光子学报  2017, Vol. 46 Issue (9): 0923004  DOI: 10.3788/gzxb20174609.0923004 0

### 引用本文

YIN Peng, XU Xi-ping, JIANG Zhao-guo, LV Jia-qi, GAO Shao-hua. Design and Analysis of Planar Solar Concentrator in Ray-leakage-free Respect[J]. Acta Photonica Sinica, 2017, 46(9): 0923004. DOI: 10.3788/gzxb20174609.0923004.

### 文章历史

(长春理工大学 光电工程学院, 长春 130022)

Design and Analysis of Planar Solar Concentrator in Ray-leakage-free Respect
YIN Peng, XU Xi-ping, JIANG Zhao-guo, LV Jia-qi, GAO Shao-hua
(College of Photoelectrical Engineering, Changchun University of Science and Technology, Changchun 130022, China)
Foundation item: The National Natural Science Foundation of China(No.61605016)
Abstract: Planar solar concentrator can provide dynamic concentration ratio, which has attracted researchers' attention.However, the decrease of the optical efficiency is not improved because of the rays-leakage from the lightguide.In order to hinder the decrease of optical efficiency from ray leakage, a new design method of the ray-leakage-free planar solar concentrator is proposed in this paper. According to the mathematical computation, refraction law and reflection law, the theoretical formula of the maximal ray-leakage-free propagating length in lightguide is derived. Furthermore, the mathematical model among the values of the parabola arbitrary coefficient, the vertex angle of air gap structure, the collector width, the collector height and the ray-leakage-free concentration ratio is established. The model of the proposed ray-leakage-free planar solar concentrator is simulated by the ray-tracing software. In consideration of Fresnel loss and material absorption, the concentration ratios of the proposed concentrators reach 698×, 857×and 1 032×with the corresponding optical efficiencies 88.2%, 85.3% and 80.2%, respectively, when the sunlight possess 0.27° divergence half angle; the concentration ratio increases further while the optical efficiency decreases slowly when the length of the lightguide exceeds the ray-leakage-free range.
Key words: Optical design    Concentration photovoltaics system    Non-imaging optics    Lightguide    Solar energy    Geometric optics    Characteristics of concentration
OCIS Codes: 230.5480;230.4040;220.0220;220.2740;220.4298;250.5460
0 引言

1 工作原理

 $y=a{{z}^{2}}\ \ \ \ \ \ \ \left( z\geqslant 1/2a \right)$ (1)
 图 1 主聚光器的修剪过程示意图 Fig.1 The schematic diagram of the changing collector

 ${{h}_{\min }}=3/4a$ (2)

 ${{h}_{\max }}=\frac{2\sqrt{\left( {{n}_{1}}+\sqrt{n_{1}^{2}-1} \right)/\left( {{n}_{1}}-\sqrt{n_{1}^{2}-1} \right)}-1}{4a}$ (3)

 ${R_{{\rm{max}}}} = \sqrt {{h^2} - \frac{{h + \sqrt {{\rm{4}}\mathit{h}{\rm{/}}a{\rm{ + }}{a^{{\rm{ - 2}}}}} }}{{2a}} + \frac{{17}}{{16{a^2}}}}$ (4)

 $\mathit{a}=2\rm{arctan }(\mathit{a}\cdot \rm{d}\mathit{x})$ (5)
 图 2 无漏光波导板的设计及光线传播路径 Fig.2 Design of the ray-leakage-free lightguide and the ray propagating path

 $\beta =\rm{arcsin}~\left( \mathit{a}\cdot \mathit{D}/\left( \rm{ }\sqrt{4\mathit{a}\cdot \mathit{h}+1}\rm{ }-1 \right) \right)$ (6)
 图 3 x-z平面边缘光线无漏光传播距离示意图 Fig.3 The schematic diagram of the edge-ray propagating length in x-z plane

 ${\mathit{L}_0} = \mathit{D}/{\rm{tan}}\ \beta$ (7)

 ${\delta _\mathit{n}} = \mathit{n}\cdot\mathit{\alpha } + \beta$ (8)
 ${\mathit{L}_\mathit{n}} = \mathit{D}\cdot{\rm{cot}}({\delta _\mathit{n}})$ (9)

 ${\mathit{\Phi }_{{\rm{in}}}} = \frac{\pi }{2} - {\delta _\mathit{n}} - \frac{\alpha }{2} \geqslant {\theta _\rm{c}}$ (10)

 $\mathit{N} \leqslant \frac{{\pi - \alpha - 2\beta - 2{\theta _\rm{c}}}}{{2\alpha }}$ (11)

 $\mathit{L} = {\mathit{L}_0} + \sum\nolimits_{n = 1}^N {{\mathit{L}_\mathit{n}} = } \frac{D}{{\tan \beta }}{\rm{ }} + \sum\nolimits_{n = 1}^N {\mathit{D} \cdot {\rm{cot}}\left( {\mathit{n}\cdot\alpha + \beta } \right)}$ (12)
2 无漏光最大聚光比的分析与讨论

 ${\rm{\eta }} = \frac{进入光电池的能量}{接收太阳能量}$ (13)

 ${\mathit{C}_{{\rm{geo}}}} = \mathit{L}/{\rm{d}}\mathit{y}$ (14)

 图 4 聚光比和反射次数与空气隙结构张角角度之间的关系 Fig.4 The relationship between the concentration ratio, reflection times and the vertex angle

 图 5 聚光比和反射次数与主聚光器高度之间的关系 Fig.5 The relationship between the concentration ratio, reflection times and the collector height

 图 6 聚光比和反射次数与主聚光器宽度之间的关系 Fig.6 The relationship between the concentration ratio, reflection times and the collector width
 图 7 光线在光波导板中的传播距离与反射次数关系 Fig.7 The schematic diagram of the relationship between the propagating length and the reflection times in the lightguide

1)Ni=Nj, LiLj

N值不变，L随着D值增大单调递减或者保持不变，如图 7(a)所示，这种情况较多发生在D值较大ΔD值较小时，首先ΔD的存在会从两方面影响光线在波导板中的传播距离：D值变大导致光线在两列空气隙结构之间传播的路径变长，意味着主聚光器宽度变大，最边缘入射光线与z轴的夹角β值变大，导致光线在每个空气隙结构上的入射角度变小.但是由于ΔD值很小，两次最边缘入射光线的β值相差不多，在每个空气隙结构入射的位置、入射角度和出射角度也相差不大，因此两次光线传播的路径几乎是相同的，所以导致第N次反射时两种情况的入射角均大于临界角.虽然D值的增加使得光线在同等入射角度情况下沿z方向传播的距离增大，但是由于D值的增大导致光线进入波导板的入射角β也有所增大，这使得光线在空气隙结构上的入射角度变小从而限制了光线在z方向的传播距离.当β增大对于传播距离的抑制作用大于D值增大对于传播距离的增加时，同样的反射次数下传播距离减小，即Li > Lj；当β增大对于传播距离的抑制作用等于D值增大对于传播距离的增加时，同样的反射次数下传播距离相同，即Li=Lj.

2)Ni > Nj, LiLj

3)Ni=Nj, Li < Lj

4)Ni > Nj, Li < Lj

 图 8 最大无漏光聚光比与主聚光器宽度和抛物线任意系数之间的关系 Fig.8 The relationship between the maximal concentration ratio, collector width and the arbitrary coefficient

3 软件仿真 3.1 无漏光实验仿真

 图 9 平板型无漏光太阳能聚光器光线追迹及聚光比变化曲线 Fig.9 Ray tracing of the planar ray-leakage-free solar concentrator and different concentration ratio curves
3.2 聚光比与聚光效率的关系

 $\bar \eta = \sum\nolimits_{i = 1}^M {{\eta _i} \cdot {S_i}/S}$ (15)

 $\eta ' = \sum\nolimits_{j = 1}^M {{{\bar \eta }_i} \cdot {\omega _i}}$ (16)

 图 10 不同主聚光器高度下，聚光比和聚光效率随着主聚光器宽度的变化 Fig.10 The concentration ratios and the optical efficiencies varying with the collector width in different collector heights

3.3 超出无漏光范围后聚光效率的下降

 图 11 不同主聚光器高度下，两种平板型聚光器超出无漏光范围后的聚光效率分布 Fig.11 The optical efficiency distribution of two kinds of planar concentrators out of the ray-leakage-free range in different collector heights

4 结论

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