Closed-Form, Analytic Solution for Diffuse Irradiance on a Tilted, Photovoltaic Collector

Continuing reductions in the installed price of solar photovoltaic (PV) modules is resulting in their deployment in low irradiance regions where the diffuse irradiation constitutes a larger proportion of the total than in high irradiance regions. It is therefore becoming increasingly important to improve the accuracy of models of diffuse irradiation by taking into account the dependence of reflections on the angle of incidence. We use the incidence angle modifier (IAM) and derive a closed-form, analytic solution to the diffuse irradiance on a tilted PV module. The result depends on the IAM parameter by 1.2%-2.1% and, for the default IAM parameter, is 3.8%-5.0% lower than an approximation that ignores IAM. The result applies directly to isotropic diffuse irradiance and the paper also shows how this result can be incorporated into models representing the anisotropic situation. A comparison is also given with an alternative to IAM for which an analytic solution is not available.