concentrating optics for photovoltaic triple … · unlike simple solar cells, solar photovoltaic...
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CONCENTRATING OPTICS FOR PHOTOVOLTAIC TRIPLE JUNCTION CELLS
by
Guillaume Butel
_____________________
A Thesis Submitted to the Faculty of the
DEPARTMENT OF OPTICAL SCIENCES
In Partial Fulfillment of the Requirements
For the Degree of
MASTER OF SCIENCES
In the Graduate College
THE UNIVERSITY OF ARIZONA
2009
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STATEMENT BY AUTHOR
This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.
Brief quotations from this thesis are allowable without special permission,
provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.
SIGNED: Guillaume Butel
APPROVAL BY THESIS DIRECTOR
This thesis has been approved on the date shown below: December, 16 2009 Dr. Roger Angel Date Professor of Astronomy
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ACKNOWLEDGEMENT I would like to thank my advisor Dr. Roger Angel for the support he gave me, the time he spent with me and the opportunity he gave me by working with him on this innovative project. I would also like to thank Tom Connors, Suresh Shivanandam and Matt Rademacher who helped me to design and set up all the experiment I realized. Tom does to 3D layout and gives me what I need to implement it into ASAP. Suresh does the electrical treatment (I-V curve) during the on-sun experiments. Matt particularly helped me setting up the on-sun experiment. I would like to thank Dr. James Burge and his PhD student Dae Wook Kim for their help in running the software ASAP; Dr. Charles Falco for his advice to solve my thin films issues. I would finally like to thank all my friends for the support they gave me during this year and a half, especially Mala Mateen, Eduardo Bendek and Stefano Young.
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Solemque suum, sua sidera norunt
Vergil, Aeneid VI, 641
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TABLE OF CONTENTS
LIST OF TABLES.........................................................................................................6 LIST OF FIGURES .......................................................................................................7 ABSTRACT...................................................................................................................9 INTRODUCTION .......................................................................................................10 CHAPTER I – DESIGN OF SOLAR ENERGY COLLECTORS USING PHOTOVOLTAIC AND THERMAL CONCENTRATION......................................12
1. Concentrating Photovoltaic (CPV) Technology ..................................................12 2. Concentrating Solar Power Technologies (CSP) with thermal conversion .........13
2.1 Trough Technology........................................................................................14 2.2 Linear Fresnel Reflector (LFR) .....................................................................14 2.3 Dish Stirling Engine.......................................................................................15 2.4 Power Tower..................................................................................................16
CHAPTER II – OPTIMIZATION OF SECONDARY CONCENTRATORS FOR RE-IMAGING CONCENTRATORS ................................................................................17
1. Core principle.......................................................................................................17 2. Imaging system description .................................................................................18 3. Different designs description ...............................................................................22 4. Solar Design – Version 1 .....................................................................................24 5. Solar Design – Version 2 .....................................................................................28 6. Solar Design – Version 3 .....................................................................................32 7. Solar Design – Version 4 .....................................................................................36 8. Solar Design – Version 5 .....................................................................................42
8.1 Initial version, 24 cells...................................................................................42 8.2 Current version, 27 cells ................................................................................44
CHAPTER III – ASAP MODELING..........................................................................49 1. Focal optimization process ..................................................................................49 2. Ray counting and statistics...................................................................................51
CHAPTER IV – END-TO-END TEST ON SUN .......................................................55 1. Purpose of the experiment ...................................................................................55 2. Description of the experiment..............................................................................56 3. Data collected and results ....................................................................................58
CHAPTER V – OPTIMIZATION OF THE PRIMARY REFLECTOR COATING..61 CONCLUSION............................................................................................................65 APPENDIX D..............................................................................................................66
APPENDIX D.2.1....................................................................................................66 APPENDIX D.2.2....................................................................................................67 APPENDIX D.2.3....................................................................................................68 APPENDIX D.3.......................................................................................................73 APPENDIX D.3.1....................................................................................................74 APPENDIX D.3.2....................................................................................................76 APPENDIX D.4.2....................................................................................................77 APPENDIX D.4.3....................................................................................................78
REFERENCES ............................................................................................................79
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LIST OF TABLES Table 2.1 – Designs overview…………………………..............................................23 Table 2.2 – Version 4 Reflectors and cells size overview……………………………37 Table 3.1 – Modeling integrating sphere rays………………………………………..53 Table 4.1 – Density calculation…………………………………………………........57 Table 4.2 – Experiment data collected……………………………………………….59 Table 5.1 – Initial number of photons………………………………………………..63 Table 5.2 – Thin film description…………………………………………………….64 Table 5.3 – Optimized photons calculations…………………………………………64
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LIST OF FIGURES Figure 1.1 – CPV Systems using dense arrays of cells (Solar Systems Inc in Australia)……………………………………………………………………………..13 Figure 1.2 – CSP Trough Technology…………………………………………….....14 Figure 1.3 – CSP LFR……………………………………………………………......14 Figure 1.4 – Dish Stirling Engine…………………………………………………….15 Figure 1.5 – PS-10 aerial view in Spain……………………………………………...16 Figure 2.1 – The whole system (left) with a zoom on the sphere (right)…………….17 Figure 2.2 – Principle 3D view, on-axis (left) and off-axis (right)………………......18 Figure 2.3 – Optical system diagram………………………………………………...19 Figure 2.4 – Imaging system description secondary reflectors layout……………….20 Figure 2.5 – Imaging system two kinds of performances……………………………20 Figure 2.6 – Filling pupil comparison……………………………………………......21 Figure 2.7 – Version 1 Zoom on a reflector………………………………………….24 Figure 2.8 – Version 1 Reflectors 3D view…………………………………………..24 Figure 2.9 – Version 1 Top view of the effective primary pupil and concentration....25 Figure 2.10 – Version 1 Cells output………………………………………………...26 Figure 2.11 – Version 1 Total power as a function of depth and angle……………...26 Figure 2.12 – Version 2 Ray paths at the focus for on and off-axis rays…………….28 Figure 2.13 – Version 2 Top view of the effective primary pupil and concentration..29 Figure 2.14 – Version 2 On-axis performance……………………………………….29 Figure 2.15 – Version 2 Horizontal off-axis performances…………………………..30 Figure 2.16 – Version 2 Diagonal off-axis performances……………………………31 Figure 2.17 – Version 3 3D view…………………………………………………….32 Figure 2.18 – Version 3 Top view of the effective primary pupil and concentration..33 Figure 2.19 – Version 3 On-axis performance with circular pupil, with (left) and without obscuration (right)…………………………………………………………...33 Figure 2.20 – Version 3 On-axis with square pupil without obscuration…………….34 Figure 2.21 – Version 3 Off-axis optical and electrical comparison…………………35 Figure 2.22 – Version 4 3D view of the output grid………………………………....36 Figure 2.23 – Version 4 Top view of the effective primary pupil……………………37 Figure 2.24 – Version 4 Ray pattern experiment description………………………...38 Figure 2.25 – Version 4 Top view of secondary reflectors of increasing depth and concentration………………………………………………………………………....38 Figure 2.26 – Version 4 Square and Twisted uniformity plot………………………..39 Figure 2.27 – Version 4 Square and twisted reflectors pattern at sweet spot………...40 Figure 2.28 – Version 4 Off-axis square uniformity plot…………………………….40 Figure 2.29 – Version 5 Reflectors 3D view…………………………………………42 Figure 2.30 – Version 5 On-axis performance……………………………………….43 Figure 2.31 – Version 5 Off-axis performances……………………………………...44 Figure 2.32 – Version 5 Final reflectors 3D top view………………………………..45 Figure 2.33 – Version 5 Top view of the effective primary pupil and concentration..45 Figure 2.34 – Version 5 Final performances…………………………………………46 Figure 2.35 – Version 5 Final reflectors back side…………………………………...47 Figure 2.36 – Version 5 Final faceted performances………………………………...47 Figure 3.1 – ASAP code diagram…………………………………………………….49 Figure 3.2 – Depth comparison, 1611 mm focal…………………………………......50
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LIST OF FIGURES – Continued Figure 3.3 – Depth comparison, 1800 mm focal……………………………………..50 Figure 3.4 – Modeling 3D view……………………………………………………...51 Figure 3.5 – Modeling number of rays……………………………………………….52 Figure 3.6 – Modeling final result……………………………………………………53 Figure 3.7 – ASAP modeling rays escape…………………………………………....54 Figure 4.1 – Version 5 Reflectors 3D view…………………………………………..55 Figure 4.2 – Experiment on-scale figure…………………………………………......56 Figure 4.3 – Experiment scheme…………………………………………………......57 Figure 4.4 – Net power plot………………………………………………………….59 Figure 4.5 – I-V curve of the cell…………………………………………………….59 Figure 5.1 – Sun spectral irradiance………………………………………………….61 Figure 5.2 – Triple junction cell spectral response…………………………………..62 Figure 5.3 – Optimization 3D plot…………………………………………………...63 Figure 5.4 – Reflectance spectrum comparison……………………………………...64
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ABSTRACT We need to create a sustainable source of energy at low-cost. Triple-junction
photovoltaic cells have shown much promise at 1000x concentration. This paper
describes improvements to an optical system for high enhanced concentration of
sunlight onto photovoltaic cells. For each critical element, primary paraboloidal
reflector, silica ball lens, secondary reflectors and triple junction cells, the goals were
twofold. First, to find the best focal ratio, the best illumination ratio, and the best
layout of the secondary reflectors, this was done using ASAP. Second, to improve the
optical throughput by optimizing the surface coatings, Macleod software was used.
On-sun tests showed that a complete end-to-end system with a single 15 mm square
triple junction cell can reach 27 % efficiency and deliver 58 W at 1000x concentration.
A new 27-cell-design is presented that is predicted to produce 2 kW for a 3.1 m
primary reflector.
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INTRODUCTION Sun-rich locations like Nevada or Spain are harvesting more and more solar
energy every year. However, current solar concentration systems have some
drawbacks. For example, one-dimensional tracking systems using thermal
conversion are often too large for practical implementation in highly-inhabited
countries like Japan and consume water. We need higher efficiency concentrators
with two-dimensional tracking which are easy to upgrade as photovoltaic cell
technology progresses. In this paper, we present a new solar concentrator design
which could help solar energy providers to meet international energy goals by
offering smaller size, lower cost, and higher efficiency.
Triple-junction photovoltaic cells which have shown much promise for two main
reasons: their conversion efficiency can reach up to 40 % at 1000x concentration,
and their low cost ($0.16 per watt at 1000x) makes them one of the best solutions
for harnessing the sun’s energy.
This paper is divided in five chapters where the improvements to the first version
of this system are developed up to the end of 2009. In the first chapter, the
different methods for obtaining electricity from sunlight are summarized as a
point of reference. The second chapter presents in detail five different designs for
concentration PV that are logically chained, where the performances of the global
system and the optimization process are described. The third chapter deals with
the modeling technique with the software ASAP to be able to simulate as
accurately as possible the system which is going to be built in the real world. The
fourth chapter presents the results of an on-sun experiment, made with a triple
junction cell which was shown to run at 27 % efficiency for the whole system.
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The fifth chapter describes the beginning of a project that consists in increasing as
much as possible the reflectance of all the critical interfaces of the system that the
sunlight meets on its path from the atmosphere to the photovoltaic cell. In this
final chapter, I illustrate the improved reflectance of the primary mirror.
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CHAPTER I – DESIGN OF SOLAR ENERGY COLLECTORS USING PHOTOVOLTAIC AND THERMAL CONCENTRATION
Unlike simple solar cells, solar photovoltaic concentrators require at least two kinds
of technology: high efficiency photovoltaic cells and optical concentrating technology.
Simple cells, like those you can find on roofs, are organized in flat panels and collect
light falling directly onto them. Since the panel cannot move, the flux is constantly
varying, according to a cosine law, during the day as the sun moves. Humans
generally require constant energy throughout the day, so the sinusoidally-varying
energy provided by simple photovoltaic panels does not optimally fulfill our energy
needs.
We could make solar panels that track the sun during the day but another issue with
panels is that the cells cost a lot. Therefore the cells used for panels must be cheap and
efficient in order to reduce the costs.
Concentrating solar energy systems allow us to use either thermal conversion or PV
systems with a reduced number of cells (and the costs) in PV systems. High efficiency
PV cells (30-40%) in concentrating systems can reach high electrical conversion.
Several projects have already been developed following these ideas.
1. Concentrating Photovoltaic (CPV) Technology
The use of III-V semiconductors has enhanced the efficiency of photovoltaic cells.
Silicon has a practical maximum of 20 % efficiency whereas current multi-junction
cells in concentrated light can reach 40 % efficiency.
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There are two main types of concentrators: reflective optics (mainly mirrors) and
refractive optics (glass or plastic structures). The reflective family can be divided into
two categories: one that uses a dense array of cells and one that uses separated solar
cells. Solar Systems Inc in Australia has developed a dense array design (Figure 1.1).
Figure 1.1 – CPV Systems using dense arrays of cells (Solar Systems in Australia)
Some specific features, like an active cooling system are needed for a dense array of
cells. One of the challenges for these systems is making the collected power uniform.
If we consider 25 cells in a square array, the concentration of light has to be adjusted
to be the same for all of the cells because the output current for cells mounted in
series will be limited by the cell that receives the lowest irradiance.
The solar panels developed by Solfocus or Amonix are examples of spread out
technology. Spread out panels have thousands of lenses on their surface in order to
concentrate the light onto individuals cells. The system can produce, depending on the
size, from several kW to a few MW.
2. Concentrating Solar Power Technologies (CSP) with thermal conversion CSP technologies are subdivided in 4 categories: trough technology, linear Fresnel
Reflector technology, Stirling Engine technology and Power Tower technology.
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2.1 Trough Technology This technology consists in heating a pipe of synthetic oil in order to convert water
into vapor that can then move a turbine. The optical component is a parabolic trough
mirror that can only track the sun in one dimension. As a result, the temperature
achieved in the tube is limited, driving down the overall efficiency. However this
technology is mature and has been used since 1980. The total installed power for a
trough system is 350 MW.
Figure 1.2 – CSP Trough Technology
2.2 Linear Fresnel Reflector (LFR) The Linear Fresnel Reflector is a modification of the Trough technology (Figure 1.3).
In the LFR, the tubes are fixed in motion but the mirrors still move to concentrate
light on the oil to heat it and create steam. The efficiency is still low, mostly because
the tracking is still one-dimensional.
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Figure 1.3 – CSP LFR
The main drawback of these two last technologies is the 1D tracking which leads to
low concentration and low thermal conversion efficeincy. This is solved in the third
system.
2.3 Dish Stirling Engine
This technology uses a 2D tracking system in order to track the sun efficiently. The
rays hit a giant dish, made with 82 mirrors that make the light focus on a Stirling
Engine that creates electricity. Each dish produces 10 to 25 kW. It is used at two
locations in California, producing 1.75 MW.
Figure 1.4 – Dish Stirling Engine
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2.4 Power Tower
This technology uses direct steam generation. It was demonstrated in the 80’s (Solar
One) and the 90’s (Solar Two) and more recently in 2005 in Spain with the PS-10
project. This technology uses dual tracking mirrors (heliostats) that concentrate the
light onto a single central receiver located at the top of the tower, as shown in Figure
1.5.
Figure 1.5 – PS-10 aerial view in Spain
The Power tower technology is now used at a smaller scale in California with the
eSolar project. The mirrors are 1/100th the size of those used in Spain where they are
120 m2. One eSolar module is composed by 12,000 mirrors divided into a north and a
south field. Each module can produce 2.5 MW. [1]
So the high concentration systems have various designs. Dr Angel’s design is a CPV
system in which the light first hits a 10 m2 silvered dish and then is directed by
multiple secondary reflectors which concentrate the light on many high-efficiency
cells. But this new design has a lot of innovative devices that we are going to show in
the second part.
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CHAPTER II – OPTIMIZATION OF SECONDARY CONCENTRATORS FOR RE-IMAGING CONCENTRATORS
1. Core principle
The core principle of this design is to focus a large amount of light by a single
reflector at a reasonable cost and distribute all this light in an array of secondary
reflectors, which will relay the concentrated light on triple junction cells. The sunlight
first hits a large back-silvered paraboloidal mirror, the primary reflector, which
focuses the light efficiently. At this focal point, the light has been concentrated once
at around 40000x. The concentrated light passes through a window into a small sealed
chamber containing many cells. Optics in the receiver are used to apportion the
incoming light evenly among many cells. This is done in two steps.
Figure 2.1 – The whole system (left) with a zoom on the sphere (right)
First, the window is made in the form of a ball lens, which maps out the light from the
intense focus within the lens into a small concave image of the primary reflector. At
this image, which is 6" square, the light is concentrated about 400x and is stabilized
against mispointing of the dish, caused by tracking errors. In the second step, the
image is divided by secondary reflectors into areas of equal power, and the light in
each area is relayed to one triple-junction cell. The relays increase the concentration
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to 1000x while preserving good uniformity of cell illumination. A powerful feature of
the optical system is that all the light is directed toward the active areas of one cell or
another. None is wasted on the light-insensitive cell edges or beyond. The following
plot clearly shows that all the rays gather at the same points on the array of
reflectors.[2]
Figure 2.2 – Principle 3D view, on-axis (left) and off-axis (right)
2. Imaging system description
This system has to achieve a very high concentration of light on the triple junction
cells. Indeed these cells require having this concentration, i.e. 1000 sun, to work at
their full power conversion efficiency (33 % - 39 % of quantum efficiency) and lower
cost per watt. To reach this performance, two concentrators are put in series and raise
the concentration from 1 to 1000 as shown in the following.
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Figure 2.3 – Optical system diagram
According to the Figure 2.2, all the rays are distributed into the secondary reflectors
and then onto the cell active area. The only optical losses of the system are due to the
interfaces of the reflecting (primary and secondary) and transmitting elements (ball
lens) and to gaps between the secondary reflectors. A first calculation of the optical
global efficiency can be made by taking 94 % for the reflectance of the two reflecting
surfaces and 92 % transmission for the ball lens, giving a total of 81.3 %. This
number is used in all the simulations to be able to compare them. To compute the
electrical power we have to multiply by the quantum efficiency of the cell: 33 % is the
number considered in the simulations. As a result the global efficiency is 27 %. The
main concept for the optical design is how to fill the pupil on the primary mirror. This
means how many cells and how to position them in order to best fit the square pupil.
Two kinds of layout for the secondary reflectors have been used as shown in the
figure below.
Sunlight
Primary mirror
Ball lens
Reflector
Escape
Hit the cell
Concentration = 1
Concentration ~ 40000 (at the focal point)
Concentration ~ 400
Concentration ~ 1000
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Figure 2.4 – Imaging system description secondary reflectors layout
The ring layout (left) is used with reflectors that are all similar size. Since the
concentration is increasing as the polar angle grows, each ring of increasing radius
yields more current (Appendix D.2.1 for detailed explanation), with all the reflectors
in one ring receive the same irradiance. Each ring can therefore be wired in series to
keep the same current along the cells of the ring. The square layout (right) is used
with varying in size reflectors so that the increase in concentration is compensated in
order to wire all the cells in series. The figure below shows the two different
performances we can obtain from the two kinds of layout.
Figure 2.5 – Imaging system two kinds of performances
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The main concept for each of the different versions is how to best fill the pupil on the
primary mirror. This means two things. First we want the largest amount of flux so
the more rays coming onto the cells the better. Second the concentration should be
adjusted to be able to wire the cells in series. As explained earlier, two kinds of
secondary array can be used to fill the square pupil: rings or squares. The number of
cells, their active area and the area of the pupil determine the geometric concentration
of the system, as indicated:
=
cell
pupil
pupil
cell
A
A
n
nConcGeo .. , A being the area and n the number of rays
The following figure shows how the filling of the pupil entrance evolved with the
different designs.
Figure 2.6 – Filling pupil comparison
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We want to have as many rays as possible globally, to increase the concentration but
those rays have to be well distributed between the cells. If the cells are wired in rings,
the area of the cells has to be adjusted to catch a number of rays that will give the
desired concentration. The concentration evolution can be seen in the Table 2.1 and in
the different tables that describe the designs in the next subsections.
3. Different designs description
The different designs are going to be exposed in the remainder of this chapter as well
as the optimization processes that have been implemented as the project was going
along.
The first design is a discovering of how the system is working and also the occasion
to learn how ASAP works and how it can be useful for our purposes. Between the
first and second design, the depth of the reflectors was optimized, going from 15 mm
to 20 mm but with equal area reflectors.
The second design is used to make the focal length vary from a slow system (1800
mm) to a faster one (1711 mm). The off-axis responses were explored in this design
as well, with again equal area reflectors.
Then the third design was meant to run experiment on the existing 1500 mm focal
length dish behind Bear Down Gym, located on the University of Arizona Campus. It
adds new constraints, on the focal length, and also adds a central obscuration to the
primary that allows three kinds of simulations with three pupils, but keeps the equal
area reflectors.
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The fourth design is the best we can make because we are using more cells which are
laid out on a curved square. This particularity is actually the best way to image the
square pupil of the primary. Another particularity is the fact that we introduced
twisted reflectors with non-square entrances to fit curved surface leading to square
output for the cell. Therefore new simulations were run to analyze those new kinds of
reflectors that use smaller cells (different area but same power). However we were not
able yet to test it on sun and this is the reason why we moved to the fifth version.
In the current 5th version that we have not fully optimized yet, we use a larger focal
length to be less sensitive to the off-axis deviation. This design uses trapezoidal
entrance apertures and strongly twisted reflectors of different area and equal power.
Their performance has been tested on-sun. The latest tested version is designed to
produce 2 kW with a 27 % overall efficiency.
The design progression is detailed in the next 5 subsections. However to grasp the
main concept you can go directly to version 4.
Here is a quick overview of the 5 designs with their main characteristics:
Primary
focal (mm) Number of cells
Power per cell
(W)
Ave. Geometric
concentration
Filling factor (%)
Design1 – Original design 1800 50 30, 35,
40 628 78.6
Design2 – Faster and optimized
1711 50 30, 35,
43 624 78
Design3 – Bear Down constraints
1537 50 30, 36,
43 619 76.6
Design4 – Current, untested, twisted
1711 80 - - -
Design5 – Current, tested, twisted 2000 26 70, 75 1259 78.4
Table 2.1 – Designs overview
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4. Solar Design – Version 1
This system has a ring-based layout as described below.
• Primary Mirror: Paraboloid, focal length 1800 mm.
• Square Pupil: 3000 mm x 3000 mm.
• Silica Sphere: Radius 75 mm. The sphere is centered at the focal point of the
parabola (i.e. z = 1800 mm).
• Distance Focus point – entrance of secondary reflectors: 117.7 mm
• Secondary reflectors: 23 mm (entrance) x 20 mm (depth) x 15 mm (cell)
Figure 2.7 – Version 1 Zoom on a reflector
The Figure 2.8 shows a close view of the secondary reflectors design:
Figure 2.8 – Version 1 Reflectors 3D view
Each ring has a specific number of reflectors in order to leave as few gaps as possible.
The fourth ring is special in the sense that it has only 8 reflectors placed 2 by 2 in the
20mm
23mm
15mm
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4 quarters of the XY plane. In the end the third and fourth ring are wired together
because we optimized them to produce the same power, by adjusting the polar angle
and the entrance aperture area. If you project the image of the rays coming onto the
cells on a plane surface, i.e. if you reverse the optical path of the rays to only consider
the rays coming onto the cells, you end up with the following spot diagram. It
represents the filling of the pupil, so only appear here the rays that made their way to
the cell. The filling factor, i.e. the geometric efficiency, of the system is in this case
78.6 %. It means that 78.6 % of the incoming rays reach a cell.
Figure 2.9 – Version 1 Top view of the effective primary pupil and concentration
As expected the size of each reflector is the same in one ring but increases as you go
off-axis. The geometric concentration increases with the polar angle as shown in the
above table. And therefore each ring is going to produce a different amount of power,
increasing with the angle. This result can be seen on the Figure 2.10 on the next page.
Concentration Ring 1 521.5 Ring 2 596 Ring 3 674.4 Ring 4 678.4
Average 628.6
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Figure 2.10 – Version 1 Cells output
The system end up with three rings of cells, connected in series, so that the power for
each ring is the one of the lowest power in the ring.
Before coming to this first result, we ran various simulations, trying to optimize the
depth of the reflectors, as it can be seen on the following plot. This plot shows 2
phenomena: the flux decrease with the angle of deviation and the flux increase with
the depth of the reflectors.
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 0.5 1 1.5 2 Theta
W
h=10
h=12
h=15
Figure 2.11 – Version 1 Total power as a function of depth and angle
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We can see how the depth of the reflectors (Z) influences the received flux. The plot
shows the total flux as a function of the off-axis angle for 3 different depths.
We came to the conclusions that the more depth the better for two reasons. First we
have more flux and second we have more space behind the cells to install all the wires,
the cooling system.
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5. Solar Design – Version 2
At this point we performed focal length optimization. The optimization process is
detailed in Chapter III.1.
In this new design, we wanted to have a faster system, which allowed us to have a
smaller total size and weight. We thus had to change the polar angles for the receiving
surface.
• Primary Mirror: Paraboloid, focal length 1711 mm.
• Square Pupil: 3000 mm x 3000 mm.
• Silica Sphere: Radius 75 mm. The sphere is centered at the focal point of the
parabola (i.e. z = 1800 mm).
• Distance Focus point – entrance of secondary reflectors: 117.7 mm
• Secondary reflectors: 23 mm (entrance) x 20 mm (depth) x 15 mm (cell)
The new system is illustrated by the following schemes:
Figure 2.12 – Version 2 Ray paths at the focus for on and off-axis rays
The geometric concentrations for the rings are slightly different from the version 1 but
the general shape is the same as shown below.
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Figure 2.13 – Version 2 Top view of the effective primary pupil and concentration
The filling factor is in this case 78 %, a bit lower than the first version.
On axis simulation
Figure 2.14 – Version 2 On-axis performance
With this new focal length, we really have a good system; this time the four rings are
distinct and can be wired out in series with four different powers.
Concentration Ring 1 521.5 Ring 2 572.5 Ring 3 658.8 Ring 4 729.3
Average 623.9
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Off axis simulations
The off-axis simulations performed were of two kinds: one kind was with the
deviation angle being vertical and the other with this angle being diagonal. They were
both done at 0.75 degree and 1 degree. This is meant to simulate the possible
deviations that may occur under some windy conditions. The diagonal (45 degree)
hurts the most. Even at 0.75 degree (blue bars), the flux stays at the same level that we
have for the on axis case. At 1 degree, the loss is not tolerable.
Figure 2.15 – Version 2 Horizontal off-axis performances
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Figure 2.16 – Version 2 Diagonal off-axis performances
The irradiance maps are in appendix D.2.2 and give a vision of how looks the
uniformity on the cells. Uniformity is something to be taken care of because it is wise
to avoid hot spots on the cells to avoid them to burn.
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6. Solar Design – Version 3
We wanted to use the previous design in the current dish that we have behind Bear
Down Gym, on campus. So we had to adapt to the constraints of this primary mirror.
The mirror has the following characteristics:
• A paraboloidal mirror of 1537 mm focal, 3.015 m of outside diameter, 1.46 m
of inside diameter limited by a circular pupil of diameter 3.015 m. So this
mirror has an obscuration ratio. Then we had to scale again all the other
devices.
• A silica sphere located at the focus of the mirror, 64.27 mm radius.
• 50 identical reflectors. They have an entrance square aperture of 23.3 mm x
23.3 mm. This surface is on a sphere of radius 100.85 mm. The center of this
sphere is the center of the silica sphere (i.e. the focal point of the parabola).
Then each reflector has a depth of 20 mm. Finally the exit surface is 15 mm x
15 mm and we assume that this surface is the photovoltaic cell. Thus the exit
surface is lying on a sphere of radius 120.85 mm, centered at the focus.
The system is illustrated by the scheme below.
Figure 2.17 – Version 3 3D view
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Figure 2.18 – Version 3 Top view of the effective primary pupil and concentration
The filling factor is in this case 76.6 %, a bit lower than the previous systems.
On axis simulations
For the on-axis simulations, we have two cases, with or without an obscuration hole in
the center. These are the optical performances:
Figure 2.19 – Version 3 On-axis performance with circular pupil, with (left) and without obscuration
(right) For now the current mirrors have an obscuration and a circular pupil. So this means
that we are in the obscuration case. To be in the case where all the four rings will be
illuminated, we need to add new panels to the existing mirror in the middle (to fill the
Concentration Ring 1 514.9 Ring 2 518.8 Ring 3 689.1 Ring 4 724.8
Average 619.3
34
obscuration hole) and in the four corners to create a square. Then we could reach this
result illustrated by the Figure 2.20 below.
Figure 2.20 – Version 3 On-axis with square pupil without obscuration
Off axis simulations
The off axis is held vertically at 3 different angles (0.5, 0.75 and 1 degree).
Here is a plot to compile all the results. All the different plots can be found in
appendix D.2.3. We compare how many rays are coming onto the cells versus how
much power is actually produced by the system, taking into account that the rings are
in series. So the cell with the least power in each ring gives the final power for the
whole ring.
35
Optical vs electrical performance comparison as a function of the off axis angle
1250
1350
1450
1550
1650
1750
1850
1950
2050
0 degree 0.5 degree 0.75 degree 1 degree
Angle
Po
wer
(W
)
Obscuration
No Obscuration
Square Pupil
Obscuration Electrical
No Obscuration Electrical
Square Pupil Electrical
Figure 2.21 – Version 3 Off-axis optical and electrical comparison
36
7. Solar Design – Version 4
The 3 first designs have now been abandoned but were very useful to define very
important parameters like the ratio between the focal and the entrance aperture radius;
or the ratio of the entrance aperture area with the cell area.
But in order to put further the imaging feature of the system, this design images a
regular square input grid at the entrance pupil onto a concave output square grid,
whereas before it was a ring output design.
Figure 2.22 – Version 4 3D view of the output grid
This design has a 4-fold symmetry so we can describe it only in the first quarter and
we end up with 14 different kinds of cells as explained in the Table 2.2.
Kind Number Depth (mm) Aperture angle (deg) Cell size (mm)
0 0 15.19 11.53 11.51 1 4 15.07 11.42 11.38 2 4 14.96 11.3 11.25 3 4 14.73 11.08 11 4 8 14.62 10.98 10.88 5 4 14.29 10.67 10.54 6 4 14.19 10.57 10.43 7 8 14.09 10.47 10.32
37
8 8 13.79 10.19 10.01 9 4 13.31 9.75 9.53
10 4 13.5 9.92 9.71 11 8 13.4 9.84 9.62 12 8 13.13 9.59 9.35 13 8 12.7 9.2 8.93 14 4 12.14 8.71 8.39
Pupil: square, 3.1 m wide Parabola dish focal: 1711.3 mm Silica Ball Diameter: 117.92 mm Radius of receiving surface from center of the ball: 91.15 mm
Table 2.2 – Version 4 Reflectors and cells size overview As shown in the above table, the cell area decreases with their distance from the
center. This was allowed for having the same power produced by each cell. Indeed the
sun irradiance increases with the angle because the irradiance is proportional to the
square of ratio of the radii as shown in appendix D.2.1. The distribution of the rays in
the cell is perfect due to the square layout and the pupil filling factor is 97.8 %. The
concentration is the same everywhere.
Figure 2.23 – Version 4 Top view of the effective primary pupil
Moreover, the imaged entrance pupil squares are no longer squares at the output.
However, the cells are still square so the reflectors are going to be twisted. So we
wanted to know how these new reflectors are behaving. Therefore we ran simulations
on single twisted reflectors to see what the limitations were for such a design. We
38
wanted to know the differences between a square cell and a twisted cell in terms of
flux received and how the twisted sides were influencing the final flux. We want to
have the maximum flux and a good uniformity on the cell.
One simulation consists in sending light from a point source to simulate the light
coming from the focus point. We only did on-axis simulations for that test. Thanks to
ASAP we were able to compute the statistics for the ray plots. We then built a
function showing how was evolving the normalized variance, E
σ, on the cell, in order
to compare the uniformity of the irradiance maps. The parameter we were using was
the relative concentration. A relative concentration of 1 is achieved when the cell
surface is the same as the entrance surface. A relative concentration of 2 is a cell area
twice smaller than the entrance area. The following plot shows how the experiment
was run, as we increased the depth (and the concentration) to see how the ray pattern
was evolving.
Figure 2.24 – Version 4 Ray pattern experiment description
The ray plots obtained for square reflectors of increasing depth but same slope angle
are illustrated in the Figure 2.25.
39
Figure 2.25 – Version 4 Top view of secondary reflectors of increasing depth and concentration
The evolution of the pattern is very interesting because this is really how the light is
hitting the cell after having hit, or not, the reflectors. In the second case, the direct
illumination becomes smaller and we begin to see the rays that bounced once or twice
on the sides. Then the relative ratio evolve as shown going from bright to dark cross
with the sweet spot in between, where the uniformity is maximum and the variance
minimum.
If now we plot the normalized variance E
σ as a function of the concentration. All the
variances were corrected with respect to the first one which was set to be 0 for a
concentration of 1.
0.000
0.439
0.308
0.113
0.233
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
1 1.5 2 2.5 3 3.5
Concentration
Co
rrec
ted
sig
ma
/ E
Square
Twisted
Figure 2.26 – Version 4 Square and Twisted uniformity plot
We can now clearly see that the ‘sweet spot’ is at the same concentration for both the
twisted and square case. This case is illustrated on figure 2.27.
40
Figure 2.27 – Version 4 Square and twisted reflectors pattern at sweet spot
We also did simulations off-axis, but this time only for the square reflectors. The
following plot shows how the uniformity evolves with the angle. The corrected curve
is the one for the on-axis case.
0.387
0.181
0.230
0.314
0.289
0.268
0.241
0.413
0.203
0.302
0.406
0.432
0.000
0.119
0.233
0.125
0.159
0.147
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
1.0000 1.5000 2.0000 2.5000 3.0000 3.5000
ConcentrationConcentrationConcentrationConcentration
σ /
<E>
σ /
<E>
σ /
<E>
σ /
<E>
Corr σ / <E>
Simu On axis
Simu 0.5 Off
Simu 1 Off
Figure 2.28 – Version 4 Off-axis square uniformity plot
The ideal concentration is, according to these plots, 2.57. Which means in term of side
dimensions a ratio of 6.157.2 = . So if we have a 15x15 mm2 chip, we should have
an entrance aperture of 24x24 mm2.
We can also notice that the 0.5 degree off axis case obtains good result, which is
going to be useful in case of errors in tracking system, or random events like wind.
41
If we come back to the 80-cell-design, we therefore can make the assumption that the
twisted reflectors are not going to behave so badly. Unfortunately we have not been
able to perform simulations on this design yet. However, this is the ultimate design
that brings at the same time a large amount of flux and efficiency (absence of gaps
between cells) and, hopefully, a good off axis performance.
42
8. Solar Design – Version 5
This design is the one we are currently working on. We went through different sub-
version for it. Thus I am going to describe the first one and the latest one for both of
which we have results.
8.1 Initial version, 24 cells
We went from the version 3 to the version 5 for several reasons:
• Increase the concentration on the cells
• Leave fewer gaps between the cells
• Use fewer cells and collect more flux
This can be done by using twisted reflectors as the following design shows:
Figure 2.29 – Version 5 Reflectors 3D view
In this design all the reflectors have twisted sides because they have trapezoidal
entrances and a square output. They are organized in two rings in order to collect all
the light coming from the primary mirror. The inner ring has 9 reflectors and the outer
ring has 15. According to the studies in the previous paragraph, the twisted reflectors
have a worse behavior on axis than the regular square ones. In that study the twist was
43
soft but in this case, especially on the inner ring, the reflectors are strongly twisted.
We will see it in the performances later on.
The focal for the system is 1537 mm. We have a 50 mm radius ball. The entrance
aperture radius is 77.3 mm. This is much shorter than all the previous designs because
we are only using 2 rings of identical reflectors in order to enhance the concentration.
The cells are 15 mm square.
The on axis results are good, because they produce a good amount of flux and the two
rings have the same unit energy. The goal is to have each cell produce the same
amount of power so that they can be in series. This is theoretically achievable because
the irradiance is increasing with the polar angle so the entrance area should be smaller
as we go off axis. We ran simulations on and off axis to see the performances of this
new system.
Figure 2.30 – Version 5 On-axis performance
So the power of every cell is almost the same as expected by the calculations. Total
power is around 70*24 = 1680 W. Now if we look off axis, the result is a bit different.
44
Figure 2.31 – Version 5 Off-axis performances
We have two rings and we can see that the second ring is behaving quite well even at
0.75 degree although the maximum power decreased from 70 W to 68 W. However
the first ring has some issues and they come from the fact that the reflectors in the
first ring are strongly twisted. The drop even happens at 0.5 degree which is not good
because this angle is a deviation we should deal with, if we have wind outside.
We went through different modifications and optimization and we finally came up
with a new design which is explained in the following.
8.2 Current version, 27 cells
The first modification was to change the primary mirror in order to test the
configuration for the final version 4 design. So the focal is 2000 mm and the outer
diameter for the primary is 3.124 m. Then the silica sphere had to be rescaled to 65.06
mm radius and finally the entrance aperture radius is 100.59 mm.
45
In order to untwist a bit the inner ring reflectors, we decided to take out one and make
the rest more square. At the same time, we added four reflectors on the four corners,
so that we can use a square pupil on the primary mirror. We adjusted the area so that
they should receive the same irradiance. This gives the following design:
Figure 2.32 – Version 5 Final reflectors 3D top view
The geometric concentration has been enhanced to double from the previous versions
as shown below. The filling factor is 78.4 %.
Figure 2.33 – Version 5 Top view of the effective primary pupil and concentration
Here is a plot of the performances for the final update:
Concentration Inner ring 1250.1 Outer ring 1256.9 4-cell ring 1288.4
Average 1259.5
46
Figure 2.34 – Version 5 Final performances
The overall result does not seem to be so good but the main reason is that we went to
a bigger focal length. We went from 70 W to 75 W on axis, a 7% increase for every
cell, meaning we now have a total power of 27*75 = 2025 W. Compared to the initial
design, we gained 20% in power. The off-axis performance is acceptable at 0.5 degree.
Indeed the inner ring (8 cells), that we wanted to correct, does not have the dip any
more. Furthermore the mean between the 0.5 degree level and the on axis level is at
the level of the outer ring (15 cells). So in case of off-axis deviation, the power will
not drop too much. Only the external ring (4 cells) has a lower level in average than
the two others.
We also have another version for the design that takes into account the feasibility of
the reflectors. Indeed how can we make twisted reflectors? Do we have the
technology yet? The goal of this alternate version is to substitute the twisted back side
of the inner ring reflectors for a faceted back side.
47
Figure 2.35 – Version 5 Final reflectors back side
The performances of the faceted version, even though much easier to make if not the
only doable, are worse. Indeed it seems that more rays manage to bounce out of the
reflector than in the twisted case. We can see that in the performance plot, Figure 2.36.
Figure 2.36 – Version 5 Final faceted performances
We are losing around 2 W per cell in the inner and outer ring, and 3 W per cell in the
external ring. This is a 2.8 % loss out of the 2025 W.
But moreover the cells lose a lot of flux at 0.5 degree. This time it is another 3 W per
cell lost in the inner ring.
48
Even though the twisted rings are a satisfactory solution, the more feasible faceted
version is not. Thus we are going to move to another design to make it both feasible
and satisfactory as performances are concerned.
49
CHAPTER III – ASAP MODELING
ASAP was very useful to do the 3D modeling and the ray tracing. I will detail two
examples of analyses we could make with ASAP. The first one is the focal
optimization and the second is how to count and sort rays.
But first of all here is a diagram of how a typical code works in ASAP. In appendix
D.3, you can find a detail of the boxes.
Figure 3.1 – ASAP code diagram
1. Focal optimization process
If we go back to the second version of the design, for which we wanted to optimize
the focal and the reflectors depth, we had to run many simulations to see where the
best performance were according to these two parameters. Actually the depth of the
reflectors was quickly decided because the noticed that between 12 mm and 20 mm,
the only difference was in the collected flux as shown on the table 2.4 in the second
chapter. The focal range was between 1611 mm and 1800 mm so we tried the two
depths at those focal lengths to see the extreme parameters were behaving.
Parameters
Coatings / media
Geometry
Analysis
50
Figure 3.2 – Depth comparison, 1611 mm focal
Figure 3.3 – Depth comparison, 1800 mm focal
In Figures 3.2 and 3.3, the variations due to the change in focal and reflectors depth
are only in terms of flux. The general behavior is strictly the same amongst all the
cells, so we chose a 20 mm depth for the reflectors to have more flux.
Then if we make the comparison for the range of focal length described before, we
have very interesting results. Two focal lengths were particularly standing out: 1637
51
mm and 1711 mm. The plots are detailed in Appendix D.3.1. Those two focal lengths
are really stable off axis even at 0.75 degree but the 1711 mm was chosen because we
had more flux in total. The 1637 mm is even more stable at 0.75 degree than the 1711
mm but each cell, except the last 8, is down 3 W, for a grand total of 126 W less.
2. Ray counting and statistics
The ray counting was particularly effective when we had to count rays that were
reflected out of the twisted reflectors after multiple reflections (version 5). We saw
the difference of about 3 % between the faceted and the twisted version of the
reflectors in the previous chapter. We can explain this difference by the statistics we
can derive from ASAP for both on and 0.5 degree off axis.
For that reason, we are using an integrating sphere around the whole system to be able
to count all the rays.
Figure 3.4 – Modeling 3D view
52
The rays are counted on various criteria and we chose to use the number of hits that
they make. To travel from the source to the cell with no secondary reflection, a ray
makes 4 hits: first the primary, second and third the silica sphere and last the cell.
Then some rays that see reflector surfaces can hit once, twice or even three times the
reflector and we end up with 5, 6 and 7 hits.
We used 786,997 rays for a total input power of 7,139 W, which means 0.00907 W
per ray.
Figure 3.5 – Modeling number of rays
The number of rays of each hits category tells us the behavior of the cell.
The phenomenon is the same in both cases:
• Same number of direct rays (4 hits)
• More 5 and 7 hits for the faceted case
• Less 6 hits for the faceted case
But the difference is the total number of rays:
53
Cells Int Sphere On axis faceted 28938 92434 On axis twisted 29685 81255
Table 3.1 – Modeling integrating sphere rays
This is a difference of 11,179 rays, or 1.778 W per cell, assuming all the 15 cells
behave the same way and that we have 26.3 % efficiency (0.33 is the quantum
efficiency and 0.813 the optical efficiency).
When we compare it to the plot of the on axis case (twisted and faceted), we obtain:
Figure 3.6 – Modeling final result
This 1.78 W difference can therefore be explained by ASAP, when each ray is
analyzed carefully. ASAP can describe the rays statistically and the understanding of
how the rays are behaving is thus easier.
The rays that we are losing between twisted and faceted case are escaping the cells as
shown below.
54
Figure 3.7 – ASAP modeling rays escape
55
CHAPTER IV – END-TO-END TEST ON SUN
1. Purpose of the experiment
This on-sun experiment is meant to calculate the overall efficiency of a single twisted
cell. Indeed to calculate the real efficiency, we must calculate the parasitic losses due
to the mechanical power of the cooling system. Then from the power produce by the
cell and by subtracting the losses, we can have the real power. Calculating the
parasitic losses is important in itself because it enables us to find the prediction we
made: there is an optimum mechanical work that maximizes the cell power.
The cell is part of a larger system which is composed by the 24 cells organized in two
rings from the version 5 of the design. Because this is an imaging system, taking a
single cell out as an example is relevant and therefore can be used to prove general
results.
The two rings are meant to collect all the light coming from a parabolic dish. Then the
light passes through a silica sphere and is finally collected in the reflectors that
concentrate light onto the cells. There are two kinds of reflectors but they both have a
trapezoidal entrance surface as shown below.
Figure 4.1 – Version 5 Reflectors 3D view
56
In this experiment however, we only consider one single cell mounted on its reflector,
as shown below.
Figure 4.2 – Experiment on-scale figure
2. Description of the experiment
The experiment is run using the active cooling system with 30% anti freeze liquid
(glycol).
To reach this goal, we have to collect different sets of data. The first set is the
mechanical parameters, like the flow rate, the pressure of the fluid, the temperature of
the fluid. Then we need the electrical parameters for the cell, like the power out of it,
the open circuit voltage (used to calculate the temperature of the cell). Finally we
need the sun parameter, i.e. its irradiance, at the specific time of the experiment.
57
With these sets of data we calculate the mechanical work of the system and then the
net power. We can then compare it to the incoming power and deduce the efficiency.
Figure 4.3 – Experiment scheme
The sun shines light through the ball and onto the cell. The active cooling system
maintains the cell at a constant temperature. The fluid is pumped from the bucket and
goes behind the cell. Then it leaves the cell, goes back to the bucket and starts the
cycle again. This fluid is composed by 30% of glycol. The density has been calculated
from tables as below, assuming the liquid temperature is about 40 degree C.
Glycol density @ 40 celsius 1.0994 Water density @ 40 celsius 0.9922 30% Glycol @ 40 celsius 1.0244
Table 4.1 – Density calculation
The incoming flux has to be calculated separately. To do that we need the DNI values
for the sun irradiance at the moment we are doing the experiment. They were
measured on campus and we asked for them afterwards. The sun irradiance was 926
W.m-2 at that time of the day.
58
Then we have to know the real area of incoming light reflected onto the cell. The
computation was done with three different methods. The first one is a direct
computation by using the counter propagation of light from the cell to the mirror. We
are able to calculate the image area by the sphere (which acts as a lens) of the
entrance trapezoid of the reflector. The second is by measuring the mask on the mirror,
calculating the angle of incidence and projecting the area to obtain the right one. The
third one is just measuring the radius between the sphere and the mirror to obtain the
magnifying factor by another method. Then we use it squared to calculate the image
area of the entrance cell.
We came to the conclusion that the useful area of the incoming flux is 0.22 m2. The
three methods are exposed in Appendix D.4.2.
3. Data collected and results
We have made several experiments that lead to very encouraging results.
We wanted to prove that we have an optimum running point as the flow rate is
concerned. Indeed if the flow rate is too low, the cell is going to run hot and have
reduced output power (0.2 % / degree C) and too much power will be used in the
pump if the flow rate is too high.
So we collect the pressure of the liquid, the flow rate, the power delivered by the cell,
the temperature before and after the cell and the open circuit voltage of the cell. With
all this data we were able to compute the Net Power, given by: WP .4− where P is the
cell power and W the mechanical work of the pump. The factor 4 allows for
conversion of electrical energy to mechanical energy of the pump.
59
Table 4.2 – Experiment data collected
This table gives the essential numbers that were used to obtain the net power. For the
detailed numbers, please go to the appendix D.4.3. If we plot the net power as a
function of the mechanical power, we find an extremum that gives us the best
pressure of liquid we should use.
Figure 4.4 – Net power plot
We can obviously see the maximum point that we were looking for (a mechanical
power of 100 mW). So there is an optimal point where we have the most net power.
This occurs for a pressure of approximately 5000 Pa, and a flow rate of 20 cm3.s-1.
From that we have the net power from the cell equals to 55.6 W. The incoming power
is 203.72 W. This gives a net efficiency of 27 %.
Figure 4.5 – I-V curve of the cell
60
The variation of power produced by the cell with the coolant temperature was
measured. The cooling system is indeed here to avoid the cell to burn but also to
allow a better performance. On the above Figure, the I-V curves of the cell give the
output power versus coolant temperature. The output power is calculated by
multiplying the voltage and the current when they are both maximum.
61
CHAPTER V – OPTIMIZATION OF THE PRIMARY REFLECTOR COATING The reflectance of the primary mirror needs to be as high as possible. The mirror is
already coated with silver which gives good performances, but now can we boost it
even more?
The optical system involves reflection or transmission by three elements, the primary
reflector, the ball lens and the secondary reflector. In this chapter we show how the
reflectance of the back-silvered primary reflector may be boosted by thin film coating.
On a primary mirror used to make the light focused in the silica ball and then and
photovoltaic cells, we wanted to increase the reflectivity by adding thin films
dielectric coating between the silver and the glass. The idea was to add a low index
material (MgF2) and a high index material (TiO2) between the glass and the silver
coating of 150 nm.
To achieve this goal we had to take into account several parameters:
- The sun spectral irradiance
- The mirror reflectivity
- The cell quantum efficiency
The sun irradiance was given by the free software SMARTS.
Sun spectral irradiance (W/m^2/nm)
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
0.00 500.00 1000.00 1500.00 2000.00
Wavelength (nm)
Figure 5.1 – Sun spectral irradiance
62
By integrating the spectrum, we find an input power of 814 W.m-2.
The mirror reflectivity is given by the software made by the company Thin Film
Center, run by Dr. Angus Macleod. We are using his software to simulate our thin
films and coating.
The spectrum for the QE of the cell was given by the manufacturer, Spectrolab.
We designed a merit function to best optimize the thickness we needed for the coating.
It is defined as the cell works. The cell is a three junction cell, with this spectrum:
Figure 5.2 – Triple junction cell spectral response
In a triple junction cell the three junctions are deposited one above the other. The
blue spectrum is absorbed in the top layer, then the red, and the infrared in the bottom
germanium layer. The same photocurrent flows from top to bottom, the same in all
three junctions. For each band, we calculated the number of photons and then the
electrical power they were creating. The three bands are defined as: λ=[350;658],
λ=[659; 887], λ=[888; 1600]. The number of photons in each band is:
∫=j
ihc
dPn ji
λ
λ
λλλ )(, , QEREP ..)( =λ being the final power received by the cell. (E is
the sun irradiance, R the mirror reflectivity and QE the cell quantum efficiency).
63
Non coated Total photons integrated 2.50E+21 ph.s-1.m-2 Photons integrated from 350 to 668 7.19E+20 ph.s-1.m-2 Photons integrated from 669 to 887 7.63E+20 ph.s-1.m-2 Photons integrated from 888 to 1600 10.2E+20 ph.s-1.m-2
Table 5.1 – Initial number of photons
A first calculation gives the number of photons above. These counts confirm what
was said before; the blue band has the lowest photon flux and is thus going to
determine the current in each band. Therefore a better way to optimize is to consider
only the two first bands.
Then the energy associated with each band is the energy of the largest wavelength (ie
658, 887, 1600 nm).
So the merit function is: 2,1
21,0
12 n
hcn
hcM
λλ+= instead of 3,2
32,1
21,0
11 n
hcn
hcn
hcM
λλλ++=
The two thin films have to have their thickness optimized, according to this function,
which places no weight in the flux beyond 890 nm. The starting point was a quarter
stacks [3] but the ‘sweet spot’ was slightly different from the classical behavior as the
3D plot below shows.
Figure 5.3 – Optimization 3D plot
64
The sweet spot is thus for two films of thickness described as follow:
Table 5.2 – Thin film description
In this optimized case the calculation of the energy per band and the number of
photons gives:
Coated with .2344 TiO2 and .1875 MgF2 Total photons integrated 2.51E+21 ph.s-1.m-2 Photons integrated from 350 to 668 7.30E+20 ph.s-1.m-2 Photons integrated from 669 to 887 7.66E+20 ph.s-1.m-2 Photons integrated from 888 to 1600 1.01E+21 ph.s-1.m-2 Merit with 3 bands 518.409 W.m-2 63.69% Merit with 2 first bands 392.544 W.m-2 48.22% Spectrum Integral 650.931 W.m-2 79.97%
Table 5.3 – Optimized photons calculations
Earlier we had a merit function for the uncoated silver equal to 47.72 %. Therefore it
is 0.5% increase between the optimized and non coated silver, which is a relative
increase of 1.04% in power. And finally the two reflectance spectrums, with the
optimization on the first two bands, are presented below.
Figure 5.4 – Reflectance spectrum comparison
―: optimized coating ---: non coated silver
65
CONCLUSION
Finally the improvements have brought a lot to the original design. They have been of
various sorts: reflectors depth, focal length, reflectance, shape of the output surface,
shape of the reflectors. The system is now able to produce over 2 kW, according to
the latest simulations. Efficient worldwide solar energy production will require
improved technologies for solar concentration and photovoltaic cells. In this paper,
we illustrated various designs including a twisted-sides solar concentrator design with
triple-junction photovoltaic cells which showed increased system power in both
simulation and experiment. The main goal was to be able to orientate the designs with
the simulations to validate the performances that we were expecting to find. The
software ASAP was really helpful on that. The system we are developing has really
interesting properties: high output power (over 2 kW), stability off-axis, high
efficiency (27 %), human size (3.1 m diameter).
This thesis concludes a one year and a half long project that will be taken further
during the next years. The next steps will be to build first the version 5 of the design
and then the version 4 once optimized. The improvement of the other reflective
surfaces has to be done. According to the latest update, the version 5.5 should be able
to produce around 2.2 kW, but it has to be validated.
66
APPENDIX D APPENDIX D.2.1
Concentration is proportional to 2
1
ER
R, RE being the entrance aperture radius from
the center of the ball to the image plane.
67
APPENDIX D.2.2
On axis irradiance map
0.75 (left) and 1 (right) degree vertical
0.75 (left) and 1 (right) degree diagonal
68
APPENDIX D.2.3
0.5 Off electrical power with obscuration
0
5
10
15
20
25
30
35
40
45C
10
C11
C12
C13
C14
C15
C16
C17
C20
0
C20
1
C20
2
C20
3
C20
4
C20
5
C20
6
C20
7
C20
8
C20
9
C21
0
C21
1
C21
2
C21
3
C30
0
C30
1
C30
2
C30
3
C30
4
C30
5
C30
6
C30
7
C30
8
C30
9
C31
0
C31
1
C31
2
C31
3
C31
4
C31
5
C31
6
C31
7
C31
8
C31
9
C40
C41
C42
C43
C44
C45
C46
C47
W
0.5 off electrical power without obscuration
0
5
10
15
20
25
30
35
40
45
C10
C11
C12
C13
C14
C15
C16
C17
C20
0
C20
1
C20
2
C20
3
C20
4
C20
5
C20
6
C20
7
C20
8
C20
9
C21
0
C21
1
C21
2
C21
3
C30
0
C30
1
C30
2
C30
3
C30
4
C30
5
C30
6
C30
7
C30
8
C30
9
C31
0
C31
1
C31
2
C31
3
C31
4
C31
5
C31
6
C31
7
C31
8
C31
9
C40
C41
C42
C43
C44
C45
C46
C47
W
69
0.5 off electrical power full square
0
5
10
15
20
25
30
35
40
45
50
C10
C11
C12
C13
C14
C15
C16
C17
C20
0
C20
1
C20
2
C20
3
C20
4
C20
5
C20
6
C20
7
C20
8
C20
9
C21
0
C21
1
C21
2
C21
3
C30
0
C30
1
C30
2
C30
3
C30
4
C30
5
C30
6
C30
7
C30
8
C30
9
C31
0
C31
1
C31
2
C31
3
C31
4
C31
5
C31
6
C31
7
C31
8
C31
9
C40
C41
C42
C43
C44
C45
C46
C47
W
0.75 off electrical power with obscuration
0
5
10
15
20
25
30
35
40
45
C10
C11
C12
C13
C14
C15
C16
C17
C20
0
C20
1
C20
2
C20
3
C20
4
C20
5
C20
6
C20
7
C20
8
C20
9
C21
0
C21
1
C21
2
C21
3
C30
0
C30
1
C30
2
C30
3
C30
4
C30
5
C30
6
C30
7
C30
8
C30
9
C31
0
C31
1
C31
2
C31
3
C31
4
C31
5
C31
6
C31
7
C31
8
C31
9
C40
C41
C42
C43
C44
C45
C46
C47
W
70
0.75 off electrical power without obscuration
0
5
10
15
20
25
30
35
40
45
C10
C11
C12
C13
C14
C15
C16
C17
C20
0
C20
1
C20
2
C20
3
C20
4
C20
5
C20
6
C20
7
C20
8
C20
9
C21
0
C21
1
C21
2
C21
3
C30
0
C30
1
C30
2
C30
3
C30
4
C30
5
C30
6
C30
7
C30
8
C30
9
C31
0
C31
1
C31
2
C31
3
C31
4
C31
5
C31
6
C31
7
C31
8
C31
9
C40
C41
C42
C43
C44
C45
C46
C47
W
0.75 off electrical power full square
0
5
10
15
20
25
30
35
40
45
50
C10
C11
C12
C13
C14
C15
C16
C17
C20
0
C20
1
C20
2
C20
3
C20
4
C20
5
C20
6
C20
7
C20
8
C20
9
C21
0
C21
1
C21
2
C21
3
C30
0
C30
1
C30
2
C30
3
C30
4
C30
5
C30
6
C30
7
C30
8
C30
9
C31
0
C31
1
C31
2
C31
3
C31
4
C31
5
C31
6
C31
7
C31
8
C31
9
C40
C41
C42
C43
C44
C45
C46
C47
W
71
1 off electrical power with obscuration
0
5
10
15
20
25
30
35
40
45
C10
C11
C12
C13
C14
C15
C16
C17
C20
0
C20
1
C20
2
C20
3
C20
4
C20
5
C20
6
C20
7
C20
8
C20
9
C21
0
C21
1
C21
2
C21
3
C30
0
C30
1
C30
2
C30
3
C30
4
C30
5
C30
6
C30
7
C30
8
C30
9
C31
0
C31
1
C31
2
C31
3
C31
4
C31
5
C31
6
C31
7
C31
8
C31
9
C40
C41
C42
C43
C44
C45
C46
C47
W
1 off electrical power without obscuration
0
5
10
15
20
25
30
35
40
45
C10
C11
C12
C13
C14
C15
C16
C17
C20
0
C20
1
C20
2
C20
3
C20
4
C20
5
C20
6
C20
7
C20
8
C20
9
C21
0
C21
1
C21
2
C21
3
C30
0
C30
1
C30
2
C30
3
C30
4
C30
5
C30
6
C30
7
C30
8
C30
9
C31
0
C31
1
C31
2
C31
3
C31
4
C31
5
C31
6
C31
7
C31
8
C31
9
C40
C41
C42
C43
C44
C45
C46
C47
W
72
1 off electrical power full square
0
5
10
15
20
25
30
35
40
45
50C
10
C11
C12
C13
C14
C15
C16
C17
C20
0
C20
1
C20
2
C20
3
C20
4
C20
5
C20
6
C20
7
C20
8
C20
9
C21
0
C21
1
C21
2
C21
3
C30
0
C30
1
C30
2
C30
3
C30
4
C30
5
C30
6
C30
7
C30
8
C30
9
C31
0
C31
1
C31
2
C31
3
C31
4
C31
5
C31
6
C31
7
C31
8
C31
9
C40
C41
C42
C43
C44
C45
C46
C47
W
73
APPENDIX D.3
Parameters
Units
Wavelength
Number of
rays
Random density of
rays
Detection: -All/certain cells -Integrating sphere
Angle of deviation
Coatings / Media Properties
Silica Transmit / Reflect / Absorb
Geometry
Parameters
Primary mirror Pupil
Sphere Other planes
Reflectors
Source grid
Analysis
Select detection
surface
Type of analysis
Type of display
74
APPENDIX D.3.1
Electrical Power for 1637 mm focal, 24*15*20, On axis
0
5
10
15
20
25
30
35
40
45
50
C10
C11
C12
C13
C14
C15
C16
C17
C200
C201
C202
C203
C204
C205
C206
C207
C208
C209
C210
C211
C212
C213
C300
C301
C302
C303
C304
C305
C306
C307
C308
C309
C310
C311
C312
C313
C314
C315
C316
C317
C318
C319
C40
C41
C42
C43
C44
C45
C46
C47
W
24*15*20 0deg
Electrical Power for 1637 mm focal, 24*15*20, Off axis horizontal
0
5
10
15
20
25
30
35
40
45
50
C10
C11
C12
C13
C14
C15
C16
C17
C200
C201
C202
C203
C204
C205
C206
C207
C208
C209
C210
C211
C212
C213
C300
C301
C302
C303
C304
C305
C306
C307
C308
C309
C310
C311
C312
C313
C314
C315
C316
C317
C318
C319
C40
C41
C42
C43
C44
C45
C46
C47
W
24*15*20 0.75deg 90
24*15*20 1deg 90
75
Electrical Power for 1711 mm focal, 24*15*20, On axis
0
5
10
15
20
25
30
35
40
45
50C
10
C11
C12
C13
C14
C15
C16
C17
C200
C201
C202
C203
C204
C205
C206
C207
C208
C209
C210
C211
C212
C213
C300
C301
C302
C303
C304
C305
C306
C307
C308
C309
C310
C311
C312
C313
C314
C315
C316
C317
C318
C319
C40
C41
C42
C43
C44
C45
C46
C47
W
24*15*20 0deg Total: 1880 W
Electrical Power for 1711 mm focal, 24*15*20, Off axis vertical
0
5
10
15
20
25
30
35
40
45
50
C10
C11
C12
C13
C14
C15
C16
C17
C200
C201
C202
C203
C204
C205
C206
C207
C208
C209
C210
C211
C212
C213
C300
C301
C302
C303
C304
C305
C306
C307
C308
C309
C310
C311
C312
C313
C314
C315
C316
C317
C318
C319
C40
C41
C42
C43
C44
C45
C46
C47
W
24*15*20 0.75deg 90
24*15*20 1deg 90
Total: 1876 WTotal: 1865 W
76
APPENDIX D.3.2
Path Rays Percent Hits Power on axis twisted 1 7987 0.269 6 2 14230 0.479 5 3 7468 0.251 4
29685 269.29 W Path Rays Percent Hits on axis faceted
1 7094 0.245 6 2 14334 0.495 5 3 7468 0.258 4 4 42 0.00145 7
28938 262.52 W 776 incoming 29714 269.6 W
.5 twisted Path Rays Percent Power Hits 1 6885 0.233 6 2 14848 0.503 5 3 7736 0.262 4 4 45 0.00153 7 29514 267.74 W .5 faceted Path Rays Percent Hits 1 5812 0.202 6 2 15069 0.525 5 3 7736 0.269 4 4 98 0.00341 7 28715 260.5 W 827 Incoming 29542 rays 268 W
77
APPENDIX D.4.2
Method 1 : calculations 25.3492 0.998 big area 456.7804 mm^2 20.955 0.825 side 18.7452 0.738 small mm in Radius from center ball to edges 81.3503 3.202768 80.08996 3.153148 79.54038 3.131511 Radius from center ball mirror 1896.872 74.68 Image dimension on mirror big 591.0757 23.2707 Big edge image Angle from big to small edge 0.268025 15.35667 rad deg Radius from point to center ball 1476.375 58.125 Medium radius 1686.624 66.4025 Image dimension on mirror height 452.0564 17.7975 Height image Image dimension on mirror small 347.9358 13.69826 Small edge image Area of image on mirror 212243.1 mm^2
0.212243 m^2 Measurement = 2nd method Small 40 cm Area 2398.445 cm^2 Big 57.3 cm 0.239845 m^2 Height 49.3 cm 0.222822 m^2 a b 2 third Theta angle (rad) 0.669569 1.103453 angle (deg) 38.36348 63.22317 angle (deg) 51.63652 26.77683 43.43282 21.71641 3rd method radius mirror 69inc 1752.6 mm radius cell 77.3 mm area ratio 514.0515 mirror area 234808.6 mm^2
0.234809 m^2 ±0.01
78
APPENDIX D.4.3 9 13 16 20 24 29 Inches
of liquid 2296.328 3316.919 4082.361 5102.952 6123.542 7399.28 Pressure
(Pa) 84 70 56 48 40 34 Flow rate
(s.L-1) 1.19E-05 1.43E-05 1.79E-05 2.08E-05 2.5E-05 2.94E-05 Flow rate
(m3.s-1) 27.337 47.385 72.900 106.312 153.089 217.626 Mech work
(mW) 55.48 56.09 56.11 56.12 55.87 55.97 Cell Power
(W) Voc 3.041 3.065 3.067 3.064 3.054 3.060 Tcell 61.66 56.08 55.47 56.21 58.57 57.24 Tin 37.5 34.6 35.4 36.8 38.9 38.6 Tout 40.6 38.2 37.8 38.2 39.5 38.8
inoutT∆ 3.1 3.6 2.4 1.4 0.6 0.2
cellT∆ 24.16 21.48 20.07 19.41 19.67 18.64
inoutT∆ *Flow 3.69E-05 5.14E-05 4.29E-05 2.92E-05 1.5E-05 5.88E-06 Incoming Power 203.72 203.72 203.72 203.72 203.72 203.72
55.48 55.771 55.879 56.043 56.024 56.091 Corrected Cell Power
55.37 55.58 55.59 55.62 55.41 55.22 Net Power (W)
Data (green rows). Calculations (white rows):
• Pressure: We convert the inches measured to Pascal by using 08.249..densityInchesp = .
• Flow rate: We convert the s.L-1 into m3.s-1. • Mechanical work: The mechanical work is obtained by Flowrate*Pressure. • Tcell: We use a plot from a publication that gives the temperature from the
open circuit voltage, Voc. • inoutT∆ : The temperature difference between Tin and Tout.
• cellT∆ : Temperature difference between Tcell and Tin.
• inoutT∆ *flow: inoutT∆ multiplied by Flow rate
• Incoming power: Sun power computed with the irradiance (926 W.m-2) and the area of the mirror (0.22 m2).
• Corrected cell power: We had to correct the cell power because as we were taking the data, the temperature wasn’t the same. It was increasing. So using the power lost per degree C of 0.11 W.degC-1 and setting the first data with the lowest pressure as the origin, we adjusted all the values.
• Net power: The net power is obtained by doing Corrected cell power – 4*Mech. Power. The multiplying factor has been evaluated previously and set to 4 as the most probable value to reality.
79
REFERENCES [1] R. Sherif, “Concentrating Solar Energy For Utility Scale Application”, Proc 2009 SPIE Vol. 7407, 740702 [2] http://www.rehnu.com [3] H.A. Macleod, Thin-Film Optical Filters, Adam Hilger Ltd., Bristol (1986)