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Optical characterisation of solar collectors
for concentration on PhotoVoltaic cells
Summary: An experimental procedure has been developed for the optical characterisation of sunlight collectors, prismatic lenses, optically designed for concentration on photovoltaic cells. The described instrumentation and measurement techniques examine the total collection efficiency of the lens, as well as the energy distribution in the image plane. A specific study has been devoted to investigate the image uniformity, separating the light contributions due to the different lens regions.
1. INTRODUCTION
The exploitation of solar energy applying an innovative technology, based on focusing the sunlight on PhotoVoltaic (PV) cells, appears to be very promising and competitive with respect to the present energy sources. The described test methodology has been elaborated, experimented and applied to provide the optical characterisation of collectors for sunlight concentration on PV cells. The collectors are optically designed to be realised in plastic and to be applied for sunlight concentration on PV cells of reduced dimensions. The collectors under examination are square-shaped prismatic lenses, with external dimensions 156mm x 156mm. The prismatic lens is composed of more than 1000 elements ("tessera") of two dimensions, 3.9mm x 3.9mm or 7.8mm x 7.8mm: the prismatic lens includes 816 tesseras of side 3.9mm and 196 tesseras of side 7.8mm. The optical project of the prismatic lens indicates that the central tesseras have larger size and are almost flat, with respect to the lateral ones. The tesseras become smaller outside of the central cross and they become more inclined as they come close to lens corners.
The test technique presented in this paper examines several samples of prismatic lens realised with different production procedures and materials on the base of the optical project. The optical project of the prismatic lens has been studied in order to concentrate the light on a squared area of 11mm X 11mm, which corresponds to the dimension of the PV cell. The optical characterisation is aimed to verify the match between the performances of the realised lens samples and the theoretical features of the designed collectors. The application to concentrate the light on PV cells requires for the image some important characteristics concerning shape and intensity values. The first fundamental feature for the image is to have a square shape that should corresponds to the entire sensitive area of the PV cell. The second requirement is to reach the maximum collection efficiency, which means focusing as much light as possible on the area of the PV cell. The third feature, essential for the maximum exploitation of the PV cells, concerns the uniformity of the beam intensity over the whole sensitive area. This characterisation of sunlight concentration on PV cells can be completed considering other aspects of the problem, which were separately investigated. The methodology for optical characterisation consists in the following measurements:
1) Tests on the total collection efficiency of the prismatic lens
2) Energy distribution assessment in the image plane of the lens and uniformity estimation
3) Identification of possible lack of uniformity in the lens performances and analysis of the light contributions pertaining to the different lens portions.
Laboratory optical set-up, measurement techniques and experimental procedures are described in Sections 2 and 3. While Sections 4 to 6 present and discuss a selection of the more interesting results of measurements and tests.
2. TOTAL "COLLECTION EFFICIENCY" MEASUREMENT
The optical characterisation of the prismatic lenses under test starts assessing the total "collection efficiency". The optical system dedicated to measure the "collection efficiency" includes two spherical mirrors of wide diameter ( 250mm ), with the first one used as collimator (M1 in Fig. 1) and the second as concentrator (M2 in Fig. 1). The procedure to assess the total "collection efficiency" of the lens is essentially represented by the measurement of two quantities: the light impinging on the lens and the light focused by the lens on the squared area (11mm x 11mm). For the measurement of the light impinging on the lens the set-up, shown in Fig. 1, includes a masking support reproducing the entrance area of the prismatic lens, which is a square of side 156mm. Then, as reported in Fig. 3, the lens under test is inserted on the masking support and placed in the region between the two mirrors, where the luminous rays are almost parallel.
The geometrical characteristics of the optical system ought to satisfy the following requirements:
· The light beam impinging on the lens ought to cover a squared area of 156mm x 156mm and should have similar divergence characteristics of the solar light (Sun Divergence: total angular aperture = 0.5°)
· The area to be controlled in the lens image plane ought to be larger than the square 11mm x 11mm (diagonal = 15.5mm)
Considering that the dimensions of the prismatic lens are so wide (156mm of side and 220mm of diagonal) to dissuade to use lenses, we have preferred to employ spherical mirrors, which, on the other hand, allow to minimise aberrations of chromatic type.
FIG. 1 Measurement of the light power impinging on the lens.
FIG. 2 Solar divergence reproduction.
The source is realised coupling a white light illuminator, with fibre output, to an integrating sphere.
The solar divergence reproduction is obtained coupling the output aperture As of the integrating sphere with the focal length L of the 1st element on the optical path (a lens in Fig. 2, the mirror M1 in the actual test set-up in Fig. 1).
Fig. 2 shows the principle for which the optical element, represented by the lens, provides a beam with increasing divergence as the dimension of the aperture As increases, corresponding to an enlargement of the source area, according to the relation:
q = arctg(As/2L)
where q is the solar divergence (total angular aperture: 2q = 0.5°); As is the aperture diameter of the integrating sphere; and L is the focal length of the collimator.
FIG. 3 Measurement of the light power collected by the lens.
In the measurement of the light impinging on the lens, using the optical system of Fig. 1, the light is reflected by mirror M2, which introduces some losses, since it does not have a perfect reflectivity (100%). To take into account this correction, the reflection coefficient of M2 is assessed employing a mask with several holes distributed over the whole aperture of the beam, sampling the mirror area in different points. Using a hole at the time, we place a photodetector behind the n-th hole to measure the incident intensity Ii,n (position "i"), then we measure the corresponding intensity reflected by the mirror Ir,n (position "r"), using the same photodetector. The local reflectivity is given by the ratio of these two quantities: Ir,n/Ii,n. The mirror reflectivity can thus be obtained by averaging the local measurement values: the mean reflectivity of M2 results to be 95.3%.
Some representative results of the described tests are reported and discussed in Section 4, examining the total "collection efficiency" measured on six samples, which represent different productions of the prismatic lens.
3. ENERGY DISTRIBUTION AND UNIFORMITY IN THE IMAGE PLANE
FIG. 4 Measurement of the energy distribution in the image plane
The second series of measurements concerns the analysis of the light in the image plane, inside and outside the nominal image, which is represented by the square 11mm x 11mm and corresponds to the effective area of the selected PhotoVoltaic cell. Using the optical set-up schematically presented in Fig. 4, these tests consist in detecting the energy distribution in the focal plane considering an area larger then the reference square of side 11mm.
As previously discussed, the application to light concentration on PV cells requires for the focused light intensity to be uniformly distributed on the PV cell area, in order to optimise the exploitation of the solar light by the PV cell surface. For this purpose it is useful to analyse this specific aspect studying every single contribution of the numerous elements composing the prismatic lens. The distribution of the luminous intensity, focused inside and outside the nominal image square, should be studied in particular in dependence on the different regions of the lens. The experimental procedure consists in masking a part of the prismatic lens to evaluate which portion of the lens is correctly focusing within the useful area, while the other zones concentrate the light outside the reference square. The aim of these tests is to individuate the lens elements concentrating the light outside of the nominal image area, in order to localise the possible defects and to determine the type of error occurred in the realisation of these lens elements.
A preliminary phase of the measurement is devoted to individuate the correct positioning of the measurement plane that should correspond to the image plane. The image plane is typically identified at the focal distance from the lens, where the image minimises its dimensions in a plane normal to the optical axis. On the other hand, for the application to PV cell concentration it is important to place the PV cell where the light intensity reaches the maximum value. Therefore for our tests, the image plane has been selected in correspondence of the obtainable maximum value for the light focused inside the 11mm x 11mm squared area. In this test plane the energy distribution can be determined by utilising the measurement procedure presented in Figure 4. The image is sampled in two orthogonal directions XY by a photodetector (PD1) with squared area of dimensions 1mm x 1mm. A motorised platform, synchronised to an acquisition system, provides the PD1 displacement at programmed steps. The sampling step is 0.5mm in horizontal direction and 1mm in vertical direction. The correspondence between plane of maximum image intensity and measurement plane is verified before stating every test, using the PD18 with side dimension 18mm. The photodetector (PD18) employed in these lens efficiency tests has a squared sensitive area that has been masked for having an area of 11mm x 11mm, thus reproducing the nominal dimensions of the image. The detected signal is acquired by a computer, which also supplies the reconstruction in the XY plane of the intensity profile, providing a 3D-graphic: a representative selection of them is presented in Section 6.
4. RESULTS OF THE TOTAL "COLLECTION EFFICIENCY" ASSESSMENT
The total "collection efficiency" R of the lens is represented by the ratio between the intensity of the light If focused in the image plane, within a squared area of 11mm x 11mm, and the light impinging on the lens Ii : R = If/Ii . The quantity Ii is obtained measuring the luminous intensity transmitted through a masking support, with a squared aperture of 156mm x 156mm corresponding to the lens dimensions, and focused by the second mirror on the photodetector PD18, as shown in Fig. 1. For the measurement of the quantity If (Fig. 3) the lens is placed on the masking support and the same photodiode (PD18) is placed in the focal plane of the lens, where it detects the light concentrated on the squared area of 11mm x 11mm. In order to obtain these nominal image dimensions the sensitive area of the PD18, which is a square of side 18mm, is partially covered.
The measurement results presented in the following table are obtained using the mirror collimator realised at the INOA laboratories with the procedure described in Section 2. The total "collection efficiency" is measured on six samples of prismatic lens. These six lenses represent three types of realisation procedures for the same optical project of the prismatic lens, as Table 1 indicates. Table 2 compares the values of total "collection efficiency" R, measured on the three different lens types, each of which is represented by a couple of samples.
Table 1- Lens samples
Table 2- Total collection efficiency
Table 2 evidence the correspondence of the two R values measured on every couple of homologous lenses, having a maximum fluctuation of ±2%. On the other hand, the three different types of lens collect the light with different values of the "collection efficiency". It is evident from Table 2 that the lenses providing the maximum light collection are Lens5 and Lens6, whose R values are slightly higher than those obtained by Lens1 and Lens2. Only Lens3 and Lens4 present a lower R level, indicating that probably the corresponding production procedure reproduces the optical project with more imperfections. Nevertheless it is important to note that all production procedures introduce several imperfections, since the theoretical value of the total "collection efficiency" is 85% and the estimation for the practical R value is 80%. Hence the production procedure needs to be improved and these tests have the purpose of individuating the error type and localising imperfections in the lens realisation.
On the base of these results, further tests and measurements are carried out with the purpose of estimating how the different areas of the lens contribute to the image formation.
5. HOW LENS AREAS CONTRIBUTE TO FORM THE IMAGE
In order to investigate, and possibly separate, the image contributions due to the different lens regions, it is necessary to select some test zones that are sufficiently large to allow to measure the light corresponding to their image contribution.
Several test areas have been individuated on the prismatic lens in correspondence with the more interesting portions of the lens. The prismatic lens is composed of 1012 squared tesseras of two dimensions: 816 tesseras of side 3.9mm and 196 tesseras of side 7.8mm for an external dimension of 156mm x 156mm. Since the light focused by a single element ("tessera") is very weak, the test areas must include several tesseras.
For separating the light contributions associated to the different test areas, some masks for the lens have been realised: Figures 5a to 5c present the masks, having as external dimension the size of the prismatic lens. The Masks are defined as follows: Mask A, the cross mask; Mask B, the central mask; Mask C, the diagonal mask; Mask D, the angular mask.
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FIG. 5a Mask A : the cross mask. |
FIG. 5b Mask B : the central mask. |
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FIG. 5c Mask C : the diagonal mask. |
FIG. 5d Mask D: the angular mask. |
Form and size of the masks have been selected on the base of the characteristics of the optical project for the prismatic lens. It is useful to remind that the lens has been conceived and realised to concentrate the solar light on a squared image of side 11mm. As already noted, the central region (rhombus) of the lens is made of larger size (7.8mm) tesseras with different inclinations. The tesseras on the central cross are almost flat, while those located far from the lens centre are more inclined. Outside of the central cross, the lens is composed of smaller size (3.9mm) tesseras, whose inclination increases as their position approaches the lens corners.
The test procedure starts by measuring the percentage of the light focused by the total area of the lens, without any mask. After this reference measurement, the different masks are applied on the prismatic lens, separately estimating for each of them the focused light. The result of these tests is the individuation of the light contribution generated by the uncovered area of the lens. Therefore the measurement with Mask A isolates the light focused by the 4 lateral squares. It is useful to note that Mask A covers the less interesting region of the lens, represented by the cross, since this is the lens portion easier to be realised, being composed of larger and almost flat tesseras. On the contrary, the elements of the prismatic lens more difficult to realise are those located at the corners, due to the fact that they are smaller than the central ones and with the highest slopes.
The test with Mask B separates the light contribution due to tesseras located near the lens corners, while using Mask C we can evidence the light focused by the 4 side triangles. Finally Mask D, being the complementary mask with respect to Mask B, eliminates the light contribution due to the four corner triangles. Figures 5a, b, c, d present the Masks A, B, C, D respectively, mounted on the prismatic lens, as they have been used in the tests. Each mask has been separately superposed on the prismatic lens: the coloured part represents the mask, thus evidencing the lens area contribution isolated in each test.
In order to individuate which portion of the lens does not contribute, as it should, the lens area percentage and the focused light percentage have been compared. This preliminary comparison is made between the contributing exposed area of the lens (expressed in percentage with respect to the total lens area) and the corresponding measured light (expressed in percentage with respect to the light focused by the total lens). Table 3 reports the measurements realised using the three masks (Mask A to Mask C) on the different lens samples. The first part (Columns 2 to 7) of the table reports the values, expressed in percentage, of the ratio "light of image obtained from masked lens"/"light of total lens image". It is interesting to compare these percentages with the area ratios "uncovered area on the masked lens"/"total lens area", which is shown in Column 8, expressed in percentage. Furthermore Column 1 specifies the portion of the lens contributing to form the image, and Column 8 quantifies the corresponding area percentage, with respect to the total lens area. The table starts from the case of lens without mask, whose light percentage is 100% and it exactly corresponds to the same value on the lens area percentage. Rows 2 and 3 report the case of Mask A: the light percentage of the four squares is about 75%, while the contributing area represents the 81% of the lens. Row 3 examines a single lateral square, whose light is about 19% of the total image light, instead of reaching 20% of the corresponding area. The more interesting results are in Rows 4 and 5 and they pertain to Mask B: the four corner triangles represent the 40% of the lens area, but their light percentage does not reach 26% of the total image light. A single corner triangle, covering 10% of the lens area, produces only 6% of the image light. Finally Rows 6 and 7 refer to Mask C case: the four side triangles represent 64% of the lens area and they give an equivalent, even higher, contribution to the image light. Correspondingly, each single side triangle is 16% of the lens area and it concentrates 16-17% of the light in the squared image.
The more remarkable result evidenced by this comparison is that the four triangular portions, near the corners, give an average contribution to the image of 6.3% of the light, while the area percentage (of each triangle) is 10.1% of the lens. The conclusion is that the lateral corners have not been correctly realised, and the image analysis confirms that they contain imperfections in the tessera realisation, which probably concern the slope of the tessera.
Table 3 - Focused light vs lens area
As indication for the lens realisation and production, these tests emphasise that the reproduction of the optical project requires to be pointed out especially in the lateral and corner areas of the lens. The samples under study have the corner tesseras insufficiently defined and not corresponding to the optical project. As a result, these tesseras do not focus the light within the image area as foreseen by the optical project. For completing the study of the problem it is useful to consider the other test results, which provides further indications to individuate the imperfections in the realisation of the tesseras composing the prismatic lens.
6. ANALYSIS IN THE IMAGE PLANE: ENERGY DISTRIBUTION AND UNIFORMITY
The analysis in the image plane examines other aspects like shape, dimension and uniformity of the image. Using the experimental set-up presented in Fig. 4 the detector performs a 2-dimensional scan of the image obtained illuminating the lens with a white light of divergence 0.5°, corresponding to the solar light. For each sample of prismatic lens, listed in Table 1, the light in the focal plane has been mapped. These maps report the profile of the luminous intensity in the image plane. Some preliminary considerations can be made on shape and dimension of the image, identified by the light map. The first check is the comparison of this mapped light distribution with the nominal image, which is the square of 11mm x 11mm. The second check is the study of fluctuations of the light map within the nominal area of the image, providing information on the uniformity of the light distribution within the image.
Measurement instrumentation and methodology are fully described in Section 3 and some representative results are reported in Figures 6 to 10, showing the image profiles measured on Lens4 and Lens6. It is useful to notice that for both lens samples the maximum value of the light does not correspond to the central part of the spot. On the contrary, these points of light intensity maximum are located within a ring near the borders. The light intensity in the central part of the image therefore results to have lower values with respect to the lateral maximum values. In all figures it is evident how the image is deformed with respect to the squared nominal shape, in particular it appears enlarged only in one direction (that has been chosen to be the horizontal axis in the tests).
With the aim of investigating the causes of image enlargement in horizontal direction (which corresponds to the deformation axis, in all tests), the image of the masked lens has been examined. These tests have the purpose of individuating which region of the lens causes the deformation and, possibly, which tesseras concentrate the light outside of the nominal image. The image produced by the lens are scanned with several profile measurements; then this operation is repeated applying on the prismatic lens the different masks. Moreover Mask D has been especially realised for this purpose: this mask covers the lens corners as Fig. 5d shows.
The 3D-profiles of the images reported in the Figures 6 to 10 have been obtained in the following conditions:
· Fig.s 6 and 7: image from the lens without any mask
· Fig. 8: image from the lens with Mask D, angular mask
· Fig. 9: image from the lens with Mask C, diagonal mask
· Fig. 10: image from the lens with Mask B, central mask
The figures indicate that a rectangular image is obtained using the lens without mask (Fig.s 6 and 7) or the lens with the central Mask B (Fig. 10), and in both cases the lens corners are uncovered. We can thus conclude that this zone of the prismatic lens generates the light outside the square of side 11mm. This result is confirmed by Fig. 10 reporting the image obtained only with the light contributions generated by the four corner triangles.
On the other hand, considering the masks covering the zones near the four corners of the squared lens, the obtained spots approaches dimensions and shape of the nominal image. These masks include, obviously, Mask D (in Fig. 5d), covering the 4 triangles on the corners (whose resulting image is in Fig. 8) and the diagonal Mask C (whose image map is in Fig. 9).
The images generated by the lens with Mask C or Mask D have almost a squared shape, with dimensions approaching 11 mm x 11 mm. Hence for attaining the required size of the nominal image it is useful to attenuate the contributions of the regions near the 4 corners of the lens, confirming the results of the tests discussed in Sect. 5.
Fig. 6 Image Profile of Lens4 without masks
Fig. 7 Image Profile of Lens6 without masks
Fig. 8 Image profile of Lens6 with Mask D.
Fig. 9 Image profile of Lens6 with Mask C.
Fig. 10 Image profile of Lens6 with Mask B.
7. CONCLUSIONS
The described methodology provides the optical characterisation of prismatic lenses, assessing the following quantities:
· Total "collection efficiency" of the lens, verifying its correspondence with the value estimated by the optical calculation.
· Separation of the single contributions of the lens regions for localising and analysing the possible defects in the lens.
· Energy distribution in the image plane of the lens, estimating its uniformity in the image plane.
The examined quantities correspond to the fundamental features that the image created by the prismatic lens should have in order to be applied to light concentration on PhotoVoltaic cells. It is useful to remind that this application to concentration on PV cells has two fundamental requirements. The solar light should be concentrated with the maximum achievable "collection efficiency" and it should be focused on the squared area of the PV cell with the maximum achievable uniformity.
The tests have examined several samples obtained from the same optical project of the prismatic lens using different realisation procedures and materials, comparing the optical characteristics to select the best product. Optical characterisation and image analysis are also addressed to identify defects and imperfections associated to every production type. It is useful to compare the test results pertaining to the last samples (Lens3 to Lens6) with the quantities measured on the first samples of the prismatic lens (Lens1 and Lens2). This comparison evidences that the measurement results do not depend on the material employed for the lens realisation.
The image analysis, emphasising the different light distributions in the X and Y directions (both orthogonal to the optical axis), indicates a probable error in the realisation of the slope of some lens tesseras. We can thus suppose that the component of the tessera slope in one direction does not correspond to the optical project specification. These imperfectly realised tesseras generates in the image the distortion and enlargement in one direction, pointed out by the image analysis and Fig.s 6 to 10. We can presume that these production errors are due to imprecision in reproducing the tessera edges (peaks and valleys); but the main cause is probably the error in the reproduction of the inclination foreseen for each tessera.
Moreover, measurements with the masked lenses confirm the defective realisation of the tesseras located at the lens corners. Considering that every small triangle covers the 10% of the total lens area, the 40% of the useful area does not contribute, as it should, to the image formation, with consequent losses in the total lens efficiency.
