 24%-efficient Si solar cellAll photon energy above Voc is lost.Energy (eV)

Review of Diodes

• Two regions: “n-type” which donate electrons and “p-type” which accept electrons

• p-n junction- diffusion of electrons and holes, current will flow readily in one direction (forward biased) but not in the other (reverse biased), this is the diode

Review of Diodes

• Making a connection from an n-type semiconductor (doped with impurities with extra electrons) to a p-type material (extra holes) induces an electric field

• This field is what separates charges generated by light• The depletion width is the region where carriers have

diffused

http://en.wikipedia.org/wiki/File:Pn-junction-equilibrium.png

The p-n Junction Diode

Voltage-Current (VI) characteristics for a diode/

0 ( -1) (8.3)dqV kTdI I e

38.90 ( -1) (at 25 C)dV

dI I e

Figure 8.15

Current in the Device:

J0: Reverse saturation current

V: Junction voltagek: Boltzmann constantT: Temperature (K)a: Ideality factor

1: ideal2: non-ideal

Photocurrent:Diode (dark) current:

Voltage (V)

Calculating Cell Parameters:

Open circuit voltage from current equation at zero current:

Solving for Voc gives:

Notes:This is for an ideal diode!! gop is proportional to light fluxVoc increases logarithmically with light flux.

Lp, Ln: Minority carrier diffusion lengths

pn, np: Minority carrier concentrations

Calculating Cell Parameters

• The previous equations in terms of the book’s notation are (just use the book equations and notation when working your problems)

• Setting I to zero, the open circuit voltage is

/0 ( -1) (8.8)qV kT

SCI I I e

0

ln 1 (8.9)SCOC

IkTVq I

+-

IV+

-LoadPV

• Add impact of parallel leakage resistance RP (want RP to be high)

• Add impact of series resistance RS (want RS to be small) due to contact between cell and wires and some from resistance of semiconductor

PV Equivalent Circuit

( ) (8.12)SC dP

VI I IR

(8.14)d SV V I R

Figure 8.22. PV Cell with parallel resistance

Vd

PV Equivalent Circuit

• Considering both RS and RP

0 exp 1 - (8.17)S S

SCP

q V I R V I RI I IkT R

Figure 8.26. Equivalent circuit for a PV Cell including series and parallel resistance

Series and Shunt Resistance Effects:Algebraically:

J JL J0 e qVJRseries / akT 1 VRshunt

Series resistance drops some voltage (reduces output voltage)

Shunt resistance drops some current (reduces output current)

Voltage & Current are coupled

Pho

tocu

rren

t so

urce D

iode

Shu

nt

resi

stan

ce

Load

Series resistance

(minimize)

(max

imiz

e)

Equivalent Circuit

Series and Shunt Resistance Effects

• Parallel (RP) – current drops by ΔI=V/RP

• Series (RS) – voltage drops by ΔV=IRS

Figure 8.23

Figure 8.25

Fill Factor and Cell Efficiency

Fill Factor (FF) =

Jmax•Vmax

Pabs = Jsc•Voc

Cell Efficiency

() =

Jsc•Voc•FFIncident Power

Jmax•Vmax

Incident Power

=

“AM 1.5” Incident Solar Power ~100 mW/cm2

JSC

Sizes important to PV

• Absorption coefficient:Thicker is better.You need at least 2 absorption

lengths even with a back surface reflector.

• Carrier diffusion length:Thinner is better.Need to be able to diffuse to

the contacts.• Optimal performance:

10 nm for organics1-2 microns for CdTe, CIS, a-

Si:H2-10 microns for GaAs20-100 microns for Si, Ge

Material Lifetime (sec) Mobility (cm2/V-sec) Ln Lp (m)

x-Si ~ 100 1350 480 590 340

CdTe ~ 0.001 3 500 0.12 1.6

GaAs ~ 0.1 8500 400 50 10

CuInSe2 ~ 0.01 800 200 3 1

a-Si ~ 0.001 1 0.05

organics ~ 0.001 10-3 0.002

Absorption of Light in the Solar Cell

Light trapping can be used to extend the path length of the light in the absorber, allowing a thinner layer to be used.

No light trapping absorption or reflection at back surface

Back surface patterned to reflect & scatter light

Front & back surface patterned to refract & scatter light