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The “Fresnel Equations” for Diffuse radiation on Inclined photovoltaic Surfaces (FEDIS)

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  • Xie, Yu
  • Sengupta, Manajit
  • Habte, Aron
  • Andreas, Afshin

Abstract

The well-known Fresnel equations solve for the reflection and transmission of light for precise incident angles. The transmission of diffuse radiation incident on a planar or domed surface is often needed for real-world applications. Due to the complexity of the Fresnel equations, the analytical solution of the integration has hitherto been unobtainable over the last centuries. Therefore, this problem was numerically solved by integrating the angular transmittances in space often leading to substantial computing burden and bias in the results. To efficiently estimate the solar energy resource for a glass-covered photovoltaic (PV) module, we derive an analytical solution of diffuse transmission based on the rigorous integration of an alternate form of the Fresnel equations. The approach leads to a simple yet accurate relative transmittance model that reconciles the solar energy sensed by pyranometers and PV panels. With limited and clearly stated approximations, the complex mathematical derivation resulted in an elegant solution. An experiment using 1-year of data at the National Renewable Energy Laboratory's (NREL's) Solar Radiation Research Laboratory (SRRL) shows that the new model dramatically decreases the disparity between the solar radiation measurements by a Kipp and Zonen CM Pyranometer 22 (CMP22) and an IMT reference cell on a 1-axis tracking system. The solution in this paper can be widely used in scientific and engineering research, development, and applications wherever the Fresnel equations are used.

Suggested Citation

  • Xie, Yu & Sengupta, Manajit & Habte, Aron & Andreas, Afshin, 2022. "The “Fresnel Equations” for Diffuse radiation on Inclined photovoltaic Surfaces (FEDIS)," Renewable and Sustainable Energy Reviews, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:rensus:v:161:y:2022:i:c:s1364032122002726
    DOI: 10.1016/j.rser.2022.112362
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    References listed on IDEAS

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    1. Sengupta, Manajit & Xie, Yu & Lopez, Anthony & Habte, Aron & Maclaurin, Galen & Shelby, James, 2018. "The National Solar Radiation Data Base (NSRDB)," Renewable and Sustainable Energy Reviews, Elsevier, vol. 89(C), pages 51-60.
    2. Wang, Lunche & Lu, Yunbo & Zou, Ling & Feng, Lan & Wei, Jing & Qin, Wenmin & Niu, Zigeng, 2019. "Prediction of diffuse solar radiation based on multiple variables in China," Renewable and Sustainable Energy Reviews, Elsevier, vol. 103(C), pages 151-216.
    3. Wang, Lunche & Kisi, Ozgur & Zounemat-Kermani, Mohammad & Salazar, Germán Ariel & Zhu, Zhongmin & Gong, Wei, 2016. "Solar radiation prediction using different techniques: model evaluation and comparison," Renewable and Sustainable Energy Reviews, Elsevier, vol. 61(C), pages 384-397.
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    1. Shi, Hongrong & Yang, Dazhi & Wang, Wenting & Fu, Disong & Gao, Ling & Zhang, Jinqiang & Hu, Bo & Shan, Yunpeng & Zhang, Yingjie & Bian, Yuxuan & Chen, Hongbin & Xia, Xiangao, 2023. "First estimation of high-resolution solar photovoltaic resource maps over China with Fengyun-4A satellite and machine learning," Renewable and Sustainable Energy Reviews, Elsevier, vol. 184(C).

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