A mathematical procedure to predict optical performance of CPCs

Abstract

To evaluate the optical performance of a CPC based concentrating photovoltaic system, it is essential to find the angular dependence of optical efficiency of compound parabolic concentrator (CPC-θe) where the incident angle of solar rays on solar cells is restricted within θe for the radiation over its acceptance angle. In this work, a mathematical procedure was developed to calculate the optical efficiency of CPC-θe for radiation incident at any angle based radiation transfer within CPC-θe. Calculations show that, given the acceptance half-angle (θa), the annual radiation of full CPC-θe increases with the increase of θe and the CPC without restriction of exit angle (CPC-90) annually collects the most radiation due to large geometry (Ct); whereas for truncated CPCs with identical θa and Ct, the annual radiation collected by CPC-θe is almost identical to that by CPC-90, even slightly higher. Calculations also indicate that the annual radiation on the absorber of CPC-θe at the angle larger than θe decrease with the increase of θe but always less than that of CPC-90, and this implies that the CPC-θe based PV system is more efficient than CPC-90 based PV system because the radiation on solar cells incident at large angle is poorly converted into electricity.