A Three-Dimensional Radiation Transfer Model to Evaluate Performance of Compound Parabolic Concentrator-Based Photovoltaic Systems

In the past, two-dimensional radiation transfer models (2-D models) were widely used to investigate the optical performance of linear compound parabolic concentrators (CPCs), in which the radiation transfer on the cross-section of CPC troughs is considered. However, the photovoltaic efficiency of solar cells depends on the real incidence angle instead of the projection incidence angle, thus 2-D models can’t reasonably evaluate the photovoltaic performance of CPC-based photovoltaic systems (CPVs). In this work, three-dimensional radiation transfer (3-D model) within CPC-θa/θe, the CPC with a maximum exit angle θe for radiation within its acceptance angle (θa), is investigated by means of vector algebra, solar geometry and imaging principle of plane mirror, and effects of geometry of CPV-θa/θe on its annual electricity generation are studied. Analysis shows that, as compared to similar photovoltaic (PV) panels, the use of CPCs makes the incident angle of solar rays on solar cells increase thus lowers the photovoltaic conversion efficiency of solar cells. Calculations show that, 2-D models can reasonably predict the optical performance of CPVs, but such models always overestimate the photovoltaic performance of CPVs, and even can’t predict the variation trend of annual power output of CPV-θa/θe with θe. Results show that, for full CPV-θa/θe with a given θa, the annual power output increases with θe first and then comes to a halt as θe > 83°, whereas for truncated CPV-θa/θe with a given geometric concentration (Ct), the annual power output decreases with θe