- Email: [email protected]
High concentration thin profile solar concentrator utilizing toroidal confocal relay
Available online at www.sciencedirect.com
ScienceDirect Solar Energy 122 (2015) 264–270 www.elsevier.com/locate/solener
High concentration thin profile solar concentrator utilizing toroidal confocal relay Chao-Wen Liang ⇑, Jhe-Syuan Lin Department of Optics and Photonics, National Central University, No. 300, Jhongda Rd., Jhongli City, Taoyuan County 32001, Taiwan, ROC Received 3 July 2014; received in revised form 29 July 2015; accepted 17 August 2015
Communicated by: Associate Editor L. Vant-Hull
Abstract A thin profile solar concentrator is designed based on the novel off-axis toroidal confocal relay design principle. The solar beam is collected, converged, re-collimated, and relayed to the solar cell simultaneously by the radially cascaded dielectric concentrator modules. This concentrator has properties of high concentrating ratio, thin aspect ratio, zero back focal distance, Gaussian irradiance profile, and single molding manufacture capability. In the Monte Carlo ray tracing simulation shown, one of the proposed concentrator designs has aspect ratio of 1/8 and achieves over 43100X peak concentration with the theoretical thermodynamic concentration limit, within the dielectric, of 71290X. Ó 2015 Elsevier Ltd. All rights reserved.
Keywords: Solar concentrator; Solar energy; Geometrical optical design; Off-axis relay
1. Introduction The concentrator photovoltaic (CPV) technology for multi-junction solar cells is considered to be one of the major solutions for renewable energy technologies. In the CPV system, the concentrator optics reduces the price per watt ratio by collecting large area sunlight and transferring the concentrated solar energy into the smaller solar cell. The CPV system with a high concentration ratio requires a solar tracker which is used to keep the concentrated solar focusing spot constantly staying on the solar cell for the maximum solar power delivery efficiency. In order to have an efficient concentrator system, the concentration ratio, the solar acceptance angle, system alignment tolerance, and cell irradiance uniformity are all important factors to be considered. ⇑
Corresponding author. E-mail address: [email protected] (C.-W. Liang).
http://dx.doi.org/10.1016/j.solener.2015.08.030 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.
The refractive Fresnel concentrator is being popularly used in the field due to its low cost and easy manufacturability with the ease of molding capability. However, most of the refractive concentrator systems have much larger system volume due to the required long back focal distance (BFD) which is defined as the distance from the concentrator to the solar cell. The long BFD poses several disadvantages to the construction of the high concentration ratio concentrator. For instance, the alignment between the solar cell and the concentrator gets more difficult with the increased length of BFD. The increased BFD also means increased weight for the rigid construction of the concentrator system which expands the weight loading for the solar tracker as well. The wind loading profile is also increased with the increased BFD. Therefore, the shortened concentrator BFD design demonstrates a compact and high precision solar tracker system and reduces the assembly process complexity.
C.-W. Liang, J.-S. Lin / Solar Energy 122 (2015) 264–270
Several researchers have proposed methods to minimize the concentrator volume by either shortening the concentrator thickness or the BFD. One of the representative designs is the non-imaging type concentrator combining the light guide panel and the micro focusing lens for coupling into the light guide panel (Karp et al., 2010). Also, the Cassegrain reflective type concentrators effectively reduce the system volume by folding the optical path (Benitez et al., 2006; Goldstein et al., 2011; Gordon, 2010; Winston and Gordon, 2005; Winston and Zhang, 2009). In one of the designs, the system flux e´tendue of the CPV system can be further improved by placing a dielectric compound confocal relay concentrator (CPC) near the focal plane of the concentrator (Winston and Gordon, 2005). The nested mirror design was developed as well to reach near the e´tendue limit performance with advantages of high concentration ratio and high e´tendue (Goldstein et al., 2011). However, since each beam relay mirror pair is independently designed, they only relay the concentrated beam once in its own optimized path. Therefore, it is inevitable to end up with a high aspect ratio concentrator design with such design approach. Another drawback is the alignment work, the nested mirror is difficult to be aligned considering the high Numerical Aperture (NA) and high incident angle on the relay mirror pair. In this paper, a novel toroidal-shaped off-axis Cassegrain relaying concentrator is proposed. This concentrator is composed of several radially cascaded toroidal paraboloid concentrator modules for a larger entrance pupil area. This proposed concentrator reaches a thin profile design with aspect ratio of 0.125 through the novel toroidal confocal relay process. Each module can simultaneously concentrate, re-collimate, and relay the collimated sunlight into the next paraboloid concentrator module in the radial direction. Therefore, this design boosts a much thinner aspect ratio and higher NA optical design than the Goldstein’s method (Goldstein et al., 2011). Besides the aspect ratio, this concentrator also has the outstanding properties of high concentrating ratio, zero back focal distance, and uniform irradiance profile. Best of all, the concentrator can be made of a single molding mass manufacture process. This molded module intrinsically aligns all optical elements of the concentrator, leaving only the silvering work of the reflective surface and the cement of the solar cell. 2. The off-axis toroidal confocal relay design The annular multi-folded lens design for a thin pancake like camera module has been developed before (Tremblay et al., 2009, 2007). In this design, the light beams enter the lens module at the edge ring of the annular concentric optics. After entering the module, the beams are then mirror-folded and relayed for multiple times in the tangential direction to image sensor located at the center of the concentric optics. The optical aberrations are then balanced in the relaying optical path by the folding aspherical mirror. The optical system is therefore composed of annu-
265
lar segments of aspherical surfaces cascaded concentrically. Since most of the inner surface area of the concentric optics is used for the beam relaying reflection, the opening entrance pupil of the whole system is literally limited to the most outer ring of the whole concentric optics. Therefore, the increased obscuration ratio limits its practical application in the concentrator in a CPV system due to the loss of incoming beam at the entrance. Though the annular multi-folded design has a very thin profile and high NA for the high concentration, it’s not practical to be used as a solar concentrator. In view of this limitation, we proposed the toroidal shaped off-axis Cassegrain relaying dielectric concentrator module with the objective of reducing the high obscuration ratio effectively while maintaining its thin profile. The system is designed with toroidal surfaces that have different curvatures in orthogonal directions. Since tangential direction is the direction of beam convergence, the tangential radius of curvature is much shorter than the revolving radius for most segments. The schematic tangential optical path of the dielectric concentrator module in the direction of concentration is illustrated in Fig. 1. In this figure, the two dielectric concentrator modules face the incoming solar beam with its surface normal parallel to the solar on-axis light path. Each of the dielectric concentrator modules is composed of two off-axis toroidal confocal optical surfaces similar to the off-axis Cassegrain telescope composed of a concave primary mirror and a convex secondary mirror. Rays propagating in the tangential direction converge to the last module where the center solar cell is located. To have the converged beam recollimated after the secondary reflecting surface, the two off-axis toroidal confocal relay surfaces within the dielectric concentrator module have to be confocal and share the same ‘‘focus ring” in the tangential direction. The concentrator has to accommodate the full solar expansion angle of 32 arc min. In Fig. 1, the concave surface SC1 of the first dielectric concentrator module converges the incoming extended solar beam onto the upper reflecting convex surface SR1. In which the extended solar beam is defined by the scope of on-axis 0° red1 line and offaxis 16 arc-min yellow line. A virtual solar image o’ is formed after SR1 forming the ‘‘focus ring” if viewed from the top of concentrator. The reflecting surface SR1 then recollimates and relays the solar beam onto the subsequent concave surface SC2. The beam 1 reflected from the surface SR1 will then be combined with incoming solar beam 2 of the secondary module and together get reflected onto the surface SR2 upon the surface SC1. To keep the same conjugate relationships for further relaying inside the concentrator, both beam 1 and beam 2 are focused to the same focal point o’’ of the surface SR2. By utilizing the off-axis confocal relaying concept, the incoming beams are cas-
1 For interpretation of color in Fig. 1, the reader is referred to the web version of this article.
266
C.-W. Liang, J.-S. Lin / Solar Energy 122 (2015) 264–270 On-axis beam1 Off-axis beam1 @ 32 arc min On-axis beam2 Off-axis beam2 @ -32 arc min O’’
Virtual Image
O’ SR1 SR2 Solid dielectric
…
SC1 SC2
Fig. 1. The cross section of the concentrator shows the off-axis relaying concept.
caded and the system throughput is increased. The dielectric concentrator modules are designed to be made of the optical glass, NBK7, with a refractive index of 1.517. Multiple dielectric concentrator modules are assembled in the aperture plane for a larger entrance pupil area and also to reach a thinner profile design. In our cascaded relay design, magnification of each relay module is an important issue due to the divergence angle of sunlight. It will affect cascaded times. Therefore, the magnification of each module in our design has to be restricted to avoid an overwhelming long focal length along the concentration direction. Fig. 2 shows one of the designs. It has three cascaded modules and all the relaying modules have their own focus ring coincident at the focal plane of three mirrors SC1, SC2 and SC3. The afocal magnification of a telescope is the ratio between the primary mirror and second mirror. Therefore, the module 1 (SC1 + SR1) provides afocal magnification of 7.5 times. The module 2 (SC2 + SR2) has the magnification of 1.47 times. The final relay surface SR3 shrinks the image further by 0.238 times with the finite conjugate magnification. Thus, such toroidal relay design doesn’t magnify the solar image as much as one would expect. Comparing the simulated ray trace
result with the paraxial image size, there is a big difference between them. This is due to the significant amount of offaxis aberration that actually dominates the size of the solar irradiance spot size. To reach a good optical design, one has to balance with the incoming beam shading from the convex surface, the number of times of relay reflections, and the entrance annular pupil size of each module for the maximum optical transfer efficiency (OTE). Since the dielectric concentrator module converges the beams in the relaying process, the more times of relay reflections from outer diameter to the center cell, the tighter the system solar tolerance will be. Also, the location of the confocal points and the curvature of the reflection surfaces both determine the system thickness and the optical path length of the entire system. In exploring those possible design spaces, we came up with two different representative designs with different design parameters as summarized in Table 1. Both the concentrator designs are assumed to utilize the silver coating with 95% reflectivity at all the inner reflecting surfaces and share the same geometrical concentration ratio rG of 1600X, where the geometrical concentration ratio rG is defined as the ratio of the concentrator entrance pupil area
Focus Ring 3 IR3= 10.195 mm
Center of sun (0 arc min ray)
Focus Ring 2 IR2=5.214 mm
Edge of sun (32 arc min ray) Edge of sun (-32 arc min ray)
Focus Ring 1 IR1=0.422 mm
Symmetric axis SR1
SR2 SR3
SC1 SC2
SC3 Final Image FR=3.3 mm
Diameter = 240 mm
Fig. 2. The rays incident the entrance pupil of the first module (or the most outter). The center ray means come from central of the sun, it is like a collimated beam light incident in solar concentrator. The other ray means come from edge of the sun, it is like a ray has 5 mrad tilt. IR is the image radius of each SC surface.
C.-W. Liang, J.-S. Lin / Solar Energy 122 (2015) 264–270
optical transfer efficiency g is unit one, optical concentration ratio r reaches its thermodynamic limit rM (Winston and Gordon, 2005).
Table 1 The design parameters table of the two concentrator designs.
Aspect ratio Thermodynamic limit concentration Peak optical concentration Averaged optical concentration 90% Acceptance angle Optical transfer efficiency
Design A
Design B
0.166 20415X 13200X 989X ±0.65° 61.79%
0.125 71290X 43100X 914X ±0.46° 57.14%
267
2
rM ¼ ½n sinðhC Þ= sinðhE Þ ¼ ðNAC =NAE Þ
2
ð1Þ
where n denotes the index of refraction of the dielectric material immersing the solar cell, hC is the half cone angle of the light which incident on the solar cell and the hE is the half solar expansion angle of 16 arc-min. Thus, when the solar cell is immersed in the dielectric material with the refractive index of 1.517, the maximum thermodynamic limit concentration rM that could be possibly achieved is limited to 106239X while hC is at its maximum angle of 90° and N.A. is numerical aperture. Note that when the solar cell is at the focus of a typical lens or mirror concentrator, the solar irradiance is maximum and uniform if the solar beam fulfills the solar cell area. However, in the proposed concentrator design, the irradiance at the solar cell is contributed from the different concentrator relaying modules that have different concentration ratios and focused spot sizes. The irradiance is not uniform even if the solar cell is located at the common focus of each cascading dielectric concentrator modules. Consequently, the optical concentration ratio is not constant over the cell and the maximum concentration ratio cannot represent a constant optical concentration
to the solar cell area. Fig. 3 shows both concentrator designs and the three dimensional view of the design B. The entrance pupil diameters of both designs are set equal. The design B has one more dielectric concentrator module and the additional central refractive dielectric concentrator module. Thus, the design B has a thinner aspect ratio of 0.125 while design A has an aspect ratio of 0.166 with just single two cascaded dielectric concentrator modules. 3. The optical concentration contributed from the cascaded module The optical concentration ratio r is defined as the ratio of the solar irradiance at the solar cell to the solar irradiance at the concentrator entrance pupil. When the solar cell is at the focus of the concentrator and the concentrator
(a)
(b)
(c) Fig. 3. (a) The concentrator design A has two cascaded dielectric concentrator module, (b) the concentrator design B has three cascaded dielectric concentrator module and a thinner profile, (c) the transparent 3D view of the concentrator design B.
268
C.-W. Liang, J.-S. Lin / Solar Energy 122 (2015) 264–270
ratio system as in the traditional concentrator optics. As a result, the averaged optical concentration ratio rA is used to define the overall effective system concentration ratio. rA ¼ rG g
ð2Þ
where g is the concentrator optical transfer efficiency which considers the factors including Fresnel refraction transmission efficiency, entrance surface shading, beam blocking, beam walk off, and the reflectivity of the reflection surface. The concentrator optical transfer efficiency g is also commonly defined as the ratio of the optical flux received by the solar cell to the optical flux entering the concentrator entrance pupil. By utilizing the relaying module, the solar irradiance profile at the solar cell is contributed from all the cascaded dielectric concentrator modules. We use design B as the model shown in Fig. 4(a). The numerical aperture is the summation of all the four ray fan angles coming from the four different modules where the ray fans are cascaded seamlessly. From the most outer to the central module, the ray fans angles boundary are 55°, 48°, 38°, and 28° respectively measured from the center axial optical axis. The NAC is then determined by the maximum ray fan boundary angle of the most outer module. Thus, the overall solar cell numerical NAC equals 1.24 and the corresponding thermo-
ɵI : 55° ɵII : 48° ɵIII : 38° ɵIV : 28°
(a)
(b) Fig. 4. (a) The NAC at the solar cell is cascaded seamlessly of the ray fans relayed from different dielectric concentrator modules and hI is 55°, hII is 48°, hIII is 38°, hIV is 28°, respectively. (b) The Gaussian like irradiance distribution at the solar cell after blurring the layered irradiance profile.
dynamic limit concentration ratio reaches as high as 71290X as predicted by the Eq. (1). High concentration ratio is reached by immersing the solar cell in a glass medium. The solar irradiance images relayed from each dielectric concentrator module are different in both their image size and concentration ratio. Therefore, paraxially, after cascading the irradiance contributions from each dielectric concentrator module, the irradiance contribution forms a ‘‘multi-layered cake” like profile at the solar cell shown in Fig. 4(b). The optics does not have an aplanatic design due to the different radius of curvature in orthogonal directions of the toroidal surface. Hence, the off-axis imaging aberration of the toroidal confocal relay mirrors, mostly the astigmatism, will blur the layered irradiance distribution into a Gaussian like profile. To verify this, the Monte Carlo simulation is performed with the incident solar full spectrum irradiance level of 1 mW/mm2. The concentrator is simulated to have its peak irradiance of 43.1 W/mm2 at the center of the Gaussian profile as shown in Fig. 5(a) which corresponds to the peak optical concentration ratio of 43100X. The peak optical concentrator ratio is therefore about 60% of the thermodynamic limit 71290X. The localized high concentration irradiance does not reduce the cell efficiency significantly, instead, the tolerance for making the optics and the alignment errors are increased by doing so (Katz et al., 2006; Korech et al., 2007). Although high concentration will improve the transfer efficiency of the solar cell, the high irradiance has the problem of thermal degradation which decreases the transfer efficiency of solar cell dramatically over the increased cell temperature (Feist et al., 2011). As a result, the effective thermal dissipation method for the accumulated heat on the solar cell is critical especially when the focused area is small. Though the proposed concentrator has the capability of the ultra-high concentration, a more uniform irradiance profile with lower concentration is still desired to address thermal dissipation concern. To achieve the goal, the converging beam can be defocused by either moving the solar cell location axially along the symmetrical axis or changing the mirror curvature of each dielectric concentrator modules. Since the light path is long from the edge concentrator model to the cell and most of the energy is contributed from the outer dielectric concentrator module, a small change of the radius of curvature of surface SC1 or SC2 will significantly change the focus spot size. The defocused irradiance profile can be achieved with a uniform distribution with its peak concentration much lowered to 1.86 W/mm2 as shown in Fig. 5(b). The optical transfer efficiency (OTE) is defined as the ratio of the optical flux entering the entrance pupil to the optical flux received at the solar cell. It depends on the Fresnel refraction transmission efficiency, entrance surface shading, beam blocking, beam walk off, the reflectivity of the reflection surface, the sun shape and beam error. In the proposed design, the concentration mechanism is achieved by mirror-relaying the beam for multiple times
C.-W. Liang, J.-S. Lin / Solar Energy 122 (2015) 264–270
269
Table 2 Coating reflectivity influence in the design B. 100% 75.49% 0% 1208X
99% 70.72% 6.32% 1131X
95% 57.14% 24.3% 914X
89% 41.70% 44.76% 667X
W/mm2
Coating reflectivity Optical transfer efficiency Thin film absorption Averaged concentration
W/mm2
(a)
for the commercial aluminum coating), simulation result shows that there is up to 44.76% loss in the transmitted light due to the thin film absorption. On the other hand, if the 95% silver coating is applied, the loss will be improved significantly to 24.3%. Therefore, the result shows that a high reflectivity coating is critical in determining the concentrator optical transfer efficiency performance. The solar alignment performance of both the concentrator designs is shown in the following Fig. 6. When the concentrator is well aligned, the concentrator design A has better optical transfer efficiency due to the reduced reflections and therefore the reduced absorption from the reflective coating. We can see that the design A has the better 90% OTE solar alignment tolerance angle of 0.65° while the design B has the 90% OTE solar alignment tolerance angle of 0.46°. Obviously, there are more beams deviated out of the system during relaying process under large solar incident angle in the design B. Considering that the design B has higher numerical aperture than design A, this simulation result seems to contradict the traditional concentrator experience where the alignment sensitivity should be reduced with the increased numerical aperture. In our confocal relay concentrator design, the overall irradiance numerical aperture at the solar cell is composed of the multiple beams coming from different dielectric concentrator modules and most of the contributed irradiance 80 70 60
(b)
in the direction from the edge to the center of the concentrator. As a result, the coating reflectivity has to be as high as possible to avoid unwanted absorption. To investigate the impacts of the coating reflectivity, four optical coatings with different reflectivity are applied in the simulation as shown in Table 2. The 100% reflectivity coating is simulated to isolate the energy loss other than the thin film absorption. As shown in Table 2, the optical transfer efficiency is 75.49% without the absorption of the thin film. If the coating reflectivity is down to 89% (typical value
50
OTE (%)
Fig. 5. (a) The Gaussian like irradiance profile at the 3 3 mm solar cell and the maximum irradiance reaches 43.1 W/mm2. (b) The defocused irradiance profile is more uniform and the maximum irradiance is reduced to 1.86 W/mm2.
Design A
40
Design B 30 20 10 0 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05 1.15 1.25
θin (degree) Fig. 6. The solar alignment performance of both concentrator designs. The finite solar expansion angle is considered and assumed to be 32 arc min. The dash line is the 90% maximum on-axis OTE which defines the tolerance of the solar alignment angle.
270
C.-W. Liang, J.-S. Lin / Solar Energy 122 (2015) 264–270
is from the outer dielectric concentrator module. After passing through each dielectric concentrator module, the width of the collimated beam is reduced in the converging and re-collimation process. Similar to the telescope optics, the magnification is increased with the reduced exit pupil collimated beam size and therefore the increased focal length. As we know that the alignment sensitivity between concentrator and solar cell is increased with BFD (Shannon, 1997), this means the alignment tolerance is reduced with the number of confocal relays. Hence, the solar alignment tolerance is reduced with the increased cascaded numerical aperture at the solar cell. It would be possible to yield a higher concentration design by cascading more dielectric concentrator modules in the radial directions. However, the reduced solar alignment tolerance and the increased reflector loss will make it less practical. 4. Conclusion The presented solar concentrator design utilizing the novel off-axis toroidal confocal relaying principle has an excellent combination of high concentration ratio and low aspect ratio. In the meantime, it also provides various advantages: The zero back focal distance feature eliminate the requirement to align the solar cell to the concentrator optics. With the low profile design and low the wind loading, the weight of the complete concentrator module is significantly reduced. Meanwhile, the concentrator design has the moderate solar acceptance angle for the solar tracker alignment tolerance. With all the above design advantages, the concentrator can even be manufactured by a single molding process for mass production. We are looking forward to the deployment of the proposed concentrator soon. Acknowledgements The authors would like to thank the National Science Council of Taiwan for financial support under Contract
No. NSC 100-2627-E-008-001. The device presented in the paper is protected under US and international patents pending. We also would like to thanks the helpful discussion from the journal editor Dr. Lorin Vant-Hull who gave us the suggestion to point out the progress of the proposed method when compared with previous arts. References Benitez, P., Cvetkovic, a., Winston, R., Reed, L., Cisneros, J., Tovar, a., Ritschel, a., Wright, J., 2006. Kohler integrating system for tandem solar cells. Imaging, 690–693. Feist, R., Mills, M., Thompson, K., Ramesh, N., 2011. Comparison of solar cell device thermal degradation and low-irradiance performance. Conf. Rec. IEEE Photovolt. Spec. Conf. 002301-002304. http://dx.doi. org/10.1109/PVSC.2011.6186414. Goldstein, A., Feuermann, D., Conley, G.D., Gordon, J.M., 2011. Nested aplanats for practical maximum-performance solar concentration. Opt. Lett. 36, 2836–2838. http://dx.doi.org/10.1364/OL.36.002836. Gordon, J.M., 2010. Aplanatic optics for solar concentration. Opt. Express 18, A41–A52. http://dx.doi.org/10.1364/OE.18.000A41. Karp, J.H., Tremblay, E.J., Ford, J.E., 2010. Planar micro-optic solar concentrator. Quantum 18, 137–144. http://dx.doi.org/10.1520/ G0173-03E01. Katz, E.a., Gordon, J.M., Tassew, W., Feuermann, D., 2006. Photovoltaic characterization of concentrator solar cells by localized irradiation. J. Appl. Phys. 100. http://dx.doi.org/10.1063/1.2266161. Korech, O., Hirsch, B., Katz, E.a., Gordon, J.M., 2007. High-flux characterization of ultrasmall multijunction concentrator solar cells. Appl. Phys. Lett. 91, 2–4. http://dx.doi.org/10.1063/1.2766666. Shannon, R.R., 1997. The Art and Science of Optical Design. Cambridge University Press, pp. 358–362. Tremblay, E.J., Stack, R.a., Morrison, R.L., Ford, J.E., 2007. Ultrathin cameras using annular folded optics. Appl. Opt. 46, 463–471. http:// dx.doi.org/10.1364/AO.46.000463. Tremblay, E.J., Stack, R.a., Morrison, R.L., Karp, J.H., For, J.E., 2009. Ultrathin four-reflection imager. Appl. Opt. 48, 343–354. http://dx.doi. org/10.1364/AO.48.000343. Winston, R., Gordon, J.M., 2005. Planar concentrators near the e´tendue limit. Opt. Lett. 30, 2617–2619. http://dx.doi.org/10.1364/ OL.30.002617. Winston, R., Zhang, W., 2009. Novel aplanatic designs. Opt. Lett. 34, 3018–3019. http://dx.doi.org/10.1364/OL.34.003018.
ScienceDirect Solar Energy 122 (2015) 264–270 www.elsevier.com/locate/solener
High concentration thin profile solar concentrator utilizing toroidal confocal relay Chao-Wen Liang ⇑, Jhe-Syuan Lin Department of Optics and Photonics, National Central University, No. 300, Jhongda Rd., Jhongli City, Taoyuan County 32001, Taiwan, ROC Received 3 July 2014; received in revised form 29 July 2015; accepted 17 August 2015
Communicated by: Associate Editor L. Vant-Hull
Abstract A thin profile solar concentrator is designed based on the novel off-axis toroidal confocal relay design principle. The solar beam is collected, converged, re-collimated, and relayed to the solar cell simultaneously by the radially cascaded dielectric concentrator modules. This concentrator has properties of high concentrating ratio, thin aspect ratio, zero back focal distance, Gaussian irradiance profile, and single molding manufacture capability. In the Monte Carlo ray tracing simulation shown, one of the proposed concentrator designs has aspect ratio of 1/8 and achieves over 43100X peak concentration with the theoretical thermodynamic concentration limit, within the dielectric, of 71290X. Ó 2015 Elsevier Ltd. All rights reserved.
Keywords: Solar concentrator; Solar energy; Geometrical optical design; Off-axis relay
1. Introduction The concentrator photovoltaic (CPV) technology for multi-junction solar cells is considered to be one of the major solutions for renewable energy technologies. In the CPV system, the concentrator optics reduces the price per watt ratio by collecting large area sunlight and transferring the concentrated solar energy into the smaller solar cell. The CPV system with a high concentration ratio requires a solar tracker which is used to keep the concentrated solar focusing spot constantly staying on the solar cell for the maximum solar power delivery efficiency. In order to have an efficient concentrator system, the concentration ratio, the solar acceptance angle, system alignment tolerance, and cell irradiance uniformity are all important factors to be considered. ⇑
Corresponding author. E-mail address: [email protected] (C.-W. Liang).
http://dx.doi.org/10.1016/j.solener.2015.08.030 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.
The refractive Fresnel concentrator is being popularly used in the field due to its low cost and easy manufacturability with the ease of molding capability. However, most of the refractive concentrator systems have much larger system volume due to the required long back focal distance (BFD) which is defined as the distance from the concentrator to the solar cell. The long BFD poses several disadvantages to the construction of the high concentration ratio concentrator. For instance, the alignment between the solar cell and the concentrator gets more difficult with the increased length of BFD. The increased BFD also means increased weight for the rigid construction of the concentrator system which expands the weight loading for the solar tracker as well. The wind loading profile is also increased with the increased BFD. Therefore, the shortened concentrator BFD design demonstrates a compact and high precision solar tracker system and reduces the assembly process complexity.
C.-W. Liang, J.-S. Lin / Solar Energy 122 (2015) 264–270
Several researchers have proposed methods to minimize the concentrator volume by either shortening the concentrator thickness or the BFD. One of the representative designs is the non-imaging type concentrator combining the light guide panel and the micro focusing lens for coupling into the light guide panel (Karp et al., 2010). Also, the Cassegrain reflective type concentrators effectively reduce the system volume by folding the optical path (Benitez et al., 2006; Goldstein et al., 2011; Gordon, 2010; Winston and Gordon, 2005; Winston and Zhang, 2009). In one of the designs, the system flux e´tendue of the CPV system can be further improved by placing a dielectric compound confocal relay concentrator (CPC) near the focal plane of the concentrator (Winston and Gordon, 2005). The nested mirror design was developed as well to reach near the e´tendue limit performance with advantages of high concentration ratio and high e´tendue (Goldstein et al., 2011). However, since each beam relay mirror pair is independently designed, they only relay the concentrated beam once in its own optimized path. Therefore, it is inevitable to end up with a high aspect ratio concentrator design with such design approach. Another drawback is the alignment work, the nested mirror is difficult to be aligned considering the high Numerical Aperture (NA) and high incident angle on the relay mirror pair. In this paper, a novel toroidal-shaped off-axis Cassegrain relaying concentrator is proposed. This concentrator is composed of several radially cascaded toroidal paraboloid concentrator modules for a larger entrance pupil area. This proposed concentrator reaches a thin profile design with aspect ratio of 0.125 through the novel toroidal confocal relay process. Each module can simultaneously concentrate, re-collimate, and relay the collimated sunlight into the next paraboloid concentrator module in the radial direction. Therefore, this design boosts a much thinner aspect ratio and higher NA optical design than the Goldstein’s method (Goldstein et al., 2011). Besides the aspect ratio, this concentrator also has the outstanding properties of high concentrating ratio, zero back focal distance, and uniform irradiance profile. Best of all, the concentrator can be made of a single molding mass manufacture process. This molded module intrinsically aligns all optical elements of the concentrator, leaving only the silvering work of the reflective surface and the cement of the solar cell. 2. The off-axis toroidal confocal relay design The annular multi-folded lens design for a thin pancake like camera module has been developed before (Tremblay et al., 2009, 2007). In this design, the light beams enter the lens module at the edge ring of the annular concentric optics. After entering the module, the beams are then mirror-folded and relayed for multiple times in the tangential direction to image sensor located at the center of the concentric optics. The optical aberrations are then balanced in the relaying optical path by the folding aspherical mirror. The optical system is therefore composed of annu-
265
lar segments of aspherical surfaces cascaded concentrically. Since most of the inner surface area of the concentric optics is used for the beam relaying reflection, the opening entrance pupil of the whole system is literally limited to the most outer ring of the whole concentric optics. Therefore, the increased obscuration ratio limits its practical application in the concentrator in a CPV system due to the loss of incoming beam at the entrance. Though the annular multi-folded design has a very thin profile and high NA for the high concentration, it’s not practical to be used as a solar concentrator. In view of this limitation, we proposed the toroidal shaped off-axis Cassegrain relaying dielectric concentrator module with the objective of reducing the high obscuration ratio effectively while maintaining its thin profile. The system is designed with toroidal surfaces that have different curvatures in orthogonal directions. Since tangential direction is the direction of beam convergence, the tangential radius of curvature is much shorter than the revolving radius for most segments. The schematic tangential optical path of the dielectric concentrator module in the direction of concentration is illustrated in Fig. 1. In this figure, the two dielectric concentrator modules face the incoming solar beam with its surface normal parallel to the solar on-axis light path. Each of the dielectric concentrator modules is composed of two off-axis toroidal confocal optical surfaces similar to the off-axis Cassegrain telescope composed of a concave primary mirror and a convex secondary mirror. Rays propagating in the tangential direction converge to the last module where the center solar cell is located. To have the converged beam recollimated after the secondary reflecting surface, the two off-axis toroidal confocal relay surfaces within the dielectric concentrator module have to be confocal and share the same ‘‘focus ring” in the tangential direction. The concentrator has to accommodate the full solar expansion angle of 32 arc min. In Fig. 1, the concave surface SC1 of the first dielectric concentrator module converges the incoming extended solar beam onto the upper reflecting convex surface SR1. In which the extended solar beam is defined by the scope of on-axis 0° red1 line and offaxis 16 arc-min yellow line. A virtual solar image o’ is formed after SR1 forming the ‘‘focus ring” if viewed from the top of concentrator. The reflecting surface SR1 then recollimates and relays the solar beam onto the subsequent concave surface SC2. The beam 1 reflected from the surface SR1 will then be combined with incoming solar beam 2 of the secondary module and together get reflected onto the surface SR2 upon the surface SC1. To keep the same conjugate relationships for further relaying inside the concentrator, both beam 1 and beam 2 are focused to the same focal point o’’ of the surface SR2. By utilizing the off-axis confocal relaying concept, the incoming beams are cas-
1 For interpretation of color in Fig. 1, the reader is referred to the web version of this article.
266
C.-W. Liang, J.-S. Lin / Solar Energy 122 (2015) 264–270 On-axis beam1 Off-axis beam1 @ 32 arc min On-axis beam2 Off-axis beam2 @ -32 arc min O’’
Virtual Image
O’ SR1 SR2 Solid dielectric
…
SC1 SC2
Fig. 1. The cross section of the concentrator shows the off-axis relaying concept.
caded and the system throughput is increased. The dielectric concentrator modules are designed to be made of the optical glass, NBK7, with a refractive index of 1.517. Multiple dielectric concentrator modules are assembled in the aperture plane for a larger entrance pupil area and also to reach a thinner profile design. In our cascaded relay design, magnification of each relay module is an important issue due to the divergence angle of sunlight. It will affect cascaded times. Therefore, the magnification of each module in our design has to be restricted to avoid an overwhelming long focal length along the concentration direction. Fig. 2 shows one of the designs. It has three cascaded modules and all the relaying modules have their own focus ring coincident at the focal plane of three mirrors SC1, SC2 and SC3. The afocal magnification of a telescope is the ratio between the primary mirror and second mirror. Therefore, the module 1 (SC1 + SR1) provides afocal magnification of 7.5 times. The module 2 (SC2 + SR2) has the magnification of 1.47 times. The final relay surface SR3 shrinks the image further by 0.238 times with the finite conjugate magnification. Thus, such toroidal relay design doesn’t magnify the solar image as much as one would expect. Comparing the simulated ray trace
result with the paraxial image size, there is a big difference between them. This is due to the significant amount of offaxis aberration that actually dominates the size of the solar irradiance spot size. To reach a good optical design, one has to balance with the incoming beam shading from the convex surface, the number of times of relay reflections, and the entrance annular pupil size of each module for the maximum optical transfer efficiency (OTE). Since the dielectric concentrator module converges the beams in the relaying process, the more times of relay reflections from outer diameter to the center cell, the tighter the system solar tolerance will be. Also, the location of the confocal points and the curvature of the reflection surfaces both determine the system thickness and the optical path length of the entire system. In exploring those possible design spaces, we came up with two different representative designs with different design parameters as summarized in Table 1. Both the concentrator designs are assumed to utilize the silver coating with 95% reflectivity at all the inner reflecting surfaces and share the same geometrical concentration ratio rG of 1600X, where the geometrical concentration ratio rG is defined as the ratio of the concentrator entrance pupil area
Focus Ring 3 IR3= 10.195 mm
Center of sun (0 arc min ray)
Focus Ring 2 IR2=5.214 mm
Edge of sun (32 arc min ray) Edge of sun (-32 arc min ray)
Focus Ring 1 IR1=0.422 mm
Symmetric axis SR1
SR2 SR3
SC1 SC2
SC3 Final Image FR=3.3 mm
Diameter = 240 mm
Fig. 2. The rays incident the entrance pupil of the first module (or the most outter). The center ray means come from central of the sun, it is like a collimated beam light incident in solar concentrator. The other ray means come from edge of the sun, it is like a ray has 5 mrad tilt. IR is the image radius of each SC surface.
C.-W. Liang, J.-S. Lin / Solar Energy 122 (2015) 264–270
optical transfer efficiency g is unit one, optical concentration ratio r reaches its thermodynamic limit rM (Winston and Gordon, 2005).
Table 1 The design parameters table of the two concentrator designs.
Aspect ratio Thermodynamic limit concentration Peak optical concentration Averaged optical concentration 90% Acceptance angle Optical transfer efficiency
Design A
Design B
0.166 20415X 13200X 989X ±0.65° 61.79%
0.125 71290X 43100X 914X ±0.46° 57.14%
267
2
rM ¼ ½n sinðhC Þ= sinðhE Þ ¼ ðNAC =NAE Þ
2
ð1Þ
where n denotes the index of refraction of the dielectric material immersing the solar cell, hC is the half cone angle of the light which incident on the solar cell and the hE is the half solar expansion angle of 16 arc-min. Thus, when the solar cell is immersed in the dielectric material with the refractive index of 1.517, the maximum thermodynamic limit concentration rM that could be possibly achieved is limited to 106239X while hC is at its maximum angle of 90° and N.A. is numerical aperture. Note that when the solar cell is at the focus of a typical lens or mirror concentrator, the solar irradiance is maximum and uniform if the solar beam fulfills the solar cell area. However, in the proposed concentrator design, the irradiance at the solar cell is contributed from the different concentrator relaying modules that have different concentration ratios and focused spot sizes. The irradiance is not uniform even if the solar cell is located at the common focus of each cascading dielectric concentrator modules. Consequently, the optical concentration ratio is not constant over the cell and the maximum concentration ratio cannot represent a constant optical concentration
to the solar cell area. Fig. 3 shows both concentrator designs and the three dimensional view of the design B. The entrance pupil diameters of both designs are set equal. The design B has one more dielectric concentrator module and the additional central refractive dielectric concentrator module. Thus, the design B has a thinner aspect ratio of 0.125 while design A has an aspect ratio of 0.166 with just single two cascaded dielectric concentrator modules. 3. The optical concentration contributed from the cascaded module The optical concentration ratio r is defined as the ratio of the solar irradiance at the solar cell to the solar irradiance at the concentrator entrance pupil. When the solar cell is at the focus of the concentrator and the concentrator
(a)
(b)
(c) Fig. 3. (a) The concentrator design A has two cascaded dielectric concentrator module, (b) the concentrator design B has three cascaded dielectric concentrator module and a thinner profile, (c) the transparent 3D view of the concentrator design B.
268
C.-W. Liang, J.-S. Lin / Solar Energy 122 (2015) 264–270
ratio system as in the traditional concentrator optics. As a result, the averaged optical concentration ratio rA is used to define the overall effective system concentration ratio. rA ¼ rG g
ð2Þ
where g is the concentrator optical transfer efficiency which considers the factors including Fresnel refraction transmission efficiency, entrance surface shading, beam blocking, beam walk off, and the reflectivity of the reflection surface. The concentrator optical transfer efficiency g is also commonly defined as the ratio of the optical flux received by the solar cell to the optical flux entering the concentrator entrance pupil. By utilizing the relaying module, the solar irradiance profile at the solar cell is contributed from all the cascaded dielectric concentrator modules. We use design B as the model shown in Fig. 4(a). The numerical aperture is the summation of all the four ray fan angles coming from the four different modules where the ray fans are cascaded seamlessly. From the most outer to the central module, the ray fans angles boundary are 55°, 48°, 38°, and 28° respectively measured from the center axial optical axis. The NAC is then determined by the maximum ray fan boundary angle of the most outer module. Thus, the overall solar cell numerical NAC equals 1.24 and the corresponding thermo-
ɵI : 55° ɵII : 48° ɵIII : 38° ɵIV : 28°
(a)
(b) Fig. 4. (a) The NAC at the solar cell is cascaded seamlessly of the ray fans relayed from different dielectric concentrator modules and hI is 55°, hII is 48°, hIII is 38°, hIV is 28°, respectively. (b) The Gaussian like irradiance distribution at the solar cell after blurring the layered irradiance profile.
dynamic limit concentration ratio reaches as high as 71290X as predicted by the Eq. (1). High concentration ratio is reached by immersing the solar cell in a glass medium. The solar irradiance images relayed from each dielectric concentrator module are different in both their image size and concentration ratio. Therefore, paraxially, after cascading the irradiance contributions from each dielectric concentrator module, the irradiance contribution forms a ‘‘multi-layered cake” like profile at the solar cell shown in Fig. 4(b). The optics does not have an aplanatic design due to the different radius of curvature in orthogonal directions of the toroidal surface. Hence, the off-axis imaging aberration of the toroidal confocal relay mirrors, mostly the astigmatism, will blur the layered irradiance distribution into a Gaussian like profile. To verify this, the Monte Carlo simulation is performed with the incident solar full spectrum irradiance level of 1 mW/mm2. The concentrator is simulated to have its peak irradiance of 43.1 W/mm2 at the center of the Gaussian profile as shown in Fig. 5(a) which corresponds to the peak optical concentration ratio of 43100X. The peak optical concentrator ratio is therefore about 60% of the thermodynamic limit 71290X. The localized high concentration irradiance does not reduce the cell efficiency significantly, instead, the tolerance for making the optics and the alignment errors are increased by doing so (Katz et al., 2006; Korech et al., 2007). Although high concentration will improve the transfer efficiency of the solar cell, the high irradiance has the problem of thermal degradation which decreases the transfer efficiency of solar cell dramatically over the increased cell temperature (Feist et al., 2011). As a result, the effective thermal dissipation method for the accumulated heat on the solar cell is critical especially when the focused area is small. Though the proposed concentrator has the capability of the ultra-high concentration, a more uniform irradiance profile with lower concentration is still desired to address thermal dissipation concern. To achieve the goal, the converging beam can be defocused by either moving the solar cell location axially along the symmetrical axis or changing the mirror curvature of each dielectric concentrator modules. Since the light path is long from the edge concentrator model to the cell and most of the energy is contributed from the outer dielectric concentrator module, a small change of the radius of curvature of surface SC1 or SC2 will significantly change the focus spot size. The defocused irradiance profile can be achieved with a uniform distribution with its peak concentration much lowered to 1.86 W/mm2 as shown in Fig. 5(b). The optical transfer efficiency (OTE) is defined as the ratio of the optical flux entering the entrance pupil to the optical flux received at the solar cell. It depends on the Fresnel refraction transmission efficiency, entrance surface shading, beam blocking, beam walk off, the reflectivity of the reflection surface, the sun shape and beam error. In the proposed design, the concentration mechanism is achieved by mirror-relaying the beam for multiple times
C.-W. Liang, J.-S. Lin / Solar Energy 122 (2015) 264–270
269
Table 2 Coating reflectivity influence in the design B. 100% 75.49% 0% 1208X
99% 70.72% 6.32% 1131X
95% 57.14% 24.3% 914X
89% 41.70% 44.76% 667X
W/mm2
Coating reflectivity Optical transfer efficiency Thin film absorption Averaged concentration
W/mm2
(a)
for the commercial aluminum coating), simulation result shows that there is up to 44.76% loss in the transmitted light due to the thin film absorption. On the other hand, if the 95% silver coating is applied, the loss will be improved significantly to 24.3%. Therefore, the result shows that a high reflectivity coating is critical in determining the concentrator optical transfer efficiency performance. The solar alignment performance of both the concentrator designs is shown in the following Fig. 6. When the concentrator is well aligned, the concentrator design A has better optical transfer efficiency due to the reduced reflections and therefore the reduced absorption from the reflective coating. We can see that the design A has the better 90% OTE solar alignment tolerance angle of 0.65° while the design B has the 90% OTE solar alignment tolerance angle of 0.46°. Obviously, there are more beams deviated out of the system during relaying process under large solar incident angle in the design B. Considering that the design B has higher numerical aperture than design A, this simulation result seems to contradict the traditional concentrator experience where the alignment sensitivity should be reduced with the increased numerical aperture. In our confocal relay concentrator design, the overall irradiance numerical aperture at the solar cell is composed of the multiple beams coming from different dielectric concentrator modules and most of the contributed irradiance 80 70 60
(b)
in the direction from the edge to the center of the concentrator. As a result, the coating reflectivity has to be as high as possible to avoid unwanted absorption. To investigate the impacts of the coating reflectivity, four optical coatings with different reflectivity are applied in the simulation as shown in Table 2. The 100% reflectivity coating is simulated to isolate the energy loss other than the thin film absorption. As shown in Table 2, the optical transfer efficiency is 75.49% without the absorption of the thin film. If the coating reflectivity is down to 89% (typical value
50
OTE (%)
Fig. 5. (a) The Gaussian like irradiance profile at the 3 3 mm solar cell and the maximum irradiance reaches 43.1 W/mm2. (b) The defocused irradiance profile is more uniform and the maximum irradiance is reduced to 1.86 W/mm2.
Design A
40
Design B 30 20 10 0 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05 1.15 1.25
θin (degree) Fig. 6. The solar alignment performance of both concentrator designs. The finite solar expansion angle is considered and assumed to be 32 arc min. The dash line is the 90% maximum on-axis OTE which defines the tolerance of the solar alignment angle.
270
C.-W. Liang, J.-S. Lin / Solar Energy 122 (2015) 264–270
is from the outer dielectric concentrator module. After passing through each dielectric concentrator module, the width of the collimated beam is reduced in the converging and re-collimation process. Similar to the telescope optics, the magnification is increased with the reduced exit pupil collimated beam size and therefore the increased focal length. As we know that the alignment sensitivity between concentrator and solar cell is increased with BFD (Shannon, 1997), this means the alignment tolerance is reduced with the number of confocal relays. Hence, the solar alignment tolerance is reduced with the increased cascaded numerical aperture at the solar cell. It would be possible to yield a higher concentration design by cascading more dielectric concentrator modules in the radial directions. However, the reduced solar alignment tolerance and the increased reflector loss will make it less practical. 4. Conclusion The presented solar concentrator design utilizing the novel off-axis toroidal confocal relaying principle has an excellent combination of high concentration ratio and low aspect ratio. In the meantime, it also provides various advantages: The zero back focal distance feature eliminate the requirement to align the solar cell to the concentrator optics. With the low profile design and low the wind loading, the weight of the complete concentrator module is significantly reduced. Meanwhile, the concentrator design has the moderate solar acceptance angle for the solar tracker alignment tolerance. With all the above design advantages, the concentrator can even be manufactured by a single molding process for mass production. We are looking forward to the deployment of the proposed concentrator soon. Acknowledgements The authors would like to thank the National Science Council of Taiwan for financial support under Contract
No. NSC 100-2627-E-008-001. The device presented in the paper is protected under US and international patents pending. We also would like to thanks the helpful discussion from the journal editor Dr. Lorin Vant-Hull who gave us the suggestion to point out the progress of the proposed method when compared with previous arts. References Benitez, P., Cvetkovic, a., Winston, R., Reed, L., Cisneros, J., Tovar, a., Ritschel, a., Wright, J., 2006. Kohler integrating system for tandem solar cells. Imaging, 690–693. Feist, R., Mills, M., Thompson, K., Ramesh, N., 2011. Comparison of solar cell device thermal degradation and low-irradiance performance. Conf. Rec. IEEE Photovolt. Spec. Conf. 002301-002304. http://dx.doi. org/10.1109/PVSC.2011.6186414. Goldstein, A., Feuermann, D., Conley, G.D., Gordon, J.M., 2011. Nested aplanats for practical maximum-performance solar concentration. Opt. Lett. 36, 2836–2838. http://dx.doi.org/10.1364/OL.36.002836. Gordon, J.M., 2010. Aplanatic optics for solar concentration. Opt. Express 18, A41–A52. http://dx.doi.org/10.1364/OE.18.000A41. Karp, J.H., Tremblay, E.J., Ford, J.E., 2010. Planar micro-optic solar concentrator. Quantum 18, 137–144. http://dx.doi.org/10.1520/ G0173-03E01. Katz, E.a., Gordon, J.M., Tassew, W., Feuermann, D., 2006. Photovoltaic characterization of concentrator solar cells by localized irradiation. J. Appl. Phys. 100. http://dx.doi.org/10.1063/1.2266161. Korech, O., Hirsch, B., Katz, E.a., Gordon, J.M., 2007. High-flux characterization of ultrasmall multijunction concentrator solar cells. Appl. Phys. Lett. 91, 2–4. http://dx.doi.org/10.1063/1.2766666. Shannon, R.R., 1997. The Art and Science of Optical Design. Cambridge University Press, pp. 358–362. Tremblay, E.J., Stack, R.a., Morrison, R.L., Ford, J.E., 2007. Ultrathin cameras using annular folded optics. Appl. Opt. 46, 463–471. http:// dx.doi.org/10.1364/AO.46.000463. Tremblay, E.J., Stack, R.a., Morrison, R.L., Karp, J.H., For, J.E., 2009. Ultrathin four-reflection imager. Appl. Opt. 48, 343–354. http://dx.doi. org/10.1364/AO.48.000343. Winston, R., Gordon, J.M., 2005. Planar concentrators near the e´tendue limit. Opt. Lett. 30, 2617–2619. http://dx.doi.org/10.1364/ OL.30.002617. Winston, R., Zhang, W., 2009. Novel aplanatic designs. Opt. Lett. 34, 3018–3019. http://dx.doi.org/10.1364/OL.34.003018.