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Renewable Energy 63 (2014) 415e425

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Renewable Energy

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Technical note

Design and evaluation of passive concentrator and reflector systemsfor bifacial solar panel on a highly cloudy region e A case studyin Malaysia

Yun Seng Lim*, Chin Kim Lo, Shin Yiing Kee, Hong Tat Ewe, Abd Rahman FaidzFaculty of Engineering and Science, Universiti Tunku Abdul Rahman, Jalan Genting Klang, 53300 Kuala Lumpur, Malaysia

a r t i c l e i n f o

Article history:Received 9 April 2013Accepted 1 October 2013Available online

Keywords:Bi-facial solar cellPassive concentrator systemPassive reflector systemLight scatterer

* Corresponding author.E-mail addresses: yslim@utar.edu.my (Y.S. Lim), uk

nicolekee88@hotmail.com (S.Y. Kee), eweht@utar.utar.edu.my (A.R. Faidz).

0960-1481/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.renene.2013.10.008

a b s t r a c t

Photovoltaic (PV) systems are the most promising renewable energy source in Malaysia because it is atropical country receiving a huge amount of solar irradiation every year. However, Malaysia is surroundedby South China Sea and Malacca Straits. The vapour from the sea water with the blow of seasonal windscauses a large amount of clouds passing over the country, hence creating the variation in the direct anddiffused sunlight throughout a day. The performance of the concentrators and reflectors for bifacial solarcells under the variation of direct and diffused sunlight has not been studied thoroughly. Therefore, severalconcentrators and reflectors havebeendesigned, constructed andplacedunder a speciallydesignedbifacialsolar panel. The setup of each concentrator and reflector is as follows; scattering particles (scatterers)sprinkled across the plane mirror under the solar panel, an array of adjustable small plane mirrors placedunderneath the solar panel, and long triangular prisms in between solar cells with a plane mirror under-neath. Another solar panel is constructed and placed on top of the planemirror as a reference. Each setup ofthe concentrators or reflectors is evaluated bymeasuring the power output of the tested and the referencepanels together throughout a day under the sun. Empirical approaches are developed to compensate foruncontrollable factors including solar cell manufacturingmismatch and unequal degradation between thetested and the reference solar panels. A few potentially working static concentrator and reflector systemsare identified based on the experimental results. An assessment is carried out to show the economicviability of the proposed setups with respect to that of the mono-crystalline solar cells.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Photovoltaic (PV) system is a promising renewable energysource on the equatorial regions due to the substantial amount ofsolar irradiation available across the regions. However, a few of theequatorial countries are surrounded by the seas where a largeamount of cloud is generated and moved to the mainland by theblow of the seasonal wind. Malaysia is one of the examples. Fig. 1shows the frequency of completely clear sky occurrences acrossthe globe [1]. It is shown that Malaysia does not have a single daywith a completely clear sky. With a large amount of clouds passingover the country, there is a variation in direct and diffused sunlightthroughout a day.

wn.cklo@gmail.com (C.K. Lo),edu.my (H.T. Ewe), faidz@

All rights reserved.

Bifacial solar cells are able to convert light into electricity withboth its front and rear sides. Their direct application is albedocollection of the Earth surface, clouds and the atmosphere: boththeir front and rear surfaces can capture direct sunlight as well asdiffused sunlight from the environment with the use of an appro-priate concentrator or reflector [2]. There are several static or non-tracking concentrators and reflectors being developed and tested,such as triangular central prism [3], equilateral triangular prismabove or below solar cells [4], RXI concentratoredielectric rodconcentrator encapsulating the solar cells [5e7], tilted groovesdielectric reflector below the solar cells [8], cylindrical reflector[4,9,10], spherical reflector [11], parabolic trough concentrator [4,7],“sea shell” collector [7,12], combined prismatic-parabola-cylindrical stationary concentrators [13], semi-transparentreflector [14], diffuse reflector [14e16], and mirror [16,17]. Theperformance of those concentrators and reflectors was mostlyevaluated in term of actual power output increase under a solarsimulator or under the sun at a specific time. However, a concen-trator system that improves much on the bifacial solar cells at aspecific time does not always improve that much at other time. This

Fig. 1. Frequency of completely clear sky occurrence across the globe (%).

Table 1Rating of an Earth-On bifacial solar cell.

Short circuitcurrent (A)

Open circuitvoltage (V)

Maximumpower (W)

Fill factor Efficiency (%)

Earth-On e 188 8.94 0.638 4.49 0.787 18.8

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phenomenon is particularly obvious on a highly clouded regionwhere the available direct and diffused sunlight can vary substan-tially throughout a day due to a large number of passing clouds overthe solar concentrator. Therefore, it is necessary to evaluate theconcentrator or reflector systems under the sun over a period oftime for accurate assessment.

The authors in [18] proposed to use mono-crystalline solar cellsto make bifacial solar cells with coloured diffuse reflector as aconcentrator. However, the mono-facial solar cells cannot be usedto represent the actual performance of the bifacial solar panel asthe uniformity of illumination on the rear sidewill affect the overallpower output of the bifacial solar panel. Comparison using themathematical model on the energy generation as described in [15]is not convincing enough because there are too many environ-mental factors to be accounted for. Factors such as connectorresistance loss, solar cell mismatch and partial shading on the rearside can reduce the performance of a real bifacial solar panel.

In this researchwork, several concentrator and reflector systemsare developed and integrated with a bifacial solar panel. The bifa-cial solar cells are the commercially available ones. The perfor-mance of each concentrator or reflector system is evaluated underthe sun over several weeks in Malaysia. The setups of the concen-trator and reflector systems are summarized as follows:-

1. Scattering particles (scatterers) sprinkled across the planemirror with the solar panel above.

2. An array of adjustable small plane mirrors placed under the bi-facial solar panel.

3. Long triangular prisms placed in between solar cells with aplane mirror underneath.

The solar panel with the concentrator or reflector is regarded asa tested panel. It is placed side by side with another bi-facial solarpanel being used as a reference with a plane mirror placed un-derneath. The power outputs of these two panels are measured byan IV plotter under the sunlight throughout several weeks for each

type of the concentrator and reflector systems. The energy outputof the tested panel per day is then determined and compared withthat of the reference panel in order to determine the increase in theenergy output contributed by each concentrator and reflector sys-tem. Empirical approaches are developed to compensate for un-controllable factors including solar cell manufacturing mismatchand unequal degradation between the tested and the referencesolar panels.

Through these experiments, it is able to identify the feasible,simple and cheap static concentrator or reflector system that canincrease the bifacial solar cells efficiency under the variation ofdirect and diffused sunlight. This paper describes the details of theresearch work and the experimental results. It begins with themethodology, followed by results and finally the conclusion.

2. Methodology

TheEarth-Onbifacial solar cell [19] isused inthisexperiment. Eachsolar cell has a dimension of 15.6 cm� 15.6 cm, rated 4.49Woutputpower, 0.79fill factorand18.8%efficiencyat the frontsideas tabulatedin Table 1. Both sides of the solar cell have similar appearance but therear side efficiency is slightly lower than the front side’s.

A bifacial solar panel comprises 6 bifacial solar cells which aresoldered in series on a transparent acrylic plate with a distance of13.5 cm between solar cells, then covered by a thin plastic film to fixtheir positions, and finally covered by another transparent acrylicplate on top as shown in Fig. 2. In the experiment, two bifacial solarpanels were put side-by-side, lifted up a distance of 10 cm from twoplane mirrors. One of the bifacial solar panels was used as a tested

Y.S. Lim et al. / Renewable Energy 63 (2014) 415e425 417

panel because it is used to evaluate the performance of theconcentrator and reflector systems. Another was used as thereference solar panel because the measurement results from testedsolar panel can be compared to the reference solar panel.

The output terminals of the solar panels are connected to an IVplotter which is able to determine IV curve of the solar panels every1e2 min. The peak power outputs of the two solar panels can bedetermined every 1e2 min.

2.1. Solar panels quality monitoring

Solar panel quality was evaluated based on its fill factor at ratedshort circuit current of 9 A. A graph of fill factor versus short circuitcurrent was plotted and curve-fitted with a 2� polynomial which fitall the curves with R2 as 0.78 to 0.99. An example of the methodwith curve fitting result in one of the measurements is shown inAppendix A. The fill factor at 9 A short circuit current was found byevaluating the polynomial with current of 9 A. Finally, a graph ofthe fill factors for all measurements arranged by the measurementdate was plotted. Significant drop in fill factor was identified fromthe graph; Measurements after the drop were treated as a new setof measurement and compensated for mismatch using mismatchfunction with different coefficients.

2.2. Mismatch compensation

Although two identical solar panels are set up under the samesunlight and environment conditions, the power outputs from thetwo panels are not exactly the same. There is a mismatch betweentwo sets of measurement results. Performance mismatch betweenthe two panels is due to manufacturing tolerance. To determine thecontribution of the concentrator or reflector system to the output of

Fig. 2. Bifacial solar panels: (1) Reference solar panel and tested solar panel with identical sexperiment setup with scatterers on the tested solar panel.

the solar panel, it is necessary to compensate every measurementmismatch with the appropriate value under the same solar panelquality. Therefore, a mismatch compensation function is used andits coefficients are determined from the mismatch in the mea-surements. This compensation function is applied to compensatethe experimental mismatch such that the power outputs of the twosolar panels are the same throughout the testing period under thesame solar panel quality. If the quality of the solar panel is changed,then a new compensation function has to be determined. The de-tails of the mismatch compensation are given in Appendix B.

The quality of the solar panel quality is changed when the per-formance of the solar panel degrades resulting in the reduced poweroutput and lowfill factor. Following are a fewknown reasons that canbe associatedwith the degradation of solar panels in this experiment:increase in series resistive loss due to degradation of solder joint be-tween solar cells and copper ribbons [20,21]; ingress ofmoisture intothe solar panels due to improper encapsulation [22,23].

2.3. Evaluation of measurement uncertainty after mismatchcompensation

Following the compensation of the mismatch as describedabove, the measurement results from the solar panels with theidentical setups contain a small amount of uncertainty. This un-certainty exists in the results even before the concentrator andreflector systems are incorporated into the tested panel. If theconcentrator or reflector system is used and the increase in theenergy output stays within the uncertainty, then the contributionof the concentrator system is negligible. This uncertainty is due toseveral uncontrollable factors such as the ambient temperature,humidity and the non-uniform distribution of solar irradianceacross the solar cells. The uncertainty of the experimental results

etup e only a plane mirror is below each solar panel; (2) Simplified illustration of the

Y.S. Lim et al. / Renewable Energy 63 (2014) 415e425418

has to be determined before evaluating the performance of theconcentrator or reflector system. The measurement uncertainty isdefined as the 95% prediction interval for a single future value of %Edif(m). The details of the calculation of 95% prediction interval aredescribed in the book of [24].

2.4. Measurement of performance increase with scatterers on themirror

Six different types of scatterers as shown in Fig. 3 are sprinkledacross the plane mirror placed under the tested solar panel:transparent glitter powder, silver glitter powder, rhinestone,reflective bead, thumb tack, and luminescent solar concentrator. Allscatterers are scattered on the mirror region not being shaded bythe solar cells as shown in Fig. 1 except luminescent solarconcentrator, which is put in the shaded area under the solar cells.However, it is unlikely to identify a region not being shaded by thesolar cells at all times because the direction of the incident sunlightvaries with time and season. Therefore, the scatterers can only beplaced on themirror regionswhere they are not shaded by the solarcells most of the time. These regions happen to be the non-shadedregions on the mirror when the sun is right above the solar cells.

The luminescent solar concentrator (LSC) is made by polymethylmethacrylate, a transparent polymer commonly known as acrylic,and rhodamine 6G, an organic luminescent dye, using cell cast

Fig. 3. Different types of scatterers in the measurement: (1) Transparent glitter powderLuminescent solar concentrator (LSC) plate.

method, where the monomer is polymerized in a water bath insidethe mould that is made of 2 pieces of thick polished glasses sepa-rated by a gasket. The details and performance of LSC are availablein the publications of [25] and [26].

2.5. Measurement of performance increase with the plane mirrorreplaced by adjustable small mirrors and car foldable silver reflector

Measurements are also carried out by replacing the planemirrorwith: 1) adjustable small mirrors tuned to focus direct sunlight tothe 6 cells during solar noon; and 2) car foldable silver reflector asshown in Fig. 4. Another measurement was made with transparentglitter powder dispersed on the adjustable small mirrors.

2.6. Measurement of performance increase by using long triangularprisms to “bend” the light via refraction

Long triangular prisms are also used to change the light direc-tion so that it enters the rear surface of the solar cells. The prismsare cut from transparent acrylic sheet (Polymethyl methacrylate)with 20 cm thickness, so that their edge surfaces form 45� withtheir bottom surfaces. Two experiments are carried out. The firstexperiment is to put the prisms right below the solar cells at theiredges. The second one is to put the prisms in between the acrylicsheets as shown in Fig. 5.

; (2) Silver glitter powder; (3) Rhinestone; (4) Reflective bead; (5) Thumb tack; (6)

Y.S. Lim et al. / Renewable Energy 63 (2014) 415e425 419

2.7. Measurement of performance improvement contributed by therear side

Plywood painted in black colour is put right below the referencesolar panel so that only the front sides of the solar cells are illu-minated, while only mirror is put under the tested solar panel tomeasure the performance increase contributed by the rear side thatis illuminated by the reflected sunlight from the plane mirror.

3. Results

3.1. Quality of solar panels over time

Fig. 6 shows the solar panel quality throughout the experimenttime period expressed in term of fill factor at rated 9 A short-circuitcurrent. Measurements from the two solar panels with identicalsetup are labelled in the figure. The mismatch compensationfunction f%Pmis(1) with its coefficient calculated from Mismatch1 isused to compensate the first 14 measurements when the testedsolar panel has higher fill factor than the reference solar panel. Thesecond compensation function f%Pmis(2) calculated from Mismatch2is used for the remaining measurements when the tested solarpanel has lower fill factor than the reference solar panel. Thecompensation of the mismatch has to be carried out before themeasurement uncertainty is determined.

3.2. Calculating measurement uncertainty after mismatchcompensation

After the power mismatch is compensated, the energy (kWh)from each solar panel can be calculated from the power profile ofthe solar panel. It is noticed that the energy of one panel is slightlydifferent from that of another panel even though the setups of thetwo solar panels are identical. The differences are shown in Fig. 7and labelled as %Edif(m) for measurements with identical setup

Fig. 4. (1) Adjustable small mirrors; (2) Car foldable silver refle

labelled as “Differencem”wherem is the time of measurement. It isshown that the uncertainties show no sign of monotonous increaseor decrease over time. This means that the uncontrollable factorsaffecting the panels are not biased, or acting more on one panelthan another.

The values of %Edif(m) are treated statistically as a set of randomvariables. The measurement uncertainty is defined as the 95%prediction interval for a single future value of %Edif(m). Therefore,the 95% prediction interval for the 17 values of %Edif(m) is calculatedas described [24]. Giving that the sample mean is 0.07%, the 95%prediction interval is calculated to be from �2.68% to 2.83%.Therefore, the uncertainty is chosen to be �2.83%.

3.3. Performance improved by using scatterers, adjustable mirrors,car foldable silver reflector, and prisms

Fig. 8 shows the contribution of various concentrator andreflector systems to the energy produced by the tested solar panelas compared to that of the reference panel. Energy generated by thesolar panel has been significantly increased by: 8.6% � 2.83% whenan array of adjustable mirrors is used under the panel; 7.1%� 2.83%when prisms are put between acrylic sheets; 4.2% � 2.83% whenadjustable mirrors are used together with transparent glitterpowder. However, it is decreased by 3.1% � 2.83% when lumines-cent solar concentrator plate is placed under the panel. In othercases, the changes are below themeasurement uncertainty of 2.83%and hence no conclusion can be made.

Figs. 9 and 10 show the power output profile for the 2 cases withsignificant increase in energy generation. Comparing the poweroutput profile of the reference solar panel with the plane mirrorand without prism: The power increases the most in solar noon butreduces in the morning and afternoonwhen adjustable mirrors areused. The power increase does not change with time when prismsare put between acrylic sheets.

ctor. (3) Experiment setup with adjustable small mirrors.

Fig. 5. Experiment setup with prisms: (1) Picture of a transparent prism at its end; (2) Simplified illustration of the experiment setup with prisms under acrylic sheet; (3) withprism between acrylic sheets.

Fig. 6. Graph of fill factor at 9 A short-circuit current for both solar panels in allmeasurements.

Fig. 7. Difference in energy generation (kWh) by solar panels with identical setup aftercompensating for mismatch in all mismatch measurements.

Y.S. Lim et al. / Renewable Energy 63 (2014) 415e425420

Fig. 8. Percentage of energy generation increase in kWh for measurements with: allscatterers, adjustable mirrors with and without transparent glitter powder as scatterer,car foldable silver reflector, and prisms. Green lines represents the measurement un-certainty. (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)

Fig. 10. (A) Power (W) and energy (kWh) output from tested solar panel with prismsbetween acrylic sheets and the reference panel; Fig. 10(B) Power increase percentage.

Y.S. Lim et al. / Renewable Energy 63 (2014) 415e425 421

3.4. Estimating the improvement in bifacial solar panel by theconcentrator and reflector systems as compared to the mono-facialsolar panel

The amount of energy produced by the tested solar panel with aplane mirror underneath is about 38.1% � 2.83% higher than that ofthe reference solar panel with its rear side being covered by theblack plywood. This result indicates that if the bifacial solar panelsare used instead of the mono-facial solar panels, there will beadditional energy of 38.1%� 2.83% to be produced. The mono-facialsolar cells are represented by the bifacial solar cells with their rearsides covered by the black plywood. This extra amount of energycan make the bifacial solar panels as an attractive option for thephotovoltaic users. The energy can be further increased if the arrayof adjustable mirrors is used to replace the plane mirror or severallong triangular prisms are placed in between solar cells above theplanemirror. This extra amount of energy can be estimatedwithoutundertaking any extra experimental measurements.

The additional energy output from bifacial solar panel will bedifferent from day to day when the trajectory of the sun changes.Fig.11(A) shows the trajectory of the sun inMalaysia. Fig.11(B) showsthe daily changes in the solar zenith angle in solar noon over a year,

Fig. 9. (A) Power (W) and energy (kWh) output from tested solar panel with adjust-able mirrors and the reference panel; Fig. 9(B) Power increase percentage.

which are calculated using PSA Algorithm [27]. Generally, the bifacialsolar panel with the plane mirror underneath generates relativelyhigh power at large solar zenith angle because the sunlight can arriveat the mirror with minimum blockage by the solar cells. Hence, therear sides of the solar cells can capture relatively high reflected sun-lightenergy. Since it is too timeconsuming to conduct theexperimentthroughout a year for each case, the experiment in this paper isconducted inaperiodwith themaximumsolar zenith angleof 12.06�,as labelled inFig.11(B). It isexpected that theadditional energyoutputfrom the bifacial solar panel should be higher than the measuredvalue of 38.1% � 2.83% because the solar zenith angle is larger than12.06� at most of the time throughout the year.

From Subsection 3.3, it is noticed that the increase in the energygenerated by the tested panel by using adjustable mirrors and theprisms are about 8.6% � 2.83% and 7.1% � 2.83%, respectively, ascompared to the reference panel. If the increases are added to38.1% � 2.83%, then the total increase in energy contributed by theconcentrator and reflector systems with respect to the mono-facialsolar panel are determined as shown in Fig. 12.

It is noticed that the maximum contribution to the energygeneration is achieved by using the array of adjustable mirrors andthen followed by the prisms. These increases in the energy gener-ation can be an attractive selling point of the bi-facial solar panelsas opposed to the mono-facial solar panels.

3.5. Comparison of the unit costs of solar electricity from varioussolar systems

An assessment is carried out to identify how the increase in theperformance of bifacial solar cells can bring down the cost of itselectricity (kWh) making this technology a potential candidate incomparison with other commonly used solar cells such as mono-crystalline solar cells in Malaysia.

The Earth-On bifacial solar cells are manufactured in Japan [19].The unit price of the bifacial solar cell with the peak power of4.49Wp from its front surface is United States Dollar (USD) 2.00/Wp

or Malaysian Ringgit (RM) 6.10/Wp based on the currency exchangeof RM 3.05/USD. Therefore, the retail price of a bifacial solar cell isUSD 8.98 or RM 27.40 per piece. According to information pub-lished in Refs. [28], the most recent retail price of the mono-crystalline solar panel in Malaysia is USD 3.27/Wp or RM 10.00/Wp.

The retail price of themono-crystalline solar panel inMalaysia ishigher than that of a bi-facial solar cell. This is because it is the

Fig. 11. (A) Illustration of solar zenith angle in solar noon; (B) The solar zenith angle at the measurement site.

Y.S. Lim et al. / Renewable Energy 63 (2014) 415e425422

panel price encompassing the labour, lamination and framing costs.Since the bifacial solar panels have not been widely used inMalaysia, the retail price of the bifacial solar panel is not availablelocally. Therefore, the retail price of a bifacial solar cell is used inthis calculation. However, it is important to highlight that theequipment used to manufacture the bifacial solar cells is the sameas that of the mono-crystalline solar cells. The main differences arethat the aluminium back surface field layer is replaced by a boronback surface field and a silicon nitride layer is used on the back sideof the bifacial cells. Therefore, the production cost of the bifacialsolar cells is similar to that of the mono-crystalline solar cells [29].To make a fair comparison, the price of a mono-crystalline solar cellused in the calculation is RM 6.10/Wp which is the same as that of abifacial solar cell without considering the costs of accessories.

In this assessment, the costs per unit of the solar electricity (RM/kWh) generated by 1 kWmono-crystalline solar cells are calculated,taking into account the lifespan and average yield of the mono-crystalline solar cells per year. It is assumed that the yearly yield of1 kW mono-crystalline solar cells in Malaysia is 1100 kWh onaverage [30]. The lifespan of the mono-crystalline is 25 yearsrespectively [25]. Therefore, the unit cost of the solar electricity from1 kW mono-crystalline is RM 0.222/kWh. The unit cost of the solarelectricity (RM/kWh) from the bifacial solar cells under a particularconcentrator system is determined depending on the number ofsolar cells required to generate 1100 kWh per year, the cost of theconcentrator system as well as the lifespan of the bifacial solar cells.

Table 2 shows the unit costs of the solar electricity by the mono-crystalline and the bifacial solar cells with the specified concen-trator and reflector systems. It is noticed that the costs of inverters,

Fig. 12. Percentage increase in energy generation of bifacial solar panel with theconcentrator and reflector systems with respect to the mono-facial solar panel.

cables, connectors and other accessories required for the solarsystems are not included into the unit costs of the solar electricity.This is because these costs are the same for all the 4 solar systems.The comparison of the unit costs of the solar electricity from the 4solar systems is not affected by the costs that are the same acrossthe systems.

It is shown that the bifacial solar cells with the plane mirrorsgenerate the cheapest electricity at the unit price of RM 0.188 perkWh. This is because, by using the plane mirrors to increase theannual energy yield, the total number of the solar cells required toproduce 1100 kWh has been reduced from 220 to 160. Thetremendous saving in the solar cells is higher than the investmenton the additional mirrors, hence making the unit cost of electricityto be the lowest. The solar panel with the prisms produces thesecond cheapest electricity at unit price of RM 0.208 per kWh. Thisis because the long triangular prisms are made of polymer and notexpensive. Also, the number of the solar cells required is reducedfrom 160 to 153. As a result, the unit cost of the solar electricitybecomes the second lowest.

Table 3 shows the sizes of the mono-crystalline and bifacialsolar cells with the specified concentrator and reflector systems.The total size of the bifacial solar panel is 40%e53% largerthan that of mono-crystalline solar panel. However, the dimen-sion in the bifacial solar panel design in this experiment is notoptimized for its cost and performance. Further simulation andverification work is required to optimize the design of the bifacialsolar panel.

4. Conclusion

The results of the experiments are relevant because the studytakes into account the daily change of the sun direction, the fluc-tuating intensity of sunlight due to the passing cloud and otherfactors such as ambient temperature and humidity.

The reference and tested solar panels are put side by sidethroughout the experiments to ensure that the two panels areexposed to the same sunlight conditions: sunlight with the samedirection and intensity. The mismatch between the results of thetwo panels is due to the manufacturing tolerance of the solar cells.The empirical approach used to compensate for the mismatch be-tween the two sets of results has been satisfactory to serve thepurpose without the need of gathering extra information such assolar cells temperature or solar irradiance. After compensating forthe mismatch, the difference between the results of the twoidentical solar panels is defined as the uncertainty which is due toother reversible factors such as temperature and humidity. Themeasurement uncertainty is then determined from the 95% pre-diction interval of the differences [24]. Besides, the fill factors of the

Table 2Solar electricity costs from mono-crystalline and bi-facial solar cells with concen-trator and reflector systems.

Mono-crystallinesolar cellsfrom Japan

Bi-facialsolar cellswith planemirror

Bi-facialsolar cellswith adjustablemirrors

Bi-facialsolar cellswith prisms

Yearly yield (kWh/kW) 1100 1100 1100 1100Price of solar cells (RM) 6100.00a 4382.24b 4163.13c 4190.52d

Cost of concentratorand >reflectorsystems for 1 kW ofsolar cells (RM)

0.00 810.00e 5200.00f 1550.00g

Total cost of solarsystemh (RM)

6100.00 4592.24 9363.13 5740.52

Unit cost of solarelectricityi (RM/kWh)

0.222j 0.188k 0.340 0.208

a The price (RM/kW) ¼ Price of solar cells (RM/Wp) � 1000. The latest retail priceof a mono-crystalline solar cell is RM 6.10/Wp.

b This price (RM/kW) ¼ Number of bifacial solar cells � Cost of each solar cell(USD/piece)*Exchange rate (RM/USD). Notice that 160 pieces of bifacial solar cellsare required to produce 1100 kWh per year. The cost of each piece of solar cell is USD8.98. The exchange rate is RM 3.05/USD.

c This price is obtained because 152 pieces of bi-facial solar cells are required toproduce 1100 kWh per year.

d This price is calculated because 153 pieces of bifacial solar cells are required toproduce 1100 kWh per year.

e The cost (RM) ¼ Cost of the total number of plane mirrors. The price of eachmirror with the dimension of 1.16 m (L)*0.73 m (W) is RM 30.00. The total numberof mirrors required for bi-facial solar cells at the capacity of 1 kW is 27.

f The cost (RM) ¼ Cost of the total number of arrays of adjustable mirrors. Thetotal estimated cost of one array of adjustable small mirror is RM 200.00. The totalnumber of arrays for the bifacial solar cells at the capacity of 0.68 kW on the frontsurface is 26.

g The cost (RM)¼ Cost of prismsþ Cost of mirrors. The cost of each long triangularacrylic prism is RM 10.00 including the cost of cutting and grinding. The totalnumber of prisms required for 0.68 kW solar panel is 77. The number of requiredplane mirrors is 26 plane mirrors.

h The cost of solar system (RM) ¼ Cost of solar cells þ Cost of concentrator orreflector system.

i Solar electricity cost (RM/kWh) ¼ Total cost of solar system/Yearly yield/Lifespan of solar cells.

j The lifespan of the mono-crystalline solar cells is 25 years [30].k The lifespan of the bifacial solar cells is 25 years, same as mono-crystalline solar

cell.

Y.S. Lim et al. / Renewable Energy 63 (2014) 415e425 423

two panels are calculated by using the same experimental resultscollected throughout the experiment period in order to indicate thequality of the solar panels. If the quality of the panel has droppeddue to other irreversible effect on the solar panels, then the

Table 3Sizes of mono-crystalline and bi-facial solar panels with concentrator and reflectorsystems.

Mono-crystallinesolar cellsfrom Japan

Bi-facialsolar cellswith planemirror

Bi-facialsolar cellswithadjustablemirrors

Bi-facial solarcells with prisms

Yearly yield (kWh/kW) 1100 1100 1100 1100Size of the solar panel

excluding frame (m2)5.35a 13.55b 12.87c 12.96d

a The size of the solar panel (m2)¼ Size of a solar cell (m2)�Number of solar cells.Each mono-crystalline solar cell is 0.156 m � 0.156 m. Notice that 220 pieces ofmono-crystalline solar cells are required to produce 1100 kWh per year.

b This size is obtained because each bifacial solar cell has a total size of(0.156 þ 0.135) m � (0.156 þ 0.135) m including the 0.135 m separation distancebetween solar cells and 160 pieces of bi-facial solar cells are required to produce1100 kWh per year.

c This size is obtained because 152 pieces of bi-facial solar cells are required toproduce 1100 kWh per year.

d This size is calculated because 153 pieces of bifacial solar cells are required toproduce 1100 kWh per year.

mismatch in the measurements has to be compensated by usingdifferent compensation coefficients.

To carry out much accurate assessment, the measurementshould be made over a period of time with the results compared interm of energy generated per year. This is because the concentratoror reflector system improving much on a particular time does notalways improve that much on other time due to the variation in thedirect and diffused sunlight caused by the passing clouds. Bycomparing the annual yields of concentrator and reflector systems,the main objective of searching for a feasible, static and cheapconcentrator and reflector systems for the bi-facial solar panel canbe achieved.

The amount of energy generated by a bifacial solar panel canbe increased by 38.1% � 2.83% with the plane mirror placed underthe bifacial solar cells. The energy can be further increased to45.2 � 5.66% or 46.7% � 5.66% respectively if the long triangularprisms are incorporated into the plane mirrors or the planemirror is replaced by adjustable small mirrors. The case study iscarried out to calculate and compare the unit cost of the solarelectricity the bifacial solar systems with that of the mono-crystalline and thin film solar cells. It is shown that the bifacialsolar panel with the plane mirrors can produce the cheapestelectricity because the saving in the number of the bifacial solarcells is more significant than the investment on the additionalmirrors. The bifacial solar panel with the additional prisms on theplane mirrors can produce the second cheapest electricitybecause of the cheap prisms being used in the panel. The unitprice of the solar electricity can be further reduced if recycledmirrors are used in the solar panel. Recycled mirrors or acrylicglasses are abundant in Malaysia. As a result, the bifacial solarpanels with mirrors or prisms will be competitive with thecommonly used solar cells in the market.

Appendix A

This section shows an example of the method of curve fitting fillfactor versus photo-generated current to calculate fill factor of allmeasurement at rated 9 A short-circuit current. The measured fillfactor and short circuit current in the first day were plotted in agraph (Fig. A1). A 2� polynomial was used to curve fit the data ofeach measurement. The fill factor for each solar panel at 9 A shortcircuit current was found by evaluating the polynomial withIsc ¼ 9 A.

Fig. A1Graph of fill factor versus short circuit current for the first measurement of theexperiment.

Y.S. Lim et al. / Renewable Energy 63 (2014) 415e425424

Appendix B

This section explains the mismatch compensation functionwithan example of the curve fitting method to find its coefficients froma mismatch measurement and shows the percentage of differencein power after the mismatch compensation in the same mismatchmeasurement.

Fig. B1Flow charts of the mismatch compensation calculation and evaluation.

Fig. B2(A) Curve fitting result and (B) residual plot of “Mismatch2” for 12:00£t<13:00.

Fig. B1 shows the flow charts for calculating the coefficients inmismatch compensation function from one of the measurementsfor the solar panels with identical setup and evaluating the methodby calculating the difference in power and energy after applying thecompensation function to the same measurement results. Themismatch compensation function, a curve fitting example thatdetermines the coefficients in mismatch compensation functionand the difference in power after applying the mismatchcompensation are shown in the following paragraphs.

The mismatch compensation function is a piecewise function oftime in 1 h interval as shown in Eq. (B1). The function defined foreach interval is a linear function of 2 variables: time and powerfrom the reference solar panel. Coefficients for each function arefound by curve-fitting a mismatch measurement data in the cor-responding time interval. A curve fitting example of “Mismatch2”measurement data for 12:00 � t < 13:00 and the correspondingresidual plot are shown in Fig. B2. It was performed using robustleast square regression with bisquare weights in MATLAB CurveFitting Tool.

f%PmisðnÞðt;P2Þ ¼

8>><>>:

c090 þ c091 tþ c092 P2ðtÞ for 09 : 00� t < 10 : 00c100 þ c101 tþ c102 P2ðtÞ for 10 : 00� t < 11 : 00

«c150 þ c151 tþ c152 P2ðtÞ for 15 : 00� t < 16 : 00

(B1)

Fig. B3 shows the percentage difference in power, aftermismatch compensation, of the measurement with two identicalsolar panel setups labelled as “Mismatch1” that is used to find thecoefficients of mismatch compensation function for the first part ofthe measurements. Fig. B4 shows that of “Mismatch2” for thesecond part. The absolute values of the differences in power forboth cases are less than 2.64%.

Fig. B4(A) Power generation from tested and reference solar panels with identicalsetups labelled “Mismatch2” after the mismatch compensation; (B) Percentage of thedifference.

Fig. B3(A) Power generation from tested and reference solar panels with identicalsetups labelled as “Mismatch1” after the mismatch compensation; (B) Percentage ofthe difference.

Y.S. Lim et al. / Renewable Energy 63 (2014) 415e425 425

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