Engineering, 2013, 5, 37-43
doi:10.4236/eng.2013.51b007 Published Online January 2013 (
Copyright © 2013 SciRes. ENG
Measurements of the Electrical Incidence Angle
Modifiers of an Asymmetrical Photovoltaic/Thermal
Compound Parabolic Concentrating-Collector
Bernardo Ricardo1*, Davidsson Henrik1, Gentile Niko1, Gomes João2, Gruffman Christian3,
Chea Luis4, Mumba Chabu5, Karlsson Björn6
1Energy and Building Design, Lund University, Lund, Sweden
2Solarus Sunpower AB, Stockholm, Sweden
3Finsun AB, Älvkarleby, Sweden
4Universidade Eduardo Mondlane, Maputo, Mozambique
5University of Zambia, Lusaka, Zambia
6Division of Energy Engineering, Mälardalen University, Västerås, Sweden
Email: *
Received 2013
Reflector edges, sharp acceptance angles and by-pass diodes introduce large variations in the electrical performance of
asymmetrical concentrating photovoltaic/thermal modules over a short incidence angle interval. It is therefore important
to quantify these impacts precisely. The impact on the electrical performance of the optical properties of an asymmetri-
cal photovoltaic/thermal CPC-collector was measured in Maputo, Mozambique. The measurements were carried out
with the focus on attaining a high resolution incidence angle modifier in both the longitudinal and transversal directions,
since large variations were expected over small angle intervals. A detailed analysis of the contribution of the diffuse
radiation to the total output was also carried out. The solar cells have an electrical efficiency of 18% while the maxi-
mum measured electrical efficiency of the collector was 13.9% per active glazed area and 20.9% per active cell area, at
25˚C. Such data make it possible to quantify not only the electrical performance for different climatic and operating
conditions but also to determine potential improvements to the collector design. The electrical output can be increased
by a number of different measures, e.g. removing the outermost cells, turning the edge cells 90˚, dividing each receiver
side into three or four parts and directing the tracking, when used, along a north-south axis.
Keywords: CPC-Collector; PVT Hybrid; Incidence Angle Modifier; Asymmetric Collector; Electrical Efficiency
1. Introduction
The electrical part of an asymmetric compound parabolic
concentrating (CPC) photovoltaic/thermal hybrid (PV/T),
collector has been investigated. The radiation is concen-
trated onto an aluminium thermal absorber on which PV
cells have been laminated. The cells were laminated on
both the upper and the lower side of the absorber. The
front side works like a standard PV module without con-
centration while the backside receives solar radiation
from a parabolic reflector such as illustrated in Figure 1.
Even though the concentration factor of the collector is
low, equal to 1.5, the PV cells can still reach high tem-
peratures. This will reduce the electric production and
cooling is required in order to maintain electrical effi-
ciency. This is carried out by running water inside the
thermal absorber. By using the heat generated in the ab-
sorber, the PV/T collector produces electricity and ther-
mal heat, see Figure 2. The PV/T system, shown in Fig-
ure 1 and Figure 2, consists of a photovoltaic module,
thermal absorber, compound reflector (parabolic and
circular), glazed protection and supporting structure. The
reflector material is made of anodised aluminium with a
solar reflection of approximately 95% [1]. The optical
axis for the reflector geometry is normal to the glass of
the collector. This defines the acceptance angle for the
irradiation of the reflector. If the radiation falls outside
this angle the reflectors do not redirect the incoming
beam radiation to the backside absorber and the optical
efficiency of the collector is thus reduced. Hence, the
optical efficiency of the collector changes throughout the
year depending on the projected solar altitude. The tilt of
the collector determines the amount of total annual irra-
diation kept within the acceptance interval [2]. The glass
cover of the collector is made of low iron glass with solar
*Corresponding author.
Copyright © 2013 SciRes. ENG
transmittance of 0.9 at normal incidence angle.
The main objective of this study was to accurately
measure the optical properties for the electrical output of
an asymmetric PV/T CPC-collector with the focus on
edge effects, bypass diodes, acceptance angle and the
contribution of diffuse radiation. This information makes
it possible to understand how to further improve the col-
lector design and estimate the expected production in
different climatic and operating conditions.
2. Method
2.1. Experimental Setup and Hybrid Design
Figure 2 describes the electrical arrangement of the solar
cells in one PV/T module. Since receiver 1 and receiver 2
are exactly the same only one of the receivers was tested.
The figure shows the collector viewed from the top. The
backside, i.e. the part that utilizes the reflector is equipped
with the same PV cell arrangement. One string consists
of 38 PV cells. Both the front side and the backside of
the receiver consist of two PV strings each. The total
number of PV cells per receiver is thus 152 cells. The PV
array is made up of six cells that have been cut into 26
mm wide pieces. The manufacturer chose to do so in
order to have a larger voltage and a smaller current for
Figure 1. The geometry of the investigated PV/T hybrid solar
Figure 2. Top view of the PV/T hybrid collector. The water
connection is in blue and the electrical connections in red.
larger irradiation levels due to the increased concentra-
tion. The total area of PV cells on a receiver was ap-
proximately 0.58 m² and the active glazed area was ap-
proximately 0.87 m² per receiver. Active glazed area was
defined as the glazed area where the incident radiation
can contribute to electricity production, i.e. the area on
top of the cells and the area on top of the reflector in
front of the cells, excluding edges, spaces between cells
and parts where there was no reflector [3]. Figure 2
shows the electrical connection in red and the water
connections in blue. Tin and Tout represent the tempera-
ture sensors placed at the inlet and outlet of the water
running inside the collector. Tmid represents the tempera-
ture sensor at the middle of the receiver.
Figure 2 also shows the size of the different electric
components in the collector. The total size of the collec-
tor is 2.31 m by 0.955 m. The length of the thermal re-
ceiver is 2.290 m and the height is 0.158 m. The size of
the PV cells is 0.148 m times 0.026 m. The active height
of the reflector is 0.292 m. The parts of the collector
which are excluded by the active glazed area are indi-
cated in the figure. The total active height of the trough is
0.44 m, i.e. the sum of the active reflector height and the
height of the PV cells.
The evaluation of the PVT hybrid collector was only
performed for the electrical part. The thermal part was
previously evaluated in [2] and further measurements are
2.2. Procedure
Since there are many factors that affect the characteristic
parameters of a solar collector the measurements have
been performed and evaluated in a specific order. The
first step was to analyze the efficiency and the tempera-
ture dependence of the PV cell module. This part was
performed while the incidence angle maximizes the elec-
trical output, i.e. close to normal incidence. Once the
temperature dependence was determined, the angular
dependence or more accurately, the incidence angle
modifier, could be measured.
In reality, it is expected that an electric load is perma-
nently connected to the PV cells and electric power is
continuously extracted at maximum power point. How-
ever, the presented method of instantaneous I-V curve
measurements simplifies the whole test procedure. These
results are less expensive and less time consuming to
achieve while still maintaining a good level of accuracy.
If an electric load were continuously connected, the ab-
sorber would be colder since a part of the incoming ra-
diation would be converted to electricity. This would
mean lower temperatures and thus slightly lower thermal
losses. This difference is however small and has little
impact on the results [3]. Since the investigated collector
has a closed structure it was not possible to measure the
Copyright © 2013 SciRes. ENG
cell temperature directly. Instead, the temperature of the
outlet water was measured. This is the limiting tempera-
ture of the whole electric output since the hottest cells in
the series connected string will limit the energy produc-
The transverse incidence angle modifier (IAMt) is de-
fined by the reduction in electrical efficiency for a given
irradiation caused by the increase of the incidence angle
between the sun and the normal to the collector in the
transverse direction (θ
). This is exemplified in the left
illustration in Figure 3. From 0˚ to +90˚ the suns direc-
tion is inside the acceptance angle of the reflector and
outside from 0˚ to -90˚. The IAM measurements are a
combination of all angular effects such as decrease of
transmission in the glazing for high incidence angles and
shading effects by edges, etc.
To be able to measure IAMt for different transverse
angles the longitudinal angle had to be kept equal to zero.
This was measured by facing the collector towards the
solar azimuth for various tilt angles. This is illustrated in
Figure 4.
The incidence angle modifier is applied for the direct
radiation only. However, even during clear days, there is
always a percentage of diffuse light that contributes to
the measured power output, which becomes relevant for
low concentrating collectors such as this one.
The fraction of useful diffuse radiation for the concen-
trating collector relative to the total diffuse radiation on
the glazed cover of the collector is described by Figure 5.
The pyranometer, labelled (A), will see
β+ of
the full sky. This is the same as for the front side of the
receiver, labelled (B). They thus see the same part of the
diffuse sky and it would be a correct assumption when a
non-concentrating collector is tested. This is however not
the case for the backside of the receiver. The acceptance
angle for the reflector blocks a substantial part of the sky.
This part is indicated with red arrows in Figure 5. The
radiation that will strike the backside of the receiver
comes from the radiation labelled (C) and is equal to the
radiation measured by the pyranometer minus half the
sky due to the acceptance angle. This is true for positive
tilt, i.e. the leftmost illustration in Figure 5.
The right-hand illustration shows the case for tilting the
reflector backwards. The pyranometer (D) and the front
side (E) of the receiver are unaffected. However, the
backside radiation (F) will be half of the sky as long as
the tilt β is less than 90°. This happens since the part out-
side the acceptance angle is now facing the ground. Thus
the part of the diffuse radiation inside the acceptance
angle is always half of the sky.
The fraction, f, of the diffuse radiation that is useful
for the collector can be calculated by summing the con-
tributions from the front side and the backside of the re-
ceiver and dividing this by the diffuse radiation measured
by the diffuse pyranometer. The front side of the receiver
accounts for one third of the total glazed area while the
backside, via the reflector, accounts for two thirds of the
total glazed area. If the collector is rotated like the left
side of the figure f will be:
( )
If the collector is rotated like the right side of the fig-
ure f will be:
( )
Figure 3. Transversal incidence angle to the left and longi-
tudinal incidence angle to the right.
Figure 4. Tilting the collector to achieve different transverse incidence angles.
Copyright © 2013 SciRes. ENG
Figure 5. Fraction of useful diffuse radiation for different
transverse incidence angles.
However, this is true for an infinitely long trough
without any shading from the edges. This is not the case
for the investigated collector. The front side of the re-
ceiver will be only slightly affected by shading and the
shading effect is thus omitted. The shading of the back-
side will be more important. This is illustrated to the
right in Figure 6.
The black arrow, labelled 1, close to normal incidence
will be reflected to the outermost PV cell. So will all rays
coming from an even lower angle, e.g. rays labelled 2
and 3. For radiation with a higher incidence angle, the
rays will be either reflected to hit another cell or be
stopped by the edges. I.e. the outermost cell can only see
roughly half of the diffuse sky. The problem is identical
for the left side of the collector. This will reduce the con-
tribution from radiation to the backside of the receiver,
i.e. (C) and (F) in Figure 5 by approximately 50%. This
will change equation (1) and equation (2) to:
( )
( )
( )
( )
( )
( )
Measurements of the IAMt were carried out by varying
the tilt β from -30° to +30°, see Figure 5. Figure 7
shows a plot of equation (3) and equation (4). The varia-
tion in the fraction of the useful diffuse radiation is small
for this tilt interval. Hence, the fraction of useful diffuse
radiation was set to be the average of its value and equal
to 50%.
Figure 6. Shading of the PV cells due to the gables of the
Figure 7. The fraction of useful diffuse radiation as a func-
tion of the collector tilt.
The longitudinal incidence angle modifier (IAMl.) was
measured while keeping a constant θt which corresponds
to the measured maximum value of IAMt.
3. Results
3.1. Theoretical Estimate of the Maximum
Output of the Collector
The produced electricity is the sum of the production on
the front and back sides, equation (5).
PPP=+ (5)
The power from the front side is the product of the cell
area, _
A, the transmission through the glass,
the efficiency of the cells,
ηo, and the total in-
coming radiation,
G, equation (6).
·· ·
PAGτη=o (6)
Due to the acceptance angle for the collector the radia-
tion has to be divided into beam and diffuse radiation.
The power from the backside is thus the sum of the two,
equation (7).
PPP=+ (7)
The electrical output from the back cells due to the
beam radiation is the product of the total width of the
cells, w, the height of the mirror, h, the transmission
through the glass,
, the reflection of the reflector, r, the
efficiency of the cells,
ηo and the beam radia-
Copyright © 2013 SciRes. ENG
. The electrical production is also dependent on
the optical efficiency. The optical efficiency,
, was
set to one in order to estimate the maximum collector
output, equation (8).
···· ·
=o (8)
The electrical output from the diffuse radiation on the
cells on the backside is calculated in equation (9). This is
the product of the cell area of the back side, _
the transmission through the glass, the reflection of the
reflector, the efficiency of the cells, the diffuse radiation
and also the optical efficiency.
···· ·
τηη=o (9)
Inserting the values presented in Table 1. into equa-
tions 5-9 gives a total maximum electrical output of
P= or
P= active glazed area
(1.74 m²).
3.2. Electrical Efficiency Dependence on
The measured electrical efficiency per cell area for the
PV/T hybrid collector at 25˚C is 20.9%, Figure 8. Ex-
pressed per active glazed area the efficiency is 13.9%.
This means that the maximum electrical power for a col-
lector is 241 W or 139 W/m2 active glazed area. As ex-
pected, this number is somewhat lower than the optimum
output of 272 W for a perfect optical efficiency. Also, the
dependence of electrical efficiency on temperature (KT)
is -0.4%/K, in good agreement with the common value
for solar cells described in literature [4].
3.3. Incidence Angle Modifiers for Beam
Figure 9 shows the electrical transverse and longitudinal
incidence angle modifiers for the beam radiation, IAMt in
blue and IAMl in red. The measured values are adjusted
for temperature variations. The sharp increase/decrease
around 0° for the IAMt is due to the radiation shifting
from outside to inside of the acceptance angle. The IAMl
for the front side and backside receivers is shown in yel-
low and green respectively. As shown, the front side re-
ceiver behaves like a flat plate solar panel. The backside
receiver is the main responsible for the efficiency drop
during low incidence angles in the longitudinal direction.
Table 1. Data for the calculation of the theoretical maxi-
mum collector output.
Acells_top (m2)
τ(-) 0.95
ηcells_(25˚C) (-)
Gtotal (W/m2)
1000 w(m) 1.976
h(m) 0.292
r(-) 0.95 Gb (W/m2)
ηopt (-) 1
Acells_back (m2)
Figure 8. Electrical efficiency dependence on the water out-
let temperature expressed per cell area.
Figure 9. Electrical transverse incidence angle modifier
(IAMt) for beam radiation in blue and the longitudinal in-
cidence angle modifier (IAMl) in red. The IAMl for the
backside and the front side of the receiver is shown in yel-
low and green respectively.
4. Discussion
Figure 9 shows that when the collector is tracking
around an axis aligned in the East-West direction it
should maintain the projected solar height over the day
between 5° and 10°. The drop in the longitudinal inci-
dence angle modifier is due to the shading caused by the
reflector edges. When 0°<θ
<30° the decrease in the
IAMl is apparent. This corresponds to partial shading on
the first cell placed at the edge of the backside receiver.
At around θl=30° the cell on the edge on the backside is
totally shaded, eliminating almost completely the pro-
duction of that string. Shading more cells when θl>30°
will not imply a further production decrease on that
string and thus, the total efficiency decrease slows down.
If there was no diode installed on the string the drop
would be double, since the strings are connected in series.
I.e. the total IAM would drop to about 0.5 and not just to
the 0.75 as seen in the figure. This is even more clearly
seen, if the numbers for the cells on the backside of the
absorber are studied. Here the value drops from 0.58 to
0.29, i.e. a 50% reduction. As can be seen from the same
Copyright © 2013 SciRes. ENG
figure the front side is less affected by the shading. The
IAMt shown in Figure 9 is in agreement with previous
measurements for the thermal production of a solar
thermal collector with the same geometry [2].
The PV/T hybrid collector is made of two different
parts. A front part where the solar cells behave like a flat
plate solar panel under no concentration and a back part
under concentration using a reflector. Since there is no
synergic effect from combining non-concentrating solar
cells with concentrating solar ones, only one of these
alternatives should be the most cost-effective way of
building a solar collector rather than a combination of
both. The choice between a concentrating or
non-concentrating system depends on the concentration
factor, the fraction of diffuse and beam irradiation in the
geographical location and the compactness needed for
the collector.
The reflector part of the collector concentrates the ra-
diation two times on the back side receiver. If the optical
efficiency is around 50%, meaning that, under optimum
conditions, the collector produces the same electrical
output as a flat plate solar panel for the same temperature.
This conclusion would change significantly, if the con-
centration factor were increased and the optical effi-
ciency maintained. Hence, the concentration factor has
an important influence on the output per cell area. One
way of increasing the concentration could be to reduce
the cell area on the backside of the receiver while using a
tracking system. This can be done by cutting the cells in
half or in thirds in the parallel direction of the busbars.
The effect of the radiation profile after reflection should
be further investigated.
As shown in Figure 8, a limitation of this study is the
reduced amount of measured data for the dependence of
efficiency on the temperature. Measurements were also
carried out with cheaper sensors in order to verify the
possibility of building low investment scientific solar
laboratories in developing countries. The overall accu-
racy of measurement with such sensors was lowered to
approximately 9%, but with a cost reduction of above
90% [5].
5. Conclusions
The optical properties of a PV/T CPC-collector were
determined. These include the electrical transverse and
longitudinal incidence angle modifiers, taking into ac-
count edge effects, by-pass diodes, acceptance angle and
diffuse radiation contribution. The measured electrical
efficiency at 25°C outlet water temperature was 20.9%
per cell area and 13.9% per active glazed area. Such effi-
ciencies occur during peak hours. During a large period
of the day the output is significantly reduced by the re-
flector edges as shown by the IAM-measurements. This
represents a big margin of improvement for the collector.
By removing the cells on the edge, turning the edge cells
90°, dividing the string into three or four parts and track-
ing the collector around an axis oriented in the North-
South direction, the collector performance can be sig-
nificantly improved and is now under study. Hence, the
annual production can become competitive with a flat
plate solar panel while, at the same time, producing hot
6. Acknowledgements
The authors are grateful to the Swedish International
Development Cooperation Agency for sponsoring the
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"Performance Evaluation of Low Concentrating Photo-
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[4] S. Wenham, M. Green, M. Watt, R. Corkish, "Applied
Photovoltaics", 2
nd edition, Earthscan, London, 2007,
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Copyright © 2013 SciRes. ENG
Pel Hybrid electric power (W)
Pel_front Hybrid electric power from front side receiver (W)
Pel_back Hybrid electric power from backside receiver (W)
Pel_back_beam Hybrid electric power from backside receiver due to beam radiation (W)
Pel_back_diff Hybrid electric power from backside receiver due to diffuse radiation
Gtotal Total irradiance (W/m²)
Gb Beam Irradiance (W/m²)
Gd Diffuse Irradiance (W/m²)
Tin Inlet water temperature (°C)
Tout Outlet water temperature (°C)
Tmid Middle water temperaure (°C)
Acells_front Cell area of the front side receiver (m²)
Acells_back Cell area of the backside receiver (m²)
β Collector tilt from horizontal (°)
f Useful fraction of diffuse radiation ) -(
τ Transmittance coefficient of glass (-)
r Reflectance coefficient of the reflector (-)
w Total width of the cells (m2)
h Height of the reflector (m2)
C Concentration factor of the collector (-)
ηcells_(25°C) Cell efficiency at 25°C (-)
ηopt Optical efficiency (-)
KT Electrical efficiency temperature dependence (%/ °C)
θ Angle of incidence onto collector (°)
θt Transverse angle of incidence onto collector (°)
θl Longitudinal angle of incidence onto collector (°)
IAMl Electrical longitudinal incidence angle modifier (-)
IAMt Electrical transverse incidence angle modifier (-)