SOLAR ELECTRICITY GENERATION SYSTEM
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 No. 12/677,208, filed September 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. Patent Nos. 4,195,913 and 5,153,780;
U.S. Published Patent Application No.: 2009/0065045;
U.S. Patent Application 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,
NM, 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%.
n 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:
dfjx.y) x - g(x
dx - f x y) + - j(x)) 2 + - h y ) + (d - (x, ) ) 2
df{x,y)
d - f x, ) + x - (x )2 + y - ft(y)) 2 + ( (x, ) )
wherein:
= for
2 2
( ) = - » o
2 2
d is the distance between the vertex and the intersection of the axis with the
array;
x is the latitudinal length of the array with an addition of a 2 cm margin;
y is the longitudinal length of the array with an addition of a 2 cm margin;
x is the projected latitudinal length of the reflecting surface on the imaginary
plane; and
Ly 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:
df{x,y) x - g(x)
dx
d - f{x,y) + - {c + - ¾( 2 + (d - f (x y
df x )
dy d- f x,y +J{x - ix + (y - A< ) ) 2 + (d - f .y)
wherein:
d is the distance between the vertex and the intersection of the axis with the
array;
x is the latitudinal length of the array with an addition of a 2 cm margin;
is the longitudinal length of the array with an addition of a 2 cm margin;
Lx is the projected latitudinal length of the reflecting surface on the imaginary
plane; and
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.
n 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 msurface 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:
dx
d - fix, y) + - ) 2 + y— y +- d f x, )
dy
d- f x,y +J (x - x + y - h y + ( - f(x,y)†
wherein:
d is the distance between the vertex and the intersection of the axis with the
array;
x is the latitudinal length of the array with an addition of a 2 cm margin;
y is the longitudinal length of the array with an addition of a 2 cm margin;
Lx is the projected latitudinal length of the reflecting surface on the imaginary
plane; and
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. B 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. IB;
Figs. D a d E 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. F & 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 - E;
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 & 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 & 3 1 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 - 31;
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 & 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 i accordance
with a preferred embodiment of the invention, and to Figs. IB 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 ce l is generally proportional to the amount of
absorbed solar radiation, hence it is desirable that a l 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 Gottingen, 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,
California, 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. IB 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. ID and IE, 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. I F & 1G,
which are together an example of MATLAB® instructions operative to calculate the
optical fill factor of the generator of Figs. 1A - IE.
f(x,y) can be obtained via the following differential equations:
d - fix, y + x ) + ( )' 2 + - ¾ ) ) '
df(x, y
dy
- f x,y + - s(x)) 2 + - y)) + (d - f x, f
where:
,g(.v) = ~ x for x e
2 2
= or y
2 2
d is the distance between the vertex 116 and the intersection of axis 118 with flat
photovoltaic module 106;
Rx is the latitudinal length of photovoltaic module 106 with an addition of a 2
cm margin;
Ry is the longitudinal length of photovoltaic module 106 with an addition of a 2
cm margin;
x is the projected length of axis 108 onto plane 120; and
y is the projected length of axis 110 onto plane 120.
Using the sequence of MATLAB® instructions shown in Figs. D and
IE, 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 = Ly = 3.46 meters, the distance d is 2 meters and the dimensions
of the photovoltaic module 106 are 10 x 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. IF & 1G, which utilizes the calculation of f(x,y) shown in
Figs. ID & IE.
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 Gottingen, 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, California, 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 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 & 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:
df{x,y) X- g x
J - x + (y y)) 2 + ( d - f x y
where:
is the distance between vertex 216 and the intersection of axis 218 with flat
photovoltaic module 206;
Rx is the latitudinal length of photovoltaic module 206 with an addition of a 2
cm margin;
Ry is the longitudinal length of photovoltaic module 206 with an addition of a 2
cm margin;
Lx is the projected length of axis 208 onto plane 220; and
Ly 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 Lx - y = 3.46 meters,
the distance d is 2 meters and the dimensions of the photovoltaic module 206 are 10 x
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 & 2G, which utilizes the calculation of f(x,y) shown in
Figs. 2D & 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 a d operative in accordance
with yet another preferred embodiment of the invention, arid 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 Gottingen, 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, California, 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 & 31,
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:
df x,y x - g x
dx
- f x,y + - * 2+ y - ( ) +
y - y
dy
d - f(x,y) + x - g + y - + ( - f x,y
where:
' "' -'
d is the distance between vertex 316 and the intersection of axis 318 with flat
photovoltaic module 306;
Rx is the latitudinal length of photovoltaic module 306 with an addition of a 2
cm margin;
Ry is the longitudinal length of photovoltaic module 306 with an addition of a 2
cm margin;
Lx is the projected length of axis 308 onto plane 320; and
Ly 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 Lx - L - 3.46 meters,
the distance d is 2 meters and the dimensions of the photovoltaic module 306 are 10 x
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 & 31, which utilizes the calculation of f(x,y) shown in
Figs. 3F & 3G.
Fig. 3J is a simplified pictorial illustration of a reflected radiation flux
distribution pattern produced by the photovoltaic solar generator of Figs. 3A - 3 1 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 i 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 31 along axis 310 and 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 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 zk =f ,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.
f(x,y) can be obtained numerically by using the following derivatives:
where:
d is the distance between vertex 316 and the intersection of axis 318 with flat
photovoltaic module 306;
x is the latitudinal length of photovoltaic module 306 with an addition of a 2
cm rg ;
Ry is the longitudinal length of photovoltaic module 306 with an addition of a 2
cm margin;
Lx is the projected length of axis 308 onto plane 320; and
Ly is the projected length of axis 310 onto plane 320.
For example, for an embodiment including a reflecting surface 302
where x = y = 3.46 meters, the distance d is 2 meters, the dimensions of the
photovoltaic module 306 are 10 x 10 centimeters and each of the four reflecting surface
segments 312 is further divided into a matrix of 9x9 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 9x9 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 &
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 can be obtained via the differential equations which describe z .= f(x,y) as
shown hereinabove. The optical fill factor is calculated using the sequence of
MATLAB® instructions shown in Figs. 4E & 4F, which utilizes the calculation oif(x,y)
shown in Figs. 4C & 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.
C L A I M S
1. A solar electricity generator including:
an array of photovoltaic power generating elements; and
a single continuous smooth solar reflecting surface, said surface
being arranged to reflect light from the sun onto said array of photovoltaic power
generating elements;
wherein:
the flux per area at a point of minimum flux per area on said array
is approximately 75% of the flux per area at a point of maximum flux per area;
the intercept factor of said array is at least 70%; and
the optical fill factor of said array is at least 60%.
2 . A solar electricity generator according to claim 1 and wherein said solar
electricity generator also includes a solar tracking system, said solar tracking system
being operative to rotate and position said reflecting surface opposite the sun throughout
the day.
3. A solar electricity generator according to either of claims 1 and 2 and
wherein said solar electricity generator provides a solar radiation concentration ratio of
500 - 1000.
4. A solar electricity generator according to any of claims 1 - 3 and
wherein:
said solar reflecting surface includes a vertex located at the center
of said reflecting surface; and
said reflecting surface is arranged generally perpendicularly to an
axis defined by said vertex and the center of said array.
5. A solar electricity generator according to claim 4 and wherein said array
is arranged in a plane which is perpendicular to said axis and is located opposite said
solar reflecting surface.
6. A solar electricity generator according to either of claims 4 and 5 and
wherein an imaginary plane is defined as perpendicularly intersecting said axis at said
vertex, and is tangent to said solar reflecting surface.
7. A solar electricity generator according to any of claims 1 - 6 and wherein
a unique 1:1 mapping of solar rays exists between said reflecting surface and said array.
8. A solar electricity generator according to either of claims 6 and 7 and
wherein the shape of said 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 said
imaginary plane and said reflecting surface;
x and y are the respective latitudinal and longitudinal distances
from coordinates x,y to said vertex on said imaginary plane; and
f(x,y) is obtained numerically via the differential equations:
x - g{x)
dx
fix, y) + ( - + ( - y + (d - f{x,y)Y
df x,y)
d
d - f x y + - + - A ) ) 2 + d - f x,y
wherein:
g ) = for x
2 2
d is the distance between said vertex and the intersection of said axis with said
array;
x is the latitudinal length of said array with an addition of a 2 cm margin;
Ry is the longitudinal length of said array with an addition of a 2 cm margin;
Lx is the projected latitudinal length of said reflecting surface on said imaginary
plane; and
y is the projected longitudinal length of said reflecting surface on said
imaginary plane.
9. 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 said surface segments being arranged
to reflect mutually overlapping fluxes of solar radiation from the sun onto said array of
photovoltaic power generating elements.
10. A solar electricity generator according to claim 9 and wherein:
said 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 said array
is approximately 90% of the flux per area at a point of maximum flux per area;
the intercept factor of said array is at least 75%; and
the optical fill factor of said array is at least 70%.
11. A solar electricity generator according to either of claims 9 and 10 and
wherein said solar electricity generator also includes a solar tracking system, said solar
tracking system being operative to rotate and position said reflecting surface opposite
the sun throughout the day.
12. A solar electricity generator according to any of claims 9 - 11 and
wherein said solar electricity generator is provides a solar radiation concentration ratio
of 500 - 1000.
13. A solar electricity generator according to any of claims 9 - 12 and
wherein:
said solar reflecting surface includes a vertex located at the center
of said reflecting surface; and
said reflecting surface is arranged generally perpendicularly to an
axis defined by said vertex and the center of said array.
14. A solar electricity generator according to claim 13 and wherein said array
is arranged in a plane which is perpendicular to said axis and is located opposite said
solar reflecting surface.
15. A solar electricity generator according to either of claims 13 and 14 and
wherein an imaginary plane is defined as perpendicularly intersecting said axis at said
vertex, and is tangent to said solar reflecting surface.
16. A solar electricity generator according to any of claims 9 - 15 and
wherein said solar reflecting surface segments are symmetric.
17. A solar electricity generator according to any of claims 13 - 16 and
wherein said solar reflecting surface segments are symmetrically arranged about said
axis.
18. A solar electricity generator according to any of claims 10 - 17 and
wherein a unique 4:1 mapping of solar rays exists between said four continuous smooth
solar reflecting surface segments and said array.
19. A solar electricity generator according to any of claims 13
wherein the shape of said 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 said
imaginary plane and said reflecting surface;
x and y are the respective latitudinal and longitudinal distances
from coordinates x,y to said vertex on said imaginary plane; and
f(x,y) is obtained numerically via the differential equations:
wherein:
d is the distance between said vertex and the intersection of said axis with said
array;
Rx is the latitudinal length of said array with an addition of a 2 cm margin;
y is the longitudinal length of said array with an addition of a 2 cm margin;
Lx is the projected latitudinal length of said reflecting surface on said imaginary
plane; and
y is the projected longitudinal length of said reflecting surface on said
imaginary plane.
20. 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 said reflecting surface,
each of said surface segments being divided into a plurality of continuous smooth solar
reflecting surface sub segments, each of said surface sub segments being arranged to
reflect mutually overlapping fluxes of solar radiation from the sun onto said array of
photovoltaic power generating elements.
21. A solar electricity generator according to claim 20 and wherein:
said solar reflecting surface is formed as four solar reflecting
surface segments, each of said 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 said array
is approximately 60% of the flux per area at a point of maximum flux per area;
the intercept factor of said array is at least 80%; and
the optical fill factor of said array is at least 60%.
22. A solar electricity generator according to claim 21 and wherein a
generally unique 16:1 mapping of solar rays exists between said reflecting surface sub
segments and said array.
23. A solar electricity generator according to claim 20 and wherein:
said solar reflecting surface is formed as four solar reflecting
surface segments, each of said 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 said array
is approximately 60% of the flux per area at a point of maximum flux per area;
the intercept factor of said array is at least 80%; and
the optical fill factor of said array is at least 60%.
24. A solar electricity generator according to claim 23 and wherein a
generally unique 81:1 mapping of solar rays exists between said reflecting surface sub
segments and said array.
25. A solar electricity generator according to any of claims 20 - 24 and
wherein said solar electricity generator also includes a solar tracking system, said solar
tracking system being operative to rotate and position said reflecting surface opposite
the sun throughout the day.
26. A solar electricity generator according to any of claims 20 - 25 and
wherein said solar electricity generator provides a solar radiation concentration ratio of
500 - 1000.
27. A solar electricity generator according to any of claims 20 - 26 and
wherein:
said solar reflecting surface includes a vertex located at the center
of said reflecting surface; and
said reflecting surface is arranged generally perpendicularly to an
axis defined by said vertex and the center of said array.
28. A solar electricity generator according to claim 27 and wherein said array
is arranged in a plane which is perpendicular to said axis and is located opposite said
solar reflecting surface.
29. A solar electricity generator according to either of claims 27 - 28 and
wherein an imaginary plane is defined as perpendicularly intersecting said axis at said
vertex, and is tangent to said solar reflecting surface.
30. A solar electricity generator according to any of claims 20 - 29 and
wherein said solar reflecting surface segments are symmetric.
31. A solar electricity generator according to any of claims 20 - 30 and
wherein 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 said individual surface sub segment between 1 and n and is the order of said
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 said
imaginary plane and said reflecting surface;
x and y are the respective latitudinal and longitudinal distances
from coordinates x,y to said vertex on said imaginary plane; and
f(x,y) is obtained numerically via the differential equations:
y - y
dy ~ f x,y) + - + - A )) + ( - f x,y
wherein:
(fe - 1)
(-!) ¾ - - - — for = 1,2, .. .7 2n 2n
/ I 2 (fe-l)i
<- - ( - - - ) fo k — 1,2, ...
2n
d is the distance between said vertex and the intersection of said axis with said
array;
Rxis the latitudinal length of said array with an addition of a 2 cm margin;
Ry is the longitudinal length of said array with an addition of a 2 cm margin;
Lx is the projected latitudinal length of said reflecting surface on said imaginary
plane; and
y is the projected longitudinal length of said reflecting surface on said
imaginary plane.