Comparative Analysis of Direct Inclined Irradiance Data Sources for Micro-Tracking Concentrator Photovoltaics
Abstract
:1. Introduction
2. Direct Inclined Irradiance Spatial Databases
2.1. Worldwide Annual DII Data from PVGIS
2.2. Comparison of Annual DII Data from PVGIS and SoDa
2.3. Comparison of DII Data from the Mathematical Model
3. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Abbreviations | |
CPV | Concentrator photovoltaics |
TICPV | Tracking-integrated CPV |
PV | Photovoltaic |
DHI | Direct horizontal irradiance (W/m2) or irradiation (kWh/m2) |
DII | Direct inclined irradiance (W/m2) or irradiation (kWh/m2) |
DNI | Direct normal irradiance (W/m2) or irradiation (kWh/m2) |
GHI | Global horizontal irradiance (W/m2) or irradiation (kWh/m2) |
GII | Global inclined irradiance (W/m2) or irradiation (kWh/m2) |
Parameters | |
GB hm(I) | Monthly average hourly direct inclined irradiance (W/m2) |
GB hm(N) | Monthly average hourly direct normal irradiance (W/m2) |
HB dm(I) | Monthly average daily direct inclined irradiation (Wh/m2) |
HB dm(N) | Monthly average daily direct normal irradiation (Wh/m2) |
HB a(S) | Annual direct inclined irradiation (Wh/m2) |
Symbols | |
α | Surface azimuth angle (rad) |
β | Surface tilt angle (rad) |
δdn | Solar declination at midday of each month (rad) |
φ | Latitude (rad) |
ωs dm | Sunrise hour angle of the midday of each month (rad) |
Solar vector | |
Normal vector to the surface of the module | |
ϴs | Angle of incidence of the beam radiation on the inclined surface (rad) |
ϴS hm | Monthly average hourly angle of incidence (rad) |
ϴzs | Solar zenith angle (rad) |
References
- Geisz, J.F.; France, R.M.; Schulte, K.L.; Steiner, M.A.; Norman, A.G.; Guthrey, H.L.; Young, M.R.; Song, T.; Moriarty, T. Six-junction III–V solar cells with 47.1% conversion efficiency under 143 Suns concentration. Nat. Energy 2020, 5, 326–335. [Google Scholar] [CrossRef]
- Perez-Higueras, P.; Fernández, E.F. High Concentrator Photovoltaics: Fundamentals, Engineering and Power Plants; Springer: Cham, Switzerland, 2015. [Google Scholar]
- Green, M.A.; Dunlop, E.D.; Hohl-Ebinger, J.; Yoshita, M.; Kopidakis, N.; Bothe, K.; Hinken, D.; Rauer, M.; Hao, X. Solar cell efficiency tables (Version 60). Prog. Photovolt. Res. Appl. 2022, 30, 687–701. [Google Scholar] [CrossRef]
- Pérez-Higueras, P.; Ferrer-Rodríguez, J.P.; Almonacid, F.; Fernández, E.F. Efficiency and acceptance angle of High Concentrator Photovoltaic modules: Current status and indoor measurements. Renew. Sustain. Energy Rev. 2018, 94, 143–153. [Google Scholar] [CrossRef]
- Talavera, D.L.; Ferrer-Rodríguez, J.P.; Pérez-Higueras, P.; Terrados, J.; Fernández, E.F. A worldwide assessment of levelised cost of electricity of HCPV systems. Energy Convers. Manag. 2016, 127, 679–692. [Google Scholar] [CrossRef]
- Algora, C.; Rey-Stolle, I. Handbook on Concentrator Photovoltaic Technology; Wiley: Hoboken, NJ, USA, 2016. [Google Scholar]
- Apostoleris, H.; Stefancich, M.; Chiesa, M. Tracking-integrated systems for concentrating photovoltaics. Nat. Energy 2016, 1, 16018. [Google Scholar] [CrossRef]
- Nardin, G.; Domínguez, C.; Aguilar, Á.F.; Anglade, L.; Duchemin, M.; Schuppisser, D.; Gerlich, F.; Ackermann, M.; Coulot, L.; Cuénod, B.; et al. Industrialization of hybrid Si/III–V and translucent planar micro-tracking modules. Prog. Photovolt. Res. Appl. 2021, 29, 819–834. [Google Scholar] [CrossRef]
- Ceballos, M.A.; Pérez-Higueras, P.J.; Fernández, E.F.; Almonacid, F. Tracking-Integrated CPV Technology: State-of-the-Art and Classification. Energies 2023, 16, 5605. [Google Scholar] [CrossRef]
- Liu, R.; Jordan, B. Daily insolation on surfaces tilted towards equator. ASHRAE Trans. 1962, 67, 526–541. [Google Scholar]
- Klein, S.A. Calculation of monthly average insolation on tilted surfaces. Sol. Energy 1977, 19, 325–329. [Google Scholar] [CrossRef]
- Hay, J.E. Calculation of monthly mean solar radiation for horizontal and inclined surfaces. Sol. Energy 1979, 23, 301–307. [Google Scholar] [CrossRef]
- Page, J.K. The estimation of monthly mean values of daily total short wave radiation on vertical and inclined surfaces from sunshine records for latitudes 40N-40S. In Proceedings of the UN Conference on New Sources of Energy, Rome, Italy, 21–31 August 1961; pp. 378–390. [Google Scholar]
- Iqbal, M. A study of Canadian diffuse and total solar radiation data—II Monthly average hourly horizontal radiation. Sol. Energy 1979, 22, 87–90. [Google Scholar] [CrossRef]
- Louche, A.; Notton, G.; Poggi, P.; Simonnot, G. Correlations for direct normal and global horizontal irradiation on a French Mediterranean site. Sol. Energy 1991, 46, 261–266. [Google Scholar] [CrossRef]
- Martins, F.R.; Pereira, E.B.; Abreu, S.L. Satellite-derived solar resource maps for Brazil under SWERA project. Sol. Energy 2007, 81, 517–528. [Google Scholar] [CrossRef]
- Ineichen, P.; Perez, R.; Kmiecik, M.; Renné, D. Modeling direct irradiance from goes visible channel using generalized cloud indices. In Proceedings of the 80th AMS Annual Meeting, Long Beach, CA, USA, 9–14 January 2000; p. 219. [Google Scholar]
- Perez, R.; Ineichen, P.; Moore, K.; Kmiecik, M.; Chain, C.; George, R.; Vignola, F. A new operational model for satellite-derived irradiances: Description and validation. Sol. Energy 2002, 73, 307–317. [Google Scholar] [CrossRef]
- Schillings, C.; Mannstein, H.; Meyer, R. Operational method for deriving high resolution direct normal irradiance from satellite data. Sol. Energy 2004, 76, 475–484. [Google Scholar] [CrossRef]
- Janjai, S. A method for estimating direct normal solar irradiation from satellite data for a tropical environment. Sol. Energy 2010, 84, 1685–1695. [Google Scholar] [CrossRef]
- Beckman, W.; Bugler, J.; Cooper, P.; Duffie, J.; Dunkle, R.; Glaser, P.; Horigome, T.; Howe, E.; Lawand, T.; van der Mersch, P.; et al. Units and symbols in solar energy. Sol. Energy 1978, 21, 65–68. [Google Scholar] [CrossRef]
- Selçuk, M.K. Glossary of terms used in solar energy. Sol. Energy 1984, 33, 97–114. [Google Scholar] [CrossRef]
- Hall, I.J.; Prairie, R.R.; Anderson, H.E.; Boes, E.C. Generation of Typical Meteorological Years for 26 SOLMET Stations; Sandia Labs.: Albuquerque, NM, USA, 1978. [Google Scholar]
- European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT). Satellite Application Facility on Climate Monitoring; European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT): Darmstadt, Germany, 2025. [Google Scholar]
- National Aeronautics and Space Administration (NASA). Prediction of Worldwide Energy Resources; National Aeronautics and Space Administration: Washington, DC, USA, 2025.
- National Renewable Energy Laboratory (NREL). National Solar Radiation Database (NSRDN); National Renewable Energy Laboratory (NREL): Golden, CO, USA, 2024.
- Meteonorm Worldwide Irradiation Data. Available online: https://meteonorm.com/ (accessed on 1 June 2025).
- Solcast a DNV Company. Available online: https://solcast.com/ (accessed on 1 June 2025).
- Photovoltaic Geographical Information System (PVGIS). Available online: https://re.jrc.ec.europa.eu/pvg_tools/es/ (accessed on 1 June 2025).
- Solar Radiation Database (SoDa) (HelioClim-3). Available online: https://www.soda-pro.com/ (accessed on 1 June 2025).
- Solargis Weather Data. Available online: https://solargis.com/ (accessed on 1 June 2025).
- Mueller, R.; Behrendt, T.; Hammer, A.; Kemper, A. A New Algorithm for the Satellite-Based Retrieval of Solar Surface Irradiance in Spectral Bands. Remote Sens. 2012, 4, 622–647. [Google Scholar] [CrossRef]
- Amillo, A.; Huld, T.; Müller, R. A New Database of Global and Direct Solar Radiation Using the Eastern Meteosat Satellite, Models and Validation. Remote Sens. 2014, 6, 8165–8189. [Google Scholar] [CrossRef]
- Golden Software (Surfer) Version 16. Available online: https://support.goldensoftware.com/hc/en-us/article_attachments/7866200064027 (accessed on 1 June 2025).
- Šúri, M.; Remund, J.; Cebecauer, T.; Hoyer-Klick, C.; Dumortier, D.; Huld, T.; Stackhouse, P.W., Jr.; Ineichen, P. Comparison of Direct Normal Irradiation Maps for Europe. In Proceedings of the SolarPACES Conference “Concentrated Solar Power and Chemical Energy Systems”, Berlin, Germany, 15–18 September 2009; pp. 1–8. [Google Scholar]
- Harsarapama, A.P.; Aryani, D.R.; Rachmansyah, D. Open-Source Satellite-Derived Solar Resource Databases Comparison and Validation for Indonesia. J. Renew. Energy 2020, 2020, 2134271. [Google Scholar] [CrossRef]
- Marchand, M.; Ghennioui, A.; Wey, E.; Wald, L. Comparison of several satellite-derived databases of surface solar radiation against ground measurement in Morocco. Adv. Sci. Res. 2018, 15, 21–29. [Google Scholar] [CrossRef]
- Hoyer-Klick, C.; Beyer, H.-G.; Dumortier, D.; Schroedter-Homscheidt, M.; Wald, L.; Martinoli, M.; Schillings, C.; Gschwind, B.; Menard, L.; Gaboardi, E.; et al. Mesor—Management and Exploitation of Solar Resource Knowledge. In Proceedings of the EUROSUN 2008, 1st International Congress on Heating, Cooling and Buildings, Lisbonne, Portugal, 7–10 October 2008. [Google Scholar]
- Viana, T.S.; Rüther, R.; Martins, F.R.; Pereira, E.B. Assessing the potential of concentrating solar photovoltaic generation in Brazil with satellite-derived direct normal irradiation. Sol. Energy 2011, 85, 486–495. [Google Scholar] [CrossRef]
- Perpiñan, O.; Lorenzo, E.; Castro, M.A.; Eyras, R. On the complexity of radiation models for PV energy production calculation. Sol. Energy 2008, 82, 125–131. [Google Scholar] [CrossRef]
- Cooper, P.I. The absorption of radiation in solar stills. Sol. Energy 1969, 12, 333–346. [Google Scholar] [CrossRef]
- Demain, C.; Journée, M.; Bertrand, C. Evaluation of different models to estimate the global solar radiation on inclined surfaces. Renew. Energy 2013, 50, 710–721. [Google Scholar] [CrossRef]
- Collares-Pereira, M.; Rabl, A. The average distribution of solar radiation-correlations between diffuse and hemispherical and between daily and hourly insolation values. Sol. Energy 1979, 22, 155–164. [Google Scholar] [CrossRef]
- Whillier, A. The determination of hourly values of total solar radiation from daily summations. Arch. Meteorol. Geophys. Bioklimatol. Ser. B 1956, 7, 197–204. [Google Scholar] [CrossRef]
- Duffie, J.A.; Beckman, W.A. Solar Engineering of Thermal Processes, 3rd ed.; Wiley: Hoboken, NJ, USA, 2006. [Google Scholar]
- Pérez-Higueras, P.J.; Rodrigo, P.; Fernández, E.F.; Almonacid, F.; Hontoria, L. A simplified method for estimating direct normal solar irradiation from global horizontal irradiation useful for CPV applications. Renew. Sustain. Energy Rev. 2012, 16, 5529–5534. [Google Scholar] [CrossRef]
GHI | GII | DHI | DNI | DII | |
---|---|---|---|---|---|
CM-SAF | + | - | + | + | - |
SSE | + | + | - | + | - |
NSRDB | + | - | + | + | - |
Meteonorm | + | + | + | + | - |
Solcast | + | - | + | + | - |
PVGIS | + | + | + | + | + |
SoDa | + | + | + | + | + |
SolarGIS | + | + | - | + | - |
PVGIS | DII | |
---|---|---|
Spatial coverage | 180° W to 180° E and 75° N to 65° S | 66° W to 66° E and 66° N to 66° S |
Spatial resolution | 0.05° × 0.05° | 0.05° × 0.05° |
Temporal resolution | Hourly data | Hourly data |
Availability period | 2005 to 2020 | 2004 to 2024 |
Access to data | Open access | Open access only from 2004 to 2006 |
N | MAD (%) | RMSD (%) | μ (%) | σ (%) | R2 | |
---|---|---|---|---|---|---|
SoDa vs. PVGIS | 40 | 8.21 | 9.94 | 4.36 | 9.48 | 0.93 |
SoDa vs. Mathematical model | 40 | 1.74 | 2.17 | 0.57 | 2.07 | 0.99 |
PVGIS vs. Mathematical model | 40 | 5.94 | 7.42 | −5.22 | 4.65 | 0.98 |
PVGIS vs. Mathematical model | 8000 | 6.08 | 6.89 | −6.27 | 3.26 | 0.99 |
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Perez-Higueras, P.; Ceballos, M.A.; Mouhib, E.; Bessa, J.G.; Montes-Romero, J.; Mata-Campos, R. Comparative Analysis of Direct Inclined Irradiance Data Sources for Micro-Tracking Concentrator Photovoltaics. Electronics 2025, 14, 2297. https://doi.org/10.3390/electronics14112297
Perez-Higueras P, Ceballos MA, Mouhib E, Bessa JG, Montes-Romero J, Mata-Campos R. Comparative Analysis of Direct Inclined Irradiance Data Sources for Micro-Tracking Concentrator Photovoltaics. Electronics. 2025; 14(11):2297. https://doi.org/10.3390/electronics14112297
Chicago/Turabian StylePerez-Higueras, Pedro, Maria A. Ceballos, Elmehdi Mouhib, Joao Gabriel Bessa, Jesus Montes-Romero, and Raul Mata-Campos. 2025. "Comparative Analysis of Direct Inclined Irradiance Data Sources for Micro-Tracking Concentrator Photovoltaics" Electronics 14, no. 11: 2297. https://doi.org/10.3390/electronics14112297
APA StylePerez-Higueras, P., Ceballos, M. A., Mouhib, E., Bessa, J. G., Montes-Romero, J., & Mata-Campos, R. (2025). Comparative Analysis of Direct Inclined Irradiance Data Sources for Micro-Tracking Concentrator Photovoltaics. Electronics, 14(11), 2297. https://doi.org/10.3390/electronics14112297