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International Journal of Solar Energy
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Bifacial Photovoltaic Panels with Sun Tracking
a
M. A. EGIDO & E. LORENZO
a
a
Institute de Energía Solar, E.T.S.I, de Telecomunicatión, Ciudad Universitaria , Madrid,
28040, Spain
Published online: 03 Apr 2007.
To cite this article: M. A. EGIDO & E. LORENZO (1986) Bifacial Photovoltaic Panels with Sun Tracking, International Journal of
Solar Energy, 4:2, 97-107, DOI: 10.1080/01425918608909842
To link to this article: http://dx.doi.org/10.1080/01425918608909842
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Int. I. Solar Energy, 1986, Vol. 4 , pp. 97-107
0142-5919/86/0402-0097$12.00/0
0 1986 Harwood Academic Publishers GmbH
Printed in the United Kingdom
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Bifacial Photovoltaic Panels with
Sun Tracking
M. A. EGlDO and E. LORENZO
lnstituto de Energfa Solar, E . T.S.I. de Telecomunicac;6n, Ciudad
Universitaria, 28040-Madrid, Spain
(Received November 25, 1985)
This paper analyzes the energy collected by bifacial photovoltaic panels that track
the sun. A theoretical model is described that calculates the collection of light by
both sides of a bifacial panel installed on a one- or two-axis tracker and placed
against a variety of surroundings. The model has been verified experimentally, and
then used to predict the annual energy collected at Madrid for a number of cases of
practical interest. The results for two-axis tracked bifacial panels show that annual
back energies of the order of 25% of the front energies can be obtained. This implies
that the total (front plus back) annual energy collected by such panels can be 80%
greater than that collected by a stationary monofacial panel, or some 30% greater
than that collected by a stationary bifacial one.
KEY WORDS: Bifacial, Photovoltaic, Panels, Sun tracking, Solar energy
I INTRODUCTION
The use of sun tracking has been widely studied as a means to
increase the energy collected by flat photovoltaic panels (I), (2).
Annual increases in collected energy as high as 40% have been
found when comparing with stationary panels.
An alternative approach to increasing the energy collected is to
use bifacial photovoltaic panels. These are composed of cells
capable of converting the light incident on both sides of the cell into
electricity, and are now manufactured industrially (3). Both sides of
such panels show a similar efficiency to that of conventional
monofacial panels. In order to increase the energy intercepted by
the back side of these panels, the surroundings (ground, walls, etc)
are generally painted white to enhance their reflectivity. In this way,
97
M. A. EGlDO AND E. LORENZO
98
for stationary panels, annual totals of energy collected by the back
sides of the up to 50% of that collected by the front sides have been
obtained (3).
This paper analyzes the conjunction of both the above ideas, that
is, bifacial panels that track the sun.
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II THEORETICAL MODEL
The model considers a flat receptor surface placed at a particular
geographic location and tracking the sun through one or two axes.
Both sides of this surface, depending on its orientation, can receive
light from the sky (the direct and diffuse) and light reflected by the
ground or surroundings (the albedo). Several authors (5), (6) have
developed mathematical models to calculate the radiation on the
front side of such a surface contributed by the direct and diffuse
radiation. Because of the low reflectivity of most natural ground
covers, these models commonly neglect the albedo. By contrast, the
model below calculates the radiation on both sides of the panel, and
gives special attention to the albedo contribution (as the reflectivity
of the surroundings of bifacial panels is generally enhanced, as
mentioned above), and to the shadowing of this albedo surface by
the .panel.
The panel surroundings are assumed to be "perfectly diffuse"
(or Lambertian) sources, in the sense that light supplied from any
direction t o an element of a surface of these surroundings is
re-emitted with an intensity proportional to the cosine of the angle
to the normal surface. Then, the power flux dER received by an
element, dSR, of the receptor surface coming from an element, dSE,
of the surroundings, where the latter emits a total energy EE, is
given by:
dER . dSR = ~ , / n i d SdQR
~ = E E / ndSE cos BE dQR
where
and i , r,
eE and
8, are defined in Figure 1. If we define
(1)
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BIFACIAL PHOTOVOLTAIC PANELS
FIGURE 1 Radiation transfer between two bodies. E is a diffuse source and R is a
black absorber.
then equation (1) can also be written as
dER = E E / n ' COS 8, ' d g E
If this equation is integrated we obtain:
The integral on the right of this equation represents the fraction
of the energy radiated from the whole source which reaches dSR. In
heat transfer text books, this is called the geometric configuration
factor or "view factor".
This factor can be conveniently obtained as follows: first, by
determining the region where the solid angle subtended by the
source from the point considered on the receptor plane intersects a
sphere of unit radius; and then by projecting this region into the
receptor plane. The area of the latter gives the view factor (7).
We now present the equations for the irradiances at the centre
points of the front and back collector surfaces. This is illustrated in
Figure 2, where, for simplicity, the surroundings are shown as a
horizontal surface.
where I*, Id and I, are the direct, diffuse and global irradiances on a
horizontal surface; p is the reflectivity of R (for further simplifica-
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M. A. EGIDO AND E. LORENZO
FIGURE 2 Sources of radiation for a receptor plane (P). The front side receives
energy proceeding from the sky (SF) and from the (horizontal) diffuse reflector
( R F ) . The posterior from SB and RE.
tion we assume p = O for the horizontal surface beyond the
whitened surface); 0, is the angle b ~ t w e e nthe vector of the position
of the sun and the vector normal to the collector surface and O2 is
the angle between the vector of the position of the sun and the
vector normal to the horizontal surface; FFSand FFR are the view
factors from the center point of the collector of the fractions of the
sky and the albedo surface as seen by the front of the collector; and
FBs,FERand Fs are the view factors from the collector center of the
fraction of the sky, the albedo surface and the shadow, as seen by
the back of the panel. Note that eqs. (7) and (8) assume that the sky
diffuse irradiance, Id, is isotropic.
The above equations were used in computer calculations to find
energy collected over a period of time. Firstly, for each hour of the
year, I, was obtained using the corresponding values of the global
horizontal data provided by the Instituto Nacional d e Meteorologia
(8) averaged over several years; and Ib and Id were found from the
Rabl and Collares Pereira correlations (9). Then B,, B,, FFs, FFRl
FBs, FERand Fs were calculated from the coordinates of the sun
BIFACIAL PHOTOVOLTAIC PANELS
101
position (10) and the type of the tracker assumed (i.e. one- or
two-axis). The hourly values were then summed to give energy
totals over time. For this, we assume that the irradiance is uniform
over the front and back surfaces of the panel.
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Ill EXPERIMENTAL MODEL VERIFICATION
The accuracy of the theoretical model was verified by constructing
small-scale physical models of three different tracking systems.
These tested two-axis, polar-axis and azimuth-axis tracking. Each
model used two 2 x 2cm photocells, one facing upward and one
facing downward, t o simulate the bifacial panel. The models were
tested outdoors over a period of several days. T o find the
irradiances that would be collected by both sides of a panel we
measured separately the short circuit currents of the corresponding
solar cells. To assure linearity, the models used low (0.3 Q .cm)
base resistivity silicon cells. In addition, we measured total irradiance on a horizontal surface, and direct irradiance normal to the
sun. The latter values were then input to the theoretical model to
derive calculated values for front and back irradiances. The
1.4
I--
-
CALCULATED VALUES
EXPERIMENTAL VALUES
FIGURE 3 Energy collected by a polar-axis tracking system. Points show values
measured with the scale models, and the solid line represents calculated values.
1M
M. A. EGIDO AND E. LORENZO
difference between the calculated values and the measured ones
was, in the worst case, less than 8%, while in the majority of the
cases the differences were less than 5%. As can be seen in Figure 3,
there is a good agreement between the theoretical model and the
experimental results.
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IV CALCULATION AND RESULTS
Once the accuracy of the theoretical model had been confirmed, we
then used it to analyse the advantages of the conjunction of bifacial
panels with trackers, and to find the optimal dimensions of such
systems that maximize energy collection, bearing in mind that the
resulting structures should be practical.
FIGURE 4 Energy collected by a two-axis tracking bifacial panel placed over a
horizontal infinite reflector, as a function of the distance to the center of the panel.
(The dimension of one side of the square panel is taken as unity). The ratio
E&,,IEFR,,
is given with reference t o the scale on the right side of the graph.
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BIFACIAL PHOTOVOLTAIC PANELS
103
The hourly and annual energies collected by both sides of a oneor two-axis perfectly tracked bifacial panel placed above a whitened
reflector area were calculated for the location of Madrid. Optimization was carried out by varying the distance between panel and
reflector; the size of the reflector; and the aspect ratio of the panel
(where the latter is defined as the relation between its length and
width).
In spite of the generality of our model, we limited our investigations to include only horizontal diffuse reflectors, (as a previous
exploration clearly showed that this case is likely to be the most
practical), and by considering only rectangular reflectors. We used
p = 0.8 to correspond to commonly available white paints.
Figure 4 shows the annual front and back energies, EF and EB,
corresponding to a two-axis tracked square panel placed above an
infinite reflector, as a function of the distance h from the center of
FIGURE 5 Annual energy collected by a two-axis tracking bifacial panel over a
horizontal square reflector, as a function of the area of the reflector normalized to
the panel area.
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104
M. A. EGIDO AND E. LORENZO
the panel to the reflector. Clearly, the maximum back energy
E,,that can be obtained in general corresponds to h = m. In this
case, the ratio EBMAx/EFmx= 0.47, and the portion of EF
resulting from the albedo component (corresponding to the third
term of equation (7)) is 12%. It is interesting to note that the E,
becomes asymptotic at relatively low values of h, which indicates
that it is possible to achieve in practical situations results that are
not too far removed from the above maximum. For example at
h ~ 0 . 7 EB/EBMAX
,
= 0.81.
As a further step in looking for a practical case, Figure 5 shows
EF and EB corresponding to h = 0.7, versus C (the ratio of the
reflector area divided by the collector area). Again, practical values
of C permit results that are relatively close to the maximum possible
value. Sp'ecifically, we found that E B / E B M , = 0.62 for C = 16.
The results improve when the aspect ratio R, of the collector
increases. As an example we analysed the case where R, = 2 and
FIGURE 6 Monthly energy collected by four different systems: 1) Two-axis
tracking with bifacial panel; 2) Polar-axis tracking with bifacial panel; 3) Stationary
bifacial panel tilted at an angle equal to latitude minus lP and 4) Stationary panel
tilted at the latitude angle.
105
BIFACIAL PHOTOVOLTAIC PANELS
C = 16. The optimum solution is that defined by h =0.5, when
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EB/EB,,, = 0.69 is obtained.
In order to compare with static monofacial panels we show in
Figure 6 the monthly values calculated over the year of the total
(front plus back) energy collected by the two-axis tracking bifacial
panel, by a stationary monofacial panel, by a stationary bifacial
panel and by a polar-axis tracking bifacial panel. Note that the
calculations for bifacial panels assume the presence of the horizontal whitened reflector surface, and that this surface is assumed
absent for the monofacial cases. The figure shows the energy gain of
the bifacial two-axis tracking combination. It is evident that this
configuration is more effective for situations with a greater consumption in summer; for example, irrigation. We also represent in
Figure 6 the values corresponding to a bifacial one-axis polar
tracking combination. It can be seen that the total annual energy
collected by the latter configuration is only 7% lower than the
corresponding two-axis case.
Figure 7 presents in more detail the comparison of the monthly
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FIGURE 7 Ratios of monthly energy collected by three different systems: (1) Ratio
of two-axis tracking bifacial panel to a stationary monofacial panel. (2) Ratio of a
two-axis tracking bifacial panel to a stationary bifacial panel. Curves l(a), (b) and (c)
show components of Curve (I), as described in the text.
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106
M. A. EGIDO AND E. LORENZO
energy collected by a tracking bifacial panel (at the optimal tilt for
year-total collection), and a fixed monfacial panel tilted at the
latitude angle. The dotted lines show the components that sum to
the total for the two-axis tracked bifacial case. These components
are the energy collected by: (la) a two-axis tracked monofacial
panel (without reflector surface); (lb) the back surface of the
bifacial panel (with reflector surface); (lc) the contribution to front
surface energy of a two-axis tracked monofacial panel due to the
reflector surface.
V CONCLUSIONS
A theoretical model for the collection of irradiance by a bifacial
photovoltaic panel tracking the sun is presented. The accuracy of
this model has been demonstrated by comparison with experiments
using small-scale physical models.
The total annual energy collected by combining the use of bifacial
panels with two-axis tracking is 80% higher than that corresponding
to a stationary monofacial panel.' With only one axis tracking,
nearly similar energy increases are obtained. In our opinion, these
results indicate the interest of the approaches examined.
Acknowledgement
The authors want to thank Roger Bentley for style correction and for helpful
suggestions in planning this paper.
References
-
D. M. Mosher. The Advantages of Sun Trackinn for Planar Silicon Solar Cells.
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