Edge effect on luminescent solar concentrators

Solar Cells, 15 (1985) 225 - 230

225

EDGE E F F E C T ON LUMINESCENT SOLAR C O N C E N T R A T O R S M. SIDRACH DE CARDONA, M. CARRASCOSA, F. MESEGUER, F. CUSSO and F. JAQUE Instituto de F(sica del Estado S61ido (C.S.I.C.) y Departamento de Optica y Estructura de la Materia, Universidad AutDnoma de Madrid, Facultad de Ciencias, Cantoblanco, 28049 Madrid (Spain)

(Received December 28, 1984; accepted May 22, 1985)

Summary The light distribution along the edge of luminescent solar concentrators has been studied experimentally and theoretically. Regular polygons with various numbers of sides have been considered. The effect of the geometrical shape on the overall conversion efficiency is discussed.

1. Introduction In the last few years the concept of the luminescent solar concentrators (LSC) has been developed [1 - 3]. These concentrators essentially consist of transparent plates {usually plastic) with luminescent molecules (mainly organic dyes) embedded in them and photovoltaic cells (PVCs) attached to the plate edges. The incident solar radiation is absorbed by the luminescent molecules and then re-emitted inside the system. A fraction of this luminescence is trapped by total internal reflection and guided to the PVCs at the collector edge. In these devices concentration is achieved because the collecting surface S is much larger than the photovoltaic cell area (lateral surface, SL). For a fixed collector thickness, the collector geometry should be suitably chosen to enhance the geometrical gain G G which is defined as the ratio G G = S / S L.

It may be seen from elementary algebra that for a regular polygon of given area, the geometrical gain increases with the number of sides N, being a minimum for a triangular shape and a maximum for a circular one. In addition, the concentrator symmetry increases with N. The light distribution along the collector edge is uniform for the circular shape b u t becomes more and more anisotropic as N decreases, with a maximum intensity at the centre of the side and a minimum at the corner [2, 4]. This anisot r o p y is particularly important if we consider the requirements for efficient photovoltaic conversion. To obtain adequate operating voltages, it will be necessary to connect in series all or a significant number of the photovoltaic 0379-6787/85/$3.30

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226 cells. Also it is well known that non-uniform illumination implies that the overall electric current is determined by the less illuminated cell. Therefore either the maximum symmetry or the maximum number of sides is desirable. Nevertheless, the ideal (circular) shape has a number of drawbacks such as the impossibility of covering a given area without leaving free spaces and the technical problem of matching a plane cell to a circular edge. For all these reasons we have studied experimentally as well as theoretically the light distribution along a luminescent solar concentrator edge for regular polygons with various numbers of sides. Its effect on the electrical efficiency (of the device LSC + PVC) is discussed.

2. Experimental details Triangular, square and hexagonal LSCs of area 0.25 m 2 were provided by Plexi S.A. with the following specifications. (a) High optical quality poly(methyl methacrylate) (PMMA) matrix (8 mm thick) doped with an organic dye is used at concentrations adequate to obtain an optical density OD = 6 that guarantees good performance [5]. (b) The dyes used, Rhodamine 6G (Lasing) and KF-241 (B.A.S.F.), have a high quantum yield and Stokes shift and their advantages in LSC operation have been previously reported [6]. Monocrystalline silicon solar cells (Solarex) with dimensions 2 × 0.8 cm 2 were optically matched to the collector edge. The cell efficiency at AM 1 illumination is 9%. Measurements were made under solar illumination with the panels tilted to face the sun. Fluctuations of the incident light during the measurements were corrected using a standard silicon reference cell.

3. Results and discussion The typical dependence of the short-circuit current on the position of the PVCs is illustrated in Fig. 1. The intensity, which has been normalized to its maximum value, decreases to 87% at the corner for a square LSC with sides 50 cm long. In order to evaluate the concentrators, measurements under two limiting conditions were performed. In the first measurement, the fraction of the panel edge not covered by the PVCs was blackened in order to avoid internal reflections at this interface. In the second one, the edge was directly in contact with the air. In such a situation a change in the refractive index from 1.49 to 1.00 produces a significant reflection. Under normal conditions, a panel whose surface is completely covered with silicon cells has a reflectivity intermediate between these two limits. The relative intensities for the various geometries studied are presented in Figs. 2a and 2b. In all cases it can be seen that the reduction in intensity becomes less pronounced as the number of sides increases. By comparing the

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two figures it can also be observed that the decrease is less pronounced, at any geometry, when the collector edge is blackened. This is to be expected because of the differences in interface reflectivity. It has also been confirmed that the light distribution is independent of the type of dye introduced in the LSCs. The light distribution along the edge and the LSC efficiency have been theoretically calculated using a Monte Carlo approach which has already been used successfully to describe the behaviour of LSCs [7]. The history of individual rays is followed from their incidence upon the top surface of the LSCs until they finally emerge through the edge faces. The wavelength of the incoming rays are selected according to the AM 1 spectral distribution and the successive events (reflection and refraction, absorption by PMMA, absorption and re-emission by the dye etc.) are considered. To handle the absorption by either the PMMA or the dye and the subsequent luminescent emission, the appropriate digitized absorption and emission spectra and the luminescent quantum yield were introduced as inputs in the Monte Carlo programme.

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Fig. 3. E x p e r i m e n t a l ( . . . . ) and theoretical ( light i n t e n s i t y d i s t r i b u t i o n f o r various LSC i n t e r f a c e s (A a n d D, b l a c k e n e d e d g e s ; B, P M M A - s i l i c o n i n t e r f a c e ; C, P M M A air i n t e r f a c e ) a n d g e o m e t r i e s : (a), s q u a r e ; (b), h e x a g o n a l .

The coordinates of emergence of those rays which finally reach the LSC edge and are absorbed by the cell are stored in order to reconstruct the light distribution. To generate this distribution, the Monte Carlo programme has handled from 50 000 to 100 000 histories. A Digital VAX 11/780 computer at the Universidad Aut6noma de Madrid was used. The theoretical distributions for a square LSC with blackened edges (curve A) and for one fully covered with silicon cells (curve B) are given in Fig. 3(a) and compared with the experimental ones for PMMA-air (curve C) and PMMA-black surface (curve D) interfaces. The same information, but for a hexagonal LSC, is given in Fig. 3(b). It can be seen that the theoretical simulation shows the same trend as the experimental values. The differences between the theoretical and experimental values for the blackened LSC can be explained by considering that in the theoretical treatment an ideal black surface (100% absorbance) has been assumed, a situation which obviously cannot be achieved in practice. A lower absorbance implies some reflection at the interface which smoothes the curvature of the light distribution. A further increase in reflectivity would be obtained in a PMMAsilicon interface in accordance with the prediction of intermediate values (curve B) between PMMA-air or PMMA-black absorbent interfaces. By comparing Figs. 3a and 3b it can be seen that a remarkable decrease occurs on going from a square to a hexagon, with a corresponding reduction in losses. Usually this effect is not taken into account in the literature or, if considered [4], it has been merely corrected by calculating the average intensity generated along the edge. Unfortunately this is not the situation in a series connection where the coupling to the less efficient cell has to be considered. Therefore, we define an edge efficiency 7~ed as the ratio between the intensity I generated in the less efficient cell (corner cell) and the intensity generated at the edge centre "r?ed =

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229 The corresponding values for different geometries are given in Table 1. It can be seen from this table that increasing the number of sides increases the value of ~?ed, which reaches a value of unity (no losses) for a circular LSC. If this ideal geometry is discarded because of the practical problem of matching the LSC with plane cells, a hexagonal LSC is a valid approximation. This LSC fully covered with silicon cells has theoretical edge losses (7%) considerably lower than those for a square (21% losses) or a triangular (51% losses) LSC. In addition, plane surfaces can be completely covered with hexagons. Their use, combined with bifacial photovoltaic cells [8] in h o n e y c o m b geometry, {Fig. 4) provides a further reduction in photovoltaic materials and hence in the final cost of photovoltaic energy. We can therefore conclude that a hexagonal LSC has not only a good geometrical gain but also a symmetry high enough to reduce losses due to edge effects, being superior to the square LSCs usually reported in the literature. TABLE 1 Values of 77ed for LSCs with different geometries LSC geometry

Circular Hexagonal Square Triangle

PMMA-silicon interface Theoretical

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Theoretical

PMMA-air interface Experimental

1,00 0.93 0.79 0.49

-0.88 0.72 0.49

1.00 0.80 0.68 0.40

-0.98 0.88 0.61

_ BIFACIAL

Fig. 4. Sketch of a bifacial concentrator using hexagonal LSCs adopting a honeycomb geometry.

Acknowledgments We wish to thank Dr. Seybold of B.A.S.F., Ludwigshafen, F.R.G., for supplying the KF-241 dye and A. Andreu of Plexi S.A., Valencia, Spain, for

230

casting the LSC with different dyes used in this paper. This work was supported by the Centro Desarrollo Tecnol6gico Industrial and by Standard El~ctrica S.A., Spain.

References W. H. Weber and J. Lambe, Appl. Opt., 15 {1976) 2299. A. Goetzberger and W. Greubel, Appl. Phys., 14 (1977) 123. R. Reisfeld and C. K. Jorgensen, Struct. Bonding, 49 (1982) 1. K. Heidler, Appl. Opt., 20 (1981) 773. M. Sidrach de Cardona, M. Carrascosa, F. Meseguer, F. Cusso and F. Jaque, Appl. Opt., 24 (1985) 2028. 6 V. Wittwer, K. Heidler, A. Zastrow and A. Goetzberger, J. Lumin., 24/25 (1981) 873. 7 M. Carrascosa, S. Unamuno and F. Agullo-Lopez, Appl. Opt., 22 (1983) 3236. 8 A. Cuevas, A. Luque, J. Eguren and J. del Alamo, Sol. Cells, 3 (1981) 337. 1 2 3 4 5