Труды Всемирного конгресса Международного общества солнечной энергии - 2007. Том 2
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Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement
612
7. ACKNOWLEDGMENTS
The work herein presented was developed under the scope
of project “POWERSOL - Mechanical Power Generation
based on Solar Thermodynamic Engines”, co-funded by the
European Commission [Contract No. 032344 (INCO)].
8. REFERENCES
(1) Gaul, H., Rabl, A., “Incidence angle modifier and
average optical efficiency of Parabolic Trough
collectors”, Journal of Solar Energy Engineering
Vol.102, 16-21, 1980.
(2) McIntire, W.R., “Factored approximations for biaxial
incident angle modifiers”, Solar Energy 29 (4), 315-322,
1982.
(3) Theunissen, P.-H., Beckman, W.A., “Solar transmittance
characteristics of evacuated tubular collectors with diffuse
back reflectors”, Solar Energy 35 (4), 311-320, 1985.
(4) Carvalho, M.J., Collares-Pereira, M., Gordon, J.M.,
“Economic optimization of stationary nonevacuated.
CPC solar collectors”, Journal of Solar Energy
Engineering Vol. 109, 40-45, 1987.
(5) Rönnelid, M., Perers, B., Karlsson, B., “On the
factorization of incidence angle modifiers for CPC
collectors”, Solar Energy 59 (4), 281-286, 1997.
(6) Nilsson, J., Brogren, M., Helgesson, A., Roos, A.,
Karlsson, B., “Biaxial model for the incidence angle
dependence of the optical efficiency of photovoltaic
systems with asymmetric reflectors”, Solar Energy 80
(9), pp. 1199-1212, 2006.
(7) Horta, P., Carvalho, M.J., Collares-Pereira, M.,
Carbajal, W., “Incidence angle modifiers for beam,
diffuse and reflected radiation: a general approach for
energy calculations”, submitted to Solar Energy, May
2007.
(8) Souka, A.F., Safwat, H.H., “Determination of the
optimum orientations for the double-exposure,
flat-plate collector and its reflectors”, Solar Energy 10
(4), 170-174.J, 1966.
(9) Tesfamichael, T., Wäckelgård, E., “Angular solar
absorptance and incident angle modifier of selective
absorbers for solar thermal collectors”, Solar Energy 10
(4), 170-174, 2000.
THE USE OF COLLECTOR EFFICIENCY TEST RESULTS IN LONG TERM
PERFORMANCE CALCULATIONS: REVISIONS AND CLARIFICATIONS IN VIEW OF
PROPER COLLECTOR CHARACTERIZATION AND INTER COMPARISON
Maria João Carvalho, Pedro Horta, João Farinha Mendes
INETI – Instituto Nacional de Engenharia Tecnologia e
Inovação, IP
Estrada do Paço do Lumiar, 22
1649-038 Lisboa, Portugal
mjoao.carvalho@ineti.pt
Manuel Collares Pereira, Wildor Maldonado Carbajal
AO SOL , Energias Renováveis, S.A .
P. Industrial do Porto Alto, Sesmaria Limpa,
2135-402 Samora Correia, Portugal
mpicp@aosol.pt
ABSTRACT
There are a growing number of solar thermal collector
types: flat plates, evacuated tubes with and without backing
reflectors and different tubular spacing, low concentration
collectors, using different types of concentrating optics.
These different concepts and designs all compete to be
more efficient or simply cheaper, easier to operate, etc. at
ever higher temperatures, and even to extend the use of
solar thermal energy in other applications beyond the most
common water heating for domestic purposes.
This means that there is a growing need for the existing and
future simulation tools to be as accurate as possible in the
treatment of these different collector types, to allow for the
proper dimensioning of solar thermal systems as well as the
proper comparison of different collector technologies for a
given application.
This paper develops a systematic approach to the problem
of the proper handling of solar radiation available to each
collector type. The proposed methodology subdivides
radiation in its different components, folding that with the
information available from efficiency curve tests (steady
state) for each collector type and the way the optics of each
particular case transforms and uses the incident solar
radiation. The suggestions made will hopefully be taken at
the level of the testing standards themselves, rendering
them more complete and general.
1. INTRODUCTION
The dimensioning of solar systems and the comparison of
solar collector performances is more and more based in
yearly operation results, obtained after the use of a growing
number of simulation tools.
In general, the available simulation tools use efficiency
curves, resulting from steady state collector testing, to
calculate instantaneous efficiency values in long term
performance calculations.
The first approach to a collector test methodology [1] was
based on flat plate collector characteristics (by far the most
common type still available). Those approaches still hold in
the present standards and do not account properly for
optical specificities of different collector types, such as
evacuated tube or CPC types, e.g.
In the present paper a calculation methodology is suggested,
after an analysis of absorber global irradiance, presented in
2. In 3, instantaneous efficiency and power calculations are
reviewed, in 4 an instantaneous power correction is
suggested and in 5 energy calculation is addressed. Finally,
a general calculation methodology is suggested in 6 and
conclusions are presented in 7.
Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement
614
2. GLOBAL IRRADIANCE AT THE ABSORBER
The total hemispherical radiation reaching a given plane
(the collector aperture plane, e.g.) results from the
summation of these different components, for a given beam
radiation incident angle, θ, and plane tilt angle, β,
according to (Rabl, 1985):
(
)
()
cos 1 cos / 2
1 cos / 2 (1)
G=I +D+
+R
θβ
β−
For all collector types, the amount of solar radiation
reaching the absorber surface is affected by a number of
optical effects related with collector geometry and optical
properties, accounted for in the incidence angle modifier
affecting the different components of solar radiation [3].
Considering these effects and their impact on the different
radiation components, the total irradiance incident on the
absorber surface can be written as:
() ()
cosG=I θKθ+K D+K R (1)
3. INSTANTANEOUS EFFICIENCY AND POWER
CALCULATIONS
The collector instantaneous efficiency may be defined as
the ratio between the useful heat delivered per aperture area
and the total irradiance of the collector aperture, according
to (2):
Qq
η= =
A
GG
(2)
The efficiency curves presently provided, after efficiency
tests according to the present standards [4,5], are based on
so-called stationary tests. According to these standards, two
kinds of efficiency curves might be provided: first (linear)
or second degree fits to efficiency points measured at
different collector temperatures.
The calculation of instantaneous power follows, from Eq.(3)
and from the efficiency curve parameters:
()
()
Q=η K θ G A a T T A−−
(3)
when a first degree fit is used for the efficiency curve, or:
()
()
()
(5)
Q=η K θ G A a T T A
TT
aA
G
−−
−
−
when a second degree fit is used for the efficiency curve.
4. INSTANTANEOUS POWER CORRECTION
A simplified calculation of the collector instantaneous
power, would result, according to Eq.(3), from the direct
multiplication of the total hemispherical radiation reaching
the aperture plane, after Eq.(1), by the instantaneous
collector efficiency as in Eq.(4) or Eq.(5), depending on the
type of approximation adopted for the efficiency curve.
Yet, a correct accounting of both the optical effects present
in a solar collector and their impact on the different
components of radiation reaching the aperture plane,
implies instead the use of the global irradiance of the
absorber surface, according to Eq.(2).
To this end, a correction to the standard efficiency curve is
required yielding a corrected efficiency to be used on
instantaneous power calculations at any given operating
temperature. From Eq.(3) follows, for the correction factor:
G
q
η ==η
GG
(4)
with irradiance values referred to efficiency test conditions,
which means that additional efficiency test information is
required: the values of diffuse and reflected radiation, tilt
angle and ground reflectivity throughout the efficiency test.
In the absence of such information, which is not included,
at present, in the efficiency test results defined in the testing
3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS
615
procedure, a compromise solution is to accept that this
correction can be made “a posteriori”.
A reasonable simplification would arise from considering a
ground reflectivity (albedo) of 0, thus eliminating the term
of ground reflected radiation, compensated by an
hemispherical diffuse radiation fraction equal to 1
(this is
equivalent to taking in all diffuse radiation, as if the ground
was not there to limit the scope of what is available).
Considering the test procedures, efficiency points must be
measured with a minimum global hemispherical radiation
in the aperture plane of 850 W/m2 and a maximum 30%
fraction of diffuse radiation. Therefore, in the absence of
information concerning diffuse radiation conditions
throughout the efficiency tests, as it is usually the case, a
diffuse radiation fraction, between 10% and 30% of the
corresponding global radiation value, could be defined. The
choice of reference values for this parameter would depend
on the efficiency test conditions.
As shown in (6), considering Eqs.(1) and (2), as well as the
reflected/diffuse radiation simplification for reference
conditions, mentioned above, the power flux variation due
to instantaneous power correction, depends only on the
value of the incidence angle modifier affecting diffuse
radiation, K
dif,h
(for the entire hemisphere, i.e., without
cutoff effects due to collector tilt angle), as well as on the
fraction of diffuse radiation adopted for collector test
reference irradiance condition, f, according to:
()
()
1
11
fK
qq
=
q
fK
ηη
η
−
−−
=
−−
(5)
The values in Table 1 show the power flux variation
resulting from the efficiency curve correction, for different
f and K
dif,h
values, which is equivalent to say different
collector test locations and different collector types:
These results show that calculation of the power flux (or
instantaneous power) based on a non-corrected efficiency
value and on absorber irradiance, as it is due to a full
accounting of the optical effects present in the collector,
leads to an underestimation of the results.
TABLE 1: POWER FLUX VARIATION FOR
DIFFERENT DIFFUSE RADIATION AND INCIDENCE
ANGLE MODIFIER CONDITIONS
f
K
dif,h
10% 20% 30%
0.9 1.01% 2.04% 3.09%
0.8 2.04% 4.17% 6.38%
0.7 3.09% 6.38% 9.89%
0.6 4.17% 8.70% 13.64%
0.5 5.26% 11.11% 17.65%
0.4 6.38% 13.64% 21.95%
0.3 7.53% 16.28% 26.58%
Moreover, it is possible to conclude that the power flux
correction depends heavily on the optical system
considered, with increased importance as the optical
complexity of the collector increases, as illustrated by K
dif,h
values calculated in (6) for a flat-plate collector (K
dif,h
= 0.9),
a non-truncated CPC with a 1.5 concentration factor (K
dif,h
= 0.54) and a non-truncated CPC with a 2.0 concentration
factor (K
dif,h
= 0.37).
5. ENERGY CALCULATIONS
The calculation of the useful energy collected within a
period, results from integration of the collector
instantaneous power according to:
Q Qdt A qdt==
∫∫
(6)
Application of the correction suggested in Eq.(7) to the
useful energy calculation leads, again, to the same constant
variation:
()
()
()
1
1
1
(9)
11
A Gdt A Gdt A G dt
QQ
=
Q
A Gdt A G dt
fK
fK
ηη ηη
ηη
ηη
η
−−
−
=
−
−
==
−−
∫∫ ∫
∫∫
Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement
616
It is important to refer, at this point, that the correction
suggested for both instantaneous power or energy
calculations, does not depend on the collector temperature
regime, as can be concluded from Eq.(7) and Eq.(9), as
illustrated in (6) with energy calculation results at different
collector temperature levels.
6. CALCULATION METHODOLOGY
In view of the above the proper sequence of calculations
leading to long term performance prediction of solar
collectors, must take into account the correction to the
efficiency curve, and all optical effects, included in the
incidence angle modifier, and is as follows:
calculation of G
col
(Eq.1) and G
abs
(Eq.2) after radiation
data for the location;
calculation of instantaneous uncorrected collector
efficiency, η, after efficiency curve parameters and G
col
value;
calculation of corrected collector efficiency, η∗, after
Eq.(7);
calculation of corrected power flux, q*, after Eq.(6), G
abs
and η∗ values;
calculation of corrected energy value after Eq.(8) and q*
value.
This approach only requires an additional information from
the collector efficiency test laboratory: the reference diffuse
fraction value, f., as in Eq.(7) and Eq.(9).
7. CONCLUSIONS
Optical properties of solar collectors affect differently the
diverse components of radiation reaching the aperture plane,
namely direct, diffuse or reflected radiation.
A correct accounting of these optical effects is achieved
after the use of proper incidence angle modifier values for
each of the different components of radiation reaching the
collector aperture plane, making it possible to calculate the
amount of irradiance reaching the absorber.
Solar collector efficiency curves are produced under clear
sky conditions. Moreover, efficiency values are calculated
in global radiation values, measured externally, in the
collector aperture plane.
A proper calculation of power flux (and energy), based on
absorber irradiance values, depends on a suitable correction
of the instantaneous collector efficiency value, which is
based on aperture irradiance.
It is shown that a suitable correction of efficiency, power
flux or energy calculations, in view of a correct accounting
of these optical effects, depends only on collector optical
properties and on reference diffuse radiation conditions for
the solar collector efficiency test.
A simple methodology, based in this correction, is
suggested for energy calculation in simulation tools.
It was shown that the adequate efficiency curve correction
affects all collector types, which highlights the importance
of adopting the suggested methodology.
Moreover, the impact of this correction in performance
calculations increases with the complexity of the optical
effects present in the collector, which renders its adoption
essential when comparing the performance of different
collector types.
This approach will only require an additional information
from the collector efficiency test laboratory: the reference
diffuse fraction value, which does not imply any additional
measurements.
8. NOMENCLATURE
A
a
- collector aperture area, [m
2
]
a
1
- global heat loss coefficient, [W/m
2
ºC]
a
2
- temperature dependent heat loss coefficient, [W/m
2
ºC
2
]
D - diffuse radiation, [W/m
2
]
f - diffuse radiation fraction
G
col
- global irradiance incident on the aperture, [W/m
2
]
G
abs
- global irradiance incident on the absorber, [W/m
2
]
I - beam radiation, [W/m
2
]
q
- power flux, [W/m
2
]
Q
- power, [W]
R
g
- ground reflected radiation, [W/m
2
]
T
a
- air temperature, [ºC]
T
f
- average heat transfer fluid temperature, [ºC]
3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS
617
β - tilt angle, [º]
η - collector efficiency
η
0
- collector optical efficiency
Κ(θ) - incidence angle modifier (IAM)
Κ
dif,d
- diffuse radiation weighted average IAM
Κ
dif,h
- hemispherical diffuse radiation weighted aver. IAM
Κ
dif,r
- reflected radiation weighted average IAM
θ - incidence angle, [º]
9. ACKNOWLEDGMENTS
The work herein presented was developed under the scope
of project “POWERSOL - Mechanical Power Generation
based on Solar Thermodynamic Engines”, co-funded by the
European Commission [Contract No. 032344 (INCO)].
10. REFERENCES
(1) Duffie, J.A., Beckman, W.A., “Flat-Plate Collector Per-
formance”. In: Duffie, J.A., Beckman, W.A., “Solar
Engineering of Thermal Processes”, John Wiley &
Sons Inc., New York, pp. 250-281, 1980.
(2) Rabl, A., “Active Solar Collectors and their
applications”, Oxford University Press, Oxford, 1985.
(3) Horta, P., Carvalho, M.J., Collares-Pereira, M., Carbajal,
W., “Incidence angle modifiers for beam, diffuse and
reflected radiation: a general approach for energy
calculations”, submitted to Solar Energy, May 2007.
(4) EN 12975-2:2006. Thermal solar systems and
components – Solar collectors – Part 2: Test Methods,
Section 6.1. European Standard, March 2006.
(5) ISO 9806-1:1994. Test methods for solar collectors –
Part 1: Thermal performance of glazed liquid heating
collectors including pressure drop.
(6) Horta, P., Carvalho, M.J., Collares-Pereira, M., Carbajal,
W., “Long term performance calculations based on
steady state efficiency test results: analysis of optical
effects affecting beam, diffuse and reflected radiation”,
submitted to Solar Energy, May 2007.
OPTICS FOR CONCENTRATION ON PV CELLS
P. Sansoni, D. Fontani, F. Francini, L. Mercatelli, D. Jafrancesco
CNR-INOA Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6 – Firenze - 50125 - Italy
paola.sansoni@inoa.it
ABSTRACT
Modern PhotoVoltaic cells and technologies for
Concentrating PhotoVoltaics require high level of solar
light concentration. The paper proposes different collectors
for the exploitation of solar light using CPV systems. Solar
concentrators have been designed to be coupled to a PV
cell with a concentration ratio exceeding 500. The paper
analyses and compares characteristics and performances of
solar collectors applied in CPV systems. Optical layout and
concentration ratio are the primary optical features, which
are essential to select the examined collector categories.
Then the analysis focuses on the comparison of the optical
characteristics that are fundamental for the application in
the domain of Concentrating PhotoVoltaics. The most
important features in case of light concentration on
PhotoVolatic cells are: collection efficiency, image size and
image uniformity.
1. CONCENTRATING PV SYSTEMS
Photovoltaic power generation using sunlight concentration
is widely experimented and applied. The introduction of
optical concentrators, especially high concentration systems,
has two positive effects: reducing the area of expensive
solar cells and increasing their efficiency. Only recently
Concentrating PhotoVoltaic (CPV) systems, using III-V
cells, have been commercialised. The main reasons for this
development are the following: (1) Improved efficiency of
CPV systems due to new solar cells made of III-V
semiconductor compounds with efficiencies of 35 % - 40 %
or more; (2) Improved size of PV installations due to the
rising and expansion of the PV application; (3) Improved
interest in alternative PV technologies both due to
government incentives and to the poor Silicon availability
as PV raw material.
In general it can be assumed that an improvement in the
volume of the CPV system reduces the costs, given that the
system provides an higher production of energy. At present
there are several examples of companies experimenting and
realising demonstrators of CPV system, mostly developing
large size modules based on III-V solar cells. We can
mention Amonix, SVV Technology, Pyron Inc. and
Concentrator Technologies LLC [1] in USA; Daido Steel
[2-5] in Japan; Green and Gold Energy and Solar Systems
[6] in Australia. Just to give an example, the Pyron
demonstrator is a 6.6 kW system that employs Fresnel
lenses to concentrate the light by a factor of 400 on
triple-junction solar cells delivered by the company
Spectrolab (USA).
In Europe, two new companies Concentrix Solar (Germany)
and Sol3G (Spain) show up. Furthermore Isofoton (Spain)
is developing III-V based CPV systems [7], working in
collaboration with the IOFFE Institute of St. Petersburg
(Russia). In Italy ENEA is developing CPV systems, using
prismatic lenses, within the PhoCUS project [8].
Concentrix Solar is a spin off from Fraunhofer ISE and
commercialises the FLATCON® technology [9]. Sol3G
develops systems for use on roof tops; they set up a 200 W
demonstration system, which is similar to the Pyron system.
3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS
619
Isofoton, in cooperation with the University of Madrid,
Instiuto Energia Solar, has developed a concentrating optic
for 1000x [7]. It exploits a total internal reflection and
refraction lens (TIR-R) with a secondary optics. In 2007
Isofoton will manufacture 5 MW of CPV modules.
The above given examples for III-V based CPV is by no
means complete. Several companies like Sharp (Japan),
Emcore (USA), SolFocus (USA) or Entech (USA) are
starting with the development of CPV prototypes using
III-V based cells. In addition, some companies like
MicroPV (USA/China) or Energy Innovations (USA),
which currently use Si concentrator solar cells, consider to
use III-V solar cells in the future.
2. OPTICS FOR CPV SYSTEMS
The concentration of solar light on small surfaces has been
studied in our Solar Collector Laboratory of CNR-INOA
since 1997. Optical configurations with increased
complexity from simple parabolic concentrators to lens
mirror combinations have been analysed and experimented
[10-13]. The possible applications relate to Photo Voltaic
sector, thermal field and internal illumination.
This paper presents two examples of solar collector
designed to focus the solar light on a circular PV cell of
diameter 2 mm with a concentration ratio of the order of
700. Typically the High Concentration PhotoVoltaic cells
(HCPV cells) are characterised by diameter/diagonal size
between 1 mm and 6 mm and concentration ratio in the
range 300-1000.
The aim of this study is to analyse and compare
characteristics and performances of solar collectors
employed in Concentrating PV systems. The proposed
collectors are named “C” optics and “T” optics.
The “C” optics, in Fig. 1, is a Cassegrain layout. In this
configuration the primary mirror is aspherical, with
entrance pupil diameter D = 55 mm, curvature radius R =
-129.03 mm and conicity k = −0.664168. The secondary
mirror of the “C” optics is spherical with D = 16.8 mm and
R = −49.03 mm; for “C” the thickness results to be 45.4
mm.
Fig. 1: Layout of “C” optics.
Fig. 2: Layout of “T” optics.
The “T” optics, in Fig. 2, has been obtained on the base of
the “tailored imaging design” [14-16] and it includes two
aspherical mirrors. For the “T” optics the primary
aspherical mirror has an entrance pupil diameter D = 55
mm and it is defined by the equation:
z = –0.0157 r
2
+0.00002 r –5.
Analogously the secondary aspherical mirror of “T” has
D = 4 mm and it is defined by the equation:
z = 0.0016 r
4
+0.00576 r
3
–0.26437 r
2
+0.00228 r –20
The thickness of the “T” optics is 15.9 mm.
Some preliminary considerations can be made regarding
optical layout and concentration ratio for “C” and “T”. The
optical parameters for the two layouts have been selected
for obtaining similar concentration ratios: 686 for “C” and
Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement
620
752 for “T”. The main drawback of “C” is the elevated
thickness value of 45 mm, especially with respect to the
“C” entrance pupil diameter of 55 mm. On the other hand
in the “T” configuration all the mirrors are aspherical, thus
requiring specific optical procedures to be realised, while
the “C” configuration is easier to be manufactured.
The comparative analysis examines collection efficiency,
image size and image uniformity, which are essential
characteristics in the Concentrating PhotoVoltaic
application.
Collection efficiency is calculated as ratio between the light
focused on the 2 mm circular area of the PV cell and the
input light. For both optics, the input light is the solar
radiation passing through the ring area obtained from the
primary mirror area subtracting the secondary mirror area,
which represents its central part.
Image diameter is measured on image profiles, obtained by
Zemax simulations (in Fig. 3 and Fig. 4), and it
corresponds to Full Width at Half Maximum.
Image uniformity is estimated from the simulated image
profile, calculating standard deviation σ of data.
Considering the image profile, between r = –1 mm and r =
1 mm, we determine the mean value of focused light; then
we calculate the standard deviation of image profile values.
The standard deviation σ results to be an “indicator of the
image disuniformity” because it is related to fluctuations of
image data.
Table 1 and Table 2 present results of collection efficiency,
image diameter and image uniformity assessment, for “C”
optics (Table 1) and “T” optics (Table 2). The analysis is
carried out considering different distances d between
optics and PV cell. For each configuration we have
examined five positions of the PV cell around the best
location. The central point is characterised by optimal
collection efficiency, image diameter approaching 2 mm
and maximum image uniformity (minimum σ value).
These optimal positions correspond to a distance d
between optics and PV cell of 37.9 mm for “C” and of
2.6 mm for “T”.
Figure 3 present image profiles pertaining to “C” optics,
while Fig. 4 shows image profiles obtained for “T” optics.
Both figures report five image profiles for each collector.
Curves of Fig. 3 pertain to the five d values in Table 1.
While profiles in Fig. 4 correspond to the d values of
Table 2.
Fig. 3: Image profiles for “C” optics.
3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS
621
TABLE 1: “C” OPTICS APPLIED TO CPV
Optics - PV
cell Distance
d (mm)
Collection
Efficiency
(%)
Image
Diameter
(mm)
“Disuniformity
Indicator”
(stand. dev. σ)
36.9 88.92 1.91 393
37.4 89.69 1.97 317
37.9 90.11 1.97 243
38.4 89.72 1.97 236
38.9 88.66 1.97 286
TABLE 2: “T” OPTICS APPLIED TO CPV
Optics - PV
cell Distance
d (mm)
Collection
Efficiency
(%)
Image
Diameter
(mm)
“Disuniformity
Indicator”
(stand. dev. σ)
1.6 98.66 1.78 928
2.1 98.74 1.84 753
2.6 98.76 1.92 572
3.1 98.71 1.96 265
3.6 97.19 2.04 165
3. CONCLUSIONS
The paper analyses and compares two optical configurations,
denominated “C” and “T”, applied to concentrate solar light
on a circular PV cell, of diameter 2 mm, with concentration
ratio around 700.
Referring to a circular area of 2 mm diameter for the image,
Table 1 and Table 2 evidence that “T” reaches higher values
of collection efficiency with respect to “C”; while the “C”
image results to be more uniform than the “T” image. In the
CPV application the image uniformity is a crucial point
because it affects the conversion efficiency of the PV cell.
For this reason it is important to examine the image profiles
of Fig. 3 and Fig. 4, studying in particular how they vary
for different distances d between PV cell and optics. The
five d values examined in Tables and Figures 3, 4 are
centred on the best condition point. This central position
corresponds to the maximum of collection efficiency,
considering the 2 mm diameter area. Then the collection
efficiency decreases from the central point to the lateral
positions.
The lateral positions around the central point are examined
to test how collection efficiency, image diameter and image
uniformity are affected by d variations.
A fundamental result is that the best condition is
maintained in all five positions for both optics. In fact the
parameters in columns 2 and 3 of Tables 1, 2 show only
minor variations. Nevertheless for both optics the collection
Fig. 4: Image profiles for “T” optics.