Patent Application: US-201314394975-A

Abstract:
one example of a solar voltaic concentrator has a primary fresnel lens with multiple panels , each of which forms a kohler integrator with a respective panel of a lenticular secondary lens . the resulting plurality of integrators all concentrate sunlight onto a common multi - junction photovoltaic cell . the integrators provide matching illumination in the different wavebands required by the different junctions . luminaires using a similar geometry are also possible .

Description:
a better understanding of various features and advantages of the present invention may be obtained by reference to the following detailed description of embodiments of the invention and accompanying drawings , which set forth illustrative embodiments in which various principles of the invention are utilized . the primary optical elements ( poe ) described in these embodiments are formed into segments , exhibiting multi - fold symmetry . in the embodiments taught in this application the secondary optical elements ( soe ) have the same multi - fold symmetry as the respective poe . each segment of the poe , along with a corresponding segment of the soe , forms one of a plurality of köhler integrator segments . the plurality of kohler integrator segments combine to concentrate incoming sunlight on a common photovoltaic cell . presently available solar cells for solar concentrators use three junctions , usually referred to as top , middle and bottom , which are sensitive to different spectral bands of the solar radiation . the semiconductor physics of the junction determine the minimum photon energy ( maximum wavelength ) of light that the junction can convert to electricity . typically , the top junction is sensitive from 350 to 690 nm , the middle junction from 690 nm to 900 nm , and the bottom junction beyond 900 nm ( a germanium bottom junction can in principle use light down to about 1800 nm , while an ingaas or ingaasnsb bottom junction can use light down to only about 1400 nm . ), the transition between the cell bands not necessarily being abrupt . when the poe is a mirror , the directions of the reflected rays are not dependent on the wavelength , and a monochromatic concentrator design is enough to predict to full spectrum performance . however , in all the present embodiments , the poe is refractive , and the variation of the refractive index of the lens material with wavelength ( usually called material dispersion , responsible for the chromatic aberration in imaging optics ) causes rays of different wavelengths to be refracted towards different directions , reaching different points of the soe . for a solar concentrator , these wavelength - dependent ray deviations for the different junction bands will cause two effects that should be taken into account : ( 1 ) there may be three different acceptance angles for the different junctions ; and ( 2 ) the irradiance distribution may also be different for the different junctions . the first effect has the consequence that the effective acceptance angle for the concentrator as a whole is the smallest of the three , limiting the cap of the device . the second effect degrades the overall solar cell efficiency , because the three junctions operate in series and the least brightly illuminated junction limits the current output of the stack . when the irradiance distributions of the wavebands used by the three junctions differ , that minimum - brightness limitation occurs locally , only partially mitigated by lateral current flows , even when the total integrated illumination of the cell is the same for the three junctions . fig1 shows one of the embodiments in the earlier u . s . pat . no . 8 , 000 , 018 b2 , in which the poe is a flat fresnel lens with 4 - fold symmetry . each of the four fresnel lens segments is part of a lens having rotational symmetry with respect to one of four axes that do not coincide with each other , and do not coincide with the center of the overall optical system . the normal - incidence rays 11 are split into four disconnected bundles to reach the four lobes of 4 - fold symmetric soe . the foci 12 of the poe lens segments are formed close to the front surface of the soe . that design ignores chromatic dispersion , and assumes that tracing a single set of rays is sufficient . the embodiments in the present application are optimized polychromatically to obtain solutions that can achieve high optical efficiency , and also correct the two effects mentioned above . that is to say , they can achieve as additional performance targets that : ( 1 ) the concentrator acceptance angle α , given by the smallest acceptance angle of the three junctions , is maximum , and ( 2 ) the irradiance distributions of the three junctions are very similar . even though the optimization described herein can be applied to a general n × m symmetric design , three specific preferred embodiments are included in this invention : a 2 × 2 symmetric with flat or dome fresnel primary , which will be referred to as 4 - fold for short ; a 3 × 3 symmetric with a flat or dome fresnel lens , which will be referred to as 9 - fold for short ; and a 2 × 1 symmetric with flat or dome fresnel primary , which will be referred to as 2 - fold for short . the performance target ( 1 ) is obtained by the poe optimization . in order to illustrate this optimization , fig2 shows a side view , in cross - section along a diagonal , of a 4 - fold soe 202 with a triple junction cell 201 being illuminated by the rays 205 of the top junction waveband , rays 204 of the middle junction waveband , and rays 203 of the bottom junction waveband . the poe ( not shown in fig2 ) is assumed to be a fresnel lens . the focal regions are located in three very different positions , 206 , 207 and 208 , shallowest for the top junction focus 206 and deepest into the soe for the bottom junction focus 208 . while in u . s . pat . no . 8 , 000 , 018 b2 only a single focal region was mentioned , the polychromatic optimization disclosed here will take into account the positions of the three foci . in the case of a flat fresnel poe , their positions cannot be controlled independently , so we can specify the position of one focus and calculate the other two . one focus can preferably be specified as the point where light of the chosen color would notionally be focused by the poe if the further refraction of the light rays by the soe did not intervene . for instance , point 209 in fig2 corresponds to such a notional focus for light of wavelength 550 nm . the two coordinates ( x m , z m ) of point 209 in the tilted coordinate system x - z shown in fig2 constitute the two parameters to vary for achieving performance target ( 1 ). therefore , the objective is to solve the mathematical problem of finding the maximum of the two - variable function α ( x m , z m ). since the definition of α = min { α ( top ), α ( middle ), α ( bottom )} is very non - linear and its derivatives are not continuous , it is useful to visualize the overall shape of this function . for instance , in the case of 4 - fold embodiments , the following inequalities hold in the neighborhood of the optimum : where α p and α d denote the parallel and diagonal acceptance angles defined in the glossary . the first two equation lines indicate that the parallel acceptance angle for the top ( short wavelength ) junction is smaller than the parallel acceptances of the other two junctions , while for the diagonal direction the bottom junction is the limiting one . the last two equation lines indicate that , for constant z m , when x m increases , the limiting parallel acceptance angle α p ( top ) increases while the limiting parallel acceptance angle α d ( bottom ) decreases . therefore , for each z m , there is compromise that is solved at the value of x m at which α p ( top )= α d ( bottom ) and then the acceptance angle α will be maximum . therefore , we have found that the maximum desired in target ( 1 ) is obtained when the top and bottom acceptance angles are balanced . the previous calculation can be done now with varying z m , and thus we can find the value of z m at which the coincident acceptance angle α p ( top )= α d ( bottom ) is a maximum , leading to the absolute maximum desired . note that since α ( top )= min { α p ( top ), α d ( top )} and α ( bottom )= min { α p ( bottom ), α d ( bottom )}, we get that α = α ( top )= α ( bottom )& lt ; α ( middle ). fig3 a shows the ray trace for the top junction spectral band on an optimized design at an incidence angle equal to 0 . 95α along the parallel direction . fig3 b shows the ray trace at the same incidence angle 0 . 95α but for the bottom junction spectral band along the diagonal direction . the 10 % drop that will occur at the incidence angle α in both direction will occur when the ray 301 that enters the soe nearest the top cusp of the soe reaches the adjacent lobe in the top junction parallel case ( fig3 a ), and when the ray 302 that enters the soe lowest down misses the target cell in the bottom junction diagonal case ( fig3 b ). since the refractive index of typical poe lens materials is not very different from middle to bottom junction bands , the focb 207 and 208 in fig2 are relatively close and the middle and bottom acceptance angles are also close . as a consequence , instead of making the parallel top acceptance angle equal to the diagonal bottom acceptance angle , the parallel top and diagonal middle acceptance angles can be made equal . this is especially adequate for the case of solar cells in which there is an excess of bottom junction photocurrent ( as in commercially available gainp — gainas — ge cells ), so that the bottom - junction current is unlikely to be limiting . in u . s . pat . no . 8 , 000 , 018 , only a monochromatic design is disclosed , and there is no mention of different parallel and diagonal acceptance angles . in u . s . pat . no . 8 , 000 , 018 , we recommended locating the single focal point either on the surface of the soe or along the chord joining the edges of the meridional curve through the optical axis of the segment , which corresponds to a point of the line z m = 0 in the present specification . as will now be shown with an example , that monochromatic design with those focus selections leads to a very low acceptance angle compared to the present polychromatic optimization , and to a poor balance between the acceptance angles of the top , middle , and bottom junctions . two 4 - fold devices with a flat fresnel lens were designed , both with geometrical concentration cg = 1024 ×, poe made of silicone on glass with dimensions 160 mm × 160 mm , soe made of savosil glass with 21 . 8 mm average diameter , gainp — gainas — ge triple junction 5 mm × 5 mm solar cell , and depth to poe diagonal ratio 1 . 08 . one of the devices was designed with the polychromatic optimization just described , while the other device was designed using the procedure disclosed in u . s . pat . no . 8 , 000 , 018 . to reproduce the monochromatic design of u . s . pat . no . 8 , 000 , 018 , the acceptance angle at the selected wavelength was maximized . the selected wavelength was 550 nm , which is centered for the top junction band . this wavelength is commonly used in optics because at that wavelength the refractive index takes approximately the value of the median of the distribution . the choice of the 550 nm wavelength was not stated in u . s . pat . no . 8 , 000 , 018 , but can be easily inferred from column 8 , lines 40 - 50 , where it is stated that a polychromatic ray trace analysis for the top junction band achieves an acceptance angle of ± 1 . 43 ° and the monochromatic analysis ± 1 . 47 ° . the proximity of these two values is consistent with the 550 nm selection . table 1 shows the comparison of the performance parameters of the two designs obtained with a ray - trace analysis : the first noticeable difference between the results for the two devices is that the focus of the 550 nm rays in the present polychromatic optimization is 5 . 1 mm away from the z m = 0 line , where the u . s . pat . no . 8 , 000 , 018 . this distance is as large as the cell side , indicating the substantial difference between this polychromatically optimized design and the ones disclosed in u . s . pat . no . 8 , 000 , 018 . the second difference is that while the acceptance angle for the three junctions is very well balanced in the polychromatic design , the bottom and middle junction acceptance angles are 30 % lower than the top junction acceptance angle in the concentrator of u . s . pat . no . 8 , 000 , 018 , so the imbalance is substantial . the third remarkable difference is that the resulting concentrator acceptance angle , given by α = min { α ( top ), α ( middle ), α ( bottom )}, and the cap , are also 30 % less in the device of u . s . pat . no . 8 , 000 , 018 . for this comparison , the u . s . pat . no . 8 , 000 , 018 concentrator was designed with the 550 nm focus located at the line z m = 0 , but , as mentioned before , in that patent we suggested as an alternative to locate the focus on the surface of the soe . that alternative selection leads to an acceptance and cap even lower than the ones shown in the above table . the poe and soe materials selected for the previous example are of special interest at present due to their expected long term durability . however , they have a relatively low refractive index ( silicone has n = 1 . 41 and savosil has n = 1 . 46 at 550 nm ) which makes their attainable acceptance angle and cap lower than with alternative materials , specially for the low depth to poe diagonal ratio ( 1 . 08 ). for instance , using pmma for the poe and b270 glass for the soe ( which have n = 1 . 49 and n = 1 . 52 , respectively ), which are also excellent candidates in terms of durability , with the same depth to poe diagonal ratio , the same design algorithm leads to a 15 % higher cap value in about 15 % thanks to their higher refractive indices . on the other hand , performance target ( 2 ), which is that the irradiance distributions of the three junctions must be very similar , is obtained by optimizing the soe . in this case , a single third design parameter is enough to obtain excellent results , and that is the point along the cell diagonal to be imaged by each quadrant on its corresponding poe sector . a central wavelength can be used for the calculations since the soe imaging required is very little affected by the chromatic dispersion due to the large field of view of view that the soe is imaging . the actual optimum position depends on the specific embodiment . for instance , in the case of concentrators with flat poes , being either 4 - fold or 9 - fold , the optimum is obtained when the selected cell diagonal point is the end of the diagonal furthest from the poe paired sector , as was disclosed in u . s . pat . no . 8 , 000 , 018 . however , for a domed poe the optimum point is the end of the diagonal closest to the paired sector . although this selection is optimum for the balance of the irradiances ( 2 ), it is not optimum for other criteria , such as the acceptance angle . for instance , fig4 a and fig4 b show the irradiance for the extreme bands of the top and bottom junctions , respectively , of a flat - poe design with pmma poe and b270 glass soe using the furthest point selection , which is the optimum for target ( 2 ) and thus they look extremely alike . on the other hand , fig4 c and fig4 d show the same graphs for a flat - poe design using the closest point selection , in which a significantly poorer uniformity balance is visible . however , the furthest - point configuration of fig4 a and 4b has a cap = 0 . 59 , while the nearest - point configuration of fig4 c and 4d achieves cap = 0 . 63 . in addition , the present polychromatic optimization makes possible a much better uniformity over the three junctions . with previous monochromatic designs , as illustrated by kritchman , ref . [ 15 ], fig9 and 10 , a too - perfect focusing at the nominal frequency sometimes resulted in a very non - uniform irradiation at that one frequency , and / or a wide variation in uniformity from one waveband to another . the following tables 2 and 3 show the numerical data describing the shape of the polychromatically optimized design just discussed whose performance data is given in the previous table 1 ). for both the poe and the soe , a cartesian coordinates system is used , with the origin at the cell center and with the x and y axes parallel to the cell sides , while the z axis is perpendicular to the cell plane . the size of the units is arbitrary , and in these units the cell active area is 5 × 5 while the poe is 160 × 160 . due to the 4 - fold symmetry , the lenses need to be described only in the quadrant x & gt ; 0 and y & gt ; 0 . both the poe and soe are symmetric with respect to the plane x = y . the surface of the soe has rotational symmetry with respect to the line joining the cell corner at x = y =− 7 . 071 and z = 0 with the poe corner at x = y = 113 . 2 , z = 244 . 5 . the soe sag list is given in table 2 : the fresnel lens segment has an axis of rotational symmetry parallel to the z axis , at x = y = 5 . 14468 , and the vertices describing its polygonal profile are given in the following table 3 : fig5 a and fig5 b disclose another preferred embodiment which consists of a 4 - fold symmetric device in which the poe is a fresnel lens 501 of a dome - like shape instead of flat . the additional degree of freedom to choose the curve of the overall profile of the fresnel lens makes it possible in the polychromatic optimization to control the positions of two foci for two junctions instead of one . fig6 illustrates the steps in the design of a domed 4 - fold concentrator . first of all , point a on the poe , placed on the optical axis , is chosen . then , point c of the soe , on the symmetry axis , is chosen , and the soe is designed as a cartesian oval coupling spherical wavefronts with origins at a and at point e on the near edge of the cell passing through c . next , point d is chosen as the point of the soe where the meridional tangent line to the soe forms a certain angle with the vertical direction ( typically 5 ° to allow for easy demolding of the soe part ). later , the poe is designed from a to b . one suitable method is described by kritchman et al ., appl . opt . 18 , 2688 - 2695 ( 1979 ), ref [ 15 ], which is incorporated herein by reference in its entirety , focusing parallel rays tilted + α ( starting from ray c and ending with ray a ) in d and focusing parallel rays tilted − α ( starting in ray d and ending with ray b ) in c , where a is the desired acceptance angle . kritchman describes only the design of a cylindrical lens , but it is within the skill in the art at the present time to generalize kritchman &# 39 ; s method to a dome lens . kritchman does not consider the possibility of a köhler configuration , but can still be used to locate the primary focus 209 . in the present embodiments , the kritchman method is modified as a polychromatic design , where rays focused in c are chosen to have a short wavelength in the solar spectrum ( e . g . 450 nm , in the top junction band ) and rays focused in d are chosen to have a long wavelength ( e . g . 1 , 000 nm , in the bottom junction band ). rays impinging within ± α on point a , after being refracted in poe and soe , will go to e . then , analogously to the polychromatic optimization described , the coordinates of points f , c and the abscissa of d are considered as the free parameters that define the space in which the acceptance angle is maximized to achieve performance target ( 1 ). domed fresnel designs can achieve lower depth to diameter ratios than flat fresnel designs ( 0 . 7 to 0 . 9 for domed fresnels compared with 0 . 9 to 1 . 2 for flat fresnels ) and higher caps due to the less constrained poe design ( up to 0 . 73 ). regarding the balanced irradiance distributions intended in performance target ( 2 ), fig7 c and fig7 d show the irradiance of a design with cg = 1 , 234 for the extreme bands of the top and bottom junctions , respectively , of a dome designed according to the previous paragraphs . it shows that the irradiances are significantly less uniform and less alike than for the flat - fresnel cases in fig4 a to 4d . the reason is that , since the lens is not flat , even if its projection on a plane normal to the sun direction is square , the angular region seen by the soe lobes is not , and the image the soe projects is very distorted and , because of the low depth to poe diagonal ratio , wavelength dependent . that design achieves a cap = 0 . 73 . if the abscissae of c and d are diminished , it is possible to provide a much more balanced uniformity , as shown in fig7 a and fig7 b , but at a lower cap = 0 . 55 . apart from the higher compactness and cap , the dome fresnel is advantageous over the flat one in its smaller soe ( this implies a lower absorption inside the material and lower cost in the glass molding process ). however , since the combination of the lens convexity and high optical efficiency can result in the facets of the dome poe having negative draft angle , the manufacturing of the dome lens becomes challenging . one technique is based on the use of pmma injection molding using a moveable mold , as the japanese company daido steel has developed for rotationally symmetric lenses , see ref . [ 5 ]. an alternative is shown in fig8 , in which the fresnel interior face of the lens is made with a spiral profile 81 ( which can be demolded by a combination of rotation and pull , as a screw ), truncated to the square projected aperture 82 . the exterior surface has the four lobes 83 to produce the desired beam separation . the spiral is constructed from a 2d polygonal profile contained in a meridional plane in three steps available in many cad software packages : ( a ) a linearly varying spiral is generated passing through the concave vertices , ( b ) the same as ( a ) for the convex vertices , and ( c ) the facet profile is swept along the spirals using the them as rails . of course , it is also possible to use the 4 - fold front surface 83 of the poe in combination with a rotationally symmetric fresnel inner surface . the following two tables 4 and 5 show the numerical data describing the shape of the polychromatically optimized dome design just discussed with cap = 0 . 73 . for both the poe and the soe , a cartesian coordinates system is defined with the origin at the cell center and with the x and y axes parallel to the cell sides , while the z axis is perpendicular to the cell plane . the size of the units is arbitrary , and in these units the cell active area is 5 × 5 while the poe is 176 × 176 . due to the 4 - fold symmetry , the lenses need to be described only in the quadrant x & gt ; 0 and y & gt ; 0 . both the poe and soe are symmetric with respect to the plane x = y . the surface of soe has rotational symmetry with respect to the line joining the cell corner at x = y = 7 . 071 and z = 0 with the poe vertex at x = y = 0 , z = 200 . the soe sag list is given in the following table 4 : the dome fresnel lens has an axis of rotational symmetry parallel to the z axis , at x = y = 5 . 211 , and the points describing the inner polygonal profile and smooth outer profile are given in the following table 5 : so far , the embodiments have had 2 × 2 symmetric units , but the polychromatic optimization described can be applied to other more general n × m schemes . fig9 shows a 1 × 2 design , in which the rectangular poe lens 91 is divided into two segments that concentrate the sun light onto a two - lobe soe lens 92 , splitting the beam into two channels that create the two foci 93 and 94 . devices with n different from m have the capacity to produce different acceptance angles in the n and m directions . this is of interest for setting the high acceptance angle direction parallel to the elevation axis , at which the mechanical constraint is higher in usual rectangular arrays . the design in fig9 has cg = 312 × and acceptance angles of ± 1 . 37 ° and 1 . 62 ° ( larger in the direction of the long side of the poe rectangle ). the acceptance of the 1 × 2 concentrator may be optimized analogously with the 2 × 2 concentrators described above . defining the “ long parallel ” direction as parallel to the edge that extends first along one segment of the primary optical element 91 and then along the other segment , and defining the “ short parallel ” direction as parallel to the orthogonal edges , the optimization can be done in three ways : ( 1 ) the simplest approach , as in the 4 - fold case , is to find the maximum at which α_long ( top )= α_long ( bottom ) and maximum . in this case α_short ( top ) and α_short ( bottom ) will not in general be equal one to another . ( 2 ) use x m , and z m to adjust the two equations α_long ( top )= α_long ( bottom ) and α_short ( top )= α_short ( bottom ). in this case along will not be maximum . ( 3 ) find the maximum at which α_short ( top )= α_short ( bottom ) and maximum . in this case α_long ( top ) and α_long ( bottom ) will not in general be equal one to another . this is the same as ( 1 ) exchanging long and short . fig1 shows a further embodiment of a köhler integrating concentrator in the form of a 3 × 3 concentrator , for which the polychromatic optimization has to be applied . the poe is a fresnel lens 100 comprising nine segments or sectors . the fresnel lens is not fully rotationally symmetric , but comprises a symmetric central sector 106 , four lateral sectors 105 , each of them symmetric with each other relative to the fresnel lens center , and four diagonal sectors 104 , also symmetric with each other relative to the fresnel lens center . the four lateral and four diagonal sectors may be made as an off - center square piece of a symmetric fresnel lens . soe lens 101 also comprises nine sectors , each aligned with corresponding sector of poe lens 100 . all nine sector pairs send the sun rays within the acceptance angle to cell 102 . compared to 4 - fold flat fresnel designs , the 9 - fold produces a higher cap ( up to 0 . 65 ) in performance target ( 1 ) and an even better uniformity and irradiance balance in performance target ( 2 ). for instance , the 9 - fold in fig1 achieves cg = 1000 × of geometrical concentration with an acceptance angle of ± 1 . 18 ° ( i . e . cap = 0 . 65 ). this device is attractive for solar cells 102 with specially high spectral sensitivity , as is expected to occur in future four and five junction solar cells . with the design of their previous u . s . pat . no . 8 , 000 , 018 , the inventors have achieved a balance no better than 0 . 7 : 1 between the top and bottom junctions , and a cap for the worst of the three wavebands no better than 0 . 40 . they believe that a balance of 0 . 75 : 1 and a cap of 0 . 45 would be obtainable by improved design . with the present devices , in contrast , a balance of at least 0 . 99 : 1 between the top and bottom junctions , and a cap for the worst of the three wavebands of at least 0 . 63 are obtainable , even with a flat primary optical element . embodiments of the present invention consistently achieve a cap greater than 0 . 45 , and a uniformity ( ratio of minimum to maximum irradiance on the cell with the sun centered on the perfect - aim position ) of at least 0 . 5 for all wavebands simultaneously . the inventors have found that with proper design a uniformity of at least ⅔ , and usually at least 0 . 8 , is consistently achievable for realistic configurations . 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