.997 Copyright © Gang Chen, MI
or 2.99irect Solar/T
hermal to
.997 Copyright © Gang Chen, MI
or 2.99irect Solar/T
hermal to
2
T
F
7 D
Electrical Energy Conversion
Review of Lecture 8
Solar spectra: AM0, AM1, AM1.5 etc. Definition of radiative properties Maximum efficiency of solar thermal engines Maximum achievable temperature
• Wavelength (frequency) selective surfaces
• Blackbody function
• Earth motion
••••
2
T
F
7 D
Electrical Energy Conversion
Contents of lecture 9
Solar hot water systems Maximum solar concentration Methods for concentration Nontracking and tracking
• Solar thermal-mechanical energy conversion
• EM wave calculation of surface properties
••••
1
2.997 Copyright ©
r 2.997 Direct S
cal Energy
ght ©
Chermal
ersion
g Chen, MI
r/Thermal to
ala
Gan
T
Fo
ola
Electri
Conversion
Solar Hot Water Systems
http://78.136.49.147/images/Solar%20Hot%20Water%20Heating %20Diagram.gif
How Much Area You Need? • 80 Gallon of Water • Start temperature Ti=15 oC • Hot water temperature Tf=60 oC
( )ifs TTmctJA −=•Δ•• η Energy Balance
hours/day5.5=Δt Specific heat c= 4180 J/kg.K Js=1000 W/m2
Thermal efficiency η=60%
A=5.1 m2
Gng
hen, MIT
or/T
to
Conv
Flat Panel Solar Hot Water Heaters
http://collector-solar.com/products/index.htm
2
Image by EERE.
Images removed due to copyright restrictions.Please also see:http://greennav.files.wordpress.com/2008/03/solar-panel.gif
http://www.mdelectric.ca/1_Pictures/GreenEnergies/GE-ViessmannCollector.jpg
Photo by szczel on Flickr.
Figure by MIT OpenCourseWare.
2.997 Copyrightang Ch
For 2.997 Direlar/T
hermal t
trical En
Conversion
97 Copyright © Gang C
97 Direct Solar/Thermal
nergy Conversion
© G
en, MIT
ct So
o
Elec
ergy
Evacuated Tube Technology
http://www.diytrade.com/china/4/products/1716424/All-Glass_Evacuated_Solar_Collector_Tube-SFVA.html
2.9
hen, MIT
For 2.9
to
Electrical E
Vacuum Tube Hot Water Heaters
Unpressurized Separate Tank Collector
3
Images removed due to copyright restrictions. Please see:
http://img.diytrade.com/cdimg/194777/1624552/0/1160536024/All-Glass_Evacuated_Solar_Collector_Tube-SFVA.jpg
http://img.diytrade.com/cdimg/194777/1624568/0/1160536058/All-Glass_Evacuated_Solar_Collector_Tube-SFVB.jpg
http://img.diytrade.com/cdimg/194777/1624573/0/1160536136/Metal-Glass_Evacuated_Solar_Collector_Tube-SFVC.jpg
Images removed due to copyright restrictions. Please see any photos of solar water heaters, such as:
http://image.made-in-china.com/2f0j00ferESMmCAVoH/Solar-Collector.jpg
http://image.made-in-china.com/2f0j00VBdtYnQhIaRE/Split-Pressurized-Solar-Water-Heater-CY-SP-24-.jpg
22.997 Copyright © Gang Chen, MIT
For .997 Direct Solar/Thermal to
Electrical Energy Conversion
Efficiency Estimation---Evacuated Tubes
Incoming Solar Radiation
sJL ••
Radiation Loss
( ) [iloss TLDQ = σπε
Thermal Efficiency
− ilossa DQQη
Din
Do
Absorbed Solar Radiation
ατ ••••= sia JLDQ
Qin Do =
4 4 ]a−Ts
⎛ πεσ T 4 4 ⎟⎞
⎜⎜ ]⎟[ατ Ta− −= = sQin Do JJs ⎝ ⎠s
2.997 Copyright © Gang Chen, MIT
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversion
Efficiency Estimation---Flat Panel
Js
Ther
mal
Insu
latio
n
Air
Rair1
Ts
Rg Rair2
Tam
4 sTσ4
amTσ
Solar In
Tam
[ ]K/W38.0026.0
1010 3
1 AAAk
dR air
air = ×
≈= −
[ ]K/W00025.02.1103.0 3
AAAk
dR
g
g g =
×≈=
−
[ ]K/W2.05 11
2 AAhARair =≈=
Ri
d
[ ]K/W3.01.0103 2
AAAk
dR i
i i =
×≈=
−
4
.997 Copyright © Gang
.997 Direct Solar/Therm
l Energy Conversion
2.997 Copyright © Gang Chen, MIT
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversion
Efficiency Estimation---Flat Panel
Js
Ther
mal
Insu
latio
n
Air Thermal Efficiency
in
lossa
Q
−=
− =
ατ
η
[ ]
[ ] [ ]44
4
2
5.5 amsams
am i
ams
gair
am
TTATTA
TTAR
TT
R
−+−=
−+−
+ +
εσ
εσT Ts −Qloss 4=
Rair R s+1
1.7[Ts − Tam ] −πεσ [T 4 −T 4 ]
J J s a s s
2
Chen, MIT
For 2
al to
Electrica
Estimated and Experimental Results
http://www.enviro-friendly.com/images/NSW-Winter-Solar-Efficiency-graph.jpg
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
40 50 60 70 80
Ther
mal
Effi
cien
cy
Temperature (oC)
5
Courtesy of Hills Solar. Used with permission.
Copyright © Gang Ch
97 Direct Solar/Thermal t
nergy Conversion
2.
T
o
Total Renewable Capacity in 2007
, MIne o
79 .9r 2 9
FE e t i al c r c l E
Weiss et al., Solar Heat Worldwide, 2009 Ed.
7 Copyright © Gang
7 Direct Solar/Therma
ergy Conversion
, MI
o2.99
ChenT
F r 2.99
l to
Electrical En
Solar Heat Utilization
Weiss et al., Solar Heat Worldwide, 2009 Ed.
6
Courtesy of IEA-SHC. Used with permission.
Courtesy of IEA-SHC. Used with permission.
ectrical
rrec
Ene 32'
Sun
= 1.495 x 1011 m= 9.3 x 107 mi
1.7%
1.27 x 107 m7900 mi
EarthSolar constant= 1367 W/m2
= 433 Btu/ft2 hr= 4.92 MJ/m2 hr{Gsc
{Distance is
1.39 x 109 m8.64 x 105 mi
ht © G
t SolaR
r θs
Energm
y Balance
er4 π or 2 n J = 4πR2 J
irss e
With Concentration
CJ = σT 4 ≤ σT 4 e c s = Js
J s ⎛ R ⎞2
Cmax = =⎜ ⎟Je ⎝ r ⎠
1 = = 46,164
sin2 θs
ang CEarth Orbital ,
Maximum Concentration of Sun Light---2nd Law Limit
Maximum concentration
7
Figure by MIT OpenCourseWare.
Figure by MIT OpenCourseWare.
Image by Robert Simmon (NASA).
Sol
y Conve
Sun 147,300,000 km152,100,000 km
September equinoxSept 22/23
March equinoxMar 20/21
PerihelionJanuary 3
DecembersolsticeDec 21/22
June solsticeJun 21/22
AphelionJuly 4
ra
997 Copyright
or 2.997 Direct S
trical Energ
.997 CopyrighG
7 Dir
a
θs
θs
Φ
θs
rθsr
d/2D/2
D/2
F
Concavefocusingmirror
.99ica
l En
2.
© Gang Chen, MIT
F
olar/Thermal to
Elec
y Conversion
Maximum Concentration of Sun Light---2nd Law Limit
nindexrefractive 4
e nCJ =
maxC =
Inside a medium of σTc
2n
sin2 θ
Achieved C=56,000
Gleckman et al., Nature, 339, 198 (1989)
o MI
,neh2D Flat Panel
sin Φ cos Φ sin 2Φ = =
3D Concentration
Φ= 2
sin d r sθ
sin D =Φr
D
cos
2
d sinθ 2sinθs s
1C = = 107max 2sinθ1 s
C = max 4sin2 θs
8
Image removed due to copyright restrictionsPlease see Fig. 1a in Gleckman, Philip, JosephO'Gallagher, and Roland Winston. "Concentration ofSunlight to Solar-surface Levels Using Non-imaging Optics."Nature 339 (1989): 198-200.
Figure by MIT OpenCourseWare.
7 Copyright © Gang Che
.997 Direct Solar/Thermal to
al Energy Conversion
θs
θs
Φ
θs
rθs
r
D/2
C = (D/2 π r sin θs = sin φ / sin θs1/π sin θs (1/π) Cmax
D/2
F
Concavefocusingmirror
n
r 2ric
.997 Copyright
997 Direct
C
A'A
θ
B' B
Reflector profile
Edge ray Wave front W
String Method
2. al
2.99
,T
FoElec
Imaging Concentration to Cylinder
From Fig.4.3: R. Winston et al., Nonimaging Optics, Elsevier, 2005
ang Chen, MIT
For
olar/Thermal to
Electric
Conversion
Nonimaging Optics
' BBABAC +=+
AC =
BAAB ''=
θsin1
' ' ==
BB
AAC
2D Concentration to Flat Plate
3D Concentration
21 ⎟⎞
⎜⎛ =C
A' B '
AA'sinθ
Maximum when θ=θs⎝sinθ ⎠
9
Figure by MIT OpenCourseWare.
Figure by MIT OpenCourseWare.
.997 Cop97
yriDi
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r/Thermal to
onversiona
.
MI
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lohrec
2
g t © Ga
T
t S
l Energy C
2D Concentration to Cylinder
Winston r Foand Hinter
rber
Energ cat iger, Solar y, 17, 255
ec (1975)
Courtesy of Elsevier, Inc., El http://www.sciencedirect.comUsed with permission.
Earth Orbital
Summer
997 Copyri
r 2.997 D.
gEquator
23.5o (22-24.5 o)
10
Winter
Images from Wikimedia Commons, http://commons.wikimedia.org
r/
onversi
2.997 Copyright © Gang Chen, MIT
For 2.997 Direct SolaThermal to
Electrical Energy C
on
Daily Insolation Variation Js
A At Noon: Q=JsA
A Q= JsAsinθ
θ
Js also varies due to path length
45o North Latitude http://www.eoearth.org/article/Daily_a nd_annual_cycles_of_temperature
2.997 Copyright © Gang Chen, MIT
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversion
Tracking
Js
A Q= JsAsinθ
θ
Q= JsA
θ
One Axis: Axis Along South-North Direction
11
Courtesy of Michael Pidwirny. Used with permission.
997 Copyright
For 2.997 Direct
ectrical Ener
ers
7 Copyright © Gang Ch
r 2.997 Direct Solar/Thermal t
Electrical Energy Conversion
ang Chen, MI
larrmal to
2.
© G
T
So/The
El
gy Conv ion
V-Trough • East-West Orientation, with
seasonal adjustment: 2.5-3 times
• South-North tracking
http://www.electricksolutions.com/cms/temp lates/electriksolutions/IMAGES/banner1.jpg Holland, Solar Energy, 13, 149 (1971)
2.99
en, MIT
Fo
o
Solar Thermal Energy Conversion ---Mechanical Systems
Handbook of Energy Efficiency and Renewable Energy
12
Courtesy of Elsevier, Inc., http://www.sciencedirect.com.Used with permission.
Images by EERE. Please also see Fig. 21-13 in Kreith, Frank, and D.Yogi Goswami. Handbook of Energy Efficiency and Renewable Energy.Boca Raton, FL: CRC Press, 2007.
97 Copyright © Gang Ch
or 2.997 Direct Solar/Thermal to
trical Energy Conversion
2.997 Copyright © G
h
For 2.997 Direct Solar/Th
Electrical Energy Conversion
2.9
en, MIT
F Elec
Solar Trough
ang C en, MIT
ermal to
Solar Trough
13
Courtesy of Plataforma Solar de Almería. Used with permission.
Image removed due to copyright restrictions.Please see Fig. 5.16 in Kaltschmitt, Martin, Wolfgang Streicher, and Andreas Weise.Renewable Energy: Technology, Economics, and Environment. New York, NY: Springer, 2007.Also see any photo of a commercial HCE, such as Schott's PTR 70.
2.997 Copyright © Gang Chen
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversion
2.997 Copyright © Gang Chen, MIT
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversion
, MITSolar Trough with
Molten Salt Storage
Price, H. Lupfert, E.“Advances in Parabolic Trough Solar Power Technology”
From J. Karni
14
Courtesy of Jacob Karni. Used with permission.
Photos by EERE, Sandia National Labs.
Courtesy of Elsevier, Inc., http://www.sciencedirect.com. Used with permission.
Image removed due to copyright restrictions.Please see any photo of a linear Fresnel lenssystem, such as http://commons.wikimedia.org/wiki/File:Fresnel_reflectors_ausra.jpg http://i.i.com.com/cnwk.1d/i/ne/p/2007/910Ausra1_550x367.jpg
997 Copyright © Gang Ch
or 2.997 Direct Solar/Thermal t
rical Energy Conversion
97 Copyright © Gang Chen, MI
or 2.997 Direct Solar/Thermal to
ectrical Energy Conversion
2.
en, MIT
F
o
Elect
Solar Trough: Concentration Ratio
Price, H. Lupfert, E.“Advances in Parabolic Trough Solar Power Technology”
2.9
T
F El
Price, H. Lupfert, E.“Advances in Parabolic Trough Solar Power Technology”
Solar Trough: Cost
15
Table removed due to copyright restrictions.Please see Table 2 in Price, Hank, et al."Advances in Parabolic Trough Solar Power Technology."Journal of Solar Energy Engineering 124 (May 2002): 109-125.
Table removed due to copyright restrictions.Please see Table 8 in Price, Hank, et al."Advances in Parabolic Trough Solar Power Technology."Journal of Solar Energy Engineering 124 (May 2002): 109-125.
opyriGang Chen,
97 Direct S/Thermal
rical Energy Con
ion
Copyright © Gang Chen,
2.997 Direct Solar/Thermal t
ectrical Energy Conversion
2.997 C ght ©
MIT
For 2.9
olar
to
Elect
vers
Trough Efficiency
“Assessment of Parabolic Trough and Power Tower Solar Technology Cost and Performance Forecasts” NREL, 2003
2.997
MIT
For
o
El
Trough Cost Breakdown
“Assessment of Parabolic Trough and Power Tower Solar Technology Cost and Performance Forecasts” NREL, 2003
16
Copyright © Gang Chen
2.997 Direct Solar/Thermal to
ical Energy Conversion
2.997
, MIT
or
Heliostat / Power Tower
l c rFE e t
2.997 Copyright © Gang Chen, MIT
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversion
From J. Karni
17
Courtesy of Jacob Karni. Used with permission.
Photo by Koza1983 on Wikipedia.
Images by EERE and Sandia National Laboratory.
yright © GChen, MIT
or 2.9
t Sohermal to
ectrical E
version
Copyright © Gang
Direct Solar/Therma
rgy Conversion
2.997 Cop
ang
F 97 Direc
lar/T
El
nergy Con
Heliostat Receiver
Handbook of Energy Efficiency and Renewable Energy
2.997
Chen, MIT
For 2.997
l to
Electrical Ene
Heliostat / Power Tower Cost
Handbook of Energy Efficiency and Renewable Energy
18
Images removed due to copyright restrictions.Please see Fig. 21-49. 21-51, and Table 21-9 in Kreith, Frank, and D.Yogi Goswami. Handbook of Energy Efficiency and Renewable Energy. Boca Raton, FL: CRC Press, 2007.
Image removed due to copyright restrictions. Please see Fig. 21-40 in Kreith, Frank, and D. Yogi Goswami.Handbook of Energy Efficiency and Renewable Energy.Boca Raton, FL: CRC Press, 2007.
pyrigGang Chen,
7 Direct S/Therm
cal Energy Convio
97 Copyright © Gang Chen,
or 2.997 Direct Solar/Thermal to
trical Energy Conversion
.99or 2
o
27 Co
ht ©
MIT
F.99
olar
al t
Electri
ersn
Heliostat / Power Tower Efficiency
“Assessment of Parabolic Trough and Power Tower Solar Technology Cost and Performance Forecasts” NREL, 2003
2.9
MIT
FElec
Dish
19
Photo from Wikimedia Commons, http://commons.wikimedia.org
2.997
Ch
For 2.997 D
Thermal to
Electrical Energ
version
opyright © Gang Chen,
97 Direct Solar/Therm
rical Energy Conversio
ol
2.9
Copyright © Gang en, MIT
irect Sar/
y Con
Dish and Stirling Engine
Kaltschmitt, M.,Wolfgang, S. Wiese, A. “Renewable Energy, technology, Economics and Enviroment”
TDish and Stirling Engine
MI
aol t
n
7 C9 .r 2 9o
e tFE
clKaltschmitt, M.,Wolfgang, S. Wiese, A. “Renewable Energy, technology, Economics and Enviroment”
20
Images removed due to copyright restrictions.Please see Fig. 5.20, 5.21, and 5.22 in Kaltschmitt, Martin, Wolfgang Streicher,and Andreas Weise. Renewable Energy: Technology,Economics, and Environment. New York, NY: Springer, 2007.
Table removed due to copyright restrictions.Please see Table 5.10 in Kaltschmitt, Martin, Wolfgang Streicher,and Andreas Weise. Renewable Energy: Technology, Economics,and Environment. New York, NY: Springer, 2007.
.997 Copyright © Gang Chen, MI
or 2.99irect Solar/T
hermal to
2
T
F
7 D
Electrical Energy Conversion
eJDH + ∂
∂ =
t
eρ=•∇ D
0=•∇ B
• Constitutive Relations
E --- Electric Field H --- Magnetic Field D --- Electric Displacement B --- Magnetic Induction Je --- Free Current Density
EM Waves
Maxwell Equations:
∂B∇ × E = −
∂t
∇ ×
D = ε E
B = μH
ε – Electric Permitivity μ – Magnetic permeability
EM Wave Propagation
2.997 Copyright © Gang Chen, MIT
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversion ⎤
⎢ ⎢ ⎣
⎡ ⎞ ⎜⎜ ⎝
⎛ •−−= kErE ˆexp),(
o o c
Ntit ω
Plane Wave Solution
⎢ ⎣
⎡ ⎛ = HrH exp),( ot
H
ω--- angular frequency k --- Wavevector
k̂ --- Unit Wavevector
N=n+iκ, Complex refractive index κ --- Extinction coefficient
• Poynting Vector (Energy Flux)
[ ]*Re 2 1)( HErS ×= πκα
4
inside A Medium
E•
k r ⎟⎟⎥
⎠⎥⎦
N k̂ • r ⎟⎟⎞⎤
⎜⎜ ⎝ co ⎠⎦
ωi− −t ⎥
= λo1 n −αxS = e E 2 k̂
2 μc Absorption
o Coefficient
21
2.997 Copyright © Gang Chen, MIT
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversion
EM Wave Reflection and Transmission at An Interface
Symbol Convention:
Field Going Out of Paper Field Going Into Paper
TM Wave = // Wave = p Wave E-Field In the Plane of Incidence:
H-Field In the Plane of Incidence:
TE Wave = Wave = s Wave
ki
Ei
Hi kr
Et
kt
θi θr
θt
n1
n2
Er
z
x
x n̂
• Snell Law
θi =θr
ti nn θθ sinsin 21 =
• Fresnel Coefficients
ti
ti
i
r
nn
nn
E
E r θθ θθ
coscos coscos
12
12
//
// // +
+− ==
t1i2
i1
i//
t//// cosncosn
cosn2E E
t θ+θ
θ ==
2
//// rR = // 1
2 // )cosRe(
)cosRe( tN
N
i
t
θ θτ =
• Reflectivity/transmissivity 2
2.997 Copyright © Gang Chen, MIT
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversion
Examples
Reflectivity as a function of the angle of incidence for a dielectric material with n=4 and for gold with N=10.8+i51.6.
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80
REF
LEC
TIVI
TY
INCIDENT ANGLE
Gold (wavelength=10um, TM)
Dielectric material (n=4, TM)
Gold (wavelength=10um, TE)
Dielectric material (n=4, TE)
Brewster Angle
22
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