We present work at the Steward Observatory Solar Lab on a high concentration photovoltaic system in which sunlight focused by a single large paraboloidal mirror powers many small triple-junction cells. The optical system is of the XRX-Köhler type, comprising the primary reflector (X) and a ball lens (R) at the focus that reimages the primary reflector onto an array of small reflectors (X) that apportion the light to the cells. We present a design methodology that provides generous tolerance to mis-pointing, uniform illumination across individual cells, minimal optical loss and even distribution between cells, for efficient series connection. An operational prototype has been constructed with a 3.3m x 3.3m square primary reflector of 2m focal length powering 36 actively cooled triple-junction cells at 1200x concentration (geometric). The measured end-to-end system conversion efficiency is 28%, including the parasitic loss of the active cooling system. Efficiency ~32% is projected for the next system.
© 2014 Optical Society of America
The goal of our research is to develop technology for solar electricity in high volume at a cost lower than any other solar energy method, competitive with fossil fuel generation. Utilizing the concept of high concentration photovoltaics (HCPV), we use novel, low cost optics to concentrate sunlight onto commercially available III-V multi-junction (MJ) cells. These MJ cells, originally developed for space, are currently twice as efficient as conventional silicon PV cells at converting sunlight into electrical energy and maintain their performance under high concentration [1,2]. As the concentration ratio of the HCPV system increases, less area of the expensive MJ cells is needed and thus the relative cost of the MJ cell to the system cost decreases . When used at high solar concentration ratios (1000-2000 Suns), the cell cost component is reduced to ~$0.10 /watt, and future large utility HCPV systems using MJ Cells approaching 50% efficiency have the potential to generate energy at cost parity with fossil fuel. This is the incentive for new more economical HCPV system designs with high concentration and high optical efficiency.
Most contemporary HCPV systems use large modules comprising an array of lens concentrators, with a single cell at each focus, and concentrations typically in the 500x to 1000x range . There has been difficulty in bringing down the cost of systems of this type to the level needed to compete with flat panel PV. Our approach to reducing cost is a simplified and more economical concentrator design in which one large glass paraboloidal mirror powers many cells packaged in a small cluster at the focus.
Back-silvered glass reflectors have a long heritage in CSP parabolic trough plants. One such case is the SEGS plant in California that has been operational since the early 1980’s. Here it has been proven that for over 15 years of service, the mirrors can still be cleaned to their as-new reflectivity of 94% . The rate of loss of panels from hail, microbursts, etc. was only 0.3% per year. More recently, anti-soiling and ultra-high reflective coatings have been developed specifically for glass reflectors. Front-surface anti-soiling coatings developed by Flabeg are claimed to have shown 50% less dust and particle adhesion since demonstrations began in 2011 , while rear-surface reflectivity boosting coatings measured independently by NREL in 2012 have demonstrated greatly enhanced optical throughput of glass reflectors, as high as 97.5% reflectivity at 500nm, with overall solar-weighted reflectance of 95.4% .
Paraboloidal dishes used to illuminate solar cells were first demonstrated in the 1960’s by Beckman et. al. of the University of Wisconsin . Their group developed a photovoltaic system that used a round, 2.2m2 paraboloidal dish concentrator to focus sunlight at a concentration ratio of 280 Suns onto 36 cm2 of silicon cell area, generating 50 W of electrical power; an efficiency of approximately 6%. This was achieved only after the challenges of reducing the series resistance of the solar cells and maintaining low enough cell temperatures were achieved. Lowering the series resistance required increasing the density of top-surface gridlines on the cells, but not so much that a significant portion of the sunlight was blocked. To maintain a low cell temperature, Beckman’s group employed a closed-loop active cooling system to run water past pin-backed solar cells, holding their temperature to only 44°C higher than ambient temperature. The parasitic power loss from the cooling system was approximately 5W, or 10% of the system’s electrical power. By contrast, our HCPV system prototype, described in Section 4.1, uses a similar active cooling system to maintain MJ Cell temperatures at only 25°C higher than ambient temperature with a parasitic loss limited to only 2% of the system’s electrical power.
While arrayed Fresnel or Cassegrain optical CPV modules focus sunlight onto individual, widely spaced MJ cells, a dish-based concentrator has the advantage of collecting a large quantity of sunlight with a single mirror and focusing the sunlight onto an array of MJ cells contained within a small package. The ‘array’ aspect is effectively moved from the collection side to the cell side. The challenge becomes the equal distribution of light at the array of cells – a condition we meet by using a unique optical technique based on Köhler illumination .
Beyond the optical benefits, the primary system advantage of a dish-based concentrator is the separation of the two-axis tracking and collection apparatus from the solar cells themselves, a system architecture that can be used to greatly simplify installation and serviceability. Ultimately, a successful CPV system will have an efficient optical concentrator with minimum production and maintenance cost while being tolerant to optical errors, minimizing the cost per kilowatt-hour of the total energy generated .
2. Paraboloidal dish concentration
Tolerance to optical errors decreases as the concentration ratio increases, a relationship based on the conservation of étendue. In short, étendue describes the angular and spatial propagation of the light through an illumination system, while the conservation of étendue explains how the relation of the angular and spatial components of the light propagation are conserved along every part of the illumination system’s light path.
2.1 Conservation of étendue
The étendue of a system is defined as 10].
Another fundamental geometric quantity is the concentration ratio, which relates the input area A to the output area A’ of the system. This quantity also represents a thermodynamic limit in the case that étendue and radiance are conserved, and is given by [12,13]
This equation is demonstrated graphically in Fig. 1 for the simple case of a round paraboloidal mirror of area A concentrating light onto a flat receiver of area A’. The incoming irradiation is incident within a cone of angular extent θ at the mirror surface, while the light exits into a cone of angular aperture θ’ at the receiver surface. Since the concentrator’s entrance aperture is normally located outside in the air, the index n is normally set to, while the index n’ of the receiver could be modified if it is placed within a medium of higher index, such as glass or acrylic.
The concept of conservation of étendue is also demonstrated in Fig. 1. The light is incident with a small angular aperture θ onto a large collection area A. For étendue to be conserved when the light is concentrated onto a smaller receiving area A’, the angular aperture of the light at that surface θ’ must increase. The concentration ratio in Eq. (3) is maximized when the light leaving the receiver surface A’ is emitted into a full hemisphere θ’ = π/2 as
From Fig. 1, we can see this would only occur in the extreme case for which the curve of the paraboloidal dish was continued around to coincide with the plane of the receiver. Given the earth’s distance from the sun, the angular size of solar radiation from the sun’s disk is a very small cone with an effective angular aperture θS = ± 0.26°. Using this angular size in Eq. (4), when the exit is also in air, n’ = 1, this results in a maximum geometric concentration ratio for solar energy of about 48,000 Suns, resulting from placing an image of the sun directly onto the receiver.
Since both thermal receivers and PV cells have lower absorption at glancing incidence angles, hemispherical illumination (as described above) is not ideal. In both applications, this maximal illumination case would require perfect sun tracking and array alignment, something that is also quite impractical. We will see in the Section 3 how a Köhler projection optic placed at the receiver location can reduce the receiver cone angle θ’, loosening alignment tolerances, while bringing the cell concentration down to manageable levels.
An additional consideration when concentrating sunlight onto solar cells is that the efficiency of the cells is improved when the illumination is more uniform. Without a secondary optical element (SOE), the illumination pattern across the cell when focusing the sunlight directly onto it would have a Gaussian profile, yielding a significantly reduced rate of electrical conversion due to series resistance losses [15,16]. Again, we will see that illumination uniformity can also be obtained by using Köhler illumination.
2.2 Concentration acceptance product
For solar concentrators, an additional equation to consider is the concentration acceptance product (CAP), defined as 17]
When the edge of the sun’s angular aperture coincides with the edge of the system’s acceptance angle, the system is still collecting all the sunlight, but when the sun is centrally aligned with the edge of the system’s acceptance angle, half of the sunlight falls outside and is no longer collected. Therefore, the system’s acceptance angle θA is reduced by about Δθ’ = −0.26° to obtain the effective acceptance angle θA*. Since this cut-off is not discrete, the effective acceptance angle is found experimentally as the location where the system’s generated power falls off to 90% of the maximum value on-axis.
3. Köhler concentrator with separated cell array
Commercial CPV systems utilizing a fast paraboloidal dish are not new. Solar Systems Pty Ltd of Australia uses a 15m diameter segmented dish to illuminate a square 0.5m dense-packed array of MJ Cells surrounded by reflectors on all sides . This design cools the dense-packed array with active liquid cooling via a heat exchanger to keep the MJ Cells at an efficient operating temperature even under concentrations exceeding 1000 Suns.
Dense-packed arrays introduce several technical challenges. One is that no provision is made to direct light away from the light-insensitive electrical bus-bars on the front surface of the arrayed cells, causing losses and reduced efficiency. Also, the illumination is not uniformly distributed across the array, causing loss of power when individual cells are connected in series. Furthermore, small mispointing of the optical axis away from the sun causes the illumination to become more uneven, further reducing power output. The heavy, high-performance trackers used to mitigate this problem through precision pointing drive up costs.
The advantages of achieving more equal concentrator cell illumination through the use of Köhler illumination design are well known [17,19]. In recent years there has been much progress made on Köhler integrators utilizing freeform Fresnel lenses and paraboloidal mirrors to achieve a CAP as high as 1.0 for reflective primary optical element (POE) designs [20–25]. In general, these systems utilize a secondary optical element (SOE) with a single refracting surface to image the POE onto a single cell to obtain good illumination uniformity. These two non-imaging elements, designed in parallel, often result in complex geometries, requiring advanced tooling techniques.
Because of free-form manufacturing limitations, these designs are limited in unit size so that a single POE is coupled to a single SOE illuminating only one cell. To increase module power, multiple units are tessellated into rectangular or hexagonal arrays with the cells separated by the width of each unit. Because of their low cell density, passive cell cooling through convection is the only economical choice to keep the cells efficiently cooled, often requiring a heatsink that transmits the heat to convective fins and adds additional mass to the system.
3.1 XRX-Köhler system
Our design seeks to merge large-scale sunlight collection and high tolerance to mispointing, while maintaining uniform illumination of an array of MJ cells with simple low-cost optics. The concentrator design utilizes a large paraboloidal collecting surface of area A to first focus sunlight into the center of a fused-silica ball lens, shown in Fig. 2. The Köhler stabilization is performed by the two refracting surfaces of this lens. Shown in Fig. 2(a), the lens images the square paraboloidal collecting mirror onto a curved image surface of area A’, achieving stabilized illumination across the curved image surface defined by the system’s Petzval curvature. Due to the imaging property of this projection optic, on-axis parallel light rays are seemingly unperturbed by the lens [Fig. 2(b)] while off-axis rays within the system’s acceptance angle are bent back onto the curved image surface by the lens [Fig. 2(c)].
After the concentrated sunlight is stabilized on the curved image surface, the light bundle then needs to be binned into equal portions and further concentrated onto each individual MJ cell in the separated array. This is achieved using a closely spaced array of reflective truncated pyramids (XTP), each located with their entrance aperture coincident with the curved image surface and their exit aperture illuminating a single concentrator cell as shown in Fig. (3).The angle and depth of each XTP is chosen such that the light reflected off their inner faces will evenly overlap onto the active cell area, even for off-axis pointing [Fig. 3(b)].
The biggest difference of our approach to this XRX-Köhler compared to an XR-Köhler or RX-Köhler is in the design methodology. Instead of specifying the POE and SOE as freeform surfaces, we limit these first 2 elements to curvatures that are easily manufactured at low volume, and very cheap to produce in high volume. The POE is simply a mirror slumped into a paraboloidal shape, which generates a high power point focus, while the SOE is a readily-fabricated quartz sphere. This creates a symmetric all-glass POE/SOE system that is easy to manufacture and align with no complex material molding. All the design complexity in splitting up the light and achieving uniformity is then left to the XTPs, which together divide the bundle of well-controlled light at the curved image plane into bins of equal flux.
3.2 XRX-Köhler optical design
The XRX-Köhler optical design is detailed in Fig. (4) . Collimated on-axis light reflects off the mirror at an angle β with the optical axis. Light rays pass through the focal point of the mirror, located inside the ball lens of radius a, before arriving at the curved image surface with radius b from the center of the ball.
In the optimization of this design, the ball lens size is first tailored as a field lens to increase the system’s acceptance angle θA. The practical limitation of the field lens to stabilize the irradiance on the receiver is defined by the focal length of the reflector f and the ball radius a. Abberations at the stabilized receiving surface remain low as long as the off-axis sun image falls within a/2 of the ball center. Thus, the maximum allowable misalignment, or acceptance angle, is given by Eq. (7) shows that as the focal length f of the mirror decreases, so does the radius of the ball lens a. The ball lens volume is proportional to the cube of the ball lens radius, so for practical purposes we desire the ball size to be minimized so that the mass and therefore cost of fused silica is reduced.
The radius of the curved image surface b is found by solving for the effective focal length of the ball lens. Assuming that the focal length of the mirror f >>a, the ball lens will act as though imaging a distant object, the mirror, onto its focal plane, the curved image surface. Given the index of fused silica at 500nm as n = 1.458, the effective focal length of the ball lens is found from the paraxial imaging relation to be 
Because of spherical aberration, the optimum location of the image surface b is actually within the paraxial focus found in Eq. (8). The best image of the concentrator over the stabilized region is actually located at an intermediate focus located between the ball lens’ paraxial and marginal foci given by 
Next, the mirror’s focal ratio, or F/# = f/D, is optimized to increase the concentration level. To find how concentration depends on the mirror’s focal length, first the distance, s, between the paraboloidal mirror surface and the focus is found using trigonometry in Fig. 4 to be
Equation (11) tells us that C1 increases across the curved image surface as reflection angle β increases away from the optical axis. Notice in Fig. 5 that the maximum reflection angle β is limited by the maximum diameter of the mirror, D. As the reflection angle β decreases, better uniformity across the curved image surface is obtained and the F/# increases (f/D>>1) with the reduced relative mirror diameter, D. However, this has an adverse effect on the system cost because as the relative mirror focal length f is increased, from Eq. (7) so does the ball radius a, if the same acceptance angle θA is to be maintained. A larger ball lens is not practical, as again we desire to reduce the mass and cost of the fused silica. Given that the ratio f/b from Eq. (11) is fixed by the desired concentration, the ratio of ball radius a to mirror diameter D (and thus β) can only be reduced by using a mirror of reduced F/#. This requirement for a small focal ratio drives the XRX-Köhler design in two important ways.
First, given a higher angle β, there will be a significant change in concentration level across the curved image surface. Using the relation given in Eq. (9), the ratio of edge C1edge to center C1center concentration depends only on F/#, and is solved to be 
As an example, the prototype system described in Section 4.1 has a fast focal ratio of F/0.46 defined from corner to corner of the square paraboloidal dish. In this system, C1 increases from 465 Suns at the center to 780 Suns at the edge of the curved image surface. To achieve equal concentration of sunlight at the cells, the design of the XTP array located at this surface must take this concentration profile into account by reducing the size of their entrance apertures, defined by α, as reflection angle β increases outward from the optical axis as shown in Fig. 5. When the entrance aperture areas are designed correctly for the integrated concentration across their entrance apertures, the integrated irradiance reaching each MJ cell will be equivalent and therefore current matched over the entire segmented array, even for off-axis pointing.
Second, because a fast paraboloid as seen from its focus subtends a wide angle, a field lens must image over a correspondingly wide field of view. This wide field of view is achieved by the symmetry of the ball lens focusing onto a deeply curved concentric image surface. By substituting Eq. (7) and Eq. (9) into Eq. (11), we find that the maximum acceptance angle is related to the central concentration by
For the prototype system of Section 4.1, the silica ball lens chosen to be used with the F/0.46 reflector to produce a geometric concentration C1 = 465 at the curved image surface will provide illumination independent of mispointing angle up to θA = 0.015rad = 0.85°. If we solve Eq. (7) with the full expression of Eq. (5) to obtain the acceptance angle for the edge of the curved image surface with C1 = 780, we obtain the same result.
3.3 XTP design for cell illumination uniformity
The final component to optimize is the array of reflective truncated pyramids (XTP) shown in Fig. 5. The XTP array serves two purposes. First, it further concentrates the sunlight by an amount C2, unique to each funnel, so as to compensate for the varying concentration C1 across the curved image plane. Second, it provides for gaps between each individual MJ cell that can be used for electrical conduction and optically inactive parts of the cell, virtually eliminating gap losses between cells found in dense-packed arrays.
The XTP design consisting of hollow metal elements with silvered reflective sides is the basis for the second ‘X’ designation in the XRX-Köhler design name, however these elements can also be replaced by an array of glass total internal reflection concentrators (TIRC). A comparison of XTP versus TIRC performance for this system shows that while the TIRC obtains a 5% better acceptance angle for the system from the increased index, the TIRC front-surface adds an additional loss that is not present in an XTP element containing an equal number of internal reflections. Due to this additional Fresnel reflection, the TIRC array forfeits a more substantial 2.5% total system efficiency loss compared to the loss from silvered, 96% reflective XTP elements in the array geometry shown in Fig. 5 .
Figure 5 shows the geometry of on-axis rays reflected off the XTP’s inner facets, whose edges are tilted from the entrance face normal by slope angle ω. The rays pass through the center of the ball lens and into the entrance aperture of the XTP at a distance b and subtending angle α from the center of the ball lens. The exit aperture of the XTP is reduced in area relative to the entrance aperture by the secondary concentration ratio given by 
This is the average XTP concentration ratio, as in general the slope angles for different sides of each XTP will be different as the concentration C1 across the curved image surface changes with reflection angle β as given by Eq. (11). For the geometry shown in Fig. 5 with the XTP depth optimized for uniform cell illumination, the preferred ratio of XTP depth t to entrance aperture width is dependent only on XTP slope angle ω and α. This is because the condition for uniform illumination on-axis occurs when the extreme edge ray reflects to strike the center of the exit aperture. Equating the half-width of the entrance face given by the incident and refracted arrays, we obtainEq. (14), the secondary concentration ratio for uniform illumination is
This relationship was used to design an XTP array model in non-sequential raytracing code. By varying the cell depth within the XTP, a raytrace was used to find the concentration level C2 that achieved the best uniformity, quantified by a merit function σ/<E> where E is the collected power and σ is the standard deviation of the irradiance. It was found that this merit function was minimized for concentration ratio C2 = 2.57x . To achieve good uniformity for off-axis pointing as well, the average concentration ratio of the funnels was designed to be a C2 = 2.5, a little less than the on-axis optimum.
If the optical throughput of the system is defined as η, then the overall concentration C seen by the cells is
If the optical throughput η = 80%, the average C1 = 500x and average C2 = 2.5x, then the system will have an overall concentration C = 1000x at the cells. It is important to note that a deeper XTP has a higher concentration C2 so that a smaller concentration C1 is required at the curved image surface. For a given overall concentration, an XRX-Köhler system with an array of deep XTP’s have increased tolerance to mispointing since the acceptance angle set by the ball lens radius in Eq. (7) applies only to the curved image surface’s concentration C1.
4. Commercial system development
Successful prototypes of the XRX-Köhler design for producing electricity from concentrated sunlight have been operating at the University of Arizona since 2010. Shown in Fig. 6(a), our optical system begins by gathering and concentrating sunlight using large, self-supporting, second-surface glass mirrors shaped at the Steward Observatory Mirror Lab, a facility principally tasked with shaping glass mirrors for the world’s largest telescopes. Unlike thick, precision telescope mirrors, the paraboloidal solar dishes are quickly slumped from inexpensive float glass. Such mirrors can be simply and inexpensively supported at 4 points within a lightweight 2-axis tracking unit that moves to follow the sun with an ideal pointing accuracy of ~0.2°.
The compact power conversion unit (PCU) package - containing the relay optics, MJ solar cells and active cooling system - is placed at the focus of the paraboloidal dish as shown in Fig. 6(b). Peak commercial MJ cell conversion efficiency is currently about 44%, and increasing at a rate of approximately 1% every year . To take full advantage of this trend, the MJ cells in our system are clustered in small packages so that they are easily replaced. By allowing the cell package to be swappable, full benefit can be taken of the continued improvement in MJ cell conversion efficiency that is expected over the next 20 years.
4.1 Prototype design
Our current operational prototype shown in Fig. 6 uses a 10m2 back-silvered dish reflector made from 4 off-axis paraboloidal segments to bring sunlight to a point focus of over 20,000 Suns. The receiver at the focus, based on the XRX-Köhler design described in Section 3, contains a fused silica ball lens [Fig. 6(d)] of 60mm radius working in conjunction with an array of reflective truncated pyramids (XTP) [Fig. 6(e)] that serve to reformat and stabilize the sunlight from the curved image surface so as to uniformly illuminate 36 MJ cells [Fig. 6(f)] with a concentration of 1000 Suns.
Each of the 15mm MJ cells in the array receive equal and nearly uniform irradiance by tailoring the entrance aperture size and thus secondary concentration level to compensate for the concentration variance over the curved image surface given by Eq. (11). This is demonstrated in Fig. 7 using the actual values for the prototype’s XTP array design. A diagonal cross-section of three XTP elements of the 6x6 array shows that as the concentration C1 increases for larger angle β the corresponding concentration C2 of the XTP decreases.
4.2 Prototype performance
The prototype was designed for C = 1000x with modeled acceptance angle θA* = 0.7° for 90% max power. From Eq. (5), this yields an effective CAP* of 0.39. The measured acceptance angle is shown in Fig. 8(a), and was found to be θA* = 0.5°, yielding an effective CAP* of 0.28 from Eq. (6). The difference in measured acceptance angle from theory is contributed by mirror deformations due to problems with prototype tracker mounting that exceeded the mechanical error budget. However, this measured acceptance angle is satisfactory because our tracking accuracy is much better than ± 0.5 degrees .
Our 1st generation prototype reflector/PCU unit consistently generated 2.2 kW of power normalized to 1kW/m2 DNI in over 200 hours of on-sun testing in 2011. The 2nd generation prototype has been in operation since June 2012 and utilizes greatly improved optical coatings to increase the optical throughput to nearly 85%. This operational prototype consistently generates 2.7 kW of power normalized to 1kW/m2 DNI and has logged over 500 hours of on-sun testing . An example day of power output is shown in Fig. 8(b). Figure 8(c) details cell temperature throughout a typical day, verifying that the cells consistently maintain an operating temperature of only 20°C above ambient . This prototype’s independently validated peak operating efficiency is 28.6%.
4.3 New system design
Having proven this system concept, work on our 3rd generation system is underway with assistance from a US Department of Energy Sunshot Incubator 7 grant aiding REhnu’s commercialization of this technology. This new system has been redesigned with a focus on manufacturability, lower cost, and a DC efficiency target of 32% or better. This system changes are detailed in Table 1. and shown in Fig. 9.The most notable change is the ¼ reduction in system size to a collector area of 2.5m2, which allowed us to reduce the PCU to a 5lb handheld unit that generates 800W of power. The active cooling heat exchanger was moved to the back of the 6.4 kW generator unit shown in Fig. 9(b), while the PCU unit is cooled through a series of injection-molded plastic manifold parts shown in Fig. 9(c).
Apart from the simplified mechanical design, the Gen 3 system also benefits significantly from a completely redesigned XTP array, only summarized here. First, the XTP-like elements are fabricated by bending, cutting, and folding a pre-silvered piece of aluminum in an origami fashion, greatly increasing reflectivity control and assembly time. Second, the illumination design places the sunlight onto only four cell planes that approximate the curved image surface, greatly simplifying the fabrication, cooling, and electrical connections since only four cell cards are needed per PCU instead of 36 individual cards in the Gen 2 system.
We present a system tailored for low cost which employs a large paraboloidal glass mirror and Köhler illumination optics to deliver uniform, concentrated sunlight to an array of MJ cells. The XRX-Köhler design is a departure from other CPV concentrators in scale, method of manufacture, and in the unique separation of collection and conversion elements. The latter property allows the possibility of economical MJ cell retrofits without dismantling the primary optic.
The XRX-Köhler’s fused silica spherical lens projects a stabilized but non-uniform image of the primary mirror onto a spherical receiving surface. An array of reflecting truncated pyramids (XTP) conforms to this stabilized image and function to distribute equal flux with very little non-uniformity while providing additional concentration. The latest prototype system, in operation since 2012, demonstrates 28.6% DC conversion efficiency and a ± 0.5 degrees acceptance angle. This acceptance angle allows a cheaper tracker than those required by CPV systems which directly image the sun onto MJ cells.
The 3rd generation system currently under development is adapted for low cost manufacture. Instead of meshing the receiving surface with individual XTP-cell pairs, each at a different plane, the cells are grouped into 4 planar quadrants which most closely approximate the concave receiving surface. New XTP-like optics divide the light evenly among the cells. Accounting for cell and optical quality improvements, we expect a 32% DC conversion efficiency.
This research was performed with generous support from Science Foundation Arizona (SFAZ), Research Corporation for Science Advancement, the Marshall Foundation, and REhnu Inc. 3rd Generation development is funded by REhnu and supported by a US Department of Energy Sunshot Incubator 7 grant #DE-EE0005982. B. Coughenour and B. Wheelwright would also like to acknowledge the Carson/REN Scholars Program for their financial support. B Wheelwright acknowledges the support of ARCS.
References and links
1. H. Cotal, C. Fetzer, J. Boisvert, G. Kinsey, R. King, P. Hebert, H. Yoon, and N. Karam, “III-V multijunction solar cells for concentrating photovoltaics,” Energy Environ. Sci. 2(2), 174–192 (2009), doi:. [CrossRef]
2. C. Pfeiffer, P. Schoffer, B. Spars, and J. Duffie, “Performance of silicon solar cells at high levels of solar radiation,” J. Eng. Power 84(1), 33–38 (1962), doi:. [CrossRef]
3. A. Lugue and V. Andreev, Concentrator Photovoltaics (Springer, 2007).
4. K. K. Chong, S. L. Lau, T. K. Yew, and C. L. Tan, “Design and development in optics of concentrator photovoltaic system,” Renew. Sustain. Energy Rev. 19, 598–612 (2013), doi:. [CrossRef]
5. H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Mahoney, and R. Gee, “Advances in parabolic trough solar power technology,” J. Sol. Energy Eng. 124(2), 109–125 (2002), doi:. [CrossRef]
6. FLABEG Holding GmbH, “Duraglare solar product information,“ (2012), Accessed 8 Nov, 2013. http://www.csp-world.com/sites/default/files/FLABEG_Solar_DuraGlare_10.pdf
7. G. P. Butel, B. M. Coughenour, H. Angus Macleod, C. E. Kennedy, and J. R. P. Angel, “Reflectance optimization of second-surface silvered glass mirrors for concentrating solar power and concentrating photovoltaics application,” J. Photon. Energy. 2(1), 021808 (2012), doi:. [CrossRef]
8. W. A. Beckman, P. Schoffer, W. R. Hartman Jr, and G. O. G. Lof, “Design considerations for a 50-watt photovoltaic power system using concentrated solar energy,” Sol. Energy 10(3), 132–136 (1966), doi:. [CrossRef]
9. J. Roger P. Angel, Photovoltaic generator with a spherical imaging lens for use with a paraboloidal solar reflector, U.S. Patent 8350145 (2013).
10. R. Koshel, Illumination Engineering (Wiley, 2013).
11. R. W. Boyd, Radiometry and the Detection of Optical Radiation (John Wiley and Sons, 1983).
12. H. Rehn, “Optical properties of elliptical reflectors,” Opt. Eng. 43(7), 1480–1488 (2004), doi:. [CrossRef]
13. R. Winston, J. Miñano, and P. Benítez, Nonimaging Optics (Elsevier Academic Press, 2005).
14. J. Chaves, Introduction to Nonimaging Optics (CRC Press/Taylor & Francis Group, 2008).
15. E. A. Katz, J. M. Gordon, and D. Feuermann, “Effects of ultra-high flux and intensity distribution in multi-junction solar cells,” Prog. Photovolt. Res. Appl. 14(4), 297–303 (2006), doi:. [CrossRef]
16. A. Braun, H. Baruch, E. A. Katz, J. M. Gordon, W. Guter, and A. W. Bett, “Localized irradiation effects on tunnel diode transitions in multi-junction concentrator solar cells,” Sol. Energy Mater. Sol. Cells 93(9), 1692–1695 (2009), doi:. [CrossRef]
17. P. Benítez, J. C. Miñano, P. Zamora, R. Mohedano, A. Cvetkovic, M. Buljan, J. Chaves, and M. Hernández, “High performance Fresnel-based photovoltaic concentrator,” Opt. Express 18(S1), A25–A40 (2010), doi:. [CrossRef] [PubMed]
18. Solar Systems Pty Ltd, “Solar Systems Brochure,” (2013), Accessed 1 Dec, 2013. http://solarsystems.com.au/wp-content/uploads/2013/07/About-Solar-Systems-Flyer1.pdf
19. W. Casserly, “Nonimaging optics: concentration and illumination,” in Handbook of Optics, 2nd ed., (McGraw-Hill, 2001).
20. M. Hernández, P. Benítez, J. C. Miñano, A. Cvetkovic, R. Mohedano, O. Dross, R. Jones, D. Whelan, G. S. Kinsey, and R. Alvarez, “XR: a high-performance PV concentrator,” Proc. SPIE 6649, 664904 (2007), doi:. [CrossRef]
21. O. Dross, R. Mohedano, M. Hernández, A. Cvetkovic, J. C. Miñano, and P. Benítez, “Köhler integrators embedded into illumination optics add functionality,” Proc. SPIE 7103, 71030G (2008), doi:. [CrossRef]
22. M. Hernández, A. Cvetkovic, P. Benítez, and J. C. Miñano, “High-performance Kohler concentrators with uniform irradiance on solar cell,” Proc. SPIE 7059, 705908 (2008), doi:. [CrossRef]
23. P. Benítez, J. C. Miñano, P. Zamora, M. Buljan, A. Cvetkovic, M. Hernández, R. Mohedano, J. Chaves, and O. Dross, “Free-form Köhler nonimaging optics for photovoltaic concentration,” Proc. SPIE 7849, 78490K (2010), doi:. [CrossRef]
24. P. Benítez, J. C. Miñano, P. Zamora, M. Hernández, and A. Cvetkovic, Köhler concentrator, U.S. Patent Publication 20100123954 (2010)
25. B. Wheelwright, “Lenticulated Köhler integrator for utility-scale CPV system.” in Renewable Energy and the Environment, Technical Digest (CD) (Optical Society of America, 2011), paper SRWC2.
26. J. Greivenkamp, Field Guide to Geometrical Optics (SPIE Press, Bellingham, Washington, 2004).
27. B. Coughenour, B. Wheelwright, and R. Angel, “Illumination characterization of glass and metal secondary concentrator elements in a photovoltaic solar concentration system,” Proc. SPIE 8468, 84680E (2012), doi:. [CrossRef]
28. G. Butel, T. Connors, B. Coughenour, and R. Angel, “Design, optimization and characterization of secondary optics for a dish-based 1000x HCPV system,” in Renewable Energy and the Environment, Technical Digest (CD) (Optical Society of America, 2011), paper SRWC3.
29. S. Kurtz, “Opportunities and Challenges for Development of a Mature Concentrating Photovoltaic Power Industry” (NREL Technical Report, 2012). http://www.nrel.gov/docs/fy13osti/43208.pdf
30. T. Stalcup, R. Angel, B. Coughenour, B. Wheelwright, T. Connors, W. Davison, D. Lesser, J. Elliott, and J. Schaefer, “Dish-based HCPV system initial on-sun performance,” Proc. SPIE 8468, 84680F (2012), doi:. [CrossRef]