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Solar Energy 88 (2013) 1–12

The design, fabrication and indoor experimental characterisationof an isolated cell photovoltaic module

Damasen Ikwaba Paul a,⇑, Mervyn Smyth b, Aggelos Zacharopoulos b, Jayanta Mondol b

a The Open University of Tanzania, P.O. Box 23409, Dar es Salaam, Tanzaniab Centre for Sustainable Technologies, School of the Built Environment, University of Ulster, Jordanstown Campus, Shore Road, Newtownabbey,

Co. Antrim, BT37 0QB, United Kingdom

Received 1 August 2012; received in revised form 14 November 2012; accepted 16 November 2012Available online 23 December 2012

Communicated by: Associate Editor Brian Norton

Abstract

A significant problem in utilising the Compound Parabolic Concentrator (CPC) in photovoltaic (PV) applications is the non-uniformillumination on the receiver which results in current reduction for PV modules in which cells are serially connected. A novel PV modulewith isolated cells, which yield high current for cells located in peak energy fluxes, has been designed and experimentally characterisedwith and without the CPC using a multi-purpose mobile solar simulator. The CPC had an acceptance half-angle of 30� and truncatedgeometrical concentration ratio of 1.96. Due to the variation in energy flux profile on each cell, it was found that the energy flux con-centration on the surface of the PV module within the CPC varied from 0.9 to 3.6, with high energy flux being concentrated at the edgesof the receiver. As a result, the cell performance parameters such as current, short-circuit current, power at maximum power point and fillfactor for the cells within the CPC varied depending on the location of the cell in the PV module. The total maximum power output forthe cells within the CPC was 25% higher than that without concentration.� 2012 Elsevier Ltd. All rights reserved.

Keywords: Non-uniform illumination; Energy flux profile; Isolated cells; Photovoltaic module; Compound Parabolic Concentrator

1. Introduction

Non-imaging1 photovoltaic (PV) concentrators have agreat potential to become the lowest-cost PV option if theillumination is uniform across the entire PV module, result-ing in an increase in current and power output. Unfortu-nately, most non-imaging concentrators that are used inPV applications such as the CPC do not produce uniform

0038-092X/$ - see front matter � 2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.solener.2012.11.009

⇑ Corresponding author. Tel.: +255 22 2266 4012; fax: +255 (0) 222668759.

E-mail address: paul.ikwaba@out.ac.tz (D.I. Paul).1 Non-imaging PV concentrator is the type of concentrating system

which is concern with the optimal transfer of light radiation between asource and a target. Unlike imaging concentrator, non-imaging PVconcentrators do not attempt to form an image of the source (Welford andWinston, 1978).

flux on the PV module (James and Williams, 1978;Edenburn and Burns, 1981; Gupta and Milnes, 1981; Pfeifferand Bihler, 1982). The non-uniformity profile on the surfaceof PV module is caused by one or a combination of follow-ing factors: (i) changes of spectral responses of light as itpasses through a concentrator (Schwartz, 1982), (ii) impro-per tracking system design (Franklin and Coventry, 2004;Schultz et al., 2012), (iii) concentrator misalignment (Antonand Sala, 2005; Mallick et al., 2006; Schultz et al., 2012),(iv) errors in the shape of concentrator profiles (Tripanag-nostopoulos, 2007), (v) mechanical failures that occur in aconcentrating system due to aging (Leutz et al., 2009), (vi)impurities in the reflector material (Hatwaambo et al.,2007), and (vii) improper concentrating system design (Sar-mah et al., 2011). The details on how each factor causesuneven flux distribution on the PV module as well as the

2 D.I. Paul et al. / Solar Energy 88 (2013) 1–12

magnitude of the effect on various PV cell parameters can befound in Baig et al. (2012).

There are two effects of non-uniform illumination on thePV module: electrical and thermal effects. The effect of non-uniform illumination on the electrical behaviour of a PVmodule is to produce ohmic drops higher than expected,because the cell operates locally at higher irradiance(Luque et al., 1998). This high ohmic drops result into aninternal current flow which is directly proportional to theirradiance and the degree of non-uniformity (Cuevas andLopez-Romero, 1984). This occurs even in open-circuitconditions. Furthermore, non-uniform illumination causesheating of a PV cell along the surface as well as non-uniformtemperature profiles across the PV module area (Nasby andSanderson, 1982). For a PV module in which cells areconnected in series, non-uniform energy flux distributionforces a highly illuminated cell to operate in a reverse biascondition which results in ‘hot spot’ caused by the rise oftemperature as resistive power dissipation increases (Cuevasand Lopez-Romero, 1984). For conventional PV modules,such a hot spot causes a reduction in power output andefficiency due to the fact that the current of the entire PVmodule depends on the least illuminated PV cell(s) (Jamesand Williams, 1978; Edenburn and Burns, 1981). Therefore,high intensity in any non-uniform concentrated PV module,which can be about 20 times that of the average intensity, islost as the intensity above that of the least illuminated cellsdo not contribute to an increase in power generation.

There has been a lot of effort to enhance performance of aconcentrated PV receiver with non-uniform energy flux dis-tribution. Early attempts to quantify the subject was takenby Edenburn and Burns (1981) who suggested the use of abypass diode to each cell to prevent the least illuminated cellfrom operating as ‘load’. In practical situations, however,one bypass diode is applied for each module to minimisecost and reduce the cell fabrication process (Anon, 2006).The number of bypass diodes determines the efficiency ofthe protection for the cells in the module. To ensure maxi-mum protection of a PV module, it has been proposed tointegrate a bypass diode across each individual cell (Suryan-to-Hasyim et al., 1986; De Boer et al., 2003) or by integrat-ing the bypass diode into the structure of each PV cell(Suryanto-Hasyim et al., 1986). These alternatives, how-ever, are not only expensive but also would result in complexcell fabrication. Furthermore, bypass diodes are not guaran-teed; when one diode fails, the diode itself become ashort-circuit (De Boer et al., 2003). Attempts to controlnon-uniform solar radiation distribution on the reflectingsurfaces of the concentrators so as to attain homogeneousillumination on the receiver have also been widelyinvestigated. For example, Burkhard and Shealy (1975),Greenman (1980), Kurzweg (1980), Gupta and Milnes(1981), Jorgensen and Wendelin (1992), Singh and Liburdy(1993), and Akbarzadeh and Wadowski (1996) suggestedthe use of specially designed concentrator profiles that focusintensity on the receiver more uniformly. The use of diffusereflector materials that result into less non-uniformity is

another method suggested by Hall et al. (2005), Nilssonet al. (2007) and Hatwaambo et al. (2008). Anotherapproach for attaining uniform flux on the receiver is theuse of small distortions in reflecting surfaces of the concen-trator (Greenman, 1980). Furthermore, in their recentreview of the causes and effects of the non-uniform illumina-tion on concentrator solar cells, Baig et al. (2012) suggestedseveral measures to reduce the effect of non-uniformity.These include (i) special concentrator cells design that needto have the right size and shape so as to account for thevariation in the flux intensity across the area, (ii) the useof secondary concentrator optical element which help inimproving the uniformity of the cell, (iii) innovative wayof tracking the sun where complete concentrating PV systemtracking or tilting the optical element of the concentrator isavoided, and (iv) proper PV cell manufacturing (copperthickness optimisation) and the use of thermal management(by using either passive or active cooling methods).

Our current study is in line with such efforts: it advancesnew knowledge on how to efficiently utilise high solar radi-ation intensity in the peak illumination regions of a PVconcentrator by using a novel isolated cells PV module.The fabrication of a PV module consisting of isolated cellsensures that there are no power output losses which arecaused by the loss of the solar irradiance in the peak energyflux regions. This is because when sharp peaks of solarradiation exists in any part of the PV module with individ-ual cells; the absorbed high solar irradiance is converted tohigh current and hence high power output.

2. Materials and methods

2.1. Design and fabrication of the isolated cells PV module

2.1.1. Photovoltaic cell solderingThe PV cells used in this study were BP Solar ‘Saturn’

cells (Zacharopoulos, 2001; Mallick and Eames, 2007).These cells have no electrical contact between the negativeand positive terminals; as a result, cell soldering wasrequired to provide connection points between the two ter-minals. For effective and identical PV cells soldering, pre-cautions were taken during manual soldering process toinsure that the recommended low temperature and equalamount of solder on the tabs were attained (Paul, 2011).

2.1.2. Design and fabrication of PV cells supporting base

The fabrication of the PV module required a suitablesupporting base plate to hold the cells in place. Usually amodule is set within an aluminium frame or occasionallywithin a stainless steel or plastic frame (Pearsall and Hill,2001). In this paper, a 6.4 mm thick Perspex block was cho-sen as supporting base because of its low cost and highstrength (Zacharopoulos, 2001). Since the module consistedof 11 cells with dimensions of 109 mm � 9 mm � 0.4 mm, aPerspex base with dimensions of 118 mm � 118 mm wasselected. To avoid short circuiting between each cell, whichcould cause ohmic losses and create hot spots, 11 rectangu-lar space blocks with dimensions of 115.0 mm � 9.1 mm

D.I. Paul et al. / Solar Energy 88 (2013) 1–12 3

and 0.4 mm deep were machined into the Perspex. The gapbetween each rectangle was 0.89 mm. A rectangular spaceblock also allowed each cell to sit between the rectangularedges avoiding dislocation. To fabricate the rectangularspace blocks, the geometry a single rectangular profile wasgenerated using Computer Aided Design software (Auto-CAD). The data was transferred to a Computerised Numer-ical Controlled (CNC) machined where 11 rectangular slotswere machined into the Perspex. Fig. 1a illustrates the detaildesign and dimensions of the supporting base whilst Fig. 1bshows the Perspex with rectangular space blocks. It shouldbe noted that Perspex is transparent to visible light; hencethe rectangular space blocks are not quite apparent inFig. 1b. A sample cell was placed in one of the rectangularblock to indicate its demarcation.

At one end of the Perspex base, a narrow slot(118 mm � 4.0 mm � 0.9 mm) was incorporated to accom-modate the thickness of the positive terminal copper rib-bon solder at the rear side of each cell so that the cell layflat against the base. Eleven holes with a diameter of5 mm each were drilled at the opposite end of the Perspexbase to permit connection of the negative terminals to thejunction box (connector board).

For the purpose of measuring the back-surface tempera-ture of each cell, holes of 2 mm diameter were drilled toenable thermocouple attachment to the rear surface of thecell. The electrical connections were made via the connectorboard which acts as the junction box. The use of a connectorboard allows a possibility of connecting cells in series, paral-lel or a combination of the two. The connector board wasfixed at the rear of the Perspex base using both M2 screwsand Araldite� 2011B adhesive. Fig. 2 details electrical con-nections where the positive terminal of each cell was serially

(a)Fig. 1. Design and fabrication of the PV cell supporting base (a) details dimensshowing the Perspex with rectangular space blocks.

connected using copper ribbon wires whilst the negative ter-minal of each cell was individually connected. Fig. 2 alsoshows how the PV cells were arranged in the supporting base.

2.1.3. Photovoltaic cells assembly and connections

The selected cells were assembled into prior preparedrectangular space blocks as shown in Fig. 3. To avoid celldislocation, small layer of Araldite� 2011B adhesive wasapplied to the surface of the rectangular blocks before plac-ing the cells. Each cell had an identification number corre-sponding to the position of the cell in the PV module. Forexample, C2 corresponds to cell number 2. Fig. 4 shows acomplete fabricated isolated cells PV module.

2.2. Design and fabrication of the symmetric CPC

A standard symmetric 2-dimensional CPC, shown inFig. 5, was designed and fabricated. The CPC had anacceptance half-angle (ha), entrance (Aa) and exit (Ar) aper-tures areas of 30�, 109 mm and 218 mm, respectively, mak-ing a geometric concentration ratio (Cg) of 2.0. The CPCwas truncated to a height of about 212 mm to enhance dif-fuse radiation collection and fabrication materials costreduction (Carvahlo et al., 1985). Aluminium sheet withreflectivity of 0.91 was used as reflector material.

2.3. Experimental test procedure

The fabricated isolated cells PV module was tested fortwo different conditions: with and without the CPC. Theseindoor experimental tests were carried out at the Centre forSustainable Technologies, University of Ulster (UK) usinga multi-purpose mobile solar simulator (Zacharopoulos

(b)Thermocouple Rectangular block

Cell

ions of the supporting base (all dimensions are in mm) and (b) photograph

Fig. 2. Detail of the electrical connections and PV cell arrangement.

PV cell

Connecting wires

Connector board

Fig. 3. The PV module after assembling a few cells.

Thermocouples Electrical connecting wires

Fig. 4. Complete isolated cells PV module.

4 D.I. Paul et al. / Solar Energy 88 (2013) 1–12

et al., 2009). The multi-purpose mobile solar simulator usesmetal halide lamps with a good spectral match to AM1.5standard solar spectrum as shown in Fig. 6. This simulatorhas a lamp-frame height which can be adjusted dependingon the requirement of the experiment. Thus, the light uni-formity of the multi-mobile solar simulator also varies withtarget area and lamp-frame distances. For example, at aheight of 1.8 m (from the target), the uniformity of about94% can be achieved on a 2.2 m � 1.5 m wide target areawhile at a distance of 2.2 m from the lamp array, the unifor-mity decreases to about 90% (Zacharopoulos et al., 2009).

The light collimation of the multi-mobile solar simulator,as measured with a 20� cone, varies from 70% to 90%, withan average value of 83% (Zacharopoulos et al., 2009). Theterm ‘83%’ signifies the percentage of light which incidenton the test target within a 20� cone. However, this non-ideal

Fig. 5. Cross-section view of a 2-dimension symmetric CPC showingdesigning parameters (Hmax is the maximum height of the CPC).

Fig. 6. The multi-mobile solar simulator spectral distribution comparedto the AM1.5 standard solar spectrum (Zacharopoulos et al., 2009).

D.I. Paul et al. / Solar Energy 88 (2013) 1–12 5

collimation of illumination had insignificant effect on theperformance since the system under test was of low concen-tration ratio (Zacharopoulos et al., 2012).

Fig. 7 details the experimental set-up for illuminationmeasurements. Measurements of illumination on the aper-ture were performed using a pyranometer and it was foundthat, at a height of 1.6 m (from the target area), the averageintensity was 615 ± 20 W/m2.

In this study, the current and voltage were measured witha Keithley 2400 SourceMeter (Anon, 1999). For the pur-pose of measuring current and voltage of an individual cell,the output from each cell was connected directly to theKeithley 2400 data acquisition through an IEEE-488 inter-face and linked to a PC, as shown in Fig. 8. A ‘linear stair-case sweep’ mode was employed for all measurements byapplying a small negative voltage of magnitude 0.01 V.The sweep voltage was increased by 0.01 V increments upto 0.8 V. For each measurement, short-circuit current(ISC), open-circuit voltage (VOC), instantaneous currentand voltage were recorded.

The Keithley 2400 SourceMeter was programmed to actas a ‘current sink’ by sourcing the voltage on the opposite

direction to that produced by the PV cell. In this set-up, theKeithley 2400 SourceMeter assumes that it is measuring acurrent from its internal source and a positive current flow‘out’ of its terminals whilst a negative current flows ‘in’. Asa result, it measures polarities opposite from what isexpected with a typical ammeter.

From the current and voltage measurements, the cur-rent–voltage (I–V) characteristics of each cell were plotted.These curves were used to extract current and voltage atmaximum power point (PMPP), IMPP and VMPP, respec-tively. The electrical conversional efficiency (g) for PV cellswithout a concentrator were calculated as (Dalal andMoore, 1977):

gð%Þ ¼ FF� IMPP � V MPP

Girr � APV

� 100 ð1Þ

while that of cells with the CPC, (gCPC), at constant tem-perature, were calculated as (Mallick and Eames, 2007):

gCPC ¼ISCðCPCÞ � V OCðCPCÞ � FF ðCPCÞ

Girr � Aaperture

ð2Þ

where Girr is the incident solar irradiance, APV is the activePV cell area and Aaperture is the aperture area of the CPCgiven as:

Aaperture ¼ APV � Cg ð3ÞIn calculating the electrical conversional efficiency of the

PV cells using either Eq. (1) or Eq. (2), the operating tem-perature of a PV cell must be constant. Since the PV mod-ule had no cooling system and the PV cells within the CPChave different flux, the following method was applied tokeep the temperature of each cell constant:

(i) The test unit (both PV module with and without theCPC) was covered before placing it on the experimen-tal rig to prevent light from the solar simulator fromreaching the PV cell which would increase the tem-perature before commencement of the experiment.

(ii) After placing the test unit on the experimental rig, thecell temperatures were allowed to stabilise (withrespect to the ambient temperature). The cover wasremoved from the test unit as quickly as possibleand the PV module was exposed to the solar simula-tor for a very short period of time (less than 1 min foreach test).

(iii) Upon completion of the current and voltage measure-ments for a single PV cell, the data collection deviceswere deactivated and the test unit was covered again.

(iv) Using a fan as a cooling system, the cells wereallowed to cool before the next experiment begins.

(v) For subsequent measurements, steps (i) to (iv) wererepeated.

The thermocouples for monitoring cell temperaturewere connected to a Data-Logger (DL2e model) and pro-grammed to take measurements every 10 s and averageevery 30 s.

Wooden frame Experimental test rig

Pyranometer

Fan

Solar simulator lamp array

Fig. 7. Experimental set-up for illumination measurements.

Fig. 8. Circuit diagram for current and voltage measurements of an individual PV cell.

6 D.I. Paul et al. / Solar Energy 88 (2013) 1–12

3. Results and discussions

3.1. Energy flux profile along the PV module

A theoretical and experimental study of energy flux dis-tribution on the PV module with CPC was carried out. Thetheoretical energy flux distribution was determined with theaid of a ray trace program (Zacharopoulos et al., 1996),where 10,000 rays, equally spaced over the aperture of

the CPC, were traced. The experimental energy flux distri-bution was determined from the ratio of short-circuit cur-rent with to short-circuit current without the CPC(Ralph, 1966). Fig. 9a shows the energy flux distributionon the surface of the PV module when the incident solarirradiance was perpendicular to the aperture of the CPC.Fig. 9b shows a photograph of a PV module inside theCPC defining the position of each cell inside the collector.As expected, both theoretical and experimental energy flux

D.I. Paul et al. / Solar Energy 88 (2013) 1–12 7

distributions are non-uniform (Welford and Winston,1978) and the agreement between theoretical and experi-mental results is very good. However, the theoretical resultshows significantly higher peaks of flux concentration com-pared to those measured experimentally. This is due to themanufacturing errors of the CPC parabolic reflectors, thelower than 100% specularity of the reflector material andthe less than perfect collimation of the multi-mobile solarsimulator light. It should be noted that the theoreticalresults assume that parabolic reflectors are specular, freeof manufacturing errors and all incident solar radiation isperfectly collimated (Welford and Winston, 1978).

As indicated in Fig. 9a, both energy flux profiles (theo-retical and experimental) have high energy flux concentra-tion at the edges of the receiver, in particular cells number 2and 10. Although theory stresses decrease in power outputdue to non-uniform illumination for the PV module inwhich cells are serially connected (James and Williams,1978), for the isolated cells PV module, the effect of non-uniform illumination will result in a power output increasefor cells located in the high energy flux areas. This is due tothe fact that the current generated by such a PV module isno longer limited by the least-illuminated cells. In this way,the fabricated isolated cells PV module operates efficientlyfor the reason that each cell performs to its potential.

3.2. Details analysis of electrical performance

3.2.1. The I–V characteristics of each cellThe effect of non-uniform illumination on the I–V char-

acteristics and other performance parameters of each cellwere investigated for various incidence angles, however,

0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10

Cell number

Ene

rgy

flux

con

cent

rati

on Theoretical

Experimental

(a)Fig. 9. (a) Theoretical and experimental energy flux distribution on the PV mmodule inside a CPC defining the position of each cell along the PV module.

this paper presents only the results for normal incidenceangle. Fig. 10 shows the I–V characteristics of each cellwith and without the CPC when the irradiance was perpen-dicular to the aperture of the CPC collector. Due to thenon-uniform illumination distribution on each cell, as indi-cated in Fig. 9a, the I–V curves varied depending on theposition of the cell in the PV module. It can be seen(Fig. 10a–f) that the I–V curves of the cells within theCPC were higher than the cells without CPC only for cellsnear the ends of the PV module (i.e., cells number 1, 2, 3, 9,10, and 11). This was a result of most light rays beingreflected near the edges of the PV module. Conversely,the I–V curves for the cells without the CPC in Fig. 10g–k were almost the same as the cells within the CPC dueto the fact that these cells had the same illumination inten-sity. The PV cells located in the middle of the CPC do not‘see’ many lamps of the solar simulator due to acceptancelimit of the CPC. It can be concluded, therefore, that whilethe peak energy flux could had be lost if the cells in the PVmodule were serially connected, the fabrication of isolatedcells PV module ensured that there is no energy loss as non-uniform illumination distribution results in higher current(and hence power output) for cells in the peak energy flux.

3.2.2. Variation of short-circuit current

Fig. 11 compares the short-circuit current of each cellwith and without the CPC. The short-circuit current for cellswithout the CPC were almost constant; the variation wasonly 7% while that of the cells within the CPC varied by76%. The variation in short-circuit currents between thecells without the CPC can be explained by the insufficientlight collimation of the solar simulator (Zacharopoulos

11

(b)

Cell No. 1 to 11

CPC

PV module

odule with the CPC (at normal incident angle). (b) A photograph of a PV

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Fig. 10. The I–V curves of each cell with and without the CPC for normal incidence angle. The irradiance on the surface of each system was constant(615 ± 20 W/m2). The average back-surface cell temperature was 17 �C and the ambient temperature was 16 �C.

8 D.I. Paul et al. / Solar Energy 88 (2013) 1–12

et al., 2009). On the other hand, the variation in short-circuitcurrents for cells within the CPC was due to non-uniformillumination among the cells. It should be noted that theeffect of non-uniform illumination in an isolated cell PVmodule results into higher short-circuit currents for cellsin the peak energy flux regions because short-circuit currentis a linear function of the light generated current which isproportional to the photon flux incident on the PV cell

(Ralph, 1966). Thus, it can be seen from Fig. 11 that theCPC had higher short-circuit current for cells located nearthe edges of the PV module due to more light rays beingfocused near the edges of the PV module. For example,the maximum ISC of 646 mA for cells within the CPC wasobserved at cell number 2 which is in an area of peak energyflux (see Fig. 9a). This value was about 75% higher than thesame PV cell in a similar position without a concentrator.

0

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Shor

t-ci

rcui

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rent

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) . without CPC

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Error V0.001±

Fig. 12. Variation in the open-circuit voltage for cells with and withoutthe CPC.

D.I. Paul et al. / Solar Energy 88 (2013) 1–12 9

The asymmetrical behaviour of ISC in Fig. 11 was aresult of asymmetric experimental energy flux distributionas can be observed in Fig. 9a. This asymmetric experimen-tal energy flux distribution is a result of insufficient lightcollimation from the solar simulator and manufacturingerrors of the CPC reflectors. Theoretically, at normal inci-dence angle, the incident irradiance should always be per-pendicular to the aperture of the CPC. However, using asolar simulator with less than perfect collimation it was dif-ficult to produce perpendicular light to every point on theaperture of the CPC because the angular size of the solarsimulator lamp ‘seen’ by a particular point on the aperturevaries with the separation distance between the solar simu-lator and the concentrator’s aperture (Kruer, 1999). Fur-thermore, in real concentrators, rays are reflected fromreflector surfaces with slope error. As a result, a reflectedray reaches the receiver at a different point from where itshould strike the receiver if the reflector was perfect.

3.2.3. Variation in open-circuit voltage

Fig. 12 compares the open-circuit voltages of each cellwith and without the CPC collector. Since the cell tempera-tures were kept constant in this experiment, it can be seenthat there was no substantial variation in open-circuit volt-ages for cells with and without concentrator. This is becausethe open-circuit voltage depends on the material character-istics of a PV cell instead of the variation in energy fluxreceived as in the case of short-circuit current. It shouldbe noted that VOC varies with saturation current and thelight-generated current (Andreev et al., 1997). However,the key factor is the saturation current as the effect of thelight-generated current is not significant. Thus, the increasein energy flux due to the use of a solar concentrator and thenon-uniform illumination did not have significant effect onthe open-circuit voltage.

3.2.4. Variation in maximum power outputFig. 13 shows the variation in maximum output power

of each cell with and without the CPC collector. It can

be seen that the power output for cells without a concentra-tor was approximately constant; it varied only by 10%(from 58 to 64 mW). The variation was mainly due toinsufficient light collimation of the solar simulator. How-ever, the power output for the cells within the CPC collec-tor varied as the intensity of light falling on the PV cellchanges. As illustrated in Fig. 13, the power output for cellswithin the CPC follows a similar profile as the experimentalenergy flux distribution on each cell. That is, the poweroutput for cells within the CPC varied from 54 mW (forcells in the least illuminated region) to 104 mW (for cellsin the peak energy flux area), with the cells near the endsof the PV module (cells number 1, 2, 3, 9, 10, and 11) per-forming much better than those at the centre. The poweroutput was higher for cells located near the edges of thePV module than those at the central region because theenergy concentration peaks on the absorber’s surface undersymmetric CPC occurs near the edges of the receiver. As aresult, the output power for cells number 1, 2, 3, 9, 10, and11 with the CPC was higher than similar cells without aconcentrator by 25%, 69%, 56%, 57%, 59%, and 55%,respectively. However, due to insufficient light collimation,the power output for cells located at the central area of thePV module (cells number 4–8) without a concentrator washigher than similar cells within the CPC by about 9%. Inspite of this, the total power output for the cells withinthe CPC was higher than similar cells without a concentra-tor by 25%.

Since the CPC used in this experiment had a truncatedgeometrical ratio of 1.96, the total maximum power outputof the PV cells within the CPC was expected to increase bya factor of 1.96. However, as observed previously, the dif-ference in power output between cells with and without theCPC was small because, for a standard PV cell, the increasein power output due to high energy flux concentration isnot directly proportional with the energy flux concentra-tion due to various resistive losses such as increased ohmiclosses (Wolf and Rauschenbach, 1963; Markvart, 1994;Leutz and Suzuki, 2001) and distributed diode factor loss(Dalal and Moore, 1977).

0

20

40

60

80

100

120

0 1 2 3 4 5 6 7 8 9 10 11

Cell number

Max

imum

pow

er (m

W)

without CPC with CPC

Fig. 13. Comparison of maximum power output for cells with andwithout the concentrator.

10 D.I. Paul et al. / Solar Energy 88 (2013) 1–12

To examine the extent of power loss on each cell due toohmic losses, the intensity concentration ratio and poweroutput ratio of each cell within the CPC were calculatedand presented in Table 1. In Table 1, the 2nd column(intensity concentration ratio) is the energy flux concentra-tion ratio; calculated as the ratio of ISC with the CPC to ISC

without the CPC. It is the same as the experimental energyflux concentration shown in Fig. 8a. On the other hand, the3rd column in Table 1 (power ratio) is the ratio of the max-imum power output of a PV cell with the CPC to the max-imum power output of the same PV cell without the CPC.The power ratio indicates the overall losses in the PV cellwith concentrator due to various system inefficiencies. Ifa PV cell is free from resistive losses, intensity concentra-tion ratio must be equal to power ratio (Ralph, 1966).On the other hand, if intensity concentration ratio isgreater than power ratio, this indicates a power loss. There-fore, it is the comparison between power ratio and intensityconcentration ratio that indicates whether there is powerloss or not.

Since the power ratio for cells number 4–8 was equal tothe intensity concentration ratio, therefore there was nopower output loss for these cells. This was due to the factthat these cells had low energy concentration, hence lowresistive losses. On the contrary, power losses of 14%,53%, 38%, 36%, 41%, and 35% were observed for cells 1,

Table 1Power output losses for each cell with the CPC collector.

Cell no. Intensity concentration ratio Power ratio Power loss (%)

1 1.4 1.2 142 3.6 1.7 533 2.6 1.6 384 0.9 0.9 05 0.9 0.9 06 0.9 0.9 07 0.9 0.9 08 0.9 0.9 09 2.5 1.6 36

10 2.7 1.6 4111 2.3 1.5 35

2, 3, 9, 10, and 11, respectively. As detailed in Table 1,the power loss varied with the position of the cell in thePV module and the illumination intensity; with the highestpower loss (53%) observed at PV cell number 2 which hadthe highest intensity concentration ratio (3.6). Theobserved power loss in Table 1 (4th column) was due to sig-nificant voltage drop around the maximum power point asa result of high series resistance of the connecting wires.From theory (Wolf and Rauschenbach, 1963), the maxi-mum power of a PV cell is obtained when the shape ofthe I–V curve is more ‘square-like’. However, when a cellundergoes a voltage drop around the maximum powerpoint it causes the cell to exhibits a more ‘rounded I–V

curve’, producing a significant reduction in maximumpower output and FF, which in turn, reduces the conver-sion efficiency. The output power and FF losses increasewith the increase in energy flux absorbed because at ahigher energy flux, the internal cell series resistanceincreases (Mitchell, 1977) and may cause a nearly straightline I–V curve as observed in Fig. 10c (cell number 2 withinthe CPC collector). To minimise the voltage drop andhence improvement in maximum power output, FF andconversion efficiency of such a PV module, a ‘4-wire remotesensing’ method for current and voltage measurement isrecommended (Paul, 2011).

3.2.5. Variation in fill factorFig. 14 illustrates the variation in FF for each cell with

and without the CPC. It can be seen that all cells without aconcentrator had constant FF of about 0.60 where as theFF for the cells within the CPC varied depending on theposition of the cell in the PV module. Comparison ofthe FF curves for the cells within the CPC indicates thatthe FF curve for each cell is the inverse of the experimentalenergy flux concentration curve shown in Fig. 10a. That is,the FF for the cells located in the peak illumination regionsdecreased due to high local concentration in the illumi-nated region which increased the resistive losses. Similarresults (but with different degree of magnitudes) have beenobserved by Araki and Yamaguchi (1997), Luque et al.(1998), Garcıa et al. (2008) and Simfukwe et al. (2011).

0

20

40

60

80

0 1 2 3 4 5 6 7 8 9 10 11

Cell number

Fill

fac

tor

(%)

without CPC with CPC

Fig. 14. Variation in FF of each cell with and without the CPC.

D.I. Paul et al. / Solar Energy 88 (2013) 1–12 11

Furthermore, decrease in FF for cells in the peak illumina-tion regions could be a result of dominance of recombina-tion mechanism in the space-charge region (Dalal andMoore, 1977; Andreev et al., 1997).

4. Conclusions

A novel isolated cells PV module has been designed, fab-ricated and experimentally characterised with and without aCPC using a multi-purpose mobile solar simulator. A theo-retical and experimental energy flux profile of cells withinthe CPC has been undertaken for normal incidence angle.Both theoretical and experimental energy flux profiles indi-cated that high energy flux concentration was observed atthe edges of the receiver as the majority of the rays wereconcentrated there. It was observed that the CPC has uni-form energy flux distribution for cells number 4–8 sinceall rays reach the PV module without reflection. Due tonon-uniform illumination, the experimental energy fluxconcentration varied from 0.9 to 3.6. As a result, cell perfor-mance parameters such as current, ISC, PMPP and FF forcells within the CPC varied depending on the location ofthe cell in the PV module. For example, the I–V curve,ISC, PMPP and FF for the cells within the CPC was higherfor cells located near the edges of the PV module than thoseat the central region because the energy concentration peakson the absorber’s surface under symmetric CPC occurs nearthe edges of the receiver. The analysis has confirmed thatthe fabrication of PV module with individual cells and theeffect of non-uniform illumination results in higher poweroutput for cells located in peak energy concentrationregions and lower power output for cells in the lower illumi-nation areas. In this way, the isolated cells PV module oper-ates efficiently for the reason that each cell performs to itspotential as the generated current is no longer limited bythe least-illuminated cell(s). To minimise the voltage dropdue to high energy flux and hence improvement in maxi-mum power output, FF and conversion efficiency, we rec-ommend the use of the 4-wire remote sensing methodsbecause this method ensures that there is no voltage dropsin the test conductor due to internal series resistance effect.

Acknowledgement

This work was supported by the Vice Chancellor’s Re-search Scholarship, University of Ulster, UK, through aPhD studentship of the corresponding author, D.I. Paul.

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