OPTICAL PROPERTIES OF V-TROUGH CONCENTRATORS

Abstract

Abstract--A new approach to study the optical behavior of V-trough concentrators is developed, based on the use of three characteristic angles defining the appearance, disappearance and return to the outside space of the cavity of a reflection mode. The probability of occurrence of a given number of reflections for beam radiation is determined as a function of these angles and the optical efficiency calculated. It is shown that the optical efficiency can be approximated by a function of two parameters, the angular acceptance function, T, and the mean number of reflections, n, as T. p,/r. Deviations between exact and approximate optical efficiency increase as n increases or as p decreases. For troughs with C _< 2.5 the maximal error for beam radiation is 3.4% for p > 0.8 (8.3% for p >-0.7). For diffuse radiation the maximal error is less than 2% for configurations whose optical efficiency is above 0.6. A further simplification was introduced to obtain the optical efficiency for diffuse radiation, approximating T by an analytical expression and n by an empirical linear function of the inverse of the vertex angle. Results accurate up to 5% for p = 0.8, were obtained. Increasing the concentration ratio, C, from 1.5 to 2.5 for a vertex angle being one third of the acceptance angle, decreased the optical efficiency from 0.74 to 0.59, for p = 0.8. For a given C, the dependence of the optical efficiency on the vertex angle is rather weak, suggesting that large trough angles might be favoured by cost-benefit analysis. INTRODUCFION V-trough cavities used in conjunction with commercial photocells can be an effective way to reduce the cost of the energy produced by photovoltaic panels. The walls of the cavity being plane, enable the use of lowcost, good-quality mirrors, with the benefit of a high optical efficiency. If at the same time the V-trough concentrator can be built at a moderate cost, the use of photovoitaic panels coupled to V-trough concentrators can result in a favourable cost-benefit ratio. The performance of the V-trough concentrator is characterized by the optical efficiency, which strongly depends on the incidence angle. It was shown by Rabl No simplified procedure is available for obtaining the optical efficiency as a function of the incidence angle. In this case the probability Pk(i) for a light ray to undergo k reflections on its passage through the op-* ISES member. tical cavity, when it reaches the aperture at an incidence angle i, has to be known. This probability can be calculated by graphical, numerical or analytical methods. The optical efficiency is then written as where M is the maximum number of reflections, for the incidence angle i. Although Pk(i) has to be obtained by detailed calculations, it will be shown that, similarly to The optical properties of V-trough concentrators were studied by Hollands [ 3 ] and some general features described by Rabl [ 4 ]. Hollands [ 3 ] calculates the effective concentration for beam radiation at the cavity absorber for several concentration ratios. The optical cavities studied i