1-kW級聚光型太陽追蹤器結構變形與追日偏差分析

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研究生：	方君元 June-Yuan Fang
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
指導教授：	林志光 Chih-Kuang Lin
口試委員:
學位類別：	碩士 Master
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
畢業學年度：	99
語文別：	英文
論文頁數：	120
中文關鍵詞：	太陽追蹤器、有限元素分析
外文關鍵詞：	solar tracker, finite element analysis
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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。

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.

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

                                

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