姓名方君元(June-Yuan Fang) 查詢紙本館藏 畢業系所機械工程學系 論文名稱1-kW級聚光型太陽追蹤器結構變形與追日偏差分析

(Analysis of Structural Deformation and Concentrator Misalignment in a 1-kW Solar Tracker)檔案[Endnote RIS 格式] [Bibtex 格式] [檢視] [下載]

- 本電子論文使用權限為同意立即開放。
- 已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
- 請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)本研究主旨在利用有限元素分析法(FEA)，探討一個1-kW級聚光型太陽光電系統之太陽追蹤器在受到重力以及風力作用之影響下，其結構變形和聚光模組的追日偏差量。研究中使用之有限元素模型是依據國立中央大學開發的太陽追蹤器實際尺寸而建立。分析的條件分別為無風之自重狀態，以及在風速為7 m/s和12 m/s之情況，在每個風速作用下又各別分為風從太陽追蹤器的正面、側面以及背面吹來三種風向。此外，在不同季節之運轉條件下，聚光模組的傾斜角度又分為三種不同的設定參數。藉由量測此太陽追蹤器二個選定位置在實際操作情況下之應變變化，與模擬結果作比對，可驗證本研究所建立的有限元素分析模型之正確性。比對結果顯示，模擬結果之應變改變趨勢和實驗結果一致，此一致性證實本研究所建立之有限元素分析模型之正確性，確實可適用於分析聚光型太陽光電系統之結構變形。

根據von Mises準則，模擬結果顯示此太陽追蹤器在受到重力加上風速為7 m/s或12 m/s的作用下，各個組件將不會有結構永久變形之情形發生。模擬結果亦顯示此追蹤器在不同追日角度下，聚光透鏡的追日偏差量的變化趨勢與其鏡面法向量方向位移大小的變化趨勢一致。因此，藉由找到擁有較大法向量方向位移的聚光透鏡，即可找到產生較大追日偏差量的聚光透鏡。所有分析情況中，在模組傾角設定為1o(夏至)時，以及風速為12 m/s從太陽追蹤器的側面吹來之情況下，聚光透鏡會有最大的追日偏差量，其值為0.142o。由於此數值小於此聚光模組的可接受角度的0.5o，所以預期此太陽追蹤器在風速為12 m/s的作用下仍可以正常運作，不會有明顯的發電效率下降，同時在正常的運作之下，不會有結構破損之情形發生。

摘要(英)The purpose of this study is to investigate the effects of gravity and wind loadings on structural deformation and concentrator misalignment in a 1-kW high concentrator photovoltaic (HCPV) system using finite element analysis (FEA) approach. A three-dimensional (3-D) FEA model was constructed for a roll-tilt form of solar tracker in an HCPV system developed at the National Central University. Several loading conditions, including gravity only and gravity plus wind speeds of 7 and 12 m/s blowing toward the front (wind direction of 0o), lateral (wind direction of 90o), and rear (wind direction of 180o) sides of the solar tracker, were applied to calculate the stress distribution and structural deformation. Three changeable tilt angles of 24.5o (the spring/autumn equinox), 1o (the summer solstice), and 48o (the winter solstice) for the concentrator modules were also taken into account. Meanwhile, the concentrator misalignment induced by the structural deformation was calculated. A comparison of the simulation and measurement results of strain change at two selected locations in the given solar tracker during field operation was made to validate the constructed FEA model. A reasonable agreement of the simulation and measurement results was found such that the constructed FEA model was validated to be effective in assessment of the structural integrity of an HCPV system.

No structural failure was predicted for all components in the given solar tracker under all the given loading conditions according to von Mises failure criterion. An agreement in the trend of variation of concentrator misalignment and normal displacement of Fresnel lens in each concentrator module was found. Therefore, the concentrator with a greater misalignment could be readily identified from the corresponding normal displacement distribution. For all the cases investigated, the maximum concentrator misalignment was of 0.142o for a wind speed of 12 m/s with wind direction of 90o for the tilt angle of 1o (the summer solstice) and it was within the range of an acceptance angle of 0.5o for the given concentrator module. Consequently, the given HCPV system can operate safely under the effects of wind speeds of 7 and 12 m/s with a good efficiency in power generation.

關鍵字(中)★ 太陽追蹤器

★ 有限元素分析關鍵字(英)★ solar tracker

★ finite element analysis論文目次LIST OF TABLES VII

LIST OF FIGURES VVIII

1. INTRODUCTION 1

1.1 High Concentrator Photovoltaic System 1

1.1.1 Concentrator module 2

1.1.2 Solar tracker 3

1.2 Literature Review for Wind Effects on Solar Tracker Structure 5

1.3 Purpose and Scope 7

2. MODELING 10

2.1 Modeling for Structural Deformation 10

2.1.1 Finite element model and material properties 10

2.1.2 Loads and boundary conditions 11

2.2 Modeling for Wind Loads 13

2.2.1 Finite element model 13

2.2.2 Physical properties and boundary conditions 14

2.3 Definition of Concentrator Misalignment 15

3. EXPERIMENTAL SETUP AND PROCEDURE 17

3.1 Experimental Setup 17

3.2 Experimental Procedure 17

4. RESULTS AND DISCUSSION 19

4.1 Effect of Gravity Only 19

4.2 Effect of a Low Wind Speed of 7 m/s 22

4.3 Effect of a Wind Speed of 12 m/s for the Tilt Angle of 24.5o 23

4.4 Effect of a Wind Speed of 12 m/s for the Tilt Angle of 1o 26

4.5 Effect of a Wind Speed of 12 m/s for the Tilt Angle of 48o 28

4.6 Overall Comparison 31

5. CONCLUSIONS 34

REFERENCES 36

TABLES 40

FIGURES 42

Table 1 Material properties of PMMA Fresnel lenses 40

Table 2 Material properties of A6N01S-T5 aluminum alloy 40

Table 3 Material properties of the aluminum frame used in the concentrator modules 40

Table 4 Material properties of C2200 copper alloy 40

Table 5 Material properties of SS400 steel 40

Table 6 Physical properties of air at an atmospheric pressure 41

Table 7 Overall comparisons of maximum stress, normal displacement, and misalignment for various combinations of wind loading and tracking angle 41

Fig. 1 Schematic of a GaInP/GaInAs/Ge triple-junction solar cell structure. [7] 42

Fig. 2 The principle of PV concentration, using Fresnel lens optics. [11] 43

Fig. 3 Major parts in an HCPV system. [10] 44

Fig. 4 Schematic of primary optics: (a) refractive lens; (b) reflective dish. [4] 45

Fig. 5 Two types of secondary optics in which the primary optics is a Fresnel lens: (a) non-imaging mirror; (b) imaging lens. [21] 46

Fig. 6 Typical structures of dual-axis solar trackers: (a) pedestal form; (b) roll-tilt form; (c) roll-tilt form with box frame; (d) turntable form. [4] 47

Fig. 7 Shade balancing principle: (a) sun-pointing sensor; (b) tilted mount of photo sensor; (c) photo sensor in a collimator. [11] 49

Fig. 8 Schematic of a concentrator module 50

Fig. 9 Schematic of the HCPV system model: (a) front view; (b) rear view 51

Fig. 10 Schematic of three selected wind directions 52

Fig. 11 Schematic of the HCPV model at hour angles of (a) 0o and (b) 75o 53

Fig. 12 Schematic of three selected tilt angles of the concentrator modules: (a) 24.5o (the spring/autumn equinox); (b) 1o (the summer solstice); (c) 48o (the winter solstice) 54

Fig. 13 Schematic of wind loading for the given HCPV model with wind blowing toward (a) the front (0o), (b) lateral (90o), and (c) rear (180o) sides of the concentrator modules 55

Fig. 14 (a) Schematic of the simplified HCPV FEA model for calculating the wind pressure; (b) schematic of the computational domain in FEA analysis 57

Fig. 15 Schematic of the computational domain and boundary conditions with wind blowing toward (a) the front (0o), (b) lateral (90o), and (c) rear (180o) sides of the concentrator modules 58

Fig. 16 (a) Wind pressure distributions on the concentrator modules and a cross-sectional view of wind vorticity and (b) velocity field of wind flow around the concentrator modules at hour angle of 60o under the effect of a wind speed of 12 m/s with direction of 90o for the tilt angle of 24.5o 60

Fig. 17 Schematic of structural deformation in a Fresnel lens for calculating the misalignment: (a) iso view; (b) a cross-sectional view 61

Fig. 18 Definition of the angle between the undeformed plane P and deformed plane P' 62

Fig. 19 Two selected locations for strain measurement: (a) a highlighted view from the FEA model; (b) the corresponding photograph 63

Fig. 20 Experimental setup for strain measurement 65

Fig. 21 Comparison of simulated and measured strain variations at various hour angles at locations S1 and S2 66

Fig. 22 Schematic of normal and parallel force components of the weight of concentrator modules 67

Fig. 23 Distributions of von Mises equivalent stress in the lower long steel beam at hour angles of (a) 0o, (b) 30o, (c) 60o, and (d) 75o for the tilt angle of 24.5o under the effect of gravity alone 68

Fig. 24 Comparisons of calculated maximum von Mises stresses in the long steel beam under the effect of gravity alone at various hour angles for three different tilt angles 70

Fig. 25 Comparisons of maximum misalignment and normal displacement of concentrator modules under the effect of gravity only at various tilt angles: (a) 24.5o; (b) 1o; (c) 48o 71

Fig. 26 Distributions of normal displacement in Fresnel lenses at hour angles of (a) 0o, (b) 30o, (c) 60o, and (d) 75o for the tilt angle of 24.5o under the effect of gravity alone 73

Fig. 27 Distributions of normal displacement in Fresnel lenses under the effect of gravity alone: (a) at hour angle of 40o for the tilt angle of 1o; (b) at hour angle of 30o for the tilt angle of 48o 75

Fig. 28 Distributions of maximum von Mises equivalent stress in the long steel beam under the effect of a wind speed of 7 m/s with wind direction of 0o for tilt angles of (a) 24.5o, (b) 1o, and (c) 48o 76

Fig. 29 Distributions of maximum von Mises equivalent stress in the long steel beam under the effect of a wind speed of 12 m/s with wind directions of (a) 0o (hour angle of 20o), (b) 90o (hour angle of 30o), and (c) 180o (hour angle of 20o) for the tilt angle of 24.5o 78

Fig. 30 Comparison of calculated maximum von Mises stresses in the long steel beam at various hour angles under the effect of gravity alone and a wind speed of 12 m/s with three specified wind directions for the tilt angle of 24.5o 80

Fig. 31 Distributions of wind pressure on the concentrator modules under the effect of a wind speed of 12 m/s with directions of (a) 0o (hour angle of 0o), (b) 90o (hour angle of 50o), and (c) 180o (hour angle of 0o) for the tilt angle of 24.5o 81

Fig. 32 Comparisons of maximum misalignment and normal displacement of concentrator modules under the effect of a wind speed of 12 m/s with directions of (a) 0o, (b) 90o, and (c) 180o for the tilt angle of 24.5o 83

Fig. 33 Distributions of normal displacement in Fresnel lenses at hour angles of (a) 0o, (b) 30o, (c) 60o, and (d) 75o for the tilt angle of 24.5o under the effect of a wind speed of 12 m/s with direction of 90o 85

Fig. 34 Distributions of maximum von Mises equivalent stress in the long steel beam under the effect of a wind speed of 12 m/s with wind directions of (a) 0o (hour angle of 20o), (b) 90o (hour angle of 40o), and (c) 180o (hour angle of 30o) for the tilt angle of 1o 87

Fig. 35 Comparison of calculated maximum von Mises stresses in the long steel beam at various hour angles under the effect of gravity alone and a wind speed of 12 m/s with three specified wind directions for the tilt angle of 1o 89

Fig. 36 Distributions of wind pressure on the concentrator modules under the effect of a wind speed of 12 m/s with wind directions of (a) 0o (hour angle of 0o) and (b) 180o (hour angle of 75o) for the tilt angle of 1o 90

Fig. 37 Comparisons of maximum misalignment and normal displacement of concentrator modules under the effect of a wind speed of 12 m/s with directions of (a) 0o, (b) 90o, and (c) 180o for the tilt angle of 1o 91

Fig. 38 Distributions of normal displacement in Fresnel lenses at hour angles of (a) 0o, (b) 30o, (c) 60o, and (d) 75o for the tilt angle of 1o under the effect of a wind speed of 12 m/s with direction of 0o 93

Fig. 39 Distributions of normal displacement in Fresnel lenses at hour angles of (a) 0o, (b)330o, (c) 60o, and (d) 75o for the tilt angle of 1o under the effect of a wind speed of 12 m/s with direction of 90o 95

Fig. 40 Distributions of maximum von Mises equivalent stress in the long steel beam under the effect of a wind speed of 12 m/s with wind directions of (a) 0o (hour angle of 20o), (b) 90o (hour angle of 40o), and (c) 180o (hour angle of 30o) for the tilt angle of 48o 97

Fig. 41 Comparison of calculated maximum von Mises stresses in the long steel beam at various hour angles under the effect of gravity alone and a wind speed of 12 m/s with three specified wind directions for the tilt angle of 48o 99

Fig. 42 Distribution of wind pressure on the concentrator modules at hour angle of 0o under the effect of a wind speed of 12 m/s with wind direction of 180o for the tilt angle of 48o 100

Fig. 43 Comparisons of maximum misalignment and normal displacement of concentrator modules under the effect of a wind speed of 12 m/s with directions of (a) 0o, (b) 90o, and (c) 180o for the tilt angle of 48o 101

Fig. 44 Distributions of normal displacement in Fresnel lenses at hour angles of (a) 0o, (b)630o, (c) 60o, and (d) 75o for the tilt angle of 48o under the effect of a wind speed of 12 m/s with direction of 180o 103

Fig. 45 Schematic of (a) boundary conditions of the bottom surface and (b) an example of wind loadings on the selected concentrator module 105

參考文獻1. R. A. Messenger and J. Ventre, Photovoltaic Systems Engineering, 2nd Ed., CRC Press, Boca Raton, FL, USA, 2003.

2. A. Goetzberger and V. U. Hoffmann, Photovoltaic Solar Energy Generation, Springer, Berlin, Germany, 2005.

3. D. Y. Goswami, F. Kreith, and J. F. Kreider, Principles of Solar Engineering, 2nd Ed., Taylor & Francis, Philadelphia, PA, USA, 1999.

4. A. Luque and S. Hegedus, Handbook of Photovoltaic Science and Engineering, John Wiley & Sons Ltd., West Sussex, England, 2003.

5. T. Markvart and L. Castaňer, Solar Cells: Materials, Manufacture and Operation, Elsevier Ltd., Oxford, UK, 2005.

6. R. R. King, D. C. Law, K. M. Edmondson, C. M. Fetzer, F. S. Kinsey, H. Yoon, R. A. Sherif, and N. H. Karam, “40% Efficient Metamorphic GaInP/GaInAs/Ge Multijunction Solar Cells,” Applied Physics Letters, Vol. 90, pp. 183516-1-183516-3, 2007.

7. C. Baur, A. W. Bett, F. Dimroth, G. Siefer, M. Meusel, W. Bensch, W. Köstler, and G. Strobl, “Triple-Junction III-V Based Concentrator Solar Cells: Perspective and Challenges,” Journal of Solar Energy Engineering, Transactions of the ASME, Vol. 129, pp. 258-265, 2007.

8. M. Yamaguchi, T. Tatsuya, K. Araki, and N. Ekins-Daukes, “Multi-Junction III-V Solar Cells: Current Status and Future Potential,” Solar Energy, Vol. 79, pp. 78-85, 2005.

9. K. Nishioka, T. Takamoto, T. Agui, M. Kaneiwa, Y. Uraoka, and T. Fuyuki, “Evaluation of InGaP/InGaAs/Ge Triple-Junction Solar Cell and Optimization of Solar Cell’s Structure Focusing on Series Resistance for High-Efficiency Concentrator Photovoltaic Systems,” Solar Energy Materials and Solar Cells, Vol. 90, pp. 1308-1321, 2006.

10. A. Luque, G. Sala, and I. Lugue-Heredia, “Photovoltaic Concentration at Onset of its Commercial Deployment,” Progress in Photovoltaics: Research and Applications, Vol. 14, pp. 413-428, 2006.

11. A. L. Luque and V. M. Andreev, Concentrator Photovoltaics, Springer-Verlag, Berlin, Germany, 2007.

12. G. Willeke, “High Concentration Photovoltaic–State-of-the-Art and Novel Concepts,” pp. 2841-2844 in Proceeding of the 3rd World Conference on Photovoltaic Energy Conversion, May 11-18, Osaka, Japan, 2003.

13. K. Araki, H. Uozumi, M. Yamaguchi, and Y. Kemmoku, “Development of a New 550x Concentrator Module with 3J Cells Performance and Reliability,” in Proceeding of the 15th International Photovoltaic Science & Engineering Conference, October 10-15, Shanghai, China, 2005.

14. M. Hein, F. Dimroth, G. Siefer, and A. W. Bett, “Characterisation of a 300x Photovoltaic Concentrator System with One-Axis Tracking,” Solar Energy Materials & Solar Cells, Vol. 75, pp. 277-283, 2003.

15. K. Araki, “500X to 1000X-R&D and Market Strategy of Daido Steel,” in Proceeding of the 4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen, March 12-16, San Lorenzo del Escorial, Spain, 2007.

16. I. Lugue-Heredia, C. Martin, M. T. Mananes, J. M. Moreno, J. L. Auger, V. Bodin, J. Alonso, V. Diaz, and G. Sala, “A Subdegree Precision Sun Tracker for 1000x Microconcentrator Modules,” in Proceeding of the 3rd World Conference on Photovoltaic Energy Conversion, May 11-18, Osaka, Japan, 2003.

17. K. Ryu, J.-G. Rhee, K.-M. Park, and J. Kim, “Concept and Design of Modular Fresnel Lenses for Concentration Solar PV System,” Solar Energy, Vol. 80, pp. 1580-1587, 2006.

18. R. Leutz, A. Suzuki, A. Akisawa, and T. Kashiwagi, “Design of a Nonimaging Fresnel Lens for Solar Concentrators,” Solar Energy, Vol. 65, pp. 379-387, 1999.

19. A. Sarno, F. Apicella, M. Pellegrino, C. Privato, and F. Roca, “Enea’s Experience on the PV-Concentrators Technology: the PhoCUS Project,” in Proceeding of the 4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen, March 12-16, San Lorenzo del Escorial, Spain, 2007.

20. P. Gleckman, “A High Concentration Rooftop Photovoltaic System,” in Proceeding of the SPIE-The International Society for Optical Engineering, August 26-28, San Diego, CA, USA, 2007.

21. T. Markvart, Solar Electricity, 2nd Ed., John Wiley & Sons Ltd., West Sussex, England, 2000.

22. F. R. Rubio, M. G. Ortega, F. Gordillo, and M. López-Martínez, “Application of New Control Strategy for Sun Tracking,” Energy Conversion and Management, Vol. 48, pp. 2174-2184, 2007.

23. P. Roth, A. Georgiev, and H. Boudinov, “Design and Construction of a System for Sun Tracking,” Renewable Energy, Vol. 29, pp. 393-402, 2004.

24. P. Roth, A. Georgiev, and H. Boudinov, “Cheap Two Axis Sun Following Device,” Energy Conversion and Management, Vol. 46, pp. 1179-1192, 2005.

25. N. H. Helwa, A. B. G. Bahgat, A. M. R. E. Shafee, and E. T. E. Shenawy, “Maximum Collectable Solar Energy by Different Solar Tracking Systems,” Energy Sources, Vol. 22, pp. 23-34, 2000.

26. K. K. Chong and C. W. Wong, “General Formula for On-Axis Sun-Tracking System and its Application in Improving Tracking Accuracy of Solar Collector,” Solar Energy, Vol. 83, pp. 298-305, 2009.

27. I. Lugue-Heredia, P. H. Magalhães, G. Quéméré, R. Cervantes, J. M. Moreno, and O. Laurent, “CPV Tracking System: Performance Issues, Specifications and Design,” in Proceeding of the 4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen, March 12-16, San Lorenzo del Escorial, Spain, 2007.

28. M. Shademan and H. Hangan, “Wind loading on Solar Panels at Different Inclination Angles,” in Proceeding of the 11th American Conference on Wind Engineering, June 22-26, San Juan, Puerto Rico, 2009.

29. A. Fage and F. C. Johansen, “On the Flow of Air Behind an Inclined Flat Plate of Infinite Span,” Proceeding of the Royal Society of London, Series A, Vol. 116, pp. 170-197, 1927.

30. S. Hernández, J. Méndez, F. Nieto, and J. Á. Jurado, “Aerodynamic Analysis of a Photovoltaic Solar Tracker,” in Proceeding of the 5th European-African Conference on Wind Engineering, July 19-23, Florence, Italy, 2009.

31. N. Naeeni and M. Yaghoubi, “Analysis of Wind Flow Around a Parabolic Collector: (1) Fluid Flow,” Renewable Energy, Vol. 32, pp. 1898-1916, 2007.

32. I. Lugue-Heredia, G. Quéméré, P. H. Magalhães, A. F. de Lerma, L. Hermanns, E. de Alarcón, and A. Luque, “Modelling Structural Flexure Effects in CPV Sun Trackers,” pp. 2105-2109 in Proceeding of 21st European Photovoltaic Solar Energy Conference, September 4-8, Dresden, Germany, 2006.

33. C. Cancro, G. Graditi, G. Leanza, F. Pascarella, A. Sarno, and D. Mancini, “Field Testing of the PhoCUS Solar Tracker by Means of a Novel Optoelectronic Device,” in Proceeding of the 4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen, March 12-16, San Lorenzo del Escorial, Spain, 2007.

指導教授林志光(Chih-Kuang Lin) 審核日期2011-7-22 推文facebook plurk twitter funp google live udn HD myshare reddit netvibes friend youpush delicious baidu