Concentration and acceptance angle

Concentrators can be accurately analysed in the framework of geometrical optics, where the light can be modelled with the ray concept. This is deduced from statistical optics [5], in which geometrical optics appears as the asymptotic limit of the electromagnetic radiation phenomenon when the fields can be approximated as globally incoherent (also called quasi-homogeneous). In this approximation sources and receivers are non-punctual (usually called extended sources and receivers) and the diffraction effects are negligible.

Assume that a certain PV concentrator, which points in one nominal direction given by the unit vector, v, ensures that all the light rays impinging on the concentrator entry aperture forming angles smaller than a with v are transmitted onto the cell with incidence angles smaller than в. Let us suppose that

the refractive index of the medium surrounding the cell is n. From the etendue conservation theorem of geometrical optics [7], it is deduced that the following inequality is verified:

Cgsin2 а < n2sin2 в (13.1)

where the geometrical concentration Cg is the ratio AE/AR, AE being the area of the projection of the entry aperture onto a plane normal to v and AR the receiver area. Equation (13.1) is valid for any contour of areas AE and AR, and v is called the normal incidence direction vector. This equation is usually referred to as the acceptance-concentration product bound. The bound n2 sin2 в is a maximum for в = 90°, i. e. when the receiver is illuminated isotropically. This situation is usually referred to as the thermodynamic limit of the concentration because surpassing this maximum bound would imply the possibility of heating a black receiver with a concentrator to a temperature higher than that of the sun, which contradicts the second principle.