4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
MIRROR REFLECTING COST EFFECTIVE PV SOLAR ENERGY
CONCENTRATING SYSTEM
V. Dallakyan, R.Vardanyan
State Engineering University of Armenia
105 Teryan Str.,375009, Yerevan, Armenia Fax: 3741 545843; E-Mail: rvardan@seua.am
ABSTRACT
To reduce the high cost of photovoltaic (PV) systems
the new cost effective mirror reflecting linear focus type
solar energy concentrating system is developed. The
concentrator system consists of flat glass mirrors, placed
under the different angles, and focusing the sun light on to
the solar sells mounted along the line. The developed PV
concentrator system has several advantages in
comparison with widely used other concentrating systems.
It is mostly protected from environmental influences (wind,
dust, rain, hail). Due to the simplified structure of
concentrating
optics,
the
standard
off-the-shelf
technologies enable low-cost manufacturing.
The cost optimization method and the computer
program for new concentrating systems design is
developed as well. The program allows to design a PV
system with the given output power, having the minimal
price. The program can be used for cost effective PV solar
energy concentrating systems design.
Besides the use of lenses, it is also possible to use
mirrors to concentrate sunlight. Solar Systems in Australia
has developed a dish concentrator PV system [5]. The
Solar Systems’ reflecting parabolic mirrors are made of
thin glass sheets, silvered on their rear surfaces, and
protected in shaped concave aluminum pans. The
EUCLIDES concentrating array consists of a mirror
reflecting parabolic trough, tracking the sun around the
horizontal axis [6].
All these designs are different, having various
structures, concentrating optics, concentration ratio,
tracking systems, solar cells’ cooling designs, and
consequently, they have different costs. Despite of
inherent cost reduction property of sun rays’
concentration, most existing PV concentrator systems are
still expensive.
In this paper the new cost effective mirror reflecting
type PV solar energy concentrator system is presented.
Our approach is based on the application of flat glass
mirrors, which are cheap, reliable and enable the low-cost
manufacturing [7].
INTRODUCTION
The high cost of photovoltaic (PV) modules makes
the use of concentrators desirable. Optical concentration
offers an attractive approach to reducing PV system’s high
cost by substituting of much of the semiconductor solar
cell area by concentrator area. It also offers other
advantages, including semiconductor solar cell increased
efficiency.
At present different types of sun concentrator
systems are used to reduce the high cost of flat PV
modules. To concentrate solar energy, designers can use
light refraction (using Fresnel lenses) or light reflection
(using mirrors).
The Fresnel lens can either be a circular lens
producing a focused spot on a single cell, or a linear lens
producing a focused line of sunlight on a row of cells.
Amonix (US, California) uses an array of point-focus
Fresnel lenses [1,2]. Fraunhofer ISE (Freiburg, Germany)
and Ioffe Institute (St. Petersburg, Russia) also use pointfocus Fresnel lenses in their concentrator PV designs [3].
The U.S. company ENTECH has developed line-focus
Fresnel lens modules [4]. Each module uses rows of
silicon cells operating at 20-suns concentration.
STRUCTURE OF PV CONCENTRATOR SYSTEM
The structure of new cost effective PV concentrator
system is a mirror reflecting linear focus type. The
concentrator system consists of flat glass mirrors, placed
under the different angles, and focusing the sun light on to
the solar sells mounted along the line.
The developed concentrator system has several
advantages in comparison with Fresnel lens concentrating
optics and mirror reflecting parabolic trough systems. It is
mostly protected from environmental influences (wind,
dust, rain, hail). Due to the simplified structure of
concentrating
optics,
the
standard
off-the-shelf
technologies enable low-cost manufacturing.
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
Fig. 1. Initial version of mirror reflecting
linear focus PV concentrator system.
The initial version of mirror reflecting linear focus PV
concentrator system is prepared and tested in outdoor
conditions during 11 years (Fig. 1). In this system five flat
glass mirrors are used to focus the solar rays on to the line
in a focus distance. The mirrors are reflecting the light
from the one side (the asymmetrical structure). The
ordinary mono-crystalline silicon solar cells with 15%
efficiency are used in this system. The heat sinks are
made of aluminum. The silicon solar cells are soldered to
the copper wafers, which are previously mechanically
connected with the heat sinks. The heat sinks are
electrically isolated from each other. The cells are
connected in series and the output 15 V voltage with
power 60 W is obtained. One axis tracker is used in this
system. During 11years of testing no damages of the PV
system are observed.
To design the new mirror reflecting cost effective PV
solar energy concentrating systems with different output
powers the special computer program is developed. The
program allows to optimize the concentration ratio and to
design a cost effective PV system, having the minimal
price.
COMPUTER PROGRAM FOR OPTIMIZATION AND
COST EFFECTIVE PV SYSTEMS DESIGN
The mathematical model of new PV concentrator
system is developed. All parameters of the system, the
influence of the temperature and concentration ratio on the
efficiency of solar cells are taken into consideration in this
model.
To determine the optimal concentration rate of mirror
reflecting linear focus PV concentrator systems, the cost
optimization method (algorithm) is developed. The method
is based on the iteration of calculations of the cost of a
concentrator system by increasing the concentration rate
in a small amount, starting from the one sun. With
increasing the concentration rate the cost of the system
decreases and after passing some minimum (optimal)
value it increases. To realize this optimization and
automated design of PV system the computer program
PVCsyst 1.2 is developed. The home page of this program
is presented in Fig. 2.
Fig. 2. Home page of computer program.
Fig. 3. Dependence of the cost of PV
system from the concentration rate.
concentrator
For the given values of generated electric power,
temperatures
(ambient
and
permissible
working
temperature of solar cells), parameters of solar cells, and
for some other input parameters, the program calculates
the prices of concentration system by changing the
concentration rate in a wide range and shows the value of
concentration rate when the minimal price of the system is
obtained. As an example, the concentration rate
optimization curve, obtained for the 1 kW PV system is
presented in Fig. 3. The other input parameters as well as
the obtained parameters of this PV system are presented
below in Table. It can be seen from the figure that the
minimal price of PV concentrator system 2.31 $/W is
obtained when the concentration rate is 22X. This value of
concentration is red colored and recommended to
designer as an optimal one. Thus, the program allows to
determine the optimal concentration rate, which provides
the minimum price of a mirror reflecting linear focus PV
concentrator system.
With the use of developed optimization method and
computer program, new mirror reflecting cost effective PV
solar energy concentrating systems are optimized and
designed. The input parameters and obtained results are
presented in Table.
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
Input parameters
Required output power
(kW)
1
10
100
Solar radiation (W)
1000
1000
1000
Tracker cost ($)
300
300
300
Efficien. of solar cell (%)
15
15
15
Dim. of solar cell (mm)
100x100 100x100 100x100
The cost of solar cell
10
10
10
Focuse distance (m)
2
2
2
Ambient temperature (C)
40
40
40
Allowed max. operation
temp. (C)
65
65
65
The cost of miror ($/m2)
25
25
25
The cost of constructive
materials ($/m)
5
5
5
Fab. cost of one array ($)
Transp. & install. ($)
200
200
200
20
200
200
Obtained results
Cost of PV system ($)
2328
11847
95245
Cost per Watt ($/W)
2.31
1.15
0.94
Concentration rate
22
29.4
43
Produced power per day
(kW*h)
5.5
57.4
583.1
1
2
10
3x8
4.3 x 19
7.2 x 24
Number of array
Dimen. of one array (m)
Cost ($/W)
3
2.5
2
1
1.5
2
1
3
0.5
Pow er (Watt)
0
2000
4000
The price of new flat mirror reflecting PV solar
energy concentrating system is compared with the price of
widely used and very similar parabolic trough linear focus
PV system (Fig.4). This comparison is realized with the
use of above mentioned program PVCsyst 1.2 and our
other program PVCsyst 3.2 developed for optimization and
design of parabolic trough PV systems.
As it could be expected, due to the high price of
mirrors of parabolic through PV systems the cost for per
watt energy of new flat glass mirror reflecting system is
smaller.
CONCLUSION
It can be seen from the Table that the PV system’s
cost per watt decreases with increasing the output power
of the system. It can be seen also that the costs of the flat
mirror reflecting linear focus PV concentrator systems are
not high in comparison with other well known PV
concentrating systems.
0
1 – Parabolic through PV system with mirror price = 100 $/m2;
2 – Parabolic through PV system with mirror price = 70 $/m2;
3 – Flat mirror reflecting PV system with mirror price = 25 $/m2.
6000
8000
10000
Fig. 4. The cost of different PV systems in versus
output power (focus distance = 1.5 m).
The developed new cost effective mirror reflecting
type PV solar energy concentrator system has several
advantages in comparison with well known systems. It is
mostly protected from environmental influences (wind,
dust, rain, hail) and has the simple structure. Due to the
simplified structure of concentrating optics, the standard
off-the-shelf technologies enable low-cost manufacturing.
The developed optimization method and computer
program allows to design the cost effective flat mirror
reflecting linear focus PV solar energy concentrating
systems.
ACKNOWLEDGEMENT
This work is supported by US Civilian Research and
Development Foundation (CRDF) and the Armenian
National Foundation for Science and Advanced
Technologies (NFSAT).
REFERENCES
[1] Stone K., Garboushian V., Hayden H. “Field
Performance and Reliability Issues of High Concentration
PV Systems”. 19th European PVSEC, Paris, 2004.
[2] Garboushian V. Continuous “Installation of
Concentrating PV in the Southwest”, 1st ICSEC, New
Orleans, 2002.
[3] Rumyantsev V., Chalov A., Ionova E., Larionov V.,
Andreev V. “Concentrator PV Modules with Multi-Junction
Cells
and
Primary/Secondary Refractive
Optical
Elements”. 19th European PVSEC, Paris, 2004.
[4] Fraas L., McConnell B. “High Power Density
Photovoltaics”. Renewable Energy World. v. 5, n. 5, 2002.
[5] www.edtekinc.com/Products/.../EDTEK_SolarCon.htm
[6] Luque J.C., Sala G., Arboiro J.C., Zamorano A.,
Minano J.C., Dramsch C. (Instituto de Energia
Solar.Universidad Politecnica de Madrid), Bruton T.,
Cunningham D. (BP Solar. Middlesex, U.K.) The
EUCLIDES Prototype: An Efficient Parabolic Trough for
PV Concentration.
[7] Vardanyan R.R. Concentrator of Solar Energy. Patent
of Armenia No 1739 A2, March, 15, 2006.
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
DAY4TM PV RECEIVERS AND HEAT SINKS FOR SUN CONCENTRATION
APPLICATIONS
L. Rubin1, V. Nebusov1, Ralf Leutz2, A. Schneider1, A Osipov1, V. Tarasenko1
Day4Energy Inc., Suite 101, 5898 Trapp Avenue, Burnaby, BC, V3N 5G4, Canada
2
Physics Department, Philipps-University, Renthof 5, 35037 Marburg, Germany
Author for correspondence: lrubin@day4energy.com, Tel.: +1-604-759-3294, Fax: +1-604-759 3295
1
ABSTRACT
The paper describes performance of Day4™
proprietary linear PV receivers and heat sinks under sun
concentrated irradiation. Paper demonstrates that novel
TM
technology allows modification of conventional
Day4
crystalline silicon PV cells so they can efficiently operate
under up to 10-suns concentrated irradiation without any
increase of their manufacturing cost. The only differences
of these cells with industrially produced ones consists of
different types of front side metallization that contains only
fingers without bus bars and back side that does not
contain Al/Ag pads. Presented results demonstrate
efficient performance of a novel heat sink that maintains
the temperature differential below 30°C between the PV
receiver and ambient even at 10-time concentration and
almost zero wind speed condition. Proposed novel
concept of PV receivers with heat sink anticipates
flexibility in adjustment to different sizes of solar cells and
types of focusing optics.
wires become soldered to front side fingers and to rear
side Al thus keeping current collecting bus bars outside
the perimeter of the solar cell. From the electrical
standpoint the electrode wires replace the conventional
screen printed bus bars and act as a distributed current
collecting system. Depending on cell size and the value of
generated current there is the possibility to use either one
bus bar (1-side lay-up) or two bus bars (2-side lay-up) at
the cell edges.
TM
Several Day4 Electrode parameters like its
resistance and shading may be easily adjusted by
changing wire diameter and spacing between neighbored
wires which guarantees its efficient employment in
different cell applications and cell sizes. For typical solar
cell applications these spacings range from 2 mm to
20 mm while wire diameter may vary in the range of 70TM
250 µm. Day4 Electrode technology anticipates that the
bus bar is used for cell interconnection in series when a
PV receiver or module is fabricated.
INTRODUCTION
SOLAR CELLS FOR UP TO 10-TIMES
CONCENTRATION APPLICATION
There are several reasons preventing sun
concentrators becoming economically feasible, namely
high costs of specialized PV cells, light focusing optics,
trackers and heat sinks. In this paper we will present
results demonstrating the possibility to produce cost
effective PV receivers and heat sinks thereby making
concentrator concept more feasible for industrial
production.
TM
technology is the
The key advantage of Day4
possibility to modify conventional crystalline silicon PV
cells so they can efficiently operate under up to 10-suns
concentrated irradiation without any increase of their
manufacturing cost. The only differences of these cells
with industrially mass produced ones consists of different
types of front side metallization that are comprised of
fingers without bus bars and back side that contains full
TM
area BSF without Ag/Al pads. The Day4 Electrode is
produced by Day4 Energy Inc. as a proprietary product
and is comprised of transparent polymeric film coated with
adhesive material and having embedded in it copper wires
coated with low melting point alloy. The electrode wires
are electrically connected to metallic bus bar [1]. A
conventional lamination process step is used to attach the
adhesive layer firmly to the solar cell surfaces after
electrode alignment. During this lamination process the
Most important for sun concentrator cell design is to
minimize series resistance thereby preventing fill factor
decline when light radiation exceeds 1-sun level [2, 3, 4].
TM
Our experiments with the Day4 Electrode
demonstrated that the new technology secures stability of
the fill factor value close to 79% on standard industrial 62
inch cells that operating under 1000 W/m with Isc value of
up to 8.5 A. It was also demonstrated that if these cells are
interconnected in series the resulting PV module does not
experience any substantial decline in fill factor value.
These results emphasize the possibility to use
Day4TMElectrode technology to develop and produce PV
receivers for low concentration applications.
The first series of experiments was focused on
TM
modification of standard solar cells with Day4 Electrodes
that should result in their ability to operate under up to 10suns. These experiments were performed with 4-inch Cz
solar cells from former RWE Schott Solar AG that
produced cells according to Day4 specification: only with a
finger grid on the front side and a full Al rear side contact.
The 4-inch semi-square cells were diced at Day4 to a size
of 50x100 mm2. A set of 4-6 cells were used for averaging
cells’ parameter variation. The cells were tested indoors at
different light intensity levels in a Berger flasher solar
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
17.2
17.0
fixed in framing, properly combined with the Fresnel lens
and illuminated inside the Berger tester using different
distances between the light source and Fresnel lens. Such
arrangements allowed extending the level of radiation
concentration up to 10-suns. Experiments with the PV
receiver demonstrated that its efficiency closely coincides
with that obtained for individual cell efficiencies: PV
receiver efficiency is kept about 16.3% at 10-suns
radiation level. It was also demonstrated that receiver
output power grew linearly with sun concentration and
reaches 75 W or about 8.3 W per each cell under about
10-suns concentration (Fig. 2).
80
70
60
50
P [Watt]
simulator by means of changing the distance between the
flash lamp and the plane where the tested cell is
positioned. The Berger tester was equipped with a special
loading unit allowing testing of single PV cells and small
modules in the range up to 12 A and 24 V. By means of
special computer simulations the finger spacing and
distance between wires were optimized in order to achieve
maximum value of fill factor and lowest shading thereby
securing cell maximum output power in the range of 1-10suns irradiation. It was estimated that optimum finger
spacing for 60 Ohm/sq. emitter is between 1-1.5 mm and
distance between electrode wires between 4-12 mm.
Upon Day4 Energy specification former RWE Schott
solar supplied cells with optimized finger spacing keeping
constant other cell parameters like silicon bulk resistance,
cell size and emitter resistance. Experiments showed that
cell efficiency reaches maximum value if distance between
electrode wires is in the range of 4-6 mm. The results for
6 mm distance between wires are shown in Fig. 1.
40
30
20
16.8
ETA [%]
Receiver without lense
Receiver with
lense
10
16.6
0
16.4
0
1
2
3
4
16.2
6
7
3
8
9
10 11
2
x 10 W/m
16.0
Figure 2: Receiver output power with and without Fresnel
lens under different light intensities.
15.8
Optimized Finger spacing
Wire gap: 6 mm
15.6
15.4
5
0
1
2
3
4
5
3
6
7
8
9
16
14
10 11
2
x 10 W/m
The initial cell efficiency of 15.8% at 1-sun gradually
increases and reaches 16.7% at 4.5-suns. Under higher
intensities cell efficiency decreases slightly but still stays
above 16.3% even at 10+-suns. The fill factor of cells with
optimized finger distance still stays above 79%. These
TM
results proved that the Day4 Electrode concept is able to
adapt industrial solar cells to operate efficiently under
intensities up to 10-suns.
DAY4™ PV RECEIVERS FOR UP TO 10-TIMES
CONCENTRATION APPLICATION
Cells with optimized finger spacing and distance
between wires were sorted and a set of 9 cells was
connected in series thereby producing a sun concentrator
PV receiver that may be used in PV systems operating at
up to 10-suns concentration. Initial PV receiver testing was
performed indoors using a Berger tester and a linear
Fresnel lens that was especially designed and built in
cooperation with Dr. Ralf Leutz, Marburg University,
Germany. Since the PV receiver is about 1 meter long
special arrangements were performed in order to achieve
uniform concentrated irradiation. The PV receiver was
Isc [A]
Figure 1: Cell efficiency with optimized finger spacing of
1.2 mm contacted by Day4TMElectrode (wire gap is 6 mm).
12
10
8
Cell parameters:
Voc = 6.08 V
Isc = 15.6 A
FF = 79.12 %
6
4
2
0
0
1
2
3
4
5
6
7
Voc [V]
Figure 3: I-V curve of PV receiver operated under 10+times concentration.
Figure 3 shows the IV curve of a PV receiver under 10+times concentration. One can see that even at this high
concentrated radiation FF value is kept at high value of
79.12%. There are strong reasons to believe that even
better results may be achieved under up to 20+-times
2
concentration if more narrow PV cells of 15x100 mm are
used.
DAY4™ PV RECEIVER FOR UP TO 5-TIMES
CONCENTRATION APPLICATION
The same testing procedure was applied for other
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
types of PV receiver that was specially built for 5-times
concentration. This receiver comprises of the same former
2
RWE Schott Solar AG cells of 50x100 mm each but with
increased 8 mm wire spacing because the current was
expected to be lower due to lower sun concentration level.
A set of 100 cells was tested using a HALM cell tester.
After sorting these cells were interconnected in series by
means of Day4 technology thereby producing a set of PV
receivers each comprising of 10 cells. These PV receivers
were tested indoors at different light intensity levels in a
Berger flasher solar simulator by means of changing the
distance between the flash lamp and the plane where the
PV receiver being tested was positioned. Detailed results
of this testing are presented in Figure 4 and Figure 5.
Receiver 2
7
Isc [A]
6
5
4
3
2
1
1
2
3
4
5
Intensity [suns]
Figure 4: Dependence of Isc value on sun concentration.
40
Receiver 2
35
Pmpp [W]
30
25
20
Table I: PV receivers in-door testing results.
Radiation on receiver
Voc
Isc
Pmpp
plane [W/m2]
[V]
[A]
[W]
15
9
10
8
5
FF
[%]
1000
2090
2330
16.58
17.12
17.23
3.28
6.86
7.63
42.84
93.27
103.49
78.84
79.40
78.68
2560
17.29
8.39
113.54
78.28
Testing results have proved that PV receivers with
proprietary heat sinks are capable of generating power of
113.54 W or 4.21 W per cell under 2560 W/m2 radiation
with FF of 78.28% while Isc exceeds 8.39 A. These results
allow estimation of PV receiver efficiency of 14.7% by
calculating it as a ratio between power value generated by
one receiver and input radiation on receiver plane.
Outdoor testing was performed using the same 3
series-interconnected PV receivers that were illuminated
by concentrated natural solar radiation using a mirror
trough concentrator with 3.5 geometrical and 2.77 optical
concentrations. Testing conditions were as follows: solar
2
radiation – 985 W/m , ambient temperature 27°C, PV
receiver temperature 57°C, wind speed 0.5 m/sec. Testing
results (Fig. 6) demonstrated that a Day4 PV receiver
comprised of 27 4” Cz cells generates Pmpp=97.5 W
2
under solar radiation of 2650 W/m on the receiver plane.
The relatively low FF value of 74.7% was a result of
increased PV receiver temperature from 25°C to 57°C.
Keeping in mind that power loss due to increased
temperature is about 16% one may estimate the value of
peak power at 25°C: Pmax=116 W or 4.3 W per cell
assuming that optical efficiency is 90% and input radiation
2
intensity is 1000 W/m . This assumption is in good
agreement with experimental data presented in Table I
obtained under PV receiver testing using a Berger tester.
7
1
2
3
4
5
Intensity [suns]
Figure 5: Dependence of Pmpp on sun concentration.
It is evident that the PV receiver continues to perform
efficiently in a wide range of light intensities ranging from
2
1000 to 5000 W/m and demonstrates only slight decrease
of FF from 79.6% to 78.6% although Isc value increases
from 1.7 A to almost 8 A and Pmpp grows from 7.80 W to
40.0 W or 4.0 W per each cell.
Current [A]
8
interconnected in series and tested indoors at different
light intensity levels in a Berger flasher solar simulator as
described above.
6
5
Voc = 15.02 V
Isc = 8.7
A
Pmpp= 97.5 W
FF = 74.7 %
Vmpp= 12.02 V
Impp= 8.12
A
4
3
2
1
0
0
2
4
6
8
10
12
14
16
Voltage [V]
DAY4™ PV RECEIVER FOR UP TO 3-TIMES
CONCENTRATION APPLICATION
Figure 6: Outdoor testing: I-V characteristics of three PV
receivers interconnected in series.
Table I contains testing results of concentrator module
comprising of 3 PV receivers each comprising of 9 Cz 4”
full square cells with attached heat sink that were
Such results have been achieved not only because of
TM
unique properties of the Day4 Electrode but also due to
the efficiency of the proprietary heat sink that managed to
keep PV receiver temperature below 60°C under almost
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
zero wind condition and ambient temperature of 27°C
2
even at concentrated solar radiation of 2770 W/m . A
controlled conventional PV panel that was positioned near
PV receivers revealed that its temperature under identical
testing conditions reaches 53°C thereby confirming that
the Day4 proprietary heat sink is capable of preserving PV
concentrator receiver temperature close to those that
experienced by a conventional PV panel.
It is important to stress out that Day4 technology is
able to customize PV receiver geometry including
modification of cells size and cell number per string,
according to a required specification based on the optical
system to be employed.
DAY4™ HEAT SINKS FOR UP TO 10-TIMES
LINEAR CONCENTRATION APPLICATION
It is well known that when a solar module operates
even under 3-4-suns concentrated radiation and at zero
wind condition its temperature grows and exceeds
ambient by more than 100°C thereby reaching a level of
≥ +130°C that eventually may destroy receiver. Besides
that, FF value also declines. Altogether these effects
provoke a decrease power output by 0.5%/ºC. In other
words if temperature increases by 50°C then power output
decreases by 25% if compared with power output at 25°C.
In order to minimize PV receiver overheating a novel
efficient heat sink was designed, built and attached to the
PV receiver rear side via a special electrically insulating
and highly thermally conductive intermediate compound.
Day4 novel sink (patent was filed on May 26th, 2006) is
made of extruded aluminum components. Its design is
characterized not only by high ratio between its weight and
heat dissipating area but also by possibility to compensate
differential between thermal expansion coefficients of
aluminum and glass that covers PV receiver front side.
Special experiments with this heat sink demonstrated
that the temperature differential between a PV receiver
2
comprised of 4” (100x100 mm ) square solar cells and
ambient does not exceed 30°C at zero wind condition
2
even under 5000 W/m radiation impact. It was further
demonstrated that the same temperature differential is
preserved for a PV receiver comprised of smaller
50x100 mm2 solar cells when it is equipped with an
adjusted heat sink and operates under not less than
2
10000 W/m radiation impact.
We also confirmed possibility to apply novel heat sink on
narrow PV receivers of 12.5 mm width that are operating
under up to 20-times concentration.
CONCLUSIONS
It is evident that due to the shortage of silicon supply
there is growing interest towards employing trackers to
increase power output from conventional PV modules and
to use sun concentrator systems. There are several
reasons why PV systems with low concentrating optics
should be considered as one of the most perspective in
terms of cost of generated solar electric energy. First of all
it is evident that low concentration optics may provide
wider acceptance angle. Therefore it has a potential to
collect higher portion of diffused solar radiation thereby
increasing annual electric energy generation. Secondly, a
low concentration system may employ less sophisticated
and low cost 1-axis tilted and even 1-axis horizontal
trackers without substantial loss of generated energy
output especially in Southern US and European areas.
And finally, a low concentration system may employ
conventional mass produced PV cells thereby providing a
realistic promise to make solar electric energy
economically feasible.
In this work we demonstrated practical possibility to use
Day4 novel technology to upgrade standard industrial
solar cells with Day4™Electrodes thereby making them
applicable for low concentration applications. We further
demonstrated possibility to design and produce linear PV
receivers within the range of from 3 and up to 20 times
sun concentration. There are no principle limitations to
develop PV receiver even for slightly higher concentration.
The cost of these PV receivers without heat sink is almost
identical to the production cost of Day4™ flat plate PV
modules of the same area although conventional PV
module generates substantially lower power when
operating under 1-sun radiation. It is evident that if low
concentration PV system employs advanced PV cells with
efficiency about 20% instead of currently available 16%
then overall cost of Wp will be decreased by 25% thus
coming closer to the target price of $2.00/Wp.
TM
In respect to the Day4 manufacturing concept there
is no economical or technological difference between
producing either sun concentrator PV receiver that
contains single string of in series connected cells or a flat
plate PV module. The only difference lies in the distance
between wires in the Day4™Electrode and optimized
spacing between front side fingers in order to achieve
maximum power output. In other words: flexibility of the
TM
technological concept makes it possible to
Day4
manufacture not a single type but a variety of PV receivers
and heat sinks using the same production platform.
ACKNOWLEDGEMENT
We would like to thank G. Rubin for fruitfull discussion
and P. Antipov for technical assistance during cell and PV
receiver assembling.
This work was supported by the IRAP NRC project
under contract number 568171.
REFERENCES
[1] German patent, DE No 102 39 845, Leonid B., Rubin,
George L. Rubin: Elektrode fuer fotovoltaische Zellen,
fotovoltaische Zelle und fotovoltaischer Module; WO
2004/021455 A1 .
[2] J. Coello, M. Castro, I. Antón, G. Sala, M.A. Vázquez,
Progress in Photovoltaics: Research and Applications,
12 (2004), p.323-331.
[3] A. Schneider, L. Rubin, G. Rubin, A. Osipov, A.
Smirnov, P. Antipov, Proceedings of the 4th WCPEC,
Hawaii, 2006, pp 2073.
[4] A. Schneider, L. Rubin, G. Rubin, Proceedings of the
st
21 European Photovoltaic Solar Energy Conference
and Exhibition, Dresden, Germany, 2006, pp 2243.
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OPTICAL ANALYSIS OF ASYMMETRIC COMPOUND PARABOLIC PHOTOVOLTAIC
CONCENTRATORS (ACPPVC) SUITABLE FOR BUILDING FAÇADE INTEGRATION
a
Yupeng Wu a, Philip C. Eames a and Mervyn Smyth b
Warwick Institute for Sustainable Energy and Resources, School of Engineering,
University of Warwick, Coventry, CV4 7AL, U.K
b
Centre for Sustainable Technologies, School of the Built Environment,
University of Ulster, Northern Ireland, BT37 0QB, U.K
Abstract
Ray-trace techniques have been used to predict the
optical performance and angular acceptance of
Asymmetric
Compound
Parabolic
Photovoltaic
Concentrator (ACPPVC) systems suitable for integration
into vertical south facing building façades. The
untruncated ACPPVC system had acceptance-half angles
of 50° and 0°, a PV width of 125mm and a geometrical
concentration ratio of 3.34. Different truncations of the
ACPPVC system were applied, with comparisons of
angular acceptance between the untruncated and
truncated systems discussed. From the simulations
undertaken, the angular acceptance was 100% within the
range of incidence angles between 0° to 50° for
untruncated and truncated systems. Increased truncation
leads to increased angular acceptance with reduced
maximum concentration. The predicted flux distributions
over the PV surface for the untruncated and truncated
systems are presented for selected angles of incidence
along with concentration ratio.
Concentrator systems which increase the solar radiation
intensity on the photovoltaic cells may reduce the system
cost, if the cost of the concentrator is less than the
photovoltaic material displaced (Rabl, 1976) (Winston et al,
2005). Non-imaging untruncated and truncated ACPPVC
systems have been analysed using ray-trace techniques
to determine their optical characteristics. The ACPPVC
system design analysed is suitable for integration onto
south facing vertical building façades in the U.K. The
untruncated ACPPVC design had acceptance-half angles
of 50° and 0°, PV absorber width of 125mm and
geometrical concentration ratio of 3.34. A schematic
illustration of the cross section of the reflector profiles
illustrating the three truncation positions investigated is
shown in figure 1. The geometrical characteristic of the
untruncated and truncated ACPPVC systems are shown in
table 1.
Introduction
Solar energy is a clean energy source with the potential to
meet the world’s energy needs. Photovoltaics convert
solar energy directly to electricity. Current low solar to
electrical conversion efficiency and high costs prevent the
wide scale adoption and use of Photovoltaic systems
(Boyle, 2004). Low concentration non-imaging Asymmetric
Compound
Parabolic
Photovoltaic
Concentrators
(ACPPVC) are suitable for building façade integration.
Table 1 Geometrical characteristics of the untruncated and
truncated ACPPVC systems
Figure 1 ACPPVC system with acceptance-half angles of 50° and 0°
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Ray trace analysis and optical performance for
the selected ACPPVC systems
All rays were assumed specular in the ray trace model, the
solar incidence angle (θ) was considered from the
horizontal as illustrated in figure 1. The aperture cover was
4mm thick low iron glass with an extinction coefficient of 4
-1
m . The reflectance of the reflectors was taken to be 0.98.
The analysis of angular acceptance and optical
efficiencies used 10,000 rays incident on the glass
aperture cover between 0° and 90° at 1° intervals. The ray
trace analysis allowed both angular acceptance function
and the optical efficiency to be determined.
Ray trace diagrams for the untruncated ACPPVC system
for a selection of solar incidence angles are shown in
figure 2. From figure 2 it can be observed that at incidence
angles of 1°, 15°, 30° and 45° (from the horizontal), all the
incident rays are incident at the PV cells. When the solar
incidence angle is 45°, a local high intensity flux can be
seen in the middle and lower part of the PV cell. This will
lead to an increase in the local temperature of the PV
cells, and potentially result in a decrease in the electrical
conversion efficiency. Decreasing the solar incidence
angle towards the horizontal, more rays are reflected onto
the absorber by reflector 1, compared to reflector 2. Ray
trace diagrams for truncation levels 1, 2 and 3 are shown
in figures 3 to 5, respectively. The ray trace diagrams of
the truncated systems are almost the same as for the
untruncated one.
The angular acceptance and optical efficiency of the
untruncated ACPPVC system are shown in figure 6. The
angular acceptance is 100% for incidence angles within 0°
to 50°. When the solar incidence angle is above 50°, the
angular acceptance rapidly drops to 0. The highest
predicted optical efficiency was 88.67% for the
untruncated ACPPVC. The angular acceptance functions
for the 4 design variations untruncated, truncation level 1,
truncation level 2 and truncation level 3 are shown in
figure 7. These systems have different geometrical
concentration ratios, but almost the same angular
acceptance functions within the range of 0° to 90°. The
untruncated system and the truncation level 1 system
have the same percentage of angular acceptance at the
same solar incidence angle. Truncation level 2 and
truncation level 3 have an increased angular acceptance
range over that of the untruncated system and the
truncation level 1 system within the solar incidence angle
range from 0° to 90°. Due to truncation of the upper and
lower reflector increasing amounts of diffuse solar
radiation can enter the ACPPVC system.
Figure 2 Illustrative ray trace diagrams for the untruncated ACPPVC system, 50 rays are shown for each diagram.
Figure 3 Illustrative ray trace diagrams for ACPPVC system truncation level 1, 50 rays are shown for each diagram.
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Figure 4 Illustrative ray trace diagrams for ACPPVC system truncation level 2, 50 rays are shown for each diagram.
Figure 5 Illustrative ray trace diagrams for ACPPVC system truncation level 3, 50 rays are shown for each diagram.
Figure 6 Angular acceptance and optical efficiency for the untrucated ACPPVC system
Figure 7 Angular acceptance functions for the untruncated and truncated ACPPVC systems
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
Energy Distribution across the PV cells
The two dimensional ray trace technique was also
employed to predict the solar radiation incident at the PV
cells. The effects of diffuse radiation were not included in
this analysis. The prediction of energy distribution across
the PV cells of the ACPPVC systems are shown in figures
2
8 and 9. 1000 W/m solar radiation has been applied at
the system apertures. Selected solar incidence angles
15°, 30° and 45° were used for this simulation. For the
untruncated ACPPVC system, from figure 8 it can be seen
that when the solar incidence angle is 15°, two peak solar
fluxes occur on the PV cells, where the PV cell near the
upper and lower reflector has a higher solar flux than in
the central region, due to the direct radiation from the sun
and reflected radiation from the upper and lower reflectors.
For the 30° solar incidence angle, the energy distribution
has the same characteristics as the 15° solar incidence
angle, two peak solar fluxes are also been on the PV cells.
For the 45° solar incidence angle, one peak solar flux only
occurs at the PV cell, due to solar radiation only being
reflected from the lower reflector. The characteristics of
the energy distributions across the PV cells for the
ACPPVC system truncation level 3 are almost the same
as those for the untruncated system shown in figure 9.
Figure 9 Energy distributions across the photovoltaic cells
of the ACPPVC System truncation level 3 for solar
incidence angles of 15°, 30° and 45° to the horizontal, the
2
incident solar radiation intensity was 1000W/m
Conclusions
A detailed analysis of the optical performance of
untruncated and truncated ACPPVC systems have been
undertaken. The angular acceptance was 100% within the
range of incidence angles between 0° to 50° for the
untruncated and truncated systems. Increased truncation
leads to increased angular acceptance with reduced
maximum concentration. Due to the reflection from the
reflectors, significant peak solar fluxes are found on the
PV cells for some incidence angles.
Acknowledgement
This work was supported by the School of Engineering,
University of Warwick through a Departmental Scholarship
to Yupeng Wu.
References
Figure 8 Energy distributions across the photovoltaic cells
of the Untruncated ACPPVC System for direct solar
incidence angles of 15°, 30° and 45° to the horizontal, the
2
incident solar radiation intensity was 1000W/m
Boyle, G (2004) Renewable Energy: Power for a
Sustainable Future. Oxford U.K Oxford University Press.
Rabl, A. (1976) Comparison of Solar Concentrators. Solar
Energy, Vol. 18, pp. 93-111
Winston, R., Miñano J. C. and Benítez, P. (2005)
Nonimaging Optics. London U.K Elsevier Academic Press.
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
LINEAR FRESNEL LENSES WITH PHOTOVOLTAICS FOR COST EFFECTIVE
ELECTRICITY GENERATION AND SOLAR CONTROL OF BUILDINGS
Y. Tripanagnostopoulos
Physics Department, University of Patras, Patra 26504, Greece
Tel:+30 2610 997472, e-mail:yiantrip@physics.upatras.gr
ABSTRACT
Linear Fresnel lenses with photovoltaics can be used
in building atria, sunspaces, etc and apart of the electricity
generation they can contribute to keep the illumination and
the interior temperature of these spaces at the comfort
level. The collection of 60%-80% of the transmitted solar
radiation by the photovoltaics leaves the rest amount to be
distributed in the interior space. The photovoltaics can be
combined with thermal absorbers to extract the heat by
water circulation, keeping their efficiency at a satisfactory
level. A system of Fresnel lens with linear absorber, to
provide electricity and heat, is presented. Design aspects
and laboratory scale experimental results are included,
giving an idea for the application of the new system.
INTRODUCTION
Several investigations result to lower the cost of
photovoltaics increasing also their electrical efficiency, but
their payback time has not been reduced enough to be
considered cost effective. The combination of solar
radiation concentration devices with PV modules is up to
now the most viable method to reduce system cost,
replacing the expensive cells with a cheaper solar
radiation concentrating system. Besides, concentrating
photovoltaics (CPV) present higher efficiency than the
typical ones, but this can be achieved in an effective way
by keeping PV module temperature as low as possible.
For PV cooling, a water or air circulation mode can be
applied to extract the heat from it, avoiding the efficiency
reduction due to the PV module temperature increase.
The concentrating solar energy systems are characterized
by their concentration ratio (CR) and can be combined
with “linear focus” (2D) or “point focus” (3D) absorbers for
low (CR<10X), medium (CR<100X) or high (CR>100X)
concentration ratio systems, respectively. Most of CPVs
must use a system to track the sun and only the very low
concentration devices can be stationary. Fresnel lenses of
inexpensive and light in weight plastic material are also
developed.
Concentrators definitely have the potential to be
comparative on cost but they must be effectively designed
to take this benefit. The solar radiation concentration
devices are the reflectors (flat, V-trough, CPC, cylindrical
parabolic, dishes etc) and the lenses (linear Fresnel
lenses, point focus Fresnel lenses, dielectric type lenses,
etc). Comparison results [1-3] give an idea about the
benefits of CPVs. Regarding high concentration Fresnel
lens type PV systems, the 240X Fresnel lens with
efficiency 20.3 % [4] the 100X Fresnel lens with CPC
refractive secondary concentrator and efficiency 26.8% [5]
and the Fresnel lens system 120X [6], can be referred. In
the range of medium CR PV systems there is a variety of
works, as the study on Fresnel optics for CPVs [7], the
development of glass type Fresnel lenses [8], and the
fabrication, installation and operation of a linear Fresnel
lens with photovoltaics [9]. A linear Fresnel type
concentrator combined with linear cells [10] and optical
results for 3D static acrylic lens concentrators, achieving a
reduction of 62% in cell surface [11] can be also referred.
Other studies on Fresnel lens type CPVs are the study on
curved surface lens to minimize focal length [12] and the
design and use of glass type Fresnel lenses [13]. In
addition, the chromatic dispersion of Fresnel lenses [14],
the truncated stationary Fresnel lenses [15] and the
performance study of a flat linear Fresnel lens collector
[16] could be mentioned. Recently, advanced technology
Fresnel lens concentrators have been developed and
commercial models are in the market, where most of them
are of 3D type and acrylic with a large number of grooves.
The use of Fresnel lenses as a transparent covering
material for lighting and energy control of internal spaces
has been introduced by Jirka et al [17]. Extending this
idea, a concept was suggested by Tripanagnostopoulos et
al, [18], combining linear Fresnel lenses with PV or hybrid
Photovoltaic/Thermal (PVT) small width absorbers, which
aim to absorb and extract the concentrated solar radiation
in the form of electricity and heat. The extracted energy
can be stored as heat (hot water storage or underground
storage) or as electricity (batteries or electricity grid), to
cover several electrical needs. The Fresnel/PVT concept
is suggested for solar control of buildings in order to keep
the illumination and the interior temperature at the comfort
level. The brief concept presentation and laboratory scale
results give an idea for the application of this new system.
THE FRESNEL/PVT CONCEPT
Fresnel lenses are optical devices for solar radiation
concentration, which are used in several solar energy
systems as the thermal collectors and photovoltaics
because of their attractive features. Their advantages are
the lower volume, weight and cost, compared to the thick
ordinary lenses. Several types of Fresnel lenses have
been investigated, consisting of linear or circular grooves.
Fresnel lenses of 2D type (linear geometry lenses) are
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
more practical than 3D type lenses (circular geometry
lenses), as they can have East-West lens axis orientation
and therefore they need less adjustments per year for
system orientation to the sun. Both sides of a Fresnel lens
could be grooved, but in practice they are grooved on the
surface facing down, having smooth their flat surface
towards the sun to reduce transmission losses and
accumulation of dust and dirt. Optical losses in a Fresnel
lens are high and are mainly due to reflection at the
interfaces, to diffraction from close groove spacing, to
absorption in the lens material, to chromatic aberration
and also to slope errors. These losses result to lower
optical performance of Fresnel lens and also to create
non-uniform illumination at the focal plane.
Fig.1 Application of Fresnel lenses to buildings
The advantage of linear Fresnel lenses to separate
the direct from the diffuse solar radiation makes them
suitable for illumination control in the building interior
spaces as atria, galleries and sunspaces (Fig.1), providing
light of suitable intensity level and without sharp contrasts.
The direct part of the incident solar radiation can be
concentrated on an absorber strip, located at the focal
position of the applied optical system and can be taken
away to achieve lower illumination level and also to avoid
the overheating of the space. The Fresnel lens is a nonimaging concentrator and therefore the refracted rays form
a diffused image of sun at the focal line, as shown in Fig.2
(left). In the same figure (Fig.2, right), six types of possible
solar radiation absorbers are included, where in the first
line are the fin with pipe type for water heating, the air duct
for air heating and the photovoltaic type absorber. In the
second line there are the hybrid PVT type absorbers for
water heating, for air heating and also for water heating
with additional glazing and thermal insulation.
Fig.2 The Fresnel lens and the linear absorbers
The Fresnel lenses can be applied on buildings to
control the light and the temperature in it. The daylight that
penetrates the transparent apertures of a building affects
the illumination and the temperature of the interior spaces.
Apart of typical windows, the sunspace, the atrium, the
gallery or other light-guide forms are used in architecture
to provide more solar radiation into the building. These
constructions are used to replace artificial illumination and
thus to save electricity, but daylight plays a more important
role considering visual comfort, communication and other
aspects. In addition, the distribution of daylight in building
spaces results in most cases to non-uniform energy flow
and therefore solar control is often necessary. In medium
and high latitude countries the amount of solar energy is
not usually enough and artificial light and heat supply is
needed in most months of the year. On the contrary, in low
latitude countries the incoming solar radiation is more than
the necessary for visual and thermal comfort and its
reduction is a common practice. Field measurements on
daylighting control have been considered for energy
saving [19] and investigations for heat transfer across a
PV wall have been determined regarding the cooling load
component [20]. In addition, flat or curved (CPC) reflectors
have been suggested to be used as lightguides and to
provide sunlight the spaces of the building interior [21,22].
Fig.3 The absorbers out (left) and on (right) focus
The linear Fresnel lens can be combined with linear
multifunction absorbers that can convert the concentrated
solar radiation into heat, electricity or both (Fig.2, right).
These compound systems can adapt illumination control
during day, as of a sunspace (Fig.3), storing the surplus
energy for space heating during night, to contribute in the
ventilation needs during day and to cover other building
electrical loads. In low intensity solar radiation, due to the
position of sun relative to the building roof (low sun
altitude) or because of the clouds, the absorbers can be
out of focus (Fig.3a) leaving the light to come in the
interior space and to keep the illumination at an
acceptable level. The distribution of the solar radiation on
cell surface and the temperature rise of it are two
problems that affect its electrical output. The uniform
distribution of the concentrated solar radiation on cell
surface and the application of a suitable cooling mode
contribute in all cases to an effective system operation,
considering the achievement of the maximum electrical
output. Non-uniformity is due to concentrator optical and
shape errors, which even if they are small they have a
significant effect on the flux profile. Another effect is that
the temperature in locations of high illuminance can be 10o
15 C higher than elsewhere in the cell, reducing the open
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
circuit voltage. In the absence of a flux modifier the
electrical losses are in the order of 5-15 %. In addition,
other optical losses due to tracking process, wind and high
ratio of diffuse solar radiation cause a further reduction of
the final system electrical output.
EXPERIMENTAL SYSTEM AND RESULTS
The passive (heat sink) or active (heat extraction by
water or air circulation) cooling of cells are usual modes to
keep their temperature at an acceptance level. As an
extension of the simple cooling mode, the hybrid PVT
solar energy systems have been investigated to provide
simultaneously electricity and hot fluid, which contributes
to a higher conversion rate of the absorbed solar radiation,
thus making the system more practical. The PVT systems
can be effectively used in applications of small available
building surfaces for system installation. Studies on PVT
solar collectors have been presented last thirty years and
among concentrating PVT systems, the use of linear
parabolic reflector [23] and Fresnel reflector [24] could be
referred.
An extensive study for performance improvement of
hybrid PVT systems has been done at the University of
Patras and new systems have been analyzed [25,26]. The
hybrid PVT systems can be combined with linear Fresnel
lenses and can be used for space heating and cooling of
building interior spaces. The Fresnel lenses with the
hybrid PVT absorbers (FRESNEL/PVT system) is a new
concept and aims to maximize the energy conversion from
Fresnel lens type solar energy systems, which can be
used as transparent material. From the performed
laboratory experiments most of the transmitted solar
radiation from the glazed roof can be absorbed, controlling
the illumination of the interior space (Fig.3b) and providing
also electricity and heat to cover several building energy
needs. The collection of 60%-80% of the transmitted solar
radiation through the transparent cover leaves the rest
amount of solar radiation to be distributed in the building
space for the illumination needs. The experiments were
performed with a simulative device and the results showed
that a considerable lighting and temperature reduction in
the interior space is achieved. The cooling effect by the
suggested system can adapt about 50% of the needs, only
from the heat extraction by the absorber operation, which
can be higher if we consider fan or AC operation by the
provided electricity from the photovoltaics. The study on
the distribution of the concentrated solar radiation on the
focal plane of a linear Fresnel lens, the effect of the
absorber size and the incidence angle on the collected
radiation and interior space temperature [27], gives a
figure of the effective use of FRESNEL/PVT system.
In hybrid PVT solar systems, the total efficiency
corresponds to the sum of both the electrical efficiency
and the thermal efficiency of the solar system for certain
operating conditions. If the electrical and the thermal
output of the system is considered together, the overall
obtained efficiency exceeds 60% for PV cooling operation
o
mode (water circulation at 20 C), while it is about 40% for
o
the usual water heating mode (water circulation at 50 C).
In the devices with low concentration photovoltaics the
obtained electrical efficiency is not considerably increased
as it is observed in devices with high concentration ratio.
In case of using pc-Si or c-Si cells, the electrical efficiency
is in the range of 10%-14% under usual operating
conditions and the rest of the above mentioned total
efficiencies are the thermal efficiencies. On the other
hand, the extraction of the great part of the incoming solar
radiation by the absorbing strips keeps the temperature of
the interior space of the simulative device at a satisfactory
o
level (reduction by 5-10 C, depending on the operating
temperature of the absorber). In this way a considerable
amount of cooling load is directly covered. Natural air
ventilation mode is necessary to be applied during periods
with high values of incident solar radiation and ambient
temperature. The suggested investigation contributes to
the extraction of a significant amount of heat from the
interior space in the form of electricity and thermal energy,
which is critical for the achievement of the comfort level in
it. In addition, an Air Conditioning system can operate by
the provided electricity from solar cells of the applied PVT
absorbers to cool building interior spaces. Regarding the
illumination control, the suggested system can avoid the
glare in the interior space and a smooth lighting without
sharp contrasts is achieved. During winter, the solar input
is some times higher than the needed and should be
extracted, being therefore converted into electricity and
heat, to cover electrical and space heating needs.
An alternative system design is the integration of the
linear Fresnel lenses on building façade or inclined roof
and the absorber to be PV cells of smaller strip width, to
receive the peak of the converged to focal line solar rays.
In this design, the non-used converged radiation and also
the diffuse radiation by the cells can be absorbed by flat or
cylindrical elements placed in a small distance from PV
strip. These elements form an air duct with system thermal
insulation and the air can circulate through it to achieve
building ventilation. In this system the cell material is
reduced (lower PV module cost) and all not-used solar
radiation by cells is absorbed for effective water heating.
In case of tubular tank absorber, it can operate as an
Integrated Collector Storage (ICS) water heater, providing
hot water without using pumps and heat exchangers. In
addition, the mass of the water in the tank has thermal
inertia (as a Trombe wall) and can achieve an extension of
building ventilation time for some more hours after sunset.
CONCLUSIONS
The concept of Fresnel lenses combined with linear
solar energy absorbers is suggested for building atria,
galleries and sunspaces to keep the illumination and the
interior temperature at the comfort level. The collection of
60%-80% of the transmitted solar radiation through the
Fresnel lens on PV or PVT absorbers leaves the rest
amount to be distributed in the interior space for the
illumination and thermal building needs. Laboratory scale
results show that the suggested system is of practical
interest for building integrated concentrating photovoltaics
(BICPVs) considering the dual operation of the system.
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systems. Solar Energy 2002, 73, 123-135.
23. Coventy J. Performance of a concentrating
photovoltaic/thermal solar collector. Solar Energy
2005, 78, 211-222.
24. Rosell J.I., Vallverdu X., Lechon M.A. and Ibanez M.
Design and simulation of a low concentrating
photovoltaic/thermal system. Energy Conversion and
Management 2005, 46, 3034-3046.
25. Tripanagnostopoulos Y., Nousia Th., Souliotis M. and
Yianoulis P. Hybrid Photovoltaic/Thermal solar
systems. Solar Energy 2002, 72, 217-234.
26. Tripanagnostopoulos Y. and Souliotis M., Battisti R.
and Corrado A. Energy, cost and LCA results of PV
and hybrid PV/T solar systems. Progress in
Photovoltaics: Res. and Applic. 2005, 13, 235-250.
27. Tripanagnostopoulos Y., Siabekou Ch. and Tonui J.K.
The Fresnel lens concept for solar control of
buildings. Solar Energy (in Press) 2007.
ACKNOWLEDGEMENTS
Thanks to the European Social Fund (ESF), Operational Program
for Educational and Vocational Training II (EPEAEK II), and
particularly the Program PYTHAGORAS II, for funding the above
work.
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
EFFECT OF A SECONDARY LINEAR CONCENTRATOR ON THE SI SOLAR CELL
ELECTRICAL PARAMETERS
Chemisana, D., Ibáñez, M., Abdel Mesih, B., Rosell, J.I.
University of Lleida, 25001, Lleida, Spain
ABSTRACT
In most photovoltaic concentrator systems the cells
are exposed to non-uniform illumination conditions with
consequent non-uniform temperature and current
distributions. Behaviour of the solar cell electrical
parameters has shown to be dissimilar according to the
illumination pattern. The non-uniform light distribution not
only affects the fill factor but also results in an open circuit
voltage reduction.
The use of secondary concentrators to modify
illumination distributions is also well known. The objective
of the work is to evaluate the increase of electrical
production of Si solar cells under linear concentration
using secondary concentrators.
The electrical output not only depends on the
uniformity of radiation but also on the local thermal and
electrical conditions of the solar cell. Therefore, it is
necessary to match all these values, the radiation pattern,
the thermal profile, and the voltage distribution over the
cell.
INTRODUCTION
Photovoltaic power generation systems at the
moment are important sources of electrical power to
replace or complement the most usual power generation
systems (which are fossil and nuclear fuels). In this field
concretely concentrator systems show a promising path to
reduce the costs of solar electricity. Currently, the prices of
solar PV systems are not economically feasible but there
are efforts to reduce these costs using concentrators.
Concentrator optics use either mirrors or lenses for
solar energy conversion. The gains that can achieved with
a Fresnel lens or a parabolic mirror are comparable and
the two configurations were developed competitively[1].
Several designs of Fresnel lenses have been
devised and tested. Flat Fresnel lenses are still in use by
some PV systems. A convex linear Fresnel lens is devised
to improve the concentration ratio and the efficiecy. Also, a
flat linear Fresnel lens in thermal energy collection is
utilized[2]. A symmetrical convex shaped Fresnel lens was
introduced and optimized and later a shaped non-imaging
Fresnel lens was presented which had an arbitrary profiles
according to the applications [3,4]. On the other hand,
mirror concentrators come in different forms; parabolic
troughs reflection concentrators, Fresnel reflection
collectors, parabolic mirror dishes, and V-trough
concentrators. In the 4 previous concentrators, the non-
uniform distribution of solar flux, at the solar cells, lowered
the efficiency of the PV power generation.
Solar concentrators suffer from inhomogeneous
illumination because they are designed in such a way so
that reflected sun rays fall exactly on the cells and do not
miss their target in case of poor tracking or structure
misalignment. This causes the electrical output of the PV
to vary and influence the distribution of currents in the
solar cell. Other factors affecting the performance are
shadowing, intensity, and spectrum due to dust,
temperature, clouds, or even pollution. The influence of
these factors can be investigated [5] using the expression:
− EG0
V
}[exp{ 1 } −1] + C3V1
I = C1G − C2T 3 exp{
kT
nVT
(1)
Eq. (1) is the mathematical expression base for the
method used here to characterize I–V curves. Where the
diode voltage V1 = V + RsI, G is the incident irradiance,
EG0 is the bandgap at 0 K and k is the Boltzmann
constant. Eq. (1) is fitted to experimental data using a nonlinear multivariable regression. A first guess of the series
resistance and the ideality factor is done. Once C1, C2 and
C3 are determined, the series resistance and the ideality
factor are numerically adjusted to obtain the best
coefficient of determination. The process is repeated until
convergence of the parameters is achieved. The
mathematical method is simple enough to be performed in
a standard spreadsheet. In this model is very important
the explicit dependence between current and temperature.
The aims of the present paper are: firsly to
determine experimentally the loss of production of a
concentrating solar cell under non-uniform illumination
distribution. Secondly, to test the improvement on
illumination distribution in a linear Fresnel concentrator
produced by a secondary concentrator. Thirdly, to
evaluate the increase of cell production thanks to the
secondary concentrator.
NUMERICAL AND EXPERIMENTAL METHODOLOGY
To determine the electrical cell parameters at
different illumination and temperature conditions,
experimental intensity and voltage measurements are
taken under concentrated radiation (1.5 suns). The
experimental work described is held on an ASE
2
monocrystalline silicon solar cell with 46.56 cm area (for
concentration uses, 10 suns).
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
measured ones in figure 3, giving a root mean square
error below 10%. Similar good fittings are obtained for the
non-uniform illumination distribution.
I(A)
The measuring device uses a halogen light source
with ± 5% uniform collimated light. A computer with a DAQ
software measures the cell performance data, the
temperature and the irradiance level and also controls an
electronic load. This allows measurement of short circuit to
open circuit conditions. We use a high speed DAQ target
(resolution 12 bits) which records the current, voltage and
temperature simultaneously. The temperature sensor is an
infrared thermometer. The negative contact in the cell is
obtained by two copper arms, and the noise is reduced
with a RC filter.
Illumination pattern on the solar cell is done using
different filters with the same mean transmittance. In the
experimental procedure Gaussian (see Fig. 1), uniform
distributions patterns were used. The filters are located
just above the solar cell.
c-Si
2
1,8
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
3
2
1
0
τ (%)
44
0,1
0,2
0,3
V(V)
Experimental data
66
0,4
0,5
0,6
Simulated data
Fig. 2. I-V adjusted curves and experimental data.
c-Si
90
2,5
The methodology developed to analyze the electrical
behavior of the solar cells is based in equation (1). In a
first step, this expression is fitted to experimental data for
uniform and Gaussian illumination patterns using different
levels of irradiance ant temperatures. In a second step the
coefficients obtained from the fittings are used to compare
electrical productions at the same irradiance and
temperature.
I sim (A)
2
Fig.1. Gaussian pattern filter
y = 0,9505x + 0,0648
R2 = 0,9808
1,5
1
0,5
0
0
0,5
1
1,5
2
I exp (A)
Fig. 3. Simulated versus measured cell intensity.
COMPARISON OF ILLUMINATION DISTRIBUTIONS
To adjust expression (1) to the ASE solar cell the I-V curve
was measured at different irradiance and temperature
conditions under uniform and non-uniform illumination
distributions. I-V curves are taken at three irradiances and
temperatures (see Table 1). Expression (1) is fitted to
these data.
-2
Curve
G (Wm )
Temp (ºC)
1
2
1000
1400
1500
29.41
47.33
3
43.42
Table 1 Illumination and temperature conditions
Figure 2 shows the results obtained for uniform
illumination pattern. The experimental curves and the
simulated ones (using the parameters shown in table 2)
are drawn. Simulated intensities are plotted against
Parameters
c-Si
C1
C2
0.00128
-53328.02358
C3
-0.10144
Rs (Ω)
N
EG (J)
0.00865
1.4973
1.7622E-19
r2
0.9802
Table 2 Model parameters derived using the regression
method.
To achieve the first objective, the adjusted I-V curves are
plotted at different irradiance and temperature conditions.
Figures 4 and 5 are an example of the results obtained.
For these graphs the irradiance assumed is 1.35 suns and
the temperature 28 ºC.
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
I(A)
2
1,8
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
0
0,1
0,2 0,3 0,4 0,5
0,6 0,7
Fig.6. Optical device
V (V)
Fig. 4. I-V curves under Gaussian (red) and uniform
(blue) illumination distributions.
0,8
P(W)
0,6
0,4
A Fresnel concentrator produces a flux distribution at
the output aperture that closely resembles the Gaussian
curve. Figure (7) shows a plot of light intensity distribution
across the target width, using OptiCAD ray-tracing
software to model the Fresnel concentrator optics. The
root mean square error (RMS) obtained for flux distribution
2
is 2.741 W/cm . Using OptiCAD the performance of the
cost-effective solution shown in figure 8 has been
evaluated. The implementation of the secondary
2
concentrator decreases the RMS to 0.1485 W/cm .
0,2
8
0
7
0
0,5
1
1,5
2
I (A)
6
5
w / cm 2 4
Fig. 5. Power curves under Gaussian (red) and
uniform (blue) illumination distributions.
For the Gaussian illumination distribution the
maximum power achieved is 0.743 W. The curve for
uniform illumination gives a maximum power of 0.759 W.
Therefore, the production for the Gaussian case is lower
than the uniform case. The small difference is small due to
the characteristics of the non-uniform pattern applied. The
transmittance varies from 44% in the sides of the cell to
90% in the center. A sharper transmittances profile would
had given a larger difference.
SECONDARY CONCENTRATOR SIMULATIONS
To achieve the second objective, secondary device
optical effects are studied applying OptiCad simulations.
The non-uniform illumination effects can be reduced with a
secondary optical device placed on the focus of the lens.
The optical system under study (see Fig. 6) is based on a
primary linear Fresnel concentrator lens (30 cm focal) and
a secondary concentrator, two parallels mirrors (reflectivity
0.88).
3
2
C7
1
0
C1
0
1
2
3
4
cm
Fig.7. Radiation pattern of the Fresnel concentrator.
To evaluate the increase of cell production thanks to
the secondary concentrator the experimental and
numerical procedure described above is applied using a
Gaussian filter which gives an illumination pattern similar
to the one obtained in figure 8. The loss of production due
to non-uniform illumination patter depends on mean
irradiance value and temperature. The mean value found
is 2.1% for irradiances between 1 and 10 suns.
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
[5] J. Rosell, M. Ibáñez. “Modelling power output in
photovoltaic modules for outdoor operating conditions”.
Energy Conversion and Management 2006, 47, pp. 24242430.
7
6
5
4
w / cm2
3
2
1
0
C6
C1
0
1
2
3
4
cm
Fig.8. Radiation pattern of the Fresnel with the
secondary optical device.
CONCLUSIONS
It is shown that the use of a simple secondary optics
device is very useful to work with linear Fresnel
concentrators due to the uniform illumination pattern
produced in the concentrating solar cells. The root mean
square error (RMS) obtained for flux distribution
2
2
decreases from a RMS 2.741 W/cm to 0.1485 W/cm in
the distribution produced by the secondary.
In accordance with previous works, it is shown that
the non-uniform illumination decreases the electric
production of the solar cells. The I-V curve fitted to the
experimental data allos the valuation of the losses in
different radiation and temperature conditions. The mean
value determined is 2.1%.
ACKNOWLEDGEMENTS
This work was supported by the MCYT (Spain) (ENE200407619).
REFERENCES
[1] Lorenzo, E., Luque, E. “Fresnel lens analysis for solar
energy applications”. Applied Optics 1981. 20(17), pp.
2941-2945.
[2] Al-Jumaily, K.E,J., Al-Kaysi, M.K.A. “The study of the
performance and efficiency of flan linear Fresnel lens
collector with sun tracking system in Iraq”. Renewable
Energy 1998. 14, pp. 41-48.
[3] Leutz, R., Suzuki, A., Akisawa, A., Kashiwagi, T.
“Design of a nonimaging Fresnel lens for solar
concentrators”. Solar Energy 1999. 65, pp. 379-387.
[4] Leutz, R., Suzuki, A., Akisawa, A., Kashiwagi, T.
“Shaped nonimaging Fresnel lenses”. Journal of Optics A:
Pure and Applied Optics 2000. 2, pp. 112-116
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
SEGMENTED CONE CONCENTRATORS: OPTICAL DESIGN
R. Leutz, L. Fu
Physics Department, Philipps-University, Renthof 5, 35037 Marburg, Germany;
ralf.leutz@physik.uni-marburg.de, phone +49-6421-2824148, fax +49-6421-2826535
L. Rubin, V. Nebusov
Day4 Energy Inc., 101 5898 Trapp Avenue, Burnaby, BC V3N 5G4, Canada
ABSTRACT
Segmented cone concentrators (or booster wings, Vtroughs) are an alternative to Fresnel lenses for low
concentration. Although the aspect ratio of a concentrator
assembled from flat mirror segments is high, it can be
designed fulfilling the conditions of uniform irradiance on
the target, and single reflection. There are two classes of
segmented cone concentrators: One class where the
mirror is directly attached to the receiver with a slope
angle smaller than π/4, and a second class characterized
by physically impossible first segment slopes, i. e. with a
gap between receiver and mirror. Both classes show very
different aspect ratios.
INTRODUCTION
The concentration ratio of segmented cone [1]
concentrators is easily found by counting the number of
images of the sun; for one segment on each side on the
receiver, the concentration ratio is three (two walls plus
receiver). The mirror walls may be segmented into two,
three, or more segments, then the concentration ratio
approaches five, seven, or more.
In this contribution we discuss the design solutions
and the optical properties of the segmented cones. We
begin with the design of single- and double-stage
segmented cones. Multiple segments are designed
numerically for any possible geometrical concentration
ratio. Physically meaningless solutions for the first (lowest)
segment lead to a novel class of cone concentrators with
moderately higher geometrical concentration ratios and
significantly reduced height.
These cones are intended as one-axis tracking linear
solar concentrators; we discuss the height vs.
concentration issue, and tracking error sensitivity. A
rendering of three different cones is shown in Fig. 1.
Figure 1: Segmented cone concentrators of similar geometrical concentration ratio. Three, four and five segments, from
left to right. The lowest segments are unphysical in the two designs on the right-hand side. Note the aspect ratios
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
ONE SEGMENT
The design of a single segment cone concentrator
with straight walls, uniform irradiance, and one reflection
per ray has been introduced 35 years ago [2]. The
geometrical concentration ratio of any concentrator is the
relation of entry aperture a to exit aperture a’ according to
Fig. 2.
Figure
2:
Figure 3: Geometrical concentration ratio and wall
inclination angle for the linear cone concentrator with one
set of wall segments. The merit function Cgeo ψ describes
the marginal change of mirror surface area (expressed by
the inclination angle) needed for an increase of the
geometrical concentration ratio
The problem is to distribute the concentrations C1
and C2 for the sets of mirror segments I and II,
respectively,
Cgeo = 1 + C1 + C 2 ,
Schematic of a segmented cone concentrator. Two paired
segments, one reflection per ray, uniform irradiance. Rays
drawn as solid lines for segment I, rays drawn as dashed
lines for segment II
With the sine-relation applied to the triangle BAA’,
we eventually obtain
Cgeo = 1 + 2 cos 2ψ .
(1)
This relation of geometrical concentration ratio and
wall inclination angle for the cone with one set of wall
segments is shown in Fig. 3. The maximum concentration
achievable in a linear cone concentrator with one pair of
straight wall segments is three. For higher concentration
ratios, an additional pair of wall segments has to be
added. The merit function in Fig. 3 is defined as Cgeo ψ,
reaching a maximum at ψ = 31°. The merit function
describes the marginal change of mirror surface area
(expressed by the inclination angle ψ which is equivalent
to the slope or derivative of the surface) needed for an
increase of the geometrical concentration ratio.
(2)
in such a way that both sets of mirror segments
illuminate the receiver completely. The law of reflection at
the mirror (Fig. 2) dictates that ψ1 = 2ψ2. Combining this
with a rewritten Eqn. 1, and Eqn. 2, yields
⎛
⎛ C −1⎞⎞
Cgeo − C 2 = 2 cos ⎜⎜ 2 arccos ⎜ 2
⎟ ⎟⎟ ,
⎝ 2 ⎠⎠
⎝
(3)
which is a transcendental equation with a numerical
solution for C2, and consequently also for C1. This
procedure allows for setting the total geometrical
concentration ratio at the start of the design process.
THREE OR MORE SEGMENTS
It is possible to design the segmented cone
concentrator with more than two segments. We shall see
that there is a small difference in the process, when
compared to the design of two sections, but that a rough
estimate of the actual concentration ratio can be obtained.
Assume that Eqs. 1-3 hold for additional elements. The
geometrical concentration ratio for a segmented cone with
n segments becomes
TWO SEGMENTS
Adding pairs of segments to the single-stage cone
results in the double-stage cone concentrator [3].
Cgeo = 1 + C1 + C2 + L + C n .
(4)
The wall inclination develops as follows,
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
ψ 1 = 2ψ 2 = 4ψ 3 = L = 2 n −1ψ n .
(5)
The sum of Eqn. 1 gives
n
⎛ 2ψ ⎞
Cgeo = 2∑ cos⎜ i−1 ⎟ ,
⎝2 ⎠
i =1
(6)
yielding the inclination angle of the first wall in a
numerical solution, and in closed form.
Figure
4:
Figure 5: Geometrical concentration ratio vs. height of
cones with three or more sets of wall segments, and
similar geometrical concentration ratios. The middle cone
IV’ is designed originally with four segments; the first
segment is nonsensical as it reflects radiation out of the
cone. Its omission creates a gap between absorber and
mirror area. The lower cone V’ is designed originally with
five segments, of which the first has been omitted
DESIGNS WITH GAPS
Corrected inclination ψ’ of the nth wall segment due to the
path of the ray r past lower segments
Reaching the third wall segment, we find that a
correction has to be introduced. Some rays reflected by
the third (top) wall travel close to the second wall segment,
and hit the first wall segment, before being rejected out of
the system. The reflected beam from the aperture of the
third segment has the width of the receiver, but not quite
the correct direction. Thus, we calculate the angle of a
virtual wall segment r extending from the edge of the
receiver to the start of the 3rd or nth wall segment, yielding
a correct inclination angle ψ’.
Having inclined the top wall segment slightly further
than the original, the beam reflected from it becomes too
wide to be accepted by the receiver. Therefore, the point
ending the top wall segment has to be recalculated as the
intersection point D of ray r’, parallel to r and the wall
segment s, as shown in Fig. 4.
The correction method yields the new rim of the
concentrator. Its geometrical concentration ratio is slightly
lower than the one put in through Eqn. 6, from which the
inclination of the first wall ψ was found.
For the first segment, the inclination angle ψ must be
positive and smaller than π/4 for the reflected ray to be
directed down towards the receiver. The mathematical
root finding procedure mentioned above yields a matching
real solution also for π/4 < ψ < π/2. Obviously, the latter
inclination makes no sense physically: all reflections on a
first segment with this inclination leave the cone.
Rays incident on the second and further segments,
however, are directed towards the target. The angle of
incidence on the target is relatively large due to the gap
left by the first segment. The smaller the aspect ratio of
the concentrator, the larger the average incidence angle
on the target. A comparison of concentration ratio vs.
height of three cones with three or more segments, two of
them designed with a nonsensical first element is given in
Fig. 5. The cones have similar geometrical concentration
ratios, the prime superscript indicates a nonsensical first
element.
It is evident from the figure that the height of the
systems reduces with the number of segments designed.
The widths of the concentrators increase.
HEIGHT VERSUS CONCENTRATION
The height of the cone is one indication for the
consumption of mirror material (in particular if all mirrors
are as steep as shown in Fig. 5), and for the sensitivity of
the cone for accepting incidence at angles other than
normal. The height of the cones I, II, III, IV of one, two,
three, four and five wall segments vs. geometrical
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
concentration ratios is plotted in Fig. 6. The height is given
in units of absorber half-width. Interestingly, the cones
designed with missing first segment (II’, III’, IV’, V’) are
lower than the corresponding segmented cones without
gaps (I, II, III, IV). This is of particular importance for actual
solar photovoltaic concentrator systems, which may have
a geometrical concentration ratio around five.
for tracking errors up to an incidence angle on the entry
aperture of 2.0°, and exceed 50% for 10°. The presented
results are obtained with a ray-tracing simulation. Cosineeffects, or shading losses are not included. The wall
reflectivity is~0.85 for all incidence angles. The simulation
includes Fresnel losses at a receiver covered with BK 7
glass.
Figure 6: Height of cones with one, two, three, four and
five sets of wall segments as function of the geometrical
concentration ratio. The height is given in units of absorber
half-width. Note that the cones designed with missing first
segment (II’, III’, IV’, V’) are lower than the corresponding
segmented cones without gaps (I, II, III, IV)
Figure 8: Irradiance distribution for typical tracking errors
on the target of the concentrator IV’ (see Figs. 5 and 7)
The irradiance distribution for typical tracking errors
on the target of the concentrator IV’ (Fig. 5) is shown in
Fig. 8. While the collection efficiency drops, the irradiance
does not develop any hot spots. The performance of a
photovoltaic cell should not be compromised.
CONCLUSIONS
It is possible to design linear cone concentrators with
multiple straight wall segments, and uniform illumination
on the receiver. Given the height of the system,
geometrical concentration ratios of five are realistic.
The introduction of a gap between the receiver and
the reflector walls reduces the height of the cone
considerably, while increasing its width. Efficiency losses
due to tracking errors are tolerable for incidence up
to 2.0°.
REFERENCES
Figure 7: Efficiency of the cones shown in Fig. 5. Raytracing results.
TRACKING ERROR SENSITIVITY AND
IRRADIANCE DISTRIBUTION
Tracking errors reduce the efficiency of the cone
concentrators according to Fig. 7 where the cones
depicted in Fig. 5 are compared. The efficiency losses
increase in linear fashion. Cone concentrators with gaps
are subject to higher losses than the cone without gap,
due to geometrical losses. Efficiency losses are below 0.2
[1] D. Williamson, Cone Channel Condenser Optics,
Journal of the Optical Society of America 42,10:712-715,
1952.
[2] K. Hollands, A Concentrator for Thin-Film Solar Cells,
Solar Energy 13:149-163, 1971.
[3] K. Mannan and R. Bannerot, Optimal Geometries for
One- and Two-Faced Symmetric Side-Wall Booster
Mirrors, Solar Energy 21:385-391, 1978.
164
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
MIRRORS BASED ON TOTAL REFLECTION FOR CONCENTRATION PV PANELS
E. Karvelas1, A. Papadopoulos1, D. Dousis1 Y. P. Markopoulos1 E. Mathioulakis2, G. Panaras2, V. Vamvakas3
and D. Davazoglou3*
2
1
Zenon S. A., Kanari 5, 15354 Glyka Nera, Attiki, Greece
NCSR “Demokritos”, Institute of Nuclear Technology and Radiation Protection, 3Institute of Microelectronics POB 60228,
15310 Agia Paraskevi, Attiki, Greece,
ABSTRACT
Mirrors based on total reflection (TRM) have been
designed and fabricated for application in concentration
PV panels. TRMs are made using glass (without any
metallization) and this renders their lifetime practically
unlimited. The approach consists in using the principle of
total reflection, which though well known since many
centuries, has never been applied in concentration PV
panels. The reason is that three axis of rotation are needed in
order to focus the reflected sunrays to the desired focal point as
opposed to two axis of rotation for the conventional mirrors.
The main breakthrough presented here is the design of
TRMs able to focus on a surface of the order of 30x10
2
mm using two axes of rotation. For the design software
based on the method of ray tracing simulation was used,
which allows for the incorporation of realistic parameters in
the calculations. To obtain focusing the straight acmes of
a typical total reflection prism were replaced by parabolic
ones. TRMs were fabricated and tested giving results in
agreement with the simulation.
INTRODUCTION
Photovoltaic (PV) cells technologically represent a
mature technology for energy production but are still very
expensive. The main reason preventing the one-sun PV
cells to be cost effective is the high price of the
semiconductor grade silicon necessary for their fabrication
when a high efficiency is desired.
One way to overcome this problem is to suppress
the factor “high price’’ using the concentrating type PVs.
Up to now this technology has not been exploited
(although it needs 500 to 1000 times less crystalline Si
than conventional PV cells) for several reasons one of
which is the cost of concentrating optics. Indeed although
mirrors are a relatively cheap material, manufacturing of
curved concentrating mirrors able to remain exposed
outdoors and sustain environmental degradation for a time
period of the order of 20 years is impossible. After a small
fraction of this period mirrors must be replaces thus
increasing the cost of the produced energy. Additionally,
the supporting structure and the sun-tracking device must
be designed for the expected wind speed during their 20year or so lifetime. Thus, the total cost of such a technical
solution using concentrating mirrors is prohibitive and
leaves little hope to reduce it at an effective level.
This study provides the solution to some of the
aforementioned problems using total reflection mirrors
(TRMs), which can be described as flat or parabolic glass
panels, made from common water-clear glass having the
rear surface curved with parallel or converging orthogonal
prisms. The sunrays coming into these panels from their
front surface (being flat or curve parabolic etc.) undergo
total reflection at the rear surface orthogonal prisms and
come out from the front side. This attractive technology
was not given any attention up to now mainly because
such mirrors need three axis of rotation in order to focus
the reflected sunrays to the desired focal point (compared
to two axis of rotation of the conventional mirrors).
The design, has shown that if one of the three
rotation axes of the TRMs pass through the focal point
then they are reduced to two, thus the TRMs developed
within the present study focus as conventional mirrors.
This last innovation has multiple implications. The
reduction of the effective surface of the reflecting mirrors
from multiple square meters (standard requirements of
conventional mirrors) to a small fraction of one square
meter for the TRMs has been achieved. In this case a low
profile arrangement of the concentrating field was selected
in order to be able to sustain the wind load when fitted to a
supporting structure and therefore reduce the design
requirements of the TRM array hyper-structure.
Additionally each TRM was designed to be in the range of
240 mm diameter, thus having the required glass volume
to be massively produced by existing automated modern
glass manufacturing processes.
DESIGN
The design of the TRM is based on the idea of the
total reflection, which is observed when a beam of light
falls on a prism. For the design the basic concept in
combination with the optical characteristics of parabolic
surfaces were investigated. More precisely, instead of
using a simple prism, an upper perfect parabolic surface
and a lower edge was designed as a perfect parabola.
Part of such a prism is shown in Figure 1. All the shown
planes P1, P2, P3 and P4 are perpendicular to the back
edge of this prism. The path that the incident on the
parabolic prism ray follows is also shown in Figure 1. The
incident ray enters the prism at the point A, which is on the
plane P1 while a small percentage of the incident energy is
reflected towards the focal point. First the ray hits the back
surface of the prism at point B, which belongs to plane P2.
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
manufacturing process capable of forming the sharp
edges of the back surface of the TRM using a cheap,
optically clear material such as, for instance, glass. In
order to evaluate the effects of the manufacturing process
on the efficiency of the system, various sizes of radii in the
formation of the back edges of the TRM were taken into
consideration in calculating the relationship between the
efficiency, nTRM, and these radii. The efficiency loss of the
TRM was calculated in relation to the respective edge radii
imposed by the manufacturing process and presented in
Figures 3(a), (b)
Fig 1. Prism design and associated sunray reflection
At this point the ray is reflected again at the opposite
surface of the prism at point C, which belongs to plane P3.
Finally, the ray is reflected out of the prism at point D,
which belongs to the plane P4. It must be noted that the
four planes P1, P2, P3 and P4 are perpendicular to the back
parabolic edge on the prism. The designed TRM is
composed by a number of parabolic prisms. The final
design is presented in figure 2. The diameter of the TRM
is of the order of 230 mm while its constituent prisms are
0
repeated every 2 .
Fig. 3. (a, Upper) Imposed radius to the edges of TRM due
to manufacturing process. (b, Lower) Efficiency loss due to
the increase of the edge radii.
Fig. 2. 3D graphical representation of the TRM optical
element.
In a mathematical limiting case when the dimensions of
each prism go to zero, the convergence surface of light
from a parallel beam becomes a point. In this limiting case
the optical system exhibits the behavior of a standard
parabolic surface. Therefore, it appears that the lateral
dimensions of the constituent parabolic prisms should be
minimized. However, practical considerations from the
manufacturing point of view impose restrictions on the
respective tolerances of the proposed design. From
theoretical projections to physical realization, significant
performance degradation is to be expected in terms of
reflection and acceptance angle due to deviations from the
ideal design. The biggest challenge in manufacturing
these optical elements is to provide a cheap
It is evident that the efficiency of the system improves as
the number of the back edges of the TRM decreases.
However, this decrease of the number of the TRM’s
“slices” produces undesirable effects such as, for instance,
the thickening of the TRM.
SIMULATIONS
Ray tracing simulations were performed using the
actual sun incident light and implementing real conditions.
In particular, the incident light was emitted from a
blackbody surface at 5840 K and equal to the size of the
surface of the sun located at a distance from the
developed Total Reflection Mirror equal to the actual sun
to earth distance. Furthermore, a Lambertian angular
distribution was used. In order to minimize the statistical
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error to values of 1% or less a large number of emitted
rays was used. The performed simulations contributed to
the successful design of the TRM by helping the designers
to pinpoint problematic areas and test the possible
remedies to various design considerations and/or
problems.
applied in order to achieve the best possible optical
surface. Additionally, special care in the machining
process was taken in order to achieve an overall radius of
the constituent prism edges in the range of .1 mm. A first
qualitative result is presented in Figures 5 (a)&(b). These
field tests are very encouraging concerning the quality and
capability of the TRM reflectivity and sun-array
concentration. Without achieving complete focus with the
sun body a fair match with simulated irradiance map (Fig.
4(a)) was achieved as presented in the photo of Figure
5(a). The Total Reflection is depicted also in visual means
in Fig. 5(b) where it is evident that the density of the
shadow created by the transparent TRM is similar with the
shadow created by a solid body.
Fig. 4. (a, Upper) Irradiance map on the focus plane
calculated with ray tracing simulation software (b, Lower)
Misalignment study.
The results of the simulation of the final TRM
design are shown in Figure 4. These results depict the
distribution of the incident rays to the PV. The size of the
PV is 30 x 10 mm (Fig. 2), located to the focus point.
Based on these simulation results the efficiency of the
optical system was calculated to be nTRM=90%. These
simulations are based on the assumption that all the
geometrical characteristics of the TRM will be met during
the manufacturing process.
MANUFACTURING
Before investigating the possibilities of molding the
TRM in glass material, in order to verify the ray tracing
simulations performed, the 3D structural model of the lens
was sent for CNC machining of a Prototype. A special
optical grade of acrylic plastic was used. After the CNC
machining of the lens an optical polishing procedure was
Fig. 5. (a) Reflection of sunrays using the TRM
Optical Prototype (b) Shadows generated by the TRM
Optical Prototype.
After the successful prototyping of TRMs on plastic,
a second generation of TRMs was produced on glass. The
manufacturing and its optimization were made in
conjunction with a glass industry. TRGs were re-designed
in order to reduce their mass to reduce the duration of
cooling after “pressing”. This was necessary because a
long duration of cooling induces stresses and therefore the
deformation of the shape of the TRGs. In Fig. 6 various
stages of the production of the second generation of glass
TRMs is shown.
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TRMs made on glass after 3 years of operation have
retained their initial performance.
Fig. 6. Various stages of the production of the second
generation of TRMs on glass.
TESTING
After fabrication TRMs were tested both at
laboratory and field conditions. The laboratory tests have
shown while the TRMs made on plastic exhibited a
performance in almost perfect agreement with the
simulation the second generation of TRMs exhibits a
concentration power of the order of 45% of the prototype
TRMs on plastic. This was attributed to the small
imperfections introduced during manufacturing of the
latter, which, as seen before, may lead to significant
reduction of performance. Imperfections were mainly
introduced during cooling of the glass and this is to be
expected since the initial temperature after “pressing” was
o
of the order of 1000 C, which was falling down to room
temperature within some minutes. In an effort to decrease
the thermal mass of the TRMs they were re-designed
several times to obtain a compromise between a small
thermal mass, i.e., small mass, and mechanical durability.
For the field testing the TRMs were installed on the
PROTEAS PV System [1, 2] (Fig. 7, a) which was a hybrid
system conceived to produce electricity with concentration
PV cells, heat in the form of hot water from the cooling of
cells and cooling power in conjunction with a small
adsorption heat pump. The main result from the field
testing was that, as expected TRMs made on glass were
much more robust than the plastic ones, which after one
year on field lost 30% of their concentration power and 50
% after the second (see Fig. 7, b). On the contrary, the
Fig. 7 (a, Upper) The installation of PROTEAS PV System.
(b, lower) Comparison of a TRM made on glass (left) and
of a plastic one (right) after two years of operation.
CONCLUSIONS
We have demonstrated the TRM, which is a novel
optical device that exploits the concept of the total
reflection in order to concentrate light on a limited area of
the order of several square centimeters for use in cent
rated PV cells. TRMs may be fabricated on glass at a
reasonably low price, using trivial manufacturing
techniques, giving a performance inferior than that of
devices made by high-precision methods but, on the other
hand, having an infinite lifetime.
ACKNOWLEDGMENTS
Financial support from E.U. is acknowledged PROTEAS
PV System, Contract No ENK6-CT-2002.
REFERENCES
[1] PROTEAS PV System, Triple hybrid concentrating
PV system for the cogeneration of electricity, heat and
cooling power, Contract No ENK6-CT-2002
[2] PROTEAS PV System, European Photovoltaics
Projects 1992-2002, Project synopses p 124-125
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OPTICAL TAILORING OF FLAT FACETED COLLECTOR FOR OPTIMAL FLUX
DISTRIBUTION ON CPV RECEIVER
Marco Stefancicha,b*, Andrea Antoninia,b, Emiliano Milana,b, Giuliano Martinellia,b, Mariangela Butturib, Paolo Zurrub,
Pierangelo di Benedettob, Davide Uderzob, Antonio Parrettac
a - University of Ferrara & CNR , Via Saragat 1 Ferrara (FE) 44100, Italy;
b - CPower srl , Via Saragat 1 Ferrara (FE) 44100, Italy;
c - ENEA Centro Ricerche “E. Clementel”, Via Martiri di Monte Sole 4, 40129 Bologna (BO), Italy
*Corresponding Author: stefancich@fe.infn.it, Phone: +39 (0)532 974329; Fax: +39 (0)532 974327;
ABSTRACT
Photovoltaic concentrator systems would lead to a
substantial reduction in the cost of the PV energy by
substituting the expensive, photovoltaic flat panels with
low cost, reflective or refractive surfaces combined with a
small area of high efficiency concentrator cells.
Reflective dish concentrators, complete with accurate
tracking, allow a good concentration levels; the use of
single, large parabolic mirrors requires a dense array of
cells at the receiver constituting the photovoltaic module.
This fact reduces significantly not only the quantity of
employed semiconductor but the size of the photovoltaic
module itself, allowing for the fabrication of this high
technological core of the system by means of the
techniques and structures of the electronic industry.
This approach has, however, other technical complexities:
the requirement of a dense array module leads to the
necessity of particular solutions for the high density
packaging of the cells and of special solutions to ensure
high uniformity of the irradiance at the receiver because of
the series connection of the solar cells. Two additional
problems tightly related to the previous are the positioning
of the bypass diodes and the necessity to ensure a
sufficient angular acceptance of the system, without
reducing the uniformity of the irradiation on the
photovoltaic devices.
In this paper some solutions at these problems adopted by
CPower srl for the development of concentrators are
presented.
INTRODUCTION
In a dish, reflective solar concentrator, the bundle of light
is directed toward a module of solar cells. To minimize
optical losses at the target, the cells must be as closely
spaced as possible. In typical dense array, the cells are
mostly series connected, to build up the voltage and keep
the current in the range of the working conditions for the
commercial inverters. Because current is almost linearly
dependent on the incident light, the current in a string of
identical solar cells will be limited by the cell with the
lowest illumination. It is therefore important to achieve an
irradiance distribution as uniform as possible at the
receiver area. Typically, for dish concentrators this is
achieved through the use of secondary flux modifiers
which disperses light at the centre of the receiver more
evenly [1-3]. However, the introduction of additional optical
parts leads to a reduction in the optical efficiency because
of the reflection at the interfaces and/or absorption of the
materials, and leads to an higher complexity in the
mechanical, thermal and optical management of the
system. Another possibility is to employ a “tailored optics”
approach for the primary collector. A particular case is a
flat facetted concentrator designs where a proper
modeling of the facets shape, dimension and position
allows to ensure a uniform illumination at the target by the
superposition of a lot of small sized, parallel bundles [4].
With this approach the defects or partially shadowing of
the large area, mirrored surface collecting the radiation
doesn’t seriously affect the illumination of the target and
the electrical output of the system, as it happens for the
traditional flat panels, or for concentrating systems
composed by arrays of concentrator-cell units.
The uniformity of irradiance at the module of PV cells is
required for all the working conditions of the system, i.e.
also under the small misalignments defining the angular
tolerance of the mechanical system parts.
FLAT FACETTED CONCENTRATORS
Using the square mirror version of the primary
concentrator with flat facetted parabolic dish as shown in
fig.(1) there are some intrinsic limitations in the achievable
light flux uniformity at the receiver. A less constrained
design based on basic triangular facets allows to
overcome these limitation obtaining, at the same time, a
mechanically continuous surface that provides significant
manufacturing advantages. The concentration level can be
freely chosen being directly connected to the number of
facets and the reproducibility and conformity of the
continuum surface to the theoretical model of the object
shape obtained can be very high with standard moulding
processes. Surface optimization can, moreover, be
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
performed by an automatic trial and error procedure aimed
at electric power maximization that takes into account the
PV panel structure.
Fig.1. Flat faceted solar dish made of an array of all
equal, squared mirrors.
To achieve an optimized concentrating surface an
automatic software procedure based on Matlab and
Tracepro has been developed; it substantially works,
starting from an initial placement of the triangular facets,
modifying the positions of the triangles vertices following a
Montecarlo approach. The quality parameter that
determines if the modified configuration is better than the
unmodified one is the simulated electrical performance of
the PV panel. The properties of the concentrated bundle
are simulated by TracePro code, where realistic
characteristics at the reflective surface are taken into
account. The optimized surface is, therefore, specific for
the chosen PV module configuration. Since the
optimization and simulation modules in the software
operate in a fully automatic mode, a very large number of
trials can be performed allowing for an highly optimal
result to be obtained. A CAD image of the so obtained
concentrator is reported in fig.(2).
As in most photovoltaic modules, in the PV panel a large
number of solar cells are series connected to reduce the
power losses related to energy transfer to the inverter and
to increase the voltage to the levels deemed acceptable
by standard conversion devices. Since, however, in a
string of series connected cells the generated current
approximately corresponds to the lower current produced
by each cell separately, all the cells should deliver similar
current. Assuming a substantial temperature uniformity the
current in each cell is essentially proportional to the level
of irradiation. So, all the cells must be equally illuminated
for optimal panel performance. In a parallel connection of
cells, on the other side, the total current is given by the
sum of those produced by each cells. Consequently, the
parallel connection appears to be more suitable for the
situations where the uniformity of illumination isn’t ensured
but it raises significant conversion problems.
On the border line of the focal region of a dish
concentrator there is an annular region of decreasing
irradiance level. This ring should be kept as thin as
possible trying to achieve a pillow box distribution. An
ideal flat facetted concentrator permits to get a distribution
closed to the optimal one, but the solar divergence, the
possible scattering of light due to the BRDF of the
reflective surface and the unavoidable fabrication
tolerances produces a ring of not negligible area.
Additionally, in condition of non ideal alignment the focus
zones moves from the desired region; as it can be
understood by simple geometrical considerations and is
represented in fig.(3). While the light distribution shape
doesn’t change significantly for small misalignments, it
shifts laterally jeopardizing the full illumination of the cell
panel.
Fig.3. Shift of the pillow box irradiance maps for a
50x optimized, flat facetted dish for misalignment at
0°, 0.5° and 1° respect to the ideal condition,
considering the solar divergence.
Fig.2. CAD representation of a dish concentrator
made of tailored triangular flat mirrors.
PANEL CONFIGURATION
To recover these optical effects some configurations of
secondary optical elements can be employed. However,
this additional object adds complexity in the system design
and realization because of its positioning, its possible
overheating, the degrading of its optical properties, etc..
For these reasons it comports additional cost at the
system. Another possible way followed by CPower srl for
its dish concentrators is based on a particular electrical
connection of the solar cells of the receiver. A ring of cells
is posed around a central region of series connected solar
cells. Half of this external ring is parallel connected with
the other half; more in particular, the cells in a string are
parallel connected to the correspondent cells on the
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opposite side of the squared module. These outer cells, in
ideal alignment conditions, are only half illuminated by the
concentrated radiation. In this way, the portion of every
solar cell which should be unirradiated recovers the part of
light at the periphery, external at the ideal pillow box;
fraction of light here reflected from the dish can be caused
by manufacturing errors of the concentrator or due to the
solar divergence. Moreover, when the focal region shifts
because of slight misalignments for tracking errors or
mechanical imperfections, these external cells recover the
light losses; this solution can cover misalignments up to
those producing a complete illumination of the external
devices and the consequential total shadowing of the
correspondent cells on the opposite side at which they are
parallel connected.
In fig.(4) the top layer of a so described module is shown
for a concentrator dish of concentration factor equal to
approximately 50x. The central region surrounded by a
continuous line and filled with crosses is the focal zone of
the concentrator under ideal alignment. All the cells are
rectangular and of same size. The cells belonging at the
external ring are positioned in order to have their longer
side perpendicular to the ring, to have approximately, the
same angular acceptance along the two axis of the square
module.
of the solar cells as well as for the positioning of bypass
diodes, elements ensuring a reduced power loss in the
case of fluctuations of the irradiance on the receiver or
degradation of the performances of some devices.
Fig.4. A detail of cells in the dense array assembly.
CONCLUSIONS
While the general design of a dish concentrator system is
essentially established there are a number of technical
solutions allowing for higher efficiencies by the reduction
of the loss mechanisms. At the same time the proposed
solutions must conform to the available industrial
techniques restricting the nature of the possible
interventions.
A deep comprehension of the loss mechanisms and a
realistic evaluation of the outcome of the proposed
solution must necessary be based on refined optoelectrical simulation the software for which has been
developed on the TracePro-Matlab development platform.
For the developed concentrator a realistic simulation of
system performances under real operating conditions has
been performed and provides, starting with cells having a
20% efficiency, global system efficiency (at the DC side) of
around 12.5%. Further optimization are being currently
considered.
ACKNOLEDGMENTS
This work was supported by the European Social Fund,
the Italian Ministry of Work and Welfare, by Regione
Emilia-Romagna and Consorzio Spinner.
Fig.4. Electrical design for the solar cells on the
module, with position of the cells adopted to recover
small tracking errors or slight light dispersion.
Another fundamental aspect regarding the dish
concentrators is the packing of the cells at the receiver.
Indeed, all the area dedicated to the interconnections
between the cells produces optical losses. However, to
ensure good electrical connections some standard
specifications of the SMD (surface mounting device)
soldering processes must be followed. An image of a
detail of a dense array module is in fig.(5). The medium
level of concentration allows us for using IMS as thermally
conductive substrate material as generally used in the
power electronics; this permits a low cost and high
flexibility for the electrical circuit design, for the connection
REFERENCES
[1] H. Ries, J.M. Gordon, M. Lasken, “High-flux
photovoltaic solar concentrators with kaleidoscope-based
optical designs”, Solar Energy 1997, 60, No.1, pp.11-16
[2] C. Bingham et al., “Concentrating Photovoltaic Module
Testing at NREL's Concentrating Solar Radiation Users
Facility”, NCPV and Solar Program Review Meeting 2003,
NREL/CD-520-33588, pp. 218-220.
[3] R. Winston, R. C. Gee, “Nonimaging light concentrator
with uniform irradiance”, Patent No.: US 6,541,694 B2,
April 1, 2003
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
[4] G. Martinelli, M. Stefancich, A. Antonini, A. Ronzoni, M.
Armani, P. Zurru, L. Pancotti, A. Parretta, "Dichroic Flat
Faceted Concentrator for PV Use", Proceedings of the
International Conference on Solar Concentrators for the
Generation of Electricity or Hydrogen 2005, 1-5 May,
Scottsdale, Arizona (USA)
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LOSS OF OPTICAL QUALITY OF A PHOTOVOLTAIC THERMAL CONCENTRATOR
DEVICE AT DIFFERENT TRACKING POSITIONS
B. Abdel Mesih, D. Chemisana, F. Badia, M. Ibañez, J.I. Rosell
Department of Medi Ambient, Universitat de Lleida, Avenue Rovira Roure 191, E25198, Lleida, Spain
ABSTRACT
The objective of this work is to apply the absorber
reflection method (ARM) implemented by Ulmer et. all to
find the loss of optical quality of a flat Fresnel-reflection
PV-T concentrator. The 11x BiFres concentrator is made
of 18 white Fresnel mirrors. The mirrors focus the
incoming rays on the thermal and PV absorber and thus all
are of equal length but at different tilt angle. The absorber
2
has 52 c-Si solar cells and a size of 0.26 m . The
concentrator is connected to two linear actuators for a 2axis sun-tracking capability. The working fluid is water. A
set of pictures were taken with a digital camera placed at a
certain distance perpendicular to the concentrator’s axis
orientated first towards it. The concentrator is then tilted at
different angles to see the effect of weight of mirrors on
the optical quality. A geometrical algorithm is used with the
aid of a numerical software to analyze the pictures. The
aim is to find the distribution of actual normal vector to
each mirror strip and compare it to the theoretical value.
Discrepancies between the previous two values mean that
reflected rays will miss the target (the absorber).
Consequently, the results of this work are used to further
obtain the power (electrical and heat) loss.
INTRODUCTION
The reflectivity of the optical parts and their
geometric precision influence the overall performance of
the PV/T concentrator systems. Any disorientation or
dents in the mirrors mean that there is a higher probability
that the reflected sun beams will miss their target which is
the photovoltaic panel and thus affect the system’s overall
thermal and electrical output. The performance of the PV/T
system is also affected by the ageing of mirrors due to
material degradation in outdoor conditions [1] and nonuniform light distribution over the PV cell [2].
An easy and effective technique suggested by Ulmer et. all
[3] is implemented to find the loss of optical quality of the
mirrors. This method is called the Absorber Reflection
Method (ARM) and is applied to the BiFres PV/T system
installed on the roof of the University of Lleida (see Fig. 1)
BiFres is an 11X system consisting of 18 white Fresnel
mirrors. The mirrors focus the incoming rays on the PV
absorber which is soldered on top of a flat plate collector
with water as the working fluid. The role of water is twofold, cool down the cells and supply hot water to a storage
tank [4].
Fig. 1 The BiFres system
The optical quality issue has been tackled before
using different methods. One of the most accurate and
precise techniques is the close range photogrammetry.
Here, coordinates of reference points on the measurement
object are calculated from a set of digital pictures taken
from different observation points using a digital camera
which can offer high-quality mega-pixel photos [5].
Photogrammetry can provide coordinate measurements
with precisions of 1:50,000 or better. The extreme
flexibility of photogrammetry to provide high accuracy
three dimensional coordinate measurements over almost
any scale makes it particularly appropriate for the
measurement
of
solar
concentrator
systems.
Photogrammetry can also provide information for the
analysis of curved shapes and surfaces, which can be
very
difficult to achieve with conventional measurement
techniques [6]. Another well known technique that has
been used since the 1970s, is the Video Scanning
Hartmann Optical Tester (VSHOT). It is a slope measuring
tool for large and imprecise reflectors. In this technique a
laser ray scans the surface automatically and detects the
reflected beam by a video camera [7,8]. Another novel
technique is used to record at night the light of a star
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
reflected by the mirrors and the images of the mirror taken
from its focal region allow the reconstruction of the slope
map. The application of this technique is particularly
simple and at very low cost in characterization of heliostats
that have a very large focal lengths of 100 meters or more
[9].
THE “ARM” METHOD
The concentrator is first set in a vertical position
with the mirrors facing the camera which is placed on a
metal mast. The mast is attached to the device’s frame
along the normal vector to the plane of the absorber at a
fixed distance S1 from the system. The focal distance f
from the absorber to the frame of the concentrator is
measured. Also other lengths are known such as the width
of the absorber, the dimensions of the concentrator
device, the distance of each mirror from the centre of the
concentrator, and the width of each mirror strip and its
inclination αd. A set of pictures are taken in this vertical
position then the concentrator is tilted to a middle position
and is finally tilted to a horizontal position. A numerical
software is used to analyze the pictures based on a
geometrical algorithm discussed in the following section.
It is important to mention that from our available
location it was not possible to get information about the
mirrors at the edges of the concentrator (mirrors
7-9 counted from the centre) unless the camera is
positioned farther away which was not possible. To solve
this problem, the absorber is replaced with a wooden
target of the same width (see Fig. 2), painted black to
observe the reflections, and situated on a sliding rail. This
gives us the opportunity to slide the absorber (target) left
and right to see the reflections on the mirrors at the edges
of the device. The algorithm includes the parameter ∆d
that represents the offset of the absorber from the centre
of the device due to such movement.
THE GEOMETRICAL ALGORITHM
The normal vector η to each mirror depends on
the tilt angle αd of the each strip as seen in Fig. 3 and
equation (1).
η = 90 − α
(1)
d
On the other hand, the normal vector
geometrically from the following relation:
is
found
⎛α +α'⎞
⎟
⎝ 2 ⎠
η = 90 − ⎜
(2)
The angle α’ is calculated as:
Xm
Xm ´
=
S1
S´
tan α ´ =
while angle
α
(3)
is found from the relation:
X 1 + ∆x − ∆d
f − ∆y
tan α =
(4)
Xm
X1
∆x
∆y
αd
η
f
∆d
S1
α´
α
Reflection of the
absorber on one
mirror strip
absorber
Camera lens
S´
α´
Camera sensor
ℓ2´
Xm´
Fig. 2 The wooden target with the reflections on the
mirrors
Fig. 3 The ARM geometrical algorithm
With the values of angles in equations 3 and 4 in hand,
both equations 1 and 2 can be compared. Discrepancies
between the two equations reflect the loss of optical
quality as shown in the values of the Root Mean Square
Errors (RMSE).
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4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
EVALUATION AND RESULTS
It is expected that the most dramatic effect in
terms of errors will be vivid when the concentrator is in the
horizontal position because the mirrors weights’ are acting
perpendicular to the concentrator. On the other hand the
lowest errors are at the vertical position while at the
horizontal position errors depend on the cosine of the tilt
angle. Also errors in the location of the camera play a very
crucial factor in calculating the RMSE because that leads
to a change in the perspective. The output of the picture
analysis is not up to the standard and shows a great error
due to the camera position on the mast. The mast tends to
slightly bend forward or to the sides as the concentrator is
moved. This leads to problems in the perspective where
sides of the concentrator which are parallel in reality, are
no longer seen parallel in the pictures. Nevertheless, the
results show that the RMSE increases with the increase of
the distance from the centre of the concentrator. That
means mirrors on the edges have higher errors than the
ones in the middle. An interpretation to that is that mirrors
have less width as we move away from the absorber to
avoid having the reflections on the back of the previous
mirror. Accordingly, wider mirrors are less susceptible to
bending. The length of the concentrator is more than 2.5
meters and practically it is not possible to transport one
sheet of mirror that long. Therefore, shorter mirrors are
supplied as a number of strips in different lengths. The
longer strips tend to bend more than the shorter ones. This
bending is obvious in locations away from the metal
guides or groves that hold the mirrors.
Other important factor is the aging of the mirrors.
The concentrator has been available on the roof of the
university for about five years including a couple of years
standing idle. The wind, rain, and dust are factors for
decreasing the efficiency of the mirrors or slightly
deforming the frame of the device with years. Also the
misalignments of the mirror strips affect the optical quality
of the reflectors. When a broken strip is replaced, the new
mirror might be shifted a few millimeters from the ideal
position. In figure 4, the reflection on two mirrors is shifted
to the right as compared to the leftmost mirror. This is an
example of the misalignment problem.
Mirror #
& location
1R
2R
3R
4R
5R
6R
7R
8R
9R
Average for
Right mirrors
1L
2L
3L
4L
5L
6L
7L
8L
9L
Average for
left mirrors
Average for
all mirrors
RMSE in mrad
Concentrator at vertical position
4,767
5,757
8,501
7,697
5,941
4,644
14,884
13,098
88,493
17,087
0,579
2,337
1,036
1,259
1,433
1,773
1,667
4,107
2,519
1,857
9,472
Table 1. The Root Mean Square Errors for the 18 mirrors
Table 1 show that results are quite reasonable for such a
system with the available experimental settings and
equipment. The left side mirrors show much lower errors
than the right ones. It is also clear that the results could
th
have been much better if the 9 mirror on the right was in
proper condition. Without this mirror the average would
have been 5 milli radians.
CONCLUSIONS
Fig. 4 Misalignment of mirrors
A summary of the results for the vertical position of the
device is presented in the following table:
The absorber reflection method has proved to be
a very effective and simple tool to assess the slope map of
the concentrator system. The method was originally
applied to parabolic trough concentrators. This work has
proved the validity of it with linear reflector systems too.
Results can be improved by accurate and precise setups,
precisely positioning the camera along the normal to the
concentrator, and using professional image analysis
software that also solves issues like perspective.
Nevertheless, the results have to be justified by comparing
it to the well established techniques of close-range
photogrammetry or VSHOT. The ARM method is useful in
determining the slope errors with the change of the angle
of the concentrator device, find the misalignments of the
mirror strips, and to improve both the device’s optical
components and structure.
175
4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen
The knowledge of the optical quality of mirrors is crucial in
further research concerning the power output of the
concentrator system.
[9] F. Arqueros, A. Jiménez a, A. Valverde. “A novel
procedure for the optical characterization of solar
concentrators”. Solar Energy 2003.75, pp.135-142.
ACKNOWLEDGMENTS
The authors would like to mention that this work is
made under the patronage of the Marie Curie Early Stage
Research Training Network. This paper is one of the
outcomes of the “SolNet” advanced solar heating and
cooling for buildings program which is the first coordinated
international PhD education program on solar thermal
engineering.
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