Patent Grant
8338693
1. Field of the Invention
The present invention relates, in general, to devices and systems for converting solar energy into electricity such as devices using the photovoltaic effect to convert solar energy directly into electricity, and, more particularly, to a PV device such as a module, array, or panel of solar cells that includes a PV enhancement (or light trapping) layer or film to better trap or capture light or rays from the Sun that are incident on a front or receiving surface of the PV device to achieve enhanced absorption and conversion of the solar energy into electricity. The PV enhancement film is adapted to reduce reflection or loss of incident light when the Sun is normal to the front surface of a solar cell (or to the solar module, array, or panel) and also at oblique angles, thus reducing the need to track the Sun's position with the PV device including the PV enhancement film.
2. Relevant Background
With the growing interest in renewable energy including use of solar power, there is an increasing demand for more efficient solar cells. Solar cells or photovoltaic (PV) cells are devices that convert solar energy into electricity by the photovoltaic effect, and solar cells are widely used in devices ranging from satellites and other applications including portable consumer electronic devices that are remote from a conventional power source. More recently, large solar power collection systems with arrays of cells or PV modules (or solar panels) are being used to supply power to electrical grids for distribution to consumers. Several concerns are limiting the implementation of solar cells including cost of materials and manufacturing, environmental concerns with materials such as lead, and low efficiency of the cells. As a result, researchers continue to look for ways to lower manufacturing costs and for ways to enhance the efficiencies of solar cells and panels, modules, or arrays that include such cells. For example, existing solar cells, such as those based on a silicon substrate, typically have efficiencies of 10 to 20 percent, and, as a result, even small increases (e.g., of one to several percent) in efficiency may represent large relative gains in being able to convert solar energy into useful electricity (e.g., an increase in efficiency of 1 to 2 percent represents a 5 to 20 percent or higher gain in efficiency for a cell design). Even with these limitations, though, the manufacture and installation of solar cells and PV arrays has expanded dramatically in recent years. Some estimates indicate that PV production has been doubling every two years making it the world's fastest growing energy technology, with about 90 percent of the capacity being grid-tied electrical systems that are ground mounted (e.g., in solar farms) or on building roofs/walls. Concerns with global warming and financial incentives provided by world governments will likely only increase the demand for PV arrays and the demand for more efficient solar cells.
Solar cells or photovoltaics (or PV devices) convert sunlight directly into electricity and generally are made of semiconducting materials similar to those used in computer chips. When sunlight is absorbed by these materials, the solar energy frees electrons loose from their atoms, which allows the electrons to flow through the material to produce electricity. The process of converting light (i.e., photons) to electricity is called the photovoltaic (PV) effect. In practice, solar cells are typically combined into modules that hold numerous cells (e.g., up to 40 or more cells, and a set of these modules (e.g., up to 10 or more) are mounted in PV arrays or solar panels that can measure up to several meters or more per side, with each cell typically only being up to 100 to 150 square centimeters in size. These flat-plate PV arrays are mounted at a fixed angle facing the Sun (e.g., south) or they may be mounted on a tracking device that follows the position of the Sun to allow them to better capture the Sun's light throughout the day. Solar cells may be formed using thin film technologies to use layers of semiconductor materials that are only a few micrometers thick.
The performance of a solar cell is measured in terms of its efficiency at turning sunlight into electricity. Only sunlight of certain energies will work efficiently to create electricity and much of this desirable energy sunlight may be reflected from the surfaces of the solar cell or absorbed by its materials without creating electricity. Due to these and other areas for loss of sunlight, a typical solar cell may have an efficiency ranging from about 5 to 20 percent, with some highly efficient solar cells claiming efficiencies of up to 22 percent or higher. For example, an energy conversion efficiency of 22 percent was announced in 2007 as being a world record event for a practical-sized (e.g., about 100 cm2), crystalline silicon-type solar cell (e.g., an HIT solar cell composed of a single thin crystalline silicon wafer surrounded by ultra-thin amorphous silicon layers). Low efficiencies mean that larger arrays are required to provide a particular amount of electricity, which increases the material and manufacturing costs. As a result, improving solar cell efficiencies while holding down the cost per cell continues to be an important goal of the solar power industry.
Even when a PV array is positioned normal to the Sun's rays, sunlight is reflected or lost to a typical solar cell, with estimates at 5 to 33 percent or more of the light being spectrally reflected and lost. In some cases, the solar cells may be protected from the environment with a glass sheet or with transparent plastic packaging. Significant efforts have been made in the solar power industry to boost efficiency by reducing reflection when the sunlight is incident at a normal angle (or when the angle of incidence is at or near zero degrees) on the PV array. Typical solutions have called for application of an antireflection coating of a material such as a SiNx layer or the like on the cell and/or upon the protective glass/plastic layer to minimize the reflection of light from this protective layer. The AR coating provides a layer or layers of material with a desirable refractive index and thickness (e.g., a quarter wavelength) to lessen reflection of sunlight at the coated surface (e.g., the planar surface of the sheet of protective glass). In some embodiments, the AR coating may be a metal fluoride combined with silica (e.g., a flouropolymer), a zinc or other metal oxide (or other transparent conductive oxide), or other material layer. Recently, coatings formed of a single-layer of porous silicon oxide have been applied to a protective glass layer to decrease glass reflection by about 3 percent at noon and by about 6 percent in mornings and evenings (e.g., when the sunlight strikes the solar cell at an oblique or non-zero incident angle). Additionally, other AR coatings are being developed including textured-dielectric coatings and multi-layered, nanostructured coatings (e.g., seven layers of silicon dioxide and titanium dioxide nanorods). While providing some improvements in light capture and efficiency of solar cells, existing AR coatings generally are most useful in controlling reflection of sunlight when the sunlight is striking the PV array at normal (e.g., near noon for many arrays) and do little to limit other types of reflection or bounce back losses.
As discussed above, the largest problem with the rapidly developing technology of photovoltaics revolves around cost-versus-efficiency. Whether traditional silicon materials are used or newer cadmium telluride or copper photovoltaic constructions are used, efficiencies are still a significant limitation on solar cell use and adoption by consumers and the power industry. While multiple-layered more expensive PV cells that are designed for concentrator systems or to absorb a wider variety of wavelengths (including the longer wave lengths) are significantly more efficient, the more elaborate and expensive multi-layer PV materials also result in increased ray loss at angles other than nearly perfect toward the Sun in both axis. This additional loss is caused by increased ray deflection as a result of cosine fall off as well as the narrow acceptance angles required by the complexity of the PV structures as they attempt to use more of the available wave lengths.
Losses in absorption into PV materials are caused by several factors. One of the factors is normal “cosine fall off” or the lack of absorption due to the incoming angle of the sunlight and the relationship of the incoming rays to the structures in the PV materials. For example, a typical solar cell will have an upper or front surface that is not perfectly planar but is instead textured or rough. This results in many of the rays simply being deflected off of the surface of the PV materials and not being absorbed. However, this phenomenon also happens even when sunlight or rays are directed directly into the PV materials at zero degrees or at a perfect angle into the PV material. Part of the reason for the deflection of the rays is that the structures within the PV materials are not flat and are for the most part three-dimensional. Incoming rays, even when perfectly aimed, are bouncing off these structures (e.g., are reflected) and are never absorbed by the solar cell.
Hence, there remains a need for improved solar cell devices/products such as PV arrays that better control reflection and/or increase the amount of incident sunlight that is absorbed by the solar cells. Preferably, the improved solar cells would have improved energy conversion efficiencies with or without tracking of the Sun's position, and the solar cells and PV arrays of solar cells would not be significantly more expensive to manufacture or require redesigns/modification of the underlying solar cell configuration or makeup.
The present invention addresses the above problems by providing photovoltaic (PV) enhancement films for use with solar panels/arrays and solar cells (or other PV devices) to increase the efficiency of the PV materials in absorbing available solar energy. Specifically, the PV enhancement films are designed to capture or trap light reflected from light-receiving surfaces of solar cells that normally would be lost and direct this reflected light back onto the light-receiving surfaces (often at a different incidence angle) for second or additional chances for absorption and conversion into electricity. The trapping or redirection of the light is achieved through the use of total internal reflection (TIR), and the PV enhancement films act to pass most incident light onto the light-receiving surface (without significant focusing) and then trap a significant portion of reflected light back to the light-receiving surface. The PV enhancement films may be formed of a plastic, glass, ceramic, or other substantially transparent material (e.g., highly light transmissive material such as an energy-cured polymer) and include a thin substrate upon which a plurality of TIR elements or structures are formed (or provided).
Each of the TIR elements is designed to receive and transmit the received light but then to direct reflected light from the solar cell back to its light-receiving surface for possible absorption. For example, the TIR elements are elongated structures that are provided with a sawtooth pattern on a side of the substrate with the triangular cross section TIR elements each providing two facets to trap light via TIR. In other cases, the TIR elements are three-dimensional (3D) structures on the surface of the substrate that each act to reflect back otherwise lost sunlight, e.g., a plurality of hemispherical/dome shaped bodies, full or truncated cone shaped bodies (frustoconical shapes), three-sided or four-sided (or more-sided) pyramids (coming to a true point/apex, to a flat/planar side/facet, to a curved, domed, or hemispherical point, or other termination), and so on. Through modeling with ray tracing computer programs, it is likely that the PV enhancement films will capture enough reflected light to significantly increase efficiencies of solar cells, solar arrays, and the like. For example, modeling indicates that use of some embodiments of the PV enhancement films will increase efficiencies up to 10 percent while other implementations may increase efficiencies up to 25 percent or more (such as in solar arrays with no tracking and with larger reflection losses during off-peak hours).
More particularly, one embodiment provides a solar cell assembly for more efficiently capturing solar energy by providing additional chances to absorb reflected sunlight. The assembly includes a solar cell (note in a solar array assembly a plurality of solar cells would be included in the assembly). The solar cell includes a light-receiving surface, and a fraction or percentage of light incident upon the light-receiving surface is reflected over a predefined range of incidence angles (e.g., most light may be absorbed in the range of −10 to 10 degrees but over at more oblique angles of incidence such as greater than 10 degrees and less than −10 degrees greater and greater portions of the light striking the solar cell may be reflected). Significantly, the solar cell assembly includes a PV enhancement film formed of substantially transparent material (such as a light-transmissive plastic) positioned to cover or abut at least a portion of the light-receiving surface (and, more typically, to cover most or all of the light-receiving surface). The PV enhancement film includes a substrate positioned proximate to or abutting (except for an optional adhesive layer affixing the film to the solar cell) the light-receiving surface. The film also includes a plurality of total internal reflection (TIR) elements on the substrate opposite the light-receiving surface. Each of the TIR elements is designed to direct at least a portion of the reflected light back toward the light-receiving surface of the solar cell.
The TIR elements transmit the light incident (or most of this received light) to the light-receiving surface (e.g., do not block or focus this light) and also direct the portion of the reflected light back to the light-receiving surface using TIR as the reflected light strikes one or more sides of the TIR elements. Each of the TIR elements may have a linear or elongated body with at least two inward angled sides. For example, the TIR elements may have triangular cross sections (e.g., as viewed on end) with sides angled inward at angles of less than about 60 degrees (e.g., of less than about 45 degrees). The TIR elements may be of like size and shape, or the TIR elements may have differing sizes (and/or shapes) such that alternating ones have differing thicknesses for example (or alternating sets of the TIR elements may be configured differently) to tune the optical effect achieved (i.e., differing TIR elements may provide better TIR trapping effects at differing incidence angles and it may be useful to select two or more of such TIR elements in a single PV enhancement film). In another example, the TIR elements are linear but include three, four, or more facets/sides such as two inward angled sides with an upper planar side positioned therebetween that is parallel to the light-receiving surface (e.g., similar to a cross of a pyramid structure). In other embodiments, the PV enhancement film may include a light receiving and trapping surface that defines the TIR elements, and this surface may have a sinusoidal shape when viewed along an edge of the PV enhancement film (e.g., to provide elongated TIR elements with a sinusoidal sectional shape). In other embodiments, the TIR elements are provided on a surface of the substrate opposite the light-receiving surface and have 3D bodies with a shape selected to provide a desired TIR effect (such as a plurality of pyramids or 3 to 4 or more-sided pyramid shapes protruding from a substrate or sheet, numerous hemispherical shaped bodies or domes, a number of cones or truncated cones, and the like). The PV enhancement film may be relatively thin and the TIR elements small to achieve the TIR trapping effect, and, in one embodiment, the TIR elements each has a base and a height less than about 10 mils in magnitude.
Generally, the present invention is directed to photovoltaic (PV) enhancement films for use in solar panels, arrays, or modules (or with individual solar cells or other PV device) to improve solar efficiencies. The PV enhancement films are adapted to be applied to existing solar arrays, panels, or modules and/or used with solar cells/PV devices during initial manufacture. The PV enhancement films each include a substrate of plastic, glass, or ceramic (e.g., a substantially transparent material such as a thin polymeric film or the like) with a plurality of total internal reflection (TIR) structures or elements on one surface. The PV enhancement film may be attached to a solar array such that TIR structure-side faces the Sun and the opposite (typically planar) side abuts the light receiving side and/or surfaces of the solar cells in the solar array. The TIR structures are each adapted to create TIR directionally toward the photovoltaic structures of the solar cells to enhance performance of the solar array (or individual PV device) by deflecting unabsorbed photons back toward the photovoltaic structures for a second (or additional) chance for absorption and conversion into electricity. Briefly, each TIR structure on the PV enhancement film acts to allow incident sunlight to pass relatively unhindered to the solar cells of the array, and, then, to trap a substantial fraction of the reflected or bounced back light with TIR causing the initially unabsorbed sunlight or rays to be returned at least one more time to the solar cell (with some rays being directed to the solar cell 2 to 5 times or more before they are either absorbed or escape the PV enhancement film and the solar array that includes such a film).
The shape of the TIR structure may vary widely to practice the invention with some TIR structures being linear with a triangular, a polygonal, an arcuate or other cross section while others are non-linear with a variety of shapes such as pyramids (three, four, or more angled sides with/without an apex (e.g., a flat or shaped peak rather than a point), domes, cones, frustoconical shapes, and hexagonal shapes (e.g., textured surfaces with domes or other side-by-side TIR elements on a surface of a sheet or film of transparent material). The angles defined by the light-receiving/trapping surfaces of the TIR structures may also vary widely from about −5 to +5 degrees with angles in the −45 to 45 degree range being desirable in some cases. Also, the size of the TIR structures may be varied to practice the invention with some embodiments utilizing TIR elements as small as about 0.25 mils (5 microns) in width while others use TIR elements up to 1 inch or more in width. The height (or thickness) may also vary again with some embodiments being very thin (e.g., about 0.25 mils or 5 microns in height) while others are relatively thick (e.g., up to about 1 inch or more in height). In one exemplary embodiment, a two or three-faceted TIR structure is utilized that is about 2 mils high and about 1 mil wide at the top planar facet or side of the structure (with the base width or pitch varying with the inward angle of the side(s) of the structure).
Electricity 120 generated by the solar cells or PV structures of the solar array 112 may be provided to a variety of end use devices such as charging electronics 130 for storage in a battery or batteries 132, a power grid 140 (e.g., for use by a utility to meet residential and commercial power demands), and/or other electrical loads 150. One of the largest problems with the use of PV arrays 112 is efficiency in converting the solar energy 104 into electricity that can be used by the end users (battery 132, power grid 140, and/or electrical load 150). Some estimate that existing solar arrays may only be 10 percent efficient in generating the electricity 120, e.g., generate 100 W/m2 from the received solar energy 104 of 1 kW/m2. There are also inefficiencies and line losses in the transmittance and storage of the electricity 120 that may result in an end-to-end efficiency of even less than 10 percent (e.g., 7 to 8 percent by some industry estimates).
The present invention is directed toward increasing the efficiency of PV devices such as the solar array 112, and the inventors recognize that a significant portion of the solar energy 104 incident upon a typical solar array 112 may be lost as shown at 106 due to reflection or bounce back. For example, losses in absorption of PV materials in the solar array 112 may be caused by normal cosine fall off or the lack of absorption due to the incoming angle of the sunlight 104 with relation to the structures in the PV materials. Even when tracking 118 is utilized, a portion 106 of the sunlight 104 is lost due to reflection (such as off of a protective glass surface, due to surface irregularities, and so on).
For example,
With reference again to
The film 114 may be retrofitted onto an existing solar array 112 or combined with new PV materials or solar cells during initial fabrication of the array 112, with either fabrication method of the array being performed relatively inexpensively (e.g., a plastic film 114 with numerous TIR structures may be attached with adhesives or other methods in a few minutes even after the array 112 is in position in a solar farm/plantation or a rooftop setting or may be laminated or otherwise applied over the solar cells of an array or over each solar cell as it is formed (e.g., the film 114 may include a plurality of segments or individual films each applied to a solar cell to form a solar cell assembly that may then be included within the array 112). The film 114 (or films as may useful to provide desired coverage of a larger array 112) may be made of a wide variety of materials such as readily available plastics that are transmissive to sunlight 104 such as a polymeric sheet or the like or made of glass or certain ceramics that are transparent or at least highly transmissive. In some embodiments, the materials used for forming the film 114 and its TIR structures/elements are chosen from glass, nearly any type of clear (i.e., transparent to translucent/less transmissive) plastic including but not limited to PET, propylene, OPP, PVC, APET, acrylic, or any clear plastic, and/or a ceramic. In many embodiments, the preferred base material is a plastic dues to its durability, low material and manufacturing costs, and light weight, and the plastic of the film 114 may be extruded, calendared, cast, or molded to provide the functional TIR structures described herein.
The TIR structures includes on the PV enhancement films of embodiments of the invention function to create TIR on the light-receiving surfaces of solar cells/PV materials, and the TIR structures may be described as “reverse funnels” for directing light.
The concept of using TIR in thin films (e.g., plastic films with a substrate with TIR structures on one side that are applied over solar cells) is believed to be a new concept. In order to use TIR as a method of turning rays or limiting loss of sunlight from a solar cell/PV material, it may be useful to describe basic physics or geometry of the angles and the resulting behavior of the rays. Sunlight or rays may enter into a transmissive TIR structure or element with refractive indexes of between 1.1 and about 2.0, with normal ideals between 1.4 and 1.65. Once rays enter the TIR structures, the rays will not exit the TIR structure if they remain within 42 degrees of parallel to the wall of the structure when striking the wall of the structure. Rays within this TIR physics law will deflect inside the TIR structure until they find an escape or are absorbed by the PV materials/solar cell and are converted into electricity. The “escape” out of the TIR structure would typically be the result of a deflection of past 42 degrees as measured from a wall of the TIR structure (e.g., an internal “surface” of a wall or facet of a TIR structure that comprises a solid body of plastic, glass, ceramic, or other highly transmissive material), creating a more direct “strike” of the surface allowing the rays to exit.
One idea supporting the invention is that many losses and decreases in efficiency in various PV films are the result of rays not being absorbed into the PV material, e.g., absorption of photons to start the photovoltaic effect (i.e., process of the electron moving down (creating a hole) to be replaced by an electron of the opposite polarity and therefore creating a flow of electrons to establish a current). Instead, the rays bounce off the three-dimensional (3D) surface or non-planar/textured surface of the PV materials or solar cell, whether the film is using silicate, cadmium telluride or other technology or materials. Since the goal of a solar cell design is for the rays to enter the PV film, and, therefore, the structures, PV films can be made of many layers, targeting the various wavelengths of the incident sunlight. Since a large portion of the solar energy lies in the shorter wavelengths for the PV process, these wavelengths are specifically targeted either on one or more layers for absorption. PV materials are often made of a pure material such as silicon mixed with tiny amounts of controlled impurities to produce controlled energy levels or bands in the material. Depending on the materials and amounts used there are valence bands and conduction bands. The photons coming from a source of light will cause electrons to occupy conduction bands that can conduct electrons to an electrode. On the other side of the material, there are holes that are effectively positive charges that were produced by the photons that traveled to the electrode on the other side of the PV material to complete the electric circuit. It is not the purpose here to dwell on these processes that are covered in solid state physics textbooks and available reference materials but to generally say that when photons are absorbed under the right conditions an electrical output will be generated.
One of the main problems with the ray absorption into PV materials is that incoming rays tend to bounce off the surface of the PV materials at extreme angles, significantly decreasing the ray's chance of absorption. This is attributed generally to a phenomenon known as cosine fall off. In this case, the incoming rays are coming in from difficult angles in the mornings, evenings, and/or differing seasons (or a combination thereof) that allow an undesirably small fraction or portion of the rays to be absorbed by the solar cell or array containing numerous solar cells. In addition, improper orientation of panels/panels with regard to the azimuth of the Sun may also contribute to or lead to loss of available solar energy.
It is important to note, however, that even with perfect tracking of the sun with PV materials, the angles of the structures themselves create a random-like mathematical percentage of rays bouncing off structures within the PV film and not being absorbed. Even short wave length rays coming in directly may hit structures or textured surfaces of a solar cell at angles that do not allow absorption (as shown in
In fact, this TIR effect may happen a few times up to dozens of times until the ray is absorbed into the PV material generating energy or exits the structure because of a deflection creating an angle that exceeds 42 degrees (a more direct “hit”) to the wall of the structure. Therefore, use of a PV enhancement film with TIR elements/structures with a solar cell/PV device in accordance of invention does not insure the absorption of each ray, but it does increase the odds of absorption by giving a portion or fraction of the unabsorbed rays another chance or opportunity at absorption by bouncing the ray back to the PV material at a different angle (at least the probability is that the ray will be incident upon the solar cell at a different angle than when first received). In many cases, a ray, if rejected again by the PV material with a deflection, will in theory have dozens more chances of absorption. Ultimately, the ray will either be absorbed or will find an exit angle from the structure that exceeds 42 degrees from parallel of the surface of the wall of exit. In ray tracing programs run by the inventors to test use of TIR structures/elements of the invention, using a 95% reflective mirrored surface in place of a light-receiving surface of a solar cell shows that rays may bounce dozens of times within the structures before exiting the structure. In other words, the TIR elements or microstructures can increase a deflected ray's odds of being absorbed by a significant amount or by many times in this TIR light-trapping process.
As shown, the PV enhancement film 420 includes a substrate 426 with a first side/surface 422 that is positioned proximate to the front or light-receiving surface 414 of the solar cell 410 (and may be considered a solar cell-facing or mating surface). The substrate 426 is generally a relatively thin layer formed of substantially transparent material (e.g., the same material as used for the TIR structures 428) and the cell-mating surface 422 often is generally planar to provide minimal interference with light passing from the PV enhancement film 420 to the cell 410. On a second side/surface 424 of the substrate 426, the PV enhancement film 420 includes a plurality of TIR structures or elements 428. The side/surface 424 may be thought of as the light-receiving surface/side of the film 420 and is spaced apart from the cell surface 414 by the thickness of the substrate 426. In this embodiment, the TIR elements 428 are two-sided or two-faceted structures with elongated bodies extending over the length (or width) of the solar cell 410 surface 414 as is shown with the length of the film, LPV film. The TIR elements 428 are linear elements with a triangular cross section in this embodiment with the two facets or sides of the structure 428 forming the sides of the triangle and the base mating with or being an integral connection with the substrate 426. The size and shape of the triangular cross section of each TIR element 428 may be varied to practice the invention, and it may be varied depending on the intended use of the cell assembly 400 (e.g., 45 degree facets may be used for a cell assembly 400 used in a solar array (see
As shown in use, a first ray 520 of sunlight is received or is incident upon a side or facet 510 of the TIR element 428 at an angle that is near normal or orthogonal (as measured from a plane orthogonal or normal to the light receiving surface 414 of the solar cell 410 with the ray 521 being shown at about −10 degrees). The received sunlight 521 is allowed to enter or pass through the TIR element 428 with some diffraction as shown with ray 522, and the ray 522 passes through the PV enhancement film 420 including the substrate 426 where it strikes the light receiving surface 414 (and/or PV structures) of cell 410. In this example, the ray 522 is not absorbed to make electricity but is instead reflected or bounced off at a different angle as shown with ray 524. The ray 524 strikes the side or facet 510 of the TIR element 428 at an angle, a, and when this angle is less than about 42 degrees (as shown), the ray is trapped by facet 520 and reflected as shown with ray 526 back toward the light receiving surface 414 of cell 410 (e.g., a TIR effect is achieved with TIR element 428). Again, the ray 526 may not be absorbed by the solar cell 410 and instead reflected/bounced back as shown at 528 where it strikes the facet 520 to again be trapped/reflected at a differing angle as ray 530. Ray 530 strikes the light receiving surface 414 of the cell 410, where it is absorbed into the cell 410 as shown with absorbed energy/ray 532.
In this example, the TIR element 428 trapped the non-absorbed rays 524, 528 using TIR and provided the solar cell 410 with two additional chances to absorb the solar energy, which otherwise would have been lost (e.g., if conventional AR coating had been used the ray 524 would likely have been lost from the assembly 400). In practice, the number of additional chances will vary widely and will likely range from 0 to 12 or more (with 0 occurring when the first reflected ray 524 strikes the facet 520 at an angle, α, greater than 42 degrees), with a general description being that the TIR element 428 acting to trap at least a fraction of the reflected light and direct it back onto the light-receiving surface 414 for one or more chances at absorption. For example, a cell 410 may experience up to 70 percent loss of sunlight due to reflection and/or bounce off of received rays from the light-receiving surface 414, and the PV enhancement film 420 with use of the TIR elements 428 (linear bodies with two-sided cross sectional shapes) may be able to force 35 percent or more of the lost sunlight to strike the light receiving surface 414 at least a second time (with some rays being trapped and forced to strike the surface 414 multiple times by the TIR element 428).
Similarly, other rays 540 may strike the TIR element 428 at differing angles (such as at more than 20 degrees as shown) and be allowed to enter the TIR element 428 as shown with ray 542. The ray 542 passes through the TIR element 428 and strikes the light-receiving surface 414 of the cell 410 where it is reflected or bounced off as ray 544. The ray 544 strikes the facet/side 520 at an angle, β, less than about 42 degrees (in this case), and is deflected as ray 546, which strikes surface 414 of cell 410 and is again reflected as ray 548. The unabsorbed ray 548 strikes facet 510 is again trapped by TIR and reflected as ray 550 toward the light-receiving surface 414, but this additional chance provided by the TIR element 428 results in the ray 550 being absorbed as shown at 554. It will be understood that
The shape of and/or wall angles the TIR element may be altered in accordance with the invention to provide better or differing TIR effects (or differing abilities to trap light on the solar cell/PV device front or light-receiving surface). For example, the inventors believe it may be beneficial to utilize TIR structures with 3 or more facets/sides to trap sunlight received over a range of angles (e.g., when tracking is not provided for a solar array or the like).
As will be understood, the PV enhancement films such as film 610 may be used with nearly any solar cell design and/or PV component where reflection or loss of incident light is a concern.
To enhance the efficiency of the cell 720, the solar cell assembly 710 includes a PV enhancement film 730 that is positioned over, and may be joined to, the front electrode 726 so as to substantially or completely cover the light-receiving surface 725. The PV enhancement film 730 is similar to the other films shown thus far in that it includes a substrate 732 of substantially transparent material upon which a plurality of linear or elongated TIR elements 734 are formed (or otherwise provided such as by a second depositing step or the like). The film 730 differs, though, as the TIR structures are formed with an arcuate light receiving/trapping surface such that each TIR structure may be considered to have a semi-circular cross section (e.g., the body of each TIR element 734 may be thought of as half or less of a cylinder). The TIR elements 734 are aligned with their elongated bodies side-by-side and with their longitudinal or central axes parallel. Again, the height and width of the TIR elements 734 may be widely varied to practice the invention and to achieve a desired TIR effect (e.g., better TIR at particular angles of incidence of received sunlight and so on to suit a particular solar cell 720). For example, each TIR element may be up to 0.25 inches in height but typically may be relatively thin such as several mils or less in height and may be up to about 1 inch in width but typically 10 or more TIR elements 734 are provided per inch of width of the film 730.
In some embodiments, PV enhancement films are provided with numerous TIR structures or elements formed upon a surface of a substrate and the TIR structures do not have elongated or linear bodies. For example,
The above description provides a general description of applications for a PV enhancement film with TIR structures or elements to improve the efficiencies of solar cells (or other PV devices) and of solar arrays, modules, and panels that incorporate such solar cells and PV enhancement films. The above description provides description of some PV enhancement films and TIR elements, and it also provides an introduction into how the TIR elements trap light using TIR to direct at least a fraction or portion of reflected (unabsorbed) sunlight back onto the solar cell/PV structures. At this point, it may be useful to provide additional explanation of the operation of TIR elements provided in PV enhancement films, and the following description provides additional embodiments of PV enhancement films along with a more detailed explanation of the optical principles utilized by the invention. Portions of the description include PV enhancement films and TIR elements shown more schematically than in prior descriptions/figures, but it will be understood that such embodiments or models used for computer-simulations and ray tracings may readily be implemented in physical products (e.g., TIR structures or elements provided on a side of a substrate or film of plastic, glass, ceramic, or substantially transparent material) for application over solar cells/solar arrays as discussed above.
This invention generally concerns the use of optical films (e.g., PV enhancement films) that make use of total internal reflection (TIR) and refraction (e.g., TIR structures or elements that provide TIR and also refraction). The TIR elements redirect sunlight reflected off the surface of a photovoltaic (PV) cell back to the cell so that energy that would be normally be lost for electrical power generation is used for (or at least available for) power generation, thus producing more power than if the cell did not have the optical or PV enhancement film as part of its assembly or covering it in a solar array. Embodiments of the invention make use of the properties of light reflection expressed by Fresnel reflection coefficients.
Relevant equations for modeling and/or evaluation of PV enhancement films and solar cells without such films can be written in the following manner: θ1=angle of incidence; θ2=angle of reflection; Rs=power in plane perpendicular to incidence; Rp=power in plane of incidence; Rs=(sin (θ2−θ1)/sin (θ2+θ1))^2; Rp=(tan(θ2−θ1)/tan(θ2+θ1))^2. A plot or graph 1200 is shown in
In this case,
For example, the TIR structure 1410 shown in
Of course, the TIR element 1410 is not able to trap all rays 1420 but, instead, only a fraction or portion of the rays 1420 is redirected toward the surface 1411 at any particular angle of incidence. For example, ray 1430 strikes facet 1414 and is received as ray 1431 for its first chance at absorption as it strikes light-receiving surface 1411. However, if it is not absorbed, the ray 1432 may be reflected in such a way from surface 1411 that is strikes facet 1416 at an angle greater than about 42 degrees. In this case, as shown, the light is lost from the TIR element 1410 as shown with ray 1433. Hence, while the PV enhancement films with TIR structures 1410 of the invention may enhance efficiency of a solar cell or PV device in receiving available sunlight, the TIR structures 1410 attempt to enhance efficiencies by increasing light capture and are designed to increase light capture for particular uses and/or solar array or cell designs (e.g., a differing TIR structure may be used for a solar array that tracks the Sun than for a solar array with no tracking).
One method of testing or verifying a design of a PV enhancement film and/or a TIR structure design is to plot ray or light intensity received by or striking a solar cell's light-receiving surface with and without use of the PV enhancement film.
For plot 1520, the light-receiving surface (such as surface 1411) was considered to have 100 percent reflection, which is not the case for PV devices but is useful for determining the functionality of a TIR structure at trapping reflected rays. As shown with line 1520, the TIR rays or redirected rays reflected from the light-receiving surface enhance the intensity of the light-receiving surface over the conventional, uncovered PV device. Use of the TIR structure with a solar cell can be seen to significantly enhance intensity when light is received at incidence angles greater than 20 degrees and less than −20 degrees (with a little loss or decrease typically occurring in the central region due to the approximately 4 percent Fresnel reflection losses associated with rays entering the TIR structure). Calculations show that the average intensity of rays with the use of the TIR structure is 0.937 while the reference intensity without a PV enhancement film is 0.699. Hence, an improvement or enhancement gain of over 30 percent (e.g., about 34 percent) is achieved with this TIR structure design.
Of course, a typical solar cell or PV device will not have 100 percent reflection from the light-receiving surface as this would not generate electricity.
Specifically, the ray tracing 1700 shows that received or originally-incident sunlight or rays 1702 may strike one a first facet/side 1714 of a TIR element 1712 (such as at an angle of incidence larger than about +/−60 degrees or the like) and enter the TIR element 1714 where it may be deflected downward to the light-receiving surface 1718. Some of the light/rays though may pass through the second facet/side 1716 as shown at 1704 to strike an adjacent TIR element 1720 upon facet/side 1722. Again, some of the light may be directed with originally incident rays 1702 striking facet/side 1722 onto light-receiving surface 1728. Other portions may pass through facet/side 1724 as shown to strike facet/side 1732 of the next TIR element 1730, where it again may be directed to the light-receiving surface 1738 with a portion of the captured/trapped light 1702 or pass through facet/side 1734 as unabsorbed light. Light reflected from the surface(s) 1718, 1728, 1738 likewise may be directed to adjacent TIR elements 1712, 1720, and/or 1730 where it may pass through or at least in part be directed to the light-receiving surfaces 1718, 1728, 1738. In this manner, the TIR elements 1712, 1720, 1730 use refraction to recapture reflected rays or transmitted rays to increase the efficiency by directing portions of originally-incident but not absorbed light onto the light-receiving surface (e.g., a surface of a solar cell or the like for absorption). This refractive collection or trapping of light may be considered additive to the overall efficiency gain provided by use of TIR elements (e.g., added to the increased intensity shown in prior figures). In other words, rays reflected and escaping one TIR element may be captured by adjacent structures where they can be again directed to the light-receiving surface.
All or a significant portion of the code or pseudocode used by the inventors in modeling and/or designing the TIR structures/elements for embodiments of PV enhancement films in accordance with the invention is provided in a program listing after this detailed description, and it is believed that this code/program listing will be useful to those skilled in the art in selecting a desirable TIR element for use with a variety of solar cells and solar arrays. The computer code was used in part to calculate the curves provided in the attached figures to determine effectiveness of TIR structures in increasing intensity upon a light-receiving surface over ranges of angles of incidence for received light. In use, after the parameters are read in off a user menu, the PV ray tracing routine is called. The computer program that is used to design and evaluate structures is a non-sequential ray tracing program designed to investigate optical structures for PV output power enhancement. The user enters values on a menu that are to be investigated, and these values such as type of structure (e.g., sawtooth, sinusoidal, cylindrical, and so on) and values for thickness, period, amplitude, and radius (if and as applicable). Deep inside the subroutine, the Fresnel reflection and transmissions are calculated in order to find the final intensity of rays striking the PV surface. The PV trace routine is called and is given in the included code/pseudocode.
The PV trace routine or program will give the user the best values found in the range of search for the TIR structure evaluated. These best values are entered into the data menu and rays are traced to evaluate the structure. Typically, 1000 rays are traced for every 2 degrees of angle between the limits of −80 degrees to +80 degrees, and the results plotted as shown in some of the above figures. To examine the rays and how they are refracted and reflected in the structures a small number of rays, e.g. 100 rays, might be used at a specific angle of interest as shown in
The inventors also modeled the PV enhancement film 732 shown in
With the above teaching in mind, one skilled in the art will readily be able to expand the concepts to arrive at numerous additional PV enhancement film and TIR structure designs to provide a particular optical effect (e.g., particular light trapping for a planned implementation or use). For example,
To enhance light capture, the assembly 2000 includes a PV enhancement film 2030 that is applied over the solar cells 2012, 2014, 2016 of the solar array 2010. The film 2030 includes a substrate or sheet 2032 of clear plastic, glass, or ceramic that is substantially transparent to light (e.g., highly transmissive) and includes a planar surface that is positioned adjacent and/or abutting light-receiving surface 2020. Upon an opposite side of the substrate 2032, a plurality of TIR elements 2034 are provided, and the elements 2034 have elongated bodies extending into the plane of the page of the drawing (e.g.,
Modeling of an embodiment of the assembly 2000 provided the graph 2100 of
Hence, it will be understood that the particular configuration of the TIR structures may be varied widely to achieve TIR/refraction-based trapping of light and to provide improved efficiency for a solar cell or solar array of cells. The particular TIR element design used may depend upon a number of factors including the material used for the film, manufacturing issues such as costs, and planned use (e.g., for a tracking or non-tracking array, to enhance light trapping at particular values of angles of incidence, and so on).
In many PV enhancement films, it may be useful to use a single TIR structure or element design. This may facilitate manufacturing and provide a consistent optical enhancement or light trapping level across the surface area of the film. However, the inventors recognize that there may be a need or desire to use two or more TIR structures (or TIR element designs) on a single PV film or in an assembly of PV films (e.g., films with differing TIR elements may be used together on a single solar array or cell to achieve a desired light-trapping effect). For example, a PV enhancement film may be provided with a sawtooth pattern of TIR elements on one side, and the TIR elements may have the same or differing pitches/base widths and/or the same or differing heights/body thicknesses to practice the invention.
In one film embodiment, the film includes a sawtooth pattern of TIR structures with a number of TIR structures of a first thickness and a number of TIR structures with a second thickness that differs from the first thickness (but with the same pitch in this case while other embodiments may differ the pitch for the two TIR structure designs). The two TIR structure embodiments may be alternated on the film or one TIR structure thickness may be provided for a first set of TIR structures and then the other TIR structure thickness may be provided for a second set of TIR structures and so on in this pattern (e.g., 10 TIR structures of the first thickness and then 10 TIR structures of the second thickness or another alternating pattern). In this manner, two light intensity or light-trapping characteristic curves may (or TIR structure functionalities) may be blended within a single PV enhancement film (or two or more films arranged upon a solar array to provide the differing TIR structures). For example, sheets or films each containing a particular TIR structure arrangement may be laid upon different portions of a solar panel of PV cells. Each location would have the optical response characteristics associated with the overlying PV enhancement film and its TIR structures. The overall effect from each location to the output of the panel or array would be an average response that may be desired by a solar array designer/user. The customer or user of the PV enhancement films could pick and choose the PV enhancement films based on their optical characteristics (e.g., in what incidence angle ranges do they provide better performance and so on) and install (in a retrofit example) or provide during manufacture the films across the PV panel or array to get the optical response they desire. Of course, three or more TIR structure designs may be used together to enhance the efficiency of a solar panel/array or a solar cell and fine tune a PV response.
The film 2330 includes a substrate or film 2332 of substantially transparent material, e.g., with a planar surface for abutting or being positioned proximate to light-receiving surface 2312. The film 2330 further includes a plurality of TIR structures upon the substrate 2332 with alternating configurations. As shown, a first configuration is represented by TIR structure 2340 that includes first and second facets 2342, 2344 (e.g., has a triangular cross section), and a second configuration is represented by TIR structure 2350 that includes first and second facets 2352, 2354 (e.g., has a triangular cross section). In this embodiment, the TIR structures 2340 and 2350 have the same base size or pitch but differing heights/thicknesses to provide differing optical characteristics (e.g., to achieve differing reflectivity or TIR effects at varying angles of incidence of sunlight upon the solar array 2310). These TIR configurations are alternated across the width or length of the light-receiving surface of the film 2330. While sawtooth designs are shown in
To evaluate the film 2330 of
The inventors recognize that many other cross sectional and overall shapes for the TIR elements may be useful to practice the invention, and many of these configurations are believed to be considered within the breadth of this description when considered alone or in combination with the attached figures. For example,
It may also be useful to further discuss the decision of whether to provide TIR elements that are pyramids and/or three-dimensional structures or that are linear triangular cross section structures. For a perfect orientation of linear triangular structures (TIR structures) to the seasonal azimuth of the Sun, the direction of the linear structures would be in a perfect North to South orientation, and the panel would be placed in a perfect orientation East and West with the panel facing the Sun at mid day perfectly with both axis points parallel to the pathway of the Sun. The above placement/use, however, can typically only be accomplished by mounting panels exactly to the azimuth of the sun in the East to West orientation. However, this is not likely or often practical, as most rooftops are not conducive to this and rather have off-angles in most cases. In addition, even if this were possible (with mounting brackets, by design, or with luck), one would still need to adjust for the seasonal azimuth to the sun to compensate for the 42-degree angular difference from summer to winter.
The testing procedure and software used to model PV enhancement films allowed the additional efficiencies obtained by using linear TIR structures to be measured and modeled in a linear diagram with triangular cross section structures (e.g., in order to observe the individual angular effects and resulting TIR with “ideal” placement), and, hence, some of the initial designs and prototypes utilized two-faceted TIR elements. Given ideal circumstances (e.g., perfect placement), the results would be measureable with these triangular structures and results documented appropriately. However, since ideal placement in the field or home use is unlikely, a three-dimensional structure such as a pyramid is believed by the inventors to provide performance enhancement at off-angles in the direction perpendicular to the linear structure (e.g., a three-faceted pyramid, a four or more sided structure, or similar cross section may be preferred in many applications). Overall, performance enhancement characteristics in non-perfect installations (most installations) may be as much as double or more using pyramidal or three-dimensional (non-linear or linear or 4 or more sided) structures. Typical placement of panels (non-ideal placement) provides not only normal cosine fall off and decreased efficiency from normal sunrise to sunset but also non-perfect placement to the seasonal azimuth of the Sun resulting in additional cosine fall off and resulting reflective losses. Since a pyramidal structure having appropriate benefiting angles in several directions increases TIR and decreases cosine fall off from several angles, overall efficiencies are improved even more than a control model with perfect placement to the Sun. In other words, a non-perfectly placed panel may achieve 10% efficiency overall without the film yet may achieve 18% or more with the pyramidal film, while only 14% may be achieved with linear structures because of the incident angles to the structures.
Numerous methods of manufacturing may be used to provide the PV enhancement films (and apply these films to existing or being fabricated cells, PV devices, and/or solar arrays). For example, various base films may be used as carriers, and the carrier film itself may or may not have photovoltaic material already applied to the film. Base films may be PET, acrylic, OPP, Polycarbonate, polyethylene (high or low density) or even thin glass. The TIR structures may be engraved into a metal, glass, ceramic, rubber, photopolymer or plastic cylinder with diamond tooling, or by a photo-polymeric exposure system, or even laser engraved. The structures may be placed into the film with a combination of heat and pressure with an embossing system in a roll form, or with a hot die stamp and platen directly onto the film itself. Conversely, they may also be cast with UV cured liquid or e-beam, or any type of energy cured polymer or solvent based polymer in roll or sheet form. One preferred method of manufacture may be electron beam casting using polymers that are engineered for durability in the sun.
Many of the above examples and evaluations were limited to a two-dimensional analysis or ray tracing of incident light. In other words, the results in the program take into account a linear structure running in a North-South direction, with the Sun rising in the East and setting in the West and with the collector optimized for the seasonality of the Sun. Therefore, it is believed that implementing the TIR structures as nonlinear, 3-dimensional shapes such as pyramids, cones, domes, frustoconical shapes, and the like may provide even better results and potentially increase the effectiveness in a real life applications exponentially. Keeping this in mind, overall increases in efficiency may go up to more than 100 percent in many cases depending upon the placement of the solar panels or PV devices with the PV enhancement films (e.g., which may be determined by roof shape not based upon optimum angular placement in residential settings and some commercial applications).
In brief, the PV enhancement films provide structures over a solar cell, a solar array, a PV film, or combined with PV film or materials, and the TIR structures are adapted to purposely create total internal reflection. The PV enhancement films (or at least the TIR structures) are made of glass, plastic, ceramics, or energy cured polymers that are substantially transparent (e.g., transmit a large portion of received light). The TIR structures may be nearly any size or thickness, but, in practice due to economic realities, manufacturing challenges, and other reasons, the TIR structures (and the films) often will be under about 100 mils in thickness and routinely under about 5 mils. Some embodiments of the PV enhancement films include elongated or linear TIR structures with two, three, or more straight (or near straight) facet or sides angling inward from the substrate of the film at 10 to 60 degrees. These structures may be saw tooth shapes (when viewed in cross or on end) with 50 degree (45 degrees may be ideal for directly overhead sun) to under 20 degree inwardly-angled sidewalls. In other embodiments, PV enhancement films may include 3D or non-elongated TIR structures that can be 3-sided to a sharp point, be hexagonal shapes to a sharp point, may be cone shaped structures 10 to 60 degrees sidewalls with a point or a flat, planar top, may be circular in cross section to form a series of domes on the PV film surface, or have other shapes to provide TIR effects in a 3D context. It should be noted that the TIR structures, including the linear lenticular-like structures with regular Pi or round radii cross sections designed to go over the top of the PV materials, do not act to “focus” the received or incident light but act to trap reflected light coming off of the covered solar cell or light-receiving surface (e.g., the lenticules of such a PV enhancement film are truncated and appear to be parts of “circles” from a side view and are not configured for focusing received light onto the solar cell). The 3D TIR structures may be dome shaped or “fly's eye” structures. Again, the TIR structures are not designed to focus light (and do not work like regular lenses), but, rather, the TIR domes sit directly on the PV materials (or are the base film for the PV materials) and act to provide TIR trapping of reflected light from the PV materials. A normal lens would have to have a height-to-width ratio of about 1.5 or 2 to 1H/W to create a focus in a linear or round lens. In contrast, the described TIR structures almost have no height (e.g., are very thin in most cases) and may be thought of as truncated “circles” or thin hemispheres sitting or positioned upon the light-receiving surface of the PV material or of the solar cell(s).
One way to understand some of the concepts of this invention is to understand that a certain percentage of rays that enter through the microstructures (e.g., TIR elements or structures) and hit the film substrate and then the PV material (or light-receiving surface of a solar cell/array) will always be lost. This is due to the relationship of the exiting angles and the point of impact of the wall and those angles (e.g., reflect in directions such that they strike the sides or facets of the TIR structures/elements at angles greater than 42 degrees). It is important to understand that the percentage of deflected rays from PV materials is much greater when the angle of the Sun in relationship to the panel (which includes the PV materials such as within solar cells) is at a greater angle, which leads to greater deflection and less efficiency, and this occurs typically when the Sun is not at perfect angles to the collector (e.g., not directly overhead at noon or the like). However, a great many of the unabsorbed rays that are deflected from the PV film will try unsuccessfully to exit the microstructures and will be deflected through TIR one or more times (e.g., to a theoretical but nearly impossible infinite number of times), and this TIR functionality of the TIR elements of the invention creates multiple chances and multiple possibilities (and practical differences in angles at every “strike”). Overall, the TIR structures provide a significant mathematical increase in probability for absorption. For instance, operation of a solar array may experience 50 percent of the rays are being lost due to cosine fall off or other structural deflections during the daytime as the Sun moves across the sky. But, with the use of the PV enhancement films designed in accordance with one or more embodiments of the invention with one or more TIR structure configuration, most of the deflections are eligible for TIR deflection back to the PV materials (or light-receiving surfaces of a solar array or solar cell or PV device).
The following formulas may be used, with actual data from PV materials for input, to test individual PV enhancement films and/or PV assemblies that include such films and TIR structures. A possible example is as follows:
X=deflected rays (70% of rays)
Z=newly absorbed rays from TIR (20% of X)
S=original efficiency (100%-70%=30% and then (0.30)(0.20)=0.06 or 6%)
H=increased efficiency: with X=70%, H=(0.20)(X)=(0.20)(0.70)=0.14
Total efficiency=S+H or, in this example, 6%+14%=20% (versus 6 percent original)
More importantly, the above was drawn from the following formula, each individual range below in angles represents an efficiency gain at each of the angles including cosine falloff as a result of the following angles times 2 (covering 140 degrees) as a result of a positive angle or a negative angle.
I=incoming rays from 60 to 70 degrees (also −60 to 70 degrees)
J=incoming rays from 50 to 60 degrees (also −50 to −60 degrees)
K=incoming rays from 40 to 50 degrees (also −40 to −50 degrees)
L=incoming rays from 30 to 40 degrees (also −30 to 40 degrees)
M=incoming rays from 20 to 30 degrees (also −20 to −30 degrees)
N=incoming rays from 10 to 20 degrees (also −10 to −20 degrees)
O=incoming rays from 0 to 10 degrees (also −10 to 0 degrees)
The above represents approximately 12 hours of daylight or sunshine. Negative numbers represent morning and positive numbers represent afternoon. Positive and negative numbers will yield the same data. For purposes of formula, each set of angles will count twice (one for negative and one for positive). Currently, this formula does not take into account angles resulting from other than ideal panel placement in a north south seasonal azimuth. The reason for this lies in the existing program, and the method of ray racing the program in a linear way and in two dimensions instead of three dimensions. This can be addressed later in future program versions. In other words, it is important to note that in these conditions further mathematical efficiency improvements would be found from this invention. Additionally, linear TIR structures may not yield the best results, and this is why several different TIR structures are and PV enhancement films are shown in the figures with non-linear or non-elongated TIR structures.
Therefore, to find the values of each value (I-O) use, V=Value (indicating total value) times 2 (not squared). For example: Total value of I=value of I×2, which takes into account the morning and evening values. For the purpose of this modeling, the rays being deflected in the ray tracing program striking the strips of absorbers will simulate absorption of the ray, when in fact that ray may be deflected again by the PV material, and then be sent back again by the microstructure. Since the inventors found it difficult to perform this rather subjective experiment with the ray tracing program, the following procedure was used to evaluate TIR structures and PV enhancement films:
Baseline
1. 50% of the “space” between the measurements of the proposed (before placing the structures) structures has 10 separate strips equating to 5% each of the total space as absorbers, and the corresponding remainder are mirrors.
2. Rays are then traced at each value (average value) in each category by changing the incoming ray angles in the programs.
3. Absorbed rays are then recorded with the same input data.
Micro Structures Addition
1. Repeat the above, only with the structures.
2. Measure the values using the structures, and calculate the increased absorption.
3. Calculate the absorption by value (angle)
4. Calculating the theoretical addition of the addition of variance in the “Y” axis describing efficiency increases in normally placed field application (imperfect placement).
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