Electrical and thermal performance evaluation of symmetric truncated C-PVT trough solar collectors with vertical bifacial receivers

Solar Energy 174 (2018) 683–690

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Electrical and thermal performance evaluation of symmetric truncated C-PVT trough solar collectors with vertical bifacial receivers

T

Diogo Cabral , Björn O. Karlsson ⁎

Department of Building, Energy and Environmental Engineering, University of Gävle, Kungsbäcksvägen 47, 801 76 Gävle, Sweden

ARTICLE INFO

ABSTRACT

Keywords: Symmetric C-PVT collector Electrical and thermal yield evaluation Bifacial receiver Ray-tracing

One way to reduce solar collectors’ production costs is to use concentrators that increase the output per photovoltaic cell. Concentrating collectors re-direct solar radiation that passes through an aperture into an absorber/ receiver. Symmetrical truncated non-tracking C-PVT trough collectors based on a parabola and compound parabolic concentrator (CPC) geometries have been developed. The collector type has a central vertical bifacial (fin) receiver and it was optimized for lower latitudes. In this paper, the electrical and thermal performance of symmetric truncated non-tracking low concentrator PVT solar collectors with vertical bifacial receivers is analysed, through a numerical ray-tracing model software and a multi-paradigm numerical computing environment. A thermal (quasi-dynamic testing method for liquid heating collectors described in the international standard for solar thermal collectors ISO 9806:2013) and electrical performance models were implemented to evaluate the design concepts. The evaluation was made for heating Domestic Hot Water for a Single Family House in Fayoum (Egypt), where CPC geometries with a concentration factor of 1.6 achieved 8 to 13%rel higher energy yields (in kWh/m2/year) than the Pure Parabola geometries.

1. Introduction Photovoltaic-Thermal (PVT) collectors are hybrid solar collectors that simultaneously generate electrical (through PV cells) and thermal energy (through the solar radiation absorbed by the PV cells that is not converted into electricity). These systems can be based on Compound Parabolic Collector (CPC) or on flat plate solar thermal (T) collectors (Sharaf and Orhan, 2015). According to Zondag (2008), PVT collectors can be classified according to their PV cell technology, design (unglazed, glazed, and concentrating), and their heat transfer medium (water and air). Concerning concentrating PVT collectors, Stine and Harrigan (1986) classified this technology as low, medium or high concentration (ratio) system, with the possibility of both stationary and tracking operation. These systems are also known by their low heat losses. Previous studies showed that the efficiency of PV cells is temperature dependent. For every degree increase in temperature, the cell efficiency decreases between around 0.3% and 0.5%, and for that reason, it is necessary to remove and harvest the excess heat. This increased PV cell temperature leads to a significant efficiency drop since the cells can reach very high temperatures. In order to carry out the excess thermal energy generated by the PV cells, a cooling fluid is used (generally water with a percentage of glycol ⁎

to prevent the fluid to freeze), which leads to a decrease in temperature on the solar cells and to higher overall efficiencies (Kramer and Helmers, 2013). This way, the waste heat harvested by the cooling fluid can be used as a cogenerated product and for heating applications (Aste et al., 2014). According to Davidsson et al. (2010), the combination of reflectors with PVTs is cost-effective since they require less reflective material and are less deep than flat one-sided absorber collectors. This technology also takes advantage of the geometry acceptance angle and the efficiency of the PV cells can be increased by actively cooling the laminated PV. Incorporating both electrical and thermal system into a single unit decreases the total area dedicated to solar energy devices, by optimizing the use of the solar resource (Lämmle et al., 2016). Nevertheless, this technology faces some challenges, such as partial shadowing. Partial shadowing has been identified by Decker and Jahn (1997), as the main cause for decreasing the energy yield of PV arrays. A Concentrating Photovoltaic-Thermal (C-PVT) non-tracking, to be able to perform at its full electrical potential (no shadowing), needs to ensure that the reflected image of the PV cells in the reflector stays as much as possible in the reflector boundaries. At lower solar altitudes (i.e. morning and afternoon), the reflected image of the PV cells in the reflector is not complete, leading to loss of power, thus lowering the

Corresponding author. E-mail address: [email protected] (D. Cabral).

https://doi.org/10.1016/j.solener.2018.09.045 Received 28 June 2018; Received in revised form 27 August 2018; Accepted 16 September 2018 0038-092X/ © 2018 Elsevier Ltd. All rights reserved.

Solar Energy 174 (2018) 683–690

D. Cabral, B.O. Karlsson

Nomenclature

c4 G Pel Qth u β c2

Symbol Description [Unit] θc acceptance half-angle [°] ambient temperature [°C] ta Gb beam irradiance [W/m2] tcell,PVT cell temperature [°C] Ci concentration factor [–] b0 constant for incident angle modifier Gd diffuse irradiance [W/m2] c5 effective thermal capacity [J/m2.K] electrical efficiency at standard testing conditions [–] ηel,STC f focal length [mm] F focus [–] x half aperture [mm] c1 heat loss coefficient at (tm − ta) = 0 [W/m2.K] θ incidence angle [°] Kθb(θL,θT) incidence angle modifier for beam radiation [–] Kθd incidence angle modifier for diffuse radiation[–] long wave irradiance (λ > 3 μm) [W/m2] El maximum efficiency [–] max tm mean fluid temperature [°C] η0,b peak collector efficiency at ΔT = 0 K [–] h receiver height [mm] ρ reflectivity [%] z reflector height [mm]

c3

sky temperature dependence of heat loss coefficient [–] solar irradiance [W/m2] specific electrical power output [W/m2] specific thermal power output [W/m2] surrounding air speed [m/s] temperature coefficient of electrical power [%/K] temperature dependence of heat loss coefficient [W/ m2.K2] wind speed dependence of heat loss coefficient [J/m3.K]

Subscripts CPC CSP C-PVT DHW IAM MaReCo MCRTM PP PR PTC PVT SFH T

energy yield. In order to avoid shadowed PV arrays from breaking down, bypass diodes are applied. This allows the current to flow in a different path at the expense of a minor fraction of the total power (Woyte et al., 2003). At lower latitudes, the solar radiation is characterised by its symmetry over the year. This implies that concentrator solar collectors should be symmetrically truncated to maximize the energy yield (Adsten et al., 2005). In order to follow the solar radiation profile, design concepts with symmetric truncated CPC and parabolic nontracking trough geometries with vertical bifacial receivers have been developed. An evaluation of the electrical and thermal performance of two symmetrical concentrating trough geometries, such as Pure Parabola (PP) and CPC is presented. These geometries were designed with the aim of lowering the shadowing effect on the PV arrays, as well as reducing the cost of solar systems, by using cheap reflectors to replace the PV cells. Several sets of ray-tracing simulations were performed in order to get the Incidence Angle Modifier (IAM) for each geometry. The data was then fed into a multi-paradigm numerical computing software (MATLAB) in order to get the IAMs. A thermal performance model based on the international standard ISO 9806:2013 and an electrical performance model suggested by Lämmle et al. (2017), have been implemented to estimate the electrical and thermal performance of the design concepts.

Compound Parabolic Collector Concentrating Solar Power Concentrating Photovoltaic-Thermal Domestic Hot Water Incidence Angle Modifier Maximum Reflector Concentration Monte Carlo Ray-Tracing Method Pure Parabola Performance ratio Parabolic Trough Collector Photovoltaic-Thermal Single-Family House Thermal

the receiver, with the amount depending on the acceptance angle of the concentrator (Duffie and Beckman, 2013). Compound Parabolic Collectors (CPC) are non-imaging concentrators that do not require a tracking system due to the ability to reflect the available beam radiation and partly diffuse radiation to the receiver. According to Rabl et al. (1980), CPC reflectors can have different configurations, such as (i) flat one-sided absorber, as in Fig. 1; (ii) flat two-sided (fin) absorber (used in this paper), as in Figs. 4 and 5; (iii) tubular absorber and (iv) wedge absorber. CPCs combine two parabolic reflectors (symmetric or asymmetric), each one of them with its own focus at the lower edge of the other parabola. Duffie and Beckman (2013) described the relation between the size of the aperture (2a) and the size of the receiver (2a′) as the concentration ratio (known as the ratio between the aperture area and the

1.1. Compound parabolic collectors Solar energy technologies, as any energy technologies, aim at providing energy at the lowest possible cost. This can be accomplished by increasing the efficiency of the systems or by decreasing the investment cost, and at the same time reduces the installation ground area (Perers and Karlsson, 1993). Concentrating solar collectors re-direct the solar radiation (both beam and diffuse radiation) that passes through an aperture into the receiver over ranges of incidence angles within wide limits (thus defining the acceptance half-angle, θc). For systems of low concentration ratio, part of the diffuse radiation will be reflected into

Fig. 1. Cross section view of a symmetrical non-truncated one-sided absorber CPC (Duffie and Beckman, 2013). 684

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receiver area). Additionally, the CPC upper reflector surfaces are parallel between each other, thus having a low contribution to the radiation reaching the absorber. The concentration factor for CPCs is presented by the following Eq. (1).

Ci =

2a 2a'

(1)

1.2. Symmetrical geometry based on maximum reflector concentration collector geometry Several studies on asymmetric concentrating solar collectors have been reported by Rabl (1976), Mills and Giutronich (1978), Welford and Winston (1989) and Tripanagnostopoulos et al. (2000). These studies led to a novel truncated geometry called Maximum Reflector Concentration (MaReCo) and the methodology for the development of this geometry is described by Adsten et al. (2005). The reflector was designed with a circular section (point 1–2, section B in Fig. 2) next to the bifacial receiver (point 1–5) and a parabola from point 2 to point 3 (truncated point, Fig. 3). The circular section reflects the light beams directly to the receiver, replacing the receiver shown in Fig. 3 by the dotted line between point 2 and the focus (F, point 5). Fig. 2 presents the basic sketch of a MaReCo design, divided into three sections A, B, and C. This revision address, amongst other geometries, a CPC trough geometry based on section B and C, presented previously in Fig. 2. The selected geometry is composed of a mirror wise version of section B and C, with a central vertical bifacial receiver as a mirror point, as shown in Fig. 3. The receiver dimensions were set to fit this geometry (point 1–5, Fig. 2) and vary in length depending on the applied geometry and concentration factor. Section B of the concentrator is composed of a 20° arc of a circle centred on the top edge of the vertical receiver and section C by a parabola with focus on f.

Fig. 2. Cross section view of the basic MaReCo design, divided into 3 main sections: A (full parabola, from point 1–4), B (circular section, from point 1–2) and C (parabola section, from point 2–3). Depending on the truncation, the position of the cover glass will vary along the extended parabola. α is the aperture tilt.

Fig. 3. Cross section view of the simulated CPC geometry with a longer vertical bifacial (fin) receiver. The geometry is divided into 2 main sections: B (circular section, from point 1–2) and C (parabola section in black, from point 2–3).

1.3. Parabolic trough collectors Parabolic trough collectors (PTC) are considered one of the most mature and commercially proven technologies in the utility-scale Concentrating Solar Power (CSP). In this review, the simulated geometries are composed of either a full parabolic section or an arc circle with a parabolic section, thus, the importance of analyzing the geometrical shape of these reflectors. Stine and Harrigan (1986) explained how a parabolic trough works, showing that all the radiation that hits the collector with the same angle as the normal of the collector will hit the focus (F). The following Eq. (2) presented by Winston et al. (1988) allows the calculation of the half aperture (x) in function of the reflector height/ truncation (z) and the focal length (f).

Fig. 4. Cross section view of the PP geometry with a longer vertical bifacial (fin) receiver, composed by one full parabola (section A, from point 1–4).

x=

f×4×z

(2)

Fig. 5. Cross-section view of PP geometries (with respective parameters), with a main section A (parabolic mirror). Left: PP 1 geometry; Right: PP 2 geometry. 685

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All the incoming light rays parallel to the axis of the parabola will be reflected towards the focus area, by definition of the focal point of a parabola. The ideal location of the receiver can be given as the focal point position, assuming that the light rays that arrive at the reflector surface are essentially parallel light rays (in tracking systems). A PP trough geometry based on section A presented in Fig. 2 has been developed and analysed. It is composed of a parabolic trough (section A, Fig. 4) with a central vertical bifacial receiver, as shown in Fig. 4. The light rays that reach the collector aperture area at a positive angle of incidence will be reflected below the focus, therefore all incoming light with a negative incidence angle will be reflected above the focus, as described by Nilsson (2005).

Table 1 Summary of the main parameters for each simulated geometries. Geometry

Concentration factor (Ci)

Reflector height (z) [mm]

Receiver height (h) [mm]

Focal length (f) [mm]

Acceptance half-angle (θc) [°]

PP 1 PP 2 CPC 3 CPC 4

1.6

75 31 75 31

56 30 56 30

27 19 48 25

– – 63 83

1.6

i. A symmetrically truncated PP reflector geometry (PP 1 and PP 2, Fig. 5). The vertical receiver has a thickness of 5 mm and a width of 30 or 56 mm. Both receiver and reflector are 2310 mm long. The reflector height varied between 31 and 75 mm. ii. A symmetrically truncated CPC reflector geometry (CPC 3 and CPC 4, Fig. 6) composed by a circular section with an arc angle of 20° (each side), complemented by a truncated parabola section. The receiver dimensions, reflector height and length are in line with the ones present above for the PP geometry.

1.4. Ray-tracing software Tonatiuh, developed by CENER, is an open source free-to-use software that focuses on the optical design simulation of complex CSP systems. Tonatiuh is based on a Monte Carlo Ray-Tracing Method (MCRTM) and it is written in C++ programming language. Provides a friendly and easy-to-use Graphics User Interface, having been experimentally validated using real data from different CSP projects (Blanco et al., 2009). The software has been under development and the latest features allow the simulation of more complex systems using more materials, a built-in tool for calculating flux distributions and the capability to import CAD files. To model the concentrating system, several nodes and sub-nodes in a tree structure must be included (the properties applied to a node also apply to all the sub-nodes). The software has more than 15 shape nodes to define the surfaces and more than 7 material nodes. After modelling the system, it is necessary to define the Sun by position, azimuth and elevation angles, and shape (Pillbox). A light source generates the light rays and calculates the ray intersection with the system surface. A specified number of rays are launched and traced from the light source into the concentrating system. The intersection of the ray with the tree structure is calculated, starting at the root node. If a ray intersects the node bounding box, the intersection is verified with that node sub-node. A more detailed description of the software can be found in Blanco et al. (2005).

The different geometries drawn in the ray-tracing software were under-dimensioned, and the number of rays launched was set and kept constant at 10,000 rays, in order to reduce the computational time. The sun shape varies widely with terrestrial location, sky conditions, and time, thus the Pillbox approximation is adequate and has been selected with a value of θmax of 4.65.10−3 rad. The optical analysis was carried out based on the assumption that the reflecting surfaces are non-ideal and free from fabrication errors. Additionally, a thorough analysis of the different geometries was established in the following Section 3. Table 1 presents a more detailed assessment regarding the main parameters of each geometry. Perers (1993, 1997) and Rönnelid et al. (1996) defined different testing procedures based on a quasi-dynamic testing methodology for conventional solar collectors. Due to testing difficulties associated with the size of concentrating solar collectors, Perers et al. (1994) defined a model to calculate the Incident Angle Modifier (IAM) of a big-size collector by means of a ray-tracing software and simulate its output power. For this reason, the analysis and design of solar concentrating systems, a MCRTM was employed, where the efficiency of each geometry at each angle (IAM) has been assessed. For this, a script file has been developed, allowing the simulation of the sun movement (performing parametrical simulations that allowed the launching of several simulations by means of a few loops). For solar energy applications, the wavelengths of importance are in the ultraviolet, visible and infrared radiation (i.e., from around 0.29 to approximately 25 μm). PV cells optimally utilize a very narrow range of the solar spectrum, therefore the radiation that is not within this range

2. Collector evaluation method To design the reflector geometry, knowledge about the angular distribution of the annual solar radiation is required. For that, each shape has been drawn independently, thus ensuring a good connection between the elements. This way, the mismatch is avoided, as it is imperative to have a perfect connection between the different collector elements, in order to collect all the launched rays. This assessment includes the following truncated symmetric reflector geometries:

Fig. 6. Cross-section view of CPC geometries (with respective parameters), divided in 2 sections: B (circular mirror) and C (parabolic mirror). Left: CPC 3 geometry; Right: CPC 4 geometry. 686

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merely warms the cells and can be used as thermal energy, thus limiting the maximum electrical efficiency. From the electrical side, the selected reflector (Almeco vega SP195) has a spectral reflectivity in the visible range of ρ = 92%, to cope with the spectral response of a silicon solar cell for wavelengths from 0.38 to around 0.78 μm. On the other hand, for the thermal side, the reflector total solar reflectance is around 95% (including ultra-violet, visible and infrared wavelengths). In order to extract the information acquired from Tonatiuh, a script has been developed and optimized. The script is composed of several lines of code in order to extract the data relative to the transversal and longitudinal IAM. The data was then fed into a multi-paradigm numerical computing software (MATLAB) in order to get the IAMs. Then, the IAMs have been employed in a thermal and electrical performance model, to evaluate the electrical and thermal yield.

the difference between mean fluid temperature tm and the ambient temperature ta. The coefficient c5 is the effective thermal capacity, which describes the dependency to the derivate in time of the mean fluid temperature dtm . The estimation of the energy yield has been done dt at a collector level, due to no knowledge about the system outside the collector array is needed. A fixed mean operating fluid temperature for heating Domestic Hot Water (DHW) is used as Tin = 40 °C and Tout = 65 °C. If the working fluid temperature varies within relatively small limits, the system can be satisfactorily simulated using the average operating temperature, thus making the comparison between different collectors more straightforward, since no system effects are included. The estimation of the electrical and thermal yields have been determined by using meteorological data records obtained from Meteonorm (2018), with hourly time steps. Fayoum is situated at latitude 29.3°N and longitude 30.8°E. The year is characterised by a global and diffuse irradiation in the horizontal plane of 1898 and 767 kWh/ m2/year, respectively. The beam irradiation at normal incidence (25° tilt) achieved 1568 kWh/m2/year.

2.1. Thermal performance model In order to accurately calculate both thermal and electrical yield of the different geometries, the collector parameters have been normalized to the gross area of the C-PVT, according to the international standard for solar thermal collectors ISO 9806:2013. The thermal and electrical parameters were obtained from previous testing reports made on C-PVT at the Solar Energy Laboratory (LES, Lisbon, 2016). The testing report is based on test methods for solar thermal collectors described in ISO 9806:2013. The collector tested at LES has the same box layout and same concentration factor as the simulated geometries. The receiver placement has been considered negligible regarding additional heat losses since the heat losses are taken into account for the ‘hot area’ (gross area of the collector). Truncation was applied to increase the optical efficiency and energy yield, therefore leading to a lower average number of reflections and to higher heat losses (Carvalho et al., 1985). As these kind of collectors (with concentration factors below 2) are coming to the market, the truncation has been selected in order to be convenient for industrial/ commercial applications. These applications require collectors with low dimensions (i.e. in-roof applications), in order to be in line with the dimensions of the asymmetric collector tested by Koronaki and Nitsas (2018). An IAM factor for diffused radiation (Kθd, given by the inverse of the geometrical concentration factor (Bernardo et al., 2011)), a heat loss coefficient (c1 = 3.155 W/m2.K), a temperature dependent heat loss coefficient (c2 = 0.022 W/m2.K2), and a collector optical efficiency for beam radiation (η0,b = 0.5) characterise the solar collectors. The quasi-dynamic performance model for liquid thermal/heating collectors has been implemented, taking into account parameters such as the dependence on direct and diffuse radiation, mean fluid temperature and incidence angle modifiers. Eq. (3) presents the energy balance equation (in W/m2) for liquid heating collectors (ISO 9806:2013) used in Solar Collector Energy Output Calculator (described in Serrats et al. (2012)).

Qth =

0, b ·(K b ( L ,

+ c4·(EL

T )·Gb

· ta 4 ) c5·

2.2. Electrical performance model A simplified electrical performance model was based in the PVT electrical performance model suggested by Lämmle et al. (2017), which takes into account different parameters, such as the instantaneous performance ratio (PR) due to incidence angle losses (PRIAM = = 1 – b0 · ( 1 − 1); Duffie and Beckman (2013)), the temperature dependence cos of the electrical efficiency (PRT = 1 − β · (tcell,PVT − ta); Skoplaki and Palyvos (2009)), and standard panel efficiency ηel,STC. The cell temperature in PVT collectors tcell,PVT presented by Lämmle et al. (2016) was simplified as the fluid mean temperature tm. Due to the concentration factor, the low irradiance behaviour PRG presented by Heydenreich et al. (2008) was not considered, thus the instantaneous specific electrical power output Pel is given by the following Eq. (4).

Pel =

where the temperature coefficient of electrical power β and the standard panel efficiency ηel,STC are 0.4%/K and 10%, respectively. 3. IAM and energy yield comparison In the following section, the electrical and thermal energy yields are presented, with reference to reflector geometry and concentration factor (through the IAMs), fluid mean temperature, tilt angle and location. Before discussing the results in more detail, Fig. 11 shows the specific yields for each geometry. A more detailed assessment of the electrical and thermal yields is presented in Appendix A (Table 2). The highest annual energy yield output has been obtained for a 25° tilt. This evaluation will focus on the thermal level of heating Domestic Hot Water (DHW) for Single Family Houses (SFH) in Fayoum, Egypt. 3.1. Comparison of C-PVT collector incidence angle modifiers

+ K d·Gd ) c1·(tm ta) c2·(tm ta )2 c3· u ·(tm ta ) dtm dt

(4)

el STC ·PRIAM · PRT · G

Incidence Angle Modifier (IAM) is known as the variance in output performance of a solar collector as the angle of the sun changes in relation to the surface of the collector, with respect to irradiance under normal incidence (Hertel et al., 2015). The longitudinal and transversal

(3)

The heat losses are given by the coefficients c1 and c2 in respect to

Table 2 Summary of the results obtained for a DHW/SFH system, including thermal and electrical yields, concentration factor, focal length, reflector and receiver height, acceptance half-angle and maximum efficiencies. Geometry

Thermal yield [kWht/m2/year]

Electrical yield [kWhe/m2/year]

Ci

f [mm]

z [mm]

h [mm]

θc [°]

ηmáx [%]

PP 1 PP 2 CPC 3 CPC 4

267 266 296 309

123 118 130 131

1.6 1.6 1.6 1.6

27 19 30 25

75 31 75 31

56 30 56 30

– – 63 83

90 90 74 79

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IAM can be obtained through the maximum efficiency, solar irradiation, efficiency at each angle and aperture area. This section presents an analysis of the results obtained for the transversal and longitudinal radiation IAM. Figs. 7–10 show both transversal and longitudinal IAM (normalized for normal incidence) for each reflector geometry. The international standard ISO 9806:2013 for solar thermal collector testing methods states that the normal incidence (equal to zero) is usually used to define the incidence angles, however other values can be used if applicable. Both PP 1 and PP 2 geometries reached a maximum efficiency of 90%. On the other hand, the CPC 3 geometry reached a maximum efficiency of 74% or 6%rel below the highest efficiency value of CPC 4. For a concentration factor of 1.6, the PP 1 geometry achieved a maximum efficiency of 18%rel higher than the one obtained for the CPC 3. Additionally, the PP 2 geometry reached a value 12%rel higher than the efficiency obtained for the CPC 4. A higher receiver will allow the collector to collect more sunlight directly into the receiver before the reflector starts to work, thus working like a PV module until the sun rays reach the acceptance incidence angle. On the other hand, the height of the receiver shadows the receiver side that is not facing the sun, leading to that only on side of the receiver works until the sunlight hits the opposite reflector. Nevertheless, a higher receiver will allow the geometry to collect the sunlight, both directly and through reflections. As expected, the whole set of simulated concept geometries have symmetrical IAMs, on both transversal and longitudinal directions. The longitudinal direction has a constant profile throughout the different simulations, as expected. Regarding the transversal IAMs, acceptance half-angles between 46° and 83° characterise the CPC geometries. Note that regardless the geometry or the receiver height, the acceptance half-angle does not change since the focal point is fixed and sets the acceptance half-angle. As can be seen in Figs. 7–10 the transversal IAMs do not ‘start’ or ‘end’ at the acceptance half-angles. This phenomenon occurs due to the receiver being longer than the focal length, thus increasing the collected solar irradiance. This phenomenon is presented by CollaresPereira et al. (1978), where it shows the increased solar irradiance that reached the absorber outside of the acceptance-half angle.

concentration factors lead to lower reflection losses, thus to higher energy yields). The energy yields of the investigated C-PVT collectors vary between 384 and 440 kWh/m2/year depending on the employed geometry. For the selected mean fluid temperature, the CPC geometry achieved higher energy yields than the PP geometry, despite having lower maximum efficiencies. The PP 2 geometry achieved an annual specific yield of 384 kWh/ m2 or 13%rel below the yield obtained for CPC 4. A specific yield of 390 kWh/m2/year was achieved for PP 1, being 8.5%rel below the highest energy yield for CPC 3. In addition, the annually received energy profile of the simulated geometries (daily average power) is in line with the average seasonal variation of the daily extra-terrestrial solar radiation for horizontal surfaces. It should be noted that the geometry with the highest energy yield has the lowest half-acceptance angle of all of the simulated geometries. Both electrical and thermal yields are higher for the CPC geometry when the same concentration factor and receiver layout is applied. 4. Summary and outlook PVT collectors co-generate electricity and heat from the same gross area, thus achieved higher energy yields. In this review, an electrical and thermal performance evaluation for this kind of systems is presented, which was obtained through a ray-tracing simulation software and a multi-paradigm numerical computing environment. The aim of these design concepts is to provide low-cost energy, by replacing partially the expensive receiver with cheap reflectors. A great part of the incoming available solar radiation will be collected without the need for tracking due to the use of reflectors and specific symmetric geometry. The CPC geometry achieved lower maximum efficiencies than the PP geometry, but on the other hand, higher annual energy yields (8 to 13%rel) have been achieved by these geometries due to their broader IAMs. Due to the symmetric reflector shape, both transversal and longitudinal IAM profiles are, as expected, symmetrical for each collector. The design concept can be refined through further studies on reflector geometry, cell temperature dependence and outdoor collector testing. Table 2 (Appendix A) gives a summary of the specific energy yield, as well as the respective efficiencies, concentration factors, focal lengths, reflector and receiver height, maximum efficiency and maximum efficiencies for all the investigated geometry technologies, as defined and discussed in Section 3.

3.2. Comparison of C-PVT collector yields The evaluation of the thermal level of heating energy was focused on heating energy for DHW/SFH, for temperatures between Tin = 40 °C and Tout = 65 °C. The concentration factor is an indicator of energy yield, which can be used to assess the performance of C-PVT collectors (since lower

Fig. 7. Normalized IAM for normal incidence (PP 1 geometry). Left: Longitudinal IAM; Right: Transversal IAM.

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Fig. 8. Normalized IAM for normal incidence (PP 2 geometry). Left: Longitudinal IAM; Right: Transversal IAM.

Fig. 9. Normalized IAM for normal incidence (CPC 3 geometry). Left: Longitudinal IAM; Right: Transversal IAM.

Fig. 10. Normalized IAM for normal incidence (CPC 4 geometry). Left: Longitudinal IAM; Right: Transversal IAM.

Acknowledgements This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Appendix A Table 2 gives a summary of the specific annual received energy, as well as the concentration factors, focal lengths, reflector and receiver height, maximum efficiency and maximum efficiencies of all investigated collector technologies described and discussed in Sections 3 and 4.

Fig. 11. Annual specific electrical (bottom, blue) and thermal (top, red) yield for a DHW/SFH system. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 689

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D. Cabral, B.O. Karlsson

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