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Abstract
Ultra-High Concentrator Photovoltaic (UHCPV) designs with up to more than 6000× geometrical concentration and optical efficiency of 80% are demonstrated in this paper by means of ray tracing simulations. These are developed based on Cassegrain-Koehler concentrators [Opt. Lett. 41(9), 1985 (2016)], with four pairs of paraboloid-hyperboloid mirrors and a central receiver composed of four Cartesian ovals of revolution. Designs at different geometrical concentrations are analyzed based on their aspect ratios (F-number). The most compact designs exhibit highest optical efficiencies. Moreover, a 3015× geometrical concentration one-cell prototype, made of aluminum and PMMA (poly(methyl methacrylate)), is fabricated and characterized indoors, achieving an effective concentration of 938 suns. This represents the CPV module with the highest geometrical concentration that has been experimentally investigated that could be found in the scientific literature.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High Concentrator Photovoltaic (HCPV) modules are known to achieve the highest efficiency (43.4%) among all existing photovoltaic (PV) technologies [1]. They utilize small solar cells and concentrator optical systems to achieve effective concentrations, Ceff (also known as the average irradiance, which is the product of the optical efficiency with the geometrical concentration), which is greater than that of 300 suns [2]. To be competitive, the development of so-called ultra-high CPV systems with Ceff exceeding that of 1000 suns could prove to be a promising strategy due to the significant reduction in the amount of semiconductor materials that can be achieved [3]. Moreover, this motivates the use of novel ultra-efficient, albeit more expensive, concentrator cells [4,5].
Few existing works have developed optical designs that achieve ultra-high (UH) concentrations [6]. Karp et al. designed a compact micro-optic waveguide to concentrate sunlight up to the intensity of around 2500 suns, assuming the optical efficiency, ηopt, to be greater than 80% [7]. Ghosal et al. announced a commercial module working at a concentration of around 950 suns [8]. Zamora et al. achieved the same results and presented experimental measurements of a Fresnel-Koehler concentrator working at the concentration of around 900 suns with ηopt≈ 80% [9]. Coughenour et al. also presented experimental measurements of a concentrator with the concentration of ∼1000 suns, with an approximate ηopt of 80% [10]. More recently, Shanks et al. demonstrated the possibility of achieving concentrations within the range of 3000-4300 suns with ηopt≈ 55%-75% [6]. The last result is promising, but future studies are still needed to achieve ultra-high levels with a better ηopt.
This study explores geometrical concentrations within 3000×-6000× by using a one-cell design previously developed by the authors based on multiple off-axis Cassegrain units to achieve the concentration of almost 1700 suns with ηopt = 73% ‒assuming that standard optical materials are used. This design, which can be called Cassegrain-Koehler as it utilizes the principle of Koehler illumination [11], is analyzed in depth in the present study. The analysis is performed theoretically in terms of the aspect ratio of the primary mirrors. Moreover, a 3015× one-cell prototype is fabricated and characterized in a CPV solar simulator to serve as a proof of concept. This represents the CPV module with the highest experimentally investigated geometrical concentration that could be found in the literature.
2. Cassegrain-Koehler-based UHCPV design
The Cassegrain-Koehler-based UHCPV design utilizes four independent optical units to concentrate sunrays on a central receiver. Primary Optical Element (POE) mirrors are paraboloids, whereas SOE (Secondary Optical Element) mirrors are hyperboloid, as depicted in Fig. 1. For each optical unit, the POE focus and the SOE near focus correspond to each other (point “F” in Fig. 1). The SOE far focus (point “G”) is located inside the correspondent Cartesian oval of revolution of the Tertiary Optical Element (TOE). The TOE is composed of four Cartesian ovals of revolution, whose length is maintained at 20 mm. This design principle can be scaled to different geometrical concentration ratios, Cg, and aspect ratios of the POE mirrors, by changing the size and focal distance of the POE mirrors, fPOE.
3. Theoretical analysis
3.1 Parametric analysis
The optical design of the Cassegrain-Koehler-based UHCPV one-cell concentrator is analyzed for different geometrical configurations while keeping the optical parameters related to the light and their interactions with the optical elements involved constant. For this purpose, optical modeling is applied in the ray tracing simulations, based on the theory described in [13] and experimentally validated in [14], in which a series of optical wavelength-dependent properties are taken into account. State-of-the-art optics are considered in this section to explore the performance limits of the proposed design. Sunrays are considered to have solar angular distribution and the standard reference terrestrial spectrum normalized to 1000 W/m2. Both dielectric elements, i.e., cover and TOE, are simulated to have antireflective coatings (ARs) of 98% transmittance. The cover is considered to be constructed from fused silica, whereas the TOE is considered to be constructed from glass Schott N-BK7. Light absorption (Beer-Lambert law) is accounted for within the TOE using a wavelength-dependent absorption coefficient. Reflectors POE and SOE are considered as the first surface mirrors accounting for 98% of the total reflectance, including reflection scattering. The ABg scatter model, which is a modified inverse-power-law-model, is used to model the roughness of the isotropic surface [15], with the following values: integrated bidirectional reflectance distribution function, BRDF = 0.01324%, and bidirectional transmission distribution function, BTDF = 0.01450%. No wavelength dependency is applied to the reflectors at this point. Finally, the solar cell is considered to be an ideal absorber.
In total, five different Cg in the range of UHCPV are considered: 2001×, 3015×, 4003×, 5028×, and 6057×. For each Cg, the F-numberPOE is varied to analyze the impact of the aspect ratio of the design on its optical performance. To standardize the analysis, every design considered was chosen to correspond to one of the following values of F-numberPOE: 0.52, 0.63, 0.75, 0.86, 0.98, or 1.09. Note that F-numberPOE is defined to be the ratio of fPOE and the length of the diagonal of the POE mirror.
However, the SOE mirrors do not impose the aforementioned constrains on Cg and F-numberPOE, and therefore, the f1-SOE value needs to be adjusted to focalize the concentrated rays on the solar cell. Then, for each Cg and F-numberPOE, a value is obtained for F-number1-SOE with the restriction of maintaining the acceptance angle (AA) at a value greater than ± 0.30°. Note that F-number1-SOE is defined to be the ratio of f1-SOE over the length of the shortest diagonal of the convex kite-like SOE. AA denotes the angle at which ηopt decreases by 10% with respect to its value under normal incidence and should be greater than ± 0.30°, which is sufficient for a typical solar tracker [6]. The F-number1-SOE values obtained for each Cg are observed to be constant, with a global deviation of only 4%. In ascending order of Cg, the observed F-number1-SOE values are 3.57, 3.43, 2.79, 2.74, and 2.49, respectively. These required F-number1-SOE values decrease with Cg as the distance between the solar cell and the SOE mirrors increases with Cg. Designs whose F-number1-SOE values for each Cg are remote from those listed, will lead to poor results for either ηopt or AA. The geometrical parameters have been summarized in Table 1.
Table 1. Geometrical parameters, optical efficiency and acceptance angle values.
3.2. Simulation results and discussion
The optical simulation results have been presented in Table 1 and summarized in Fig. 2, in which ηopt has been plotted versus F-numberPOE, for each Cg.
Fig. 2. ηopt of the investigated designs as a function of the F-numberPOE and depending on Cg. The shadowed area represents the rejected designs, i.e., those with ηopt < 78% or AA < ±0.30°.
For each value of F-numberPOE, only designs with relatively good performance are considered, i.e., AA > ±0.30° and ηopt > 78%. Note that certain cases under study do not satisfy both criteria, e.g., Cg = 6057× and F-numberPOE lower than 0.75. These designs, which do not correspond to the aforementioned criteria, approximately correspond to the shadowed area depicted in Fig. 2.
ηopt ranges from a minimum of 78.7% (Cg = 6057×, F-numberPOE = 0.98) to a maximum of 83.7% (Cg = 2001×, F-numberPOE = 0.52), and decreases, in general, with F-numberPOE values, independent of Cg. The decreasing trend in ηopt with respect to F-numberPOE holds, in general, for all the analyzed Cg. Therefore, the most compact designs (ones with the lowest aspect ratio) perform the best at concentrating sunrays on the solar cell. This is due to two primary reasons: the lower apparent size of the solar cell as observed by the SOE mirrors, and the longer optical path of the concentrated rays−especially those between the SOE mirrors and the TOE. Both effects tend to reduce the probability of a concentrated ray reaching the solar cell.
Corresponding to a specific value of F-numberPOE, ηopt is inversely proportional to Cg. For instance, corresponding to F-numberPOE = 0.86 and ascending order of Cg, the corresponding ηopt values are 82.5%, 82.3%, 81.8%, 80.6%, and 79.9%. As Cg increases, the dimensions of POE and SOE mirrors also increase relative to the solar cell (with fixed area). This causes wider ray beams to impinge on the TOE and the solar cell, and therefore, increases the difficulty of concentrating the sunrays onto the solar cell.
Designs with a fixed F-numberPOE increase in height, h, as Cg is increased. For example, in the case of F-numberPOE = 0.86, the h values are 132 mm, 158 mm, 178 mm, 194 mm, and 210 mm, respectively. Note that the change in h ranges from 86 mm (Cg = 2001× and F-numberPOE = 0.52) to 227 mm (Cg = 6057× and F-numberPOE = 0.98).
The lowest value of the acceptance angle proposed in the designs is ± 0.30° (especially in cases with higher Cg), whereas the designs with lowest Cg exhibit the greatest AA values. This is the case of designs with Cg = 2001× and F-numberPOE = 0.63, with AA = ±0.44°.
4. 3015× One-cell prototype
4.1. Design and fabrication
The design that has been selected to be fabricated in this study has a geometrical concentration of 3015×, with the total length of the POE mirror plates being 151 mm and a height of around 125 mm. It is designed to have the following focal distances: fPOE = 135.04 mm, f1-SOE = 131 mm, and f2-SOE = 25 mm. The corresponding F-numbers are F-numberPOE = 0.63 and F-number1-SOE = 2.72. Note that these values of F-number1-SOE are lower than those obtained from theoretical analysis in subsection 3.2, where it was estimated to be 3.43. The reason for this variation is that, with a lower F-number1-SOE, the AA of the design selected for fabrication is expected to be higher than that of the design considered in Table 1. Thus, this value increases the probability of obtaining a prototype suitable for a real sun tracker. However, the low value may result in a reduction in the expected optical ηopt.
The mechanical design of the UHCPV one-cell prototype follows the poka-yoke methodology: every part fits in only one specified orientation. For instance, the SOE mirrors are inserted on the PMMA (poly(methyl methacrylate)) cover and no further orientation adjustment is allowed after the screws are tightened. The PMMA cover (of 6 mm depth) affixes the SOE mirrors in the correct position and orientation. Moreover, the TOE is modified to have a truncated inverted pyramidal base that corresponds to the solar cell surface. Figure 3 depicts a transverse cut along a diagonal of the 3D model of the selected design (left), and (right) a detailed view of the TOE along with the solar cell receiver.
Fig. 3. (Left) Transverse diagonal cut of the 3D design of the UHCPV one-cell prototype. (Right) Detail of the TOE along with the solar cell receiver.
The UHCPV one-cell prototype is fabricated using PMMA and aluminum, which are standard and relatively inexpensive materials. Polishing is the only optical surface treatment applied. The triple-junction, 3J, AZUR SPACE solar cell is a square of 5.5 mm length, with spectral response, SRsubcell(λ), as given in Fig. 7. Figure 4 presents a photograph of the UHCPV one-cell prototype (left) and details of an SOE mirror (top right) and the TOE (bottom right). The polished surface of the SOE can be also seen.
Fig. 4. (Left) Photograph of the UHCPV one-cell prototype. (Top right) detail of an SOE mirror along with the polished surface. (Bottom right) Detail of the TOE.
4.2 Experimental setup
Indoor characterization is performed using the CPV Solar Simulator Helios 3198. This multi-flash solar simulator produces an angular distribution of rays of ± 0.3°, similar to real sunrays. The spectral distribution of the flash light is that of a Xenon discharge lamp and, from the point of view of the typical 3J solar cell, is equivalent to that of the sunrays. This CPV solar simulator is of class AAA and is a characterization tool widely used in CPV [16,17]. The I-V characteristics are obtained under conditions equivalent to concentrator standard test conditions (CSTC), i.e., DNI (Direct Normal Irradiance) = 1000 W/m2, spectrum SMR(top/mid) = 1 ± 0.01, and ambient temperature = 25 °C. The spectrum is monitored using a Tri-Band spectro-heliometer from Solar Added Value using the Spectral Matching Ratio (SMR) between the top and the middle subcells—known as the SMR(top/mid) metric [18]. SMR(top/mid) evaluates the spectral balance of the incoming light with respect to the top and middle isotype-component cells. The UHCPV one-cell prototype is mounted on the support structure of the solar simulator (Fig. 4-left). In addition, the uniformity profiles on the solar cell surface are obtained using the set-up introduced in [19]. This consists of a Lambertian diffuser and a CCD camera, as well as various non-neutral filters to correspond to the SR(λ) of the camera and that of each subcell.
4.3 Experimental results
The electrical characterization of the UHCPV one-cell prototype at CSTC yielded the following electrical values: (short-circuit current) Isc = 4.342 A, (voltage at open circuit) Voc = 3.20 V, (maximum power) Pmp = 10.50 W, (fill factor) FF = 75.7% and efficiency = 11.5%. This characterization corresponds to an effective concentration, Ceff = Cg· ηopt, of 938 suns, i.e., the Isc measured is 938 times higher than its calibrated Isc value (4.63 × 10−3 A) under the illumination of 1 sun. Such a value of Ceff implies an ηopt of 31%.
This ηopt value is lower than expected and can be attributed to several factors: i) greater light scattering on the optical surfaces than expected, ii) light spillage from the solar cell surface due to deficient optical coupling between the TOE and the solar cell, and iii) an excessive top-subcell current limitation, as depicted in Fig. 5-left, where the subcell's current limitation diagram has been presented [18]. The ratio of the normalized current of the UHCPV one-cell prototype and the effective irradiance measured by the top subcell remains constant up to around SMR(top/mid) = 1.12. Therefore, the top subcell limits the current up to the blue-rich spectral condition of the incoming irradiance. This may be attributed to greater absorption of irradiance in the top subcell range than expected. This point will be further discussed below. The current limitation effect in the top-subcell was not observed in Fresnel refractive (PMMA) concentrators that had been previously investigated [13]. Future research can analyze the source of those losses to improve the UHCPV one-cell prototype.
Fig. 5. (Left) Subcell current limitation diagram. (Right) Simulated and experimental acceptance angle curves.
With regard to the measured angular tolerance (consult Fig. 5-right, black points), the experimental acceptance angle is around ± 0.30°.
With regard to the uniformity of the generated Jsc,subcell, Fig. 6 demonstrates both the simulated Jsc,subcell plots obtained via ray tracing of the top (left) and middle (right) subcells. The associated experimental measurement has been explained in section 4.2. The measured results demonstrate relatively good uniformity, i.e., a peak-to-average (PAR) ratio of 2.2 for the top subcell and that of 2.3 for the middle subcell.
Fig. 6. Simulated short-circuit current density plots of the top and middle subcells, as well as acquired pictures (CCD camera) of concentrated light for the spectral ranges of the top and middle subcells.
4.4 Comparison of experimental results with those obtained via optical modeling
The properties of the elements described in sub-section 4.1 (fabricated materials instead of state-of-the-art materials) are included in the ray-tracing optical modeling, to compare its results with the experimental results and achieve a better understanding of the UHCPV one-cell prototype. For transparent elements, refractive index and absorption coefficient of PMMA, αP, are included in the ray tracing simulations. The mirrors are modeled using the wavelength-dependent reflectance measured in our institution, using a Cary 4000UV-Vis spectrophotometer, from a polished planar plate sample made of aluminum. This reflectance is relatively low: 86% at 550 nm. These optical properties have been summarized in Fig. 7. The ABg scatter model is also applied, as discussed in Section 3 (theoretical analysis).The 3J solar cell is modeled using the SRsubcell (λ) values (consult Fig. 7).
Fig. 7. Material and surface properties included in the optical simulations: spectral response of each subcell, absorption coefficient of PMMA and reflectance of aluminum.
These new optical simulation results obtained using inexpensive fabricated materials, exhibit an ηopt of 58.1% (3J solar cell is considered), which implies an effective concentration of 1753 suns (≈87% higher than the measured). Note that, in this case, three subcells are considered to calculate ηopt. Thus, in this case, ηopt can be considered as the polychromatic optical efficiency [20], and therefore, its value may be lower than the case in which the solar cell is considered to be an ideal absorber. The simulation results for short-circuit current density values, Jsc,subcell, are 27.4 A/cm2 (top subcell), 28.2 A/cm2 (middle subcell), and 28.7 A/cm2 (bottom subcell). SMR(top/mid) results achieve the value 0.98 (≈10% lower spectral losses than measured), which corresponds to the so called “red-rich” spectral conditions, although it is very close to unity [21]. The lower SMR(top/mid) value obtained from the simulation can be attributed to absorption of short-wavelength light by the aluminum surfaces of POE and SOE. This also confirms the top cell's experimentally measured current limitation, but to a lesser extent. Therefore, it indicates that there could be additional optical losses at shorter wavelengths that could explain the lower performance of the UHCPV one-cell prototype at those intervals. The study of other causes to explain the lower optical efficiency obtained, such as issues like additional light scattering or light spillage as previously mentioned, will be the aim of future works in this field.
The optical modeled acceptance angle was detected to be ± 0.41° (consult Fig. 5-right, red points). This is ≈0.1° higher than the measured result (an increase of ≈37%). The sharper drop in the AA values compared to the measurements may be attributed to the effect of imperfections that may be present in the fabricated elements on the optical surfaces. These may provoke the rays to be scattered to a greater extent than in the simulations. The measured patterns presented in Fig. 6 indicate that the illumination uniformity is similar to the simulated Jsc,subcell results, with PAR values of 4.0 for the top subcell and 4.1 for the middle subcell. The results concerning AA and illumination uniformity confirm that, despite the optical losses encountered, the geometrical design and construction of this UHCPV one-cell prototype is correct in terms of the position and alignment of the optical elements.
5. Conclusions and future work
This study analyzed the design limits of Cassegrain-Koehler ultra-high concentrator photovoltaic modules (UHCPV) [12]. First, a parametric analysis based on the aspect ratio (F-number) of the primary mirrors at different geometrical concentration ratios was carried out. Concentrations of up to almost 5000 suns were theoretically achieved via ray tracing simulations over a 5.5 mm side solar cell using TracePro optomechanical software. Optical efficiencies of up to almost 84% were estimated for designs at 2000× the geometrical concentration ratio, whereas it only decreased to 80% for the design at 6056×. The most compact designs were the most efficient independent of the geometrical concentration ratio. This is an interesting conclusion, as one of the main intentions of the design proposed is to increase the compactness of CPV modules, to reduce the amount of materials, loads supported by the trackers, etc. Moreover, none of the designs analyzed had an acceptance angle lower than ± 0.30°.
To test the theoretical design, a 3015× one-cell prototype was fabricated and characterized in a CPV solar simulator. It utilized inexpensive materials, such as PMMA (polymethyl methacrylate) and aluminum. The UHCPV one-cell prototype achieved up to around 938 suns of effective concentration. This represents the CPV module with the highest experimentally investigated geometrical concentration that could be found in existing literature. It corresponded with an optical efficiency of 31%, which is lower than the optically modeled efficiency (58%). An evinced excessive top-subcell current limitation may be the cause of the lower optical performance obtained, apart from other possible problems, such as light scattering on the surfaces or light spillage on the solar cell. The UHCPV one-cell prototype recorded a worse acceptance angle value (±0.30°) than the simulation one (±0.41°) but was still very close to it. The geometrical design was also validated via the experimental results based on the images of the concentrated light in the light homogenizer element (TOE).
In future works, the identification of the source of the top-subcell current limitation, as well as that of the lower optical efficiency, needs to be carried out. Light scattering on surfaces is to be checked, and the soundness of the optical coupling between the TOE and the solar cell must also be verified. To improve the performance of the UHCPV one-cell prototype, materials with higher optical quality and better surface finishing (better polishing, antireflective coating, highly reflective coatings, etc.) may be needed. Moreover, scaling such designs to micro-concentrators and the feasibility of their fabrications are to be investigated.
Funding
European Regional Development Fund (ENE2016-78251-R); Ministerio de Ciencia, Innovación y Universidades (RYC-2017-21910).
Acknowledgments
The authors thank Lambda Research Co. for its donation of TracePro optical software. The authors also want to thank the CICT-UJA (Centro de Instrumentación Científico-Técnica of the University of Jaén) and the Fundación Andaltec I + D+i.
Disclosures
The authors declare no conflicts of interest.
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