EE 237: Solar Energy Conversion Week 2: Limits to Solar Energy ...
EE 237: Solar Energy Conversion Week 2: Limits to Solar Energy Conversion April 10 2013
tanford University
1
Recap: Solar Radiation
tanford University
2
Recap: Solar Radiation Direct, Diffuse, Albedo AM 1.5 G AM 1.5 D
Difference between AM 1.5G vs. AM 1.5D ? D = Direct, G = Global = Direct + Diffuse + .. tanford University
3
Recap: Air Mass
tanford University
4
Recap: optimal tilt and direction
Which panel is at higher latitude ?
tanford University
5
View for mere mortals
tanford University
6
Optical tilt and air mass
Earth titled 23.5 degree about the axis tanford University
7
1-axis Tracking
Why insolation not constant with tracking ? tanford University
8
Todays lecture : Limits of Solar Energy Conversion • Shockley-Queisser limit • Tiedje – Yablonovitch limit • Landsberg Limit • Black body limit
tanford University
EE 237 : Aneesh Nainani
9
Three generations of photovoltaics
Bright outlook for solar cells, Physics World, 2007
Beating the S-Q limit - battle cry for III-gen PV tanford University
EE 237 : Aneesh Nainani
10
Basics: Planck’s constant
tanford University
EE 237 : Aneesh Nainani
11
Basics: Laws of thermodynamics
First Law:
Second Law:
tanford University
EE 237 : Aneesh Nainani
12
How do I calculate efficiencies ?
tanford University
EE 237 : Aneesh Nainani
13
Saving the world: one electron pair at a time Generation
tanford University
EE 237 : Aneesh Nainani
14
Solar Cell Efficiency ElectronEnergy(Output) Optical-Electrical Energy = Conversion Efficiency PhotonEnergy(Input)
Solar Spectrum
Energy Conversion Efficiency of Silicon Cell
λ < Eg Silicon
1 Junction Silicon Solar Cell
λ > Eg
Max. Theoretical Efficiency ? What's missing in this analysis ?
tanford University
15
Shockley-Queisser limit
Planck’s Law
tanford University
16
Shockley-Queisser limit
tanford University
17
Saving the world: one electron pair at a time Generation
Rad. Recomb.
tanford University
EE 237 : Aneesh Nainani
18
Shockley-Queisser limit
Assumptions • • • • •
Concentration of one sun Sun and cell as black body Absorption: Step function Infinite mobility Loss mechanism: Radiative recombination
tanford University
19
How to calculate radiative recombination ? Tc Tc
Cell in equilibrium TA = Tc V=0
p n
V=0 tanford University
20
How to calculate radiative recombination ? Tc Tc
Cell not in equilibrium V=V
p n
V=V tanford University
21
Shockley-Queisser limit
tanford University
EE 237 : Aneesh Nainani
22
Shockley-Queisser limit
Assuming sun to be Black body at 6000K
tanford University
23
Shockley-Queisser limit Taking AM 1.5G
tanford University
24
Saving the world: one electron pair at a time Generation
SRH
Auger
Rad. Recomb.
Free carrier absorb. tanford University
EE 237 : Aneesh Nainani
25
Tiedje – Yablonovitch limit Assumptions • Concentration of one sun • Sun and cell as black body • AM 1.5G • Absorption: Step function • Finite absorption co-eff
Shockley
Queisser 1961
• Infinite mobility • Loss mechanisms • Radiative recombination • Auger • Free carrier absorption
tanford University
26
Tiedje – Yablonovitch limit Assumptions • SQ: Absorption: Step function • TJ: Actual absorption coefficient
tanford University
27
Tiedje – Yablonovitch limit
tanford University
28
Tiedje – Yablonovitch limit
tanford University
29
PS1: Multi Junction Solar Cell Optical-Electrical Energy Conversion Efficiency
=
PhotonEnergy(Input) ElectronEnergy(Output)
Energy Conversion Efficiency of Silicon Cell
Energy Conversion Efficiency of MJ Cell
λ < Eg Silicon
1 Junction Silicon Solar Cell
Material 1
3 Junction Solar Cell Stack
Material 2
λ > Eg tanford University
Max. Theoretical Efficiency ~32%
Material 3
Theoretical Efficiency 48% 30
PS1: Multi Junction Cell
I Cell 2
Cell 1 Cell 2
tanford University
Cell 1
EE 237 : Aneesh Nainani
31
SQ Limits for Multi Junction Cell • • • • •
1 cell: 32%, 41% [1-sun, concentrated] 2 cell: 42, 55% 3 cell: 48%, 63% 4 cell: 52%, 67% .. Infinite cell: 86%
tanford University
EE 237 : Aneesh Nainani
32
Thermodynamic Limits : Carnot Efficiency
tanford University
EE 237 : Aneesh Nainani
33
Landsberg Limit
tanford University
EE 237 : Aneesh Nainani
34
Blackbody radiation Entropy in convertor during absorption
Entropy in convertor during emission
tanford University
EE 237 : Aneesh Nainani
35
Blackbody radiation
tanford University
EE 237 : Aneesh Nainani
36
Blackbody radiation Limit of Thermophotovoltaics (TPV)
More on TPV in week 9 tanford University
EE 237 : Aneesh Nainani
37
SQ Limits for Multi Junction Cell • • • • •
1 cell: 32%, 41% [1-sun, concentrated] 2 cell: 42, 55% 3 cell: 48%, 63% 4 cell: 52%, 67% .. Infinite cell: 86% • Limit for any solar cell with reciprocal optics
• Black body limit (TPV): 85% • Thermodynamic (Landsberg) Limit: 93 % • Requires non-reciprocal elements • Carnot efficiency (not possible for solar): 95% tanford University
EE 237 : Aneesh Nainani
38
Suggested Reading • Sunlight / Tracking • Applied Photovoltaics, Chapter 1 • http://bit.ly/115DsyO • Solar Energy Limits • S-Q limit: HO#1 on the class website (original paper) • S-Q limit: http://sjbyrnes.com/sq.pdf • T-Y limit: HO #2 on the class website • Thermodynamic Limits • Third Generation Photovoltaics, M A Green, Chapter 3 (not free but good) • Handbook of Photovoltaics, Chapter 4, http://bit.ly/XPtTQg tanford University
EE 237 : Aneesh Nainani
39
tanford University
1
Recap: Solar Radiation
tanford University
2
Recap: Solar Radiation Direct, Diffuse, Albedo AM 1.5 G AM 1.5 D
Difference between AM 1.5G vs. AM 1.5D ? D = Direct, G = Global = Direct + Diffuse + .. tanford University
3
Recap: Air Mass
tanford University
4
Recap: optimal tilt and direction
Which panel is at higher latitude ?
tanford University
5
View for mere mortals
tanford University
6
Optical tilt and air mass
Earth titled 23.5 degree about the axis tanford University
7
1-axis Tracking
Why insolation not constant with tracking ? tanford University
8
Todays lecture : Limits of Solar Energy Conversion • Shockley-Queisser limit • Tiedje – Yablonovitch limit • Landsberg Limit • Black body limit
tanford University
EE 237 : Aneesh Nainani
9
Three generations of photovoltaics
Bright outlook for solar cells, Physics World, 2007
Beating the S-Q limit - battle cry for III-gen PV tanford University
EE 237 : Aneesh Nainani
10
Basics: Planck’s constant
tanford University
EE 237 : Aneesh Nainani
11
Basics: Laws of thermodynamics
First Law:
Second Law:
tanford University
EE 237 : Aneesh Nainani
12
How do I calculate efficiencies ?
tanford University
EE 237 : Aneesh Nainani
13
Saving the world: one electron pair at a time Generation
tanford University
EE 237 : Aneesh Nainani
14
Solar Cell Efficiency ElectronEnergy(Output) Optical-Electrical Energy = Conversion Efficiency PhotonEnergy(Input)
Solar Spectrum
Energy Conversion Efficiency of Silicon Cell
λ < Eg Silicon
1 Junction Silicon Solar Cell
λ > Eg
Max. Theoretical Efficiency ? What's missing in this analysis ?
tanford University
15
Shockley-Queisser limit
Planck’s Law
tanford University
16
Shockley-Queisser limit
tanford University
17
Saving the world: one electron pair at a time Generation
Rad. Recomb.
tanford University
EE 237 : Aneesh Nainani
18
Shockley-Queisser limit
Assumptions • • • • •
Concentration of one sun Sun and cell as black body Absorption: Step function Infinite mobility Loss mechanism: Radiative recombination
tanford University
19
How to calculate radiative recombination ? Tc Tc
Cell in equilibrium TA = Tc V=0
p n
V=0 tanford University
20
How to calculate radiative recombination ? Tc Tc
Cell not in equilibrium V=V
p n
V=V tanford University
21
Shockley-Queisser limit
tanford University
EE 237 : Aneesh Nainani
22
Shockley-Queisser limit
Assuming sun to be Black body at 6000K
tanford University
23
Shockley-Queisser limit Taking AM 1.5G
tanford University
24
Saving the world: one electron pair at a time Generation
SRH
Auger
Rad. Recomb.
Free carrier absorb. tanford University
EE 237 : Aneesh Nainani
25
Tiedje – Yablonovitch limit Assumptions • Concentration of one sun • Sun and cell as black body • AM 1.5G • Absorption: Step function • Finite absorption co-eff
Shockley
Queisser 1961
• Infinite mobility • Loss mechanisms • Radiative recombination • Auger • Free carrier absorption
tanford University
26
Tiedje – Yablonovitch limit Assumptions • SQ: Absorption: Step function • TJ: Actual absorption coefficient
tanford University
27
Tiedje – Yablonovitch limit
tanford University
28
Tiedje – Yablonovitch limit
tanford University
29
PS1: Multi Junction Solar Cell Optical-Electrical Energy Conversion Efficiency
=
PhotonEnergy(Input) ElectronEnergy(Output)
Energy Conversion Efficiency of Silicon Cell
Energy Conversion Efficiency of MJ Cell
λ < Eg Silicon
1 Junction Silicon Solar Cell
Material 1
3 Junction Solar Cell Stack
Material 2
λ > Eg tanford University
Max. Theoretical Efficiency ~32%
Material 3
Theoretical Efficiency 48% 30
PS1: Multi Junction Cell
I Cell 2
Cell 1 Cell 2
tanford University
Cell 1
EE 237 : Aneesh Nainani
31
SQ Limits for Multi Junction Cell • • • • •
1 cell: 32%, 41% [1-sun, concentrated] 2 cell: 42, 55% 3 cell: 48%, 63% 4 cell: 52%, 67% .. Infinite cell: 86%
tanford University
EE 237 : Aneesh Nainani
32
Thermodynamic Limits : Carnot Efficiency
tanford University
EE 237 : Aneesh Nainani
33
Landsberg Limit
tanford University
EE 237 : Aneesh Nainani
34
Blackbody radiation Entropy in convertor during absorption
Entropy in convertor during emission
tanford University
EE 237 : Aneesh Nainani
35
Blackbody radiation
tanford University
EE 237 : Aneesh Nainani
36
Blackbody radiation Limit of Thermophotovoltaics (TPV)
More on TPV in week 9 tanford University
EE 237 : Aneesh Nainani
37
SQ Limits for Multi Junction Cell • • • • •
1 cell: 32%, 41% [1-sun, concentrated] 2 cell: 42, 55% 3 cell: 48%, 63% 4 cell: 52%, 67% .. Infinite cell: 86% • Limit for any solar cell with reciprocal optics
• Black body limit (TPV): 85% • Thermodynamic (Landsberg) Limit: 93 % • Requires non-reciprocal elements • Carnot efficiency (not possible for solar): 95% tanford University
EE 237 : Aneesh Nainani
38
Suggested Reading • Sunlight / Tracking • Applied Photovoltaics, Chapter 1 • http://bit.ly/115DsyO • Solar Energy Limits • S-Q limit: HO#1 on the class website (original paper) • S-Q limit: http://sjbyrnes.com/sq.pdf • T-Y limit: HO #2 on the class website • Thermodynamic Limits • Third Generation Photovoltaics, M A Green, Chapter 3 (not free but good) • Handbook of Photovoltaics, Chapter 4, http://bit.ly/XPtTQg tanford University
EE 237 : Aneesh Nainani
39
