Chapter 5 pv systems april 11 2011

 A material or device that is capable of converting the energy contained in photons of light into an electrical voltage and current is said to be photovoltaic..  Altitude angle at sol

 A material or device that is capable of converting the

energy contained in photons of light into an electrical

voltage and current is said to be photovoltaic

 A photon with short enough wavelength and high enough energy can cause an electron in a photovoltaic material to break free of the atom that holds it

 If a nearby electric field is provided, those electrons can be swept toward a metallic contact where they can emerge as

 Spurred on by the emerging energy crises of the 1970s, the

development work supported by the space program began to pay off back on the ground

 By the late 1980s, higher efficiencies (Fig 8.1) and lower

costs (Fig 8.2) brought PVs closer to reality, and they began

to find application in many offgrid terrestrial applications

such as pocket calculators, off-shore buoys, highway lights,

signs and emergency call boxes, rural water pumping, and

small home systems

• While the amortized cost of

photovoltaic power did drop

dramatically in the 1990s, a

decade later it is still about

double what it needs to be to

compete without subsidies in

more general situations

Figure 8.1 Best laboratory PV cell efficiencies for various technologies (From National Center for Photovoltaics, www.nrel.gov/ncpv 2003

Critics of this decline point to the government’s lack of enthusiasm to fund PV R&D By comparison, Japan’s R&D budget is almost an order of magnitude greater

Figure 8.2 Possible evolution of turn-key PV system

prices

 Before we can talk about solar power, we need

to talk about the sun

 Need to know how much sunlight is available

 Can predict where the sun is at any time

 Insolation : incident so lar radiation

 Want to determine the average daily insolation

at a site

 Want to be able to chose effective locations and panel tilts of solar panels

 The sun

◦ 1.4 million km in diameter

◦ 3.8 x 10 20 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

 Plank’s law – wavelengths emitted by a blackbody depend on temperature

8

5

3.74 10

(7.1)14400

Source: en.wikipedia.org/wiki/Electromagnetic_radiation

Visible light has a wavelength of between 0.4 and 0.7 μm, with

ultraviolet values immediately shorter, and infrared immediately longer

The earth as a blackbody

Figure 7.1

Area under curve is the total radiant power emitted

 Total radiant power emitted is given by the

Stefan –Boltzman law of radiation

 The wavelength at which the emissive power

per unit area reaches its maximum point

• λmax =0.5 μm for the sun , T = 5800 K

• λmax = 10.1 μm for the earth (as a blackbody), T = 288 K

Figure 7.2

• h1 = path length through atmosphere with sun

 Air mass ratio of 1 (―AM1‖) means sun is directly

overhead

 AM0 means no atmosphere

 AM1.5 is assumed average at the earth’s surface

2 1

1

sin

h m



Figure 7.3

• m increases as the sun appearslower in

the sky

• Notice there is a large

loss towards the blue end for higher m , which is why the sun appears reddish at sun rise and sun set

 One revolution every 365.25 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 one day, the earth rotates 360.99˚

 The earth sweeps out what is called the ecliptic plane

 Earth’s spin axis is currently 23.45˚

 Equinox – equal day and night, on March 21

and September 21

 Winter solstice – North Pole is tilted furthest

from the sun

 Summer solstice – North Pole is tilted closest to the sun

Figure 7.5

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

 Solar 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

 Predict where the sun will be in the sky at any time

 Pick the best tilt angles for photovoltaic (PV) panels

Figure 7.6

Solar declination

 Solar noon – sun is

directly over the

 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

 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

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

 Zenith – perpendicular axis at a site

Figure 7.9

 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

 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

Figure 7.10 Azimuth Angle

Altitude 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)

sin   cos cos cosL  H sin sin (7.8) L 

• Test to determine if the angle magnitude is less than

or greater than 90˚ with respect to true south-

 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)

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

 Two possible azimuth angles exist

 Apply the test (7.11)

 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

 Trees to the southeast, small building to the

southwest

 Can estimate the amount of energy lost to

shading

Figure 7.15

 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

Source: NYTimes, 4/7/08

 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

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

Time Zone Local Time Meridian

 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

 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

 Find Eastern Daylight Time for solar noon in

Boston (longitude 71.1˚ W) on July 1

 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

 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 cosL  H sin sin (7.8) L 

sin   cos cos cosL  H sin sinL   0 (7.15)

 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

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

 Diffuse radiation IDC – scattered by molecules in the atmosphere

 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/m 2

 n = day number

2 0

 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

 Can treat attenuation as an exponential decay function

(7.21)

km B

I  Ae

• k = optical depth

• m = air mass ratio from (7.4)

(7.21)

km B

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

 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, r, ranging down from 0.8 for clean snow to 0.1 for a shingle roof

cos

BC B

 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, west]

east- Ballpark figures for tracking system benefits

are about 20% more for a single axis, and 25 to 30% more for a two axis

 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

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

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

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

 When Prof Chapman built a new house in

Urbana in 2007 he added some solar PV

 His system has 14 modules

with 205 W each, for a

total of 2870W He has

a 3300 W inverter

 Total cost was about $27,000,

but tax credits reduced it

to $16,900

 He should be getting about 3700 kWh per year

Source: www.patrickchapman.com/solar.htm

Solar Intensity: Atmospheric Effects

Sunlight at sea level

at 40° N Lattitude at noon (AM1.5)

• Accelerated lifetime testing

•30 year outdoor test is difficult

•Damp heat, light soak, etc

• Inverter & system design

•Micro-inverters, blocking diodes, reliability

Short-circuit current

Maximum Power Point

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

 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

metal.svg

state is the Fermi distribution

probability of finding an electron is 0.5

 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

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

Cut-off wavelength

Table 8.2 Band Gap and Cut-off Wavelength Above Which Electron

Excitation Doesn’t Occur

•The gaps between allowable energy bands are called forbidden bands, the most important of which is the gap separating the

conduction band from the highest filled band below it

•The energy that an electron must acquire to jump across the

forbidden band to the conduction band is called the band-gap energy, designated Eg

•The units for band-gap energy are usually electron-volts (eV), where one electron-volt is the energy that an electron acquires when its voltage is increased by 1 V (1 eV = 1.6 × 10−19 J)

•The band-gap Eg for silicon is 1.12 eV, which means an electron needs to acquire that much energy to free itself from the

electrostatic force that ties it to its own nucleus—that is, to jump into the conduction band

When a photon with more than 1.12 eV of energy is absorbed by a solar cell, a single electron may jump to the conduction band

When it does so, it leaves behind a nucleus with a +4 charge that now

has only three electrons attached to it

That is, there is a net positive charge, called a hole, associated with that nucleus as shown in Fig 8.7a Unless there is some way to sweep the electrons away from the holes, they will eventually recombine, obliterating both the hole and electron as in

Fig 8.7b

When recombination occurs, the energy that had been associated with the electron

in the conduction band is released as a photon, which is the basis for light-emitting diodes (LEDs)

Figure 8.7 A photon with sufficient energy can create

a hole–electron pair as in (a).The electron can

recombine with the hole, releasing a photon of energy

(b)

Figure 8.8 When a hole is filled by a nearby valence electron, the hole appears to move

Example 8.1 Photons to Create Hole–Electron Pairs in Silicon What maximum

wavelength can a photon have to create hole–electron pairs in silicon? What

minimum frequency is that? Silicon has a band gap of 1.12 eV and 1 eV = 1.6 ×

For a silicon photovoltaic cell, photons with wavelength greater than 1 11 μm

have energy hν less than the 1.12-eV band-gap energy needed to excite an

electron None of those photons create hole–electron pairs capable of carrying current, so all of their energy is wasted It just heats the cell On the other

hand, photons with wavelengths shorter than 1 11 μm have more than enough

energy to excite an electron Since one photon can excite only one electron, any

extra energy above the 1.12 eV needed is also dissipated as waste heat in the

cell Figure 8.9 uses a plot of (8.2) to illustrate this important concept The band gaps for other photovoltaic materials—gallium arsenide (GaAs), cadmium telluride (CdTe), and indium phosphide (InP), in addition to silicon—are shown in

Table 8.2

Figure 8.9 Photons with

wavelengths above 1.11 μm

don’t have the 1.12 eV needed

to excite an electron, and this

energy is lost Photons with

shorter wavelengths have more

than enough energy, but any

energy above 1.12 eV is wasted

as well