Corrections to anisotropic diffuse radiation model


Solar energy is the energy comes from radiant light of the Sun. Solar energy is the most abundant form of energy on earth and can be harnessed using a range of ever-evolving technologies, such as: solar heating, photovoltaics, solar thermal energy, solar architecture, molten salt power plants and artificial photosynthesis. The most popular harnessing technique is the use of photovoltaic modules, colloquially termed solar panels, mainly in solar farms. Technically, photovoltaic fields are deployed in multiple rows, therefore the second and subsequent rows see the sky dome with a smaller angle than the first (front) row. Obscuring part of the sky on the second row by the front row affects the amount of the diffuse incident radiation on the second row. As the diffuse radiation depends on atmospheric conditions, a relative large number of diffuse radiation models have been proposed. These models are based on isotropic and on anisotropic models. Generally, the anisotropic models are based on the isotropic model and include circumsolar radiation and horizon brightening. These models were developed for a single row only; therefore, these models require modifications for multiple rows.

Typically, solar diffuse radiation models are based on isotropic and on anisotropic models. The diffuse radiation components are a combination of three fractions: isotropic diffuse, circumsolar diffuse and horizon brightening. Therefore, to address the aforementioned shortfall, researchers from the School of Electrical Engineering at Tel Aviv University in Israel: Yehya Massalha and A. Aronescu and led by Professor Joseph Appelbaum proposed to modify the current anisotropic model by three factors: Sky view factor of a second row-depending on the field parameters and being constant, correction to circumsolar brightening- time dependent and the correction to horizon brightening- time dependent. Their work is currently published in the research journal, Solar Energy.

Noteworthy studies have demonstrated that horizon brightening contributes 0.1% of diffuse incident irradiation in Klucher model. Thus, the research team developed a modified model of the Klucher anisotropic model for diffuse radiation. The researchers compared the differences in the diffuse incident irradiation on rows for isotropic, anisotropic and modified anisotropic (Klucher) models for the first and the second row.

The authors reported that the for latitude 32 N° and relative low percentage of diffuse radiation the horizon brightening may not be considered in the anisotropic Klucher model as it constitutes only about 0.1. Remarkably, Professor Joseph Appelbaum and his colleagues further reported that the isotropic model resulted in 9.56% less annual diffuse incident irradiation as compared to Klucher original model for the front row, and the isotropic model resulted in 5.83% less annual diffuse incident irradiation compared to the modified Klucher model for the second and subsequent rows.

In summary, the Tel Aviv University scientists developed a reliable modification of the anisotropic model by three factors: sky view factor of a second row, correction to circumsolar brightening and correction to horizon brightening. Overall, the main modification of the model contained correction to the circumsolar radiation and the sky view factor for the second row and the subsequent rows. Consequently, other anisotropic models may adopt necessary modifications.  In a statement to Advances in Engineering, Professor Joseph Appelbaum pointed out that their proposed modified anisotropic model enables one to calculate the incident solar radiation on photovoltaic fields more accurately.


J. Appelbaum, Y. Massalha, A. Aronescu. Corrections to anisotropic diffuse radiation model. Solar Energy, volume 193 (2019) page 523–528.

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