Patent Publication Number: US-9893223-B2

Title: Solar electricity generation system

Description:
REFERENCE TO RELATED APPLICATIONS 
     Reference is made to the following patents and patent applications, owned by assignee, the disclosures of which are hereby incorporated by reference: 
     U.S. Published Patent Application No. 2009/0065045; and 
     U.S. patent application Ser. No. 12/677,208, filed Sep. 10, 2008 and entitled “SOLAR ELECTRICITY GENERATION SYSTEM”. 
     FIELD OF THE INVENTION 
     The present invention relates to photovoltaic power generation. 
     BACKGROUND OF THE INVENTION 
     The following publications are believed to represent the current state of the art:
     U.S. Pat. Nos. 4,195,913 and 5,153,780;   U.S. Published Patent Application No.: 2009/0065045;   U.S. patent application Ser. No. 12/677,208;   

     Concentrators employing spherical concave reflective elements suitable for photovoltaic power generation are discussed by Authier, B. and Hill, L., 1980, “High Concentration Solar Collector of the Stepped Spherical Type: Optical Design Characteristics,” Applied Optics, Vol 19, No. 20, pp. 3554-3561; 
     Concentrators designed for photovoltaic applications are discussed by Kurzweg, U. H., 1980, “Characteristics of Axicon Concentrators for Use in Photovoltaic Energy Conversion”, Solar Energy, Vol. 24, pp. 411-412; 
     Swanson, R. M., July 1988, “Photovoltaic Dish Solar-Electric Generator”, Proceedings of the Joint Crystalline Cell Research, and Concentrating Collector Projects Review SAND88-0522, Sandia National Laboratories, Albuquerque, N. Mex., pp. 109-119 discuss a parabolic dish in conjugation with a diffuser. 
     SUMMARY OF THE INVENTION 
     The present invention seeks to provide improved systems for photovoltaic power generation. 
     There is thus provided in accordance with a preferred embodiment of the present invention a solar electricity generator including an array of photovoltaic power generating elements, and a single continuous smooth solar reflecting surface, the surface being arranged to reflect light from the sun onto the array of photovoltaic power generating elements, wherein the flux per area at a point of minimum flux per area on the array is approximately 75% of the flux per area at a point of maximum flux per area, the intercept factor of the array is at least 70%, and the optical fill factor of the array is at least 60%. 
     In accordance with a preferred embodiment of the present invention, the solar electricity generator also includes a solar tracking system, the solar tracking system being operative to rotate and position the reflecting surface opposite the sun throughout the day. Preferably, the solar electricity generator provides a solar radiation concentration ratio of 500-1000. Additionally, the solar reflecting surface includes a vertex located at the center of the reflecting surface, and the reflecting surface is arranged generally perpendicularly to an axis defined by the vertex and the center of the array. 
     Preferably, the array is arranged in a plane which is perpendicular to the axis and is located opposite the solar reflecting surface. Additionally, an imaginary plane is defined as perpendicularly intersecting the axis at the vertex, and is tangent to the solar reflecting surface. 
     In accordance with a preferred embodiment of the present invention, a unique 1:1 mapping of solar rays exists between the reflecting surface and the array. Additionally, the shape of the reflecting surface is described by a mathematical function z=f(x,y) wherein z is the distance between a set of coordinates x,y on the imaginary plane and the reflecting surface, x and y are the respective latitudinal and longitudinal distances from coordinates x,y to the vertex on the imaginary plane, and f(x,y) is obtained numerically via the differential equations: 
     
       
         
           
             
               
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     L y  is the projected longitudinal length of the reflecting surface on the imaginary plane. 
     There is also provided in accordance with another preferred embodiment of the present invention a solar electricity generator including an array of photovoltaic power generating elements, and a solar reflecting surface formed as a plurality of continuous smooth solar reflecting surface segments, each of the surface segments being arranged to reflect mutually overlapping fluxes of solar radiation from the sun onto the array of photovoltaic power generating elements. 
     In accordance with a preferred embodiment of the present invention, the solar reflecting surface is formed as four continuous smooth solar reflecting surface segments, and wherein the flux per area at a point of minimum flux per area on the array is approximately 90% of the flux per area at a point of maximum flux per area, the intercept factor of the array is at least 75%, and the optical fill factor of the array is at least 70%. 
     Preferably, the solar electricity generator also includes a solar tracking system, the solar tracking system being operative to rotate and position the reflecting surface opposite the sun throughout the day. Preferably, the solar electricity generator is provides a solar radiation concentration ratio of 500-1000. 
     In accordance with a preferred embodiment of the present invention, the solar reflecting surface includes a vertex located at the center of the reflecting surface, and the reflecting surface is arranged generally perpendicularly to an axis defined by the vertex and the center of the array. Additionally, the array is arranged in a plane which is perpendicular to the axis and is located opposite the solar reflecting surface. Additionally, an imaginary plane is defined as perpendicularly intersecting the axis at the vertex, and is tangent to the solar reflecting surface. 
     Preferably, the solar reflecting surface segments are symmetric. Preferably, the solar reflecting surface segments are symmetrically arranged about the axis. 
     In accordance with a preferred embodiment of the present invention, a unique 4:1 mapping of solar rays exists between the four continuous smooth solar reflecting surface segments and the array. Additionally, the shape of the reflecting surface is described by a mathematical function z=f(x,y) wherein z is the distance between a set of coordinates x,y on the imaginary plane and the reflecting surface, x and y are the respective latitudinal and longitudinal distances from coordinates x,y to the vertex on the imaginary plane, and f(x,y) is obtained numerically via the differential equations: 
     
       
         
           
             
               
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     d is the distance between the vertex and the intersection of the axis with the array; 
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     R y  is the longitudinal length of the array with an addition of a 2 cm margin; 
     L x  is the projected latitudinal length of the reflecting surface on the imaginary plane; and 
     L y  is the projected longitudinal length of the reflecting surface on the imaginary plane. 
     There is further provided in accordance with yet another preferred embodiment of the present invention a solar electricity generator including an array of photovoltaic power generating elements, and a solar reflecting surface formed as a plurality of solar reflecting surface segments arranged symmetrically about the center of the reflecting surface, each of the surface segments being divided into a plurality of continuous smooth solar reflecting surface sub segments, each of the surface sub segments being arranged to reflect mutually overlapping fluxes of solar radiation from the sun onto the array of photovoltaic power generating elements. 
     In accordance with a preferred embodiment of the present invention, the solar reflecting surface is formed as four solar reflecting surface segments, each of the surface segments being divided into four continuous smooth solar reflecting surface sub segments, and wherein the flux per area at a point of minimum flux per area on the array is approximately 60% of the flux per area at a point of maximum flux per area, the intercept factor of the array is at least 80%, and the optical fill factor of the array is at least 60%. Additionally, a generally unique 16:1 mapping of solar rays exists between the reflecting surface sub segments and the array. 
     In accordance with a preferred embodiment of the present invention, the solar reflecting surface is formed as four solar reflecting surface segments, each of the surface segments being divided into eighty one continuous smooth solar reflecting surface sub segments, and wherein the flux per area at a point of minimum flux per area on the array is approximately 60% of the flux per area at a point of maximum flux per area, the intercept factor of the array is at least 80%, and the optical fill factor of the array is at least 60%. Additionally, a generally unique 81:1 mapping of solar rays exists between the reflecting surface sub segments and the array. 
     Preferably, the solar electricity generator also includes a solar tracking system, the solar tracking system being operative to rotate and position the reflecting surface opposite the sun throughout the day. Preferably, the solar electricity generator provides a solar radiation concentration ratio of 500-1000. 
     In accordance with a preferred embodiment of the present invention, the solar reflecting surface includes a vertex located at the center of the reflecting surface, and the reflecting surface is arranged generally perpendicularly to an axis defined by the vertex and the center of the array. Additionally, the array is arranged in a plane which is perpendicular to the axis and is located opposite the solar reflecting surface. Additionally, an imaginary plane is defined as perpendicularly intersecting the axis at the vertex, and is tangent to the solar reflecting surface. Preferably, the solar reflecting surface segments are symmetric. 
     In accordance with a preferred embodiment of the present invention, for a matrix of n by m surface sub segments of a surface segment, wherein the coordinates of an individual surface sub segment are denoted as k,j, where k is the order of the individual surface sub segment between 1 and n and j is the order of the individual surface sub segment between 1 and m, the shape of the individual surface sub segment at coordinates k,j is described by a mathematical function z=f(x,y) wherein z is the distance between a set of coordinates x,y on the imaginary plane and the reflecting surface, x and y are the respective latitudinal and longitudinal distances from coordinates x,y to the vertex on the imaginary plane, and f(x,y) is obtained numerically via the differential equations: 
     
       
         
           
             
               
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                                 = 
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                                 … 
                                 ⁢ 
                                 
                                     
                                 
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                                       ( 
                                       
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                                       ( 
                                       
                                         
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                                             ⁢ 
                                             
                                                 
                                             
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                                             my 
                                           
                                           
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                                             y 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
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                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   y 
                                 
                                 ∈ 
                                 
                                   [ 
                                   
                                     
                                       - 
                                       
                                         
                                           jL 
                                           y 
                                         
                                         
                                           2 
                                           ⁢ 
                                           
                                               
                                           
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                                             ( 
                                             
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                                               - 
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                                             ) 
                                           
                                           ⁢ 
                                           
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                                             y 
                                           
                                         
                                         
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                                           ⁢ 
                                           
                                               
                                           
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                                   ) 
                                 
                               
                               , 
                             
                           
                         
                         
                           
                             
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   j 
                                   = 
                                   1 
                                 
                                 , 
                                 2 
                                 , 
                                 
                                   … 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   m 
                                 
                               
                             
                           
                         
                       
                       ; 
                     
                   
                 
               
             
           
         
       
     
     d is the distance between the vertex and the intersection of the axis with the array; 
     R x  is the latitudinal length of the array with an addition of a 2 cm margin; 
     R y  is the longitudinal length of the array with an addition of a 2 cm margin; 
     L x  is the projected latitudinal length of the reflecting surface on the imaginary plane; and 
     L y  is the projected longitudinal length of the reflecting surface on the imaginary plane. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will be understood and appreciated more fully from the following detailed description, taken in conjunction with the drawings in which: 
         FIG. 1A  is a simplified pictorial illustration of a photovoltaic solar generator constructed and operative in accordance with a preferred embodiment of the invention; 
         FIG. 1B  is a simplified pictorial illustration of a smooth generally concave reflecting surface which is part of the photovoltaic solar generator of  FIG. 1A ; 
         FIG. 1C  is a simplified sectional illustration of the smooth generally concave reflecting surface of  FIG. 1B ; 
         FIGS. 1D and 1E  are together an example of a sequence of MATLAB® instructions operative to calculate part of the shape of the reflecting surface of the generator of  FIGS. 1A-1C ; 
         FIGS. 1F &amp; 1G  are together an example of MATLAB® instructions operative to calculate the optical fill factor of the reflecting surface of the generator of  FIGS. 1A-1E ; 
         FIG. 1H  is a simplified pictorial illustration of a reflected radiation flux distribution pattern produced by the photovoltaic solar generator of  FIGS. 1A-1G ; 
         FIG. 2A  is a simplified pictorial illustration of a photovoltaic solar generator constructed and operative in accordance with another preferred embodiment of the invention; 
         FIG. 2B  is a simplified pictorial illustration of a smooth generally concave reflecting surface which is part of the photovoltaic solar generator of  FIG. 2A ; 
         FIG. 2C  is a simplified sectional illustration of the smooth generally concave reflecting surface of  FIG. 2B ; 
         FIGS. 2D and 2E  are together an example of a sequence of MATLAB® instructions operative to calculate part of the shape of the reflecting surface of the generator of  FIGS. 2A-2C ; 
         FIGS. 2F &amp; 2G  are together an example of MATLAB® instructions operative to calculate the optical fill factor of the reflecting surface of the generator of  FIGS. 2A-2E ; 
         FIG. 2H  is a simplified pictorial illustration of a reflected radiation flux distribution pattern produced by the photovoltaic solar generator of  FIGS. 2A-2G ; 
         FIG. 3A  is a simplified pictorial illustration of a photovoltaic solar generator constructed and operative in accordance with yet another preferred embodiment of the invention; 
         FIG. 3B  is a simplified pictorial illustration of a smooth generally concave reflecting surface which is part of the photovoltaic solar generator of  FIG. 3A ; 
         FIG. 3C  is a simplified sectional illustration of the smooth generally concave reflecting surface of  FIG. 3B ; 
         FIG. 3D  is a simplified pictorial illustration of a reflected radiation flux distribution pattern produced by a part of the photovoltaic solar generator of  FIG. 3A ; 
         FIG. 3E  is a simplified pictorial illustration of a reflected radiation flux distribution pattern produced by another part of the photovoltaic solar generator of  FIG. 3A ; 
         FIGS. 3F and 3G  are together an example of a sequence of MATLAB® instructions operative to calculate part of the shape of the reflecting surface of the generator of  FIGS. 3A-3E ; 
         FIGS. 3H &amp; 3I  are together an example of MATLAB® instructions operative to calculate the optical fill factor of the reflecting surface of the generator of  FIGS. 3A-3G ; 
         FIG. 3J  is a simplified pictorial illustration of a reflected radiation flux distribution pattern produced by the photovoltaic solar generator of  FIGS. 3A-3I ; 
         FIG. 4A  is a simplified illustration of a reflected radiation flux distribution pattern produced by a part of a photovoltaic solar generator constructed and operative in accordance with yet another preferred embodiment of the invention; 
         FIG. 4B  is a simplified illustration of a reflected radiation flux distribution pattern produced by the photovoltaic solar generator of  FIG. 4A ; 
         FIGS. 4C and 4D  are together an example of a sequence of MATLAB® instructions operative to calculate part of the shape of the reflecting surface of the generator of  FIGS. 4A and 4B ; 
         FIGS. 4E &amp; 4F  are together an example of MATLAB® instructions operative to calculate the optical fill factor of the reflecting surface of the generator of  FIGS. 4A-4D ; and 
         FIG. 4G  is a simplified pictorial illustration of a reflected radiation flux distribution pattern produced by the photovoltaic solar generator of  FIG. 4A . 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Reference is now made to  FIG. 1A , which is a simplified pictorial illustration of a photovoltaic solar generator constructed and operative in accordance with a preferred embodiment of the invention, and to  FIGS. 1B and 1C , which are simplified respective pictorial and sectional illustrations of a smooth generally concave reflecting surface which is part of the photovoltaic solar generator of  FIG. 1A . 
     As known to persons skilled in the art, the overall electric current produced by an array of photovoltaic cells connected in series is limited by the photovoltaic cell which generates the weakest current. Therefore, it is desirable that all cells generate a generally equal electric current. It is appreciated that the current generated by an individual photovoltaic cell is generally proportional to the amount of absorbed solar radiation, hence it is desirable that all cells in the array absorb a generally equal amount of solar radiation. 
     As is also known to persons skilled in the art, a non-uniform flux of incident radiation on an individual photovoltaic cell causes a reduction in the power generating efficiency of the photovoltaic cell. Thus, it is desirable to achieve a uniform flux of radiation over each of the individual photovoltaic cells as well as over the entire array. 
     As seen in  FIG. 1A , there is provided a photovoltaic solar generator  100  having a single continuous smooth generally concave reflecting surface  102  mounted upon a solar tracking system  104  such as a PESOS® SFC 30 Tracking System, commercially available from PAIRAN Elektronik GmbH of Göttingen, Germany. The photovoltaic solar generator  100  also includes a flat photovoltaic module  106  including a multiplicity of photovoltaic cells such as SPECTROLAB CDO-100-C3MJ Concentrator Solar Cells, commercially available from SPECTROLAB Inc. of Sylmar, Calif., located opposite the reflecting surface  102 . The reflecting surface  102  reflects a generally uniform flux of solar radiation onto the flat photovoltaic module  106  located opposite the reflecting surface  102 , preferably defining a concentration ratio of 500-1000, whereby the optimal distance between the reflecting surface  102  and the photovoltaic module  106  is determined by the shape of the reflecting surface  102 , as will be explained hereinbelow. 
     The uniformity of the flux of radiation impinging on the array of photovoltaic cells can be measured by the optical fill factor of the system. It is therefore an objective of the present invention to achieve a maximum optical fill factor of the system. 
     Throughout, the term “optical fill factor” of an array of photovoltaic cells is defined to mean the ratio between the amount of radiation that would impinge upon an array had the flux of impinging radiation been uniform at a level matching the level of impinging radiation at the points on the array receiving the lowest level of impinging radiation, and the total amount of radiation actually impinging upon the array. This ratio is shown in  FIG. 1A  as the ratio between area A and the combination of areas A and B. 
     In addition to achieving maximum uniformity of the flux of radiation impinging on the array of photovoltaic cells, it is an objective of the present invention to maximize the intercept factor of the system. Throughout, the term “intercept factor” is defined to mean the fraction of radiation reflected by the surface that impinges on the absorbing surface of the receiver. 
     As also seen in  FIG. 1A , a first curved axis  108  of surface  102  perpendicularly intersects a second curved axis  110  of surface  102  at a vertex  116  located at the center of surface  102 . 
     As seen in  FIGS. 1B and 1C  and as mentioned hereinabove, the reflecting surface  102  reflects a generally uniform flux of solar radiation onto the flat photovoltaic module  106 . As also seen in  FIG. 1C , the reflecting surface  102  is arranged generally perpendicularly to an axis  118  defined by the vertex  116  and the photovoltaic module  106 , whereby the photovoltaic module  106  is symmetrically arranged about axis  118  in a plane perpendicular thereto. The solar tracking system  104  is operative to rotate and position the reflecting surface  102  opposite the sun throughout the day, thereby aligning axis  118  with the sun. A plane  120  is defined as perpendicularly intersecting axis  118  at vertex  116 . 
     It is a particular feature of this embodiment of the present invention that the single continuous smooth generally concave reflecting surface  102  is shaped so that a unique 1:1 mapping of solar rays exists between the reflecting surface  102  and the photovoltaic module  106 . 
     The shape of the reflecting surface  102  can be described by a mathematical function z=f(x,y) where z is the distance between a set of coordinates x,y on plane  120  and the reflecting surface  102 , and where coordinates x and y are the distances relative to vertex  116  on a projection of axis  108  and  110  onto plane  120 . 
     Reference is now made to  FIGS. 1D and 1E , which are together an example of a sequence of MATLAB® instructions operative to calculate part of the shape of the reflecting surface of the generator of  FIGS. 1A-1C , and to  FIGS. 1F &amp; 1G , which are together an example of MATLAB® instructions operative to calculate the optical fill factor of the generator of  FIGS. 1A-1E . 
     f(x,y) can be obtained via the following differential equations: 
     
       
         
           
             
               
                 ∂ 
                 
                   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 
                       
                     
                   
                 
               
             
             ; 
           
         
       
       
         
           
             where 
             ⁢ 
             
               : 
             
           
         
       
       
         
           
             
               
                 g 
                 ⁡ 
                 
                   ( 
                   x 
                   ) 
                 
               
               = 
               
                 
                   
                     
                       R 
                       x 
                     
                     
                       L 
                       x 
                     
                   
                   ⁢ 
                   x 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   for 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   x 
                 
                 ∈ 
                 
                   [ 
                   
                     
                       - 
                       
                         
                           L 
                           x 
                         
                         2 
                       
                     
                     , 
                     
                       
                         L 
                         x 
                       
                       2 
                     
                   
                   ] 
                 
               
             
             ; 
           
         
       
       
         
           
             
               
                 h 
                 ⁡ 
                 
                   ( 
                   y 
                   ) 
                 
               
               = 
               
                 
                   
                     
                       R 
                       y 
                     
                     
                       L 
                       y 
                     
                   
                   ⁢ 
                   y 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   for 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   y 
                 
                 ∈ 
                 
                   [ 
                   
                     
                       - 
                       
                         
                           L 
                           y 
                         
                         2 
                       
                     
                     , 
                     
                       
                         L 
                         y 
                       
                       2 
                     
                   
                   ] 
                 
               
             
             ; 
           
         
       
     
     d is the distance between the vertex  116  and the intersection of axis  118  with flat photovoltaic module  106 ; 
     R x  is the latitudinal length of photovoltaic module  106  with an addition of a 2 cm margin; 
     R y  is the longitudinal length of photovoltaic module  106  with an addition of a 2 cm margin; 
     L x  is the projected length of axis  108  onto plane  120 ; and 
     L y  is the projected length of axis  110  onto plane  120 . 
     Using the sequence of MATLAB® instructions shown in  FIGS. 1D and 1E , f(x,y) for one quarter of the reflecting surface  102  can be obtained numerically via the above equations. Due to the symmetry of reflecting surface  102 , f(x,y) for the remaining quarters of surface  102  can be extrapolated using the above calculation for a single quarter. 
     For example, for a single continuous smooth generally concave reflecting surface  102  where L x =L y =3.46 meters, the distance d is 2 meters and the dimensions of the photovoltaic module  106  are 10×10 centimeters, the value of z is calculated to vary between 0 at vertex  116  and 73.5 centimeters at each of the corners of reflecting surface  102 . The total flux of solar radiation impinging upon the photovoltaic module  106  is calculated to be approximately 833 suns, whereby the flux per area at a point on the photovoltaic module  106  of minimum flux per area is approximately 75% of the flux per area at a point on the photovoltaic module  106  of maximum flux per area. The intercept factor of the photovoltaic module  106  is calculated to be no less than 70%, and the optical fill factor is calculated to be no less than 60%. 
     The optical fill factor is calculated using the sequence of MATLAB® instructions shown in  FIGS. 1F &amp; 1G , which utilizes the calculation of f(x,y) shown in  FIGS. 1D &amp; 1E . 
     It is appreciated that although  FIGS. 1A-1C  illustrate reflecting surface  102  as being a unitary reflecting surface, for considerations relating for example to manufacturing and shipping, alternative embodiments of the present invention may include a plurality of surface segments assembled to form reflecting surface  102 . 
       FIG. 1H  is a simplified pictorial illustration of a reflected radiation flux distribution pattern produced by the photovoltaic solar generator of  FIGS. 1A-1G  on the flat photovoltaic module  106 . As seen in  FIG. 1H , the reflected radiation flux pattern produced on the flat photovoltaic module  106  is generally uniform in intensity over the entirety of photovoltaic module  106 , and tapers off steeply at the edges thereof. 
     Reference is now made to  FIG. 2A , which is a simplified pictorial illustration of a photovoltaic solar generator constructed and operative in accordance with another preferred embodiment of the invention, and to  FIGS. 2B and 2C , which are simplified respective pictorial and sectional illustrations of a smooth generally concave reflecting surface which is part of the photovoltaic solar generator of  FIG. 2A . 
     As seen in  FIG. 2A , there is provided a photovoltaic solar generator  200  having a smooth generally concave reflecting surface  202  mounted upon a solar tracking system  204  such as a PESOS® SFC 30 Tracking System, commercially available from PAIRAN Elektronik GmbH of Göttingen, Germany. The photovoltaic solar generator  200  also includes a flat photovoltaic module  206  including a multiplicity of photovoltaic cells such as SPECTROLAB CDO-100-C3MJ Concentrator Solar Cells, commercially available from SPECTROLAB Inc. of Sylmar, Calif., located opposite the reflecting surface  202 . The reflecting surface  202  reflects a generally uniform flux of solar radiation onto the flat photovoltaic module  206  located opposite the reflecting surface  202 , preferably defining a concentration ratio of 500-1000, whereby the optimal distance between the reflecting surface  202  and the photovoltaic module  206  is determined by the shape of the reflecting surface  202 , as will be explained hereinbelow. 
     As also seen in  FIG. 2A , a first curved axis  208  of surface  202  perpendicularly intersects a second curved axis  210  of surface  202 . Axis  208  and axis  210  divide the reflecting surface  202  into four planar symmetric and continuous smooth generally concave reflecting surface segments  212 . A vertex  216  is defined by the intersection of axis  208  and  210 . 
     As seen in  FIGS. 2B and 2C  and as mentioned hereinabove, the reflecting surface  202  reflects a generally uniform flux of solar radiation onto the flat photovoltaic module  206 . As also seen in  FIG. 2C , the reflecting surface  202  is arranged generally perpendicularly to an axis  218  defined by the vertex  216  and the photovoltaic module  206 , whereby the photovoltaic module  206  is symmetrically arranged about axis  218  in a plane perpendicular thereto. The solar tracking system  204  is operative to rotate and position the reflecting surface  202  opposite the sun throughout the day, thereby aligning axis  218  with the sun. A plane  220  is defined as perpendicularly intersecting axis  218  at vertex  216 . 
     It is a particular feature of this embodiment of the present invention that the reflecting surface  202  is shaped so that a 4:1 mapping of solar rays exists between the four continuous smooth generally concave reflecting surface segments  212  and the photovoltaic module  206 . This arrangement, whereby the photovoltaic module  206  receives four overlapping and generally evenly distributed fluxes of solar radiation, provides for a generally uniform flux of solar radiation on the photovoltaic module  206  even in the case of damage to a limited region of one of the reflecting surface segments  212 . 
     The shape of the reflecting surface  202  can be described by a mathematical function z=f(x,y) where z is the distance between a set of coordinates x,y on plane  220  and the reflecting surface  202 , and where coordinates x and y are the distances relative to vertex  216  on a projection of axis  208  and  210  onto plane  220 . 
     Reference is now made to  FIGS. 2D and 2E , which are together an example of a sequence of MATLAB® instructions operative to calculate part of the shape of the reflecting surface of the generator of  FIGS. 2A-2C , and to  FIGS. 2F &amp; 2G , which are together an example of MATLAB® instructions operative to calculate the optical fill factor of the generator of  FIGS. 2A-2E . 
     f(x,y) can be obtained via the following differential equations: 
     
       
         
           
             
               
                 ∂ 
                 
                   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 
                       
                     
                   
                 
               
             
             ; 
           
         
       
       
         
           
             where 
             ⁢ 
             
               : 
             
           
         
       
       
         
           
             
               g 
               ⁡ 
               
                 ( 
                 x 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         
                           
                             
                               R 
                               x 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     x 
                                   
                                   
                                     L 
                                     x 
                                   
                                 
                                 - 
                                 
                                   1 
                                   2 
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           for 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           x 
                         
                         ∈ 
                         
                           ( 
                           
                             0 
                             , 
                             
                               
                                 L 
                                 x 
                               
                               / 
                               2 
                             
                           
                           ] 
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               R 
                               x 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     x 
                                   
                                   
                                     L 
                                     x 
                                   
                                 
                                 + 
                                 
                                   1 
                                   2 
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           for 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           x 
                         
                         ∈ 
                         
                           [ 
                           
                             
                               
                                 - 
                                 
                                   L 
                                   x 
                                 
                               
                               / 
                               2 
                             
                             , 
                             0 
                           
                           ) 
                         
                       
                     
                   
                 
                 ; 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     h 
                     ⁡ 
                     
                       ( 
                       y 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     R 
                                     y 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           y 
                                         
                                         
                                           L 
                                           y 
                                         
                                       
                                       - 
                                       
                                         1 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 for 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 y 
                               
                               ∈ 
                               
                                 ( 
                                 
                                   0 
                                   , 
                                   
                                     
                                       L 
                                       y 
                                     
                                     / 
                                     2 
                                   
                                 
                                 ] 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     R 
                                     y 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           y 
                                         
                                         
                                           L 
                                           y 
                                         
                                       
                                       + 
                                       
                                         1 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 for 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 y 
                               
                               ∈ 
                               
                                 [ 
                                 
                                   
                                     
                                       - 
                                       
                                         L 
                                         y 
                                       
                                     
                                     / 
                                     2 
                                   
                                   , 
                                   0 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ; 
                     
                   
                 
               
             
           
         
       
     
     d is the distance between vertex  216  and the intersection of axis  218  with flat photovoltaic module  206 ; 
     R x  is the latitudinal length of photovoltaic module  206  with an addition of a 2 cm margin; 
     R y  is the longitudinal length of photovoltaic module  206  with an addition of a 2 cm margin; 
     L x  is the projected length of axis  208  onto plane  220 ; and 
     L y  is the projected length of axis  210  onto plane  220 . 
     Using the sequence of MATLAB® instructions shown in  FIGS. 2D and 2E , f(x,y) for one quarter of the reflecting surface  202  can be obtained numerically via the above equations. Due to the symmetry of reflecting surface  202 , f(x,y) for the remaining quarters of surface  202  can be extrapolated using the above calculation for a single quarter. 
     For example, for a reflecting surface  202  where L x =L y =3.46 meters, the distance d is 2 meters and the dimensions of the photovoltaic module  206  are 10×10 centimeters, the value of z is calculated to vary between 0 at vertex  216  and 76.5 centimeters at each of the corners of reflecting surface  202 . The total flux of solar radiation impinging upon the photovoltaic module  206  is calculated to be approximately 833 suns, whereby the flux per area at a point on the photovoltaic module  206  of minimum flux per area is approximately 90% of the flux per area at a point on the photovoltaic module  206  of maximum flux per area. The intercept factor of the photovoltaic module  206  is calculated to be no less than 75%, and the optical fill factor is calculated to be no less than 70%. 
     The optical fill factor is calculated using the sequence of MATLAB® instructions shown in  FIGS. 2F &amp; 2G , which utilizes the calculation of f(x,y) shown in  FIGS. 2D &amp; 2E . 
       FIG. 2H  is a simplified pictorial illustration of a reflected radiation flux distribution pattern produced by the photovoltaic solar generator of  FIGS. 2A-2G  on the flat photovoltaic module  206 . As seen in  FIG. 2H , the reflected radiation flux pattern produced on the flat photovoltaic module  206  is generally uniform in intensity over the entirety of photovoltaic module  206 , and tapers off steeply at the edges thereof. 
     Reference is now made to  FIG. 3A , which is a simplified pictorial illustration of a photovoltaic solar generator constructed and operative in accordance with yet another preferred embodiment of the invention, and to  FIGS. 3B and 3C , which are simplified respective pictorial and sectional illustrations of a smooth generally concave reflecting surface which is part of the photovoltaic solar generator of  FIG. 3A . 
     As seen in  FIG. 3A , there is provided a photovoltaic solar generator  300  having a smooth generally concave reflecting surface  302  mounted upon a solar tracking system  304  such as a PESOS® SFC 30 Tracking System, commercially available from PAIRAN Elektronik GmbH of Göttingen, Germany. The photovoltaic solar generator  300  also includes a flat photovoltaic module  306  including a multiplicity of photovoltaic cells such as SPECTROLAB CDO-100-C3MJ Concentrator Solar Cells, commercially available from SPECTROLAB Inc. of Sylmar, Calif., located opposite the reflecting surface  302 . The reflecting surface  302  reflects a generally uniform flux of solar radiation onto the flat photovoltaic module  306  located opposite the reflecting surface  302 , preferably defining a concentration ratio of 500-1000, whereby the optimal distance between the reflecting surface  302  and the photovoltaic module  306  is determined by the shape of the reflecting surface  302 , as will be explained hereinbelow. 
     As also seen in  FIG. 3A , a first curved axis  308  of surface  302  perpendicularly intersects a second curved axis  310  of surface  302 . Axis  308  and axis  310  divide the reflecting surface  302  into four planar symmetric and generally concave reflecting surface segments  312 . Each of the four reflecting surface segments  312  is further divided into four generally equally sized reflecting surface sub segments  314 . A vertex  316  is defined by the intersection of axis  308  and  310 . 
     As seen in  FIGS. 3B and 3C  and as mentioned hereinabove, the reflecting surface  302  reflects a generally uniform flux of solar radiation onto the flat photovoltaic module  306 . As also seen in  FIG. 3C , the reflecting surface  302  is arranged generally perpendicularly to an axis  318  defined by the vertex  316  and the photovoltaic module  306 , whereby the photovoltaic module  306  is symmetrically arranged about axis  318  in a plane perpendicular thereto. The solar tracking system  304  is operative to rotate and position the reflecting surface  302  opposite the sun throughout the day, thereby aligning axis  318  with the sun. A plane  320  is defined as perpendicularly intersecting axis  318  at vertex  316 . 
     It is a particular feature of this embodiment of the present invention that the reflecting surface  302  is shaped so that a 4:1 mapping of solar rays exists between the four reflecting surface sub segments  314  adjacent to vertex  316  and the photovoltaic module  306 , whereby each of the four reflecting surface sub segments  314  adjacent to vertex  316  reflects a generally equal amount of solar radiation onto the photovoltaic module  306 , thereby producing a generally uniform flux of solar radiation on the photovoltaic module  306 . This arrangement, whereby the photovoltaic module  306  receives four overlapping and generally evenly distributed fluxes of solar radiation, provides for a generally uniform flux of solar radiation on the photovoltaic module  306  even in the case of damage to a limited region of one of the four reflecting surface sub segments  314  adjacent to vertex  316 . 
     Reference is now made to  FIG. 3D , which is a simplified pictorial illustration of reflected radiation flux distribution pattern produced by one of the four reflecting surface sub segments  314  adjacent to vertex  316  on the photovoltaic module  306 , and is a part of the photovoltaic solar generator of  FIG. 3A , and to  FIG. 3E  which is a simplified pictorial illustration of reflected radiation flux distribution pattern produced by one of the twelve reflecting surface sub segments  314  which are not adjacent to vertex  316  on the photovoltaic module  306 , and is a part of the photovoltaic solar generator of  FIG. 3A . 
     In addition to the aforementioned 4:1 mapping between the four reflecting surface sub segments  314  adjacent to vertex  316  and the flat photovoltaic module  306 , the shape of reflecting surface  302  also provides for a mapping between each of the twelve reflecting surface sub segments  314  which are not adjacent to vertex  316  and the flat photovoltaic module  306 . Each of the twelve reflecting surface sub segments  314  which are not adjacent to vertex  316  reflects a generally equal and overlapping flux of solar radiation onto the flat photovoltaic module  306 , thereby producing an additional generally uniform flux of solar radiation on the flat photovoltaic module  306  which is superimposed over the generally uniform flux of solar radiation reflected by the four reflecting surface sub segments  314  adjacent to vertex  316 . However, as seen in  FIGS. 3D and 3E , the radiation flux distribution pattern produced by one of the twelve reflecting surface sub segments  314  which are not adjacent to vertex  316  is not entirely superimposed over the radiation flux distribution pattern produced by the four reflecting surface sub segments  314  adjacent to vertex  316 . 
     The shape of the reflecting surface  302  can be described by a mathematical function z=f(x,y) where z is the distance between a set of coordinates x,y on plane  320  and the reflecting surface  302 , and where coordinates x and y are the distances relative to vertex  316  on a projection of axis  308  and  310  onto plane  320 . 
     Reference is now made to  FIGS. 3F and 3G , which are together an example of a sequence of MATLAB® instructions operative to calculate part of the shape of the reflecting surface of the generator of  FIGS. 3A-3E , and to  FIGS. 3H &amp; 3I , which are together an example of MATLAB® instructions operative to calculate the optical fill factor of the generator of  FIGS. 3A-3G . 
     f(x,y) can be obtained via the following differential equations: 
     
       
         
           
             
               
                 ∂ 
                 
                   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 
                       
                     
                   
                 
               
             
             ; 
           
         
       
       
         
           
             where 
             ⁢ 
             
               : 
             
           
         
       
       
         
           
             
               g 
               ⁡ 
               
                 ( 
                 x 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         
                           
                             
                               R 
                               x 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     4 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     x 
                                   
                                   
                                     L 
                                     x 
                                   
                                 
                                 - 
                                 
                                   1 
                                   2 
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           for 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           x 
                         
                         ∈ 
                         
                           ( 
                           
                             0 
                             , 
                             
                               
                                 L 
                                 x 
                               
                               / 
                               4 
                             
                           
                           ] 
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               R 
                               x 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   - 
                                   
                                     
                                       4 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       x 
                                     
                                     
                                       L 
                                       x 
                                     
                                   
                                 
                                 + 
                                 
                                   3 
                                   2 
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           for 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           x 
                         
                         ∈ 
                         
                           [ 
                           
                             
                               
                                 L 
                                 x 
                               
                               / 
                               4 
                             
                             , 
                             
                               
                                 L 
                                 x 
                               
                               / 
                               2 
                             
                           
                           ] 
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               R 
                               x 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     4 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     x 
                                   
                                   
                                     L 
                                     x 
                                   
                                 
                                 + 
                                 
                                   1 
                                   2 
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           for 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           x 
                         
                         ∈ 
                         
                           [ 
                           
                             
                               
                                 - 
                                 
                                   L 
                                   x 
                                 
                               
                               / 
                               4 
                             
                             , 
                             0 
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               R 
                               x 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   - 
                                   
                                     
                                       4 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       x 
                                     
                                     
                                       L 
                                       x 
                                     
                                   
                                 
                                 - 
                                 
                                   3 
                                   2 
                                 
                               
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                           ⁢ 
                           
                               
                           
                           ⁢ 
                           for 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           x 
                         
                         ∈ 
                         
                           [ 
                           
                             
                               
                                 - 
                                 
                                   L 
                                   x 
                                 
                               
                               / 
                               2 
                             
                             , 
                             
                               
                                 - 
                                 
                                   L 
                                   x 
                                 
                               
                               / 
                               4 
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 ; 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     h 
                     ⁡ 
                     
                       ( 
                       y 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 
                                   
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                                     y 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
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                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 for 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 y 
                               
                               ∈ 
                               
                                 ( 
                                 
                                   0 
                                   , 
                                   
                                     
                                       L 
                                       y 
                                     
                                     / 
                                     4 
                                   
                                 
                                 ] 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     R 
                                     y 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         - 
                                         
                                           
                                             4 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             y 
                                           
                                           
                                             L 
                                             y 
                                           
                                         
                                       
                                       + 
                                       
                                         3 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 for 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 y 
                               
                               ∈ 
                               
                                 [ 
                                 
                                   
                                     
                                       L 
                                       y 
                                     
                                     / 
                                     4 
                                   
                                   , 
                                   
                                     
                                       L 
                                       y 
                                     
                                     / 
                                     2 
                                   
                                 
                                 ] 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     R 
                                     y 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           ⁢ 
                                           
                                               
                                           
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                                           y 
                                         
                                         
                                           L 
                                           y 
                                         
                                       
                                       + 
                                       
                                         1 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 for 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 y 
                               
                               ∈ 
                               
                                 [ 
                                 
                                   
                                     
                                       - 
                                       
                                         L 
                                         y 
                                       
                                     
                                     / 
                                     4 
                                   
                                   , 
                                   0 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     R 
                                     y 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         - 
                                         
                                           
                                             4 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             y 
                                           
                                           
                                             L 
                                             y 
                                           
                                         
                                       
                                       - 
                                       
                                         3 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 for 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 y 
                               
                               ∈ 
                               
                                 [ 
                                 
                                   
                                     
                                       - 
                                       
                                         L 
                                         y 
                                       
                                     
                                     / 
                                     2 
                                   
                                   , 
                                   
                                     
                                       - 
                                       
                                         L 
                                         y 
                                       
                                     
                                     / 
                                     4 
                                   
                                 
                                 ] 
                               
                             
                           
                         
                       
                       ; 
                     
                   
                 
               
             
           
         
       
     
     d is the distance between vertex  316  and the intersection of axis  318  with flat photovoltaic module  306 ; 
     R x  is the latitudinal length of photovoltaic module  306  with an addition of a 2 cm margin; 
     R y  is the longitudinal length of photovoltaic module  306  with an addition of a 2 cm margin; 
     L x  is the projected length of axis  308  onto plane  320 ; and 
     L y  is the projected length of axis  310  onto plane  320 . 
     Using the sequence of MATLAB® instructions shown in  FIGS. 3F and 3G , f(x,y) for one quarter of the reflecting surface  302  can be obtained numerically via the above equations. Due to the symmetry of reflecting surface  302 , f(x,y) for the remaining quarters of surface  302  can be extrapolated using the above calculation for a single quarter. 
     For example, for a reflecting surface  302  where L x =L y =3.46 meters, the distance d is 2 meters and the dimensions of the photovoltaic module  306  are 10×10 centimeters, the value of z is calculated to vary between 0 at vertex  316  and 75.5 centimeters at each of the corners of reflecting surface  302 . The flux of solar radiation impinging upon the photovoltaic module  306  is calculated to be approximately 833 suns, whereby the flux per area at a point on the photovoltaic module  306  of minimum flux per area is approximately 60% of the flux per area at a point on the photovoltaic module  306  of maximum flux per area. The intercept factor of the photovoltaic module  306  is calculated to be no less than 80%, and the optical fill factor is calculated to be no less than 60%. 
     The optical fill factor is calculated using the sequence of MATLAB® instructions shown in  FIGS. 3H &amp; 3I , which utilizes the calculation of f(x,y) shown in  FIGS. 3F &amp; 3G . 
       FIG. 3J  is a simplified pictorial illustration of a reflected radiation flux distribution pattern produced by the photovoltaic solar generator of  FIGS. 3A-3I  on the flat photovoltaic module  306 . As seen in  FIG. 3J , the reflected radiation flux pattern produced on the flat photovoltaic module  306  is generally uniform in intensity over the entirety of photovoltaic module  306 , and tapers off steeply at the edges thereof. 
     It is appreciated that in alternative embodiments of the present invention, reflecting surface segments  312  may be divided into any number of generally equally sized reflecting surface sub segments, creating a matrix of surface sub segments, wherein each of the surface sub segments is larger than the flat photovoltaic module  306 , and whereby each of the surface sub segments reflects a generally equal and overlapping generally uniform flux of solar radiation onto the photovoltaic module  306 . It is noted that while the surface sub segments adjacent to vertex  316  reflect generally equal and overlapping fluxes of solar radiation onto the entirety of photovoltaic module  306 , surface sub segments which are not adjacent to vertex  316  reflect fluxes of solar radiation which are not entirely overlapping and that do not cover the entirety of photovoltaic module  306 . 
     For a matrix of n by m surface sub segments, where n is the number of sub segments from vertex  316  to the edge of the surface segment  312  along axis  308 , m is the number of surface sub segments from vertex  316  to the edge of the surface segment  312  along axis  310  and 
                 R   x       (       L   x     /   n     )       =       R   y       (       L   y     /   m     )             
the coordinates of an individual surface sub segment are denoted as k,j, where k is the order of the individual surface sub segment on axis  308  between 1 and n, and j is the order of the individual surface sub segment on axis  310  between 1 and m.
 
     The shape of the individual surface sub segment at coordinates k,j can be described by a mathematical function z k,j =f (x,y) where z k,j  is the distance between a set of coordinates x,y on plane  320  and the reflecting surface  302 , and where coordinates x and y are the distances relative to vertex  316  on a projection of axis  308  and  310  onto plane  320 . 
     f(x,y) can be obtained numerically by using the following derivatives: 
     
       
         
           
             
               
                 ∂ 
                 
                   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 
                     
                   
                 
               
             
           
         
       
       
         
           
             where 
             ⁢ 
             
               : 
             
           
         
       
       
         
           
             
               g 
               ⁡ 
               
                 ( 
                 x 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   - 
                                   1 
                                 
                                 ) 
                               
                               k 
                             
                             ⁢ 
                             
                               
                                 R 
                                 x 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   - 
                                   
                                     1 
                                     2 
                                   
                                   - 
                                   
                                     
                                       2 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       nx 
                                     
                                     
                                       L 
                                       x 
                                     
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             for 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             x 
                           
                           ∈ 
                           
                             ⌊ 
                             
                               
                                 
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   L 
                                 
                                 
                                   2 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   n 
                                 
                               
                               , 
                               
                                 
                                   kL 
                                   x 
                                 
                                 
                                   2 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   n 
                                 
                               
                             
                             ⌋ 
                           
                         
                         , 
                         
                           k 
                           = 
                           1 
                         
                         , 
                         2 
                         , 
                         
                           … 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           n 
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   - 
                                   1 
                                 
                                 ) 
                               
                               k 
                             
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     d is the distance between vertex  316  and the intersection of axis  318  with flat photovoltaic module  306 ; 
     R x  is the latitudinal length of photovoltaic module  306  with an addition of a 2 cm margin; 
     R y  is the longitudinal length of photovoltaic module  306  with an addition of a 2 cm margin; 
     L x  is the projected length of axis  308  onto plane  320 ; and 
     L y  is the projected length of axis  310  onto plane  320 . 
     For example, for an embodiment including a reflecting surface  302  where L x =L y =3.46 meters, the distance d is 2 meters, the dimensions of the photovoltaic module  306  are 10×10 centimeters and each of the four reflecting surface segments  312  is further divided into a matrix of 9×9 generally equally sized reflecting surface sub segments, the value of z is calculated to vary between 0 at vertex  316  and 75.6 centimeters at each of the corners of reflecting surface  302 . The flux of solar radiation impinging upon the photovoltaic module  306  is calculated to be approximately 833 suns, whereby the flux per area at a point on the photovoltaic module  306  of minimum flux per area is approximately 60% of the flux per area at a point on the photovoltaic module  306  of maximum flux per area. The intercept factor of the photovoltaic module  306  is calculated to be no less than 80%, and the optical fill factor is calculated to be no less than 60%. This embodiment is further described hereinbelow in conjunction with  FIGS. 4A-4C . 
     Reference is now made to  FIG. 4A , which is a simplified illustration of a reflected radiation flux distribution pattern produced by a part of a photovoltaic solar generator constructed and operative in accordance with yet another preferred embodiment of the invention, and to  FIG. 4B , which is a simplified illustration of a reflected radiation flux distribution pattern produced by the photovoltaic solar generator of  FIG. 4A . 
     In the embodiment of  FIGS. 4A and 4B , two perpendicularly intersecting curved axis of a smooth generally concave reflecting surface divide the reflecting surface into four planar symmetric and generally concave reflecting surface segments. Each of the four reflecting surface segments is further divided into a 9×9 matrix of eighty one generally equally sized reflecting surface sub segments. 
       FIG. 4A  illustrates the reflected radiation flux distribution pattern produced by one of the four reflecting surface segments on a photovoltaic module which is part of the solar generator. As seen in  FIG. 4A , the reflected radiation flux distribution pattern produced by one of the four reflecting surface segments is generally, but not entirely, uniform over the photovoltaic module. The radiation flux distribution is provided by the eighty one generally overlapping fluxes of radiation produced by the eighty one generally equally sized reflecting surface sub segments of one of the four reflecting surface segments. This arrangement, whereby the photovoltaic module receives eighty one overlapping and generally evenly distributed fluxes of solar radiation, provides for a generally uniform flux of solar radiation on the photovoltaic module even in the case of damage to a limited region of one of the eighty one sub segments. 
       FIG. 4B  illustrates the reflected radiation flux distribution pattern produced by the entire reflecting surface on a photovoltaic module which is part of the solar generator. As seen in  FIG. 4B , the reflected radiation flux distribution pattern produced by the entire reflecting surface is generally uniform over the photovoltaic module. This arrangement, whereby the photovoltaic module receives four overlapping and generally evenly distributed fluxes of solar radiation provided by the four reflecting surface segments, provides for a generally uniform flux of solar radiation on the photovoltaic module even in the case of damage to a limited region of one of the four reflecting surface segments. 
     Reference is now made to  FIGS. 4C and 4D , which are together an example of a sequence of MATLAB® instructions operative to calculate part of the shape of the reflecting surface of the generator of  FIGS. 4A and 4B , and to  FIGS. 4E &amp; 4F , which are together an example of MATLAB® instructions operative to calculate the optical fill factor of the generator of  FIGS. 4A-4D . 
     Using the sequence of MATLAB® instructions shown in  FIGS. 4C and 4D , z k,j  can be obtained via the differential equations which describe z k,j =f (x,y) as shown hereinabove. The optical fill factor is calculated using the sequence of MATLAB® instructions shown in  FIGS. 4E &amp; 4F , which utilizes the calculation off(x,y) shown in  FIGS. 4C &amp; 4D . 
       FIG. 4G  is a simplified pictorial illustration of a reflected radiation flux distribution pattern produced by the photovoltaic solar generator of  FIGS. 4A-4F  on a flat photovoltaic module. As seen in  FIG. 4G , the reflected radiation flux pattern produced on the flat photovoltaic module is generally uniform in intensity over the entirety of photovoltaic module, and tapers off steeply at the edges thereof. 
     It will be appreciated by persons skilled in the art that the present invention is not limited by what has been particularly shown and described hereinabove. Rather the scope of the present invention includes both combinations and subcombinations of various features described hereinabove as well as variations and modifications thereof which are not in the prior art.