Hi,
Looking over the SAM Photovoltaic Model Technical Reference Update here -
www.nrel.gov/docs/fy18osti/67399.pdf
, equation 9.9 (page 41) specifies the reduced sky diffuse irradiance as -
G_sky_red = G_d - G_dh( 1 - cos(psi/2)^2 ) *(N_rows-1)/N_rows (9.9)
The relation between G_dh and G_d is specified by Eq. 9.7 -
G_dh = G_d * (2/ (1+cos(beta_s)) (9.7)
The two equations considered together for an interior row amount to -
G_sky_red_int = G_dh*( (1 + cos(beta_s)/2 - (1 - cos(psi/2)^2 ) ).
which simplifies to -
G_sky_red_int = G_dh * (cos(beta_s) + cos(psi) )/2
This does not appear to be correct. Consider rotating the (2D) scene by an angle beta_s around the bottom of the interior row, thereby making this row horizontal. The ground is now sloped upwards at an angle beta_s and the row in front of it is slopes at an angle (beta_s + psi) to the horizontal. In this rotated scene, the shaded row sees the isotropic sky on one (higher) side, and the sky obstructed by the combination of the ground and the adjacent row on the other side. It cannot distinguish between the two, and sees only one continuous obstruction. The correct formula is therefore -
G_sky_red_int = G_dh*( 1 + cos( beta_s + psi))/2
This correct view factor is reported for example, as equation 14 of the following publication -
www.sciencedirect.com/science/article/pii/S0038092X21000633
regards,
