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Abstract
A microtracking concentrator photovoltaics (CPV) module with a bi-convex aspheric lens array was designed, and its performance was numerically and experimentally verified. The lens shape was optimized considering the yearly incidence characteristics of direct solar radiation. The lens optimized at 127 × was found to converge 68.7% of the yearly cumulative direct solar radiation to solar cells and to be robust against changes in installation azimuth and tilt angles. The incidence-angle characteristics of a prototype lens agreed well with the design analysis. In an outdoor test using a prototype microtracking CPV module with an optimized lens and a triple-junction solar cell, the power generation was 1.32 times higher than that of the 17%-efficient Si cell and nearly 30% module conversion efficiency was achieved under clear sky conditions.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Currently, the highest reported conversion efficiency of the silicon (Si) solar cell—the most popular type of solar cell—is over 26% [1], which is relatively close to the theoretical conversion efficiency (29.43% [2]). In contrast, the conversion efficiencies of III-V compound multijunction solar cells continue to be significantly improved, and its highest reported conversion efficiency thus far is 46.0% at 508 suns [3]. Concentrator photovoltaics (CPV) has been developed because the multijunction cell is expensive although highly efficient. In the CPV, inexpensive concentrator optics collects sunlight into a small-area multijunction cell so that high-efficiency power generation can be achieved with relatively low cell usage. Consequently, the cell cost is remarkably reduced in a high-concentration CPV.
However, such a high-concentration CPV requires a mechanical solar tracking device (hereinafter referred to as “tracker”). In general, many CPV modules are mounted on the tracker. In order to maintain rigidity for tracking accuracy even in strong wind, it is necessary to increase the tracker size, which increases the system cost. Furthermore, to avoid interference among the trackers in the tracker array, the area of the installation site must be greater than the total area of the modules, i.e., the ground coverage ratio of the CPV tracker array tends to be less than that of the conventional photovoltaic (PV) module.
Recently, tracking-integrated systems have been developed to solve the abovementioned issues. In tracking-integrated systems, since the tracking mechanism is built in the CPV module, the CPV module can be mounted on the fixed mount that has been used for the conventional PV module. Tracking-integrated systems are roughly classified into beam-steering and microtracking systems [4]. A beam-steering system consists of a beam-steering optical element, fixed concentrating optical element, and fixed PV cell. The beam-steering element collimates sunlight so that it is perpendicularly incident on the concentrating optical element such as a Fresnel lens, which collects collimated sunlight into the PV cell. While a geometrical concentration ratio of 500 × to 1000 × can be achieved, the system tends to be complicated and have a high optical loss at such concentration ratios. Previous studies have proposed mirror-based [5], rotating-prism-based [6,7], and electrowetting-based [8–10] beam-steering CPV systems. However, none of these have been realized on a practical module scale. On the other hand, a microtracking system consists of concentrating optical elements and a movable photovoltaic (PV) cell. A compact internal tracking mechanism incorporated in the module moves the PV cell to the focused spot, thereby maintaining the concentrating performance, i.e., optical efficiency. Duerr et al. introduced an advanced optical design using the Simultaneous Multiple Surface (SMS) algorithm for a microtracking system with laterally moving plano-convex lenses [11,12]. Several microtracking systems with a laterally-moving lightguide have been studied [13–17]; for example, Liu et al. devised a system for which optical analysis and tests demonstrated optical efficiencies of 65% or greater at incidence angles less than 24° [16,17].
Lim et al. designed a unique and compact three-axis tracking mechanism using two actuators and demonstrated tracking for 8 h in an outdoor test using a prototype module [18]. Price et al. designed a planar microtracking CPV module with a novel focusing system in which a laterally (two-dimensionally) movable PV cell is sandwiched by a lens and a mirror via an index-matching fluid, and its prototype module achieved a module conversion efficiency of ∼30% in an outdoor test under clear sky conditions. This module generated 1.54 times more electricity than a 17%-efficient commercial flat Si PV module per day [19–21]. Although these previous studies have shown the potential for microtracking with advanced focusing systems, the systems appear complicated and might present difficulties in scaling up the system. Thus, there is room for exploring a simpler focusing system and a tracking mechanism with a higher optical efficiency for a wider angle of incidence. In the present study, we design a simpler microtracking CPV module (127 × ) consisting of a fixed bi-convex aspheric lens array and a three-dimensionally movable PV cell array, and report the results of lens design analysis and an outdoor test using the prototype module. The convex bi-aspheric lens is a well-known lens widely used in various optical applications. However, its potential for microtracking CPV applications has not been investigated to date.
2. Design concept
Figure 1 shows the design concept of the proposed microtracking CPV module. This module consists of a micro-lens array, PV-cell array, compact tracking mechanism, and housing. The lens aperture is hexagonal and has a smaller Fresnel loss than a quadrangular aperture, and the lens array has a one-piece structure with a small alignment error. A mechanism similar to that reported by Lim et al. [18] was adopted, in which the tracking operation in the Z direction is performed passively in conjunction with the tracking operation in the XY direction. This tracking mechanism enables three-axis tracking with only two actuators, thereby reducing the cost. The tracking mechanism consists of a plate on which the PV cell array is mounted, ball foot, ball guide, and XY actuators. The ball-foot diameter and the curved surface shape of the ball guide determine the tracking trajectory of the PV cell. Since this module is fixed, a wide acceptance angle is required for the concentrator system. Furthermore, the variation in the position of the focused spot with respect to the change in the incidence angle needs to be smooth and continuous. In this study, we adopt a bi-convex aspheric lens, which has been widely used for various optical instruments, and verify the performance of the concentrator system. The secondary optical element, which is often attached on the PV cell in the conventional high-concentration CPV to widen the acceptance angle, was not considered in this study to keep the optical system as simple as possible.
Fig. 1 Design concept of the proposed microtracking CPV module with a bi-convex aspheric lens array.
3. Lens design analysis
Since the incidence angle of direct solar radiation to a fixed module varies with the season and time, the concentrator system needs to be evaluated by annual analysis. In this study, the yearly cumulative solar radiation energy Eannual collected on the PV cell was used as an evaluation index. The optimum lens shape is the shape that maximizes Eannual, which is defined as follows:
where θi, E(θi), and ηopt(θi) are the incidence angle [°], yearly cumulative direct solar radiation incident on the lens aperture [kWh/(m2⋅year)] at the incidence angle θi, and the optical efficiency of the concentrator system at the incidence angle θi, respectively. The optical efficiency is the ratio of the energy collected in the PV cell to the total direct solar radiation incident on the lens aperture. E(θi) was calculated from AMeDAS weather extended data (installation location: Tokyo, latitude: 35.69°, longitude: 139.76°). The inclination angle of the module is assumed to be the same as the latitude of the installation site, and the module is assumed to be oriented toward the south.Figure 2 shows the optical simulation model of the bi-convex aspheric lens, while Table 1 lists the simulation conditions. The model is a monolithic lens array with seven lenses in order to consider cross-talk between adjacent lenses. Optical efficiency for the center lens was calculated from the incident energy at the projected aperture area of the center lens and the energy captured by the PV cell. The geometrical concentration ratio was set at 127 × . Even in such a moderate concentration ratio, the III-V compound multi-junction cell still exhibits a cell efficiency over 40% (which is the reported experimental value for a triple-junction cell [22]), and the required tracking accuracy is low compared to that for a high-concentration ratio such as 600 × or higher. In addition, the research and development of lower-cost multijunction cells, such as III-V/Si cells, are rapidly progressing. Optical simulation software (CYBERNET Co., Ltd., LightTools 8.4) was used for ray-tracing analysis. The top and bottom faces of the lens are aspherical, and the lens aperture is hexagonal. The hexagonal shape decreases the inclination of the curved surface at the end of the lens and reduces the reflection losses (Fresnel loss). Polymethyl methacrylate (PMMA), often used for injection-molded lenses, was used as the lens material. The lens shape of the top and bottom curved surfaces is expressed as follows:
where ctop, cbottom, ktop, kbottom, and t denote the curvature of the top and bottom surfaces, conic constant of the top and bottom surfaces, and lens thickness, respectively. The combination of these five variables that yields the maximum is determined through a global optimization technique. An in-house macro program has been developed for the global optimization and implemented by using LightTools. Since the outer shape of the lens is not circular but rather hexagonal, the optical efficiency may slightly vary, not only with but also with ϕ ′, as shown in Fig. 2(b). When searching for the optimal lens shape, ηopt(θi) is treated as the average in the case of ϕ ′ = 0°, 10°, 20°, and 30°, as expressed in the following equation:
Table 1. Optical simulation conditions
We moved the position of the PV cell in ray-tracing analysis and found the coordinates with the highest ηopt(θi); this position is defined as the focused-spot position. Table 2 lists the optimum shape parameters of the bi-convex aspheric lens yielding the maximum Eannual as well as the search range of each parameter.
Table 2. Optimization parameters [search range] (optimized value)
The black curve in Fig. 3 shows E(θi) for this module. When the module tilt angle is the same as the latitude of the installation site, E(θi) peaks at an incidence-angle range of 22–25°, irrespective of the installation location. The orange line shows the E(θi)⋅ηopt(θi) of the microtracking system using the designed lens. For comparison, the purple line shows the result when using a plano-convex aspheric lens with the same geometrical concentration ratio, which has advantages such as ease of manufacturing, cleanability of the front surface, and elimination of cross-talk between adjacent lenses at the front surface. It is confirmed that the optimized bi-convex lens can converge 68.7% of the annual direct solar radiation incident on the lens aperture into the PV cell, which is approximately 1.7 times greater than that for the optimized plano-convex lens.
Fig. 3 Simulated annual direct irradiation on the PV cell concentrated by microtracking with the optimized bi-convex aspheric lens array. The result of the optimized plano-convex aspheric lens array with the same geometrical concentration ratio is also plotted for comparison.
Figure 4 shows the simulated incidence-angle characteristics of the optimized bi-convex and plano-convex aspheric lenses with the illustrations of traced rays at on-axis and off-axis conditions. The bi-convex lens exhibits significantly better optical efficiency over large incidence angles. In addition, the bi-convex lens exhibits shorter focal length and shorter moving distance of the focused-spot position.
Fig. 4 Simulated incidence-angle dependency of the optimized bi-convex and plano-convex aspheric lens array (ϕ ′ = 0°). Adjacent lenses are hidden in the illustrations.
The azimuth angle and inclination angle of the microtracking module are not necessarily set at an inclination angle facing south and equal to the latitude. Therefore, the influence of the installation azimuth angle ϕ and the inclination angle φ on Eannual was calculated for the optimized bi-convex aspheric lens. Figure 5(a) shows the inclination-angle dependence of Eannual. Here, E0 indicates the Eannual value at ϕ = 0° and φ = 35.67° given in the lens design analysis. For ϕ = 0°, Eannual can be 90% or more of E0 in the range 20° ≤ φ ≤ 60°. Figure 5(b) shows the azimuth-angle dependence of Eannual. For φ = 35.67°, Eannual can be 90% or more of E0 in the range 40° ≤ ϕ ≤ 40°. These results indicate that the proposed module has some degree of robustness against changes in the installation azimuth angle and inclination angle.
Fig. 5 Tolerance to tilt angle and azimuth angle of the microtracking module with the designed bi-convex aspheric lens array.
To verify the validity of the design, a test unit composed of a lens and PV cell was prototyped, and the optical efficiency and focused-spot position were measured. Figure 6 illustrates the indoor test apparatus. We used an in-house highly collimated solar simulator as the light source [23]. The prototype unit was mounted on a rotating stage, which could arbitrarily change the incidence angle. The monolithic lens array with the optimum shape parameter was manufactured by machining PMMA in a plastic lens manufacturer. Shape error of the manufactured lens from the designed shape was measured with a hi-precision three-dimensional shape measurement instrument. The peak-to-valley value of the shape error was less than 3 μm. Similar to the simulation model, seven PMMA lenses with the optimum shape parameter were arranged, and light concentrated by the central lens was made incident on the PV cell. A typical triple-junction (3-junction) cell (GaInP/GaInAs/Ge, nominal cell efficiency 42.5% at 1000 suns, 25 °C, AM 1.5D spectrum) was used for the PV cell. The area of the PV cell was the same as that in the simulation, i.e., 1 × 1 mm2. The PV cell was mounted on an off-the-shelf XZ stage, and the focused-spot position of the lens was detected by manually adjusting the XZ stage by 0.05-mm steps in each direction. Figure 7(a) shows the measurement result of the optical efficiency for ϕ ′ = 0°. The experimental values agreed well with simulated values. Both experimental and simulated values show a high optical efficiency at θi ≤ 50°(acceptance angle of ± 40°), which decreases rapidly at θi > 50°.
Fig. 7 Comparison between measured and simulated incidence-angle dependency of the optimized bi-convex aspheric lens array (ϕ ′ = 0°).
Overall, the experimental values are slightly greater than the simulated values because the standard solar spectrum AM 1.5D used in the optical simulation and the experimental spectrum are slightly different. Figure 7(b) shows the relationship between the focused-spot position and the incidence angle for ϕ ′ = 0°. The black solid line and red dots show the simulated curve and experimental values, respectively, and they are in good agreement. The focused-spot position changes smoothly and continuously with respect to θi and varies within 1% with the change in ϕ ′; therefore, the present microtracking is easy to perform. The radius of the focused spot tends to increase in proportion to the decrease in the optical efficiency. For θi > 55°, the focused spot is not actually a “spot” but rather a “spread area.” Accordingly, the experimental data was not plotted.
4. Outdoor test with prototype module
A prototype module, consisting of the designed lens, 3-junction solar cell, and microtracking mechanism shown in Fig. 1, was built and an outdoor test was conducted in Takasaki City (latitude: 36.3°, longitude: 139.0°, Japan). Figure 8 shows the appearance, components, and tracking mechanism of the prototype module. The three-dimensional tracking motion is driven by two sets of motors/gears. As shown in Fig. 8(c), the long hole guides/pins on the gears enable lateral (XY direction) motion of the PV cell; simultaneously, the ball foots/guides passively enable vertical (Z direction) motion of the PV cell. The motors, gears, ball guides, and ball foots of the tracking mechanism are designed such that they can be used without modification even when the module size is 1 m × 1 m. Estimated friction in the ball foot/guide is relatively small compared to the force produced by the motor. However, it should be noted that, upon scaling to a larger area, the accuracy of cell-lens alignment becomes an issue. Parallelism of the motion between lens arrays and cell arrays must be accurate enough, especially when the module is installed at a higher inclination angle, because mechanics at the ball foot/guide may be affected by the force of gravity; moreover, supporting pillars must be inserted at certain intervals to keep the center of the lens array from sagging. Although the present experimental system works well without these issues, further study for improvements in the tracking mechanism and module design is necessary.
Fig. 8 Prototype microtracking CPV module with the designed bi-convex aspheric lens array and a triple-junction solar cell.
The prototype module faced south and was installed at an inclination angle equal to the latitude of the installation location. A combination of an open control and a feedback control was used for the tracking methodology. The two motors were basically controlled by the open control along with the orbit of the sun calculated from the information of the installation location and date. The feedback control was intermittently performed in 30-min intervals to correct the PV cell position to the position where the short-circuit current value became maximum, by monitoring the current-voltage (I-V) characteristic of the PV cell with an I-V tester. To compare the power generation with that of a flat Si PV module, the I-V characteristics of a crystalline Si cell (nominal cell efficiency 17.2% at 1 sun, 25 °C, AM 1.5G spectrum) arranged side-by-side with the prototype module were also measured. Direct normal irradiance (DNI) was measured using a pyrheliometer (not shown in Fig. 8) and converted to direct tilted irradiance (DTI).
Figure 9 shows the time variation of DTI and I-V characteristics of the module under clear sky conditions. The daily mean ratio of diffuse component to global solar irradiation was 0.19, which is almost equivalent to the annual mean value for a typical sunny location. Measurement data when the rate of change of DTI exceeded 5 W/(m2⋅s) were excluded to avoid errors due to the time constant of the measurement system. The maximum power output of the prototype module Pmax exceeded that of the Si cell at almost all times during the day. The reason why Pmax suddenly decreased from 15:08 is that the tracking mechanism interfered with the module housing and the tracking was stopped. This problem can be simply solved by improving the module structure to modify the shapes of mechanical parts. The fill factor FF and open-circuit voltage Voc of the triple-junction solar cell were always stable in the ranges of 0.831−0.868 and 2.78−2.86 V, respectively, up to 15:08. The module conversion efficiency peaked at solar culmination, and the maximum value was 29.7%. Here, the module conversion efficiency is defined as the ratio of the PV cell power to the solar radiation incoming over the module aperture area. In the case of the microtracking CPV module, the projected area of the single lens is used as the module aperture area and direct solar irradiance is used as the solar radiation. In the case of the Si cell, the cell area is used as the module aperture area and global solar irradiance is used as the solar radiation. The power generation per unit lens aperture area integrated over the entire test time is 929 Wh/m2, which is 1.32 times greater than that of the 17%-efficient Si cell (701 Wh/m2). This result implies that the present microtracking CPV module has the potential to generate greater power than the conventional flat Si PV module in a typical sunny location, although the flat Si PV module does not require complicated tracking and it can generate power not only from direct sunlight but also from diffuse sunlight.
Fig. 9 Measured daily performance of the prototype microtracking CPV module compared with a 17%-efficient conventional PV module (Si cell).
Figure 10 shows a comparison between the simulated value of optical efficiency and the experimental value. Experimental values were calculated from the cell’s short-circuit current. Although they are in good agreement at θi < 30°, the experimental value gradually becomes lower than the simulated value at θi > 30°. The alignment error between the lens and the tracking mechanism is the main possible reason for this discrepancy. The experimental optical efficiency integrated over the entire test time reached 93% of the simulated efficiency. During the experiment, optical efficiency of the present CPV system was as high as 0.74 where the 3-junction cell was supposed to be illuminated at ∼100 sun. The 3-junction cell used in the experiment exhibits a cell efficiency of 30.3% and 36.9% at 1 sun and 100 sun conditions, respectively, which were measured by an indoor test using a high-flux solar simulator. Thus, it can be said that the present CPV system increased the cell efficiency by a factor of ∼1.2. Furthermore, if a 3-junction cell optimized for the ∼100 sun condition is employed, the cell efficiency of ∼40% [22] can be obtained and the power generation amount and the module conversion efficiency are further improved.
5. Conclusion
A microtracking CPV module was designed by combining a bi-convex aspheric lens array and a built-in tracking mechanism. The lens shape was optimized considering the yearly incidence characteristics of direct solar radiation. The lens optimized at 127 × was found to converge 68.7% of the yearly cumulative direct solar radiation to PV cells and to be robust against changes in installation azimuth and tilt angles. The incidence-angle characteristics of the prototype lens agreed well with the lens design analysis. In the outdoor test using the prototype microtracking CPV module with an optimized lens and triple-junction solar cell under clear sky conditions, the power generation per unit module area per day was 1.32 times higher than that of the 17%-efficient Si cell, which simulated the conventional Si PV module. The module conversion efficiency reached almost 30%, which is comparable to the highest record currently reported in the literature. Furthermore, the daily variation in optical efficiency of the module was in good agreement with the analysis. These results validate the proposed optical design and demonstrate the performance of the proposed module concept. Since the triple-junction solar cell used in this experiment was originally designed for a higher concentration ratio, i.e., 1000 sun, it was used under a far-off-design condition. By using a dedicated triple-junction solar cell, the performance can be improved further. The present results elucidate that even a bi-convex aspheric lens—a very common lens—has the potential to be useful for microtracking CPV systems if it is used with a tracking mechanism accommodating three-dimensional PV cell movement and also used with a moderate geometrical concentration ratio ∼100 ×. A major challenge will be to maintain the performance with a relatively low cost increase when the module size is increased to the meter scale. Such a practical tracking-integrated system will play an important role in mitigating restrictions on the installation requirements of CPV systems due to trackers and in effectively utilizing multi-junction solar cells, which will become more efficient in the near future.
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