The Hay and Davies diffuse model divides the sky diffuse irradiance into isotropic and circumsolar components. Horizon brightening is not included. An anisotropy index, $$A_i$$ , is defined as:
$$A_i= frac{DNI}{E_{a}}$$,
where $$DNI$$ is the direct normal irradiance and $$E_a$$ is the extraterrestrial radiation.
The Hay and Davies model formulation for sky diffuse radiation is:
$$E_d-DHI times left[A_i R_b + left( 1-A_i right) frac{1+ cos left( theta_T right)}{2} right]$$,
where $$DHI$$ is the diffuse horizontal irradiance, $$R_b=cos(AOI)/cos(Z)$$, $$AOI$$ is the angle of incidence, $$Z$$ is the solar zenith, and $$theta_T$$ is the tilt angle of the array.
This model is implemented in the PV_LIB Toolbox as the function: pvl_haydavies1980.
References:
- [1] Loutzenhiser P.G. et al. “Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation” 2007, Solar Energy vol. 81. pp. 254-267
- [2] Hay, J.E., Davies, J.A., 1980. Calculations of the solar radiation incident on an inclined surface. In: Hay, J.E., Won, T.K. (Eds.), Proc. of First Canadian Solar Radiation Data Workshop, 59. Ministry of Supply and Services, Canada.