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Bifacial Photovoltaic Panels with Sun TrackingM. A. EGIDO a & E. LORENZO aa Institute de Energa Solar, E.T.S.I, de Telecomunicatin, Ciudad Universitaria, Madrid,28040, SpainVersion of record first published: 03 Apr 2007.

To cite this article: M. A. EGIDO & E. LORENZO (1986): Bifacial Photovoltaic Panels with Sun Tracking, International Journal ofSolar Energy, 4:2, 97-107

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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

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,

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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.

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 to 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 S ~ dQR = E E / n dSE cos BE dQR (1) where

and i , r, eE and 8, are defined in Figure 1. If we define

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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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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~ tween the 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; FFS and 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, FER and 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 de 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, FER and Fs were calculated from the coordinates of the sun

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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.

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, to 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 ir- radiance 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

I---- - CALCULATED VALUES 1.4 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.

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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.

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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The hourly and annual energies collected by both sides of a one- or two-axis perfectly tracked bifacial panel placed above a whitened reflector area were calculated for the location of Madrid. Optimiza- tion 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 investiga- tions 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 EB/EBM, = 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.

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BIFACIAL PHOTOVOLTAIC PANELS 105

C = 16. The optimum solution is that defined by h =0.5, when 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 horizon- tal 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 con- sumption 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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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. Solar Energy W, 91-97 (1973. - G. W. Rhodes el al . , The ARC0 One-Megawatt Photovoltaic Power Plant. 5th Photovoltaic Solar Enerev Conference. Athens. 1983. G. Sala er PI., Albedo &llecting ~hotovoltaic~ower Plant. 5th EC Photovol- taic Solar Energy Conference. Athens, 1983. A. Cuevas et al., 50 Per Cent More Output Power From an Albedo-Collecting Flat Panel Using Bifacial Solar Cells. Solar Energy, 29, 419-420 (1982). S. A. Klein. Calculation of Monthly Average Insolation on Tilted Surfaces. Solar Energy 19, 325-329 (1977). T. M. Klutcher, Evaluation of Models to Predict Insolation on Tilted Surfaces. Solar Energy 23, 111-114 (1979).

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7. G. H. Derrick, A Three-Dimensional Analogue of the Hottel String Constmc- tion for Radiation Transfer. Oprica Acra 32, 39-60 (1985).

8. Instituto Nacional de Meteorologia, Radicai6n Solar en Espafia. Ministerio de Transportes, Turisrno y Comunicaciones, D-44 (1984).

9. M. Collares-Pereira and Ari Rabl, The Average Distribution of Solar Radiation-Correlations Between Diffuse and Hemispherical and Between Daily and Hourly Insolation Values. Solar Energy 22, 155-164 (1979).

10. R. Walraven, Calculating the Position of the Sun. Solar Energy 20, 393-397 (1978).

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