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applied
sciences
Article
A Novel Concentrator Photovoltaic (CPV) System
with the Improvement of Irradiance Uniformity and
the Capturing of Diffuse Solar Radiation
Nguyen Xuan Tien and Seoyong Shin *
Department of Information and Communication Engineering, Myongji University, Yongin 17058, Korea;
nxtien@gmail.com
*Correspondence: sshin@mju.ac.kr; Tel.: +82-31-330-6768
Academic Editors: Frede Blaabjerg and Yongheng Yang
Received: 16 June 2016; Accepted: 6 September 2016; Published: 8 September 2016
Abstract:
This paper proposes a novel concentrator photovoltaic (CPV) system with improved
irradiation uniformity and system efficiency. CPV technology is very promising its for highly efficient
solar energy conversion. A conventional CPV system usually uses only one optical component,
such as a refractive Fresnel lens or a reflective parabolic dish, to collect and concentrate solar radiation
on the solar cell surface. Such a system creates strongly non-uniform irradiation distribution on the
solar cell, which tends to cause hot spots, current mismatch, and degrades the overall efficiency of
the system. Additionally, a high-concentration CPV system is unable to collect diffuse solar radiation.
In this paper, we propose a novel CPV system with improved irradiation uniformity and collection of
diffuse solar radiation. The proposed system uses a Fresnel lens as a primary optical element (POE)
to concentrate and focus the sunlight and a plano-concave lens as a secondary optical element (SOE)
to uniformly distribute the sunlight over the surface of multi-junction (MJ) solar cells. By using the
SOE, the irradiance uniformity is significantly improved in the system. Additionally, the proposed
system also captures diffuse solar radiation by using an additional low-cost solar cell surrounding
MJ cells. In our system, incident direct solar radiation is captured by MJ solar cells, whereas incident
diffuse solar radiation is captured by the low-cost solar cell. Simulation models were developed
using a commercial optical simulation tool (LightTools
™
). The irradiance uniformity and efficiency
of the proposed CPV system were analyzed, evaluated, and compared with those of conventional
CPV systems. The analyzed and simulated results show that the CPV system significantly improves
the irradiance uniformity as well as the system efficiency compared to the conventional CPV systems.
Numerically, for our simulation models, the designed CPV with the SOE and low-cost cell provided
an optical power ratio increase of about 17.12% compared to the conventional CPV without the
low-cost cell, and about 10.26% compared to the conventional CPV without using both the SOE and
additional low-cost cell.
Keywords:
concentrator photovoltaic (CPV); Fresnel-lens-based CPV; CPV with irradiance
uniformity; CPV for capturing diffuse radiation
1. Introduction
Today, concentrator photovoltaic (CPV) systems are used to increase the effectiveness of
photovoltaic (PV) systems using reflective material, lenses, or mirrors to concentrate sunlight on highly
efficient solar cells [
1
]. CPV systems convert solar energy to electricity efficiently by concentrating
and focusing incident solar radiation on high-efficiency multi-junction (MJ) solar cells. A typical CPV
system consists of a solar concentrator, MJ solar cells, and a sun tracking system. In a CPV system,
solar radiation is concentrated and focused on MJ solar cells through the solar concentrator. Since the
Appl. Sci. 2016,6, 251; doi:10.3390/app6090251 www.mdpi.com/journal/applsci
Appl. Sci. 2016,6, 251 2 of 15
system requires direct sunlight, the concentrator and solar cells require the use of a sun tracking system
to follow the sun’s trajectory and optimize the incident solar radiation [2].
The solar concentrator could be a Fresnel lens [
3
], a parabolic concentrator [
4
], a compound
parabolic concentrator (CPC) [
5
], a parabolic trough concentrator [
6
], and others [
7
–
9
]. An ideal CPV
system is expected to distribute the concentrated sunlight uniformly to the solar cell. However, the use
of concentrators causes non-uniform illumination [
2
]. The non-uniformity of the incident illumination
is found in all CPV systems and has been a well-known problem in the CPV systems [
10
]. For CPV
systems, the illumination non-uniformity causes effects in two basic categories of electrical and thermal
impacts that are described in detail in [
2
,
10
–
12
]. Several approaches have been proposed and developed
to improve the illumination non-uniformity in CPV systems. These approaches can be classified into
two categories: concentrator-design-based and secondary optical element (SOE)-based approaches.
Concentrator-design-based approaches modify and focus on designs of the solar concentrator
to solve the illumination non-uniformity problem. Non-imaging Fresnel lenses are designed with
the objective of concentrating light rather than forming an image. The main goal of the design of a
non-imaging Fresnel lens is to maximize the energy and flux uniformity of solar radiation concentrated
by the lens [
13
,
14
]. Stefancich et al. [
15
] proposed a two-dimensional single optical element system for
integrating both the concentrating and spectral splitting actions. Solid transparent dispersive prisms
are designed to deflect and split a polychromatic collimated light beam from a given direction onto
the same area of a receiving target. The resulting concentrated and spectrally divided beam is simply
obtained by the superimposition of each prism contribution. The solar cell intercepts the beam exiting
from the prism ensemble. Later, these authors proposed the design of a three-dimensional point-focus
spectral splitting solar concentrator system [16] to minimize the optical loss.
SOE-based approaches, called two-stage systems, utilize an SOE, such as a lens, a reflector, or a
CPC, located before the solar cell to improve the irradiation uniformity. Ning et al. [
17
] presented a
two-stage CPV system with a Fresnel lens as the primary optical element (POE) and a dielectric totally
internally reflecting non-imaging concentrator as the SOE. The two-stage design provided both a
higher concentration and a more uniform flux distribution on the PV cell. Meng et al. [
18
] investigated
a design of a symmetrical two-stage flat reflected concentrator (STFC), which used reflectors to
provide uniform sunlight distribution over the solar cell. The design consisted of two symmetrical
off-axis concentrators and inclined flat reflectors. The incident solar radiation was concentrated by the
primary off-axis concentrators and diffused by the secondary planes. A Fresnel–Köhler technology was
developed [
19
–
21
]. The Fresnel–Köhler technology was based on Köhler integration. The principles of
the general design procedure were described in [
22
]. The main idea of the design was to concentrate
the incident solar radiation through Köhler integrator pairs divided in four or nine channels, and each
channel consists of two optical elements, a Fresnel lens as the POE, and a free-form surface as the SOE.
The design improved the uniformity of irradiance distribution on the solar cell. Chen and Chiang [
23
]
proposed the design of three types of SOE for Fresnel lens-based CPV units to achieve high optical
efficiency and improve the irradiance uniformity. Some concentration systems have been also proposed
for daylighting systems [
23
–
26
]. Ullah and Shin [
24
,
25
] presented two light concentration systems
to capture sunlight and then focus it over a small area. The first approach used two concave and
convex parabolic reflectors: the concave parabolic reflector captured sunlight and directed the sunlight
toward the convex parabolic reflector, which illuminates a bundle of optical fibers. In the second
approach, a Fresnel lens was used to focus direct sunlight on a collimating lens, which illuminates a
bundle of optical fibers. Furthermore, the authors presented the development of these two systems
using a parabolic trough and a linear Fresnel lens [
26
]. Vu and Shin [
27
] proposed a combination
of linear Fresnel lenses and a stepped thickness waveguide to concentrate the solar energy for a
daylighting system.
Additionally, CPV systems cannot capture diffuse solar radiation because of the narrow acceptance
angle of the concentrators, so the use of the systems in regions of medium direct normal irradiation
(DNI) is not cost effective [
28
]. In other words, the CPV systems are not suitable for medium DNI
regions, such as Korea and Japan. Benitez et al. [
29
] proposed and invented a CPV system that uses
Appl. Sci. 2016,6, 251 3 of 15
auxiliary cells to collect diffuse solar radiation. The invention comprises a combination of two types
of solar cells in a single module. The main cell is located at the focal spot of the concentrator and a
low-cost secondary solar cell is added to the concentrator, surrounding the main cell. Direct solar
radiation is concentrated upon the main cell, while diffuse solar radiation is collected by the low-cost
secondary solar cell. This concept was implemented in [
28
,
30
] using a prototype CPV module with an
additional cell. In the implementation, a silicon solar cell was installed onto a CPV module. In this
experiment, direct solar radiation is concentrated by a Fresnel lens onto a triple-junction solar cell,
whereas diffuse solar radiation is collected by the additional solar cell. The experimental results
showed that the electricity generated by the experimented CPV module with the additional crystalline
silicon solar cell is greater than that for a conventional CPV module by an improvement factor of
1.44 when the mean ratio of diffuse normal irradiation to global normal irradiation is 0.4. In other
words, the experimental results showed that the experimented CPV module provided a conversion
efficiency increase of 44% compared to the conventional CPV module. Therefore, the CPV system with
the additional solar cell improves the system efficiency compared to the conventional CPV systems,
especially in medium DNI regions.
However, there is no CPV system with irradiance uniformity that can capture diffuse solar
radiation and no CPV system with diffuse solar radiation collection that uses an SOE to improve
the irradiance uniformity. In other words, there is no study that integrates both the improvement of
irradiance uniformity and the collection of diffuse solar radiation into a CPV system. In this paper,
we propose a novel CPV system that combines both features of the abovementioned CPV systems,
including the improvement of irradiation uniformity and the collection of diffuse solar radiation.
The proposed system includes several CPV units and an additional low-cost solar cell. Each CPV unit
consists of a Fresnel lens as the POE, a plano-concave lens as the SOE, and a multi-junction solar cell.
For each CPV unit, the Fresnel lens concentrates and focuses the sunlight on the SOE and the SOE then
spreads the sunlight over the MJ solar cell. By using the SOE, the irradiance uniformity is significantly
improved in the CPV unit. In addition, the proposed system also captures diffuse solar radiation by
using the additional low-cost solar cell. Therefore, the proposed CPV system significantly improves
irradiance uniformity and system efficiency.
The rest of the paper is organized as follows. Section 2describes the proposed CPV system.
Simulation models are modeled using the commercial optical simulation tool LightTools
™
(Synopsys’s
Optical Solutions Group, Mountain View, CA, USA), and the system performance is analyzed and
evaluated in Section 3. Finally, in Section 4, we provide our conclusions.
2. The Proposed CPV System
The proposed CPV system includes an array of CPV units and an additional low-cost solar cell.
Each CPV unit consists of a Fresnel lens as the POE, a plano-concave lens as the SOE, and an MJ solar
cell. A silicon (Si) solar cell surrounds plano-concave lenses of the CPV units to capture diffuse solar
radiation. Each CPV unit highly concentrates and uniformly distributes direct solar radiation on its MJ
solar cell through its POE and SOE, whereas the Si solar cell captures diffuse solar radiation.
The design and layout of the proposed system are shown in Figures 1and 2, respectively.
Appl.Sci.2016,6,2513of15
mediumDNIregions,suchasKoreaandJapan.Benitezetal.[29]proposedandinventedaCPV
systemthatusesauxiliarycellstocollectdiffusesolarradiation.Theinventioncomprisesa
combinationoftwotypesofsolarcellsinasinglemodule.Themaincellislocatedatthefocalspotof
theconcentratorandalow‐costsecondarysolarcellisaddedtotheconcentrator,surroundingthe
maincell.Directsolarradiationisconcentrateduponthemaincell,whilediffusesolarradiationis
collectedbythelow‐costsecondarysolarcell.Thisconceptwasimplementedin[28,30]usinga
prototypeCPVmodulewithanadditionalcell.Intheimplementation,asiliconsolarcellwas
installedontoaCPVmodule.Inthisexperiment,directsolarradiationisconcentratedbyaFresnel
lensontoatriple‐junctionsolarcell,whereasdiffusesolarradiationiscollectedbytheadditionalsolar
cell.TheexperimentalresultsshowedthattheelectricitygeneratedbytheexperimentedCPVmodule
withtheadditionalcrystallinesiliconsolarcellisgreaterthanthatforaconventionalCPVmodule
byanimprovementfactorof1.44whenthemeanratioofdiffusenormalirradiationtoglobalnormal
irradiationis0.4.Inotherwords,theexperimentalresultsshowedthattheexperimentedCPVmodule
providedaconversionefficiencyincreaseof44%comparedtotheconventionalCPVmodule.
Therefore,theCPVsystemwiththeadditionalsolarcellimprovesthesystemefficiencycomparedto
theconventionalCPVsystems,especiallyinmediumDNIregions.
However,thereisnoCPVsystemwithirradianceuniformitythatcancapturediffusesolar
radiationandnoCPVsystemwithdiffusesolarradiationcollectionthatusesanSOEtoimprovethe
irradianceuniformity.Inotherwords,thereisnostudythatintegratesboththeimprovementof
irradianceuniformityandthecollectionofdiffusesolarradiationintoaCPVsystem.Inthispaper,
weproposeanovelCPVsystemthatcombinesbothfeaturesoftheabovementionedCPVsystems,
includingtheimprovementofirradiationuniformityandthecollectionofdiffusesolarradiation.The
proposedsystemincludesseveralCPVunitsandanadditionallow‐costsolarcell.EachCPVunit
consistsofaFresnellensasthePOE,aplano‐concavelensastheSOE,andamulti‐junctionsolarcell.
ForeachCPVunit,theFresnellensconcentratesandfocusesthesunlightontheSOEandtheSOE
thenspreadsthesunlightovertheMJsolarcell.ByusingtheSOE,theirradianceuniformityis
significantlyimprovedintheCPVunit.Inaddition,theproposedsystemalsocapturesdiffusesolar
radiationbyusingtheadditionallow‐costsolarcell.Therefore,theproposedCPVsystem
significantlyimprovesirradianceuniformityandsystemefficiency.
Therestofthepaperisorganizedasfollows.Section2describestheproposedCPVsystem.
SimulationmodelsaremodeledusingthecommercialopticalsimulationtoolLightTools™
(Synopsys’sOpticalSolutionsGroup,MountainView,CA,USA),andthesystemperformanceis
analyzedandevaluatedinSection3.Finally,inSection4,weprovideourconclusions.
2.TheProposedCPVSystem
TheproposedCPVsystemincludesanarrayofCPVunitsandanadditionallow‐costsolarcell.
EachCPVunitconsistsofaFresnellensasthePOE,aplano‐concavelensastheSOE,andanMJsolar
cell.Asilicon(Si)solarcellsurroundsplano‐concavelensesoftheCPVunitstocapturediffusesolar
radiation.EachCPVunithighlyconcentratesanduniformlydistributesdirectsolarradiationonits
MJsolarcellthroughitsPOEandSOE,whereastheSisolarcellcapturesdiffusesolarradiation.
ThedesignandlayoutoftheproposedsystemareshowninFigures1and2,respectively.
Figure 1. Design of the proposed concentrator photovoltaic (CPV) system. Si, silicon.
Appl. Sci. 2016,6, 251 4 of 15
Appl.Sci.2016,6,2514of15
Figure1.Designoftheproposedconcentratorphotovoltaic(CPV)system.Si,silicon.
Figure2.ArraylayoutoftheCPVsystem.MJ,multi‐junction.
2.1.ImprovingIrradianceUniformity
IntheproposedCPVsystem,anarrayofFresnellensesisusedasthePOE.Fresnellensesare
usedassolarconcentratorssincetheyofferhighopticalefficiencyalongwithminimalweightanda
lowcost[31].Plano‐concavelensesareusedtoexpandlightbeamsinopticalsystems.Theyareused
inCPVsystemstoimprovetheirradianceuniformityofthesystems.IneachdesignedCPVunit,a
plano‐concavelensischosenastheSOEtoimprovetheirradianceuniformitysinceplano‐concave
lensesareverycommonproductsinthemarketandhavealowcostcomparedtoothersophisticated
SOEtypes,suchasKöhlerintegration‐basedSOEs[19–21]andothers[23].ThedesignoftheCPVunit
isshowninFigure3.
Figure3.DesignoftheproposedCPVunitwiththesecondaryopticalelement(SOE).
ThePOE(Fresnellens)isusedtoconcentrateincidentsolarradiationintotheSOE.TheSOE
(plano‐concavelens)isusedtoredirectthesunlightintotheMJsolarcellandtouniformlydistribute
theirradiationonthesolarcell.Therefore,thedesignedCPVunitsignificantlyimprovesthe
irradianceuniformitycomparedtotheconventionalCPV.
Theeffectivefocallength(EFL)oftheFresnellensiscalculatedasfollows:
1,(1)
whereistherefractiveindexandistheradiusoftheFresnellens.
Thefocallengthoftheplano‐concavelensiscalculatedby[32]:
Figure 2. Array layout of the CPV system. MJ, multi-junction.
2.1. Improving Irradiance Uniformity
In the proposed CPV system, an array of Fresnel lenses is used as the POE. Fresnel lenses are
used as solar concentrators since they offer high optical efficiency along with minimal weight and
a low cost [
31
]. Plano-concave lenses are used to expand light beams in optical systems. They are
used in CPV systems to improve the irradiance uniformity of the systems. In each designed CPV unit,
a plano-concave lens is chosen as the SOE to improve the irradiance uniformity since plano-concave
lenses are very common products in the market and have a low cost compared to other sophisticated
SOE types, such as Köhler integration-based SOEs [
19
–
21
] and others [
23
]. The design of the CPV unit
is shown in Figure 3.
Appl.Sci.2016,6,2514of15
Figure1.Designoftheproposedconcentratorphotovoltaic(CPV)system.Si,silicon.
Figure2.ArraylayoutoftheCPVsystem.MJ,multi‐junction.
2.1.ImprovingIrradianceUniformity
IntheproposedCPVsystem,anarrayofFresnellensesisusedasthePOE.Fresnellensesare
usedassolarconcentratorssincetheyofferhighopticalefficiencyalongwithminimalweightanda
lowcost[31].Plano‐concavelensesareusedtoexpandlightbeamsinopticalsystems.Theyareused
inCPVsystemstoimprovetheirradianceuniformityofthesystems.IneachdesignedCPVunit,a
plano‐concavelensischosenastheSOEtoimprovetheirradianceuniformitysinceplano‐concave
lensesareverycommonproductsinthemarketandhavealowcostcomparedtoothersophisticated
SOEtypes,suchasKöhlerintegration‐basedSOEs[19–21]andothers[23].ThedesignoftheCPVunit
isshowninFigure3.
Figure3.DesignoftheproposedCPVunitwiththesecondaryopticalelement(SOE).
ThePOE(Fresnellens)isusedtoconcentrateincidentsolarradiationintotheSOE.TheSOE
(plano‐concavelens)isusedtoredirectthesunlightintotheMJsolarcellandtouniformlydistribute
theirradiationonthesolarcell.Therefore,thedesignedCPVunitsignificantlyimprovesthe
irradianceuniformitycomparedtotheconventionalCPV.
Theeffectivefocallength(EFL)oftheFresnellensiscalculatedasfollows:
1,(1)
whereistherefractiveindexandistheradiusoftheFresnellens.
Thefocallengthoftheplano‐concavelensiscalculatedby[32]:
Figure 3. Design of the proposed CPV unit with the secondary optical element (SOE).
The POE (Fresnel lens) is used to concentrate incident solar radiation into the SOE. The SOE
(plano-concave lens) is used to redirect the sunlight into the MJ solar cell and to uniformly distribute
the irradiation on the solar cell. Therefore, the designed CPV unit significantly improves the irradiance
uniformity compared to the conventional CPV.
The effective focal length (EFL) of the Fresnel lens is calculated as follows:
EFL =r
n−1, (1)
where nis the refractive index and ris the radius of the Fresnel lens.
Appl. Sci. 2016,6, 251 5 of 15
The focal length of the plano-concave lens is calculated by [32]:
f=Dp
2×N A , (2)
where NA is numerical aperture of the Fresnel lens and Dpis diameter of the plano-concave lens.
In our proposed system, the material used for the Fresnel lens is polymethyl methacrylate (PMMA)
with a refractive index of 1.494. The material used for the plano-concave lens is borosilicate glass
N-BK7 with a refractive index of 1.52. Table 1summarizes the design parameters of the CPV unit.
Table 1. Design parameters of the concentrator photovoltaic (CPV) unit.
Parameter Value
Focal length of the Fresnel lens 300 mm
Size of the Fresnel lens 300 mm ×300 mm
Thickness of the Fresnel lens 3 mm
Material of the Fresnel lens PMMA 1
Focal length of the plano-concave lens 25 mm
Diameter of the plano-concave lens 21.5 mm
Thickness of the plano-concave lens 2 mm
Material of the plano-concave lens N-BK7 2
Distance between the POE 3and SOE 4283 mm
Diameter of the multi-junction solar cell 20 mm
1
PMMA: Polymethyl methacrylate;
2
N-BK7: Borosilicate glass.
3
POE, primary optical element.
4
SOE,
secondary optical element.
2.2. Capturing Diffuse Solar Radiation
Figure 4shows the configuration of the proposed CPV unit for capturing diffuse solar radiation
through the Si solar cell.
Appl.Sci.2016,6,2515of15
2,(2)
whereisnumericalapertureoftheFresnellensandisdiameteroftheplano‐concavelens.
Inourproposedsystem,thematerialusedfortheFresnellensispolymethylmethacrylate
(PMMA)witharefractiveindexof1.494.Thematerialusedfortheplano‐concavelensisborosilicate
glassN‐BK7witharefractiveindexof1.52.Table1summarizesthedesignparametersoftheCPV
unit.
Table1.Designparametersoftheconcentratorphotovoltaic(CPV)unit.
Parameter Value
FocallengthoftheFresnellens300mm
SizeoftheFresnellens300mm×300mm
ThicknessoftheFresnellens3mm
MaterialoftheFresnellensPMMA1
Focallengthoftheplano‐concavelens25mm
Diameteroftheplano‐concavelens21.5mm
Thicknessoftheplano‐concavelens2mm
Materialoftheplano‐concavelensN‐BK72
DistancebetweenthePOE3andSOE4283mm
Diameterofthemulti‐junctionsolarcell20mm
1PMMA:Polymethylmethacrylate;2N‐BK7:Borosilicateglass.3POE,primaryopticalelement.
4SOE,secondaryopticalelement.
2.2.CapturingDiffuseSolarRadiation
Figure4showstheconfigurationoftheproposedCPVunitforcapturingdiffusesolarradiation
throughtheSisolarcell.
Figure4.DesignoftheproposedCPVunitwiththeSOEandlow‐costcell.
Figure5showsray‐tracingoftheCPVunitwiththeSisolarcell.ThesizeoftheSisolarcellis
equaltosizeofthearrayofFresnellensesoftheCPVsystem.
ThelayoutoftheproposedCPVsystemwiththearrayofnineCPVunitsandtheadditionalSi
solarcellisshowninFigure2.Inthedesign,directsunraysareconcentratedbytheFresnellenses
Figure 4. Design of the proposed CPV unit with the SOE and low-cost cell.
Figure 5shows ray-tracing of the CPV unit with the Si solar cell. The size of the Si solar cell is
equal to size of the array of Fresnel lenses of the CPV system.
Appl. Sci. 2016,6, 251 6 of 15
Appl.Sci.2016,6,2516of15
andredirectedanddistributeduniformlybytheplano‐concavelensesontheMJsolarcells.Diffuse
sunraysfromtheskyandthroughtheFresnellensesarethencollectedbytheadditionalSisolarcell.
Additionally,directraysthatarehitoutsidetheFresnellensregionarealsocapturedbytheSisolar
cell.
Figure5.Ray‐tracingofthedesignedCPVunitwiththeSOEandSisolarcell.
3.PerformanceAnalysisandSimulations
3.1.IrradianceUniformityvs.OpticalLoss
AddingtheSOEtotheCPVunitimprovestheirradianceuniformitybutcausesopticallossin
theunit.Thissectionanalyzes,evaluates,andcomparestheirradianceuniformityandoptical
efficiencyoftheproposedCPVunittotheconventionalCPVunit.Inthiscase,theadditionalSicell
isnotincludedintheanalysisandevaluation.Inotherwords,theconsideredCPVunitcontainsthe
MJsolarcell,butnottheSisolarcell.
ThegeometricalstructureoftheproposedCPVunitwasdesignedandsimulatedbyusingthe
commercialopticalmodelingsoftware,LightTools™[33].Inourdesignandsimulations,thematerial
usedfortheFresnellenswasPMMAwitharefractiveindexof1.49.Thematerialusedfortheplano‐
concavelenswasborosilicateglassN‐BK7witharefractiveindexof1.52.Thesimulationparameters
werethesameasthoseofthedesignshowninTable1.SincetheLightToolssoftwaredoesnot
supportscirclesolarcells,squaresolarcellswithsizeof20mm×20mmwereusedinthesimulation
models.
Ray‐tracinglayoutsoftheconventionalCPVunitandtheproposedCPVunitwiththeSOEare
showninFigure6a,b,respectively.IntheproposedCPVunit,thePOEconcentratedandfocused
directsunraysontheSOE’ssurface,andthentheSOEdistributedthesunraysoverthesolarcell
uniformly,asshowninFigure6b.
Figure 5. Ray-tracing of the designed CPV unit with the SOE and Si solar cell.
The layout of the proposed CPV system with the array of nine CPV units and the additional
Si solar cell is shown in Figure 2. In the design, direct sunrays are concentrated by the Fresnel
lenses and redirected and distributed uniformly by the plano-concave lenses on the MJ solar cells.
Diffuse sunrays from the sky and through the Fresnel lenses are then collected by the additional Si
solar cell. Additionally, direct rays that are hit outside the Fresnel lens region are also captured by the
Si solar cell.
3. Performance Analysis and Simulations
3.1. Irradiance Uniformity vs. Optical Loss
Adding the SOE to the CPV unit improves the irradiance uniformity but causes optical loss in the
unit. This section analyzes, evaluates, and compares the irradiance uniformity and optical efficiency of
the proposed CPV unit to the conventional CPV unit. In this case, the additional Si cell is not included
in the analysis and evaluation. In other words, the considered CPV unit contains the MJ solar cell,
but not the Si solar cell.
The geometrical structure of the proposed CPV unit was designed and simulated by using
the commercial optical modeling software, LightTools
™
[
33
]. In our design and simulations, the
material used for the Fresnel lens was PMMA with a refractive index of 1.49. The material used for
the plano-concave lens was borosilicate glass N-BK7 with a refractive index of 1.52. The simulation
parameters were the same as those of the design shown in Table 1. Since the LightTools software
does not supports circle solar cells, square solar cells with size of 20 mm
×
20 mm were used in the
simulation models.
Ray-tracing layouts of the conventional CPV unit and the proposed CPV unit with the SOE are
shown in Figure 6a,b, respectively. In the proposed CPV unit, the POE concentrated and focused direct
sunrays on the SOE’s surface, and then the SOE distributed the sun rays over the solar cell uniformly,
as shown in Figure 6b.
Appl. Sci. 2016,6, 251 7 of 15
Appl.Sci.2016,6,2517of15
(a)(b)
Figure6.LayoutofCPVunitsunderray‐tracingsimulation:(a)aconventionalCPVunit;and(b)the
proposedCPVunit.
3.1.1.IrradianceUniformity
Toevaluateandcomparetheirradianceuniformity,theirradiationdistributionofboththe
conventionalandproposedCPVunitswasmeasured.Figure7a,bshowtheirradiationdistribution
oftheconventionalandproposedCPVunits,respectively.Thesimulatedresultsshowedthatthe
proposedCPVunitwiththeSOEgavebetteruniformirradiancedistributionoverthesolarcellthan
theconventionalCPVwithouttheSOE.
(a)
(b)
Figure7.Irradiancedistributiononthesolarcell:(a)theconventionalCPVunit;and(b)theproposed
CPVunit.
Figure 6.
Layout of CPV units under ray-tracing simulation: (
a
) a conventional CPV unit; and (
b
) the
proposed CPV unit.
3.1.1. Irradiance Uniformity
To evaluate and compare the irradiance uniformity, the irradiation distribution of both the
conventional and proposed CPV units was measured. Figure 7a,b show the irradiation distribution
of the conventional and proposed CPV units, respectively. The simulated results showed that the
proposed CPV unit with the SOE gave better uniform irradiance distribution over the solar cell than
the conventional CPV without the SOE.
Appl.Sci.2016,6,2517of15
(a)(b)
Figure6.LayoutofCPVunitsunderray‐tracingsimulation:(a)aconventionalCPVunit;and(b)the
proposedCPVunit.
3.1.1.IrradianceUniformity
Toevaluateandcomparetheirradianceuniformity,theirradiationdistributionofboththe
conventionalandproposedCPVunitswasmeasured.Figure7a,bshowtheirradiationdistribution
oftheconventionalandproposedCPVunits,respectively.Thesimulatedresultsshowedthatthe
proposedCPVunitwiththeSOEgavebetteruniformirradiancedistributionoverthesolarcellthan
theconventionalCPVwithouttheSOE.
(a)
(b)
Figure7.Irradiancedistributiononthesolarcell:(a)theconventionalCPVunit;and(b)theproposed
CPVunit.
Figure 7.
Irradiance distribution on the solar cell: (
a
) the conventional CPV unit; and (
b
) the proposed
CPV unit.
3.1.2. Optical Loss
An optical loss factor
l
was used to analyze and evaluate the optical efficiency of the proposed
CPV with the SOE compared with that of a conventional CPV.
The optical loss factor lis determined by:
l=ηC
opt_CPV −ηD
opt_CPV
ηC
opt_CPV
, (3)
Appl. Sci. 2016,6, 251 8 of 15
where
ηC
opt_CPV
and
ηD
opt_CPV
are the optical efficiency of the conventional and proposed CPV
units, respectively:
ηC
opt_CPV =PC
in_cell
Pin_FL
, (4)
ηD
opt_CPV =PD
in_cell
Pin_FL
, (5)
where
PC
in_cell
and
PD
in_cell
is the incident solar power received at the MJ solar cell of the conventional
and proposed CPV units, respectively, and
Pin_FL
is the incident solar radiation hit on the Fresnel
lens’s surface.
Equation (3) is then re-written as follows:
l=PC
in_cell −PD
in_cell
PC
in_cell
. (6)
Several simulations were conducted with various sunlight vertical incident luminous flux values
to evaluate the loss factor of the proposed CPV unit. The incident power received at the solar cell
was recorded in the simulations. Figure 8a shows the incident power received at the solar cell of both
conventional and proposed CPV units, and Figure 8b shows the optical loss of the proposed CPV
unit compared to the conventional CPV unit. The simulation results showed that the loss factor of
the proposed CPV unit was 5.86%. In other words, the proposed CPV unit with the SOE resulted in
optical loss of 5.86% compared to the conventional CPV unit without the SOE.
Appl.Sci.2016,6,2518of15
3.1.2.OpticalLoss
Anopticallossfactorwasusedtoanalyzeandevaluatetheopticalefficiencyoftheproposed
CPVwiththeSOEcomparedwiththatofaconventionalCPV.
Theopticallossfactorisdeterminedby:
η
_
η
_
η
_
,(3)
whereη_
andη_
aretheopticalefficiencyoftheconventionalandproposedCPVunits,
respectively:
η
_
_
_
,(4)
η
_
_
_
,(5)
where_
and_
istheincidentsolarpowerreceivedattheMJsolarcelloftheconventional
andproposedCPVunits,respectively,and_istheincidentsolarradiationhitontheFresnel
lens’ssurface.
Equation(3)isthenre‐writtenasfollows:
_
_
_
.(6)
Severalsimulationswereconductedwithvarioussunlightverticalincidentluminousfluxvalues
toevaluatethelossfactoroftheproposedCPVunit.Theincidentpowerreceivedatthesolarcellwas
recordedinthesimulations.Figure8ashowstheincidentpowerreceivedatthesolarcellofboth
conventionalandproposedCPVunits,andFigure8bshowstheopticallossoftheproposedCPV
unitcomparedtotheconventionalCPVunit.Thesimulationresultsshowedthatthelossfactorofthe
proposedCPVunitwas5.86%.Inotherwords,theproposedCPVunitwiththeSOEresultedin
opticallossof5.86%comparedtotheconventionalCPVunitwithouttheSOE.
(a)(b)
Figure8.(a)comparisonofincidentpowerreceivedatthecellsoftheconventionalandproposed
CPVunits;and(b)opticallossoftheproposedCPVunitcomparedtotheconventionalCPVunit.
3.1.3.AcceptanceAngle
IntheCPVfield,anacceptanceangleistheincidenceangleatwhichtheconcentratorcollects
90%oftheon‐axispower.Theacceptanceanglehasatradeoffwiththeconcentration.Increasingthe
acceptanceanglereducestheconcentrationpermanently[34].Thistradeoffisdescribedthroughthe
concentration‐acceptanceangleproduct(CAP),beinganappropriatemeritfunctionfora
concentrator:
Figure 8.
(
a
) comparison of incident power received at the cells of the conventional and proposed CPV
units; and (b) optical loss of the proposed CPV unit compared to the conventional CPV unit.
3.1.3. Acceptance Angle
In the CPV field, an acceptance angle is the incidence angle at which the concentrator collects
90% of the on-axis power. The acceptance angle has a tradeoff with the concentration. Increasing the
acceptance angle reduces the concentration permanently [
34
]. This tradeoff is described through the
concentration-acceptance angle product (CAP), being an appropriate merit function for a concentrator:
CAP =qCgsin α, (7)
where
α
is the acceptance angle, and
Cg
is the geometric concentration, defined as the ratio of the
concentrator aperture area to solar cell area [19].
Appl. Sci. 2016,6, 251 9 of 15
Figure 9a,b demonstrate the ray-tracing results of the conventional and proposed CPV units,
respectively, when the incidence angle is 1.2◦.
Appl.Sci.2016,6,2519of15
sinα,(7)
whereαistheacceptanceangle,andisthegeometricconcentration,definedastheratioofthe
concentratorapertureareatosolarcellarea[19].
Figure9a,bdemonstratetheray‐tracingresultsoftheconventionalandproposedCPVunits,
respectively,whentheincidenceangleis1.2°.
(a)(b)
Figure9.Ray‐tracingatincidenceangleof1.2°:(a)theconventionalCPVunit;and(b)theproposed
CPVunit.
Theray‐tracingresultsshowedthattheproposedCPVunitwithusingasimpleplano‐concave
lensastheSOEreducedafewincidenceangleofsunrayscomparedtotheconventionalCPVunit.
ThisresultedinasmallreductionintheacceptanceangleoftheproposedCPVunit.Toacertain
degree,however,usingaccuratetwo‐axissuntrackingsystemintheproposedCPVsystemcan
overcometheproblem.
Figure10showstheangulartransmissioncurveforbothCPVunits.Thesimulationresultsshow
thattheproposedCPVunithasa90%acceptanceangleof1.05°,whichisalittlelessthanthe
conventionalCPVunit,whoseacceptanceangleisabout1.16°.
Figure10.Theangulartransmissioncurvevs.incidentangleforbothconventionalandproposedCPV
units.
3.1.4.Discussion
UsingtheSOE,theproposedCPVunitaddedanadditionalopticallosstothesystem.However,
theopticallossof5.86%causedbytheSOEfoundinthesimulationissmallandcanbecompensated
forusingtheSilow‐costcelltocapturediffusesolarradiation,whichisdiscussedinthenextsection.
Meanwhile,byusingtheSOE,theproposedCPVunitsignificantlyimprovedtheirradiance
Figure 9.
Ray-tracing at incidence angle of 1.2
◦
: (
a
) the conventional CPV unit; and (
b
) the proposed
CPV unit.
The ray-tracing results showed that the proposed CPV unit with using a simple plano-concave
lens as the SOE reduced a few incidence angle of sunrays compared to the conventional CPV unit.
This resulted in a small reduction in the acceptance angle of the proposed CPV unit. To a certain degree,
however, using accurate two-axis sun tracking system in the proposed CPV system can overcome
the problem.
Figure 10 shows the angular transmission curve for both CPV units. The simulation results
show that the proposed CPV unit has a 90% acceptance angle of
±
1.05
◦
, which is a little less than the
conventional CPV unit, whose acceptance angle is about ±1.16◦.
Appl.Sci.2016,6,2519of15
sinα,(7)
whereαistheacceptanceangle,andisthegeometricconcentration,definedastheratioofthe
concentratorapertureareatosolarcellarea[19].
Figure9a,bdemonstratetheray‐tracingresultsoftheconventionalandproposedCPVunits,
respectively,whentheincidenceangleis1.2°.
(a)(b)
Figure9.Ray‐tracingatincidenceangleof1.2°:(a)theconventionalCPVunit;and(b)theproposed
CPVunit.
Theray‐tracingresultsshowedthattheproposedCPVunitwithusingasimpleplano‐concave
lensastheSOEreducedafewincidenceangleofsunrayscomparedtotheconventionalCPVunit.
ThisresultedinasmallreductionintheacceptanceangleoftheproposedCPVunit.Toacertain
degree,however,usingaccuratetwo‐axissuntrackingsystemintheproposedCPVsystemcan
overcometheproblem.
Figure10showstheangulartransmissioncurveforbothCPVunits.Thesimulationresultsshow
thattheproposedCPVunithasa90%acceptanceangleof1.05°,whichisalittlelessthanthe
conventionalCPVunit,whoseacceptanceangleisabout1.16°.
Figure10.Theangulartransmissioncurvevs.incidentangleforbothconventionalandproposedCPV
units.
3.1.4.Discussion
UsingtheSOE,theproposedCPVunitaddedanadditionalopticallosstothesystem.However,
theopticallossof5.86%causedbytheSOEfoundinthesimulationissmallandcanbecompensated
forusingtheSilow‐costcelltocapturediffusesolarradiation,whichisdiscussedinthenextsection.
Meanwhile,byusingtheSOE,theproposedCPVunitsignificantlyimprovedtheirradiance
Figure 10.
The angular transmission curve vs. incident angle for both conventional and proposed
CPV units.
3.1.4. Discussion
Using the SOE, the proposed CPV unit added an additional optical loss to the system. However,
the optical loss of 5.86% caused by the SOE found in the simulation is small and can be compensated
for using the Si low-cost cell to capture diffuse solar radiation, which is discussed in the next section.
Meanwhile, by using the SOE, the proposed CPV unit significantly improved the irradiance uniformity
compared to the conventional CPV unit without the SOE, resulting in the elimination of hot spots and
increasing the performance and lifetime of the solar cell.
Additionally, using an existing simple plano-concave lens as the SOE resulted in a small reduction
of the acceptance angle of the proposed CPV system. The problem can be resolved by designing a new
Appl. Sci. 2016,6, 251 10 of 15
SOE type in order to improve not only the irradiation uniformity, but also the acceptance angle of the
proposed CPV system.
3.2. System Efficiency
This section describes the system efficiency analysis of the proposed CPV system with the Si solar
cell for capturing diffuse solar radiation compared to the conventional CPV system without using the
additional solar cell.
A CPV system consisting of an CPV unit and an Si low-cost solar cell was considered. The design
of the CPV system is shown in Figure 4, and its ray-tracing layout is shown in Figure 5.
3.2.1. Optical Power Ratio
The optical power ratio of the CPV unit is simply defined as the ratio of the solar radiation
received by the solar cells to the solar radiation hit on the Fresnel lens’s surface.
The optical power ratio is calculated by:
ηopt_CPV =Pin_cell
Pin_FL
, (8)
where
Pin_cell
is the incident solar radiation received at the solar cells and
Pin_FL
is incident solar
radiation hit on the Fresnel lens’s surface of the CPV unit.
For the proposed CPV unit, the incident solar radiation received at the solar cells including the
MJ solar cell and the Si solar cell is determined by:
Pin_cell =Pin_MJ_cell +Pin_Si_cell, (9)
where
Pin_MJ_cell
and
Pin_Si_cell
are the incident solar radiation received at the MJ and Si solar
cells, respectively.
To evaluate the efficiency of the designed CPV units, the following CPV units were considered,
including a CPV unit without the SOE and the additional low-cost cell, a CPV unit with the SOE, and
the designed CPV unit with both the SOE and the additional low-cost cell. The models of these CPV
units are shown in Figure 11a–c, respectively.
Appl.Sci.2016,6,25110of15
uniformitycomparedtotheconventionalCPVunitwithouttheSOE,resultingintheeliminationof
hotspotsandincreasingtheperformanceandlifetimeofthesolarcell.
Additionally,usinganexistingsimpleplano‐concavelensastheSOEresultedinasmall
reductionoftheacceptanceangleoftheproposedCPVsystem.Theproblemcanberesolvedby
designinganewSOEtypeinordertoimprovenotonlytheirradiationuniformity,butalsothe
acceptanceangleoftheproposedCPVsystem.
3.2.SystemEfficiency
ThissectiondescribesthesystemefficiencyanalysisoftheproposedCPVsystemwiththeSi
solarcellforcapturingdiffusesolarradiationcomparedtotheconventionalCPVsystemwithout
usingtheadditionalsolarcell.
ACPVsystemconsistingofanCPVunitandanSilow‐costsolarcellwasconsidered.Thedesign
oftheCPVsystemisshowninFigure4,anditsray‐tracinglayoutisshowninFigure5.
3.2.1.OpticalPowerRatio
TheopticalpowerratiooftheCPVunitissimplydefinedastheratioofthesolarradiation
receivedbythesolarcellstothesolarradiationhitontheFresnellens’ssurface.
Theopticalpowerratioiscalculatedby:
η
_
_
_
,(8)
where_istheincidentsolarradiationreceivedatthesolarcellsandP_isincidentsolar
radiationhitontheFresnellens’ssurfaceoftheCPVunit.
FortheproposedCPVunit,theincidentsolarradiationreceivedatthesolarcellsincludingthe
MJsolarcellandtheSisolarcellisdeterminedby:
_
_
_
_
_
,(9)
where__and__aretheincidentsolarradiationreceivedattheMJandSisolarcells,
respectively.
ToevaluatetheefficiencyofthedesignedCPVunits,thefollowingCPVunitswereconsidered,
includingaCPVunitwithouttheSOEandtheadditionallow‐costcell,aCPVunitwiththeSOE,and
thedesignedCPVunitwithboththeSOEandtheadditionallow‐costcell.ThemodelsoftheseCPV
unitsareshowninFigure11a–c,respectively.
SimulationswereconductedusingLightTools™toevaluateandcomparetheopticalpowerratio
ofthedesignedCPVunitwiththatoftheotherCPVunits.TheopticalpowerratiooftheCPVunits
inthesimulationswasrecordedandisshowninFigure12a,b,respectively.Thesimulationresults
showedthattheopticalpowerratioofthedesignedCPVunitisbetterthanthatoftheotherCPV
units.
(a)(b) (c)
Figure11.CPVunits:(a)theCPVunitwithouttheSOEandlow‐costcell;(b)theCPVunitwiththe
SOE;and(c)thedesignedCPVunitwithboththeSOEandlow‐costcell.
Figure 11.
CPV units: (
a
) the CPV unit without the SOE and low-cost cell; (
b
) the CPV unit with the
SOE; and (c) the designed CPV unit with both the SOE and low-cost cell.
Simulations were conducted using LightTools
™
to evaluate and compare the optical power ratio
of the designed CPV unit with that of the other CPV units. The optical power ratio of the CPV units
in the simulations was recorded and is shown in Figure 12a,b, respectively. The simulation results
showed that the optical power ratio of the designed CPV unit is better than that of the other CPV units.
Appl. Sci. 2016,6, 251 11 of 15
Appl.Sci.2016,6,25111of15
(a)(b)
Figure12.(a)comparisonofincidentsolarpowerreceivedatthesolarcellsofCPVunits;and(b)
comparisonoftheopticalpowerratiobetweenCPVunits.
3.2.2.SystemConversionEfficiency
ConversionefficiencyisameasureusedtoanalyzeandevaluatetheperformanceofaCPV
system.ConversionefficiencyisdefinedastheratioofenergyoutputfromtheCPVsystemtoinput
energyfromthesun.TheefficiencyofaCPVsystemdependsontheconversionefficiencyofsolar
cellsusedinthesystem,theopticalefficiencyoftheCPVunits,andthespectrumandintensityofthe
incidentsunlight.
Thetotalsolarradiationonahorizontalsurface,denotedbyG,isthesumofhorizontalbeam
(direct)solarradiationanddiffusesolarradiation[1]:
,(10)
whereisbeamradiationonahorizontalsurface(directnormalirradiation),isdiffuse
radiationonahorizontalsurface,andisglobalhorizontalirradiation.
TheconversionefficiencyofaconventionalCPVsystem,denotedbyη,isgivenby[28]:
ηη
_
η
_
,(11)
where_and_aretheopticalefficiencyoftheCPVbasedondirectsolarradiationand
theconversionefficiencyoftheMJsolarcell,respectively.
TheproposedCPVsystemcapturesbothdirectanddiffusesolarradiation,soitsconversion
efficiencydependsonnotonlydirectsolarradiation,butalsodiffusesolarradiation.Theconversion
efficiencyofthedesignedCPVsystem,denotedbyη,canbecalculatedby[28]:
ηη
_
η
_
η
_
η
_
,(12)
whereη_andη_aretheopticalefficiencyoftheSilow‐costsolarcellbasedondiffusesolar
radiationandtheconversionefficiencyoftheSisolarcell,respectively.
Animprovementfactorofsystemefficiencywasusedtoanalyzeandevaluatethesystem
efficiencyoftheproposedCPVsystemwiththeSilow‐costsolarcellcomparedwiththatofthe
conventionalCPVsystemwithoutthelow‐costsolarcell.
Theimprovementfactorisdeterminedasfollows:
ηη
η.(13)
Bysubstituting(11)and(12)into(13),theimprovementfactorisre‐writtenasfollows:
η
_
η
_
η
_
η
_
.(14)
Figure 12.
(
a
) comparison of incident solar power received at the solar cells of CPV units; and
(b) comparison of the optical power ratio between CPV units.
3.2.2. System Conversion Efficiency
Conversion efficiency is a measure used to analyze and evaluate the performance of a CPV system.
Conversion efficiency is defined as the ratio of energy output from the CPV system to input energy
from the sun. The efficiency of a CPV system depends on the conversion efficiency of solar cells
used in the system, the optical efficiency of the CPV units, and the spectrum and intensity of the
incident sunlight.
The total solar radiation on a horizontal surface, denoted by G, is the sum of horizontal beam
(direct) solar radiation and diffuse solar radiation [1]:
G=GB+GD, (10)
where
GB
is beam radiation on a horizontal surface (direct normal irradiation),
GD
is diffuse radiation
on a horizontal surface, and Gis global horizontal irradiation.
The conversion efficiency of a conventional CPV system, denoted by ηC, is given by [28]:
ηC=ηopt_CPVηcell_CPV GB
G, (11)
where
ηopt_CPV
and
ηcell_CPV
are the optical efficiency of the CPV based on direct solar radiation and
the conversion efficiency of the MJ solar cell, respectively.
The proposed CPV system captures both direct and diffuse solar radiation, so its conversion
efficiency depends on not only direct solar radiation, but also diffuse solar radiation. The conversion
efficiency of the designed CPV system, denoted by ηD, can be calculated by [28]:
ηD=ηopt_CPVηcell_CPV GB+ηopt_PVηcell_PVGD
G, (12)
where
ηopt_PV
and
ηcell_PV
are the optical efficiency of the Si low-cost solar cell based on diffuse solar
radiation and the conversion efficiency of the Si solar cell, respectively.
An improvement factor of system efficiency
f
was used to analyze and evaluate the system
efficiency of the proposed CPV system with the Si low-cost solar cell compared with that of the
conventional CPV system without the low-cost solar cell.
The improvement factor fis determined as follows:
f=ηD−ηC
ηC
. (13)
Appl. Sci. 2016,6, 251 12 of 15
By substituting (11) and (12) into (13), the improvement factor fis re-written as follows:
f=ηopt_PVηcell_PV
ηopt_CPVηcell_CPV
×GD
GB
. (14)
Let τand ρbe:
τ=ηopt_CPVηcell_CPV
ηopt_PVηcell_PV
, (15)
ρ=GD
G, (16)
where
τ
is the ratio of the conversion efficiency of the MJ solar cell to that of the Si solar cell in the
CPV system, and
ρ
is the diffuse-to-global ratio, or the ratio of diffuse solar radiation to the global
solar radiation.
The improvement factor fis then determined as follows:
f=ρ
τ(1−ρ). (17)
Figure 13 shows the improvement factor
f
values for seven
ρ
values (0.1
÷
0.7) with
τ=
1, 2,
and 3, respectively. For
τ=
2, an improvement
f
of 33.3% is expected for a medium DNI region with
ρ∼
=0.4, whereas an improvement fof 12.5% is expected for a high DNI region with ρ∼
=0.2.
Appl.Sci.2016,6,25112of15
Letτandρbe:
τη
_
η
_
η
_
η
_
,(15)
ρ
,(16)
whereτistheratiooftheconversionefficiencyoftheMJsolarcelltothatoftheSisolarcellinthe
CPVsystem,andρisthediffuse‐to‐globalratio,ortheratioofdiffusesolarradiationtotheglobal
solarradiation.
Theimprovementfactoristhendeterminedasfollows:
ρ
τ1ρ.(17)
Figure13showstheimprovementfactorvaluesforsevenρvalues(0.10.7)withτ1,
2,and3,respectively.Forτ2,animprovementof33.3%isexpectedforamediumDNIregion
withρ≅0.4,whereasanimprovementof12.5%isexpectedforahighDNIregionwithρ≅0.2.
Figure13.Improvementfactorvs.diffuse‐to‐globalratio.
3.2.3.SystemCost
ToevaluateandcomparethecostefficiencyoftheproposedCPVsystemwithanadditionallow‐
costsolarcelltothatoftheconventionalCPVsystemwithouttheadditionallow‐costsolarcell,the
following“meritfunction”Risusedasthecapitalcostofannualelectricalenergydelivered.SinceR
isexpressedascostperunitofpower,lowvaluesofRaremoremeritorious[29]:
$
.(18)
ThemeritfunctionRandenergyoutputEoftheconventionalCPVsystemaredeterminedas
follows[29]:
,(19)
η
_
η
_
,(20)
whereandisthecapitalcostofannualgeneratedelectricalenergyandthenominalannual
DCelectricalenergydensityoftheconventionalCPVsystem,respectively.andarethe
coststhatareproportionaltosystementryaperturearea(themodulecover,frame,trackingsystem,
thestructuralsupportingbeams,landuse,etc.),andsystempower(inverter,etc.),respectively.
andarecommontotherespectiveCPVsystems;andisthecostspecifictotheuseof
thehighefficiencyMJcells(MJcells,heatsink,etc.).
Figure 13. Improvement factor vs. diffuse-to-global ratio.
3.2.3. System Cost
To evaluate and compare the cost efficiency of the proposed CPV system with an additional
low-cost solar cell to that of the conventional CPV system without the additional low-cost solar cell, the
following “merit function” Ris used as the capital cost of annual electrical energy delivered. Since Ris
expressed as cost per unit of power, low values of Rare more meritorious [29]:
R=system cost ($)
annual nominal generated electrical energy (kWh). (18)
The merit function Rand energy output Eof the conventional CPV system are determined as
follows [29]:
RC=C0+CCPV
EC
+Cnon−cell, (19)
EC=GB×ηcell_CPVηopt_CPV, (20)
Appl. Sci. 2016,6, 251 13 of 15
where
RC
and
EC
is the capital cost of annual generated electrical energy and the nominal annual DC
electrical energy density of the conventional CPV system, respectively.
C0
and
Cnon−cell
are the costs
that are proportional to system entry aperture area (the module cover, frame, tracking system, the
structural supporting beams, land use, etc.), and system power (inverter, etc.), respectively.
C0
and
Cnon−cell
are common to the respective CPV systems; and
CCPV
is the cost specific to the use of the
high efficiency MJ cells (MJ cells, heat sink, etc.).
The merit function and energy output of the proposed CPV system with the additional low-cost
solar cell are calculated as follows [29]:
RD=C0+CCPV +CPV
ED
+Cnon−cell, (21)
ED=GB×ηcell_CPVηopt_CPV +GD×ηcell_PVηopt_PV , (22)
where
RD
and
ED
is the capital cost of annual generated electrical energy and the nominal annual DC
electrical energy density of the proposed CPV system, respectively; and
CPV
is the cost specific to the
use of the additional low-cost solar cell.
Some experimental results [
28
–
30
] showed that the CPV system with the additional low-cost
solar cell outperformed the conventional CPV without the additional solar cell, with
ED/EC=
1.15.
The addition of the low-cost solar cell to the CPV system resulted in 15% more electricity generated
per dollar.
3.2.4. Discussion
Numerically, for our simulations, the proposed CPV unit with the SOE and the Si low-cost cell
(Figure 11c) provided an optical power ratio increase of about 17.12% compared to the conventional
CPV unit without using the additional low-cost cell (Figure 11b), and about 10.26% compared to
the conventional CPV unit without using both the SOE and the additional low-cost cell (Figure 11a).
In other words, the optical power ratio of the proposed CPV unit is better than that of the other CPV
units. By using both the SOE and the additional low-cost cell, the proposed CPV not only improves
the irradiance uniformity but also increases the optical power ratio of the system.
For the system conversion efficiency, the conversion efficiency ratio
τ
depends on the type of MJ
and additional low-cost solar cells as well as the optical system. The improvement factor decreases
with an increasing ratio
τ
because the electricity generated by the MJ solar cell is high compared to
that generated by the Si solar cell. The ratio
ρ
depends on the atmospheric conditions, e.g., the annual
mean value for a medium DNI region, such as Korea or Japan, is
ρ∼
=
0.4, while that for a high DNI
region, such as Phoenix (USA), is
ρ∼
=
0.2 [
28
]. The improvement factor increases with an increasing
ratio
ρ
because the amount of diffuse solar radiation collected by the additional solar cell increases
compared to that for direct solar radiation concentrated on the MJ solar cell.
Since the proposed CPV system uses an additional low-cost solar cell, the cost of the system is
higher than that of conventional CPV systems. However, the proposed system uses low-cost optical
components, including Fresnel and plano-concave lenses, and an additional low-cost cell; the cost
of the system is thus not much higher than that of the conventional CPV systems. The use of the
additional low-cost solar cell resulted in more electricity generated per dollar.
4. Conclusions
In this paper, we proposed a novel CPV system to improve both irradiation uniformity and
system efficiency. Each CPV unit of the proposed system uses a Fresnel lens as the POE associated
with a plano-concave lens as the SOE to highly concentrate and uniformly distribute the sunlight
over a MJ solar cell. By using the SOE, the irradiance uniformity is significantly improved in the
system. Additionally, the system also uses an additional low-cost solar cell to harvest diffuse solar
radiation. The direct solar radiation is concentrated and focused by the Fresnel lenses and then
Appl. Sci. 2016,6, 251 14 of 15
distributed uniformly by the plano-concave lenses on the MJ solar cells, whereas the diffuse solar
radiation is captured by the low-cost solar cell. Therefore, the conversion efficiency of the designed
system is significantly increased. The analyzed and simulated results show that the proposed CPV
system significantly improves both the irradiance uniformity and the system efficiency compared to
the conventional CPV systems. Numerically, for our simulation models, the designed CPV with the
SOE and low-cost solar cell provided the optical power ratio increase of about 17.12% compared to
the conventional CPV without the low-cost cell, and about 10.26% compared to the conventional CPV
without using both the SOE and additional low-cost cell. The study is the first to integrate both the
improvement of irradiance uniformity and the collection of diffuse solar radiation into a CPV system.
The proposed CPV system is very suitable for medium DNI regions, such as Korea and Japan.
Our future work is to design a new SOE type that is used to replace the simple plano-concave
lens of the CPV unit in order to improve not only the irradiation uniformity, but also the acceptance
angle of the proposed CPV system.
Acknowledgments:
This work was supported by the National Research Foundation of Korea (NRF) grant funded
by the Korea government (MSIP) (No. 2014R1A2A1A11051888).
Author Contributions:
Nguyen Xuan Tien and Seoyong Shin conceived of and developed the ideas behind
the research. Nguyen Xuan Tien performed the performance analysis and simulations, and wrote the paper.
Seoyong Shin supervised the research.
Conflicts of Interest: The authors declare no conflict of interest.
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