A Concentrator Photovoltaic System Based on a Combination ... - MDPI

energies Article

A Concentrator Photovoltaic System Based on a Combination of Prism-Compound Parabolic Concentrators Ngoc Hai Vu and Seoyong Shin * Department of Information and Communication Engineering, Myongji University, San 38-2 Nam-dong, Yongin 449-728, Korea; [email protected] * Correspondence: [email protected]; Tel.: +82-102-709-6483 Academic Editor: Jean-Michel Nunzi Received: 31 May 2016; Accepted: 5 August 2016; Published: 16 August 2016

Abstract: We present a cost-effective concentrating photovoltaic system composed of a prism and a compound parabolic concentrator (P-CPC). In this approach, the primary collector consists of a prism, a solid compound parabolic concentrator (CPC), and a slab waveguide. The prism, which is placed on the input aperture of CPC, directs the incoming sunlight beam to be parallel with the main axes of parabolic rims of CPC. Then, the sunlight is reflected at the parabolic rims and concentrated at the focal point of these parabolas. A slab waveguide is coupled at the output aperture of the CPC to collect focused sunlight beams and to guide them to the solar cell. The optical system was modeled and simulated with commercial ray tracing software (LightTools™). Simulation results show that the optical efficiency of a P-CPC can achieve up to 89%. when the concentration ratio of the P-CPC is fixed at 50. We also determine an optimal geometric structure of P-CPC based on simulation. Because of the simplicity of the P-CPC structure, a lower-cost mass production process is possible. A simulation based on optimal structure of P-CPC was performed and the results also shown that P-CPC has high angular tolerance for input sunlight. The high tolerance of the input angle of sunlight allows P-CPC solar concentrator utilize a single sun tracking system instead of a highly precise dual suntracking system as cost effective solution. Keywords: concentrator photovoltaic; compound parabolic concentrator; solar cell

1. Introduction Concentrator photovoltaic (CPV) technology is an effective means of reducing the use of solar cell material. A CPV system utilizes the optical concentrator to focus sunlight to small solar cells [1]. The CPV systems in use today can be divided into two main categories: Fresnel lens refractors (or parabolic reflectors) and compound parabolic concentrators (CPCs) [2–5]. A typical system using a Fresnel lens, as shown in Figure 1a, consists of a primary concentrating optical element (Fresnel lens) that concentrates the solar radiation and a secondary optical element [6]. However, in order to collect light efficiently, it is necessary to concentrate the sunlight at a high ratio, which requires extremely precise alignment and a precise electromechanical sun tracking system to focus sunlight onto the surface of solar cells [7]. These features make it difficult for most Fresnel lens solar collectors for CPV applications to provide a cost-effective solution and become successful in the market. The concept of a CPC as a solar concentrator has been interested in the field of CPV typically only for low concentration (50), meanwhile it maintains the advantages of CPCs, such as low fabrication costs and onlow solar cells (>50), meanwhilewhich it maintains of CPCs, suchofasmass lowproducing fabrication costs alignment requirements, facilitatesthe theadvantages viable commercialization costand low alignment requirements, which of facilitates thesystem, viable design commercialization of their masseffects producing effective CPV systems. The components the optical parameters and on the optical performance are discussed Sections 2 and 3 in detail. The CPV system using the

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cost-effective CPV Energies 2016, 9, 645

systems. The components of the optical system, design parameters and 3their of 13 effects on the optical performance are discussed Sections 2 and 3 in detail. The CPV system using the combination combination of of prism-CPC prism-CPC (P-CPC) (P-CPC) described described in in this this study study is is aa new new design design that that shows shows the potential potential for in bulk. bulk. for cost-effectiveness cost-effectiveness when when it it is is manufactured manufactured in 2. Proposed ProposedSunlight SunlightConcentrator Concentratorof ofCPV CPVSystem System 2. In this this section, section, we we introduce introduce the the conceptual conceptual design design and and working working principle principle of of the the combination combination of of In prism-CPC. The The idea idea is is based based on a CPC that has been used for many different applications, ranging ranging prism-CPC. from high-energy high-energy physics physics to to solar solar energy energy collection. collection. To To modify modify CPCs CPCs for for our our purpose, purpose, we we recall recall the the from theory of of conventional conventional CPCs. CPCs. A A symmetrical symmetrical CPC CPC consists consists of of two two identical identical parabolic parabolic reflectors reflectors that that theory funnel radiation radiation from from the the aperture aperture to the absorber [12]. The The right-hand right-hand side side and and the the left-hand left-hand side side funnel parabolas are areaxisymmetric. axisymmetric.The The focuses of the parabolas that form theofbase of the CPC are parabolas focuses of the twotwo parabolas that form the base the CPC are shown shown in Figure 2a. When a sunlight is parallel to the main parabolicrim, rim,ititwill will be be in Figure 2a. When a sunlight beambeam is parallel to the main axisaxis of of thethe parabolic concentrated on on the the focus focus of of the the parabola, parabola, as as illustrated illustrated in in Figure Figure 2b. A A solid solid dielectric dielectric CPC CPC is is filled filled concentrated When the the incidence incidence angles angles with dielectric materials, such as poly-methyl methacrylate (PMMA) [13]. When of the incoming incoming rays rays are smaller than the acceptance acceptance angle, angle, the the rays would would undergo undergo total total internal internal of reflection or mirror reflection to reach the base of the CPC [14]. reflection [14].

Figure CPC; and and (b) (b)ray raytracing tracingofofthe thesunlight sunlightbeam beamthat thatis is parallel axis Figure 2. 2. (a) (a) A A symmetrical symmetrical CPC; parallel toto thethe axis of of parabolic rim. thethe parabolic rim.

In this study, we propose a new way of using a solid dielectric CPC that utilizes the imaging In this study, we propose a new way of using a solid dielectric CPC that utilizes the imaging optics properties of a CPC which is a non-imaging optics device. Figure 3 shows the physical layout optics properties of a CPC which is a non-imaging optics device. Figure 3 shows the physical layout of of our proposed solar concentration device based on a P-CPC combination. The prism is placed at the our proposed solar concentration device based on a P-CPC combination. The prism is placed at the top top of a CPC and can change the direction of an incoming solar ray. A PMMA slab is attached to the of a CPC and can change the direction of an incoming solar ray. A PMMA slab is attached to the base base of the CPC, and multi-junction solar cells are placed on two edges of the slab. With the of the CPC, and multi-junction solar cells are placed on two edges of the slab. With the appropriate appropriate prism angle, the direct sunlight is refracted at two sides of the prism and is divided into prism angle, the direct sunlight is refracted at two sides of the prism and is divided into two separate two separate beams that are parallel to the axes of the two parabolic rims of the CPC. After reflection beams that are parallel to the axes of the two parabolic rims of the CPC. After reflection at the wall of at the wall of the CPC, two beams are focused at the focal points of the parabola, as shown in Figure the CPC, two beams are focused at the focal points of the parabola, as shown in Figure 3b. The light 3b. The light propagates by reflection inside the slab waveguide to reach the solar cell on the edge. propagates by reflection inside the slab waveguide to reach the solar cell on the edge.

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Figure 3. (a) Physical layout of P-CPC; and (b) mechanism of sunlight concentration by ray tracing. Figure 3. (a) Physical layout of P-CPC; and (b) mechanism of sunlight concentration by ray tracing.

Figure 4 shows the method to calculate the structure of the prism based on the acceptance angle Figure 4 shows the method calculate the structure of the based on the acceptance of the CPC. The incident angle to i of the sunlight ray at the edge of prism the prism is equal to angle α of theangle Figure 3. (a) Physical layout of P-CPC; and (b) mechanism of sunlight concentration by ray tracing. of theprism CPC.(The incident angle θ the sunlight ray at the edge the prism equal to angle i = α). The refracted ray be in the direction of theofparabolic rimisaxis of the CPC α of i ofshould (acceptance angle of CPC:  acc). Based on Snell’s law, the relationship between  i andrim  acc axis is shown in CPC the prism (θ = α). The refracted ray should be in the direction of the parabolic of the i Figure 4 shows the method to calculate the structure of the prism based on the acceptance angle Equation (1): (acceptance angle ofincident CPC: θangle onsunlight Snell’s ray law,atthe between θ and θacc αisofshown of the CPC. The i of the therelationship edge of the prism is equal to angle the in acc ). Based i

prism(1): (i = α). The refracted ray should in the direction of the parabolic rim axis of the CPC Equation (1) sin θbe 𝑖 = 𝑛𝑃 sin(θ𝑖 − θ𝑎𝑐𝑐 ) (acceptance angle of CPC: acc). Basedsinθ on Snell’s law, the relationship between  i and acc is shown in = n sin θ − θ ( ) acc P i i

(1)

where nP is the refractive index of the prism. Solving Equation (1), we can find the structure of the Equation (1): prism. CPV system, theofeffective sunlight collecting area is(1), calculated the the product of CPCof the where nP isFor thethis refractive index the prism. Solving Equation we canbyfind structure (1) sin θis 𝑛𝑃 sin(θ𝑖 − θFigure length and input size D (the input size D indicated in 3b). The output apertures are two 𝑖 = 𝑎𝑐𝑐 ) prism. For this CPV system, the effective sunlight collecting area is calculated by the product of edges ofnPthe slabrefractive waveguide whose areaprism. is the multiplication of the length of the CPC by thickness d is the the Equation we can structure of the CPC where length and input size Dindex (the of input size DSolving is indicated in (1), Figure 3b).find Thethe output apertures are (parameter d is also indicated in Figure 3b). Therefore, the geometric concentration ratio of the system, prism.of For this CPV system, the effective sunlight collecting area isofcalculated byof the product of CPC two edges the slab waveguide whose area is the multiplication the length the CPC by thickness C R, is the input size D divided by two times the waveguide thickness, as shown in Equation (2). length and input size D (the input size D is indicated in Figure 3b). The output apertures are two

d (parameter d is also indicated in Figure 3b). Therefore, the geometric concentration ratio of the edges of the slab waveguide whose area is the multiplication of the𝐷length of the CPC by thickness d 𝐶𝑃𝐶 𝑙𝑒𝑛𝑔𝑡ℎ system, CR , is the input size D divided (2). 𝐶𝑅 =by two times the waveguide = thickness, as shown in Equation (2) (parameter d is also indicated in Figure23b). Therefore,𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 the geometric × 𝑤𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒 2𝑑concentration ratio of the system, CR, is the input size D divided by two times CPC the waveguide thickness, D as shown in Equation (2). length

CR =

𝐶𝑅 =

= 𝐶𝑃𝐶 𝑙𝑒𝑛𝑔𝑡ℎ 2 × waveguide thickness = 𝐷2d 2 × 𝑤𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠

2𝑑

(2)

(2)

Figure 4. The relationship between the prism structure and the acceptance angle of the CPC.

The design of the CPV system powered by renewable solar energy was presented in this section. The sunlight concentrator researched in this study is composed of a prism, a CPC, and a slab Figure 4. The relationship betweenthe theprism prism structure acceptance angle of the Figure 4. The relationship between structureand andthe the acceptance angle of CPC. the CPC. waveguide. The concentrator is supposed to be equipped with a tracking system to collect sunlight in theThe normal direction [15].system Two solar cell strings are attached the output aperturesinofthis thesection. optical design of the CPV powered by renewable solarat energy was presented The design of the CPV system powered by renewable solar energy was presented in section. concentrator to absorb sunlight and to convert the sunlight into electrical energy. The components of The sunlight concentrator researched in this study is composed of a prism, a CPC, and this a slab the optical system, the design parameters, and their effects on the optical performance are discussed The sunlight concentrator researched in this study is composed prism, asystem CPC, to and a slabsunlight waveguide. waveguide. The concentrator is supposed to be equipped withofa atracking collect in detailis insupposed the following section. The concentrator be equipped with aare tracking to collect sunlight in optical the normal in more the normal direction [15].toTwo solar cell strings attachedsystem at the output apertures of the concentrator to absorb sunlight andare to convert theat sunlight into electrical energy. The components of direction [15]. Two solar cell strings attached the output apertures of the optical concentrator the optical system, the design parameters, and their effects on the optical performance are discussed to absorb sunlight and to convert the sunlight into electrical energy. The components of the optical in more detail inparameters, the followingand section. system, the design their effects on the optical performance are discussed in more detail in the following section.

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3. Optical Analysis and Performance 3. Optical Analysis and Performance

Optical modelling plays a crucial role in the efficiency evaluation of an optical system. Optical optical modelling plays asoftware crucial role in the efficiency evaluation of an optical system. The was The commercial modeling LightTools™ (Synopsys Inc., San Frrancisco, CA, USA) commercial optical modeling software LightTools™ (Synopsys Inc., San Frrancisco, CA, USA) was used to design and simulate the geometrical structure of the P-CPC solar concentration system [16]. used to design and simulate the geometrical structure of the P-CPC solar concentration system [16]. In the designed system, one of the most common optical plastics, poly-methyl methacrylate (PMMA) In the designed system, one of the most common optical plastics, poly-methyl methacrylate (PMMA) with with a refractive index of ofnPMMA 1.49,was was selected the prism, and slab waveguide. a refractive index nPMMA == 1.49, selected for for the prism, CPC, CPC, and slab waveguide. To To evaluate weinserted insertedthree threeluminous luminous flux receivers in simulation the simulation model, evaluatethe thelosses lossesin inthe the system, system, we flux receivers in the model, as shown in Figure 5. 5. as shown in Figure

Figure 5. The simulationstructure structure for analysis. Figure 5. The simulation foroptical opticalefficiency efficiency analysis.

The optical efficiency, which is simply defined as the ratio of the output luminous flux to the

The efficiency, which isofsimply defined the ratio losses. of the output luminous flux to the inputoptical luminous flux, is a function the reflection andasabsorption input luminous flux, is a function of the reflection and absorption losses. 𝐹𝑙𝑢𝑥 𝑜𝑛 𝑅𝑒𝑐𝑒𝑖𝑣𝑒𝑟 2 + 𝐹𝑙𝑢𝑥 𝑜𝑛 𝑅𝑒𝑐𝑒𝑖𝑣𝑒𝑟 3 =

(3)

𝐹𝑙𝑢𝑥 𝑜𝑛 𝑅𝑒𝑐𝑒𝑖𝑣𝑒𝑟 1 Flux on Receiver 2 + Flux on Receiver 3 η = The efficiency of the system depends on the shape of the CPC Flux on Receiver 1 and the system concentration ratio.

(3)

These problems are discussed in detail in Sections 3.1 and 3.2.

The efficiency of the system depends on the shape of the CPC and the system concentration ratio. Optimization of the Shape in of the CPCin Sections 3.1 and 3.2. These3.1. problems are discussed detail The loss mechanism is illustrated by ray tracing, as shown in Figure 6. The Fresnel reflection

3.1. Optimization of the Shape of the CPC losses occur at the boundaries where the light passes from one region to another with different refractive indices. In this proposed system, Fresnel at the 6. surface of the prism. Otherlosses The loss mechanism is illustrated by ray the tracing, as losses shownoccur in Figure The Fresnel reflection at the conjunction between solarfrom cells and edgesto ofanother the waveguide can be reduced occurFresnel at the loss boundaries where the light the passes onethe region with different refractive to below 0.1% by filling the gap with the index-matching gel, and then it can be ignored in comparison indices. In this proposed system, the Fresnel losses occur at the surface of the prism. Other Fresnel loss with other losses. The leak at the parabolic wall of the CPC and the bottom surface of the slab at the conjunction between the solar cells and the edges of the waveguide can be reduced to below 0.1% waveguide are also important and can significantly affect the final efficiency of the system. These by filling gap with the index-matching andsatisfy then it can beinternal ignored in comparison with other kindsthe of losses are caused by some rays thatgel, cannot the total reflection (TIR) condition losses. The leak at the parabolic wall of the CPC and the bottom surface of the slab waveguide inside the P-CPC concentrator. These losses depend on the shape of the CPC and can be prevented are also important andCPC can and significantly affecthave the final efficiency the system. Thesecoating kinds of losses are when the solid slab waveguide a mirror coating.ofHowever, the mirror usually caused that cannot satisfy total reflection, internal reflection (TIR)can condition hasby a some lower rays reflectance than the total the internal so the coating have a inside positivethe or P-CPC a negative effect the optical performance of a P-CPC. Applying a mirror coating process concentrator. Theseonlosses depend on the shape of the CPC and can be prevented whenalso themakes solid CPC the system more have costly.a mirror coating. However, the mirror coating usually has a lower reflectance and slab waveguide In order to quantify the effect of CPC shapecan on the efficiency of the a parametric analysis than the total internal reflection, so the coating have a positive orsystem, a negative effect on the optical was carried out whilst varying its CPC concentration ratio, CCPC. The CCPC is defined by the ratio performance of a P-CPC. Applying a mirror coating process also makes the system more costly. between the input aperture size and the output aperture size of the CPC. The changing of the CCPC In order to quantify the effect of CPC shape on the efficiency of the system, a parametric analysis does not affect the geometric concentration ratio of the system, CR which was defined by Equation 2. was carried varyingofitsthe CPC ratio, Cto is defined CPC CPCThe We fixedout thewhilst input aperture CPCconcentration (input size of system) D. =The 200 C mm. thicknessby ofthe the ratio between the input aperture size and the output aperture size of the CPC. The changing of the slab waveguide is d = 2 mm. Based on Equation (2), the concentration ratio of the system achieves CRCCPC does =not geometric concentration ratio of theCPC system, CR which was defined 50.affect Based the on this, the geometry model of the sample was created in LightTools™ forby rayEquation tracing (2). We fixed the input aperture of the CPC (input size of system) to D = 200 mm. The thickness of the slab waveguide is d = 2 mm. Based on Equation (2), the concentration ratio of the system achieves CR = 50. Based on this, the geometry model of the sample CPC was created in LightTools™ for ray

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tracing analysis. The LightTools™ used the to study the of behavior of rays analysis. The LightTools™ softwaresoftware was also was usedalso to study behavior rays within the within P-CPC the for Energies 2016,structures. 9, 645 CPC structures. 6 of 13 was P-CPC forCPC different A total 1000traced rays were traced [4]. The ray-tracing analysis different A total of 1000 raysofwere [4]. The ray-tracing analysis was conducted conducted for a fewCPC different CPC structures. Figurethe 7 shows the variation of theconcentration P-CPC concentration for a few different structures. Figure 7 shows variation of the P-CPC system analysis. The LightTools™ software was also used to study the behavior of rays within the P-CPC for system with different with different CCPC. CCPC . different CPC structures. A total of 1000 rays were traced [4]. The ray-tracing analysis was conducted for a few different CPC structures. Figure 7 shows the variation of the P-CPC concentration system with different CCPC.

Figure 6. Loss mechanism of the system. Figure thesystem. system. Figure6.6.Loss Loss mechanism mechanism ofofthe

Figure 7. Schematic diagram of ray-tracing results for the P-CPC concentration system with different

Figure 7. Schematic diagram of ray-tracing results for the P-CPC concentration system with different Figure 7. Schematic diagram shapes of CPCs that have Cof CPCray-tracing = 2.5; 3.5 andresults 4.5. for the P-CPC concentration system with different shapes of CPCs that have C = 2.5; 3.5 and 4.5. shapes of CPCs that have CCPC CPC = 2.5; 3.5 and 4.5. It is clear from Figure 7 that as the CCPC increases, the incident angle of sunlight at the surface of theisprism decreases, so77Fresnel also decreases. The leak at the parabolic rim and the slab It clear from from Figure thatas asloss theC CCPC increases, the incident angle sunlight the surface Figure that the the incident angle ofof sunlight at at the surface of CPCincreases, waveguide also change with different C CPCs. In order to optimize the structure of P-CPC for maximum of the prism decreases, Fresnelloss lossalso alsodecreases. decreases.The Theleak leakatatthe theparabolic parabolic rim rim and and the the slab the prism decreases, soso Fresnel efficiency, we carried out a simulation with several different CPC concentration ratio CCPC ranging waveguide s. In Inorder order to tooptimize optimize the the structure structure of P-CPC P-CPC for maximum waveguide also also change change with with different differentCCCPC CPCs. from 2 to 8 in 0.5 increments. Figure 8 shows the variation of optical efficiencies at different CCPC efficiency, we carried out a simulation with several different CPC concentration we carried out a simulation with several different CPC concentrationratio ratioCCCPC CPC ranging concentration ratios for the CPC. The simulation for optical efficiency of a sunlight concentrator based 2 to 88 in increments. Figure 88 shows the of efficiencies at C CPC fromon in 0.5 0.5 increments. shows the variation variation of optical optical efficiencies at different different a P-CPC was implemented. In the implementation we included material attenuation, Fresnel CCPC concentration ratios for the sunlight concentration ratios CPC. The simulation for optical efficiency of a sunlight concentrator based reflection losses, and geometrical losses (the leak at the parabolic wall of the CPC and the bottom on a surface P-CPC the implementation included material attenuation, P-CPCofwas was implemented. the implemented. slab waveguide).InFigure 8 shows that CCPC we = 3.5 is the optimal value for the CPC Fresnel to obtainlosses, the highest of 89%. reflection and efficiency geometrical losses (the leak at the parabolic wall of the CPC and the bottom

surface of the slab waveguide). = 3.5 3.5 is is the the optimal optimal value value for for the CPC to waveguide). Figure 8 shows that C CCPC CPC = obtain the highest efficiency of 89%.

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Figure 8. Variation of optical efficiencies at different CCPC concentration ratios for the CPC.

Figure 8. Variation of optical efficiencies at different CCPC concentration ratios for the CPC.

3.2. The Dependence of Efficiency on theefficiencies System Concentration Ratio CR Figure 8. Variation of optical at different CCPC concentration ratios for the CPC.

3.2. The Dependence of Efficiency on the System Concentration Ratio CR

The prism attached at the top of the CPC to direct the sunlight beam is shown in Figure 3. 3.2. The Dependence of Efficiency on the System Concentration Ratio CR

However, prism hasatanthe inherent the dispersion of the solar spectrum. For The prismtheattached top ofdisadvantage, the CPC towhich directis the sunlight beam is shown in Figure 3. attached the thespectrum CPC to direct the sunlight beam is shown Figure 3. CPV The systems, the dispersion of top the of solar range is is very because leads to an However, theprism prism has anatinherent disadvantage, which theimportant dispersion of theitin solar spectrum. However, the prism has inherent disadvantage, which isrange the dispersion of the solar spectrum. For essential decrease the an optical efficiency and concentration ratio of systems. Figure 9 illustrates For CPV systems, theindispersion of the solar spectrum is the very important because it leads CPV systems, the dispersion of the solar spectrum range is very important because it leads to an schematically how the sunlight beam passes through a P-CPC via a dispersion mechanism. The to an essential decrease in the optical efficiency and concentration ratio of the systems. Figure 9 essential decrease in the optical efficiency and concentration ratio of the systems. Figure 9 illustrates sunlight is dispersed at the focal point of the P-CPC due to the wavelength dependence of the illustrates schematically how the sunlight beam passes through a P-CPC via a dispersion mechanism. schematically how theprism sunlight beamThe passes through P-CPC viahow a dispersion mechanism. refractive index of the material. focused area aalso defines big the sun’s image willThe be The sunlight is dispersed atthe thefocal focalpoint pointofofthe theP-CPC P-CPC due to the wavelength dependence sunlight is dispersed at due to the wavelength dependence of slab theof the at the focal point, and it affects the coupling between the CPC and the slab waveguide. Larger refractive index of the prism material. The focused areaalso also defines how big the sun’s image will refractive index of the prism material. The focused area how big the sun’s image will be waveguide thickness will capture more focused sunlight butdefines will decrease the concentration ratio of be at theat focal point, and it affects the coupling between the CPC and the slab waveguide. Larger focal point, and it affects the coupling between the CPC and the slab waveguide. Larger slab slab thethe system. waveguide thickness capture morefocused focused sunlight sunlight but thethe concentration ratio ratio of of waveguide thickness willwill capture more butwill willdecrease decrease concentration the system. the system.

Figure 9. Mechanism of dispersion inside the P-CPC.

We used ray tracing in LightTools™ to analyze the dependence of efficiency on the thickness of Figure 9. Mechanism of dispersion inside the P-CPC. Figure 9. Mechanism of dispersion inside the P-CPC. the slab waveguide that is governed by the dispersion phenomenon. The sunlight source used in the We used ray tracing in LightTools™ to the analyze efficiency on the thickness analysis, generated by LightTools™, was in rangethe of dependence 250–2500 nmof[17]. The input aperture sizeof is the slab waveguide governed byof the phenomenon. sunlight source the fixed at D = 200tracing mm,that and thickness the slab waveguide d variesThe from 1efficiency mm to 2 mm inthe thein step We used ray inisthe LightTools™ todispersion analyze the dependence of onused thickness generated by LightTools™, was thedispersion range of 250–2500 The input aperture sizeused is in ofslab 0.2 mm. This means the concentration ratio C R decreases from nm 100[17]. to 50The in the step ofsource 10. Figure of theanalysis, waveguide that is governed by in the phenomenon. sunlight fixed at D = 200 mm, and the thickness of the slab waveguide d varies from 1 mm to 2 mm in the step 10a illustrates the P-CPC structures with some different slab waveguide thicknesses, d = 1 mm, 1.5 the analysis, generated by LightTools™, was in the range of 250–2500 nm [17]. The input aperture of 0.2 mm. This means the concentration ratio CR decreases from 100 to 50 in the step of 10. Figure size is fixed at D = 200 mm, and the thickness of the slab waveguide d varies from 1 mm to 2 mm in 10a illustrates the P-CPC structures with some different slab waveguide thicknesses, d = 1 mm, 1.5

the step of 0.2 mm. This means the concentration ratio CR decreases from 100 to 50 in the step of 10. Figure 10a illustrates the P-CPC structures with some different slab waveguide thicknesses, d = 1 mm,

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1.5 mm, and 2 2mm, 10b shows showsthe thesimulated simulated optical efficiency at different system mm, and mm,respectively. respectively. Figure Figure 10b optical efficiency at different system concentration ratios. It can be seen that because of dispersion, system efficiency η decreases almost concentration ratios. It can be seen that because of dispersion, system efficiency η decreases almost linearly the increase ofRC R. The lowerconcentration concentration ratio higher optical efficiency, linearly withwith the increase of C . The lower ratiocan canprovide provide higher optical efficiency, also increases requirement solarcells. cells. but it but alsoitincreases the the areaarea requirement ofofsolar

Figure 10. (a) The variation of the P-CPC shape; and (b) the variation of optical efficiency at different

Figure 10. (a) The variation of the P-CPC shape; and (b) the variation of optical efficiency at different system concentration ratios (CR). system concentration ratios (CR ).

3.3. Tolerance of the System

3.3. Tolerance of the System

For proper operation of the proposed solar concentration system, direct sunlight should always

For proper operation theof proposed solar concentration system, direct always be parallel to the mainofaxis the P-CPC. This is a difficult task because thesunlight positionshould of the sun is be always and led us toThis use is a sun tracking system. Thethe required accuracy theissun parallel to thechanging, main axis of this the P-CPC. a difficult task because position of theof sun always tracking is determined the tracking solar concentrating collector’s angle of tolerance [18–21]. The changing, andsystem this led us to use abysun system. The required accuracy of the sun tracking tolerance of the system the acceptable angular deviationangle of theof sunlight direction from thetolerance two system is determined by theissolar concentrating collector’s tolerance [18–21]. The main axes of the system within the allowable efficiency loss. It is defined as the angle where of the system is the acceptable angular deviation of the sunlight direction from the two main the axes of efficiency drops by 10% [22]. The acceptance angle determines the required accuracy of the tracking the system within the allowable efficiency loss. It is defined as the angle where the efficiency drops system mounted on the concentrator. The dependence of the optical efficiency of the system on by 10% [22]. The acceptance angle determines the required accuracy of the tracking system mounted angular deviation along the north-south (NS) and east-west (EW) direction is very different because on thetheconcentrator. dependence of the optical efficiency of the system angular of deviation system is not The symmetric. We examined the efficiency with different angularondeviations the alongsunlight the north-south (NS) and east-west (EW) direction is very different because the system is not direction along the NS and EW directions. The alignment of the system along the NS and symmetric. We examined the efficiency with different angular deviations of the sunlight direction EW directions is shown in Figure 11. 12aEW shows the optical efficiency output to thealong angular the EW is along the Figure NS and directions. The alignment of relative the system thedeviation NS and along EW directions direction, and Figure 12b shows a graph of efficiency versus angular deviation along the NS direction. shown in Figure 11. The simulation results thatefficiency the tolerance is more than ±6° the EW direction, far EW Figure 12a shows theshow optical output relative to along the angular deviationwhich alongis the larger than that for the EW direction (±0.5°). This indicates that, by using a P-CPC, the acceptance direction, and Figure 12b shows a graph of efficiency versus angular deviation along the NS direction. angle along the EW direction can be greatly increased without sacrificing optical efficiency too much. The simulation results show that the tolerance is more than ±6◦ along the EW direction, which is far Therefore, unlike the conventional lens or parabolic mirror system for concentrators, the proposed larger than that for the EW direction (±0.5◦ ). This indicates that, by using a P-CPC, the acceptance angle along the EW direction can be greatly increased without sacrificing optical efficiency too much. Therefore, unlike the conventional lens or parabolic mirror system for concentrators, the proposed P-CPC system can lower the accuracy requirements along the EW direction, and this reduces the

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Energies 2016, 9, 645can lower the accuracy requirements along the EW direction, and this reduces the 9 of 13 P-CPC system cost cost of the tracking system. As the size of the slab waveguide becomes larger, the focused light from of the tracking system. As the size of the slab waveguide becomes larger, without the focused lightdecoupled. from the the primary CPC can be transferred more effectively to the waveguide being A P-CPC system can lower the accuracy requirements along the EW direction, and this reduces the cost primary CPC can be transferred more effectively to the waveguide without being decoupled. A volumetric increase of theAs slab while keeping the input aperture the same gives of the tracking system. the waveguide size of the slab waveguide becomes larger, the focused light from thebetter volumetric increase of the slab waveguide while keeping the input aperture the same gives better tracking tolerance along the NS direction. However, increasing the acceptance angle reduces primary CPC can be transferred more effectively to the waveguide without being decoupled. A the tracking tolerance along the NS direction. However, increasing the acceptance angle reduces the concentration dramatically. tolerance and concentration be kept in volumetricratio increase of the slabTherefore, waveguidethe while keeping thethe input aperture theratio sameshould gives better concentration ratio dramatically. Therefore, the tolerance and the concentration ratio should be kept tracking along the NS direction. However, increasing the acceptance angle reduces the balance in thetolerance system design. in balance in the system design.

concentration ratio dramatically. Therefore, the tolerance and the concentration ratio should be kept in balance in the system design.

Figure 11. The alignment of the system along the NS and EW directions.

Figure 11. The alignment of the system along the NS and EW directions. Figure 11. The alignment of the system along the NS and EW directions.

Figure 12. Variation of optical efficiency of the concentrator at different angular deviations along the (a) EW direction; and (b) NS direction. Figure 12. Variation of optical efficiency of the concentrator at different angular deviations along the Figure 12. Variation of optical efficiency of the concentrator at different angular deviations along the (a) EW direction; and (b) NS direction.

(a) EW direction; and (b) NS direction.

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3.4. Irradiance Distribution on the Surface of the Solar Cell 3.4. Irradiance Distribution on the Surface of the Solar Cell Besides concentration and the tolerance angle, an optical PV concentrator must achieve other and theuniformity tolerance angle, optical concentrator must achievethe other goalsBesides [7]. Oneconcentration of these is irradiance on thean cell. This isPV important not only because cell goals [7]. One of these is irradiance uniformity on the cell. This is important not only because the cell efficiency depends on it but also to assure long-term cell and concentrator reliability. High flux contrast efficiency depends oncauses it butserious also toresistance assure long-term cell and concentrator reliability. High flux across the cell surface losses, although this is less dramatic in multi-junction contrast across the cell surface causes serious resistance losses, although this is less dramatic in comes multisolar cells than in silicon cells. Another limitation specific to multi-junction cells, however, junction solar cells than in silicon Another limitation specific to multi-junction cells, however, from tunnel diodes that need to becells. operating in their tunneling regime. This limits the irradiance at comes from tunnel diodes that need to be operating in their tunneling regime. This limits the any point of the cell. Additionally, if different wavelengths have a different irradiance distribution irradiance any point of the cell. if differentofwavelengths a different irradiance (which hasatbeen referred to as theAdditionally, chromatic aberration irradiance),have the cell efficiency can be distribution (which has been referred to as the chromatic aberration of irradiance), the cell efficiency significantly affected due to a local current mismatch between the top and middle junctions. In this can be significantly affected the dueslab to awaveguide local current mismatch between the and middle junctions. proposed solar concentrator, works as a homogenizer fortop attaining good irradiance In this proposed solar concentrator, the slab waveguide works as a homogenizer for attaining uniformity on the solar cells. With a slab waveguide homogenizer, the solar cell is glued togood two irradiance uniformity onreaches the solar cells. slab waveguide homogenizer, the solar glued edges; most of the light the cellWith after abouncing off the waveguide surfaces by cell TIR is[23–25]. to two edges; most of the reaches cell after bouncing the waveguide by TIR [23– The light distribution onlight the cell can the be made uniform afteroffsufficient lengthsurfaces of slab waveguide. 25]. The light distribution on the cell surface can be made of slab waveguide. The uniformity of irradiation on the of theuniform solar cellafter wassufficient evaluatedlength and simulated using the The uniformity of irradiation on the surface of the solar cell was evaluated and simulated using the same optical software (LightTools™). There are two solar cells which are attached at two exit ports same optical software (LightTools™). There are two solar cells which are attached at two exit ports of P-CPC, but they have the same uniformity because of symmetry property of P-CPC. We analyzed of P-CPC, but they haveone theexit same uniformity because of symmetry property of P-CPC. We analyzed the uniformity at only port. Figure 13a,b shows 2D and 3D irradiance distribution graph the uniformity at only one exit port. Figure 13a,b shows 2D and 3D irradiance distribution graph on 2 2, on the exit port. The maximum irradiance was 330 W/m , the minimum irradiation was 285 W/m 2, the minimum irradiation was 285 W/m2, and the exit port. The maximum irradiance was 330 W/m and the average irradiance was 299 W/m2 . A uniformity Equation (4) [26] was adopted to calculate the uniformity average irradiance 299 W/m2. which A uniformity [26] that was the adopted to calculate the the of P-CPCwas concentrator, reachedEquation 92.5%. It (4) is clear proposed P-CPC can uniformity of P-CPC concentrator, which reached 92.5%. It is clear that the proposed P-CPC can provide excellent irradiance uniformity on the cell. provide excellent irradiance uniformity on the cell. Maximum Irradiation − Minimum Irradiation Uni f ormity = (1 − − 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐼𝑟𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 − 𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝐼𝑟𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛))××100% (4) 𝑈𝑛𝑖𝑓𝑜𝑟𝑚𝑖𝑡𝑦 = (1 100% (4) ×𝐴𝑣𝑒𝑟𝑎𝑔𝑒 Average irradiation 22 × 𝑖𝑟𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛

13. (a) 3D irradiance irradiance Figure 13. (a) A A 2D 2D irradiance irradiance distributions distributions on on the the exit exit port of P-CPC; and (b) a 3D distributions on the exit port port of of P-CPC. P-CPC.

3.5. Proposed Large-Scale System and Discussion As an initiative for a cost-effective large-scale solar concentration system, 10 P-CPCs are placed together. These systems share a sun tracking system, a battery bank, and other infrastructure. The

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3.5. Proposed Large-Scale System and Discussion As an initiative for a cost-effective large-scale solar concentration system, 10 P-CPCs are placed together. These systems share a sun tracking system, a battery bank, and other infrastructure. Energies 9, 645 a linear array of P-CPCs. A schematic description of a sunlight 11 ofcollector 13 The system will2016, include for a large-scale CPV system is shown in Figure 14. The concentration ratio of this system is flexible, system will include a linear array of P-CPCs. A schematic description of a sunlight collector for a dependinglarge-scale on the thickness ofisthe waveguide. ForThe different concentration CPV system shown in Figure 14. concentration ratio of thisratios, systemdifferent is flexible,solar cells depending on the thickness of the waveguide. For different concentration ratios, different solarmulti-junction cells can be used. For high concentration systems of CR = 50 proposed in this study, III–V can be used. For high concentration systems of CR = 50 proposed in this study, III–V multi-junction solar cells are suggested. Multi-junction solar cells made of III–V compound semiconductors can have solar cells are suggested. Multi-junction solar cells made of III–V compound semiconductors can have efficienciesefficiencies of moreofthan Although they expensive, smaller sizecells solar more40%. than 40%. Although theyare are expensive, thethe smaller size solar for cells higherfor higher concentration ratios would makemake the the system more concentration ratios would system more cost-effective. cost-effective.

Figure 14. Proposed large-scale CPV system based on P-CPCs.

Figure 14. Proposed large-scale CPV system based on P-CPCs. To evaluate the performance of the large scale CPV system, the irradiation from the sunlight was calculated at performance different times ofofday LightTools™. The simulation considers the direct normal To evaluate the thebylarge scale CPV system, the irradiation from the sunlight irradiance solar spectrum, generated by LightTools™, as the incident irradiance input parameter. was calculated at different times of day by LightTools™. The simulation considers the direct normal Here, let us look at the solar irradiation for a summer day as an example. The highest solar elevation irradiance(zenith) solar spectrum, generated LightTools™, the[27]. incident irradiance inputweparameter. angle at the site is 76°, andby it takes place at 12:30as p.m. To achieve direct sunlight, Here, let us look that at the irradiation for awith summer day as device an example. highestmodule solar elevation assume thesolar CPV system is mounted a sun tracking to rotate The concentrator 2 as shown in Figure 14. ◦ toward the sun all time of the day. The area of the sunlight collector is 2 m (zenith) angle at the site is 76 , and it takes place at 12:30 p.m. [27]. To achieve direct sunlight, Figure 15 shows the power of sunlight at the collecting surface of CPV system and output power at we assume that the CPV system is mounted with a sun tracking device to rotate concentrator different times. The total output energy per day can be calculated by integration of output power module toward the sunonall time The along area aofday the sunlight is 2multim2 as shown over time. Based Figure 15, of the the total day. solar energy at the output iscollector 18 KWh. Using in Figure 14. Figure 15cells shows the of sunlight at the collecting surface of CPV and output junction solar made of power III–V compound semiconductors which have efficiencies of system more than 40%, the system canThe generate 7.2 KWh of electricity day. power at different times. totalabout output energy per dayper can be calculated by integration of output The P–CPC concept introduced here fulfills the requirements for a concentrator of a CPV system, power over time. Based on Figure 15, the total solar energy along a day at the output is 18 KWh. such as a high concentration ratio and a highly uniform distribution of radiance on the surface of Using multi-junction solar the cells of III–V compound which have efficiencies of solar cells. Reducing usemade of materials will also contribute semiconductors to reduced manufacturing costs, reduced 2016, 9,the 645 moreEnergies thansupplier 40%, system can generate aboutrecycling 7.2 KWh of electricity per fabrication day. management costs, and reduced costs. To achieve low costs, it is12 of 13 necessary to have one component, one material, and one manufacturing process for the concentrator design. The P-CPC concept proposed here meets all these requirements. It is made of a single component and a single material, and it uses a single manufacturing process, such as injection molding and/or extrusion, which is suitable for mass production. These features have resulted in reduced manufacturing costs [28].

Figure 15. Power of sunlight thecollecting collecting surface surface (input and output power fromfrom solar solar Figure 15. Power of sunlight atatthe (inputpower) power) and output power concentration system at different times of the day. concentration system at different times of the day.

4. Conclusions A CPV system using P-CPCs has been designed and discussed. To explore the practical performance of the proposed system, a sample optical system was modeled and simulated with LightTools™. The simulation results indicate that 89% optical efficiency was achieved at Cgeo = 50 for the proposed concentrator system. In addition, the angular tolerance (acceptance angles) in the NS

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The P–CPC concept introduced here fulfills the requirements for a concentrator of a CPV system, such as a high concentration ratio and a highly uniform distribution of radiance on the surface of solar cells. Reducing the use of materials will also contribute to reduced manufacturing costs, reduced supplier management costs, and reduced recycling costs. To achieve low fabrication costs, it is necessary to have one component, one material, and one manufacturing process for the concentrator design. The P-CPC concept proposed here meets all these requirements. It is made of a single component and a single material, and it uses a single manufacturing process, such as injection molding and/or extrusion, which is suitable for mass production. These features have resulted in reduced manufacturing costs [28]. 4. Conclusions A CPV system using P-CPCs has been designed and discussed. To explore the practical performance of the proposed system, a sample optical system was modeled and simulated with LightTools™. The simulation results indicate that 89% optical efficiency was achieved at Cgeo = 50 for the proposed concentrator system. In addition, the angular tolerance (acceptance angles) in the NS and the EW directions was also analyzed. By using a P-CPC, an acceptance angle of ±6◦ was achieved in the EW direction. This allows us to use a less accurate sun tracking system, such as a seasonal sun tracking system along the EW direction, as a cost-effective solution. This study is the first to use a combination of a prism and a CPC for a solar concentration system. The proposed system is very suitable for large-scale purposes. It shows great potential for commercial- and industrial-scale CPV applications. In the future, we will try to implement experimentation under real conditions to verify the accuracy of the simulation and the commercial viability of the system. Acknowledgments: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (No. 2014R1A2A1A11051888). Author Contributions: Ngoc Hai Vu and Seoyong Shin conceived and developed the original ideas. Ngoc Hai Vu carried out the performance analysis and simulations and wrote the paper. Seoyong Shin supervised the research and finalized the paper. Conflicts of Interest: The authors declare no conflict of interest.

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