A mathematical procedure to predict optical performance of CPCs

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-θ_e ) where the incident angle of solar rays on solar cells is restricted within θ_e for the radiation over its acceptance angle. In this work, a mathematical procedure was developed to calculate the optical efficiency of CPC-θ_e for radiation incident at any angle based radiation transfer within CPC-θ_e . Calculations show that, given the acceptance half-angle (θ_a ), the annual radiation of full CPC-θ_e increases with the increase of θ_e and the CPC without restriction of exit angle (CPC-90) annually collects the most radiation due to large geometry (C_t ); whereas for truncated CPCs with identical θa and C_t , the annual radiation collected by CPC-θ_e is almost identical to that by CPC-90, even slightly higher. Calculations also indicate that the annual radiation on the absorber of CPC-θ_e at the angle larger than θ_e decrease with the increase of θ_e but always less than that of CPC-90, and this implies that the CPC-θ_e 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.