Effective incidence angles of sky-diffuse and ground-reflected irradiance for various incidence angle modifier types

A logical contradiction is pointed out involving the employment of some commonly used formulae for effective diffuse and reflected angles, when simulating the total irradiance on a tilted solar collector, in situations where the incidence angle modifier of the collector is known. By re-deriving the appropriate formulae for these effective incidence angles, it is found that the error involved in using the commonly used formulae is quite small in most practical cases. Differences are particularly small in the case of conventional photovoltaic panels, but may reach figures in the neighborhood of 5% for solar-thermal collectors.

► Effective diffuse and reflected incident angles depend on incident-angle-modifier.
► Within the isotropic approximation this dependence is shown to be weak.
► For non-isotropic models it is advisable to derive model-specific effective angles.
► A convenient formalism is presented for effecting such calculations.