CN103314454A - 太阳能发电系统 - Google Patents

太阳能发电系统 Download PDF

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CN103314454A
CN103314454A CN2011800650790A CN201180065079A CN103314454A CN 103314454 A CN103314454 A CN 103314454A CN 2011800650790 A CN2011800650790 A CN 2011800650790A CN 201180065079 A CN201180065079 A CN 201180065079A CN 103314454 A CN103314454 A CN 103314454A
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solar
reflecting surface
solar generator
energy reflection
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CN103314454B (zh
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R·莫兰
H·查耶特
O·考斯特
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Solaero Solar Power Inc
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Zenith Solar Ltd
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    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01LSEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
    • H01L31/00Semiconductor devices sensitive to infrared radiation, light, electromagnetic radiation of shorter wavelength or corpuscular radiation and specially adapted either for the conversion of the energy of such radiation into electrical energy or for the control of electrical energy by such radiation; Processes or apparatus specially adapted for the manufacture or treatment thereof or of parts thereof; Details thereof
    • H01L31/04Semiconductor devices sensitive to infrared radiation, light, electromagnetic radiation of shorter wavelength or corpuscular radiation and specially adapted either for the conversion of the energy of such radiation into electrical energy or for the control of electrical energy by such radiation; Processes or apparatus specially adapted for the manufacture or treatment thereof or of parts thereof; Details thereof adapted as photovoltaic [PV] conversion devices
    • H01L31/054Optical elements directly associated or integrated with the PV cell, e.g. light-reflecting means or light-concentrating means
    • H01L31/0547Optical elements directly associated or integrated with the PV cell, e.g. light-reflecting means or light-concentrating means comprising light concentrating means of the reflecting type, e.g. parabolic mirrors, concentrators using total internal reflection
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24HEATING; RANGES; VENTILATING
    • F24SSOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S23/00Arrangements for concentrating solar-rays for solar heat collectors
    • F24S23/70Arrangements for concentrating solar-rays for solar heat collectors with reflectors
    • F24S2023/83Other shapes
    • F24S2023/832Other shapes curved
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24HEATING; RANGES; VENTILATING
    • F24SSOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S23/00Arrangements for concentrating solar-rays for solar heat collectors
    • F24S23/70Arrangements for concentrating solar-rays for solar heat collectors with reflectors
    • F24S23/80Arrangements for concentrating solar-rays for solar heat collectors with reflectors having discontinuous faces
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00Energy generation through renewable energy sources
    • Y02E10/50Photovoltaic [PV] energy
    • Y02E10/52PV systems with concentrators

Abstract

一种太阳能发电机,包括光伏发电元件的阵列,以及单个连续的平滑太阳能反射表面,所述表面被布置成将来自太阳的光反射到所述光伏发电元件的阵列上,其中,在所述阵列上每单位面积最小通量的点处的每单位面积通量约为在每单位面积最大通量的点处的每单位面积通量的75%,所述阵列的截断因子至少为70%,并且所述阵列的光学填充因子至少为60%。

Description

太阳能发电系统
相关申请的引用
参考了受让人所拥有的以下专利和专利申请,其公开内容通过引用并入本文:
美国公开专利申请No.2009/0065045;以及
于2008年9月10日提交的题为“SOLAR ELECTRICITY GENERATIONSYSTEM”的美国专利申请No.12/677,208。
技术领域
本发明涉及光伏发电。
背景技术
认为以下公开代表了本领域的现有技术:
美国专利No.4,195,913和5,153,780;
美国公开专利申请No.2009/0065045;
美国专利申请No.12/677,208;
Authier,B.和Hill,L在1980年的“High Concentration Solar Collector ofthe Stepped Spherical Type:Optical Design Characteristics”(Applied Optics,Vol19,No.20,pp.3554-3561)中讨论了使用适合于光伏发电的凹球面反射元件的聚能器;
Kurzweg,U.H.在1980年的“Characteristics of Axicon Concentrators forUse in Photovoltaic Energy Conversion”(Solar Energy,Vol.24,pp.411-412)中讨论了为光伏应用设计的聚能器;
Swanson,R.M在1988年7月的“Photovoltaic Dish Solar-ElectricGenerator”(Proceedings of the Joint Crystalline Cell Research,andConcentrating Collector Projects Review SAND88-0522,Sandia NationalLaboratories,Albuquerque,NM,pp.109-119)中讨论了与漫射器相结合的抛物柱面反射器。
发明内容
本发明寻求提供用于光伏发电的改进的系统。
因此,根据本发明的优选实施例提供了一种太阳能发电机,包括光伏发电元件的阵列,以及单个连续的平滑太阳能反射表面,所述表面被布置成将来自太阳的光反射到所述光伏发电元件的阵列上,其中,在所述阵列上每单位面积最小通量的点处的每单位面积通量约为在每单位面积最大通量的点处的每单位面积通量的75%,所述阵列的截断因子(intercept factor)至少为70%,并且所述阵列的光学填充因子至少为60%。
根据本发明的优选实施例,所述太阳能发电机还包括太阳能跟踪系统,所述太阳能跟踪系统用于使所述反射表面旋转并且定位成全天都对着太阳。优选地,所述太阳能发电机提供500-1000的太阳能辐射聚光比。另外,所述太阳能反射表面包括位于所述反射表面的中心处的顶点,并且所述反射表面被布置成大致上垂直于由所述顶点和所述阵列的中心所定义的轴。
优选地,所述阵列被布置在垂直于所述轴的平面中并且被定位成与所述太阳能反射表面相对。另外,将虚平面定义为在所述顶点处与所述轴垂直相交,并且与所述太阳能反射表面相切。
根据本发明的优选实施例,在所述反射表面与所述阵列之间存在太阳光线的唯一1:1映射。另外,所述反射表面的形状由数学函数z=f(x,y)来描述,其中,z是在虚平面上的一组坐标x,y与反射表面之间的距离,x和y分别是从坐标x,y到虚平面上的顶点的横向和纵向距离,经由以下微分方程在数学上获得f(x,y):
∂ f ( x , y ) ∂ x = x - g ( x ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2
∂ f ( x , y ) ∂ y = y - h ( y ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2 ;
其中:
g ( x ) = R x L x x , 其中 x ∈ [ - L x 2 , L x 2 ] ;
h ( y ) = R y L y y , 其中 y ∈ [ - L y 2 , L y 2 ] ;
d是所述轴和阵列的相交点与所述顶点之间的距离;
Rx是添加了2cm裕度(margin)的阵列的横向长度;
Ry是添加了2cm裕度的阵列的纵向长度;
Lx是反射表面在虚平面上的投影横向长度;以及
Ly是反射表面在虚平面上的投影纵向长度。
根据本发明的另一优选实施例还提供了一种太阳能发电机,包括光伏发电元件的阵列,以及形成为多个连续的平滑太阳能反射表面段的太阳能反射表面,每一个表面段被布置成将来自太阳的太阳能辐射的相互重叠的通量反射到光伏发电元件的阵列上。
根据本发明的优选实施例,所述太阳能反射表面被形成为四个连续的平滑太阳能反射表面段,其中,在所述阵列上每单位面积最小通量的点处的每单位面积通量约为在每单位面积最大通量的点处的每单位面积通量的90%,所述阵列的截断因子至少为75%,并且所述阵列的光学填充因子至少为70%。
优选地,所述太阳能发电机还包括太阳能跟踪系统,所述太阳能跟踪系统用于使所述反射表面旋转并且定位成全天都对着太阳。优选地,所述太阳能发电机提供500-1000的太阳能辐射聚光比。
根据本发明的优选实施例,所述太阳能反射表面包括位于所述反射表面的中心处的顶点,并且所述反射表面被布置成大致上垂直于由所述顶点和所述阵列的中心所定义的轴。另外,所述阵列被布置在垂直于所述轴的平面中并且被定位成与所述太阳能反射表面相对。另外,虚平面被定义为在所述顶点处与所述轴垂直相交,并且与所述太阳能反射表面相切。
优选地,所述太阳能反射表面段是对称的。优选地,所述太阳能反射表面段围绕所述轴对称地布置。
根据本发明的优选实施例,在四个连续的平滑太阳能反射表面段与所述阵列之间存在太阳光线的唯一4:1映射。另外,所述反射表面的形状由数学函数z=f(x,y)来描述,其中,z是在虚平面上的一组坐标x,y与反射表面之间的距离,x和y分别是从坐标x,y到虚平面上的顶点的横向和纵向距离,经由以下微分方程在数学上获得f(x,y):
∂ f ( x , y ) ∂ x = x - g ( x ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2
∂ f ( x , y ) ∂ y = y - h ( y ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2 ;
其中:
Figure BDA00003513612300043
Figure BDA00003513612300044
d是轴和阵列的相交点与所述顶点之间的距离;
Rx是添加了2cm裕度的阵列的横向长度;
Ry是添加了2cm裕度的阵列的纵向长度;
Lx是反射表面在虚平面上的投影横向长度;以及
Ly是反射表面在虚平面上的投影纵向长度。
根据本发明的再一优选实施例,还提供了一种太阳能发电机,包括光伏发电元件的阵列,以及形成为多个太阳能反射表面段的太阳能反射表面,所述多个太阳能反射表面段相对于所述反射表面的中心对称布置,每一个表面段被划分为多个连续的平滑太阳能反射表面子段,每一个表面子段被布置成将来自太阳的太阳能辐射的相互重叠的通量反射到光伏发电元件的阵列上。
根据本发明的优选实施例,所述太阳能反射表面形成为四个太阳能反射表面段,每一个表面段被划分为四个连续的平滑太阳能反射表面子段,其中,在所述阵列上每单位面积最小通量的点处的每单位面积通量约为在每单位面积最大通量的点处的每单位面积通量的60%,所述阵列的截断因子至少为80%,并且所述阵列的光学填充因子至少为60%。另外,在反射表面子段与所述阵列之间存在太阳光线的大致上唯一16:1映射。
根据本发明的优选实施例,所述太阳能反射表面被形成为四个太阳能反射表面段,每一个表面段被划分为81个连续的平滑太阳能反射表面子段,其中,在所述阵列上每单位面积最小通量的点处的每单位面积通量约为在每单位面积最大通量的点处的每单位面积通量的60%,所述阵列的截断因子至少为80%,并且所述阵列的光学填充因子至少为60%。另外,在反射表面子段与所述阵列之间存在太阳光线的大致上唯一81:1映射。
优选地,所述太阳能发电机还包括太阳能跟踪系统,所述太阳能跟踪系统用于使所述反射表面旋转并且定位成全天都对着太阳。优选地,所述太阳能发电机提供500-1000的太阳能辐射聚光比。
根据本发明的优选实施例,所述太阳能反射表面包括位于所述反射表面中心处的顶点,所述反射表面被布置成大致上垂直于由所述顶点和所述阵列的中心所定义的轴。另外,所述阵列被布置在垂直于所述轴的平面中并且被定位成与所述太阳能反射表面相对。另外,虚平面被定义为在所述顶点处与所述轴垂直相交,并与所述太阳能反射表面相切。优选地,所述太阳能反射表面段是对称的。
根据本发明的优选实施例,对于表面段的n×m个表面子段的矩阵,其中,各表面子段的坐标表示为k,j,其中k是在1与n之间的各表面子段的顺序,j是在1与m之间的各表面子段的顺序,在坐标k,j处的各表面子段的形状由数学函数z=f(x,y)来描述,其中,z是在虚平面上的一组坐标x,y与反射表面之间的距离,x和y分别是从坐标x,y到虚平面上的顶点的横向和纵向距离,经由以下微分方程在数学上获得f(x,y):
∂ f ( x , y ) ∂ x = x - g ( x ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2
∂ f ( x , y ) ∂ y = y - h ( y ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2 ;
其中:
Figure BDA00003513612300061
Figure BDA00003513612300062
d是轴和阵列的相交点与顶点之间的距离;
Rx是添加了2cm裕度的阵列的横向长度;
Ry是添加了2cm裕度的阵列的纵向长度;
Lx是反射表面在虚平面上的投影横向长度;及
Ly是反射表面在虚平面上的投影纵向长度。
附图说明
根据下面结合附图给出的详细说明,将会更充分地理解并领悟本发明,在附图中:
图1A是根据本发明优选实施例构建和操作的光伏太阳能发电机的简化示意图;
图1B是作为图1A的光伏太阳能发电机的一部分的大致上平滑的凹反射表面的简化示意图;
图1C是图1B的大致上平滑的凹反射表面的简化截面图;
图1D和1E一起是指令序列的示例,其用于计算图1A-1C的发电机的反射表面部分形状;
图1F&1G一起是
Figure BDA00003513612300064
指令的示例,其用于计算图1A-1E的发电机的反射表面的光学填充因子;
图1H是由图1A-1G的光伏太阳能发电机生成的反射辐射通量分布图的简化示意图;
图2A是根据本发明另一优选实施例构建和操作的光伏太阳能发电机的简化示意图;
图2B是作为图2A的光伏太阳能发电机的一部分的大致上平滑的凹反射表面的简化示意图;
图2C是图2B的大致上平滑的凹反射表面的简化截面图;
图2D与2E一起是
Figure BDA00003513612300071
指令序列的示例,其用于计算图2A-2C的发电机的反射表面部分形状;
图2F&2G一起是
Figure BDA00003513612300072
指令的示例,其用于计算图2A-2E的发电机的反射表面的光学填充因子;
图2H是由图2A-2G的光伏太阳能发电机生成的反射辐射通量分布图的简化示意图;
图3A是根据本发明再一优选实施例构建和操作的光伏太阳能发电机的简化示意图;
图3B是作为图3A的光伏太阳能发电机的一部分的大致上平滑的凹反射表面的简化示意图;
图3C是图3B的大致上平滑的凹反射表面的简化截面图;
图3D是由图3A的光伏太阳能发电机的一部分生成的反射辐射通量分布图的简化示意图;
图3E是由图3A的光伏太阳能发电机的另一部分生成的反射辐射通量分布图的简化示意图;
图3F与3G一起是
Figure BDA00003513612300073
指令序列的示例,其用于计算图3A-3E的发电机的反射表面部分形状;
图3H&3I一起是
Figure BDA00003513612300074
指令的示例,其用于计算图3A-3G的发电机的反射表面的光学填充因子;
图3J是由图3A-3I的光伏太阳能发电机生成的反射辐射通量分布图的简化示意图;
图4A是由根据本发明又一优选实施例构建和操作的光伏太阳能发电机的一部分生成的反射辐射通量分布图的简化示意图;
图4B是由图4A的光伏太阳能发电机生成的反射辐射通量分布图的简化示意图;
图4C与4D一起是
Figure BDA00003513612300075
指令序列的示例,其用于计算图4A和4B的发电机的反射表面部分形状;
图4E&4F一起是
Figure BDA00003513612300081
指令的示例,其用于计算图4A-4D的发电机的反射表面的光学填充因子;以及
图4G是由图4A的光伏太阳能发电机生成的反射辐射通量分布图的简化示意图。
具体实施方式
现在参考图1A和1B-1C,图1A是根据本发明优选实施例构建和操作的光伏太阳能发电机的简化示意图,并且图1B和1C分别是作为图1A的光伏太阳能发电机的一部分的大致上平滑的凹反射表面的简化示意图和截面图。
如本领域技术人员公知的,由串联连接的光伏电池阵列生成的总电流受到生成最微弱电流的光伏电池的限制。因此,希望所有电池生成大致上相等的电流。应该意识到,由单个光伏电池所生成的电流通常与所吸收的太阳能辐射的量成比例,因此希望阵列中的所有电池都吸收大致上等量的太阳能辐射。
同样如本领域技术人员公知的,单个光伏电池上的入射辐射的非均匀通量导致光伏电池的发电效率减小。因此,希望在每一单个光伏电池上以及在整个阵列上实现均匀的辐射通量。
如图1A所示,提供了一种光伏太阳能发电机100,其具有单个连续大致上平滑的凹反射表面102,所述凹反射表面102安装在太阳能跟踪系统104上,所述太阳能跟踪系统104例如是
Figure BDA00003513612300082
SFC30追踪系统,可以从德国的PAIRAN Elektronik GmbH of
Figure BDA00003513612300083
购买到。光伏太阳能发电机100还包括定位成与反射表面102相对的平坦光伏模块106,所述光伏模块106包括诸如SPECTROLAB CDO-100-C3MJ Concentrator Solar Cells的多个光伏电池,其可以从加利福尼亚的SPECTROLAB Inc.of Sylmar购买到。反射表面102将大致上均匀的太阳能辐射的通量反射到位于反射表面102对面的平坦光伏模块106上,优选定义500-1000的聚光比,从而反射表面102与光伏模块106之间的最佳距离由反射表面102的形状来确定,如下文将解释的。
可以通过系统的光学填充因子来测量入射到光伏电池阵列上的辐射通量的均匀性。因此本发明的目的在于实现系统的最大光学填充因子。
在全文中,术语光伏电池阵列的“光学填充因子”被定义为表示在如果入射辐射的通量与接收最低水平入射辐射的阵列上的点处的入射辐射的水平相匹配的水平是均匀的情况下,应当入射到阵列上的辐射的量与实际入射到阵列上的辐射的总量之间的比率。该比率在图1A中示出为面积A与面积A和B的组合之间的比率。
除了实现入射到光伏电池阵列上的辐射的通量的最大均匀性以外,本发明的目的在于使得系统的截断因子最大化。在全文中,术语“截断因子”被定义为表示由表面反射的入射到接收器的吸收表面上的辐射的分数。
同样如图1A中所示,表面102的第一曲轴(curved axis)108在位于表面102的中心的顶点116处与表面102的第二曲轴110垂直相交。
如图1B和1C中所示以及如上所述,反射表面102将大致上均匀的太阳能辐射的通量反射到平坦光伏模块106上。还如图1C中所示,反射表面102被布置成大致上垂直于由顶点116与光伏模块106定义的轴118,从而在与轴118垂直的平面中相对于轴118对称布置光伏模块106。太阳能跟踪系统104用于使反射表面102旋转并且定位成全天都对着太阳,从而使轴118与太阳对准。平面120被定义为在顶点116处与轴118垂直相交。
本发明的这个实施例的特定特征是被成形为单个连续大致上平滑的凹反射表面102,使得太阳光线的唯一1:1映射存在于反射表面102与光伏模块106之间。
反射表面102的形状可以由数学函数z=f(x,y)来描述,其中,z是在平面120上的一组坐标x,y与反射表面102之间的距离,其中坐标x和y是在将轴108和110投影到平面120上时相对于顶点116的距离。
现在参考图1D和1E以及图1F&1G,图1D和1E一起是
Figure BDA00003513612300091
指令序列的示例,其用于计算图1A-1C的发电机的反射表面部分形状,并且图1F&1G一起是
Figure BDA00003513612300092
指令的示例,其用于计算图1A-1E的发电机的反射表面的光学填充因子。
可以经由以下微分方程获得f(x,y):
∂ f ( x , y ) ∂ x = x - g ( x ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2
∂ f ( x , y ) ∂ y = y - h ( y ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2 ;
其中:
g ( x ) = R x L x x , 其中 x ∈ [ - L x 2 , L x 2 ] ;
h ( y ) = R y L y y , 其中 y ∈ [ - L y 2 , L y 2 ] ;
d是轴118和平坦光伏模块106的相交点与顶点116之间的距离;
Rx是添加了2cm裕度的光伏模块106的横向长度;
Ry是添加了2cm裕度的光伏模块106的纵向长度;
Lx是轴108在平面120上的投影长度;及
Ly是轴110在平面120上的投影长度。
使用图1D和1E中所示的
Figure BDA00003513612300107
指令序列,可以经由以上方程在数学上获得针对反射表面102的一个象限的f(x,y)。由于反射表面102的对称性,使用以上针对单个象限的计算可以外推针对表面102的剩余象限的f(x,y)。
例如,对于单个连续大致上平滑的凹反射表面102,在此Lx=Ly=3.46米,距离d是2米,光伏模块106的尺寸是10×10厘米,z的值被计算为在位于顶点116的0与位于反射表面102的每一个角处的73.5厘米之间变化。入射到光伏模块106上的太阳能辐射的总通量计算约为833sun,从而在每单位面积最小通量的光伏模块106上的点处的每单位面积通量约为在每单位面积最大通量的光伏模块106上的点处的每单位面积通量的75%。光伏模块106的截断因子计算为不小于70%,光学填充因子计算为不小于60%。
使用图1F&1G中所示的
Figure BDA00003513612300108
指令序列来计算光学填充因子,其利用了图1D&1E中所示的f(x,y)的计算。
应该理解,尽管图1A-1C将反射表面102示出为整体反射表面,出于例如与制造和运输有关的考虑,本发明替换实施例可以包括组装形成反射表面102的多个表面段。
图1H是由图1A-1G的光伏太阳能发电机在平坦光伏模块106上生成的反射辐射通量分布图的简化示意图。如图1H中所示,在平坦光伏模块106上生成的反射辐射通量分布图在整个光伏模块106上就强度而言大致上是均匀的,在其边缘处急剧减小。
现在参考图2A以及2B和2C,图2A是根据本发明另一优选实施例构建和操作的光伏太阳能发电机的简化示意图,图2B和2C分别是作为图2A的光伏太阳能发电机的一部分的大致上平滑的凹反射表面的简化示意图和截面图。
如图2A中所示,提供了一种光伏太阳能发电机200,其具有大致上平滑的凹反射表面202,所述凹反射表面202安装在太阳能跟踪系统204上,所述太阳能跟踪系统204例如是
Figure BDA00003513612300111
SFC30追踪系统,可以从德国的PAIRAN Elektronik GmbH of
Figure BDA00003513612300112
购买到。光伏太阳能发电机200还包括定位成与反射表面202相对的平坦光伏模块206,所述光伏模块206包括诸如SPECTROLAB CDO-100-C3MJ Concentrator Solar Cells的多个光伏电池,其可以从加利福尼亚的SPECTROLAB Inc.of Sylmar购买到。反射表面202将大致上均匀的太阳能辐射的通量反射到位于反射表面202对面的平坦光伏模块206上,优选定义500-1000的聚光比,从而反射表面202与光伏模块206之间的最佳距离由反射表面202的形状来确定,如下文将解释的。
同样如图2A中所示,表面202的第一曲轴208与表面202的第二曲轴210垂直相交。轴208与轴210将反射表面202划分为四个平面对称且连续大致上平滑的凹反射表面段212。由轴208与210的相交点来定义顶点216。
如图2B和2C中所示以及如上所述,反射表面202将大致上均匀的太阳能辐射的通量反射到平坦光伏模块206上。同样如图2C中所示,反射表面202被布置成大致上垂直于由顶点216与光伏模块206定义的轴218,从而在与轴218垂直的平面中相对于轴218对称布置光伏模块206。太阳能跟踪系统204用于使反射表面202旋转并且定位成全天都对着太阳,从而使轴218与太阳对准。平面220被定义为在顶点216处与轴218垂直相交。
本发明的这个实施例的特定特征是反射表面202被成形使得太阳光线的4:1映射存在于四个连续大致上平滑的凹反射表面段212与光伏模块106之间。即使在一个反射表面段212的有限区域受损的情况下,这种布置也提供了在光伏模块206上的大致上均匀的太阳能辐射的通量,从而光伏模块206接收四个重叠且大致上均匀分布的太阳能辐射的通量。
反射表面202的形状可以由数学函数z=f(x,y)来描述,其中,z是在平面220上的一组坐标x,y与反射表面202之间的距离,其中坐标x和y是将轴208和210投影到平面220上时相对于顶点216的距离。
现在参考图2D和2E以及图2F&2G,图2D和2E一起是
Figure BDA00003513612300121
指令序列的示例,其用于计算图2A-2C的发电机的反射表面部分形状,图2F&2G一起是
Figure BDA00003513612300122
指令的示例,其用于计算图2A-2E的发电机的光学填充因子。
可以经由以下微分方程获得f(x,y):
∂ f ( x , y ) ∂ x = x - g ( x ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2
∂ f ( x , y ) ∂ y = y - h ( y ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2 ;
其中:
Figure BDA00003513612300126
d是轴218和平坦光伏模块206的相交点与顶点216之间的距离;
Rx是添加了2cm裕度的光伏模块206的横向长度;
Ry是添加了2cm裕度的光伏模块206的纵向长度;
Lx是轴208在平面220上的投影长度;以及
Ly是轴210在平面220上的投影长度。
使用图2D和2E中所示的
Figure BDA00003513612300127
指令序列,可以经由以上方程在数学上获得针对反射表面202的一个象限的f(x,y)。由于反射表面202的对称性,可以使用以上针对单个象限的计算外推针对表面202的剩余象限的f(x,y)。
例如,对于反射表面202,其中Lx=Ly=3.46米,距离d是2米,光伏模块206的尺寸是10×10厘米,z的值被计算为在顶点216处的0与反射表面202的每一个角处的76.5厘米之间变化。入射到光伏模块206上的太阳能辐射的总通量被计算约为833sun,从而在每单位面积最小通量的光伏模块206上的点处的每单位面积通量约为在每单位面积最大通量的光伏模块206上的点处的每单位面积通量的90%。光伏模块206的截断因子被计算为不小于75%,光学填充因子被计算为不小于70%。
使用图2F&2G中所示的
Figure BDA00003513612300131
指令序列来计算光学填充因子,其利用了图2D&2E中所示的f(x,y)的计算。
图2H是由图2A-2G的光伏太阳能发电机在平坦光伏模块206上生成的反射辐射通量分布图的简化示意图,如图2H中所示,在平坦光伏模块206上生成的反射辐射通量分布图在整个光伏模块206上就强度而言大致上是均匀的,在其边缘急剧减小。
现在参考图3A以及3B和3C,图3A是根据本发明再一优选实施例构建和操作的光伏太阳能发电机的简化示意图,图3B和3C分别是作为图3A的光伏太阳能发电机的一部分的大致上平滑的凹反射表面的简化示意图和截面图。
如图3A中所示,提供了一种光伏太阳能发电机300,其具有大致上平滑的凹反射表面302,所述凹反射表面302安装在太阳能跟踪系统304上,所述太阳能跟踪系统304例如是
Figure BDA00003513612300132
SFC30追踪系统,可以从德国的PAIRAN Elektronik GmbH of
Figure BDA00003513612300133
购买到。光伏太阳能发电机300还包括定位成与反射表面302相对的平坦光伏模块306,所述光伏模块306包括诸如SPECTROLAB CDO-100-C3MJ Concentrator Solar Cells的多个光伏电池,其可以从加利福尼亚的SPECTROLAB Inc.of Sylmar购买到。反射表面302将大致上均匀的太阳能辐射的通量反射到位于反射表面302对面的平坦光伏模块306上,优选定义500-1000的聚光比,从而反射表面302与光伏模块306之间的最佳距离由反射表面302的形状来确定,如下文将解释的。
同样如图3A中所示,表面302的第一曲轴308与表面302的第二曲轴310垂直相交。轴308与轴310将反射表面302划分为四个平面对称且大致上凹反射表面段312。四个反射表面段312中的每一个都进一步划分为四个尺寸大致上相等的反射表面子段314。由轴308与310的相交点来定义顶点316。
如图3B和3C中所示以及如上所述,反射表面302将大致上均匀的太阳能辐射的通量反射到平坦光伏模块306上。同样如图3C中所示,反射表面302被布置成大致上垂直于由顶点316与光伏模块306定义的轴318,从而在与轴318垂直的平面中相对于轴318对称布置光伏模块306。太阳能跟踪系统304用于使反射表面302旋转并且定位成全天都对着太阳,从而使轴318与太阳对准。平面320被定义为在顶点316处与轴318垂直相交。
本发明的这个实施例的特定特征是反射表面302被成形为使得太阳光线的4:1映射存在于与顶点316相邻的四个反射表面子段314与光伏模块106之间,从而与顶点316相邻的四个反射表面子段314中的每一个都将大致上等量的太阳能辐射反射到光伏模块306上,从而在光伏模块306上生成大致上均匀的太阳能辐射的通量。即使在与顶点316相邻的四个反射表面子段314中的一个的有限区域受损的情况下,这种布置也提供了在光伏模块306上的大致上均匀的太阳能辐射的通量,从而光伏模块306接收四个重叠且大致上均匀分布的太阳能辐射的通量。
现在参考图3D和图3E,图3D是由与顶点316相邻的四个反射表面子段314中的一个在光伏模块306上生成的反射辐射通量分布图的简化示意图,并且是图3A的光伏太阳能发电机的一部分,图3E是由与顶点316不相邻的12个反射表面子段314中的一个在光伏模块306上生成的反射辐射通量分布图的简化示意图,并且是图3A的光伏太阳能发电机的一部分。
除了在与顶点316相邻的四个反射表面子段314与平坦光伏模块306之间的上述4:1映射之外,反射表面302的形状还提供了在与顶点316不相邻的12个反射表面子段314中的每一个与平坦光伏模块306之间的映射。与顶点316不相邻的12个反射表面子段314中的每一个都将大致上相等且重叠的太阳能辐射的通量反射到平坦光伏模块306上,从而在平坦光伏模块306上生成额外的大致上均匀的太阳能辐射的通量,其叠加到由与顶点316相邻的四个反射表面子段314反射的大致上均匀的太阳能辐射的通量上。然而,如图3D和3E中所示,由与顶点316不相邻的12个反射表面子段314中的一个生成的辐射通量分布图没有完全叠加到由与顶点316相邻的四个反射表面子段314生成的辐射通量分布图上。
反射表面302的形状可以由数学函数z=f(x,y)来描述,其中,z是在平面320上的一组坐标x,y与反射表面302之间的距离,其中坐标x和y是将轴308和310投影到平面320时相对于顶点316的距离。
现在参考图3F和3G以及图3H&3I,图3F和3G一起是
Figure BDA00003513612300151
指令序列的示例,其用于计算图3A-3E的发电机的反射表面部分形状,图3H&3I一起是
Figure BDA00003513612300152
指令的示例,其用于计算图3A-3G的发电机的光学填充因子。
可以经由以下微分方程获得f(x,y):
∂ f ( x , y ) ∂ x = x - g ( x ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2
∂ f ( x , y ) ∂ y = y - h ( y ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2 ;
其中:
Figure BDA00003513612300156
d是轴318和平坦光伏模块306的相交点与顶点316之间的距离;
Rx是添加了2cm裕度的光伏模块306的横向长度;
Ry是添加了2cm裕度的光伏模块306的纵向长度;
Lx是轴308在平面320上的投影长度;以及
Ly是轴310在平面320上的投影长度。
使用图3F和3G中所示的指令序列,可以经由以上方程在数学上获得针对反射表面302的一个象限的f(x,y)。由于反射表面302的对称性,使用以上针对单个象限的计算可以外推针对表面302的剩余象限的f(x,y)。
例如,对于反射表面302,其中Lx=Ly=3.46米,距离d是2米,光伏模块306的尺寸是10×10厘米,z的值被计算为在顶点316处的0与反射表面302的每一个角处的75.5厘米之间变化。入射到光伏模块306上的太阳能辐射的通量计算约为833sun,由此,在每单位面积最小通量的光伏模块306上的点处的每单位面积通量约为在每单位面积最大通量的光伏模块306上的点处的每单位面积通量的60%。光伏模块306的截断因子被计算为不小于80%,光学填充因子被计算为不小于60%。
使用图3H&3I中所示的
Figure BDA00003513612300162
指令序列来计算光学填充因子,其利用了图3F&3G中所示的f(x,y)的计算。
图3J是由图3A-3I的光伏太阳能发电机在平坦光伏模块306上生成的反射辐射通量分布图的简化示意图,如图3J中所示,在平坦光伏模块306上生成的反射辐射通量分布图在整个光伏模块306上就强度而言大致上是均匀的,在其边缘急剧减小。
应该理解,在本发明的替代实施例中,可以将反射表面段312划分为任意数量的尺寸大致上相等的反射表面子段,生成表面子段的矩阵,其中,每一个表面子段都大于平坦光伏模块306,从而每一个表面子段都将大致上相等且重叠的大致上均匀的太阳能辐射的通量反射到光伏模块306上。应该注意,尽管与顶点316相邻的表面子段将大致上相等且重叠的太阳能辐射的通量反射到整个光伏模块306上,但与顶点316不相邻的表面子段反射不完全重叠并且没有覆盖整个光伏模块306的太阳能辐射。
对于n×m个表面子段的矩阵,其中,n是沿轴308从顶点316到表面段312的边缘的子段数量,m是沿轴310从顶点316到表面段312的边缘的子段数量,并且
Figure BDA00003513612300171
单个表面子段的坐标表示为k,j,其中,k是在1与n之间的在轴308上的单个表面子段的顺序,j是在1与m之间的在轴310上的单个表面子段的顺序。
在坐标k,j处的单个表面子段的形状可以由数学函数zk,j=f(x,y)来描述,其中,zk,j是在平面320上的一组坐标x,y与反射表面302之间的距离,其中坐标x和y是将轴308和310投影到平面320上时相对于顶点316距离。
通过使用以下的导数可以在数学上获得f(x,y):
∂ f ( x , y ) ∂ x = x - g ( x ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2
∂ f ( x , y ) ∂ y = y - h ( y ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2 ;
其中:
Figure BDA00003513612300174
Figure BDA00003513612300175
d是轴318和平坦光伏模块306的相交点与顶点316之间的距离;
Rx是添加了2cm裕度的光伏模块306的横向长度;
Ry是添加了2cm裕度的光伏模块306的纵向长度;
Lx是轴308在平面320上的投影长度;及
Ly是轴310在平面320上的投影长度。
例如,对于包括反射表面302的实施例,其中Lx=Ly=3.46米,距离d是2米,光伏模块306的尺寸是10×10厘米,四个反射表面段312中的每一个都进一步被划分为9×9个尺寸大致上相等的反射表面子段的矩阵,z的值被计算为在顶点316处的0与反射表面302的每一个角处的75.6厘米之间变化。入射到光伏模块306上的太阳能辐射的通量计算约为833sun,从而在每单位面积最小通量的光伏模块306上的点处的每单位面积通量约为在每单位面积最大通量的光伏模块306上的点处的每单位面积通量的60%。光伏模块306的截断因子被计算为不小于80%,光学填充因子被计算为不小于60%。以下结合图4A-4C来进一步说明这个实施例。
现在参考图4A和图4B,图4A是由根据本发明又一优选实施例构建和操作的光伏太阳能发电机的一部分生成的反射辐射通量分布图的简化示意图,图4B是由图4A的光伏太阳能发电机生成的反射辐射通量分布图的简化示意图。
在图4A和4B的实施例中,大致上平滑的凹反射表面的两条垂直相交的曲轴将反射表面划分为四个平面对称且大致上凹反射表面段。四个反射表面段中的每一个都进一步被划分为81个尺寸大致上相等的反射表面子段的9×9矩阵。
图4A示出了由四个反射表面段中的一个在作为太阳能发电机一部分的光伏模块上生成的反射辐射通量分布图。如图4A中所示,由四个反射表面段中的一个生成的反射辐射通量分布图在光伏模块上大致上是均匀的,但不是完全均匀的。经由由四个反射表面段中的一个的81个尺寸大致上相等的反射表面子段生成的81个大致上重叠的辐射的通量提供辐射通量分布。即使在81个子段中的一个的有限区域受损的情况下,这种布置也提供了在光伏模块上的大致上均匀的太阳能辐射的通量,从而光伏模块接收81个重叠并且大致上均匀分布的太阳能辐射的通量。
图4B示出了由作为太阳能发电机的一部分的光伏模块上的整个反射表面生成的反射辐射通量分布图。如图4B中所示,由整个反射表面生成的反射辐射通量分布图在光伏模块上是大致上均匀的。即使在四个反射表面段中的一个的有限区域受损的情况下,这种布置也提供了在光伏模块上的大致上均匀的太阳能辐射的通量,从而光伏模块接收由四个反射表面段提供的四个重叠并且大致上均匀分布的太阳能辐射的通量。
现在参考图4C、4D以及图4E&4F,图4C和4D一起作为
Figure BDA00003513612300181
指令序列的示例,其用于计算图4A和4B的发电机的反射表面部分形状,图4E&4F一起作为指令的示例,其用于计算图4A-4D的发电机的光学填充因子。
使用图4C和4D中所示的
Figure BDA00003513612300192
指令序列,可以经由如上所示的描述zk,j=f(x,y)的微分方程来获得zk,j。使用图4E&4F中所示的
Figure BDA00003513612300193
指令序列来计算光学填充因子,其利用了图4C&4D中所示的f(x,y)的计算。
图4G是由图4A-4F的光伏太阳能发电机在平坦光伏模块上生成的反射辐射通量分布图的简化示意图。如图4G中所示,在平坦光伏模块上生成的反射辐射通量分布图在整个光伏模块上就强度而言大致上是均匀的,在其边缘急剧减小。
本领域技术人员应该理解,本发明不限于上文中具体所示和所述的。相反地,本发明的范围包括现有技术中所没有的上文所述的多个特征及其变化和修改的组合和子组合。

Claims (31)

1.一种太阳能发电机,包括:
光伏发电元件的阵列;以及
单个连续的平滑太阳能反射表面,所述表面被布置成将来自太阳的光反射到所述光伏发电元件的阵列上;
其中:
在所述阵列上每单位面积最小通量的点处的每单位面积通量约为在每单位面积最大通量的点处的每单位面积通量的75%;
所述阵列的截断因子至少为70%;并且
所述阵列的光学填充因子至少为60%。
2.根据权利要求1所述的太阳能发电机,其中,所述太阳能发电机还包括太阳能跟踪系统,所述太阳能跟踪系统用于使所述反射表面旋转并且定位成全天都对着太阳。
3.根据权利要求1和2中的任一项所述的太阳能发电机,其中,所述太阳能发电机提供500-1000的太阳能辐射聚光比。
4.根据权利要求1-3中的任一项所述的太阳能发电机,其中:
所述太阳能反射表面包括位于所述反射表面中心处的顶点;并且
所述反射表面被布置成大致上垂直于由所述顶点和所述阵列的中心定义的轴。
5.根据权利要求4所述的太阳能发电机,其中,所述阵列被布置在垂直于所述轴的平面中并且被定位成与所述太阳能反射表面相对。
6.根据权利要求4和5中的任一项所述的太阳能发电机,其中,虚平面被定义为在所述顶点处与所述轴垂直相交,并且与所述太阳能反射表面相切。
7.根据权利要求1-6中的任一项所述的太阳能发电机,其中,在所述反射表面与所述阵列之间存在太阳光线的唯一1:1映射。
8.根据权利要求6和7中的任一项所述的太阳能发电机,其中,所述反射表面的形状由数学函数z=f(x,y)来描述,其中:
z是在所述虚平面上的一组坐标x,y与所述反射表面之间的距离;
x和y分别是从坐标x,y到所述虚平面上的所述顶点的横向和纵向距离;并且
经由以下微分方程在数学上获得f(x,y):
∂ f ( x , y ) ∂ x = x - g ( x ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2
∂ f ( x , y ) ∂ y = y - h ( y ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2 ;
其中:
g ( x ) = R x L x x , 其中 x ∈ [ - L x 2 , L x 2 ] ;
h ( y ) = R y L y y , 其中 y ∈ [ - L y 2 , L y 2 ] ;
d是所述轴和所述阵列的相交点与所述顶点之间的距离;
Rx是添加了2cm裕度的所述阵列的横向长度;
Ry是添加了2cm裕度的所述阵列的纵向长度;
Lx是所述反射表面在所述虚平面上的投影横向长度;以及
Ly是所述反射表面在所述虚平面上的投影纵向长度。
9.一种太阳能发电机,包括:
光伏发电元件的阵列;以及
太阳能反射表面,其形成为多个连续的平滑太阳能反射表面段,所述表面段中的每一个被布置成以将来自太阳的太阳能辐射的相互重叠的通量反射到所述光伏发电元件的阵列上。
10.根据权利要求9所述的太阳能发电机,其中:
所述太阳能反射表面被形成为四个连续的平滑太阳能反射表面段,并且其中:
在所述阵列上每单位面积最小通量的点处的每单位面积通量约为在每单位面积最大通量的点处的每单位面积通量的90%;
所述阵列的截断因子至少为75%;并且
所述阵列的光学填充因子至少为70%。
11.根据权利要求9和10中的任一项所述的太阳能发电机,其中,所述太阳能发电机还包括太阳能跟踪系统,所述太阳能跟踪系统用于使所述反射表面旋转并且定位成全天都对着太阳。
12.根据权利要求9-11中的任一项所述的太阳能发电机,其中,所述太阳能发电机提供500-1000的太阳能辐射聚光比。
13.根据权利要求9-12中的任一项所述的太阳能发电机,其中:
所述太阳能反射表面包括位于所述反射表面的中心处的顶点;并且
所述反射表面被布置成大致上垂直于由所述顶点和所述阵列的中心定义的轴。
14.根据权利要求13所述的太阳能发电机,其中,所述阵列被布置在垂直于所述轴的平面中并且被定位成与所述太阳能反射表面相对。
15.根据权利要求13和14中的任一项所述的太阳能发电机,其中,虚平面被定义为在所述顶点处与所述轴垂直相交,并且与所述太阳能反射表面相切。
16.根据权利要求9-15中的任一项所述的太阳能发电机,其中,所述太阳能反射表面段是对称的。
17.根据权利要求13-16中的任一项所述的太阳能发电机,其中,所述太阳能反射表面段围绕所述轴对称地布置。
18.根据权利要求10-17中的任一项所述的太阳能发电机,其中,在所述四个连续的平滑太阳能反射表面段与所述阵列之间存在太阳光线的唯一4:1映射。
19.根据权利要求13-18中的任一项所述的太阳能发电机,其中,所述反射表面的形状由数学函数z=f(x,y)来描述,其中,
z是在所述虚平面上的一组坐标x,y与所述反射表面之间的距离,
x和y分别是从坐标x,y到所述虚平面上的所述顶点的横向和纵向距离;并且
经由以下微分方程在数学上获得f(x,y):
∂ f ( x , y ) ∂ x = x - g ( x ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2
∂ f ( x , y ) ∂ y = y - h ( y ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2 ;
其中:
Figure FDA00003513612200043
Figure FDA00003513612200044
d是所述轴和所述阵列的相交点与所述顶点之间的距离;
Rx是添加了2cm裕度的所述阵列的横向长度;
Ry是添加了2cm裕度的所述阵列的纵向长度;
Lx是所述反射表面在所述虚平面上的投影横向长度;以及
Ly是所述反射表面在所述虚平面上的投影纵向长度。
20.一种太阳能发电机,包括:
光伏发电元件的阵列;以及
太阳能反射表面,其形成为围绕所述反射表面的中心对称布置的多个太阳能反射表面段,所述表面段中的每一个被划分为多个连续的平滑太阳能反射表面子段,所述表面子段中的每一个被布置成将来自太阳的太阳能辐射的相互重叠的通量反射到所述光伏发电元件的阵列上。
21.根据权利要求20所述的太阳能发电机,其中:
所述太阳能反射表面形成为四个太阳能反射表面段,所述表面段中的每一个被划分为四个连续的平滑太阳能反射表面子段,并且其中:
在所述阵列上每单位面积最小通量的点处的每单位面积通量约为在每单位面积最大通量的点处的每单位面积通量的60%;
所述阵列的截断因子至少为80%;并且
所述阵列的光学填充因子至少为60%。
22.根据权利要求21所述的太阳能发电机,其中,所述反射表面子段与所述阵列之间存在太阳光线的大致上唯一16:1映射。
23.根据权利要求20所述的太阳能发电机,其中:
所述太阳能反射表面形成为四个太阳能反射表面段,所述表面段中的每一个被划分为81个连续的平滑太阳能反射表面子段,并且其中:
在所述阵列上每单位面积最小通量的点处的每单位面积通量约为在每单位面积最大通量的点处的每单位面积通量的60%;
所述阵列的截断因子至少为80%;并且
所述阵列的光学填充因子至少为60%。
24.根据权利要求23所述的太阳能发电机,其中,在所述反射表面子段与所述阵列之间存在太阳光线的大致上唯一81:1映射。
25.根据权利要求20-24中的任一项所述的太阳能发电机,其中,所述太阳能发电机还包括太阳能跟踪系统,所述太阳能跟踪系统用于使所述反射表面旋转并且定位成全天都对着太阳。
26.根据权利要求20-25中的任一项所述的太阳能发电机,其中,所述太阳能发电机提供500-1000的太阳能辐射聚光比。
27.根据权利要求20-26中的任一项所述的太阳能发电机,其中:
所述太阳能反射表面包括位于所述反射表面的中心处的顶点;并且
所述反射表面被布置成大致上垂直于由所述顶点和所述阵列的中心定义的轴。
28.根据权利要求27所述的太阳能发电机,其中,所述阵列被布置在垂直于所述轴的平面中并且被定位成与所述太阳能反射表面相对。
29.根据权利要求27-28中的任一项所述的太阳能发电机,其中,虚平面被定义为在所述顶点处与所述轴垂直相交,并且与所述太阳能反射表面相切。
30.根据权利要求20-29中的任一项所述的太阳能发电机,其中,所述太阳能反射表面段是对称的。
31.根据权利要求20-30中的任一项所述的太阳能发电机,其中,对于表面段的n×m个表面子段的矩阵,其中各表面子段的坐标表示为k,j,其中k是在1与n之间的所述各表面子段的顺序,j是在1与m之间的所述各表面子段的顺序,在坐标k,j处的各表面子段的形状由数学函数z=f(x,y)来描述,其中:
z是在所述虚平面上的一组坐标x,y与所述反射表面之间的距离;
x和y分别是从坐标x,y到所述虚平面上的所述顶点的横向和纵向距离;
并且
经由以下微分方程在数学上获得f(x,y):
∂ f ( x , y ) ∂ x = x - g ( x ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2
∂ f ( x , y ) ∂ y = y - h ( y ) d - f ( x , y ) + ( x - g ( x ) ) 2 + ( y - h ( y ) ) 2 + ( d - f ( x , y ) ) 2 ;
其中:
Figure FDA00003513612200073
Figure FDA00003513612200074
d是所述轴和所述阵列的相交点与所述顶点之间的距离;
Rx是添加了2cm裕度的所述阵列的横向长度;
Ry是添加了2cm裕度的所述阵列的纵向长度;
Lx是所述反射表面在所述虚平面上的投影横向长度;以及
Ly是所述反射表面在所述虚平面上的投影纵向长度。
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