A Three-Dimensional Radiation Transfer Model to Evaluate Performance of Compound Parabolic Concentrator-Based Photovoltaic Systems
Abstract
:1. Introduction
2. Optical and Photovoltaic Conversion Efficiency of CPVs
2.1. Equation of Reflectors of CPC-θa/θe
2.2. Coordinate System to Determine the Vector of Solar Rays
2.3. Photovoltaic Conversion Efficiency of Solar Cells
2.4. Optical and Photovoltaic Conversion Efficiency of CPVs
2.4.1. Calculation of f1 and η1
2.4.2. Calculation of f2 and η2
2.4.3. Calculation of f3 and η3
2.4.4. Calculation of f4 and η4
2.4.5. Calculation of and
2.4.6. Calculation of and
3. Annual Optical and Photovoltaic Performance of CPVs
4. Numerical Approach
5. Results and Discussions
5.1. Annual Collectible Radiation
5.2. Annual Photovoltaic Performance of CPVs
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Glossary
Ct | geometric concentration of truncated CPVs (dimensionless) |
Cpv | annual power output increase factor of CPVs as compared to similar non-concentrating PV panel (dimensionless) |
optical efficiency factor of CPVs (dimensionless) | |
H | daily radiation (J/m2) |
ht | height of CPVs (m) |
I | instantaneous radiation intensity (W/m2) |
Vector of solar rays incident on point M of reflectors; | |
Vector of the normal to reflectors at point M | |
Incident solar vector | |
reflective solar vector from point M of reflectors | |
Pa | annual power output from CPVs (MJ/m2) |
Pa,0 | annual power output from similar PV panel without using CPCs (MJ/m2) |
Sa | annual radiation collected by CPVs (MJ/m2) |
t | solar time (s) |
Greek Letters
tilt-angle of CPVs’ aperture from the horizon (rad.) | |
declination of the Sun (rad.) | |
polar angle of point M on parabolic reflectors (rad.) | |
photovoltaic conversion efficiency of CPVs (dimensionless) | |
photovoltaic conversion efficiency of solar cells as the function of (dimensionless) | |
tilt-angle of any line relative to x-axis (rad.) | |
site latitude (rad.) | |
acceptance half-angle of CPCs (rad.) | |
maximum exit angle of CPC-/ for radiation over its acceptance angle (rad.) | |
solar incident angle on the aperture of CPVs (rad.) | |
solar incident angle on solar cells of CPVs (rad.) | |
solar incident angle at point M of reflectors (rad.) | |
solar exit angle from point M of reflectors relative to the negative x-axis (rad.) | |
projected angle of incident solar rays on the cross-section of CPC-troughs (rad.) | |
projected angle of solar ray reflecting from M of reflectors (rad.) | |
edge-ray angle of truncated CPCs (rad.) | |
reflectivity of reflectors (set to be 0.9 in this work) | |
opening angle of V-trough formed by two plane mirrors of CPC-/ (rad.) | |
day length (s) | |
hour angle (rad.) |
Subscripts
0 | sunset |
a | annual |
abs | absorber of CPCs; solar cells of CPVs |
ap | aperture |
b | beam radiation |
c | critical value |
i | incident solar ray |
r | reflective solar ray; right reflector |
pl | plane mirror |
Appendix A
Appendix A.1. For the Case of
Appendix A.2. For the Case of <
Appendix A.3. For the Case of <
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Tang, J.; Yu, Y.; Tang, R. A Three-Dimensional Radiation Transfer Model to Evaluate Performance of Compound Parabolic Concentrator-Based Photovoltaic Systems. Energies 2018, 11, 896. https://doi.org/10.3390/en11040896
Tang J, Yu Y, Tang R. A Three-Dimensional Radiation Transfer Model to Evaluate Performance of Compound Parabolic Concentrator-Based Photovoltaic Systems. Energies. 2018; 11(4):896. https://doi.org/10.3390/en11040896
Chicago/Turabian StyleTang, Jingjing, Yamei Yu, and Runsheng Tang. 2018. "A Three-Dimensional Radiation Transfer Model to Evaluate Performance of Compound Parabolic Concentrator-Based Photovoltaic Systems" Energies 11, no. 4: 896. https://doi.org/10.3390/en11040896