This study proposed a planar solar concentrator featuring alignment-free total-internal-reflection (TIR) collectors and an innovative compound tracker. The compound tracker, combining a mechanical single-axis tracker and scrollable prism sheets, can achieve a performance on a par with dual-axis tracking while reducing the cost of the tracking system and increasing its robustness. The alignment-free TIR collectors are assembled on the waveguide without requiring alignment, so the planar concentrator is relatively easily manufactured and markedly increases the feasibility for use in large concentrators. Further, the identical TIR collector is applicable to various-sized waveguide slab without requiring modification, which facilitates flexibility regarding the size of the waveguide slab. In the simulation model, the thickness of the slab was 2 mm, and its maximal length reached 6 m. With an average angular tolerance of , and after considering both the Fresnel loss and the angular spread of the sun, the simulation indicates that the waveguide concentrator of a 1000-mm length provides the optical efficiencies of 62–77% at the irradiance concentrations of 387–688, and the one of a 2000-mm length provides the optical efficiencies of 52–64.5% at the irradiance concentrations of 645–1148. Alternatively, if a 100-mm horizontally staggered waveguide slab is collocated with the alignment-free TIR collectors, the optical efficiency would be greatly improved up to 91.5% at an irradiance concentration of 1098 (Cgeo = 1200X).
© 2014 Optical Society of America
As a type of green energy, solar energy has been attracting increasing attention in recent years. Common ways of harvesting solar energy include photovoltaics (PV), solar thermal, and daylighting. Because PV cells are composed of costly semiconductor materials, optical concentrators known as solar concentrators are commonly used to reduce the necessary area of PV cells; PV cells employing a solar concentrator are called concentration photovoltaics (CPV). In addition, commercial multi-junction CPV technologies have already demonstrated solar-cell efficiencies of approximately 40% under a highly concentrated solar irradiation of hundreds to thousands of suns . Under these highly concentrated solar irradiations, the cost of operating CPV depends largely on the employed optical system. Solar thermal technology can be used for household heat exchangers and in power plants. Solar thermal used in power generation also requires an optical concentrator to attain a sufficiently high temperature to heat boilers. Daylighting involves collecting natural sunlight for interior illumination. For illumination inside buildings, the collected sunlight is typically guided through a duct or a fiber bundle. To reduce the volume of the duct or facilitate coupling with the fiber bundle, an optical concentrator must be used to concentrate the sunlight. Therefore, optical concentrators play a crucial role in harvesting solar energy. Optical concentrators can be divided into two types: the traditional type composed of lenses or mirrors; and the planar type, based on a waveguide slab. Numerous designs related to the traditional concentrator have been proposed, which can provide a considerable concentration ratio, but requires a sophisticated dual-axis tracker and typically a large space . The planar concentrator can provide a concentration ratio ranging from high to low, and its advantages include a compact volume and a light weight. In addition, whether a tracker is necessary for the planar concentrator depends on the concentration ratio determined by its design. High-ratio concentrators require a sophisticated dual-axis tracker, whereas those with a low ratio can operate with a relatively simple single-axis tracker; even various specific designs do not require a tracker. Thus, the planar concentrator features a compact volume and light weight; provides the design flexibility for a wide range of applications. Consequently, numerous designs associated with the planar concentrator have been proposed in recent years. Related designs are discussed in the following.
A planar concentrator is equivalent to a device that divides a single large concentrated element into an array of millimeter-sized optics (e.g. lens array) coupled to a common slab waveguide. The light entering each small aperture are focused on localized fold mirrors embedded on the bottom of the waveguide. These localized fold mirrors are called coupling microstructures, and reflect light at predicted angles, causing it to propagate in the waveguide through total internal reflection (TIR); thus, the light from thousands of small apertures is guided to the ends of the waveguide . The concentration ratio of a basic planar concentrator is equivalent to the ratio of the waveguide length to the slab thickness, independent of the slab width. The concentration ratio of the planar concentrator determines its application. Planar concentrators with a high concentration ratio are typically used mainly for PV and solar-thermal applications that must overcome light leakage during light propagation in a waveguide. Because the coupling microstructures on the waveguide surface couple light into the waveguide, and also decouple the light guided in the waveguide in subsequent interactions, the decoupling loss increases with the waveguide length. Moreover, to prevent the light from being decoupled, an air gap must exist between the array of optics and the slab waveguide, which is adverse to the alignment of the optics and coupling microstructure. Although employing a transparent adhesive material with a low refractive index can replace the air gap, the low refractive index adhesion inevitably facilitates the decoupling of the propagating light. To manage the decoupling loss, various designs of the waveguide and coupler geometries were proposed. Stepped (or taper) and horizontally staggered waveguides have been proposed to reduce or eliminate interactions with the coupling microstructure [4,5]. These designs can support the efficient propagation of guided light in the waveguide only for a limited length; hence, the concentration value or total flux is limited. Another proposed approach for reducing decoupling loss involves introducing a bypass element—a “dimple”—which diverts the guided light around the coupling microstructures . However, each bypass-prism reflection adds to the angular spectrum of the guided light. Therefore, multiple prism reflections cause rays to break the TIR, and ultimately limit the concentration ratio. To address this issue, an approach combining a bypass element and a tapper waveguide was proposed . In principle, this design can yield a high efficiency at higher concentrations, but the complex profile of the dimple is not conducive for manufacture. Moreover, the fillet inevitably existing in the dimple must substantially increase the decoupling loss. These designs require an accurate alignment of the lens array and the coupling microstructure, which is difficult to be achieved when assembling a large product. In addition to these approaches, others have been proposed. For example, employing an additional optical element such as a compound parabolic concentrator (CPC) attached to the end of the waveguide; alternatively, waveguides are radially arranged to enhance the concentration of the guided light [4,8,9].
In other cases, planar concentrators with medium and low concentrations were adopted in daylighting; these are occasionally called planar sunlight collectors. Because of its compact size and light weight, the planar collector can be directly integrated into the canopy or window to guide the sunlight into the area to be illuminated [10–12]. Some planar sunlight collectors have been installed on the roofs of buildings to collect and concentrate sunlight; the concentrated light has been guided into the buildings for illumination [13–15]. Sunlight collectors have also been combined with artificial light sources to form hybrid lighting systems [14,16]. In addition, the planar collector and PV cells can be integrated into windows for both daylighting and electricity generation . Concentrator systems with lower concentration levels typically alleviate the tolerance on the tracking system. For a lower concentration ratio, a planar concentrator combining single-axis tracking with a microlens array capable of small lateral transitions can increase the tracking tolerance by up to 10°; if the single-axis tracker is combined with cylindrical lenses, even the planar concentrator does not require tracking during the day [18–20]. Another proposed approach combined small lateral translations and adequately designed lenses of lower off-axis aberrations to accomplish dual-axis tracking without requiring a tracker . Luminescent solar concentrators (LSCs) with a planar waveguide doped with phosphors also do not require a tracker [22,23]. However, LSCs exhibit a considerably low optical efficiency. In addition to these approaches, other specific concepts featuring free of a tracker have been proposed, which are currently, however, problematic for commercial use [24,25].
According to this review, planar concentrators with a high concentration level need sophisticated dual-axis tracing systems and must reduce the decoupling effect of coupling microstructures on the waveguide as low as possible. Although planar concentrators with low to medium concentration levels reduce the dependence on sophisticated tracing systems, they have the disadvantage of low efficiency. Tracker-free systems are either too inefficient or not conducive for commercialization. Therefore, this paper proposes a novel planar-concentrator design that not only displays a favorable optical efficiency at a high concentration ratio but also reduces the dependence on sophisticated tracing systems. The proposed planar concentrator features a newly designed waveguide concentrator and an innovative tracking method; the waveguide concentrator, using a waveguide slab to carry the TIR collectors without requiring alignment, can be relatively easily manufactured, especially for a large product; the innovative tracking method combines a single-axis tracker and scrollable microstructure sheets as a replacement for the sophisticated dual-axis tracker.
2. Design concept and model principles
To improve the optical efficiency of the planar concentrator at a high concentration ratio, the coupling microstructures must be minimized. Consequently, such a design must depend on a sophisticated dual-axis tracker to precisely trace the sun, and therefore, raises costs. Moreover, the tolerance of the alignment between the lens array and the coupling microstructure array must become critical. Therefore, this paper proposes a novel planar solar concentrator that provides good efficiency at a high concentration ratio, and requires a relatively simple tracker with a reasonable tolerance. Moreover, the planar concentrator uses TIR collectors that do not necessitate aligning with the coupling microstructures. The proposed planar solar concentrator comprises two subsystems: a waveguide concentrator and a compound tracker. The waveguide concentrator consists of an array of TIR collectors, coupling inlets, and a slab waveguide; and the compound tracker includes a single-axis tracker and scrollable microstructure sheets. These components are detailed in the following.
2.1 TIR collector
Different from the common refractive collector composed of lenses, the TIR collector reflects the incident light to converge at the coupling inlet through the TIR. The advantages of the TIR collector include being alignment-free and exhibiting less Fresnel loss. To reflect the normal incident sunlight and cause it to converge at a focal point, the TIR collector has a parabolic TIR surface. For simplicity, consider a parabola with its minimum passing the coordinate origin, which is expressed as
Thus, the focal point is at . If the sunlight enters along the z-axis, it is reflected to converge onto the focal point. Because the reflected sunlight is meant to enter the waveguide slab below, only the portion of the parabolic surface above the focal plane is reserved. Because the incident angle at the intersection of the parabolic and focal plane is 45 o, the TIR collector must be composed of a material with a refractive index above 1.42, so that the incident light can be reflected through the TIR. The reserved portion of the parabolic surface is calculated as follows and shown in Fig. 1::
Because the portion of the parabolic surface below the focal plane is removed and replaced with a flat bottom, the light incident on the flat bottom is directly transmitted through the waveguide slab, and cannot propagate in the waveguide slab; consequently, the optical efficiency decreases. Moreover, the symmetric parabolic surface causes the reflected light entering the waveguide slab to propagate toward its opposite ends as shown in Fig. 2(a), thereby reducing the concentration ratio by 50%. Therefore, only the right half of the remaining parabolic surface is retained and further modified, as shown in Figs. 2(b) and 2(c). Figure 2(c) shows that the modified TIR collector has two surfaces composed of the portion of the same paraboloid, exhibiting a constant displacement between each other along the z-axis; the inner surface is called the first paraboloid; the outer surface is called the second paraboloid. When the TIR collectors are placed near each other, the flat bottom of the posterior TIR collector is shielded by the second paraboloid of the anterior TIR collector; consequently, the light leakage from the flat bottom decreases. The shield ratio is defined as the shield area of the flat bottom over the area of the flat bottom. A higher shield ratio lessens the occurrence of light leakage in the flat bottom. However, the modified TIR collector shown in Fig. 2(c) has a thicker central portion than its both outer margins (i.e., the space of the central portion between the first and second paraboloids is larger than that of both outer margins). Consequently, the light incident on both outer margins is reflected by the second paraboloid and then easily blocked by the first paraboloid. Furthermore, although the light incident on both outer margins is reflected into the waveguide slab, some of them leaks out from both sides of the waveguide slab without propagating to the end of it, as shown in Fig. 2(d). Therefore, both outer portions of the TIR collector are trimmed off, as shown in Fig. 2(e), to ensure that all reflected light enters the waveguide slab and propagates to its end.
Because the top surface of the final modified TIR collector in Fig. 2(e) is quadrilateral, with two pairs of substantial parallel sides, the shield ratio can be approximated asFig. 2(c). The projected length c depends on the height of the TIR collector h, and the relationship is derived from (1) and (3):
To ensure that the coupled light (i.e., the light reflected by the TIR collector) continues to propagate in the waveguide slab through the TIR, the angle at which the reflected light is incident on the waveguide slab must be larger than the critical angle. As expressed in Eq. (2), the light reflected by the higher portion of the paraboloid is incident on the waveguide slab at a smaller angle, and therefore, the height of the TIR collector must be limited. If the material of the waveguide slab has a refractive index n, the tangential slope at the top of the second paraboloid can be expressed as
If the gap between the TIR collectors is neglected, the pitch of the array of the TIR collectors is approximately ; consequently, Eq. (4) can be expressed as
From the equations, the dimensions of the TIR collector can be determined accordingly. First, the material of the TIR collector is selected and the refractive index determined. Second, an appropriate maximal height hmax of the TIR collector is identified before determining the parabola coefficient from Eqs. (6) and (7). Third, the height of the TIR collector h is determined from Eq. (8) according to a predetermined shield ratio. The height of the TIR collector h must be less than the maximal height.
2.2 Coupling inlet
A coupling inlet is the junction of each TIR collector and the waveguide slab, through which the light focused by the TIR collector enters the waveguide slab below. Because the field angle of the sun itself is 0.52°, the sunlight is focused onto a spot, rather than on a point; therefore, the coupling inlet must have a sufficiently large area for the focused light to pass through. In addition, the TIR collector focuses the light within a larger spot area if tracking tolerance is considered. Thus, a coupling inlet with a larger area contributes to an increased coupling efficiency. However, a coupling inlet with a larger area also raises the probability of the light propagating in the waveguide slab to be emitted from the coupling inlet, thereby reducing the propagation efficiency. Because the total optical efficiency depends on the product of the coupling efficiency and the propagation efficiency, securing a balance between the two is critical. The resulting shape and size of the area of the coupling inlet depend on the dimensions of the TIR collector and the level of tracking tolerance; to optimize both, implementation of the simulation analysis is required, which is detailed in Section 3.1. The initial coupling inlet is design as shown in Fig. 3.To insulate the TIR collector from the waveguide slab excluding the junction, the flat bottom of the TIR collector is replaced with a conic surface that is centered at the focus point of the second paraboloid (i.e. the origin of the coordinates in Fig. 3) and at an 2° angle to the horizontal plane (x-y plane). The coupling inlet is placed at the focus, and the cross-section of the junction is quadrilateral, except for the portion of the coupling inlet protruding out of the first paraboloid, which is shaped as a taper to avoid interference with other TIR collector closely placed in front of it. Compared with typical coupling microstructures (i.e., prisms or folded mirrors) used in the collectors composed of a microlens array, the proposed coupling-inlet design has the following advantages: First, the coupling inlet has a flat bottom and does not sink into the waveguide slab; and thus, the probability of interaction between the propagating light and the coupling inlet decreases, thereby increasing the propagation efficiency. Second, the angular distribution of the light guided into the waveguide slab by the coupling inlet is closer to the horizontal plane than that of the light guided by the coupling prisms, causing the guided light to propagate further.
2.3 Waveguide slab
The waveguide slab is composed of an appropriate transparent material such as PMMA (Poly methyl methacrylate), PC (Polycarbonate), and glass; and is connected to the TIR collector via the coupling inlet. The function of the waveguide slab is to facilitate the propagation of light from the coupling inlet to the end of the slab through the TIR to enable the light to become concentrated. The geometric concentration is expressed asFig. 4, causing the light to converge in a smaller area.
2.4 Compound tracker
Because the TIR collector requires that the sunlight irradiate along the y-axis (referring to Fig. 2) to reflect the sunlight onto a miniscule spot, a tracker is essential. The proposed tracker is a compound tracker composed of a mechanical single-axis tracker and scrollable microstructure sheets, and thus, achieves the tracking function of a dual-axis tracker. The tracking mechanism is illustrated in Fig. 5.A single-axis tracker is employed to rotate both the waveguide concentrator and the scrollable microstructure sheets around the x-axis to trace the sun’s locus from east to west; this enables the sun to be situated exactly on the x’-y’ plane of the local coordinates on the waveguide concentrator, as shown in Fig. 5(a). Because of the angle between the equatorial and the ecliptic plane, the sun still exhibits an angle γ to the y-axis after the single-axis tracker rotates the waveguide concentrator. Therefore, the microstructure sheet with prisms is employed to deflect the sunlight to enter the TIR collector along the y’-axis (the normal of the waveguide concentrator), as shown in Fig. 5(b).
Because the TIR collector is sensitive to the direction of the incident light, the angle of the prism must be precisely determined based on angle γ. However, because angle γ varies over time, the annual variation of angle γ must be predicted to determine the corresponding angles of the prism, and then separately fabricate every prism sheet for each corresponding angle. All the prism sheets are integrated on a continuous substrate to enable scrolling. The roll of prism sheets is supported by a pair of rollers atop the waveguide concentrator; thus, the appropriate prism sheets are moved to the top of the waveguide concentrator for different angles of γ by rotating the rollers, so that the sunlight can be deflected to enter the TIR collector along its normal. In principle, the sunlight can be deflected according to the intended direction by using an appropriate prism sheet, but whether this is a feasible solution remains unclear. If angle γ has a large varying range, the number of required prism sheets is so high that the roll consequently becomes too voluminous; hence, this idea is impractical. Therefore, the varying range of the angle γ for every day of the year must first be calculated.
As shown in Fig. 6, the sun in the sky is positioned by r、azimuth angle Az, elevation angle Ae . The position of the sun in the Cartesian coordinate system can be determined using the following coordinate-system transformation:
Considering the variation of the locus of the sun over the course of the four seasons, the entire apparatus, the tracker included, is mounted on a platform with a tilt angle of to the horizontal (ground), enabling the sun to irradiate on the normal of the waveguide concentrator at noon on the spring and autumnal equinoxes, as shown in Fig. 7(a).Thus, the position of the sun can be expressed in the local coordinate system of the platform as follows:
As the sun moves from east to west in the sky, the single-axis tracker prompts both the waveguide concentrator and the rollers of the scrollable prism sheets to rotate around the x’-axis. If they are rotated by angle , as shown in Fig. 7(b), the position of the sun can be expressed in the local coordinate system of the waveguide concentrator as follows:
To ensure that the sun irradiates exactly on the plane, angle , as modified by the single-axis tracker, can be expressed as
After the waveguide concentrator and rollers are rotated by the degree of angle , the sun irradiates exactly on the plane, and the sunlight is incident on the TIR collector at an angle with the (the normal of the TIR collectors):Fig. 7(c).
Data from Taiwan’s Central Weather Bureau were obtained to identify the positions (r, Az, Ae) of the sun in the sky related to Taipei through 2014; consequently, angle any given day in 2014 can be calculated using Eqs. (10)-(19), as shown in Fig. 8.The horizontal axis in Fig. 8 represents the date for the interval scale in months; Figs. 8(a) and 8(b) show the inclined angle of the platform at angles of 0 o and 25 o to the ground, respectively. Figure 8 indicates that the maximal varying range of angle within one day decreases from 16 o to 0.13 o; the average daily varying range measured only 0.26 o, and equivalently, the average weekly varying range measured 1.8°. If the designed tolerance of the TIR collectors is (considering the subtended angle of the sun), the prism sheet must be changed on average every four days. For angle varying from −23.5 o to 23.5 o within one year, 47 prism sheets satisfy the requirement for one year if the prism sheet is designed according to a 1° interval of the annual angle ; thus, the roll of prism sheets does not occupy too much space. If a more accurate control is required for reducing the tolerance to , 94 prism sheets satisfy the requirement for one year. In this case, the prism sheet must be changed on average every two days, and the machine loading is not too heavy. In addition, angle gradually begins decreasing from 23.5 o on the winter solstice to −23.5 o on the summer solstice; it then gradually increases to 23.5 o when approaching the next winter solstice. Therefore, all of the prism sheets are sequentially arranged on a continuous substrate, according to the order of the variation of the angle (i.e., the cycle of applying a roll of prism sheets begins on the winter solstice and ends with the summer solstice). In the beginning, the rollers rotate counterclockwise to feed the prism sheets from one roller to the other; after the summer solstice, the rollers rotate clockwise to return the prism sheets to the original roller, as shown in Fig. 9. Therefore, the rollers do not rotate back and forth frequently, thus reducing the probability of mechanical failure.
3. Simulation results and discussion
In the optical model of this study, the TIR collector has a pitch of 10 mm, a height of 15 mm, and a width of 15 mm; the waveguide slab has a thickness of 2 mm, a width of 300 mm, and a length of 6 m; the TIR collector and slab are composed of PMMA. The spectral range of the incident light was selected within the visible spectrum (400–700 nm) in AM1.5 solar spectrum. The ray-tracing software LightTools 8.0 was used to implemented simulations. The simulations on the design of the coupling inlet, the efficiency of the waveguide concentrator, and the effects of the prism sheet on deflecting sunlight are detailed in the following.
3.1 Design of the coupling inlet
To maximize the amount of light coupled into the waveguide slab, the coupling inlet must be enlarged, although a larger coupling inlet results in more decoupling loss. However, because the system requires a reasonable tolerance for feasibility, an appropriate area for the coupling inlet is essential. The tolerance was set to for the rotation angle of the x-axis and the z-axis (i.e., respectively). The related simulation results regarding the illumination on the coupling inlet are shown in Fig. 10(a).The optimal area of the coupling inlet is determined by superimposing all of the illumination distributions, as shown in Fig. 10(a). The range of is from 0 to 1, and therefore, is asymmetric. The optimal area is a trapezoid with two base widths of 0.9 mm and 0.3 mm, and a height of 1.05 mm, as shown in Fig. 10(b). The results of the simulation for the coupling efficiency of the optimal coupling inlet with the variations of angles are shown in Fig. 10(c). Figure 10(c) Indicates the optimal direction of the light incident on the TIR collectors at and . Although the tolerance for is slightly less than , the tolerance for is ; therefore, the average tolerance is . Moreover, the coupling efficiency is more sensitive to variations of angle ; therefore, a single-axis tracker was used to accurately control angle and use the scrollable prism sheets to compensate for angle .
3.2 Scrollable prism sheets
Afterward, the prism profile according to angle of the incident light was determined. The prism profile is shown in the upper left inset of Fig. 11, and the base angles of the prism corresponding to angle are shown in Fig. 11. The prism is facing downward, and the transmission is almost 100% for all of the base angles, excluding the Fresnel loss.
3.3 Optical efficiency of the waveguide concentrator
Finally, the simulation for the optical efficiency of the waveguide concentrator based on various geometrical concentrations was implemented. In the optical model, the waveguide slab had a thickness of 2 mm, a width of 300 mm, and a length of 6 m, with 12,000 TIR collectors on its surface. The simulation considered the Fresnel loss and angular spread of the sun; and its results are displayed in Fig. 12.The figure indicates the optical efficiencies of the waveguide concentrators as follows. The waveguide concentrators of a 1000-mm length (Cgeo = 500X) reaches 77% at an irradiance concentration of 387, and the one of a 2000-mm length (Cgeo = 1000X) reaches 64.5% at an irradiance concentration of 645. Moreover, if the waveguide concentrator is attached to a rectangular CPC with a concentration factor of 1.5, the waveguide concentrator of a 1000-mm length reaches 75% at an irradiance concentration of 560, and the one of a 2000-mm length reaches 62.2% at an irradiance concentration of 930. Furthermore, if the waveguide concentrator is attached to a rectangular CPC with a higher concentration factor of 2.3, the waveguide concentrator of a 1000-mm length reaches 62% at an irradiance concentration of 688; the one of a 2000-mm length reaches 52% at an irradiance concentration of 1148; and the maximal practical irradiance concentration is beyond 1800. Obviously, the attached CPC can markedly increase the irradiance concentration but slightly reduce the optical efficiency. In addition, although the optical efficiency decreased with an increase in concentration, the drop in optical efficiency gradually declined as the propagation distance increased. This is because the flat-bottom coupling inlet does not spread the angular spectrum of the light propagated in the waveguide slab compared with protrusive coupling microstructures. Consequently, after a certain propagation distance, the propagation light with a larger angular spectrum was decoupled, and the remaining propagation light with a small angular spectrum was not decoupled easily. Therefore, the total irradiance flux output of a waveguide concentrator can be considerably high for a long waveguide concentrator, which is applicable to daylighting and solar-thermal applications.
3.4 TIR collectors collocating with a horizontally staggered waveguide slab
Although the large planar concentrator can output a high total irradiance flux, its optical efficiency is not as high as that of planar concentrators presented in certain studies. Therefore, we tried to adopt a horizontally staggered waveguide slab to improve optical efficiency. In the case, ten TIR collectors were collocated with a horizontally staggered waveguide slab, and an additional 2D CPC with a concentration factor of 4.0 was attached to the end of the waveguide slab, as shown in Fig. 13.The horizontally staggered waveguide slab is appropriately a triangle of 100 mm X 10 mm and has a thickness of 0.5 mm; and its hypotenuse has nine step increases of 1 mm. Moreover, every injection end at the step increases of the slab has an inclined facet at an angle of 12° with the horizontal level to direct the injected light to propagate in the slab within from the horizontal level. The collecting area composed of ten TIR collectors is ; and thereby the geometric concentration was 1200 (including the concentration factor of the CPC). The simulation results indicated that the optical efficiency was greatly improved up to 91.5%. By contrast, for the combination of a 1500-mm long, 2-mm thick rectangular waveguide slab and a CPC with a concentration factor of 1.5, it provided an optical efficiency of 69% at geometric concentration of 1125 (referring to Fig. 12).
3.5 Light absorption of materials depending on light spectrum
Because PV cells made of various materials have different spectral response characteristics, the spectral range of the light to be collected depends on the PV materials. For example, the spectral response of amorphous Si is approximately within the visible spectrum; that of crystalline Si is approximately within the spectrum of 400–1100 nm; and that of GaAs is approximately within the spectrum of 500–900 nm. However, light absorption occurring in a waveguide concentrator depends on both the material of the waveguide slab and the spectrum of the collected light. The absorbed light is converted the heat and induces the thermal effect on the waveguide concentrator, which reduces the lifetime of the concentrator. Therefore, selecting the appropriate material according to the spectrum of the light to be collected is important. Regarding the various spectrum of the light to be collected, we implemented the simulations for the waveguide slab made of PMMA and BK7, respectively, to evaluate the light absorption; and the simulation results are listed in Table 1. Table 1 indicates that the absorption increases with the increased length; consequently optical efficiency decreases. Moreover, PMMA has less absorption and better optical efficiency than BK7 for the visible light, but has a dramatic rise in absorption and drop in optical efficiency for the light with a spectral range of 400–1100 nm. It is mainly because PMMA has high absorption for the near infrared. By contrast, BK7 performs without difference between the two spectra. Higher absorption means more heat is generated. Therefore, if the collected light is visible, a slab made of PMMA is a good choice because it can provide higher optical efficiency and less absorption; less weight is another plus. However, if the collected light is within a spectral range of 400–1100 nm, BK7 performs better than PMMA. Otherwise, a horizontally staggered waveguide slab is another good choice to provide an excellent optical efficiency with a high concentration level in a shorter length. Because shorter staggered waveguide slab can reduce absorption, it can be made of either PMMA or BK7 for collecting the light with a spectral range of 400–1100 nm.
Another thermal concern is to remove the heat generated on the PV cell with a high concentration level. Because the PV cell is linearly arranged on the exit end of the waveguide slab, a passive cooling plate could be easily integrated to the cell. Moreover, the temperature of the linearly arranged PV cell is generally lower than the PV cell in the point focus system. According to the thermal analysis of a similar case with a concentration of 1000 proposed by the literature, the maximum temperature of a linearly arranged PV cell irradiated by a 1000X concentration with a 500W/m2 is 75 °C, which is acceptable for the PV cell. More details can refer to Ref .
3.6 Manufactural impacts and concerns
The geometric structures of the planar concentrator are relative simple, so the ray-tracing software can accurately simulate the optical behavior of the planar concentrator. The difference between the simulation and experimental results is mainly because of manufacture tolerance and material absorption. For example, small coupling microstructures are likely to exhibit fillets to induce stray light, and thereby the optical efficiency drops. In Ref , the practical optical efficiency was only 32.4% for 37.5X as compared with the simulation value 91%. By contrast, our design involving a flat-bottom coupling inlet does not have fillets sunk in the waveguide slab to result in an optical efficiency drop. Moreover, the alignment-free TIR collector is advantageous for manufacturing. Therefore, the practical efficiency of the proposed planar concentrator would be expected closer to the ideal value. In addition, the proposed planar concentrator has the following limitations: First, efficiently assembling the TIR collectors and securing them on the waveguide slab is complicated, especially for ensuring that only the coupling inlet adheres to the slab. Perhaps a UV-curing adhesive is an effective solution. Second, the planar concentrator requires transparent housing to protect the prism sheets from wind and dust. Third, an infrared shielding is needed to keep infrared from being converted to heat in the waveguide slab, especially for a large planar concentrator.
The proposed planar solar concentrator features an alignment-free TIR collector and an innovative compound tracker. The compound tracker, comprising a mechanical single-axis tracker and scrollable prism sheets, can achieve a performance on a par with dual-axis tracking. Using a mechanical single-axis tracker can reduce the cost of the tracking system and increase its robustness. The alignment-free TIR collector has various advantages. First, the TIR collector does not require an alignment with the coupling microstructure, which is advantageous for manufacturing, and markedly increases the feasibility for use in large concentrators. Second, the TIR collector has a substantially smaller f-number (1.25) than the typical microlens used in other planar concentrators; therefore, based on the same area of receiving light, it is thinner. Third, the size of the proposed planar concentrator is flexible. The size of the waveguide slab is determined by the requirements, and its surface is fitted with identical TIR collectors regardless of the size. Moreover, Size variations in the waveguide slab do not affect the optical efficiency on condition that the geometric concentration (i.e. length/thickness) is unchanged. Furthermore, the size flexibility means that the concentration can be adjusted according to the requirements, and such flexibility is crucial for practical applications. By contrast, some planar concentrators with a high optical efficiency function only at an optimal length in the tens or hundreds of millimeters, and hence, their total irradiance flux output is limited. Finally, the alignment-free TIR collector is compatible with other techniques involving stagger waveguides and dimple microstructures. We adopt a horizontally staggered waveguide slab to improve the optical efficiency up to 91.5% with a geometric concentration of 1200.
This study proposed a planar solar concentrator consisted of an innovative compound tracker and a waveguide slab carrying alignment-free TIR collectors. The compound tracker, combining a mechanical single-axis tracker and scrollable prism sheets, can achieve a performance on a par with dual-axis tracking. Using a mechanical single-axis tracker can reduce the cost of the tracking system and increase its robustness. With the designed tolerance of the TIR collectors by (considering the subtended angle of the sun), the prism sheet must be changed on average every four days, and thereby 47 prism sheets satisfy the requirement for one year if the prism sheet is designed according to a 1° interval of the annual variation of angle ; with the tolerance by , 94 prism sheets satisfy the requirement for one year, and the prism sheet must be changed on average every two days. The alignment-free TIR collectors are assembled on the waveguide without requiring alignment, so the planar concentrator is relatively easily manufactured, especially for a large product. Moreover, the identical TIR collector is applicable to various-sized waveguide slab, thereby providing flexibility regarding the size of the waveguide slab. In the simulation model, the thickness of the slab was 2 mm, and its maximal length reached 6 m. With an average angular tolerance of, and after considering both the Fresnel loss and the angular spread of the sun, the simulation indicates the optical efficiencies of the waveguide concentrators as follows. The waveguide concentrator of a 1000-mm length (Cgeo = 500X) reaches 77% at an irradiance concentration of 387, and the one of a 2000-mm length (Cgeo = 1000X) reaches 64.5% at an irradiance concentration of 645. Moreover, if the waveguide concentrator is attached to a rectangular CPC with a concentration factor of 1.5, the waveguide concentrator of a 1000-mm length reaches 75% at an irradiance concentration of 560, and the one of a 2000-mm length reaches 62.2% at an irradiance concentration of 930. Furthermore, if the waveguide concentrator is attached to a rectangular CPC with a higher concentration factor of 2.3, the waveguide concentrator of a 1000-mm length reaches 62% at an irradiance concentration of 688; the one of a 2000-mm length reaches 52% at an irradiance concentration of 1148; and the maximal practical irradiance concentration is beyond 1800. Finally, if a 100-mm horizontally staggered waveguide slab and a CPC with a concentration factor of 4 are adopted, the optical efficiency would be greatly improved up to 91.5% at an irradiance concentration of 1098 (Cgeo = 1200X).
This study was sponsored by Ministry of Science and technology of Taiwan under Grant No. NSC 102-2221-E-008-028 and MOST 103-2221-E-003 006 -MY2.
References and links
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