Abstract

The method of detailed balance, introduced by Shockley and Queisser, is often used to find an upper theoretical limit for the efficiency of semiconductor pn-junction based photovoltaics. Typically the solar cell is assumed to be at an ambient temperature of 300 K. In this paper, we describe and analyze the use of radiative cooling techniques to lower the solar cell temperature below the ambient to surpass the detailed balance limit for a cell in contact with an ideal heat sink. We show that by combining specifically designed radiative cooling structures with solar cells, efficiencies higher than the limiting efficiency achievable at 300 K can be obtained for solar cells in both terrestrial and extraterrestrial environments. We show that our proposed structure yields an efficiency 0.87% higher than a typical PV module at operating temperatures in a terrestrial application. We also demonstrate an efficiency advantage of 0.4-2.6% for solar cells in an extraterrestrial environment in near-earth orbit.

© 2015 Optical Society of America

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References

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  1. W. Shockley and H. J. Queisser, “Detailed balance limit of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
    [Crossref]
  2. T. T. Chow, “A review on photovoltaic/thermal hybrid solar technology,” Appl. Energy 87(2), 365–379 (2010).
    [Crossref]
  3. A. Akbarzadeh and T. Wadowski, “Heat pipe-based cooling systems for photovoltaic cells under concentrated solar radiation,” Appl. Therm. Eng. 16(1), 81–87 (1996).
    [Crossref]
  4. G. Sala, “Cooling of solar cells” in Cells and Optics for Photovoltaic Concentration, A. Luque and G. L. Araújo, eds. (Adam Hilger, 1989).
  5. L. Zhu, A. Raman, K. X. Wang, M. A. Anoma, and S. Fan, “Radiative cooling of solar cells,” Optica 1(1), 32–38 (2014).
    [Crossref]
  6. S. Catalanotti, V. Cuomo, G. Piro, D. Ruggi, V. Silvestrini, and G. Troise, “The radiative cooling of selective surfaces,” Sol. Energy 17(2), 83–89 (1975).
    [Crossref]
  7. B. Bartoli, S. Catalanotti, B. Coluzzi, V. Cuomo, V. Silvestrini, and G. Troise, “Nocturnal and diurnal performances of selective radiators,” Appl. Energy 3(4), 267–286 (1977).
    [Crossref]
  8. C. G. Granqvist and A. Hjortsberg, “Surfaces for radiative cooling: silicon monoxide films on aluminum,” Appl. Phys. Lett. 36(2), 139–141 (1980).
    [Crossref]
  9. C. G. Granqvist and A. Hjortsberg, “Radiative cooling to low temperatures: general considerations and application to selectively emitting SiO films,” J. Appl. Phys. 52(6), 4205–4220 (1981).
    [Crossref]
  10. P. Berdahl, “Radiative cooling with MgO and/or LiF layers,” Appl. Opt. 23(3), 370–372 (1984).
    [Crossref] [PubMed]
  11. A. Harrison and M. Walton, “Radiative cooling of TiO2 white paint,” Sol. Energy 20(2), 185–188 (1978).
    [Crossref]
  12. M. Muselli, “Passive cooling for air-conditioning energy savings with new radiative low-cost coatings,” Energy Build. 42(6), 945–954 (2010).
    [Crossref]
  13. L. Zhu, A. Raman, and S. Fan, “Color-preserving daytime radiative cooling,” Appl. Phys. Lett. 103(22), 223902 (2013).
    [Crossref]
  14. E. Rephaeli, A. Raman, and S. Fan, “Ultrabroadband photonic structures to achieve high-performance daytime radiative cooling,” Nano Lett. 13(4), 1457–1461 (2013).
    [PubMed]
  15. A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, “Passive radiative cooling below ambient air temperature under direct sunlight,” Nature 515(7528), 540–544 (2014).
    [Crossref] [PubMed]
  16. S. Bailey and R. Raffaelle, “Space solar cells and arrays” in Handbook of Photovoltaic Science and Engineering, A. Luque and S. Hegedus, ed. (John Wiley and Sons, 2005).
  17. P. Würfel, S. Finkbeiner, and E. Daub, “Generalized planck’s radiation law for luminescence via indirect transitions,” Appl. Phys., A Mater. Sci. Process. 60(1), 67–70 (1995).
    [Crossref]
  18. Gemini Observatory, IR Transmission Spectra, http://www.gemini.edu/?q=node/10789 .
  19. IEC 61215, “Crystalline silicon terrestrial photovoltaic modules—design qualification and type approval,” 2nd ed. (2005).
  20. R. G. Ross and M. I. Smokler, “Electricity from photovoltaic solar cells: flat-plate solar array project final report,” http://authors.library.caltech.edu/15040/1/JPLPub86-31volVI.pdf (1986).
  21. R. G. Ross., “Flat-plate photovoltaic array design optimization,” in Proceedings of IEEE Conference on Photovoltaic Specialist Conference, (IEEE, 1980), pp. 1126–1132.

2014 (2)

A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, “Passive radiative cooling below ambient air temperature under direct sunlight,” Nature 515(7528), 540–544 (2014).
[Crossref] [PubMed]

L. Zhu, A. Raman, K. X. Wang, M. A. Anoma, and S. Fan, “Radiative cooling of solar cells,” Optica 1(1), 32–38 (2014).
[Crossref]

2013 (2)

L. Zhu, A. Raman, and S. Fan, “Color-preserving daytime radiative cooling,” Appl. Phys. Lett. 103(22), 223902 (2013).
[Crossref]

E. Rephaeli, A. Raman, and S. Fan, “Ultrabroadband photonic structures to achieve high-performance daytime radiative cooling,” Nano Lett. 13(4), 1457–1461 (2013).
[PubMed]

2010 (2)

T. T. Chow, “A review on photovoltaic/thermal hybrid solar technology,” Appl. Energy 87(2), 365–379 (2010).
[Crossref]

M. Muselli, “Passive cooling for air-conditioning energy savings with new radiative low-cost coatings,” Energy Build. 42(6), 945–954 (2010).
[Crossref]

1996 (1)

A. Akbarzadeh and T. Wadowski, “Heat pipe-based cooling systems for photovoltaic cells under concentrated solar radiation,” Appl. Therm. Eng. 16(1), 81–87 (1996).
[Crossref]

1995 (1)

P. Würfel, S. Finkbeiner, and E. Daub, “Generalized planck’s radiation law for luminescence via indirect transitions,” Appl. Phys., A Mater. Sci. Process. 60(1), 67–70 (1995).
[Crossref]

1984 (1)

1981 (1)

C. G. Granqvist and A. Hjortsberg, “Radiative cooling to low temperatures: general considerations and application to selectively emitting SiO films,” J. Appl. Phys. 52(6), 4205–4220 (1981).
[Crossref]

1980 (1)

C. G. Granqvist and A. Hjortsberg, “Surfaces for radiative cooling: silicon monoxide films on aluminum,” Appl. Phys. Lett. 36(2), 139–141 (1980).
[Crossref]

1978 (1)

A. Harrison and M. Walton, “Radiative cooling of TiO2 white paint,” Sol. Energy 20(2), 185–188 (1978).
[Crossref]

1977 (1)

B. Bartoli, S. Catalanotti, B. Coluzzi, V. Cuomo, V. Silvestrini, and G. Troise, “Nocturnal and diurnal performances of selective radiators,” Appl. Energy 3(4), 267–286 (1977).
[Crossref]

1975 (1)

S. Catalanotti, V. Cuomo, G. Piro, D. Ruggi, V. Silvestrini, and G. Troise, “The radiative cooling of selective surfaces,” Sol. Energy 17(2), 83–89 (1975).
[Crossref]

1961 (1)

W. Shockley and H. J. Queisser, “Detailed balance limit of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[Crossref]

Akbarzadeh, A.

A. Akbarzadeh and T. Wadowski, “Heat pipe-based cooling systems for photovoltaic cells under concentrated solar radiation,” Appl. Therm. Eng. 16(1), 81–87 (1996).
[Crossref]

Anoma, M. A.

L. Zhu, A. Raman, K. X. Wang, M. A. Anoma, and S. Fan, “Radiative cooling of solar cells,” Optica 1(1), 32–38 (2014).
[Crossref]

A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, “Passive radiative cooling below ambient air temperature under direct sunlight,” Nature 515(7528), 540–544 (2014).
[Crossref] [PubMed]

Bartoli, B.

B. Bartoli, S. Catalanotti, B. Coluzzi, V. Cuomo, V. Silvestrini, and G. Troise, “Nocturnal and diurnal performances of selective radiators,” Appl. Energy 3(4), 267–286 (1977).
[Crossref]

Berdahl, P.

Catalanotti, S.

B. Bartoli, S. Catalanotti, B. Coluzzi, V. Cuomo, V. Silvestrini, and G. Troise, “Nocturnal and diurnal performances of selective radiators,” Appl. Energy 3(4), 267–286 (1977).
[Crossref]

S. Catalanotti, V. Cuomo, G. Piro, D. Ruggi, V. Silvestrini, and G. Troise, “The radiative cooling of selective surfaces,” Sol. Energy 17(2), 83–89 (1975).
[Crossref]

Chow, T. T.

T. T. Chow, “A review on photovoltaic/thermal hybrid solar technology,” Appl. Energy 87(2), 365–379 (2010).
[Crossref]

Coluzzi, B.

B. Bartoli, S. Catalanotti, B. Coluzzi, V. Cuomo, V. Silvestrini, and G. Troise, “Nocturnal and diurnal performances of selective radiators,” Appl. Energy 3(4), 267–286 (1977).
[Crossref]

Cuomo, V.

B. Bartoli, S. Catalanotti, B. Coluzzi, V. Cuomo, V. Silvestrini, and G. Troise, “Nocturnal and diurnal performances of selective radiators,” Appl. Energy 3(4), 267–286 (1977).
[Crossref]

S. Catalanotti, V. Cuomo, G. Piro, D. Ruggi, V. Silvestrini, and G. Troise, “The radiative cooling of selective surfaces,” Sol. Energy 17(2), 83–89 (1975).
[Crossref]

Daub, E.

P. Würfel, S. Finkbeiner, and E. Daub, “Generalized planck’s radiation law for luminescence via indirect transitions,” Appl. Phys., A Mater. Sci. Process. 60(1), 67–70 (1995).
[Crossref]

Fan, S.

A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, “Passive radiative cooling below ambient air temperature under direct sunlight,” Nature 515(7528), 540–544 (2014).
[Crossref] [PubMed]

L. Zhu, A. Raman, K. X. Wang, M. A. Anoma, and S. Fan, “Radiative cooling of solar cells,” Optica 1(1), 32–38 (2014).
[Crossref]

E. Rephaeli, A. Raman, and S. Fan, “Ultrabroadband photonic structures to achieve high-performance daytime radiative cooling,” Nano Lett. 13(4), 1457–1461 (2013).
[PubMed]

L. Zhu, A. Raman, and S. Fan, “Color-preserving daytime radiative cooling,” Appl. Phys. Lett. 103(22), 223902 (2013).
[Crossref]

Finkbeiner, S.

P. Würfel, S. Finkbeiner, and E. Daub, “Generalized planck’s radiation law for luminescence via indirect transitions,” Appl. Phys., A Mater. Sci. Process. 60(1), 67–70 (1995).
[Crossref]

Granqvist, C. G.

C. G. Granqvist and A. Hjortsberg, “Radiative cooling to low temperatures: general considerations and application to selectively emitting SiO films,” J. Appl. Phys. 52(6), 4205–4220 (1981).
[Crossref]

C. G. Granqvist and A. Hjortsberg, “Surfaces for radiative cooling: silicon monoxide films on aluminum,” Appl. Phys. Lett. 36(2), 139–141 (1980).
[Crossref]

Harrison, A.

A. Harrison and M. Walton, “Radiative cooling of TiO2 white paint,” Sol. Energy 20(2), 185–188 (1978).
[Crossref]

Hjortsberg, A.

C. G. Granqvist and A. Hjortsberg, “Radiative cooling to low temperatures: general considerations and application to selectively emitting SiO films,” J. Appl. Phys. 52(6), 4205–4220 (1981).
[Crossref]

C. G. Granqvist and A. Hjortsberg, “Surfaces for radiative cooling: silicon monoxide films on aluminum,” Appl. Phys. Lett. 36(2), 139–141 (1980).
[Crossref]

Muselli, M.

M. Muselli, “Passive cooling for air-conditioning energy savings with new radiative low-cost coatings,” Energy Build. 42(6), 945–954 (2010).
[Crossref]

Piro, G.

S. Catalanotti, V. Cuomo, G. Piro, D. Ruggi, V. Silvestrini, and G. Troise, “The radiative cooling of selective surfaces,” Sol. Energy 17(2), 83–89 (1975).
[Crossref]

Queisser, H. J.

W. Shockley and H. J. Queisser, “Detailed balance limit of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[Crossref]

Raman, A.

L. Zhu, A. Raman, K. X. Wang, M. A. Anoma, and S. Fan, “Radiative cooling of solar cells,” Optica 1(1), 32–38 (2014).
[Crossref]

L. Zhu, A. Raman, and S. Fan, “Color-preserving daytime radiative cooling,” Appl. Phys. Lett. 103(22), 223902 (2013).
[Crossref]

E. Rephaeli, A. Raman, and S. Fan, “Ultrabroadband photonic structures to achieve high-performance daytime radiative cooling,” Nano Lett. 13(4), 1457–1461 (2013).
[PubMed]

Raman, A. P.

A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, “Passive radiative cooling below ambient air temperature under direct sunlight,” Nature 515(7528), 540–544 (2014).
[Crossref] [PubMed]

Rephaeli, E.

A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, “Passive radiative cooling below ambient air temperature under direct sunlight,” Nature 515(7528), 540–544 (2014).
[Crossref] [PubMed]

E. Rephaeli, A. Raman, and S. Fan, “Ultrabroadband photonic structures to achieve high-performance daytime radiative cooling,” Nano Lett. 13(4), 1457–1461 (2013).
[PubMed]

Ross, R. G.

R. G. Ross and M. I. Smokler, “Electricity from photovoltaic solar cells: flat-plate solar array project final report,” http://authors.library.caltech.edu/15040/1/JPLPub86-31volVI.pdf (1986).

R. G. Ross., “Flat-plate photovoltaic array design optimization,” in Proceedings of IEEE Conference on Photovoltaic Specialist Conference, (IEEE, 1980), pp. 1126–1132.

Ruggi, D.

S. Catalanotti, V. Cuomo, G. Piro, D. Ruggi, V. Silvestrini, and G. Troise, “The radiative cooling of selective surfaces,” Sol. Energy 17(2), 83–89 (1975).
[Crossref]

Shockley, W.

W. Shockley and H. J. Queisser, “Detailed balance limit of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[Crossref]

Silvestrini, V.

B. Bartoli, S. Catalanotti, B. Coluzzi, V. Cuomo, V. Silvestrini, and G. Troise, “Nocturnal and diurnal performances of selective radiators,” Appl. Energy 3(4), 267–286 (1977).
[Crossref]

S. Catalanotti, V. Cuomo, G. Piro, D. Ruggi, V. Silvestrini, and G. Troise, “The radiative cooling of selective surfaces,” Sol. Energy 17(2), 83–89 (1975).
[Crossref]

Smokler, M. I.

R. G. Ross and M. I. Smokler, “Electricity from photovoltaic solar cells: flat-plate solar array project final report,” http://authors.library.caltech.edu/15040/1/JPLPub86-31volVI.pdf (1986).

Troise, G.

B. Bartoli, S. Catalanotti, B. Coluzzi, V. Cuomo, V. Silvestrini, and G. Troise, “Nocturnal and diurnal performances of selective radiators,” Appl. Energy 3(4), 267–286 (1977).
[Crossref]

S. Catalanotti, V. Cuomo, G. Piro, D. Ruggi, V. Silvestrini, and G. Troise, “The radiative cooling of selective surfaces,” Sol. Energy 17(2), 83–89 (1975).
[Crossref]

Wadowski, T.

A. Akbarzadeh and T. Wadowski, “Heat pipe-based cooling systems for photovoltaic cells under concentrated solar radiation,” Appl. Therm. Eng. 16(1), 81–87 (1996).
[Crossref]

Walton, M.

A. Harrison and M. Walton, “Radiative cooling of TiO2 white paint,” Sol. Energy 20(2), 185–188 (1978).
[Crossref]

Wang, K. X.

Würfel, P.

P. Würfel, S. Finkbeiner, and E. Daub, “Generalized planck’s radiation law for luminescence via indirect transitions,” Appl. Phys., A Mater. Sci. Process. 60(1), 67–70 (1995).
[Crossref]

Zhu, L.

A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, “Passive radiative cooling below ambient air temperature under direct sunlight,” Nature 515(7528), 540–544 (2014).
[Crossref] [PubMed]

L. Zhu, A. Raman, K. X. Wang, M. A. Anoma, and S. Fan, “Radiative cooling of solar cells,” Optica 1(1), 32–38 (2014).
[Crossref]

L. Zhu, A. Raman, and S. Fan, “Color-preserving daytime radiative cooling,” Appl. Phys. Lett. 103(22), 223902 (2013).
[Crossref]

Appl. Energy (2)

T. T. Chow, “A review on photovoltaic/thermal hybrid solar technology,” Appl. Energy 87(2), 365–379 (2010).
[Crossref]

B. Bartoli, S. Catalanotti, B. Coluzzi, V. Cuomo, V. Silvestrini, and G. Troise, “Nocturnal and diurnal performances of selective radiators,” Appl. Energy 3(4), 267–286 (1977).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

C. G. Granqvist and A. Hjortsberg, “Surfaces for radiative cooling: silicon monoxide films on aluminum,” Appl. Phys. Lett. 36(2), 139–141 (1980).
[Crossref]

L. Zhu, A. Raman, and S. Fan, “Color-preserving daytime radiative cooling,” Appl. Phys. Lett. 103(22), 223902 (2013).
[Crossref]

Appl. Phys., A Mater. Sci. Process. (1)

P. Würfel, S. Finkbeiner, and E. Daub, “Generalized planck’s radiation law for luminescence via indirect transitions,” Appl. Phys., A Mater. Sci. Process. 60(1), 67–70 (1995).
[Crossref]

Appl. Therm. Eng. (1)

A. Akbarzadeh and T. Wadowski, “Heat pipe-based cooling systems for photovoltaic cells under concentrated solar radiation,” Appl. Therm. Eng. 16(1), 81–87 (1996).
[Crossref]

Energy Build. (1)

M. Muselli, “Passive cooling for air-conditioning energy savings with new radiative low-cost coatings,” Energy Build. 42(6), 945–954 (2010).
[Crossref]

J. Appl. Phys. (2)

W. Shockley and H. J. Queisser, “Detailed balance limit of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[Crossref]

C. G. Granqvist and A. Hjortsberg, “Radiative cooling to low temperatures: general considerations and application to selectively emitting SiO films,” J. Appl. Phys. 52(6), 4205–4220 (1981).
[Crossref]

Nano Lett. (1)

E. Rephaeli, A. Raman, and S. Fan, “Ultrabroadband photonic structures to achieve high-performance daytime radiative cooling,” Nano Lett. 13(4), 1457–1461 (2013).
[PubMed]

Nature (1)

A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, “Passive radiative cooling below ambient air temperature under direct sunlight,” Nature 515(7528), 540–544 (2014).
[Crossref] [PubMed]

Optica (1)

Sol. Energy (2)

S. Catalanotti, V. Cuomo, G. Piro, D. Ruggi, V. Silvestrini, and G. Troise, “The radiative cooling of selective surfaces,” Sol. Energy 17(2), 83–89 (1975).
[Crossref]

A. Harrison and M. Walton, “Radiative cooling of TiO2 white paint,” Sol. Energy 20(2), 185–188 (1978).
[Crossref]

Other (6)

G. Sala, “Cooling of solar cells” in Cells and Optics for Photovoltaic Concentration, A. Luque and G. L. Araújo, eds. (Adam Hilger, 1989).

S. Bailey and R. Raffaelle, “Space solar cells and arrays” in Handbook of Photovoltaic Science and Engineering, A. Luque and S. Hegedus, ed. (John Wiley and Sons, 2005).

Gemini Observatory, IR Transmission Spectra, http://www.gemini.edu/?q=node/10789 .

IEC 61215, “Crystalline silicon terrestrial photovoltaic modules—design qualification and type approval,” 2nd ed. (2005).

R. G. Ross and M. I. Smokler, “Electricity from photovoltaic solar cells: flat-plate solar array project final report,” http://authors.library.caltech.edu/15040/1/JPLPub86-31volVI.pdf (1986).

R. G. Ross., “Flat-plate photovoltaic array design optimization,” in Proceedings of IEEE Conference on Photovoltaic Specialist Conference, (IEEE, 1980), pp. 1126–1132.

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Figures (5)

Fig. 1
Fig. 1 Contour plot of efficiency as a function of solar cell temperature and bandgap energy for the (a) AM0 (extraterrestrial) spectrum and (b) the AM1.5G (terrestrial) spectrum using the principle of detailed balance. Lower temperatures result in higher maximum power conversion efficiencies.
Fig. 2
Fig. 2 Schematic of the proposed structure consisting of a solar cell coupled to a selective thermal emitter with back mirror. The solar cell absorbs above-bandgap illumination from the sun (left). The radiative cooler emits (and hence absorbs) strongly in the atmospheric transparency window in the mid-infrared range between 8 and 26 μm (right).
Fig. 3
Fig. 3 Contour plot of cooling power for a hybrid structure consisting of a solar cell thermally coupled to a radiative cooler that can emit into 8 to 26 μm infrared region. The black curve indicates the steady state temperature of the structure placed in ambient at 300 K. Positive values of the cooling power result in a reduction of the cell temperature.
Fig. 4
Fig. 4 (a) Efficiency comparison of the proposed structure, solar cells operating at 300 K, and a typical solar cell characterized by a NOCT of 321 K, i.e. a cell operating at 335 K. (b) Steady state temperature as a function of bandgap energy for the structure with a radiative cooler emitting in the 8-26 μm range. Vertical dashed and solid lines indicate the bandgaps of GaAs and Si, respectively.
Fig. 5
Fig. 5 (a) Efficiency comparison of the radiatively cooled solar cell operating at temperatures between 300 and 500 K under AM 0 illumination. The efficiency of the proposed structure, drawn in black, is greater than that of solar cells with a temperature of 300 K for all Eg > 1.36 eV. (b) The temperature of the proposed structure as a function of material bandgap energy.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

P n e t = P r a d , c o o l e r + P r a d , c e l l + P e l e c t r i c a l P a t m P a b s o r b e d
n ( E , T , V ) = 2 E 2 h 3 c 2 ( e E q V k T 1 )
P r a d , c o o l e r A = d Ω cos θ 0 E n ( E , T , V = 0 ) ε ( E , θ ) d E ,
P r a d , c e l l A = E g d Ω cos θ E g 2 E 2 h 3 c 2 ( e E q V max k T 1 ) d E .
P a t m A = d Ω cos θ 0 E n ( E , T a m b , V = 0 ) ε ( E , θ ) ε a t m ( E , θ ) d E ,
ε a t m ( E , θ ) = 1 t ( E ) 1 cos θ
P a b s o r b e d A = E g n A M 1.5 ( E ) d E ,
T c e l l = T a i r + ( N O C T 293.15 80 ) S ,
P n e t = P r a d , c o o l e r + P r a d , c e l l + P e l e c t r i c a l P a b s o r b e d .

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