SESSION 1B
CONCENTRATOR OPTICS AND TRACKING
ANTONIO MARTÍ AND KENJI ARAKI, CHAIRPERSONS OF THE SESSION 1B
VALERY D. RUMYANTSEV FROM IOFFE PHYSICO-TECHNICAL INSTITUTE PRESENTS HIS PAPER:
SOLAR CONCENTRATOR MODULES WITH FRESNEL LENS PANELS
LEWIS FRAAS FROM JX CRYSTALS, INC. PRESENTS HIS PAPER:
POSSIBLE IMPROVEMENTS IN THE CASSEGRAINIAN PV MODULE
RICHARD L. JOHNSON JR. FROM PRACTICAL INSTRUMENTS, INC. PRESENTS HIS PAPER:
HYBRID OPTIC DESIGN FOR CONCENTRATOR PANELS
RALF LEUTZ FROM PHILIPPS-UNIVERSITY MARBURG PRESENTS HIS PAPER:
NONIMAGING FLAT FRESNEL LENSES
MAXIM Z. SHVARTS FROM IOFFE PHYSICO-TECHNICAL INSTITUTE PRESENTS HIS PAPER:
THE NEW APPROACH TO DESIGN OF FRESNEL LENS SUNLIGHT CONCENTRATOR
ROBERT A. MACDONALD FROM SOLFOCUS, INC. PRESENTS HIS PAPER:
ACCEPTANCE ANGLE REQUIREMENTS FOR POINT FOCUS CPV SYSTEMS
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
SOLAR CONCENTRATOR MODULES WITH FRESNEL LENS PANELS
V.D.Rumyantsev, A.E.Chalov, N.Yu.Davidyuk, E.A.Ionova, N.A.Sadchikov, V.M.Andreev
Ioffe Physico-Technical Institute, 26 Polytechnicheskaya str., St.-Petersburg, 194021, Russia
ABSTRACT
A promising way for solar concentrator module design
is the use of the highly-efficient multijunction III-V cells
together with small-aperture area Fresnel-type solar
concentrators. In the developed modules, the 50x 50 cm2
2
panels of integrated Fresnel lenses (each lens is 4x4 cm
in aperture area) have a composite structure: microprisms
are formed from transparent silicone contacting with glass
sheet. A comprehensive analysis has been conducted
concerning concentration properties of the lenses. Such a
lens material parameter as refraction index and its
dependence on wavelength was involved in computer
modeling and measurement procedure at optical efficiency
evaluation. As a result, lens profile was under optimization
bearing in view different aspects, such as focal distance,
receiver diameter, sun illumination spectrum, sensitivity
spectra of the sub-cells in a triple-junction cell and others.
Overall conversion efficiency in a test module of described
design as high as 26.5% has been measured.
INTRODUCTION
One of the tendencies in concentrator photovoltaics
development is a concept of decrease in the concentrator
and cell dimensions on retention of a high sunlight
concentration ratio. The first experimental modules of such
a type consisted of a panel of lenses, each of 1 x 1 or 2 x
2
2 cm , focusing radiation on the AlGaAs/GaAs cells of
sub-millimeter size [1,2]. At that time, formulated were
main advantages of a module with small-aperture area
concentrators: the requirements are essentially lowered
imposed on the capability of heat sinking material to
conduct heat, on its thermal expansion coefficient and on
its thickness. The focal distance of such lenses appears to
be comparable with the structural thickness of the
conventional modules without concentrators. The
advantages of the small-size concentrator cells are the
following: lower ohmic losses at collection of lower current
in the conditions of non-uniform light intensity distribution
at high local photocurrent density; higher cell chip
throughput from a wafer; possibility to apply the highproductive mounting methods. This approach resulted in
creation of the “all-glass” photovoltaic modules with III-V
cells and panels of small-aperture area Fresnel lenses
2
(each lens is 4 x 4 cm ) [3-5]. The lens panels had a
“glass-silicone” composite structure. In recent works [6-8],
Fresnel lenses are arranged on a common superstrate in
a view of a panel of 12x12 lenses. One-junction cells as
2
small as 2x2 mm and 1.7 mm in designated area
diameter operating at mean concentration ratio of about
700x are used in the PV modules [8] (see photograph in
Figure 1).
Figure 1. Array of the full-size concentrator modules [8].
In the case of use of the multijunction cells, two
additional advantages may be noted for the modules of
the described design. First of them is connected with lens
structure: specific IR absorbtion in silicone microprisms
with small average thickness may be disregarded at
analysis of bottom sub-cell operation. The second may be
formulated as lower sensitivity of small-size cells to
chromatic aberrations of the refracting concentrators.
Negative influence of this type of illumination nonuniformity can not be compensated by use of more dense
contact grid, because lateral currents arise between subcells inside the cell structure.
In present work a comprehensive analysis has been
conducted regarding to concentration properties of the
lenses matched in an optimum way with III-V triplejunction cells. Lens profile was under optimization bearing
in view refraction index of silicone and its dependence on
wavelength, focal distance, receiver diameter, sun
illumination spectrum, sensitivity spectra of the sub-cells in
a triple-junction cell and others. Overall conversion
efficiency in test modules of described design as high as
26.5% has been measured.
COMPUTER MODEL
Optical diagram for computer simulation of lens
operation is shown in Figure 2. Sunrays with divergence,
corresponding to sundisk size, are incident upon the lens
surface. After serial reflections and refractions on the airglass-silicone-air interfaces, they rich focal plane, where a
receiver is situated. Overlapping the elliptical light spots
33
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
from different parts of the lens forms distribution of light
intensity along the focal plane. Receiver of diameter d can
accept certain part of light. This amount of light, divided by
total amount of light, incident within lens aperture area and
spectral range of receiver sensitivity, is defined as lens
optical efficiency with respect to given receiver diameter.
diameter should be as close (one to others) as possible for
all of three spectral bands to eliminate negative action of
the lateral currents flowing inside the cell structure.
RESULTS: NORMAL POSITIONING
Contours of the light distributions along receiver
radius, as well as lens optical efficiencies for each of three
spectral bands (for top, middle and bottom sub-cells) at
receiver diameter variation are shown in Figure 3.
G la s s
6
5
INITIAL DATA FOR COMPUTER SIMULATION
Lens optical efficiency versus receiver diameter for
different lens focal distances F was under consideration in
computer simulation. Incidence angle of the sunrays upon
lens surface was varied as well. Solar spectral curve AM
1.5d low AOD together with spectral sensitivity curves for
a triple-junction InGaP/GaAs/Ge cell (for the case of a
balance between photocurrent densities in the top and
middle sub-cells, but excess of photocurrent in the bottom
Ge sub-cell) were involved. Also, dependence of silicone
refraction index on wavelength, measured within spectral
range of λ=400÷1700 nm, was introduced in the
calculations. Light absorption in glass sheet and thin
silicone microprisms is believed to be insignificant. Glass
and silicone have no antireflection coatings. Lens aperture
2
area is 40x40 mm at grooves pitch of 0.25 mm. Ideally
smooth facets at sharp profile of the grooves is supposed
as well.
It should be noted, that distance F is defined as a
focal one only by convention, because focusing the
different spectral bands takes place at different distances
from the lens. Actually, this is a distance, at which given
receiver should be situated in given lens design. Result of
calculation is a set of refracting angles in microprisms, at
which optimum defocusing takes place for all of three
spectral bands (corresponding to top, middle and bottom
sub-cells), keeping up a balance between photon fluxes
for top and middle sub-cells at possibly highest optical
efficiency with respect to a given receiver diameter. Also,
drop of optical efficiency in spectral band for bottom subcell should be compensated by excess of photocurrent in
it. Finally, contours of light distributions within receiver
90
80
3
70
2
60
1
50
0
40
6
100
5
4
F=65
3
2
e f f ic ie n c y , %
Figure 2. Optical layout for computer simulation.
F=85
O p t ic a l
F o c a l p la n e
C o n c e n t r a t io n r a t io x 1 0 3 , s u n s
S ilic o n e
Focal distance (F)
4
100
1
0
6
5
4
90
80
70
60
50
40
100
F=45
90
80
3
70
2
60
1
50
0
40
0.0 0.2 0.4 0.6 0.8 1.0 1.0 1.2 1.4 1.6 1.8 2.0
Dist. along reciever radius, mm
Reciever diameter, mm
Figure 3. On the left: plots of sun concentration ratio on
distance along receiver radius for the lenses with F=45, 65
and 85 mm. On the right: lens optical efficiencies for
different receiver diameters. Solid lines correspond to
spectral band suitable for top sub-cell in a triple junction
photoreceiver, dotted and chain lines correspond to the
middle and bottom sub-cells, respectively.
34
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
In Figure 3, focal distances in interval of F =45÷85
mm, and cell diameters in interval of d=1÷2 mm, are under
consideration. At shorter F, lens optical efficiencies begin
to be unacceptably low, whereas at longer ones off-normal
acceptance angle of the concentrator system is too small
(see below). For all F in above interval, lens profile can be
optimized for minimization of a difference in light
distribution contours for top and middle sub-cells. At the
same time, contour for bottom sub-cell is sufficiently
different. Remembering that there exists an excess of
photocurrent in Ge sub-cell (up to 1.5 times), one can
expect almost full coincidence of the contours for all the
sub-cells in the case of F=85 mm. Lens optical efficiencies
as high as 90% may be expected employing the cells with
d≥1.6 mm. For shorter F, equalization of the currents
begins to be more problematic for central cell areas, but it
is achieved over total cell area at d≥1.2 mm and any F
from regarding interval. Optical efficiencies at shorter F
have a tendency to be lower.
The most important difference between lenses of
different focal distances consists in much higher sun
concentration ratios (C) in receiver center, realizing by
lenses with shorter F. This is quite right for top- and
middle-cell contours, where C~2500x at F=85 mm, with
increase up to C~5500x at F=45 mm. For contour of IR
light it has a minor effect.
RESULTS: OFF-NORMAL POSITIONING
Another difference is revealed at consideration of an
off-normal behavior of the concentrator system.
Corresponding data are shown in Figure 4.
Receiver diameter is 1.7 mm
Optical efficiency,%
It is seen from the presented results that the intervals
of F=45÷85 mm and d=1.2÷2 mm can be supposed at
development of the practical concentrator systems. On the
other hand, these results did not include additional optical
losses arising at lens fabrication. Although lens
manufacturing method itself is characterized by a very
high accuracy of the mould copying at polymerization of
silicone, mould manufacturing process is not always
perfect to produce quite sharp edges of the prisms by
diamond cutting tool. It can be considered, that
manufacturing errors degrade the performance of the
optical concentrators to a greater extent at shorter focal
distances, than at longer ones. However, shorter-in-focaldistance modules can be more appropriate for designer.
Such modules may have a lower weight for the cost of the
smaller module walls, or they expected to be more
aesthetically attractive, even if overall module efficiency is
limited by optical efficiency of the concentrators.
One of the most important features of a concentrator
is its capability to ensure a high mean sun concentration at
local values as low as possible. This mitigates
requirements to peak current density of the tunnel p-n
junctions in triple-junction cell structure. Very often the
cells can not be used in the high-concentration PV
systems due to peak tunnel current limitations.
Nevertheless, properly designed cells (for inctance, of
Spectrolab, Inc.) demonstrate actual capacity for work at
concentration ratios as high as 2000÷6000 suns [9].
OPTICAL EFFICIENCY IN PRACTICAL LENSES
A setup with flash lamp and achromatic objective
optics has been used for recording the light intensity
contours. This was carried out by means of the spectrally
filtered GaAs and GaSb cells through a hole of 0.15 mm in
diameter (see Figure 5). Long focus of practical lenses
waschosen (F=85 mm), taking into account the highest
optical efficiency, predicted by theory, and high expected
surface quality of the smaller in depth grooves in lens
mould, fabricated by diamond cutting. Reasonable
agreement with theory was observed.
100
F=65 mm
90
DISCUSSION OF THE THEORETICAL RESULTS
80
F=45 mm
70
F=85 mm
60
to p
m id d le
b o tto m
50
0,0
0,2
0,4
0,6
Off normal angle, degrees
Figure 4. Off-normal curves for concentrator systems with
one and the same receiver diameter d=1.7 mm and
different lens focal distances.
It is seen from the Figure, that a wider off-normal curve
inheres in a system with shorter focal distance. On the
other hand, advantage of the system with F=45 mm in
comparison with that of F=65 mm is realized only at low
enough optical efficiency. Regarding to the system with
F=85 mm, it is characterized by the curve with almost flat
part within ±0.2 degree of arc range, which can be
ensured in the trackers developed by us earlier [6, 8].
Light intensity, relative units
1 .0
0 .8
0 .6
0 .4
0 .2
0 .0
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
1 .2
1 .4
1 .6
1 .8
2 .0
D is ta n c e a c r o s s r e c e iv e r d ia m e te r , m m
Figure 5. Experimental contours of the light intensity
distributions in focal spot of the lens with F=85 mm for
spectral bands corresponding to top, middle and bottom
sub-cells.
35
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
MEASUREMENTS OF THE TEST MODULES
WITH FRESNEL LENS PANELS
Operational abilities of the modules with Fresnel lens
panels have been checked in respect to overall conversion
efficiency by fabricating and outdoor measurements of test
modules of reduced sizes. The modules similar to those
described in [7] have been equipped with GaInP/GaAs/Ge
triple-junction cells produced by Spectrolab, Inc. The cells
were characterized by conversion efficiencies around 3234% (AM 1.5d) at indoor flash measurements at
concentration ratio of about 1000x.
In a module with 8-lens panel (2x4 lenses), the cells of
2 mm in diameter were mounted, being connected in
parallel. Hermetically sealed module was installed on the
sun tracking system. After the first outdoor
characterization by manual I-V measurement equipment
and by an automatic outdoor tester, the module was
characterized indoors by a large-area flash solar tester [7]
to compare corresponding results for outdoor and indoor
measurements (see Figure 6). Overall module conversion
efficiency as high as 26.5% was measured assuming cell
temperature of 25C.
8-lens test module
1,2
1,0
Current, A
0,8
Isc=1.1 A
Voc=2.88 V
Im=1.061 A
Vm=2.538 V
Pm=2.693 W
FF=85%
Eff=24.55%
(no temp. corr.)
o
Tamb=25 C
0,6
0,4
0,2
Isc=1.1 A
Voc=2.999 V
Im=1.031 A
Vm=2.818 V
Pm=2.905 W
FF=88.05%
Eff=26.48%
(temp. corr.)
2
Ec=857 W/m
0,0
0,0
0,5
1,0
1,5
Voltage, V
2,0
2,5
3,0
Figure 6. Illuminated I-V curves measured on the 8-lens
test module outdoors (St. Petersburg, June 16, 2006, 16
h. 43 m., ambient Т=25C, solid line) and indoors by a flash
simulator (dashed line). Cell temperature is about 50C
outdoors and 25C indoors.
CONCLUSION
Highly efficient multijunction cell is a key element of a
concentrator PV system. Actual efficient functioning of this
element is not possible without proper matching of its
characreristics with those of the concentrator. Smallaperture area Fresnel lenses with composite “glasssilicone” structure demonstrate good potential for practical
use. Optical simulation simplifies the performance
evaluation of the concentrators, and may assist with the
choice of solar concentrator parameters.
ACKNOWLEDGEMENTS
This work has been supported by the European
Commission within the project FULLSPECTRUM of the VI
Framework Program under contract no. SES6-CT-2003502620, and by the Russian Foundation for the Basic
Research (Grant 05-08-18189).
REFERENCES
[1] V.M. Andreev, A.A. Alaev, A,B. Guchmazov, V.S.
Kalinovsky, V.R. Larionov, K.Ya. Rasulov, V. D.
Rumyantsev, “High-efficiency AlGaAs-heterophotocells
operating with lens panels as the solar energy
concentrators”, Proc. of the all-Union Conference
“Photovoltaic phenomena in semiconductors”, Tashkent,
1989, 305-306 (in Russian).
[2] V.M. Andreev, V.R. Larionov, V.D. Rumyantsev, M.Z.
Shvarts, “High-efficiency solar concentrating GaAsth
AlGaAs modules with small-size lens units”, 11
European Photovoltaic Solar Energy Conference and
Exhibition – Book of Abstracts; abstract No 1A.15,
Montreux, Switzerland, 12-16 October, 1992.
[3] Project: INTAS96-1887, “Photovoltaic installation with
sunlight concentrators”, Final Report, 2000.
[4] V.D. Rumyantsev, V.M. Andreev, A.W. Bett, F.
Dimroth, M. Hein, G. Lange, M.Z. Shvarts, O.V. Sulima
“Progress in development of all-glass terrestrial
concentrator modules based on composite Fresnel
lenses and III-V solar cells”, Proceedings of the 28th
PVSC, Anhorage, Alaska, 2000, 1169-1172.
[5] A.W. Bett, C. Baur, F. Dimroth, G. Lange, M. Meusel,
S. van Riesen, G. Siefer, V.M. Andreev, V.D.
TM
Rumyantsev, N.A. Sadchikov, “FLATCON –modules:
technology and characterization”, Proceedings of 3rd
World Conference on Photovoltaic Energy Conversion
(2003) 3O-D9-05.
[6] V.D. Rumyantsev, A.E. Chalov, E.A. Ionova, V.R.
Larionov, N.A. Sadchikov, V.M. Andreev, “Practical
design of PV modules and trackers for very high solar
concentration”, Proc. on CD of the Second Int. Conf. on
Solar Concentrators for the Generation of Electricity or
Hydrogen, Scottsdale, Arizona, May 2005.
[7] V.D. Rumyantsev, N.A. Sadchikov, A.E. Chalov, E.A.
Ionova D.J. Friedman, G. Glenn, “Terrestrial
concentrator PV modules based on GaInP/GaAs/Ge TJ
cells and minilens panels”, ”, Proceedings of the IEEE
4th World Conference on Photovoltaic Energy
Conversion, Hawaii, May 7-12, 2006, pp. 632-635.
[8]
V.D.Rumyantsev,
N.A.Sadchikov,
A.E.Chalov,
E.A.Ionova, V.R.Larionov, V.M.Andreev, G.R.Smekens,
E.W.Merkle
“Pilot
installation
with
“all-glass”
st
concentrator PV modules”, Proceedings at the 21
European Photovoltaic Solar Energy Conference,
Dresden, 2006, pp. 2097-2100.
[9] V.M. Andreev, E.A. Ionova, V.R. Larionov, V.D.
Rumyantsev, M.Z. Shvarts, G. Glenn, “Tunnel diode
revealing peculiarities at I-V measurements in
multijunction III-V solar cells”, Proceedings of the IEEE
4th World Conference on Photovoltaic Energy
Conversion, Hawaii, May 7-12, 2006, pp. 799-802.
36
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
POSSIBLE IMPROVEMENTS IN THE CASSEGRAINIAN PV MODULE
1
L. Fraas1, J. Avery1, L. Minkin1, and E. Shifman2
JX Crystals Inc, 1105 12th Ave NW, Suite A2, Issaquah, WA 98027,
2
Concentrated Solar Energy, Las Vegas, NV
lfraas@jxcrystals.com
ABSTRACT
A Dual-Focus Cassegrainian module using a
dichroic secondary mirror is reported with an outdoor
measured efficiency of 30.8% at operating temperature.
This Dual-Focus Cassegrainian module used 32% efficient
dual junction cells at the center of the primary mirror along
with a second 6% efficient GaSb booster cell behind a
dichroic secondary. Herein, it is noted that a string of dual
junction InGaP/GaInAs cells series connected with a string
of GaSb cells outperforms a module with traditional
monolithic triple junction cells both because of the higher
voltage generated in the GaSb cell and also because the
cells in our Dual-Focus Cassegrainian module operate at
lower temperatures since the heat load is divided.
CASSEGRAINIAN MODULE
The Cassegrainian solar concentrator module
concept shown in figures 1 uses a primary mirror with a
dichroic secondary mirror to split the solar spectrum into
two parts and direct the infrared and near visible portions
of the spectrum to two separate cell locations [1, 2., 3].
Figure 2 shows a photograph of one of our Duel-Focus
Cassegrainian modules. The primary mirror in this module
has dimensions of 25 cm by 25 cm. This prototype solar
concentrator PV module used InGaP/GaAs dual junction
(DJ) cells located at the near-visible focus at the center of
the primary and GaSb infrared solar cells located behind
the secondary.
Cassegrain PV Module
GaSb
Cell
GaSb IRIR
Cell
InGaP/GaAs
InGaP/GaAs
2J Cell
2J Cell
33% Efficient PV Module
Figure 1: Dual-Focus Cassegrainian module concept.
Figure 2: Photograph of a Dual-Focus Cassegrainian
module in outdoor testing.
Cassegrainian modules using first and second
iteration cells were mounted on an Array Technologies 2axis tracker and measured in outdoor sunlight as shown in
figure 3. The results for the first iteration have been
reported previously [2]. Note in figure 3 that instruments
for measuring the direct and global solar flux are also
mounted on this tracker. The results for the second
iteration cells are summarized in table I.
Table I: Performance Summary
Packaged
Projected Measure
Measure
Cells at
STC with at
Module
STC
90%
Operate
at STC
Optical
Temp
(April 28)
Effic
(April 28)
DJ Cell 17.4 W
15.7 W
14.4 W
15.1 W
Power
DJ Cell 31.5%
28.4%
26.1%
27.3%
Effic.
IR Cell
3.64 W
3.28 W
2.6 W
3.1 W
Power
IR Cell
6.6%
5.9%
4.7%
5.6%
Effic.
Sum
21 W
19 W
17 W
18.7 W
Power
Sum
38.1%
34.3%
30.8%
32.9%
Effic.
NIP DNI = 0.92; Area = 600 cm2; Input Power = 55.2 W
37
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
front sheet with holes where IR cell packages complete
with heat sinks and the dichroic secondary mirror are
mounted. An array of primary mirrors is then mounted on
posts extending up from the back sheet and then these 3
arrays are captured by side-wall aluminum extrusions.
Cassegrain Panel
Components
1. Glass plate window with
IR cell assemblies.
2. Back panel with visible
light sensitive cell
assemblies.
3. Primary mirrors.
4. Aluminum frame
extrusions.
5. Power out junction box.
Figure 3: Photograph of 3 Cassegrainian modules
mounted on a 2-axis solar tracker with associated
illuminated current vs voltage measurement equipment
and direct and global solar intensity monitors.
Referring to column 3 in table I, at actual
operating temperature, the power produced by the DJ cell
was 14.4 W and the power produced by the IR cell was
2.6 W for a combined electrical output power of 17 W.
The direct solar intensity reading was 919 W / m2. So for
the module area of 600 cm2, the input power was 55.2 W.
These numbers translate to a module efficiency of 30.8%.
From the Voc readings for the two cells, we can
also determine the individual cell temperatures. The DJ
cell was operating at 12.5 C above ambient and the IR cell
was operating at 30 C above ambient. The DJ cell
temperature is really remarkable given that it was
operating at a geometric concentration ratio of 1200 suns.
While the IR cell operating temperature is acceptable,
there is room for improvement in the IR heat sink fin
design to decrease that cells operating temperature still
further.
CASSEGRAINIAN PANEL DESIGN
Having now demonstrated a respectable
Cassegrainian module, we are now moving on to a full
size panel. Here, we define a module as a complete set
of unique cell and optical components and a panel as an
array of modules. Figure 4 shows a Cassegrainian panel
consisting of a 3 by 6 array of modules. As this figure
shows, this panel consists of a metal back sheet with an
array of holes where DJ cell packages complete with heat
sinks are mounted. The panel also comprises a glass
Figure 4: Cassegrainian panel design. This particular
panel is a 3 x 6 array with dimensions of 750 mm x 1500
mm, about the same size as a silicon 180 W panel.
However, extrapolating from column 2 in table III, this
panel should produce 340 W.
OPTIMAL CELL SELECTION
Our dichroic-secondary Cassegrain module design
actually guarantees a panel performance greater than can
be achieved with today’s monolithic triple junction cells
alone. Higher combined cell efficiencies can result by
simply combining the GaSb cell as a booster cell along
with a monolithic InGaP/GaAs/Ge triple junction cell.
Since the Ge cell in the triple-junction cell produces
current in excess of that available to the InGaP and GaAs
cells, the reflection-to-transmission wavelength for the
dichroic filter can be adjusted to provide just enough
current to the Ge cell. Then the excess IR photons are
transmitted to the GaSb cell.
Figure 5 will aid in
understanding how this can work. Notice the 4 plateaus in
the accumulated Jsc curve in this figure. There is a
plateau at 35 mA/cm2 and 0.9 microns corresponding to a
water vapor absorption line just below the GaAs band
edge. The InGaP and GaAs cells share this current with
half each. Next notice that there is another plateau at 52
38
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
mA/cm2 at about 1.4 microns. Setting the dichroic
transition wavelength now at 1.4 microns will give 5235=17 mA/cm2 to the Ge cell. This then leaves another
10 mA/cm2 for the GaSb cell. Notice that the 4th plateau
at 1.8 microns indicates that there is really no current
available in the interval between the GaSb band edge at
1.8 microns and the Ge band edge at 2 microns. We
calculate then that the GaSb cell should be able to add
another 2.5 percentage points to the triple junction
demonstrated efficiency of 39% to bring the total to 41.5%.
Table II: Cell performance predictions for series
conneccted 2J and 3J Dual-Focus Cassegrainian panel
configurations.
Cell
Composition
Series 2J
Panel
GaAs(0.95)
P(0.05)
Al(0.95)
Ga(0.05)As
GaSb
Series 3J
Panel
In(0.6)
Ga(0.4)P
Ga(0.9)
In(0.1)As
GaSb
Figure 5: Graph showing the current available from the
terrestrial spectrum as a function of the longest
wavelength that a given semiconductor can absorb.
While using an existing triple junction cell with a
GaSb cell might be a fast path to higher efficiency, 2
terminal wiring of a production panel would present
problems. Our wiring plan for our Dual-Focus
Cassegrainian panel as shown in figure 6 is to
interconnect all of the cells of both types in series. With
this in mind and referring to column 3 in table I, more work
on the visible light sensitive cell is required.
We see 2 possible options as summarized in
table II.
For low cell cost, we can use a simple
GaAs(0.95)P)0.05) single junction cell array series
connected with the GaSb IR cell array with all cells
operating at about 10 Amps [4]. This option should allow a
panel efficiency of over 30%. Alternately for still higher
panel efficiency, indium can be added in both junctions in
an In(0.6)Ga(0.4)P / Ga(0.9)In(0.1)As DJ cell and a cell
array of this type can then be series connected with the
GaSb IR cell array operating at a current of about 7 Amps
[4]. This option should allow a panel efficiency of over
35%.
Current
Partition
AM1.5
1sun
Theory
Jsc
(mA/cm2)
Cut-on
Wavelength
(microns)
Eg
(eV)
Practical
Target
Efficiency
45%
27.9
0.82
1.5
24.3%
45%
27.9
0.82
1.5
24.3%
55%
34.1
1.77
0.7
11.5%
35.8%
30%
18.6
0.73
1.7
19.6%
30%
18.6
0.99
1.25
12.8%
40%
24.8
1.77
0.7
8.5%
40.9%
Of these two alternate choices for cell sets, we
prefer the InGaP/GaInAs-GaSb 3 junction cell set both
because the panel efficiency will be the highest but also
because the heat load on the GaSb cell will be reduced
relative to either the InGaP/GaAs already demonstrated
case or the hypothetical GaAsP case.
LOW COST PRIMARY MIRROR
Before a Dual-Focus Cassegrainian panel can be
produced as a product, the optical components will need
to be developed. We start here with a discussion of the
primary mirror. There are potentially near term and
longer-term solutions to the problem of low cost mirror
manufacturing. Perhaps the long-term solution will be a
dedicated specially designed coating machine for the
deposition of mirror films on preformed mirror substrates.
However, herein, we describe a compromise
nearer term low-cost mirror fabrication scenario. We can
address the low cost primary mirror issue by taking
advantage of the fact that two separate companies now
make low cost mirror material in a roll to roll process. This
is the material that we are using on our 3-sun project. It
costs about $20 per square meter. There are two
requirements for making Cassegrain primary mirrors.
There is a forming requirement and a coating requirement.
Our thesis is that forming is much cheaper than coating
and coating in a roll to roll process will be much cheaper
than batch coating a parabolic formed part. So we plan to
first coat a film (which is already being done) and then
apply the coated film to a formed substrate as shown in
figure 7.
The result can be a lower cost primary mirror
made by coating a flat aluminum sheet, then stamping
radial slits followed by forming into a final parabolic shape.
The slits minimize distortion of the coated surface and
coating in the flat form minimizes costs. The primary mirror
photo in figure 8 lends credibility to the proposed
fabrication concept.
Figure 6: All cells in a panel are wired in one series string.
39
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
cooler, there is an additional voltage advantage for the
Dual-Focus case of 3 x 30 x 2 mV = 0.18 V. Combining
these 2 effects gives a voltage advantage of 0.38 V and
that will translate to a 4 percentage-point advantage in
higher conversion efficiency for the Dual-Focus
configuration.
Unfortunately, efficiency and performance are not
really the problems for this proposed configuration. The
problem is funding for system integration and
manufacturing scale up.
REFERENCES
[1] Lewis M. Fraas, J. E. Avery, H. X. Huang, E. Shifman,
K. Edmondson, R.R. King, “Toward 40% and Higher
st
Multijunction Cells in a New Cassegrain PV Module”, 31
IEEE PVSC, Florida, USA (Jan. 2005).
[2] L. Fraas, J. Avery, H. Huang, Leonid Minkin, She Hui,
Eli Shifman, “Towards a 33% Efficient Cassegrainian
Solar Module”, Shanghai, October 2005.
Figure 7: The 4 steps in a hypothetical Cassegrainian
mirror fabrication process shown are as follows:
•
Step 1: Roll to roll mirror coating on plastic
film
•
Step 2: Cut flat form leaf pattern
•
Step 3: Vacuum pickup with ball transfer tool
•
Step4: Apply adhesive and press into mirror
support parquet
[3] L. Fraas J. Avery, H. Huang, Leonid Minkin, and Eli
Shifman, “Demonstration of a 33% Efficient Cassegrainian
Solar Module”, 4th World Conference on Photovoltaic
Energy Conversion, Hawaii, May 2006.
[4] Lewis M. Fraas, Patent pending
Figure 8: Primary mirror formed from patterned flat sheet.
CONCLUSION
The Dual-Focus Cassegrainian module described
here can have a significantly higher energy conversion
efficiency relative to a concentrator panel using just
monolithic triple junction cells.
This higher conversion efficiency is a result of 2
benefits. First, the GaSb cell can produce a higher
voltage relative to a Ge cell by at least 0.2 V if all cells are
operated at 25 C. However, because the Dual-Focus cell
configuration splits the heat loads, there is an additional
advantage for the Dual-Focus cell configuration. If the
cells in the Dual-Focus Cassegrainian panel operate 30 C
40
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
HYBRID OPTIC DESIGN FOR CONCENTRATOR PANELS
R.L. Johnson Jr.
Practical Instruments, 133 N. San Gabriel Blvd. Suite 205, Pasadena, CA 91107, USA
ABSTRACT
CONCENTRATING TROUGH
Practical
Instruments’
Heliotube™
integrates
individually articulating concentrator troughs into a flat
panel format compatible with rooftop installation methods.
Heliotube’s hybrid optical design provides 10x geomtetric
concentration with a ±2° acceptance angle. Each trough
has a hybrid primary optic comprising a parabolic reflector
and a Fresnel lens arranged in parallel such that the lens
concentrates rays near the optical axis and the reflector
concentrates rays farther from the axis. This lens-reflector
combination enables Heliotube to have a height/width ratio
suitable for densely packing troughs while utilizing the full
aperture of each trough to collect sunlight. Additionally,
the lens-reflector combination allows Heliotube to track the
sun daily in one axis while mitigating the effect of seasonal
sun variations. Furthermore, the optical design provides
sufficient field of view to self-power the tracking electronics
using diffuse sky radiation when not pointed at the sun.
Each concentrator trough (Fig. 2) includes an acrylic
Fresnel cover, a parabolic reflective trough constructed
from MIRO™[1], and a photovoltaic receiver comprising
14 solar cells. The trough fully encloses the receiver
protecting it from the environment. The two end caps
provide the pivot axis about which the trough is rotated to
track the sun. Within the panel, troughs are connected by
a common link arm and are articulated in unison using a
single motor. Additionally some troughs house wide and
narrow angle sun sensors used by the panel control
electronics to sense the relative sun position.
Concentrating Solar Panel
By packaging concentrating troughs into a solar
panel format, Heliotube (Fig. 1) combines the cost saving
advantages of concentrator technology with the installation
convenience and market acceptability of traditional flat
panels. Heliotube conforms to accepted mounting and
wiring practices facilitated by its relatively low profile and
ability to self-power. The combination of intelligent closed
loop sun tracking and novel optical design enable
2
Heliotube to provide an equivalent W/m solar panel at a
fraction of the cost of traditional solar panels.
Fig. 2. Trough Concentrator
HYBRID OPTICS
Fig. 1. Heliotube: Concentrating Solar Panel
Heliotube’s patent pending optical design is a 1D
prime focus concentrator that combines the best aspects
of reflective and refractive components. Rather than
having a single element concentrate the entire entrance
aperture, the hybrid optic approach splits the aperture
between a reflective trough and a refractive lens. As
illustrated in Fig. 3, the parabolic trough reflects rays
farthest from the optical axis onto the receiver located at
the bottom of the trough. In contrast, the Fresnel lens
refracts rays near the optical axis onto the receiver.
Splitting the aperture in this way overcomes problems
associated with purely reflective and refractive solutions.
41
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
that has a greater wind profile and less “panel-like”
characteristics.
Fresnel Lens
Fig. 3. Hybrid Optic
Reflective Trough
The active area of the reflective trough has a
compound parabolic concentrator (CPC) profile.
A
property of CPCs and other bottom focusing reflectors is
that rays closer to the optical axis strike the focal plane
with a larger angle of incidence than rays at the outer
edge of the reflector. Because of total internal reflection
(TIR) at the receiver encapsulant interface, there is a limit
to the incidence angle at which rays will be absorbed by
the cells. To address this issue, CPC designs typically
have either a large height/width ratio or incorporate a
collimating secondary optic between the primary and the
receiver. In either case, these solutions result in a
concentrator with a unfavorable height/width ratio for a
given concentration level. Fig. 4 compares a CPC with the
same concentration ratio to Heliotiube’s hybrid optic.
Heliotube incorporates a four zone 1D Fresnel lens
with an aperture 52% of the full trough aperture. Having
four zones allows for a sufficiently thin lens while
minimizing scattering losses at the zone boundaries. In
contrast, a full aperture Fresnel lens would either require a
much larger thickness or significantly more zones for a
given focal length. Rays farther away from the optical axis
require more bending which makes a Fresnel less efficient
at the edges and exhibit increased chromatic aberration.
From a manufacturing standpoint, fewer large zones allow
the lens to be made using standard and less costly
injection molding techniques.
Concentration, Acceptance Angle, & Beam Uniformity
Heliotube troughs provide a 10x geometric
concentration with an acceptance angle of ±2°. The
nominal design has a 5” aperture, a 0.5” receiver and a
height/width ratio ≈ 1. Taking into consideration the
scattering and absorption losses of the reflector and lens,
each trough has an 8x optical concentration factor. The
acceptance angle allows for mispointing due to
mechanical variations and control errors. Fig. 5 plots
normalized flux as a function of input angle.
Fig. 5. Acceptance Angle Performance
Fig. 4. Hybrid Optic vs. CPC
In order to concentrate the full aperture, the CPC exit
aperture must be the same size as the receiver. To
comparably limit the angle incidence the slope at the
bottom of the CPC must be the same as the slope of
hybrid optic reflector at the edge of its active region.
Consequently the CPC design has a height/width ratio
several times that of the hybrid optic design. Such large
height/width ratios make it impossible for individual
troughs to articulate and be closely spaced. One option
would be to have fixed troughs on an articulating panel,
however this would not allow the panel to lie flat on a roof
and would require larger more expensive tracking
solutions. Another option would be to space the troughs
far apart resulting in very few troughs per panel or very
large panels. Either of these options result in a taller panel
Beam uniformity is often a concern with
concentrators because highly non-uniform beams can
result in localized hot spots that reduce cell efficiency [2].
The beam profile is shown in Fig. 6 for on axis and off axis
conditions for a 1 W ½° source. On axis, both reflector
and lens concentrate onto the center 1/3 of the receiver
resulting in a localized concentration of 24x. The off axis
conditions reveal that the hybrid optic helps maintain
beam uniformity because the focal spots generated by the
reflector and lens translate in opposite directions as the
input beam moves off-axis. As a result, the flux density
never exceeds the on-axis condition over the entire
acceptance angle. By optimizing the receiver for the onaxis concentration, Heliotube avoids hot spots and can
operate efficiently over its acceptance range.
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
On Axis
1° Off Axis
1000
1000
Trough
Lens
100
1
-0.3
-0.2
-0.1
0.1
0
0.1
0.2
0.3
10
W/cm2
W/cm2
100
Combined
10
1
-0.3
-0.2
-0.1
0.1
0.001
0.001
0.0001
0.0001
x(in)
1000
1000
100
100
0
0.1
0.2
0.3
W/cm2
W/cm2
0.1
0.3
Effects Of φ
10
1
-0.1
0.2
2° Off Axis
10
-0.2
0.1
x(in)
1.5° Off Axis
-0.3
0
0.01
0.01
-0.3
1
-0.2
Trough
Lens
Combined
0.01
0.001
0.0001
-0.1
0.1
0
0.1
0.2
0.3
0.01
0.001
0.0001
x(in)
optical axis. As a result, when the troughs are aligned to
the sun’s longitude angle θ, the sun’s position relative to
the troughs’ optical axis can be characterized by the
latitude angle φ.
x(in)
Fig. 6. On & Off Axis Beam Profile
TRACKING
In order to generate significant power, Heliotube
must align its troughs with the sun.
Sun sensors
incorporated into some of the troughs provide feedback to
the control system in order to articulate the troughs to
track the sun’s longitude as it moves across the sky. By
tracking the sun, Heliotube generates peak power
throughout a longer portion of the day.
Elevation Tracking
Fig. 7 shows a normalized flux profile as a function of
declination angle. Between 0 and 25 degrees Heliotube
generates full power as all tubes are fully illuminated. As
the declination angle increases beyond 25 degrees,
adjacent tubes begin to shadow each other reducing
incident solar flux and the panel output.
Latitude angle affects the reflective and refractive
components of Heliotube differently. The reason for this is
because reflection is a linear operation allowing the
principle of superposition to be applied; whereas refraction
is a non-linear operation and superposition cannot be
applied.
When the trough is aligned to the sun’s longitude
angle, incident rays have a component that is parallel to
the optical axis (z) and a component that is parallel to the
axis of rotation (y). In the case of a reflective surface, the
z components get concentrated along the x-axis but the y
components are not affected because they are parallel to
the reflection plane. Consequently, the reflector exhibits
no aberrations from off-axis rays that are parallel to optical
plane. The incident flux on the receiver is therefore just
the cosine projection of solar vector onto the reflector’s
aperture
In the case of the Fresnel lens, Snell’s Law cannot
be applied separately in each axis. Consequently the
component of the refracted ray parallel to the x-axis is a
function of φ as is the component parallel to the y-axis.
The net result is that the effective focal length of the
Fresnel decreases as φ increases.
This effect is
illustrated in Fig. 8 in which the rays traced are parallel to
the optical plane but off-axis relative to the y-z plane by 20
degrees.
Heliotube
1
Normalized Flux
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
70
80
90
100
θ(°)
Fig. 7. Normalized Flux vs. Declination Angle
Seasonal Variations
Because the panel is a single axis tracker it does not
account for seasonal variations in the sun’s latitude angle.
Consequently, the tracking control system can only align
the optical plane of each trough to the sun and not the
Fig. 8. Off Axis Aberration
Rays reflecting off of the trough are focused correctly
on the receiver. Rays refracted by the Fresnel lens come
to a focus in front of the receiver. In this particular case,
the aberration does not cause rays to miss the receiver
and therefore the solar flux on the receiver follows the
cosine law. As φ increases, however, the aberration
eventually causes rays to miss the receiver and the
receiver flux decreases. Combining the off axis effects of
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
the reflector and the lens according to the contributions of
the respective apertures yields the following plot of flux
versus off-axis latitude angle (Fig. 9).
field of view is provided by the non-concentrating windows
in the cover between the lens and the reflector. Fig. 11
illustrates Heliotube’s field of view with respect to diffuse
sky radiation.
1
Reflector
Lens
Heliotube
Normalized Flux
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
70
80
Φ(°)
Fig. 9. Heliotube’s Latitude Angle Performance
Figure 9 indicates that the hybrid optic has a ±25°
degree window where the lens is unaffected by latitude
induced aberration. In contrast, a comparable full aperture
Fresnel would exhibit a much narrower window.
Consequently, such a concentrator is required to track
both sun axes. In order to lie flat on the roof, panels
incorporating lens-only concentrators could be mounted
on large rotation platforms. Such platforms are generally
expensive and do not conform to typical panel mounting
practices. Alternatively, such panels could be tilted
seasonally either by automated or manual means. In
either case, having to track in the second axis results in
less – flat panel-like systems. Because the hybrid optic
approach limits the effects of the latitude aberration,
Heliotube is able to track in one axis only with an
estimated annualized performance degradation of less
than 10%.
Fig. 10. Diffuse Sky Field Of View
CONCLUSION
Heliotube’s hybrid optic design delivers a simple and
effective solution enabling concentrator technology to
compete in the rooftop solar market. At present Practical
Instruments is taking Heliotube from the prototype pictured
in Fig. 11 into production. As we work to fine tune
manufacturing issues, we are confident that the
advantages of using the hybrid optical design will enable
us to deliver a reliable and less expensive concentrating
alternative to traditional solar panels.
SELF POWERING
Providing an external power source to bootstrap a
concentrator’s tracking control system is a barrier for many
installers of traditional photovoltaic systems. Battery and
other energy storage solutions could be employed but
have limited lifetime issues. Borrowing power from the
grid is also possible, but adds another level of installation
complexity and isolation problems.
Heliotube overcomes this hurdle by providing a fully
solar self-powered solution. By combining low power
intelligent control system techniques and the hybrid optical
design, Heliotube generates sufficient power to track even
when not pointed at the sun. In fact, Heliotube is able to
self-power each morning as the sun rises in the east while
its troughs are facing west.
The key to self-powering is the hybrid optics ability to
collect enough diffuse radiation from the sky. Whereas
most concentrator designs have a field of view limited to
the acceptance angle of the concentrating optics,
Heliotube’s, hybrid optic approach provides a 30° field of
view by which the receiver can see the sky. This added
Fig. 11. Prototype On The Rooftop
FINAL NOTE
At the time of this writing, Practical Instruments is in
the process of changing its name to Soliant Energy.
REFERENCES
[1] MIRO is a registered trademark of Alanod
[2] E.T.Franlin, J.S. Coventry. “Effects of Highly Nonuniform Illumination Distribution on Electrical Performance
of Solar Cells”. Proc. 40th ANZSES Conference,
Newcastle, Australia, November 2002.
44
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
NONIMAGING FLAT FRESNEL LENSES
R. Leutz
Physics Department, Philipps-University, Renthof 5, 35037 Marburg, Germany;
ralf.leutz@physik.uni-marburg.de, phone +49-6421-2824148, fax +49-6421-2826535
ABSTRACT
Nonimaging flat Fresnel lenses are designed based
on imaging flat Fresnel lenses. The flat Fresnel lens has
three geometrical degrees of freedom: two surfaces and
the decoupling of the local slope of the prism from the
global shape of the lens. The third degree of freedom is
used to create a finite size focal area illuminated with a
prescribed irradiance pattern. The lenses show
moderately increased tracking sensitivites but are
characterized by the absence of hot spots. The maximum
concentration ratio along with dispersion are discussed.
This sounds simple, but it takes the flat Fresnel lens
one step beyond its image as the aspheric version of the
plano-convex singlet lens. Just as the aspherical lens (or
the Fresnel lens) can be designed to correct spherical
aberrations, it can be used to create a defined irradiation
pattern.
This paper discusses possibilities to customize the
design of flat Fresnel lenses for solar applications,
i. e. deterministic aberrations detailed in this paper, as
compared to point-focussing, and blue-edge, or red-edge
designs [1,2]. The analysis encompasses tracking
sensitivity, and irradiance distribution on the target, as
caused by the design of those nonimaging flat Fresnel
lenses.
INTRODUCTION
DESIGN STRATEGIES
Is it possible to design nonimaging flat Fresnel
lenses? How many degrees of freedom does the flat
Fresnel lens have? The answer is three; two for its two
surfaces, and one for decoupling the global shape of the
lens and the local slope of the prisms. A change of
material could be regarded as the fourth degree of
freedom, but this is equivalent to changing the prism
angle, or the refractive power of the lens.
The upper surface of the simple Fresnel lens is flat.
This leaves two degrees of freedom. One is used to focus
the light onto the focal point. The second degree of
freedom (the fact that each prism can be oriented
independently) may be used to spread the focus
deterministically (or statistically) around the focal point,
creating a defined irradiance distribution on the receiver.
Figure 1 shows the design strategies explored in the
cause of this work. The standard point focus design
(Fig. 1a) often yields a hot spot target irradiance pattern
which for all but the highest concentration ratios may be
only partially illuminating the cell. Partial illumination of the
cell generally is inefficient. Fig. 1b shows a fixed focal
area. Blue-edge or red-edge designs are similar to this
concept. Focussing all rays onto a ring (assuming the
design is rotationally symmetric, or 3D) on the target leads
to a doughnut-shaped irradiance distribution. Depending
on concentration ratio, this may result in good irradiance
uniformity.
The irradiance distribution on the target depends on
three factors, the cosine of the impinging ray (its projected
Figure 1: Strategies for the design of flat Fresnel lenses, (a) point focus design, (b) fixed focal area, (c) statistical or
folding focus design
45
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
width), the dispersion of the lens (the beam width depends
on the spectrum of the incident light, and the prism
material and angle), and the divergence angle of the
source. The half angle of the solar disk is 0.28°. For
extremely high concentration ratios well above
10.000 suns, sunshape (the brightness variations across
the solar disk) must be considered.
IRRADIANCE AND BEAM SPREAD
The irradiance distribution on the target of a
refractive concentrator depends on the three beam spread
factors cosine-effect, dispersion, and sunshape.
Dispersion is the most critical of the three, as shown in
Figs. 4-6.
The geometrical concentration ratio, hence the size
of the nominal focal area, receiver or cells size, interacts
with the three beam spread factors cosine-effect,
dispersion, and sunshape. The higher the geometrical
ratio of the lens, the more likely it is that the cross-section
of the beam exceeds the size of the target. In that case,
the strategy of point-focussing yields acceptable results in
terms of irradiance distribution.
Typical concentration ratios of flat Fresnel lenses for
photovoltaic applications are in the range of 500 suns. The
geometrical concentration ratio is defined as
r2
C = lens
2
rrec
⇔
rrec = 0.045 rlens ,
(1)
Figure 4: Irradiance distribution on the target of a lens
designed with focal rings rings of equal area (Fig. 3).
Monochromatic and parallel incidence. Note the doughnutshape of the distribution
where the indices define the radii of the lens and the
receiver, respectively. Whether the spread of the
dispersed beam is larger or smaller than the target
depends on the focal length and aspect ratio of the
concentrator.
When the beam spread is much smaller than the
receiver size, the folding focus design of Fig. 1c can be
used to modify irradiance patterns. The folding of the
focus moves the intersection with the receiver plane of any
ray from a given prism to a defined location. In a first-order
approximation for three-dimensional (3D) systems the
irradiance decreases with the square of the distance from
the optical axis of the system. Therefore, it makes sense
to increase the density of rays with increasing radius, as
shown in a comparison in Figs. 2 and 3.
Figure 2: Ray footprint of
lens designed with equal
spacing between rays on
the target
Figure 3: Ray footprint of
lens designed for uniform
irradiance on the target
The design in Fig. 3 tends to deliver a more uniform
irradiance distribution on the target. The dependence of
the resulting irradiance pattern on the factors affecting the
beam spread are discussed in the following section.
Figure 5: Irradiance distribution on the target of a lens
designed with focal rings rings of equal area (Fig. 3).
Monochromatic incidence and sunshape 0.28°
Figure 6: Irradiance distribution on the target of a lens
designed with focal rings rings of equal area (Fig. 3).
Sunshape 0.28° and solar spectrum 300-1900 nm. The
shape of the distribution shows a moderate hot spot
All ray-tracing simulations in Figs. 4-6 were
performed with an identical lens. The results indicate the
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
importance of the dispersion for the shape of the
irradiance distribution on the receiver. Further
modifications of the design are required to soften the
moderate hot spot observed in Fig. 6.
FURTHER DESIGN TACTICS
The design strategy outlined above can be modified
and changed in detail in order to achieve a prescribed
irradiance distribution and concentration. These tactics
allow for the elimination of hot spots in the center of the
receiver.
For the three strategies pictured in Fig. 1, typical
irradiance distributions are given in Fig. 7, for threedimensional flat Fresnel lenses.
Figure 8: Tracking sensitivity for the lenses with irradiance
distributions shown in Fig. 7. Increased uniformity of the
irradiance on the target leads to moderately higher
tracking sensitivity
Why is it impossible to create a ‘pillbox’-shape of the
irradiance distribution in Fig. 7? The beam spread
depends on dispersion and size of the solar disk. The
cosine-effect may be neglected in the following
considerations, as its influence on beam spread depends
on prism size. Accordingly, the cosine-effect is small for
small prisms.
The dispersion can be calculated. The rotation of a
ray at a prism is [2,3]
Figure 7: Irradiance distributions on the target for the
design strategies shown in Fig. 1, ‘off-focus’ refers to the
strategy in Fig. 1b. Note how the peak irradiance is
reduced in favour of a lower concentration ratio. The
concentrator is rotationally symmetric
As an extreme example, the lens named ‘random
focus 0.75 lens’ is a design where a focal area defined to
have a radius 75% of the nominal radius for the desired
concentration ratio of 500 suns is illuminated randomly.
This is, first, not very scientific (I noted above that the
density of rays must be increased squarely with radius),
and, secondly, results in a random pattern of prism angles
at the lens, which may be cumbersome to manufacture.
dϕ =
t dn
∆λ .
l dλ
(2)
The lengths t and l describe the prism angle. For the
solar spectrum, and the appropriate refractive indices of
PMMA, with the solar half-angle already added, the beam
spread can be expressed as a length, shown in Fig. 9.
The lens design tactics in Fig. 7 have a significant
influence on the required tracking accurracy of the lenses.
As expected, the efficiency of the lens is reduced if the
light is not focused to a central point. Any tracking
misalignment moves the focus out of the center. For the
point focus design it simply takes longest to move rays off
the target, as shown in Fig. 8.
While the lenses with better uniformity of the
irradiation on the target suffer from a moderate increase of
tracking sensitivity, it should be noted that the conversion
efficiency of the photovoltaic cell will increase with better
uniformity.
Figure 9: Width of the beam relative to nominal target, for
a geometrical concentration ratio of 500 suns. The aspect
ratio of the lens is 0.5
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
From Fig. 9, it is clear that the geometrical
concentration ratio of 500 suns is high enough to cause a
beam spread large enough for tailored ‘pillbox’-shaped
irradiance distributions to become impossible.
Due to lack of space, I would like to discuss the
details leading to Fig. 9 in a future paper [4], based on the
observations for the maximum concentration ratio of
refractive concentrators [5].
CONCLUSIONS
Nonimaging flat Fresnel lenses can be designed. It is
possible to tailor the irradiance distribution on the target
within bounds. The design strategies may be combined
with tactics fine tuning the irradiance pattern. It is
important that the number of prisms is high for statistical
reasons. It is equally important to understand what the
influence of the concentration ratio in combination with the
beam spread and aspect ratio on the irradiance
distribution are.
Further work will focus on the description of the
beam spread function due to cosine-effect, dispersion, and
sunshape, in order to find a suitable set of parameters
both for nonimaging lens design and for choosing the best
speed of a flat Fresnel lens for a given acceptance,
concentration and tracking sensitivity.
ACKNOWLEDGEMENTS
I would like to thank Jeff Gordon for the initial
discussions on this subject in Tokyo years ago, and
Harald Ries for his ideas concerning the folding of the rays
onto the target.
REFERENCES
[1] L.W. James and J.K. Williams, Fresnel Optics for Solar
Concentration on Photovoltaic Cells, in: Proceedings of
the 13th IEEE Photovoltaic Specialists Conference, 1978,
673-679.
[2] R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses:
Design and Performance of Solar Concentrators,
Springer Verlag, Heidelberg, 2001.
[3] M. Born and E. Wolf, Principles of Optics, 6th ed.,
Pergamon, Oxford, 1989.
[4] R. Leutz and L. Fu, Dispersion in Tailored Fresnel
Lens Concentrators, abstract submitted for the ISES Solar
World Congress 2007, Beijing, China.
[5] R. Leutz and H. Ries, Concentration Limit of Solar
Fresnel Lenses, in: Proceedings of the ISES Solar World
Congress 2003, Göteborg, Sweden.
48
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
THE NEW APPROACH TO DESIGN OF FRESNEL LENS SUNLIGHT CONCENTRATOR
1
V.A. Grilikhes1, V.M. Andreev1, A.A. Soluyanov2, E.V. Vlasova2, M.Z. Shvarts1
Ioffe Physico-Technical Institute, 26 Polytechnicheskaya str., St.-Petersburg, 194021, Russia
2
Technoexan LTD, 26 Polytechnicheskaya str., St.-Petersburg, 194021, Russia
Tel.: +7(812) 292 7394; fax: +7(812) 297 1017; e-mail: gril@scell.ioffe.rssi.ru
ABSTRACT
GEOMETRICAL OPTICS CONCEPT
A new approach to designing Fresnel lenses as
sunlight concentrators based on search of the optimal
combination of dimension of a lens, its focal distance and
the refracting surface profile parameters, which ensures
the maximum average concentration, is presented.
Realization of the approach is illustrated on the example of
flat-plane Fresnel lenses with point focus using the
concepts of geometrical and power optics.
It has been shown that in using the proposed
procedure, the negative effect of chromatic aberration on
the concentrating capability of a lens may be decreased in
1.5–2 times. The validity of the choice of the lens design
parameters depend strongly on the accuracy in
determining the dependence of its material refraction
index on wavelength.
To account for the physical essence of the proposed
approach, it is appropriate to consider the problem in the
geometrical optics approximation. It is known [12] that,
when there is no CA, the concentration ratio of an ideal
max
is determined by its opening angle (or by the
lens Cg
ratio of the diameter 2rl to the focal distance f ) and by the
angular diameter of the sun 2φs = 32'. At the optimum ratio
rl / f =1, the Cgmax value is 11500 and the focal spot radius
is approximately in 107 times smaller than the lens radius.
The presence of CA, which stems from the
dependence of the refractive index of the lens material on
the radiation wavelength, n=n(λ), leads to a significant
increase in the focal spot radius rs and, as a result, to the
considerable decrease of the geometrical concentration
2
Cg=(rl /rs) .
Figure 1 shows schematically how a sunlight beam
passing through the terminal tooth of a lens decomposes
due to light dispersion into several monochromatic beams
(each with its own wavelength) with an angular divergence
of 2φs.
INTRODUCTION
Different lens sunlight concentrators find expanding
application in photovoltaic installations [1-4]. The main
disadvantage of lenses as concentrators is conditioned
with the chromatic aberrations (CA), which, at the wide
range of the sunlight spectrum and finite angular
dimension of the Sun, leads to “blurring” of the
concentrated radiation in the plane of the photoreceiver
location and to the considerable decrease in the average
level of the photoreceiver irradiance.
This negative effect can be essentially diminished by
a correct choice of the optimum combination of the lens
dimension, its focal distance and optical parameters
determining the refracting surface profile. The optimization
criterion is the maximum of the average sunlight
concentration corresponding to the focal spot minimum
size. The optical parameter controlling the profile of the
lens at its preassigned dimensions and focal distance is
the refractive index, the values of which are taken from its
precisely determined dependence on wavelength for a
chosen lens material. Any optimization procedure may be
used for solving the problem.
Such is suggested general approach for designing
lens concentrators, which will be illustrated by an example
of choosing design parameters of flat-plane Fresnel lenses
(FL), being among the most promising ones for solar
photovoltaic installations [5-9]. All calculations were
performed with using two concentration process models
based on the geometrical optics and photometry (power
optics) concepts [10, 11].
r α2
n α
α1
rl
t
h/2
α
h
θ UV
f
θ IR
β UV
β IR
ϕS
FUV
F0
FIR
rUV
rIR
Fig.1. Schematic diagram of sunlight beam dispersion on
the terminal tooth of a Fresnel lens
49
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
rl − t / 2
ncalc ⋅ ( rl − t / 2) 2 + f 2 − f
,
(1)
where t is the step of the lens profile [13].
Taking into account that, after refraction in the UV
range, the maximum deviation from the axis is observed
for the extreme ray with the largest angle (α1) and in the IR
range with the smallest angle (α2) of incidence, it is
expedient to restrict the consideration to these two cases:
α1 = α + ϕ S ; α 2 = α − ϕ S
(2)
The angles of refraction for the rays arriving from the
periphery of the Sun disk for the UV and IR spectrum
regions are related to the corresponding angles of
incidence via the Snell law as
β UV = arcsin( nUV ⋅ sin α 1 )
β IR = arcsin( nIR ⋅ sin α 2 )
(3)
where nUV and nIR are the refractive indexes of the lens
material, which correspond to the extreme wavelengths in
the UV and IR spectral regions, respectively.
The angles between the extreme refracted rays and
the optical axis of the lens in the UV and IR spectral
regions are defined as:
θ UV = β UV − α ; θ IR = β IR − α
(4)
The radii of focal spots determined by the points of
intersection of the extreme refracted UV and IR rays with
the focal plane are, respectively
rUV = ( f + h / 2) ⋅ tgθ UV − rl
rIR = rl − ( f + h / 2) ⋅ tgθ IR
;
1.5
IR
1.4
1.3
UV
1.2
ncalc = 1.5087
1.45
UV
1.40
1.35
IR
1.30
ncalc = 1.5059
UV
1.6
1.5
1.4
1.3
IR
1.2
50
60
70
80
90
100
Focal distance, mm
Fig. 2. The dependences of the UV and IR focal spot radii
on the focal distance f calculated with allowance for CA at
various values of the ncalc .
(5)
where h = t ⋅ tan α is the Fresnel lens tooth height.
The latter two formulae show that the radii of the UV
and IR spots depend on the focal distance and the lens
size, and also on θUV and θIR angles, which are determined
not only by f and rl , but also by three values of the
refraction index – one chosen for calculation of the lens
profile and two corresponding to extreme wavelengths in
the considered range (see expressions 1-4).
It follows from the formulae (5) that at the
preassigned lens radius, there exist values of the focal
distances ensuring minimal radii of the focal spots for each
extreme wavelength of a range due to that angles θUV and
θIR decrease with increasing f.
The calculations were performed at fixed rl =20 mm
and t = 0.3 mm for wavelengths of the solar radiation
ncalc = 1.5114
1.6
1.5087
Geometrical concentration
α = arctg
spectrum within 0.35 –0.92 µm and for the ncalc variation
from 1.525 to 1.495 in accordance with the experimental
dispersion curve n(λ) for the lens material.
The dependences of the UV and IR focal spot radii
on the focal distance at different ncalc values are presented
in Figure 2, from which it follows that minimum spot radius
values for UV and IR radiation correspond to different
focal distances. To determine the geometrical
concentration ratio at any focal distance, one has to
choose the greatest radius of two. The corresponding
dependences of the geometrical concentration ratio on the
focal distance are shown in Figure 3 for different ncalc
values. The plot indicates that at each ncalc value there
exists a maximum of the geometrical concentration
corresponding either to the minimal IR spot (left side
curves), or to the minimal UV spot (right side curves), of to
the equality of the spots (middle curves). Besides, it is
clear that there is the only combination of the ncalc and f,
which ensures the greatest maximum of the geometrical
concentration ratio.
Focal spot radius, mm
The central ray of a beam with the wavelength
corresponding to the refractive index ncalc chosen for
calculations of the Fresnel lens profile strikes the center F0
of the focal spot. Beams with wavelengths other than that
corresponding to ncalc will cross the optical axis above (UV
radiation) or below (IR radiation) the focal plane, thus
forming additional foci (FUV and FIR , respectively) on the
optical axis. In this case, the spot radius in the focal plane
will be determined by its intersection with the extreme ray
of the beam with the wavelength at the corresponding end
of the radiation spectrum in the UV or IR region.
The radii of the focal spots of corresponding extreme
rays of the UV and IR beams (rUV and rIR, respectively)
can be determined as follows (see Fig. 1). The angle of
incidence of the central ray of the sunlight beam on the
lens face is determined as:
225
1.5093
220
1.5082
215
210
205
1.5099
1.5073
200
195
190
ncalc=1.5114
185
1.5059
180
175
50
55
60
65
70
75
80
85
90
Focal distance, mm
Fig. 3. Geometrical concentration coefficient Cg versus
focal distance f calculated with allowance for CA at various
values of the ncalc .
50
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
profile corresponding to these parameters and hence the
geometrical concentration can be increased in 1.5-2 times.
2.0
min
200
180
1.8
160
1.6
140
120
1.4
100
opt
calc
n
80
1.496
Minimum focal spot radius rs
Maximum geometric concentration Cgmax
220
, mm
2.2
240
1.2
1.500
1.504
1.508
1.512
1.516
1.520
1.524
1.528
Refractive index ncalc
max
and
Fig. 4. Maximum geometrical concentration Cg
minimum focal spot radius rsmin versus refractive index
ncalc.
POWER OPTICS (PHOTOMETRY) CONCEPT
0.7
0.5
2500
Local concentration
300
0.8
2000
250
0.9
1500
200
150
1000
100
0.4
50
0
-1.0
-0.5
0.0
0.5
Radius, mm
1.0
max values on the n
Cav
calc , which indicates that at Kint = 0.95
the choice of optimal designed lens parameters allows to
obtain the average concentration on a receiver of
appropriate size close to 800 X. The plot also shows that
an error in choosing ncalc in the third digit results in a
significant decrease in the average concentration.
800
500
0
-1.0
-0.5
0.0
Radius, mm
0.5
r0.95
rs
1.0
Fig. 5. Spectral (left) and integral (right) OPCs of
2
40 x 40 mm Fresnel lens.
750
4
700
3
5
6 2
650
1
600
f opt
550
50
60
70
80
90
100
Focal distance, mm
Fig. 6. Average concentration ratio versus focal distance f
at different refractive indexes ncalc (Kint = 0.95): 1-1.51301;
2-1.51150; 3-1.51011; 4-1.50879; 5-1.50754; 6-1.50637.
Maximum average concentration Cav
λ = 0.6 µm
350
max
shows that at each ncalc there exists a maximum Cav
value and a corresponding to it optimum f value. However,
only one of these combinations ensures obtaining the
greatest among maximum ones average concentrations.
Figure 7 presents the dependence of the maximum
max
In choosing optimum design parameters of practical
FL on the grounds of the power optics (photometry),
basically the same approach as on the geometrical optics
concept is valid. However, the basis of the calculations are
the optical-power characteristics (OPC) of the lens, which
characterize the concentrated radiation density distribution
in its focal plane. Figure 5 presents the spectral and
2
integral OPC of a 40 x 40 mm Fresnel lens with the
profile step of 0.3 mm. As in the case of the geometrical
optics concept, in calculations, the precisely determined
dispersion curve n(λ) for a chosen lens material was used.
Calculation of OPC was carried out with using the
procedure presented by us in [14].
In determining average values of the concentration
ratio, considered is not the whole area of the focal spot
with radius rs , but the area of the circle, which collects the
95-98% of the concentrated radiation power. The latter
allows obtaining a higher average concentration on a
receiver without essential losses of the total radiation
power passed through the lens. The ratio of the radiation
power on the receiver to the total concentrated radiation
power is characterized by the intersection factor Kint .
Figure 6 presents dependencies of the average
concentration ratio (Cav) on the focal distance f at different
values of the refractive index ncalc and Kint = 0.95. The plot
Average concentration Cav
This is illustrated by Figure 4, which presents the
dependences of maximal values of geometrical
concentration ratio and minimal focal spot radii on ncalc . It
is seen, to what extent the maximum concentration is
sensitive to the accuracy of ncalc selection. Thus, the
influence of CA can essentially lowered down by correct
opt
and f opt and the lens
choosing the combination of ncalc
850
800
750
700
650
600
550
500
450
nopt=1.50879
1.503
1.506
1.509
1.512
1.515
Refractive index n
calc
max
Fig. 7. The maximum average concentration ratio Cav
versus material refractive index ncalc (Kint = 0.95).
51
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
CONCLUSION
In conclusion, additional two circumstances should
be pointed out:
- when a lens with optimal parameters is designed, one
may consider the problem on the choice of the size of the
solar cell (SC), which must be placed in the focal plane of
the such lens. For this, on the basis of the integral OPC of
the designed lens, the dependencies of Cav and of optical
efficiency ηoptical on the SC radius can be plotted (see
Fig.8). The plot shows that in choosing the SC radius it is
necessary to allow for two contradictory tendencies: in
increasing Cav , the “FL – SC” system optical efficiency
decreases, and vise versa the average concentration ratio
decreases with rising ηoptical . The ultimate choice is
determined by economical considerations with allowing for
the operational factors;
- if in the focal plane a multijunction SC is located, the
principal approach in designing the optimal lens profile
remains the same. However, the criterion for choosing
lens parameters changes: instead of the average
concentration maximum in the focal plane (i.e. on SC),
average concentration values are given for separate
photoactive junctions of SC.
1.0
0.8
2000
0.6
1500
0.4
1000
0.2
500
0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Optical efficiency, ηoptical
Average concentration Cav
2500
0.0
Solar cell radius, mm
Fig. 8. Dependencies of Cav and of optical efficiency ηoptical
on the SC radius for optimal Fresnel lens.
SUMMARY
The physical essence of the proposed approach to
the search of optimal design parameters of a FL sunlight
concentrator has been revealed on the example of solving
the problem with using the geometrical optics concept. It
has been seen that for a lens of any material there exists
the only combination of optimum values of lens size, lens
focal distance and refraction index ncalc used for the profile
calculation, which ensures the maximum concentration of
sunlight.
To determine the optimal design parameters of
practical lens, the power (photometric) concept has been
used based on calculation of spectral and integral
distributions of the concentrated radiation density on a
receiver. The analysis has shown that the possibility to
achieve the maximum radiation concentration depends in
decisive degree on the correct choice of ncalc from the
precisely determined lens material dispersion curve.
It has been also established that in choosing the size
of SC placed in the focal plane of FL with optimal
parameters, it is necessary to take into account the
contradictory effect of the SC radius on the average
concentration and the optical efficiency of the “FL-SC”
system.
ACKNOWLEGEMENTS
The authors would like to thank N.Kh.Timoshina for
the technical assistance.
This work has been supported by the Russian
Foundation for the Basic Research (Grant 05-08-33603).
REFERENCES
[1] R. Leutz, et al. “Nonimaging Freslen Lens
Concentrators for Photovoltaic Application”. Proc. ISEC
Solar World Congress, Jerusalem, Israel, 1999
[2] V. Andreev, et al. “Space Photovoltaic Modules with
Short-focal-length Linear Refractive Concentrators”. Proc.
th
of the 16 European PVSEC, 2000, on CD.
[3] A. Terao, et al. “New Development on the Flatplate
th
Micro-concentrator Module”. Proc. of the 3 WCPVEC,
Osaca, Yapan, 2003
[4] K. Araki, et al. “A 550 x Concentrator System with
Dome-shaped Fresnel Lenses - Reliability and Cost”.
Proc. of the 20th EPVSEC, Barcelona, Spain, 2005, on CD
[5] V. Grilikhes, et al. “Indoor and outdoor testing of space
concentrator AlGaAs/GaAs photovoltaic modules with
th
Fresnel lenses”. Proc. of the 25 IEEE PVSC, 1996. pp
345-348.
[6] R. Leutz, et al. “Development and design of solar
engineering Fresnel lenses”. Proc. of Symposium on
Energy Engineering, 2000. 2, pp. 759-765.
[7] V. Rumyantsev, et al. “Terrestrial and space
concentrator PV modules with composite (glass-silicon)
th
Fresnel Lenses”. Proc. of the 29 IEEE PVSC, 2002.
p.1596-1599.
[8] H. Cotal, R. Sherif. “The effect of chromatic aberration
on the performance of GaInP/GaAs/Ge concentrator solar
St
cells from Fresnel optics”. Proc. of the 31 IEEE PVSC,
2005. pp 747-750.
[9] V. Rumyantsev, et al. “Terrestrial concentrator PV
modules based on GaInP/GaAs/Ge TJ cells and minilens
th
panels”. Proc. of the 4 WCPEC, 2006, on CD.
[10] V. Grilikhes, et al. “Effect of Chromatic Aberration on
the Concentration of Solar Radiation by Fresnel Lenses”.
Technical Physics Letters, 2006. 32 No 12, pp. 1039-1042
[11] E. Bobkova, V. Grilikhes, A. Soluyanov, M. Shvarts.
“The method for choosing the optimal parameters of flatplane Fresnel lenses, intended for sunlight concentration”,
Geliotekhnica, 2006. No 3 pp. 50-57, (Translated into
English in Applied Solar Energy)
[12] V. Weinberg. “Optical in the solar power plants”.
Laningrad, Oborongiz, 1959. 256 p.
[13] E. Tver’yanovich “Profiles of Solar-Engineering
Fresnel Lenses”. Geliotekhnica, 1984. No 6, pp. 31-34,
(Translated into English in Applied Solar Energy).
[14] A. Soluyanov, V. Grilikhes. “Methods of Calculation of
Fresnel lenses as Sunlight Concentrators”. Geliotekhnica,
1993. No 5 pp. 48-53, (Translated into English in Applied
Solar Energy).
52
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
ACCEPTANCE ANGLE REQUIREMENTS FOR POINT FOCUS CPV SYSTEMS
S Cowley, S Horne, S Jensen, R MacDonald
SolFocus, Inc., 3333 Coyote Hill Rd., Palo Alto, CA 94304, USA
ABSTRACT
High concentration photovoltaic designs that
dramatically reduce the active area of semiconductors
increase the requirement for accurate tracking. The
increasingly common point focus designs with geometric
concentration above 400 can require tracking accuracy in
two dimensions of 0.1 to 1 degrees for a single point focus
element. Wiring these elements in series significantly
reduces the angular acceptance of complete panels and
arrays. We present results of models and measurements
examining the impact of acceptance angle properties of
individual units and the impact on cascaded arrays. The
analysis is used to determine the accuracy requirements
of two-axis trackers for high concentration PV systems.
behavior of acceptance angle in cascaded arrays and to
further assess the effectiveness of ISC measurements in
determining acceptance angle.
Precision, two-axis trackers for CPV systems require
high accuracy controllers [4], high stiffness structural
elements, and precision, low backlash drives, all of which
add cost to the complete CPV system. The cost of these
tracker components are strongly dependent on the
tracking accuracy required by the concentrators, as
described by the acceptance angle of the complete array.
For example, the cost of a tracker frame can be reduced
by over 25% by relaxing its bending/flexure requirement
from 0.1 to 0.4 degrees, as shown in Figure 1.
Tracker Cost
INTRODUCTION
The acceptance angle for a complete array of point
focus, mini-concentrators will depend on many component
and system level factors such as the optical design, the
manufacturing variation of optical components, the
manufacturing tolerances of the panel assembly, the
alignment tolerances of panels to the tracker, and the
electrical topology of the panel array.
Previously
published measurements of acceptance angle on CPV
modules suggest that acceptance angle can be measured
using either the short-circuit current (Isc) or the module
power at maximum power point (PMPP).[3] We present
results of acceptance angle measurements on individual
mini-concentrators as well as complete panels to show the
Relative Cost
Market interest in high concentration photovoltaic
systems has been rekindled by the dramatic growth and
commercial success of large scale flat plate photovoltaic
(PV) systems and the coincident silicon supply shortage.
Novel point focus, high concentration optical designs and
successful commercialization of high efficiency, multijunction PV cells fuel the promise of concentrator
photovoltaic (CPV) systems.[1], [2] Point focus designs
based on mini-concentrators allow CPV systems to be
constructed from panels that emulate flat plate
technologies, except that they require much more
accurate mechanical tracking. The tracking accuracy
mandated by the acceptance angle of the complete array
has a strong impact on total equipment cost. Acceptance
angle, commonly defined as the 90% power point for a
concentrator, also has a strong impact on installation costs
and system performance. A thorough understanding of
acceptance angle is therefore invaluable in reduction of
the overall cost of electricity for CPV systems.
100%
90%
80%
70%
Total
Frame
60%
50%
0.1
0.2
0.3
Flexure (degrees)
0.4
Fig. 1. Sensitivity of cost to flexure for a specific 2axis azimuth-elevation tracker
The reduced tracker costs afforded by relaxed flexure
tolerances favors panels with wider acceptance angles,
and factors which affect the acceptance angle by tenths of
a degree can have a meaningful impact.
One important effect is the electrical interconnection
between individual mini-concentrators within a panel and
between panels on a tracker array. Conventional wiring
approaches call for string voltages of 400 V or more,
representing well over 100 multi-junction cells wired in
series. This degree of concatenation has the potential to
dramatically narrow the effective acceptance angle of such
a string.
53
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
SYSTEM DESCRIPTION
Measurements were taken on SolFocus Gen1
panels mounted on a two-axis azimuth elevation drive.
The Gen1 panel, shown in Figure 2, is constructed from
16 power units wired in series. Each power unit includes
two mirrors and a tapered rod, providing a net
concentration of approximately 500, along with a bypass
diode. The tapered rod enhances the acceptance angle of
the power unit to approximately +/-1 degree.
pole determines the tracker axes of rotation.
Rotation of the module axes maps out a grid of
measurement points relative to the Sun’s position.
The panel was brought on sun then, under program
control, was moved in a 15 x 15 grid centered on the sun
with 0. 3o step size (Fig. 3). Between discrete grid steps,
the tracker continued to move with the sun to ensure
consistent relative pointing errors through the test
program. At every point on the grid, the following data
were taken: ISC for each of the 16 power units, and panel
IV characteristic. The complete set of data collection
required approximately 30 minutes. Measurements were
taken close to solar noon in order to minimize spectral and
intensity variation. All data was normalized using solar
intensity
readings
from
a
Normal
Incidence
Pyroheliometer.
RESULTS
Fig. 2. SolFocus CPV panel
Panels under test were mounted on a Wattsun
225 tracker driven by a custom digital controller. This
system featured minimum step size of 0.1o, angular
o
accuracy of +/-0.25 , and angular repeatability of
o
approximately 0.2 . The tests were carried out during
minimal wind conditions to minimize frame flex, and drive
errors were minimized through calibration in the controller.
The panel was set up so that the short-circuit current
(ISC) of each power unit could be individually measured,
and panel ISC and power output data taken without any
wiring change. Switching was accomplished using a high
current programmable switch. Power unit and panel level
Isc were measured by a programmable electronic load
under GPIB control, while the panel Isc and IV curves were
obtained from a high speed, 4-Quadrant programmable
power supply.
Short circuit current measurements were made for
each separate power unit and for the panel at each of the
mapping points described above. In addition, an IV curve
was taken for the panel at each of these points.
Unfortunately at this time, equipment limitations precluded
us taking IV curves for each power unit.
Fig. 4. Acceptance angle map of representative
power unit. Horizontal and vertical axes represent
azimuth and elevation angular offsets from the sun,
respectively, in degrees. Contour lines represent
10% gradations of ISC.
Fig. 3. Measurement pattern: The desired axes of
Sun
4 .2
4 .2
Measurement
Points
As a preliminary measurement, ISC maps were
produced for each power unit. A representative sample is
shown in Figure 3 above. This figure illustrates two
characteristics of the power unit:
•
a wide acceptance angle of over +/- 1o, indicating a
well fabricated and assembled unit, and
•
an error in pointing, with the power unit “looking”
approximately 0.15 o to the right of the optical axis.
All 16 power units on the panel exhibited wide
o
acceptance angles, with pointing errors of less than 0.5 ,
as indicated in Figure 5 below.
rotation lie in the plane of the panel, whereas the
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
numbers of power units maintained high power unit ISC.
The others were running at lower current levels, or had
completely shut down as the sun had moved out of their
field of view. We made two observations from this:
•
Driving the panel ISC from a small number of power
units can only be done if the bypass diodes around
the non-performing power units were conducting.
Bypass diodes can provide more than insurance
against a cell failure; they may also affect the
acceptance angle.
•
Panel ISC is probably a good indicator of acceptance
angle in the area where all or most of the power units
are contributing to the panel output. Power, however,
is an aggregation of the output power of all
contributors, and so panel ISC measurements will
overestimate the acceptance angle when further from
the sun.
Fig. 5. Distribution of cell pointing for a panel
The above two data sets were generated as
standard output from our manufacturing tests, and gave us
sufficient confidence in the panel to continue analysis.
In order to understand the correlation between
power unit and panel acceptance angles, using ISC as a
measure, the graph of Figure 6 was produced. All colored
hexagons on this graph represent a point within the panel
ISC acceptance angle limit. In other words, at each of these
points, the panel ISC was within 90% of the maximum ISC.
A separate series of ISC measurements was made on
individual power units across the same position grid. The
numbers within the hexagons (and the color-coding)
represent the number of individual power units that were
measured stand-alone to be within 90% of the panel’s ISC
at that position.
Panel power output as a function of off-axis angle
and ISC data were then compared to determine the utility of
ISC as a gauge of acceptance angle. In the following
graph, the red curve shows the panel power produced at a
certain angle from the sun (in either azimuth or elevation),
normalized to the maximum power produced. The panel
acceptance angle, defined as the 90% point, is measured
to be +/- 1o. The green curve indicates the ISC as a
function of the angle (or radius) from the sun. It has also
been normalized.
Fig. 7. Comparison of off-axis behaviour of ISC and
PMPP
Fig. 6. Distribution of cell pointing for a panel
At the center of the panel’s field of view, all 16 power
units were at or above 90% of the panel’s ISC, indicating
that they were all contributing to the output power.
However, at the periphery of the field of view, smaller
The graph clearly shows that at the 90% points the
panel ISC measurements overestimate the acceptance
angle. In addition, as the angle from the sun becomes
greater and more bypass diodes are activated, the
estimation of power by the ISC method becomes less
accurate.
In order to fully understand the above, SolFocus is
building a complete analytical model that will calculate
55
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
electrical properties as a function of key power unit
parameters and allow Monte-Carlo analysis of critical
manufacturing process variations. As a precursor to that,
inspection of a simple model showed that the panel IV
curves (reproduced here in Figure 8) were behaving
consistently, and that the bypass diodes were working as
expected.
th
Reduction”. Procedings of the 20 European Photovoltaic
Solar Energy Conference, Barcelona, June 6-10, 2005.
.
[3] A.W. Bett, C. Baur, F. Dimroth, H. Lerchenmüller, G.
Siefer, G. Willeke, “The FLATCON Concentrator PVtechnology”. Procedings of the International Conference
on Solar Concentrators for the Generation of Electricity or
Hydrogen, Scottsdale, AZ, May1-5, 2005.
[4] I. Luque-Heredia, J.M. Moreno, G. Quéméré,
R.Cervantes, P.H. Magalhães. “CPV Sun Tracking at
Inspira”. Procedings of the International Conference on
Solar Concentrators for the Generation of Electricity or
Hydrogen, Scottsdale, AZ, May1-5, 2005.
Fig. 8. Panel IV measurements as a function of offaxis position
SUMMARY
The results shown above indicate that the
acceptance angle of a well-aligned CPV panel is very
close to that of its constituent power units. Furthermore,
when the panel is operating on axis, i.e. aligned to the
sun, measurements of panel ISC can be used to
characterize the angular dependence of panel output
power, consistent with the findings by Bett, et al.[3] As the
panel is moved off-axis measurements of ISC less
accurately predict the total panel power at its maximum
operating voltage due to the presence of bypass diodes
across each PV cell.
Clearly, the use of secondary optics and bypass
diodes to broaden acceptance angle of a string of cells
allows the system designer to relax critical tracker
tolerances such as stiffness and backlash. This permits
lower cost structural designs to be used in conjunction
with high concentration panels. A comprehensive
analytical model of these effects in mini-concentrator
systems that will help further define panel manufacturing
tolerances is currently under development.
REFERENCES
[1] R.M. Swanson, "The Promise of Concentrators",
Progress in Photovoltaic Res. Appl., 8, pp. 93-111, 2000.
[2] J. Luther, A. Luque, A.W. Bett, F. Dimroth, H.
Lerchenmuller, G. Sala, C. Algora, “Concentration
Photovoltaics for Highest Efficiencies and Cost
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