CONCENTRATING OPTICS FOR PHOTOVOLTAIC TRIPLE … · Unlike simple solar cells, solar photovoltaic...

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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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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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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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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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


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


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:


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 %.


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.


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)

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