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Infrared Transmission Efficiency of Refractive and Reflective Non- Imaging Devices for a Full-Spectrum Solar Energy System Dan Dye* and Byard Wood Mechanical Engineering, Mail Stop 312, University of Nevada, Reno Reno, NV 89557 ABSTRACT A solar collector/receiver for a full-spectrum solar energy system is being designed by a research team lead by Oak Ridge National Laboratory and the University of Nevada, Reno1,2. This solar energy system is unique in that it utilizes the majority of the solar spectrum. The collector/receiver is a modified Cassegrain system that uses a large parabolic mirror and a secondary mirror comprised of multiple planar segments. The secondary mirror segments are coated with a spectrally selective cold mirror coating that lets the infrared (IR) energy pass through while reflecting the visible light. The focus of this paper is on determining whether a refractive or a reflective non-imaging (NI) tube will produce the most uniform irradiance of the IR energy on the thermophotovoltaic (TPV) array. It has been shown that a rectangular NI tube will work well for the prototype system3. The results herein show that a reflective NI tube will perform best for this system, with a short length, minimum/maximum flux ratio of 0.94 and power output of 37W. It is also shown that a square shaped TPV array can increase the optical efficiency by 9% and the overall system efficiency by 2%. Keywords: non-imaging device; thermophotovoltaic; infrared; full-spectrum; solar energy 1. INTRODUCTION A full-spectrum solar energy system combining daylighting and electric power generation is under development. The concept for this system is shown in Figure 1. The visible portion of the solar spectrum is separated from the IR and concentrated for transmittance of the daylight via fiber optics to hybrid luminaries. The IR spectrum is concentrated and directed onto a TPV array behind the secondary mirror for electric power generation. The IR energy that passes through the secondary mirror will be directed to the TPV array shown in Figure 2. Work has been performed to determine the optimum shape of a NI device to homogenize the IR flux concentrated by the primary parabolic mirror incident on the gallium antimonide (GaSb) TPV array. The results of that research show that a rectangular tube would perform the best as the NI device. In general, square NI tubes show the most promise4, but due to the silhouette of the current TPV array, other cross sections have been investigated. The next step is to determine if a total internal reflecting (TIR) or a hollow internal reflecting (HIR) system would work the best for this prototype system. The average incident angle at the focal plane is approximately 49 degrees, so reflection losses are expected at the entrance of the TIR tube. The HIR tube will not have the entrance aperture losses, but the advantage of the refractive TIR system is that the average incident angle at the exit aperture will decrease to about 31 degrees, while the reflective HIR system will retain the higher angles. To determine which type of NI device would perform the best for the benchmark TPV array, two different configurations have been investigated: an HIR and a TIR system with rectangular cross-sectional shape. The results of the detailed analysis have been used to determine which system has the highest energy transfer efficiency. A second generation TPV array is suggested. This array has a close to square silhouette and the HIR and TIR NI tubes will be used to compare this system to the benchmark, or first generation, system. It is expected that the second generation system will have a higher efficiency from the NI optics entrance to exit aperture due to more useable area at the exit aperture. But, compared to the IR losses at the secondary mirror, this gain in NI optics efficiency may be negligible. * email@example.com; phone 775 784-6735; fax 775 784-1701; energy.unr.edu 166 Nonimaging Optics: Maximum Efficiency Light Transfer VII, edited by Roland Winston, Proceedings of SPIE Vol. 5185 (SPIE, Bellingham, WA, 2004) · 0277-786X/04/$15 · doi: 10.1117/12.506318 Figure 1: Full-Spectrum Solar Energy System Figure 2: 100-Cell GaSb TPV Array For more efficient energy transfer, a square-shaped TPV array is suggested. Based on the test data from the original TPV array5, each cell in the array has a voltage at the maximum power point of Vmax = 0.345 V and an open circuit voltage of Voc = 0.477 V. The dimensions of each cell are approximately 16.33 mm x 10.85 mm. Using this data, a possible array could have 96 cells, which will have Voc = 45.8 V, Vmax = 33.1 V, and outside dimensions of 13 cm x 13 cm. This array has been used in the analysis as a possible second generation TPV array. Figure 3 shows the comparison of the 100 cell array and the proposed 96 cell array. This second generation array will reduce the unused area at the exit aperture of the NI tube, as well as allow for the use of a square NI tube. This should produce a more homogenized flux across the array surface as well as increase the maximum power output of the array. Proc. of SPIE Vol. 5185 167 Figure 3a: 100 Cell Figure 3b: 96 Cell Figure 3: 100 cell and proposed 96 cell TPV arrays 2. METHODOLOGY Solid models of the collector/receiver system and all optical components were built within TracePro version 3.0. The system was modeled with the surface properties of the primary and secondary mirrors, as shown in Figures 4 and 5. For the refractive TIR NI tube, silica was used as the material, and for the HIR NI tube, an average wall reflectivity of 97% was used. For the ray source of the model, the 0.7 to 1.8 µm spectrum of Air Mass 1.5 was used, with approximately 12.5 million rays per square meter traced. Primary Mirror Reflectivity Secondary Mirror Transmissivity 100 100 90 80 60 80 40 70 20 60 0 0.5 1.0 1.5 2.0 2.5 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Wavelength [ m] Wavelength [ m] Figure 4. Primary Parabolic Mirror Spectral Response Figure 5. Secondary Mirror Spectral Response Once the system model is built, the NI tube is placed with the entrance aperture at the focal point of the primary mirror. The TPV array is then placed near the focal point in the NI tube, moved incrementally down the NI tube away from the focal point, and a TracePro file is generated for each location. A Scheme code is written which runs TracePro through the batch of files and the results are saved for post-processing in Excel 2002. Once the data is in Excel, it can be processed to provide useful information about the flux distribution across the array surface and the surfaces of other system components, as well as the angular distribution of the incident rays on a surface. 168 Proc. of SPIE Vol. 5185 3. DATA The data generated by TracePro can be used to produce figures that show how the minimum cell flux, homogeneity of the flux, and the maximum array output vary with the NI tube length. The angular distribution of the rays on the TPV array can also be collected and processed with a statistical package. Figure 6 shows a histogram of the incident angles at the focal plane. The angles normal to the focal plane of the parabolic mirror are conserved inside the HIR tube, so this distribution is the same for the entrance and exit apertures of the HIR tube. Figure 7 shows a histogram of the incident angles at the exit aperture of the TIR tube. These rays have been refracted, and some of the steeper rays have been lost due to Fresnel losses, so the distribution is quite a bit different. As shown, the rays inside the HIR tube range from 22 to 69 degrees, while in the TIR tube they range from about 14.5 to 40 degrees. HIR Tube Exit Apeture Angular Distribution TIR Tube Exit Apeture Angular Distribution 1400 100% 100% Frequency 90% 2000 Frequency 90% 1200 Cumulative % Cumulative % 80% 80% 1000 70% 70% 1500 60% Frequency 60% Frequency 800 50% 50% 1000 600 40% 40% 400 30% 30% 500 20% 20% 200 10% 10% 0 0% 0 0% 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 14.5 17 19.5 22 24.5 27 29.5 32 34.5 37 39.5 Angle [deg] Angle [deg] Figure 6: HIR Tube Angular Distribution Figure 7: TIR Tube Angular Distribution Figures 8 and 9 show the minimum to maximum flux ratio versus the distance of the array from the focal point, or the NI tube length. These figures show how well the flux has been homogenized. Due to the fact that the rays entering the TIR tube are refracted and act as though the system had a longer f/D ratio, the system requires a significantly longer NI tube length to homogenize the flux. 100 Cell Array Min/Max Ratio 96 Cell Array Min/Max Ratio 1 1 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 Ratio Ratio 0.5 0.5 0.4 0.4 0.3 HIR Tube 0.3 TIR Tube HIR Tube 0.2 0.2 TIR Tube 0.1 0.1 0 0 0 200 400 600 800 1000 0 200 400 600 800 1000 NI Tube Length [mm] NI Tube Length [mm] Figure 8: 100 Cell Array Min/Max Flux Ratio Figure 9: 96 Cell Array Min/Max Flux Ratio Proc. of SPIE Vol. 5185 169 Figures 10 and 11 show the maximum power output from the TPV array. The output of the TPV array is driven by the minimum cell flux on the array. The maximum power output is then simply the minimum flux multiplied by the array area and then multiplied by the efficiency of the GaSb cells, which is estimated to be 18%. Again, the HIR tube produces results with a shorter tube length than the TIR tube. After a maximum is reached, the HIR tube shows a decrease in the power output as the length is increased, due to reflective losses inside the tube, while the TIR tube does not show a significant decrease. This is for a perfect TIR tube though. Dirt, imperfections, and surface roughness will obviously decrease the transmission of the TIR tube with increased length as well. 100 Cell TPV Array Power Output 96 Cell TPV Power Output 40 50 35 45 40 30 35 25 Power [W] Power [W] 30 20 25 20 15 HIR Tube 15 10 HIR Tube TIR Tube TIR Tube 10 5 5 0 0 0 200 400 600 800 1000 0 100 200 300 400 500 600 700 800 900 1000 NI Tube Length [mm] NI Tube Length [mm] Figure 10: 100 Cell Array Power Generation Figure 11: 96 Cell Array Power Generation 4. RESULTS The results from the raytrace analysis are presented below in Tables 1 and 2. For both the 96 cell and 100 cell arrays, the outputs from the two different NI tubes are comparable. From Air Mass 1.5, there is approximately 395 W/m2 IR energy available in the spectrum used for this analysis, and the benchmark system collects about 404 W. The predicted outputs from the 100 cell array are 37 W from the HIR tube and 36 W from the TIR tube. The predicted outputs from the 96 cell array are 44 W from both the TIR and HIR tubes. This is an increase in power production of almost 19% by simply changing the shape of the TPV array. The optical system efficiency of the 100 cell array systems is about 51%, and for the 96 cell array systems it is about 60%. With the IR energy conversion efficiency of the TPV cells accounted for, the overall system efficiency for the 100 cell and 96 cell arrays are 9% and 11%, respectively. Table 1: Comparison Between HIR and TIR Tubes for the 100 Cell TPV Array 100 Cell TPV Array HIR Tube TIR Tube Peak min/max ratio 0.94 0.93 Distance from focal point [mm] 515 810 Peak Minimum Cell Watts 2.05 2.02 Distance from focal point [mm] 190 660 1 Maximum available power [W] 205 202 Power Transfer Efficiency 51 50 Maximum power output2 [W] 37 36 Overall System Efficiency [%] 9 9 1 Minimum cell power multiplied by the number of cells 2 Maximum power available multiplied by an efficiency of 18% 170 Proc. of SPIE Vol. 5185 Table 2: Comparison Between HIR and TIR Tubes for the 96 Cell TPV Array 96 Cell TPV Array HIR Tube TIR Tube Peak min/avg ratio 0.95 0.94 Distance from focal point [mm] 480 900 Peak Minimum Cell Watts 2.52 2.55 Distance from focal point [mm] 180 800 Maximum available power1 [W] 242 245 Power Transfer Efficiency 60 61 Maximum power output2 [W] 44 44 Overall System Efficiency [%] 11 11 1 Minimum cell power multiplied by the number of cells 2 Maximum power available multiplied by an efficiency of 18% 5. CONCLUSIONS For the current TPV array, the structure of the array’s cells essentially necessitates the use of an HIR tube. The cells are stacked in a shingle-fashion, thus there is not a planar front surface. A TIR tube induces losses at both the entrance and exit apertures, as well as being longer and probably more expensive than the HIR tube. These factors lead to the decision to use an HIR tube. Tests must be performed on the GaSb TPV cells in order to determine their response to the angle of incidence of the incoming rays. How the performance decreases with incident angle will play a role in the development of the full-spectrum collector/receiver. An HIR tube with a length of 190mm will produce the maximum power output for the 100 cell array. For the 96 cell array, a tube length of 180mm is required. It is noted that the best min/max flux ratio is achieved at a substantially longer tube length in both cases; 515mm and 480mm respectively. A NI device might be used in the full-spectrum solar energy system in a location other than in front of the TPV array. If thermal management issues are overcome, the fiber optic cables might be centered in a bundle instead of arranged around the axis in an array of individual fibers. If the fibers are put into a bundle, this could possibly relax the stringent tracking and alignment requirements of the system. If a bundle is used, then a NI device could be beneficial because the individual fibers in the bundle would receive a more uniform flux, thus the output of all fibers pulled from the bundle would be nearly equal. Simple, preliminary tests show that the min/max ratio with a non-imaging device in front of a fiber bundle can be on the order of 0.9, as expected. With a circular tube in front of the fibers, instead of a square- shaped NI tube, the min/max ratio could be very poor. Work will be performed to determine whether this is of concern. ACKNOWLEDGMENTS This project is funded in part by DOE Cooperative Agreement DE-FC26-01NT41164. Thanks are due to the Energy Systems Laboratory at the University of Nevada, Reno, Oak Ridge National Laboratory, and all of the Adaptive Full- Spectrum Solar Energy Systems team members. REFERENCES 1. Wood, B.D., Muhs, J., “Adaptive Full-Spectrum Solar Energy Systems”, NETL Report # 41164R02, 8/31/2002 2. J. Muhs, “Design and Analysis of Hybrid Solar Lighting and Full-Spectrum Solar Energy Systems,” American Solar Energy Society, SOLAR2000 Proc. of SPIE Vol. 5185 171 3. Dye, D., Wood, B.D., Fraas, L., and Muhs, J., “Optical Design of an Infrared Non-Imaging Device for a Full- Spectrum Solar Energy System,” Proceedings of the ASME International Solar Energy Society Conference, Hawaii, 2003 4. O’Gallagher, J.J, Winston, R. and Gee, R., “NonImaging Solar Concentrator with Near Uniform Irradiance for Photovoltaic Arrays,” Nonimaging Optics: Maximum Efficiency Light Transfer VI, Proceedings of SPIE Vol. 4446 (2001) 5. L.M. Fraas, W.E. Daniels, J. Muhs, “Infrared Photovoltaics for Combined Solar Lighting and Electricity for Buildings,” Proceedings of 17th European Photovoltaic Solar Energy Conference, (2001) 172 Proc. of SPIE Vol. 5185
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