A theoretical study on performance and design optimization of linear dielectric compound parabolic concentrating photovoltaic systems

To investigate solar leakage and effects of the geometry of linear dielectric compound parabolic concentrator with a restricted exit angle (DCPC-θ_a/θ_e) on the performance of DCPC-θ_a/θ_e -based photovoltaic systems (DCPV-θ_a/θ_e), a three-dimensional radiation transfer model based on solar geometry and vector algebra is suggested. Analysis shows that the annual radiation loss due to leakage is sensitive to the geometry of DCPCs and tilt-angle adjustment strategy, and the optimal qe,opt for minimizing annual leakage is the one that makes the incidence angle of solar rays on the plane wall equal to the critical incidence angle for total internal reflection at solar-noon in solstices and days when tilt-angle adjustment from site latitude is made for DCPV with the aperture's tilt-angle being yearly fixed, and adjusted two and four times, respectively. It is found that annual radiation leakage is considerable small, for DCPVs with qe < θ_eθ_opt, almost all leaked radiation comes from sky diffuse radiation, whereas for θ_e = 90°, most of leakage is attributed to direct sunlight. As compared to similar non-concentrating solar cells, more radiation arrives annually on solar cells of DCPV-θ_a/θ_e at small angles thanks to refraction of radiation on the aperture, hence, under same operation conditions, the annual average photovoltaic efficiency of solar cells for concentrated radiation is even higher. Analysis also shows that the power increase of DCPVs, being much less than the geometric concentration of DCPCs (Ct), is mainly attributable to optical loss due to absorption of solar rays on the way to the solar cells, and the power loss due to leakage of radiation is not significant. From the point of annual electricity generation, for full DCPVs with a given qa, DCPV-qa/90 are favorable, and for truncated DCPVs with given qa and Ct, DCPVs with θ_e < 90 are favorable; whereas from the point of contribution per unit volume of dielectric to the annual electricity generation, the situation is reversed.