Effect of Reflector Geometry in the Annual Received Radiation

Article Effect of Reﬂector Geometry in the Annual Received Radiation of Low Concentration Photovoltaic Systems

João Paulo N. Torres 1,* ID , Carlos A. F. Fernandes 1, João Gomes 2, Bonﬁglio Luc 3, Giovinazzo Carine 3, Olle Olsson 2 and P. J. Costa Branco 4 ID

1 Instituto de Telecomunicações, Instituto Superior Técnico, Universidade de Lisboa, 1649-004 Lisboa, Portugal; [email protected] 2 Department of Building, Energy and Environmental Engineering, University of Gävle, 801 76 Gävle, Sweden; [email protected] (J.G.); [email protected] (O.O.) 3 Ecole Polytechnique Universitaire de Montpellier, 34095 Montpellier, France; lucbonﬁ[email protected] (B.L.); [email protected] (G.C.) 4 Associated Laboratory for Energy, Transports and Aeronautics, Institute of Mechanical Engineering (LAETA, IDMEC), Instituto Superior Técnico, Universidade de Lisboa, 1649-004 Lisboa, Portugal; [email protected] * Correspondence: [email protected]; Tel.: +351-910086958

Received: 6 June 2018; Accepted: 14 July 2018; Published: 19 July 2018

Abstract: Solar concentrator photovoltaic collectors are able to deliver energy at higher temperatures for the same irradiances, since they are related to smaller areas for which heat losses occur. However, to ensure the system reliability, adequate collector geometry and appropriate choice of the materials used in these systems will be crucial. The present work focuses on the re-design of the Concentrating Photovoltaic system (C-PV) collector reflector presently manufactured by the company Solarus, together with an analysis based on the annual assessment of the solar irradiance in the collector. An open-source ray tracing code (Soltrace) is used to accomplish the modelling of optical systems in concentrating solar power applications. Symmetric parabolic reflector configurations are seen to improve the PV system performance when compared to the conventional structures currently used by Solarus. The parabolic geometries, using either symmetrically or asymmetrically placed receivers inside the collector, accomplished both the performance and cost-effectiveness goals: for almost the same area or costs, the new proposals for the PV system may be in some cases 70% more effective as far as energy output is concerned.

Keywords: concentrating photovoltaic (C-PV) solar systems; maximum reﬂector collector (MaReCo); ray-tracing; reﬂector design; Soltrace

1. Introduction Modernisation plays a considerable role in the change of the people’s behaviours. People’s behaviour towards energy is not only related to the way energy is produced but also how and why it is consumed. Conventional forms of electricity generation are today still mostly based on fossil fuel, ranging from coal-based steam plants to gas boilers. In the recent years, humanity has made overwhelming advances in its capacity to improve life quality; however, in this worthy quest, mankind has created a series of new challenges that need to be tackled. Global warming is likely the most urgent of all since it threatens the continued existence of man on earth. This way, serious steps are being taken like the Paris climate agreement [1]. As mentioned, a glance at the present situation regarding the production of electricity and heat, renewable resources play a massive part in mainstream energy production and feed in the grid. By the end of 2016, 303 GW of photovoltaic system (PV) has been

Energies 2018, 11, 1878; doi:10.3390/en11071878 www.mdpi.com/journal/energies Energies 2018, 11, 1878 2 of 15 installed all over the world [2], 16 countries installed at least 500 MW of PV [3], Germany ranks first in solar PV per capita with 511 watts/capita [4,5]. Economics is currently mentioning it as one of a crucial aspect of sustainability, dealing mainly with the energy efficiency [6]. In 2011 (Energy Policies of International Energy Agency Countries-Sweden, 2013 Review), in Sweden, 56.7% of total electricity came from the renewable energy sources, and in the fifth place in the electricity produced from the renewable energy sources ranking. Portugal appears in the seventh position, with 47%. The world energy consumption at the moment is 10 terawatts (TW) per year [7]. By the year 2050, the expected energy consumption would be 30 TW [8]. The conclusion is an additional 20 TW of a CO2 free energy source is required to balance the demand. One solution to stabilise CO2 might be to use photovoltaics (PV) and other renewables like for example hydro and wind for electricity (10 TW) and hydrogen for transportation (10 TW) [8]. Hence solar energy will play an essential role in the future and nowadays it is considered as the “tipping point” for the PV systems [9]. Solar energy, an inexhaustible resource, clean and non-polluting as it may have seen, however, it is not an easy task to make the most out of it [10]. Its potential lies in the method and the techniques used for the maximum efficiency possible. Several systems have been developed to use the solar energy, for example with Flat-plate solar panels [11] or with concentrated solar power (CSP) systems [12]. These systems are some of the ways to generate power from the sun. The CSP systems could be used to extract heat from the sun, in this case, it is a thermal system [13], or it could be used to convert solar energy in electricity, and in this case, it is a concentrating photovoltaic system (C-PV) [14]. In a situation where it is necessary to reach high levels of energy conversion, C-PV technology plays an important role. Linking an optical device between the light source and the receiver/absorber, the efficiency of the collector energy conversion related to the photoelectric effect will be theoretically higher. The improvement will increase with the concentrator factor C, which represents the ratio of the total energy collected in the concentrator collector and the total energy received in the flat collector. There are three different C-PV systems:

• Low concentration (LC-PV): C between 1 and 40 suns [15]; • Medium concentration (MC-PV): C between 40 and 300 suns [16]; • High concentration (HC-PV): C between 300 and 2000 suns [16].

However, these systems also present some disadvantages that need to take into account. Namely:

• Concentration implies losses, as the reflectivity of the reflector is never 100%. A high quality reflector has 95% reflectance, which implies 5% losses. If there are multiple reflections, the reflectance losses are compounded. • The redirection of the rays can lead to a situation in which the light does not reach the target (receiver), leading to a steep decrease in the collector efficiency. This happens when the angle is outside of the reflectors acceptance angle or due to imperfections in the shape of the concentration. • Concentrating collectors receive 1/C of the diffuse radiation. This means that a collector with concentration factor of two will receive 50% of the diffuse solar radiation, while a high concentration collector will receiver close to 0%. This effect is particularly relevant in locations, such as Berlin or Paris, where diffuse radiation accounts for approximately 50% of the annual solar radiation.

Stationary collectors usually present C up to 5. Higher values of C can be reached but require tracking systems [17]. However, tracking systems are more complex, and they are related to higher installation and management costs. Solarus standard reflector is designed to be used in a non-tracking system. Along with the usual partial shading effects, related to several effects (clouds, reflector boundaries, shadows, dust, or any dirtiness), the use of reflectors in stationary solar C-PV collectors usually cause Energies 2018, 11, 1878 3 of 15 Energies 2018, 11, x FOR PEER REVIEW 3 of 15 Energies 2018, 11, x FOR PEER REVIEW 3 of 15 usually cause non-uniform light distribution along the PV cells string. This in turn can create hot non-uniformusually cause light non distribution-uniform li alongght distribution the PV cells along string. the This PV in cells turn string. can create This hot in spotsturn resultingcan create in hot aging spots resulting in aging or permanent damage. When cells are entirely shaded, the hot spot evidence orspots permanent resulting damage. in aging When or permanent cells are entirely damage shaded,. When cells the hot are spot entirely evidence shaded, may the prevent hot spot the evidence triggering may prevent the triggering of the bypass (BP) diode [18], resulting in the increased temperature that may prevent the triggering of the bypass (BP) diode [18], resulting in the increased temperature that of thewill bypass degrade (BP) the diode solar [ 18panel.], resulting in the increased temperature that will degrade the solar panel. will degrade the solar panel. In mismatchingIn mismatching operating operating conditions conditions for for example, example, due due to to aging, aging, manufacturing manufacturing tolerances, tolerances, In mismatching operating conditions for example, due to aging, manufacturing tolerances, differentdifferent orientation orientation of theof the solar solar panels, panels, the the PV PV system system energetic energetic efficiencyefficiency is strongly compromised. compromised. different orientation of the solar panels, the PV system energetic efficiency is strongly compromised. To mitigateTo mitigate these thes effects,e effects, a re-design a re-design searching searching for for alternatives alternatives concerning concerning thethe geometry of of the the C C-PV-PV To mitigate these effects, a re-design searching for alternatives concerning the geometry of the C-PV collectorscollectors is imperative is imperative [19 [,2019,].20]. collectors is imperative [19,20]. TheseThese systems, systems, are are classified classified as as [21 []:21 Parabolic]: Parabolic trough; trough; Central Central Receiver/Solar Receiver/Solar Tower; Tower; Parabolic Parabolic These systems, are classified as [21]: Parabolic trough; Central Receiver/Solar Tower; Parabolic dish;dish; Linear Linear Fresnel Fresnel Collector; Collector; Compound Compoun Parabolicd Parabolic Collector Collector (CPC), and(CPC) Maximum, and Maximum Reflector Reflector Collector dish; Linear Fresnel Collector; Compound Parabolic Collector (CPC), and Maximum Reflector (MaReCo).Collector (MaReCo). Collector (MaReCo). It isIt essential is essential to giveto give an an overview overview regarding regarding the the last last two, two, since since itit isis thethe structurestructure mostly mostly used used in in It is essential to give an overview regarding the last two, since it is the structure mostly used in the market. thethe market. market. The CPC system has two, parabolic reflectors with different focal points. In Figure 1, the basic TheThe CPC CPC system system has has two,two, parabolicparabolic reflectorsreflectors with with different different focal focal poin points.ts. In InFigure Figure 1, 1the, the basic basic shape of the collector is shown [22]. shapeshape of of the the collector collector is is shown shown [[2222].].

Figure 1. Compound Parabolic Collector (CPC) [22]. FigureFigure 1.1. Compound Parabolic Parabolic Collector Collector (CPC) (CPC) [22]. [22 ].

The aperture d2 in the bottom of Figure 1 is the distance between the focuses of the two parabolas, The aperture d2 in the bottom of Figure 1 is the distance between the focuses of the two parabolas, AThe and aperture B, and dit2 isin the the receiver bottom of(solar Figure cells)1 is location. the distance The betweentwo parabolas the focuses reflect of the the incoming two parabolas, solar A and B, and it is the receiver (solar cells) location. The two parabolas reflect the incoming solar A andradiation B, and on it the is the receiver. receiver There (solar is symmetry cells) location. between The the two focal parabolas point and reflectthe axis the of incomingthe compound solar radiation on the receiver. There is symmetry between the focal point and the axis of the compound radiationparabolic on the collector. receiver. The There acceptance is symmetry angle between between both the focal controls point the and amount the axis of oflight the that compound can be parabolic collector. The acceptance angle between both controls the amount of light that can be parabolicreflected collector. and finally The end acceptance up on the anglereceiver. between The interesting both controls fact is, the only amount an incident of light ray that that falls can in be reflected and finally end up on the receiver. The interesting fact is, only an incident ray that falls in reflectedthe acceptance and finally angle end range up on will the definitely receiver. Thebe reflected interesting by both fact is,reflectors only an and incident reach ray the thatreceiver falls [22]. in the the acceptance angle range will definitely be reflected by both reflectors and reach the receiver [22]. acceptanceThe angle Maximum range Reflector will definitely Collector be reflected system (MaReCo) by both reflectors is an asymmetrical and reach thetruncated receiver trough [22].-like The Maximum Reflector Collector system (MaReCo) is an asymmetrical truncated trough-like CPCThe collector. Maximum It Reflectoris mainly Collectordesigned systemfor higher (MaReCo) latitudes is [22]. an asymmetrical It is a non-tracking truncated coll trough-likeector with a CPC bi- CPC collector. It is mainly designed for higher latitudes [22]. It is a non-tracking collector with a bi- collector.facial It absorber. is mainly The designed bi-facialfor absorber higher helps latitudes to minimise [22]. It is the a non-tracking absorber area, collector and subsequently with a bi-facial the facial absorber. The bi-facial absorber helps to minimise the absorber area, and subsequently the absorber.production The bi-facial costs. It absorber is generally helps used to minimise from stand the-alone absorber mounting area, and on subsequently the ground to the the production roof top production costs. It is generally used from stand-alone mounting on the ground to the roof top integration [23]. costs.integration It is generally [23]. used from stand-alone mounting on the ground to the roof top integration [23]. A basic structure of a CPC system is shown in Figure 2. The reflector has three parts; A: the AA basic basic structure structure of of aa CPCCPC systemsystem is shown in Figure Figure 22.. The The reflector reflector has has three three parts; parts; A: A: the the upper parabolic reflector between points 2 and 3 with the reflection focus on the top of the absorber; upperupper parabolic parabolic reflector reflector between between pointspoints 2 and 3 3 with with the the reflection reflection focus focus on on the the top top of ofthe the absorber; absorber; B: a circular section between points 1 and 2. This part transfers the light onto the absorber and C: the B:B: a circulara circular section section between between pointspoints 11 andand 2. This part part transfers transfers the the light light onto onto the the abs absorberorber and and C: the C: the lower parabolic part between points 4 and 1. lowerlower parabolic parabolic part part between between points points 44 andand 1.

Figure 2. Basic structure of Maximum Reflector Collector (MaReCo) [23]. FigureFigure 2. 2.Basic Basic structurestructure of Maximum Reflector Reﬂector Collector Collector (MaReCo) (MaReCo) [23]. [23 ]. Energies 2018, 11, x FOR PEER REVIEW 4 of 15

Energies 2018, 11, 1878 4 of 15 EnergiesIn Figure 2018, 11 2,, x ϕ FOR is thePEER aperture REVIEW tilt angle and β is the absorber inclination angle. The cover glass4 of is 15 attached between points 3 and 4. The position of the cover glass depends on the location of the In Figure 2, ϕ is the aperture tilt angle and β is the absorber inclination angle. The cover glass is reflectorIn Figurealong the2, φ extendedis the aperture parabolas tilt anglewhere and the βmaximumis the absorber annual inclination irradiation angle. onto the The aperture cover glass is attached between points 3 and 4. The position of the cover glass depends on the location of the obtainedis attached [23]. between points 3 and 4. The position of the cover glass depends on the location of the reflector along the extended parabolas where the maximum annual irradiation onto the aperture is reﬂectorA diagram along of the the extended stand-alone parabolas MaReCo where is in the Figure maximum 3. The annualMaReCo irradiation structure ontocould the be aperture dived in is obtained [23]. fiveobtained different [23 ]. types of prototypes; the stand-alone MaReCo; the roof-integrated MaReCo; the A diagram of the stand-alone MaReCo is in Figure 3. The MaReCo structure could be dived in east/westA diagram MaReCo; of the the spring/fall stand-alone MaReCo; MaReCo the is wall in Figure MaReCo3. The, and MaReCo the Solarus structure Power could Collector. be dived The in five different types of prototypes; the stand-alone MaReCo; the roof-integrated MaReCo; the standﬁve- differentalone MaReCo types of has prototypes; a cover the glass stand-alone with a tilt MaReCo; of 30° thein this roof-integrated cases for Stockholm MaReCo; the conditions, east/west east/west MaReCo; the spring/fall MaReCo; the wall MaReCo, and the Solarus Power Collector. The concerningMaReCo; thethe spring/fallhorizontal. MaReCo; The upper the and wall lower MaReCo, acceptance and the angle Solarus are Power65° and Collector. 20°, respectively. The stand-alone It has stand-alone MaReCo has a cover glass with◦ a tilt of 30° in this cases for Stockholm conditions, a MaReCoconcentration has a area cover [23] glass of C withi = 2.2 a. tilt of 30 in this cases for Stockholm conditions, concerning the concerning the horizontal. The upper and lower acceptance angle are 65° and 20°, respectively. It has horizontal. The upper and lower acceptance angle are 65◦ and 20◦, respectively. It has a concentration a concentration area [23] of Ci = 2.2. area [23] of Ci = 2.2.

Figure 3. Diagram of stand-alone MaReCo for Stockholm conditions with cover glass angle of 30° [15]. Figure 3. Diagram of stand-alone MaReCo for Stockholm conditions with cover glass angle of 30◦ [15]. TheFigure roof 3.-integrated Diagram of MaReCostand-alone is MaReCo specially for designing Stockholm forconditions roof implementation. with cover glass angle In this of 30° case, [15]. the cover glass starts where the circular part of MaReCo ends which means the glass is between points 2 TheThe roof-integratedroof-integrated MaReCo MaReCo is speciallyis specially designing designing for rooffor roof implementation. implementation. In this In case, this thecase, cover the and 4 in Figure 2. Hence, there is no upper parabolic reflector, and so the absorber is placed right glasscover starts glass where starts thewhere circular the circular part of MaReCopart of MaReCo ends which ends means which the means glass the is between glass is between points 2 andpoints 4 in 2 under the cover. Since this collector is placed on the roof of a building, it is tilt with the roof angle. Figureand 4 2in. Hence, Figure there 2. Hence, is no upperthere parabolicis no upper reflector, parabolic and soreflector, the absorber and so is placedthe absorber right under is placed the cover. right All radiations ranging from incidence angles between 0° to 60° is accepted by the reflector. The angle Sinceunder this the collector cover. Since is placed this oncollector the roof is of placed a building, on the it roof is tilt of with a building, the roof angle.it is tilt All with radiations the roof ranging angle. 60° is determined by the roof angl◦ e, and◦ the reflector receives radiation angles ◦from the horizon to fromAll radiations incidence ranging angles between from incidence 0 to 60 anglesis accepted between by the 0° to reflector. 60° is accepted The angle by 60 theis reflector. determined The by angle the the glass normal. The collector behaves similarly to a flat plate collector above 60° with an absorber roof60° is angle, determined and the reflectorby the roof receives angle, radiation and the angles reflector from receives the horizon radiation to the angles glass normal. from the The horizon collector to area of one third of the aperture area which is the ◦front side of the absorber. It has a concentration behavesthe glass similarly normal. toThe a flatcollector plate collectorbehaves similarly above 60 towith a flat an plate absorber collector area above of one 60° third with of the an apertureabsorber area of Ci = 1.5 when the roof is 30° tilt concerning the horizon. A diagram of roof-integrated MaReCo ◦ areaarea whichof one is third thefront of the side aperture of the absorber.area which It hasis the a concentration front side of the area absorber. of Ci = 1.5 It whenhas a theconcentration roof is 30 is in Figure 4. tiltarea concerning of Ci = 1.5 thewhen horizon. the roof A is diagram 30° tilt concerning of roof-integrated the horizon. MaReCo A diagram is in Figure of roof4. -integrated MaReCo is in Figure 4.

Figure 4. Diagram of roof integrated MaReCo [23]. Figure 4. Diagram of roof integrated MaReCo [23]. The east/west MaReCoFigure with 4. a concentrationDiagram of roof area integrated of 2.0 MaReCo is designed [23].for exceptional cases when theThe roofs east/west are not alignedMaReCo in with the east/west a concentration direction. area In of this 2.0 case,is designed the reﬂector for exceptional axes are aligned cases when in the the roofs are not aligned in the east/west direction. In this case, the reflector axes◦ are aligned◦ in the east/westThe east/west direction thatMaReCo is; it iswith tilted a concentration along the roof. area Radiations of 2.0 is in designed the range for of exceptional 20 to 90 are cases accepted when east/west direction that is; it is tilted along the roof. Radiations in the range of 20° to 90° are accepted asthe seen roofs in are Figure not5 .aligned in the east/west direction. In this case, the reflector axes are aligned in the as seen in Figure 5. east/west direction that is; it is tilted along the roof. Radiations in the range of 20° to 90° are accepted as seen in Figure 5. Energies 2018, 11, 1878 5 of 15 Energies 2018, 11, x FOR PEER REVIEW 5 of 15 EnergiesEnergies 2018 2018, ,11 11, ,x x FOR FOR PEER PEER REVIEW REVIEW 55 of of 15 15

FigureFigure 5.5. Diagram of east/westeast/west MaReCo MaReCo with with 70° 70◦ opticaloptical axis axis from from the the cover cover glass glass [ [2323].]. FigureFigure 5. 5. Diagram Diagram of of east/west east/west MaReCo MaReCo with with 70° 70° optical optical axis axis from from the the cover cover glass glass [ 23[23].]. The spring/fall MaReCo is another prototype, is used to maximise the efficiency of the system TheTheThe spring/fallspring/fall spring/fall MaReCo MaReCo is is another another prototype, prototype, is is usedused used toto to maximisemaximise maximise thethe the efﬁciencyefficiency efficiency ofof of thethe the systemsystem system during the spring and the fall. Radiations with angles below 15°◦ will be reflected outside the collector. duringduringduring thethe the springspring spring andand and thethe the fall.fall. fall. RadiationsRadiations Radiations withwith with anglesangles angles belowbelow below 1515° 15° will will be be reflected reﬂected reflected outside outside the the collector. collector. In this prototype the absorber is placed just below the cover glass. The spring/fall MaReCo has a InInIn thisthis this prototypeprototype prototype thethe the absorberabsorber absorber isis is placed placed placed just just just below below below the the the cover cover cover glass. glass. glass. The The The spring/fall spring/fall spring/fall MaReCoMaReCo MaReCo hashas has aa a i concentration area of C i= 1.8. Figure 6 shows a diagram of spring/fall MaReCo. concentrationconcentrationconcentration areaarea area ofof ofC C iC =i= = 1.8.1.8. 1.8. Figure Figure6 6 6shows shows shows a a diagrama diagram diagram of of of spring/fall spring/fal spring/fall l MaReCo.MaReCo. MaReCo.

FigureFigure 6.6. DiagramDiagram ofof spring/fallspring/fall MaReCo MaReCo for for roof roof tilt 30° 30◦ [[2323].]. FigureFigure 6. 6. Diagram Diagram of of spring/fall spring/fall MaReCo MaReCo for for roof roof tilt tilt 30° 30° [ 23[23].]. An alternative to the east/west MaReCo or the spring/fall MaReCo is the wall MaReCo. It is a AnAnAn alternativealternative alternative toto to thethe the east/west east/west east/west MaReCoMaReCo MaReCo oror or thethe the spring/fallspring/fall spring/fall MaReCoMaReCo isis the the wallwall wall MaReCo.MaReCo. MaReCo. ItIt It isis is aa a i collector which can be installed on a wall with C i= 2.2 for the concentration area and a range between collectorcollectorcollector which which which can can can be be be installed installed installed on on on a a a wall wall wall with with withC C C= i= = 2.22.2 2.2 for for the the concentration concentration areaarea area andand and aa a rangerange range betweenbetween between 25° and 90° for the acceptance angle. The absorberi is also placed just below the cover glass. Figure 7 2525°25°◦ andand and 9090° 90°◦ forfor for thethe the acceptanceacceptance acceptance angle.angle. angle. TheThe The absorberabsorber absorber isis is alsoalso also placedplaced placed justjust just belowbelow below thethe the covercover cover glass.glass. glass. FigureFigure Figure7 7 7 shows a diagram of the wall MaReCo. showsshowsshows aa a diagramdiagram diagram ofof of thethe the wallwall wall MaReCo.MaReCo MaReCo. .

Figure 7. Diagram of wall MaReCo designed for south facing with optical axis at 25° from the horizon FigureFigureFigure 7.7. 7. Diagram Diagram of of of wall wall wall MaReCo MaReCo MaReCo designed designed designed for for forsouth south south facing facing facing with with withoptical optical optical axis axis at at axis 25° 25° from at from 25 ◦the thefrom horiz horiz theonon [23]. horizon[23].[23]. [23]. A photovoltaic thermal (PVT) hybrid system is the combination of a hybrid PV and a solar- AA p photovoltaichotovoltaic thermal thermal (PVT) (PVT) hybrid hybrid system system is is the the combination combination of of a a hybrid hybrid PV PV and and a a solar solar-- thermalA photovoltaic system. This thermal system (PVT) is anhybrid alternative system is environmentally the combination of friendly a hybrid way PV and which a solar-thermal offers both thermalthermal system. system. This This system system is is an an alternative alternative environmentally environmentally friendly friendly way way which which offers offers both both system.thermal, This as wellsystem as is electrical an alternative output environmentally from a single friendly unit. The way system which offers allows both the thermal, simultaneous as well thermal,thermal, as as well well as as electrical electrical output output from from a a single single unit. unit. TheThe system system allows allows the the simultaneous simultaneous asacquisition electrical of output both fromelectrical a single and unit. thermal The systemoutputs allows while the at simultaneousthe same time acquisition there is a reduction of both electrical in the acquisitionacquisition of of both both electrical electrical and and thermal thermal outputs outputs while while at at the the same same time time there there is is a a reduction reduction in in the the andPV module thermal electrical outputs while efficiency at the b samey preventing time there the is atemperature reduction in theincrease PV module in the electricalsolar cells efficiency caused by PVPV module module electrical electrical efficiency efficiency b byy preventing preventing the the temperature temperature increase increase in in the the solar solar cells cells caused caused by by preventingthe solar radiation the temperature. The loss increase reduction in the is solarachieved cells due caused to the by theuse solar of coolant radiation. (water) The, loss which reduction flows thethe solar solar radiation radiation. .The The loss loss reduction reduction is is achieved achieved due due to to the the use use of of coolant coolant (water) (water), ,which which flows flows isthrough achieved the due solar to collector the use of unit coolant [24]. (water), which flows through the solar collector unit [24]. throughthrough the the solar solar collector collector unit unit [24]. [24]. This paper is intended to expand a previous work of the authors [25] [25] and it is organised as ThisThis paper paper is is intended intended to to expand expand a a previous previous work work of of the the authors authors [25] [25] and and it it is is organised organised as as follows: Section 22 describesdescribes thethe SolarusSolarus PVTPVT solarsolar collector,collector, whichwhich waswas usedused toto validatevalidate thethe model;model; follows:follows: Section Section 2 2 describes describes the the Solarus Solarus PVT PVT solar solar collector, collector, which which was was used used to to validate validate the the model model; ; Section 3 describes the accomplished methodology to define the C-PV collector geometry related to SectionSection 3 3 describes describes the the accomplished accomplished methodology methodology to to define define the the C C-PV-PV collector collector geometry geometry related related to to Energies 2018, 11, 1878 6 of 15

Section3 describes the accomplished methodology to define the C-PV collector geometry related to the optical analysis tool designated by Soltrace; Section4 makes a comparison, in terms of a cost-effectiveness analysis, between the conventional MaReCo Solarus configurations and the new configurations, which use symmetrical parabolic geometries for the collector-reflector. The assessment takes into account the influence of the irradiance and the receiver location inside the collector for different zones of the globe. In Section5, some conclusions are summarised, and future trends to the next step of this work are made in Section6.

2. Solarus Concentrating Photovoltaic (C-PV) Collector Solarus concentrator collector is hybrid (PV plus thermal, or PVT), operates without a tracking system [26] and it is specially designed for roof applications in northern countries in Europe. The PVT Solarus collector belongs to the compound parabolic collector (CPC) type, which is commonly known as the maximum reflector concentrator (MaReCo) family [27] already described in the introduction [28–30]. It is formed by a reflector with two asymmetrical truncated parabolic sections separated by a circular section (compound parabolic concentrator, CPC), a flat receiver with solar cells in both sides and bi-facial absorbers. The reflector geometry is designed for high latitudes with the goal of adjusting the output of the collector to better suit the relatively flat heat demand of domestic hot water application. The electric part of each module consists of strings of 38 series-connected cells cut into 1/6 size or 19 series-connected cells cut 1/3 size (The standard cell is 0.156 × 0.156 m2). To fit the collector design, the cell is cut to 0.148 × 0.156 m2. When the larger dimension is cut into three slices, it results in a solar cell, known as 1/3 cell, whose area is 0.148 × 0.052 m2; if it is divided into six slices, a solar 1/6 is formed (0.148 × 0.026 m2). The panel has several parallel connected strings distributed over two similar troughs. For example, in Figure8, there are 152 PV solar cells of 1/6 type. All dimensions are expressed in mm. The length of the receiver Lr is 148 mm; the aperture length Laper is 192 mm. Water connection for cooling is represented in blue; electric connections are represented in red.

Figure 8. Top view of the photovoltaic thermal (PVT) Solarus AB panel.

Some structural parameters that describe the collector are schematically shown in Figure9. Energies 2018, 11, 1878 7 of 15

Figure 9. Standard Solarus concentrating photovoltaic thermal (C-PVT) collector.

Other parameters related to the location and installation details of the solar panel are equally important for its complete description: the latitude (N or S), the longitude (W or E), the elevation solar angle αS, the tilt θt and the azimuthal angle γ (Figure 10).

Figure 10. Schematic representation of the azimuthal, altitude, and tilt angles for a given solar cell panel.

The aluminum reflector concentrated the sum rays into the thermal absorber. The acceptance angle for the reflector is defined by the optical axis direction related to the reflector. The collector optical efficiency changes throughout the year. The collector tilt (the angle that the glass cover of the collector makes with ground) defines the total annual irradiation falling within the acceptance interval. Considering anisotropic light sources, the concentrator factor related to typical MaReCo Solarus [22] structures is roughly 1.4 to 1.5 suns. In the results, this geometry will be considered as a standard geometry and it is schematically represented in Figure8. Photos with the top and side views are shown in Figure 11.

Figure 11. Solarus C-PVT panel: (a) the top view and (b) side view.

Some features of the standard Solarus concentrating photovoltaic thermal (C-PVT) collector can be found in [25]. Energies 2018, 11, 1878 8 of 15

A new reﬂector design by Solarus for lower latitudes was being designed to reach new markets and gain competitiveness against the conventional PV and thermal systems. The new reﬂector has the following dimensions 56 mm wide and 2310 mm long for the receiver, as shown in Figure 12.

Figure 12. Standard Solarus collector absorber.

The solar collector is anodised aluminium reﬂector surface, and it is cover with a low iron glass. The optical properties of the reﬂector, glass and plastic gables are summarised in Table1.

Table 1. Summary of the properties of optical elements.

Optical Elements Optical Properties Reﬂector Reﬂectance (Measured according to norm ASTM891-87) = 95% Transmittance (Measured according to norm ISO9050 for solar thermal) = 95% Glass Refractive index = 1.52 Transmittance = 91% Plastic gables Refractive index = 1.492

3. Efficiency Calculation Methodology and Collector Geometries Understanding the conversion processes that are associated with solar resources requires specialised modelling tools to predict system and economic performances. One of the most important aspects concerns the collector design. For energy calculations in the receiver ray tracing software (Soltrace) are often used. In paper [27], it is possible to find an explanation of the simulation procedure adopted for the asymmetric Solarus collectors. In this paper, Soltrace software was used. Since the early 1960’s, when the first general ray-tracing procedures were described [31], a long road has been travelled, due to the need for designing and modelling solar concentrating systems. From the late 1980’s several optical specific commercial design codes have been developed by the National Renewable Energy Laboratory (NREL), but they were not general and flexible enough for a suitable analysis: a deeper insight into physical and engineering aspects was required. Based on a Monte-Carlo methodology [32], Soltrace was the answer. The main idea is to select a given number of rays and traced his trajectory through the system when they come across various optical interactions. Some of these interactions are probabilistic while others are deterministic [32]. In each simulation, the program uses the well-known Fresnel equations. First, in Soltrace, a solar ray could be absorbed, and if it is this the case, the program moves on to the next solar ray. If it is not absorbed, it is necessary to generate a random number between 0 and 1 to find if the solar ray is reflected or transmitted. If the reflectance defined in the program is smaller than this random number the solar ray is reflected at the specular angle, if it is not, the solar ray is transmitted. It is possible to lunch a certain number of rays for a specific sun position. At the end of the simulation, the program counts the number of rays with an associated power that reaches the receiver. In Figure 13, there is an example of a Soltrace simulation. Energies 2018, 11, 1878 9 of 15

Figure 13. Soltrace simulation. Solar ray’s interaction with a parabolic surface.

Basically Ntot solar rays are traced from the sun through the system, towards the aperture area of the collector, while encountering various optical interactions. Accuracy increases with Ntot, but the use of larger ray numbers means more processing time. A compromise shall be taken, accordingly to the desired result and the situation under analysis. For instance, relative changes in the optical efficiency for different sun angles is not as exigent (as far as Ntot is concerned) as when one needs a more accurate assessment to the flux distribution on the receiver. The particular site latitude and time (day of the year and local solar hour) shall be included in the set of data. From this information, the sun position is calculated (azimuth and elevation). The simulation analysis will allow the collected solar annual energy in each new structure to be assessed and compared to the standard C-PVT Solarus collector. The gain [32] is given by: E − E G = new standard (1) Estandard where Enew and Estandard are the annual flux of energy for the new CPC and the standard Solarus collector, respectively. If the gain is positive, this means a new CPC with a better performance than the standard ones. The concentration factor for 2D concentrating systems (linear: parabolic, circular, MaReCo trough collectors) is given by: 1 C = (2) 2sin(θ) For MaReCo with acceptance angles of 90◦, C = 1.414. According to [27], and using geometrical considerations, the linear concentrating factor is given by:

Aapert C = (3) Arec

In (3), Aapert and Arec are the aperture and the receiver areas, respectively. Taking into account the values referred for the standard collector is concentration factor is around 1.44. Nevertheless, lower acceptance angles shall increase C. Although concentration reduces the costs, it also reduces the annual output. Due to the reﬂection losses, a CPC collector will always receive less energy per m2 of aperture than a ﬂat receiver. The CPC collector annual energy percentage ηE is given by:

Enew ηE = (4) Eﬂat Energies 2018, 11, 1878 10 of 15

The main goal is a percentage value as higher as possible. The idea is to find a new design that allows to receive as much energy as the flat collector, but at a lower cost. This will represent an upgrade. Three new geometries were proposed for lower latitudes (In the presented examples, simulations were carried out for Lisbon (Lat = 38◦, 420 N, Long = 9◦, 80 W) and Luanda (Lat = 8◦, 500 S, Long = 13◦, 140 E)). Two of them present symmetric geometries (parabolic reflector and receivers symmetrically placed) and the third has a parabolic reflector but with an asymmetrically placed receiver as standard MaReCo. For lower latitudes, the geometry symmetry increase is expected to improve the collector performance since the solar radiation difference between the winter and summer is not as large as it is in Sweden. All collectors present the same height and aperture area (Figure 14).

Figure 14. Collector structures: (a) P1—standard MaReCo; (b) P2—Parabolic Reflector; Asymmetric Receiver; (c) P3—Parabolic Reflector; Symmetric Horizontal Receiver; and (d) P4—Parabolic Reflector; Symmetric Vertical Receiver.

4. Results

4.1. Structures Analysed In this section several results were acquired for the structures previous described in Figure 14. The main idea was to redesign the reflector quipping the same area of the standard MaReCo collector and inspect who the reflector geometry affects the total energy collected. For that proposed, the performance of each collector structure was studied for three latitudes in the solstices. The results presented in this section were obtained using Soltrace software. In the simulations, it has considered that the collector model is ideal. This means that: (i) the optical properties are ideal (no optical errors); (ii) the reflector reflectivity is 100%; (iii) the plastic side gables, the frame and the cover glass were not drawn in the 3D model; and (iv) the thickness of the absorber is negligible (2 mm), whereas the current absorber is around 11.4 mm.

4.2. The Latitude and Tilt Effects on the Studied Structures Three latitudes were considered: Gävle in Sweden, Lisbon in Portugal, and Luanda in Angola, for two situations: winter and summer solstices for each of the four geometries: standard with two different receiver positions as well as symmetric and asymmetric parabolic. Validation of the methodology described in Section2 was conducted by comparing the results with the simulation results concerning the current Energies 2018, 11, 1878 11 of 15

Solarus solar panels presented in [33], which uses Tonatiuh software. Results related with the solar panel efficiencies are presented in Figure 15 when the tilt of the PVT system is zero. The figure shows that, for Lisbon, the geometry that captures the most amount of solar radiation in the solstice day is P4, the symmetrical collector with a vertical receiver. In spite of being a good solution for winter solstice, geometry P3 has a poor performance during the Summer solstice in Lisbon, due to the high elevation solar angles. The lateral collected power, which is more clearly seen during the winter solstice in Gävle and Lisbon, is associated to the transparent gambles in all existent structures (photos of Figure 11, concerning the double trough C-PVT Solarus panel).

Figure 15. Collected energy per time along the solstices for the standard and proposed structures, when tilt is zero in (a) Lisbon, (b) Gavle, and (c) Luanda. P1—standard MaReCo; P2—Parabolic Reflector; Asymmetric Receiver; P3—Parabolic Reflector; Symmetric Horizontal Receiver; P4—Parabolic Reflector; Symmetric Vertical Receiver. Energies 2018, 11, 1878 12 of 15

Considering Gävle at zero tilt, the best option presented in Figure7 is the P3 structure. It is worth noticing, that P4 is also a good solution for summertime. The distribution, along the day, in this case is more uniform, which is advantageous for the beginning and the end of the day, where the demands should be higher for grid or off-grid habitation segments or markets. However, during the winter solstice, the produced energy by P4 is negligible, due to the small elevation solar angles. Therefore, this solution should be rejected. For the location of Luanda, and keeping in mind that this city is located in the southern hemisphere close to the equator, on the 21st of December, the Sun will be higher than on the 21st of June. This explains why, during December, P3 is not a good option, in spite of presenting a good performance in June. Some other conclusions may be highlighted, for example, the fact that: (i) P4 geometry is adequate for both solstices and (ii) standard Solarus collectors is not optimized for locations near the equator. The collector tilt variation has a significant influence on the panel efficiency. For Gavle it has been referred that the increase of tilt angles can lead to substantial improvement, being the best performances achieved for tilts around 30◦ [34]. Also important to notice is that for tilts greater than 45◦, due to a steep decrease of the acceptable angles during the Summer solstice, the collected energy almost vanishes, leading to a cut-off phenomenon [35]. By comparative analysis of the geometries under study, and considering the case of Gävle, it is apparent from Figure 16 that geometry P4 is the best option, presenting good performances either in summer or winter, whereas P2 is good in winter but less so in summer. For a tilt of 30◦, the P4 geometry shows, according to (1), the output can increase in Gavle by 70%, being similar to the results presented in Lisbon for a more disadvantageous situation (tilt 0◦), as seen in Figure 15a).

Figure 16. Collected energy per unit time along the solstices for the standard and proposed structures, when tilt is 30◦ in Gävle.

4.3. Potential Choices The simulation results have shown that for all situations, there is always at least one of the new proposals that presents better performances than the MaReCo geometry. For example, in Lisbon with tilt 0◦ or in Gavle with tilt 30◦, using the maximum values of energy per unit time (around midday), the proposed conﬁguration P4 reaches gains around 70%. Using (4), it is straightforward to show that:

Enew = (1 + ηE). (5) Estandard

As expected, an increase of 170% in the collected energy is foreseen in Gävle for the summer solstice case, when compared to a symmetric C-PVT structure with horizontal receiver and a tilt of 30◦ (Figure8). It is also worth referring, that all the proposed conﬁgurations have the same total collector area, which means that the involved costs are comparable. Costs represent an important issue for industrial applications. Energies 2018, 11, 1878 13 of 15

Finally, it is important to highlight that although the outputs during the solstices are a useful indication, further study needs to be performed, as the annual output is, in the end, the most important result.

5. Conclusions Alternative geometries for C-PV collectors have been studied using ray trace software Soltrace. In this paper, it has been considered three locations (Gavle, Lisbon, and Luanda) and simulation analysis have been presented for winter and summer solstices. A comparative analysis with the current MaReCo C-PVT has been assessed. In all situations, there was at least one of the new proposals that correspond to an improvement of the power production when compared to the current collector. However, the assessment should be done for the full extent of the year. The simulation method using Soltrace is a useful tool to investigate the effect of the collector geometry on the energy output in a simpler, faster, and cheaper way than using the experimental methods. The simulation results are important input data for the electrical and thermal description of the collector [36]. These studies reveal crucial for panel manufacturers that wish to reach emerging markets. Current investments and commitments must be made to further objectives in a near future. Compromises will always be taken into account, following which the ﬁnal decision will be made.

6. Future Work The best CPV geometry optimisation procedure is a complex process since there is a large amount of parameters that need to be considered simultaneously. For instance, the sun position and the latitude of the system installation that affects the system performance. The results shown in the present paper for three different latitudes provides important insights on how the configuration of the concentrator and the position of the receiver in the concentrator affects the CPV performance. It is crucial in a future work and using the same CPV configurations, to implement an optimisation algorithm. With this algorithm, it is possible to optimise these structures regarding the several parameters that affect his performance. Several optimisation algorithms can be used to optimise these structures. We are going to focus our attention in the machine learning algorithms and the genetic algorithms. The first one, has already been used to directly predict and optimise the best collector geometries in several cases [37,38], similar to the second one [39].

Author Contributions: J.P.N.T. performed all the simulations and post-processing, analysed the results, and wrote the manuscript. C.A.F.F., J.G., B.L., G.C., O.O. and P.J.C.B. analysed the simulation results and revised the manuscript. All authors read and approved the final manuscript. Acknowledgments: This work was supported by FCT, through IDMEC, under LAETA, project UID/EMS/ 50022/2013 and under IT, project UID/EEA/50008/2013. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

2 Aapert aperture area of the collector (m ) 2 Arcev receiver area (m ) C concentration factor

Eﬂat Energy produced by the ﬂat panel (W·h) Enew Energy produced by the new geometry (W·h) Estandard Energy produced by MaRECo structure (W·h) G gain or energy ratio Ntot number of total rays in the simulation Greek Symbols ◦ αs elevation solar angle ( ) ν incident angle (◦) Energies 2018, 11, 1878 14 of 15

ηE electrical efﬁciency ◦ θa acceptance angle ( ) ◦ θt tilt angle of the glass cover ( ) Acronyms and abbreviations BP Bypass CPC Compound Parabolic Concentrator C-PV Concentrating Photovolaitc CSP Concentrated solar power HC-PV High Concentration Photovoltaic LC-PV Low Concentration Photovoltaic MC-PV Medium Concentration Photovoltaic MaReCo Maximum Reﬂector Collector PV Photovoltaic PVT Photovoltaic and Thermal

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