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Abstract
Ultra-high concentrator photovoltaic systems aim to enhance the conversion efficiency of sunlight and to reduce the cost of electricity. However, it is still necessary to develop optical systems with higher efficiencies and angular tolerances for them to become a reality. This Letter proposes a novel design that is able to achieve a geometric concentration of ${4096{\times}}$. The system consists of four concentrator units based on parabolic mirrors and optical guides that concentrate the sunlight onto a single cell. Additionally, a preliminary proof-of-concept module has been assembled for validation purposes. The novel design exceeds the optical efficiency of the existing systems, ${\approx} {{84}}\%$, and offers almost double acceptance angles, ${{\approx} {0.6}}^\circ$.
© 2021 Optical Society of America
Ultra-high concentrator photovoltaics (UHCPV) with intensities ${\gt}{{2000}}\;{\rm{suns}}$ (${{1}}\;{\rm{sun}}\;{ = }\;{{1000}}\;{\rm{W}}\cdot{{\rm{m}}^{- 2}}$) is a promising route to achieve a novel high-efficiency and low-cost PV technology [1]. These extreme concentrations allow the area of the cell to be strongly reduced, which is the most expensive part of system, and the theoretical efficiency of the cell to be increased [2–4]. Despite its potential, UHCPV is still under development, and important efforts are still needed (a) to analyze different architectures of solar cells with efficiencies peaking at ultra-high (UH) concentrations [4–7], (b) to propose a cooling system that is able to remove the extreme heat waste and avoid overheating of the cells [8], and (c) to develop novel concentrator photovoltaics (CPV) optics with a high optical performance and angular tolerance [9–12]. These constraints need to be eliminated to decrease the system cost while improving the efficiency and reliability. This Letter is focused on the presentation of a novel UHCPV optical configuration.
Today, only a few works in the literature report optical systems that are able to achieve UH levels. Karp et al. developed a complex waveguide system with an optical efficiency $({\eta _{\rm{opt}}}) \approx {{80}}\%$ at an effective concentration $({{{C}}_{\rm{eff}}})\;{\rm{of}} \,\approx {{2400}}\;{\rm{suns}}$ [9]. Miñano et al. achieved a ${{{C}}_{\rm{eff}}}$ close to 2000 suns with a ${\eta _{\rm{opt}}}$ of 82.5% and an acceptance angle by means of free form secondary optics [10]. Shanks et al. developed a system with a geometrical concentration (${{{C}}_g}$) of ${5800{\times}}$ that could achieve ${{{C}}_{\rm{eff}}}$ of 3000 and 4400 suns and ${\eta _{\rm{opt}}}$ of 55% and 75%, respectively, depending on the materials used, and a maximum AA of 0.4º [13]. Ferrer et al. presented the state-of-the-art UHCPV optical system that could obtain ${{{C}}_g}$ within ${2000{\times}}- {6000{\times}}$ [11]. This module shows the possibility of reaching a ${{{C}}_{\rm{eff}}} \approx {{5000}}\;{\rm{suns}}$ with a ${\eta _{\rm{opt}}}$ of 80% and an AA of 0.3º.
This Letter offers a novel optical configuration that is able to achieve superior ${\eta _{\rm{opt}}}$ and AA to the state-of-the-art designs. The UHCPV proposed is formed by four symmetric and independent optical units that concentrate the sunlight on a single solar cell. This concept is similar to the previously discussed by Ferrer–Rodriguez et al. [11,14] and by Shanks et al. [13]. However, in this case, a novel optical configuration that uses optical guides to further increase the optical performance is proposed. Each optical unit consists of two optical elements: a square parabolic mirror (primary optical element [POE]) and a curved optical guide (secondary optical element [SOE]). The sunlight is concentrated in two optical steps per optical unit; see Fig. 1 (left). First, the direct incident sunrays reach the parabolic mirror and are reflected towards its focal point. Secondly, the optical guide, with the input surface located at the focal point of the POE mirror, guides the rays toward the cell surface by total internal reflection (TIR). In this configuration, the input area of the optical guide is reduced proportionally with length. With this strategy and the ability to scale the system, the total concentration falling on the solar cell can be increased by adding multiple independent units without drastically increasing the optical losses.
Fig. 1. Left: UHCPV module scheme. (1) The sunlight falls on the surface of the POE mirror; (2) it is reflected towards the focal of the mirror “f,” which corresponds to the input optical guide surface; and (3) the optical guide leads the radiation to the solar cell (4) by reducing its diameter with length. Right: fused silica absorption and spectral response of the MJ solar cell considered.
The total geometric concentration ratio of the system investigated in this Letter, defined as the ratio between the total area of the POEs to the cell area, is ${{{C}}_g} = {{4096{\times}}}$. At this stage, four pairs of POE–SOE units are considered. Each individual parabolic mirror has a size of ${{32}}\;{\rm{mm}} \times {{32}}\;{\rm{mm}}$ with a focal distance of 45.25 mm, and the solar cell has a size of ${{1}}\;{\rm{mm}} \times {{1}}\;{\rm{mm}}$. This solar cell area has been selected to reduce the heat power waste at UH levels and to ensure its operating temperature within the safe limits, i.e., a temperature below 80–100°C [8,15]. As previously mentioned, the optical guide diameter is reduced through its length, i.e., the input and output surfaces are different. In order to find the best design, an optimization process has been carried out. As a first step in the design, the output guide area was fixed at a diameter of 0.45 mm, while the input size was varied. To obtain the optimal input diameter, a range of concentrations between ${500{\times}}$ and ${1400{\times}}$ per concentrator sub-unit (${\rm{POE}} + {\rm{optical}}\;{\rm{guide}}$) was investigated.
The optical simulations were performed using the TracePro ray tracing software and considering the Concentrator Standard Test Conditions (CSTC): ${{1000}}\;{\rm{W/}}{{\rm{m}}^2}$, AM1.5D reference spectrum (${\rm{SMRs}} = {{1}}$), and 25 °C cell temperature. The angular size of the sun (4.7 mrad) is also considered. The optical model used, early introduced by the authors, takes into account the absorption and angular properties of the optical elements and solar cell under consideration. Further details of this optical model and about its experimental validation can be found in the previous work of the authors [16,17]. In this investigation, the mirrors have been simulated as “perfect mirrors” with 98% reflectance and the following features: absorptance = 0.02, specular reflectivity = 0.9786, and integrated bidirectional reflectance distribution function = 0.001324 using the ABg scatter model. The material used for the optical guide was simulated as fused silica, and the cell is a standard triple junction solar cell composed of GaInP/GaInAs/Ge. Fig. 1 (right) shows the spectral response of each subcell, input spectrum, and fused silica absorption attenuation profile.
The optical design presents symmetry around the normal at the solar cell’s center. Each of the four optical units corresponds to a similar squared portion of the module. Therefore, in order to realize the optimization of the optical guide, only a quarter part of the total system is studied. The ${\eta _{\rm{opt}}}$ and AA will be considered as figures of merit for carrying out the optimization process. The results obtained for different input-to-output ratios of the ${\eta _{\rm{opt}}}$ and AA are shown in Fig. 2. This figure shows how both parameters present an inverse relationship. As the ${\eta _{\rm{opt}}}$ decreases with the variation of the ratio, the AA increases. This implies that it is necessary to consider a trade-off between both magnitudes to decide the final optical design, e.g., to achieve a high AA without drastically reducing the ${\eta _{\rm{opt}}}$. Based on this, an input-to-output ratio of 2.84 has been selected, which corresponds to an optical guide input diameter of 1.28 mm. Hence, the ${{{C}}_g}$ of each sub-unit is ${796{\times}}$. This factor dominates the overall optical performance of the module and would allow record acceptance angles at UH concentrations to be achieved.
Fig. 2. Optimization of the geometry of the optical guide for a single concentrator unit (${\rm{POE}} + {\rm{guide}}$): the optical efficiency versus acceptance angle is shown. The input-to-output ratio is related to the geometrical concentration of the optical guide.
After selecting the optical guide geometry, the optical characteristics of the complete system have been obtained. Figure 3 shows a detail of the ray tracing, while Table 1 summarizes the main results. Regarding the ${\eta _{\rm{opt}}}$, a high value of 84.7% has been obtained, which implies a ${{{C}}_{\rm{eff}}}$ of 3468 suns. This is approximately 10% higher than the best optical design presented by Shanks et al., and 2%–5% higher than the designs with similar ${{{C}}_g}$ introduced by Ferrer et al. With regards to the AA, a state-of-the-art value of 0.61º for a module working at such extreme concentrations levels has been obtained. This is ${\approx} {{2}}$ times higher the AA obtained by Ferrer et al. and 1.5 higher than the Shanks et al. design. The high optical performance of the proposed design in terms of ${\eta _{\rm{opt}}}$ and AA compared with the previous UHCPV modules also can be explained through the concentration–acceptance angle product (CAP), which is 0.68. The CAP is an indicator parameter of how close the system is of reaching the ideal maximum concentration. This CAP value is indeed 1.5 times higher than the best commercial CPV modules with ${{{C}}_g}$ within ${500{\times}}- {1300{\times}}$ [18].
Fig. 3. Left: ray tracing of the system. Right: irradiance map of the incident rays on the solar cell (top) and sunlight reflection over the focal of the mirror (bottom).
Table 1. Summary of Geometrical and Simulated Parameters
The proposed optical system also provides good results concerning the spectral irradiance and uniformity over the solar cell surface. As can be seen in Table 1, the spectral-matching ratio (SMR) [19] between the top and middle subcells is ${\approx} {{1}}$. This indicates that the optical system is not significantly modifying the input spectral irradiance. Hence, no optical losses due to current mismatching issues among the subcells of the (MJ) cell are produced. This SMR value is considerably better than standard systems based on (PMMA) Fresnel lenses and SOEs with ${{{C}}_g}\; \approx \;{550{\times}}$, which usually tend to diminish the current of the top subcell, i.e., a SMR (top/mid) ${\approx} \;{0.96}$ [16,17], so the overall ${\eta _{\rm{opt}}}$. Finally, the uniformity of the irradiance falling on the solar cell can be considered adequate for the extreme concentration investigated. Figure 3 (right-top) shows the irradiance distribution map over the solar cell surface. As can be seen, the output of each optical guide produces a non-uniform distribution over the cell, leaving part of it under dark conditions. Despite this, the uniformity, quantified through the peak-to-average ratio (PAR), is relatively low for a simulated value. This is due to the fact that the four optical guides act as diffusers that spread the light over the solar cell. Indeed, PAR values above 10 are usually found for standard CPV optical units based on Fresnel lenses without the use of homogenizers [20], which is also in agreement with the simulations conducted by the authors [16,17]. Further designs will also investigate the use of interface layers to couple the guides and the MJ cells to achieve PAR values ${\approx} {{2}}$ similar to standard POE–SOE configurations.
It is also interesting to analyze the cause of the optical loss (L) that occurs in each $i$-optical step. This is useful towards future designs with a higher optical performance. The different losses can be explained due to the following factors: (1) reflection of the mirrors, (2) attenuation and reflection on the guides, (3) breakage of the TIR, (4) bending of the optical guides, and (5) optical mismatches among the optical units. The values of these losses are shown in Table 2. The losses are obtained as ${L_{i}} = (1 - {\eta _{{\rm opt}\,(i - 1)}}/{\eta _{{\rm opt}\,(i)}})$, while the overall optical $L$ is obtained as ${L_{\rm{global}}} = (1 - {\eta _{\rm{opt}}})$. As can be seen, the decrease of the diameter of the guide is the main cause of the reduction of the final ${\eta _{\rm{opt}}}$, followed by the reflectance and attenuation of the guides.
Table 2. Detailed List of Optical Efficiency and Optical Losses
In addition to the simulations, we have conducted a preliminary experimental investigation of the configuration; see Fig. 4. For doing this, we have considered the same Fresnel lens and MJ solar cell used earlier in [16,17]. In this case, the module is composed of four PMMA Fresnel lenses, each with a 135 mm side, four optical guides with a fixed diameter of 2 mm and a length of 50 cm, and a MJ solar cell with an area of ${5.5} \times {5.5}\;{\rm{mm}}^2$. Hence, the total concentration of the system is ${\approx} {2400{\times}}$. The materials and absorption properties of the optical guides and MJ cell are the same as those shown in Fig. 1, while details of the Fresnel lens could be found in the references above. The Fresnel POEs have been provided by ORAFOL Fresnel Optics GmbH, the optical guides by Fiberguide Industries Inc., and the MJ cell by AZUR SPACE Solar Power GmbH.
Fig. 4. Left: prototype module consisting of four Fresnel lenses and four optical guides on a solar cell. Right: experimental comparison of two normalized I-V characteristic curves (top) and measured uniformity pattern on the cell surface (bottom).
The main drawback of this assembly is related to the use of the Fresnel lens as a POE and the fixed diameter of the optical guide. Fresnel lenses are known to have an important chromatic aberration. This increases the size of the light spot, since each wavelength of the spectral irradiance is focused in a different location. In addition, in this case, the available optical guides have a constant diameter with length. As a consequence, the input area cannot be adjusted to the light spot to receive all the irradiance coming from the POE. These limitations result in a poor optical efficiency. Indeed, an ${\eta _{\rm{opt}}}$ of 25.8% has been obtained according to the ray-tracing simulations. Despite this, we think the experimental investigation serves to partially validate the optical concept based on multiple POEs and optical guides, as well as to quantify the accuracy of the simulation procedure. Additionally, it helps to identify manufacturing and assembling challenges for future modules with more optimal features.
The experimental investigation of the module has been conducted at the indoor CPV facilities of the University of Jaén; see also Refs. [11,14,16,17] for further details of the experimental setup. The module was mounted on the supporting structure of the Helios 3198 CPV solar simulator and aligned to the direct input irradiance. The I-V characteristics of the module have been obtained at conditions equivalent to the CSTC by adjusting the irradiance, monitoring the spectrum through component solar cells (${\rm{SMRs}}\; \approx \;{{1}}$) [19], and maintaining the room temperature at 25ºC. Based on this, a maximum ${\eta _{\rm{opt}}}$ of 23.1% has been experimentally obtained (${{{C}}_{\rm{eff}}} = {{556}}\;{\rm{suns}}$); see Refs. [16,18] for details of this calculation. This value could be considered to be in agreement with the result obtained in the ray-tracing optical simulations considering the features of the module prototype and CSTC, a difference of only 2.7%. The expected lower value of the experimental ${\eta _{\rm{opt}}}$ can be attributed to additional effects not considering during the simulations, e.g., manufacturing tolerances and mounting errors. For instance, we have found small breaks on the optical guide surfaces, probably originating during the manual mounting of the module, which produce light leaks. In addition, the optical guides have been cut and polished manually. Due to this, the input and output surface present a non-negligible roughness that also contributes to increase the Fresnel losses at the interfaces. The recorded I-V characteristics have also been compared with a CPV system only composed of a Fresnel lens and a cell; see Fig. 4 (right-top). The later has a ${{{C}}_{\rm{eff}}}$ of 434 suns. This value is almost the same as the UHCPV module under investigation. Hence, additional effects on the MJ cell caused by a different operating concentration are diminished. The fill factor (FF) of the UHCPV module is 84.9%, while it is only 77.2% for the standard. This better performance could be attributed to the better irradiance uniformity anticipated in the simulations. In order to go deeper on this, Fig. 4 (right-bottom) shows the irradiance map on the solar cell surface recorded with a Si-based CCD camera following the procedure described in [21]. As can be seen, the output of each optical guide can be clearly observed. However, the PAR value is significantly better than for the standard CPV module. A low PAR of 1.45 has been found for the UHCPV module, while it is 2.85 for the standard. This provides further evidences of the adequate uniformity produced by the proposed optical configuration. This is fundamental to limit the non-uniformity losses caused by extreme concentrations at some points of the MJ solar cells that could reduce the FF, and thus the efficiency, of the UHCPV module.
In conclusion, we have proposed a UH optical configuration formed by four symmetrical optical units made up of small mirrors and optical guides that send the rays to a central receiver. The simulations indicate its feasibility and a higher optical performance compared with current UH designs. Considering a system with a ${{{C}}_g} = {4096{\times}}$, we have obtained a ${\eta _{\rm{opt}}}\; \approx \;{{85}}\%$ and an ${\rm{AA}} = {0.61}^\circ$. These values of ${\eta _{\rm{opt}}}$ and AA are, respectively, around 2%–10% and 1.5–2 times higher than the state-of-the-art optical designs. Additionally, a high CAP of 0.68 has been obtained. This is around 1.5 higher than today’s best standard CPV modules. In addition, the optical system has proven to produce an adequate spectrum, ${\rm{SMR}}\; \approx \;{{1}}$, and uniformity, a PAR within 4.8–5.2, on the cell surface. The optical configuration and simulation procedure has been validated indoors by means of a solar simulator. In this sense, a preliminary UHCPV module with a ${{{C}}_g}$ of around ${2400{\times}}$ made up of four POE Fresnel lenses and optical guides with a fixed diameter that focuses the light on a single MJ cell has been investigated. Based on this, a difference of only 2.7% between the simulations and experimental results has been found. Future work will focus on the study of different optical materials to reduce the optical losses. Additionally, the most convenient procedure for fabricating the different optical elements will be discussed. Based on this, a design with the optimum configuration is aimed to be manufactured and experimentally investigated to completely investigate the potential of the concept.
Funding
Junta de Andalucía (PAIDI 2020: P18-RT-1595); Agencia Estatal de Investigación (BEAGAL18/00164, PID2019-106497RB-I00/AEI/10.13039/501100011033, RYC-2017-21910).
Acknowledgment
The authors are grateful for the donation of TracePro optical software by the Lambda Research Corporation. P. Rodrigo and E. Fernández, respectively, thank the AEI because of the 2020-2024 BEAGAL18/00164 and the RYC-2017-21910 fellowships.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this Letter are not publicly available at this time but may be obtained from the authors upon reasonable request.
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