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Abstract
A bidirectional planar-displacement waveguide tracker was devised to replace the traditional two-axis tracking system for high-concentration photovoltaics, with improved module thickness, optical field uniformity, and current matching. The concentrating magnification reaches 725 times, and the sun tracking angle is more than 170°, which is equivalent to 11.3 tracking hours per day. The module thickness is only 6.16 cm. This design enabled us to place the module flat on the ground, in which swing was not required. This will greatly improve the mechanical strength and the lifetime of the module and solve the development dilemma faced by III-V multijunction solar cells.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Monolithic III-V multijunction solar cells have been mainly developed in conjunction with a two-axis tracking system for solar concentrators to form a high-concentration photovoltaic module [1], where the optical system comprises of Fresnel lens and secondary optical elements of various shapes [2]. Considering the solar cell cost, the optical system was mainly designed to have a high-concentration ratio. However, this led to problems such as a rise in solar cell temperature, drop in efficiency [3], and a reduction of the solar tracking tolerance angle to below 1° [4]. Moreover, many mechanical problems were found in the actual modular products following long-term outdoor-operation tests. For example, the large and heavy modules resulted in a substantial increase in material and labor costs [5]; long-term exposure to wind caused static and dynamic deformation of the material, which reduced the solar tracking tolerance [6]; and a long-term operation in a harsh environment caused demagnetization of the motor [7]. Abovementioned disadvantages made it difficult to develop the two-axis tracking system for solar concentrators. To improve the two-axis tracking system, Lee et al. have designed a microcell array using a three-dimensional movable photovoltaic to replace the tracking system [8]. Liu et al. have designed a waveguide with a 45° wedge to collect the sun light, which focused on the concentrating lens, and the collected sun light could propagate to the edge of the photovoltaic module to reduce the working temperature [9]. Vu et al. have also designed a prism waveguide to collect the focused sun light reflected by a curved mirror [10]. This design can divide the different wavelength sunlight to different photovoltaics to improve the efficiency. Recently, Price et al. have combined a concentrating lens and a curved reflector to focus the sun light on a plane [11]. A movable solar cell was placed on the plane in between the lens and reflector to absorb the sun light. So, the movable solar cell could track the sun light on a two-dimensional plane to replace the two-axis tracking system. The concentration ratio of this design is ∼200 times with a wide sunlight zenith angle ∼60°. Then, they published another design with 660 times concentration ratio, and the workable zenith angle of ∼70° [12]. Solar cells were located at the center of these two designs, and the working temperature increased as the operation time increased. To prevent the cells from getting damaged due to high temperature, the cooling mechanism has to be considered without blocking the incident light.
Furthermore, the optical system design for concentrating solar cells has to be considered for the quantum efficiency of III-V multijunction solar cells of each absorption junction. The AM1.5D full-wavelength solar spectrum, which was used to calculate the overall efficiency, is not accurate. If the number of electron–hole pairs in the three absorber junctions does not match, the solar cell efficiency will be limited for the current mismatch [13–16]. Therefore, it is very important to refer to the quantum efficiency of the three absorption junctions of the solar cell when designing and optimizing the optical system. Additionally, the sunlight illuminance on the surface of the solar cell is not distributed evenly in the high-concentration system. Several researchers have identified that non-uniform illuminance distribution can decrease the solar cell efficiency and also damage the solar cell [17–21]. So evenly distributing the sun light on the surface of the solar cell is also very important.
In this research, a bidirectional planar-displacement waveguide tracker integrated with a concentrating lens, curved reflector, and movable waveguide was designed to replace the traditional two-axis tracking system for solar concentrators. Non-sequential lighting simulation software was used for efficiency and uniformity analysis. This allows the modules to be placed horizontally; the same applies to the silicon solar cell, using bidirectional plane displacement of the waveguide responsible for solar tracking. Additionally, considering the quantum efficiency of each junction of the III-V multijunction solar cell in the simulation, the conversion efficiency is maximized through the design and optimization of the optical system in conjunction with the corresponding absorption spectrum.
2. Optimization design method
The III-V multijunction solar cell in this research composed of three absorption junctions [22]. Photocurrent is generated through the photoelectric effect induced in each junction of the solar cell. Figure 1(a) shows the quantum efficiency of the III-V multijunction solar cell [23]. The three junctions are arranged in series. The top junction absorbs the short wavelength and the bottom one absorbs the long wavelength. The total output current is limited by the top junction. In this junction, the short-wavelength photo current must be increased to the maximum value to achieve output of maximum efficiency. In the design of the bidirectional planar-displacement waveguide tracker, both the cumulative photon flux of the AM1.5G solar spectrum and the quantum efficiency of each wavelength of the III-V multijunction solar cell need to be taken into account. According to the absorption spectrum of the three junctions, the absorption wavelengths can be roughly divided into three bands: 300–660 nm, 660–890 nm, and 890–1900 nm. Figure 1(b) displays the product of the cumulative photon number corresponding to the AM1.5G solar spectrum [24] and the solar cell quantum efficiency.
Fig. 1. Flux performance of the III-V multijunction solar cell to the generated electron holes by each absorption junction under the illumination of AM1.5G solar spectrum (a) External quantum efficiency of the III-V multijunction solar cell and (b) number of electron–hole pairs generated by the III-V multijunction solar cell in different wavelength ranges.
The result represents the number of electron–hole pairs generated by the solar cell per square centimeter per second. The cumulative numbers of electron–hole pairs corresponding to the absorption wavelength of 300–660 nm, 660–890 nm, 890–1900 nm are 8.2 × 1016 #/cm2 sec, 8.39 × 1016 #/cm2 sec, and 1.17 × 1017 #/cm2 sec respectively, indicating that in the optical system design, the conversion efficiency of the top junction which absorbs short wavelength must be increased as much as possible, while that of the electron–hole pairs entering the bottom junction, which absorbs long wavelength, has to be decreased to reduce the heat accumulated by the excessive carriers, to avoid component degradation. The efficiency of the continuous solar spectrum of AM1.5G in the absorption wavelength of 300–1900 nm is simulated using the optical system simulation software, with the conversion efficiency of each absorption layer in the solar spectrum wavelength ranges of 300–660 nm, 660–890 nm, and 890–1900 nm analyzed simultaneously.
Figures 2(a) and 2(b) show the side view and the top view of the optical system architecture. Considering the cost competitiveness of solar cells, in the simulation of optimization, the case of normal sunlight incident was included, which had the advantage of achieving a concentration ratio of over 725. The first optical element was a concentrating lens of diameter 76 mm, which was responsible for increasing the light concentration ratio for the solar cell. The sunlight would be reflected by the second optical reflector with a diameter of 76 mm. When the focal points corresponding to different zenith angle could form a Petzval curvature [25], the optical reflector mirror could correct the Petzval curvature by optimizing the surface curvature and curvature constant. The sunlight of different zenith angle could be focused on the same plane, and the waveguide only needed to move on the plane to complete the sun tracking. Filling high-refractive index oil in between the condenser and the optical reflector can increase the daily sunlight acceptance angle. The third optical element was a long straight movable waveguide with a reflective wedge with a length of 76 mm, width of 2.5 mm, and height of 2.5 mm. The waveguide is covered by a transparent glass tube, and air is filled in between the transparent glass tube and the waveguide to increase the total reflection angle. Figure 2(a) shows the detail of the reflective wedge; there is a piece of flat glass placed near the focus of the second optical reflector, with the refractive index lower than that of the waveguide and refractive index oil. The refractive index of the refractive index oil, waveguide, and flat glass are 1.71, 1.9, and 1.47, respectively. Flat glass can couple the sunlight from the refractive index oil into the waveguide. Through the characteristics of the reflective wedge and total reflection of the waveguide, the sunlight was focused on the side-oriented solar cell with a length of 2.5 mm and width of 2.5 mm for power generation. In practical situations, reducing the module thickness can increase module mechanical strength and reduce the material cost. The side-oriented characteristic allowed the module to be thinner with the overall optical system thickness less than 6.16 cm, which would also facilitate the installation of heat dissipation systems inside the module.
Fig. 2. Optical system of the bidirectional planar-displacement waveguide tracker (a) side view and (b) top view.
With the advancement of multilayer film technology or etching technology, Fresnel reflection loss can be reduced by a broadband anti-reflection design or lens surface etching [26]. Each optical component in this research was considered to have a broadband anti-reflection surface to eliminate the Fresnel reflection loss. In terms of tracking the sun, the sun has both zenith angle and declination angle according to the daily and seasonal changes [27]. The zenith angle is the changing angle of the 24 hours a day, and the four seasons are mainly due to the change of the Sun’s declination angle. Place the solar cell module facing the equator, and the declination angle of the sun will only move back and forth within ±23.5°. Therefore, it is already the most extreme situation at a declination angle of ±23.5°. In this study, the bidirectional planar-displacement waveguide tracker will be designed and optimized for declination angle of 0° and ±23.5° with different zenith angles.
3. Results and discussion
The applied optical system with high concentration and wide angles would cause different aberrations. Therefore, it was necessary to optimize the surface curvature of the concentrating lens and the optical reflector so as to focus the light of different wavelengths. Design parameters are shown in Table 1. NFK56 and TAFD17 were used as the material of the concentrating lens and the optical reflector. The aspheric function of the reflector was used for optimization. Aspheric coefficients are shown in Table 2. Finally, the thickness of the two lenses was optimized to be less than 25 mm, with the thickness of the overall optical system being 6.16 cm. Note that the straight waveguide was not included in the lens optimization because it was necessary to maximize the efficiency of short wavelengths on the focal plane to ensure that considerable short-wavelength light could be transmitted to the solar cell through the previously installed waveguide. Figure 3 shows the efficiency distribution of the incident light on the focal plane, where the light with three wavelength bands enters the optical system at different angles. In order to achieve a maximum coupling efficiency, the aberration of the optical system has to be calculated. Besides, the size of the focal plane was restricted to 2.5 × 2.5 mm to match the cross section of the solar cell. After optimization, the zenith angle exceeds 170°, which is equivalent to 11.3 hours per day. Concentrating lens and optical reflector were designed to achieve maximum efficiency as short-wavelength light entered the system at a zenith angle of ±20°–±85°, while the long-wavelength light-based efficiency was significantly reduced at various zenith angle, which would help reduce the generation of excessive carriers in solar cells.
Fig. 3. Conversion efficiency of short-, medium-, and long-wavelength light incident on the receiver of the optical system at different zenith angles.
Table 1. Design parameters of concentrating lens and optical reflector
Table 2. Optical reflector aspheric coefficient
Figure 4 is the light field diagram with 0° declination angle and zenith angles of 0°, 40°, and 85° on the focal plane. High-energy condensing points are generated at different zenith angles. It shows the phenomenon of uneven light field, especially when the zenith angle is 0°, as shown in Fig. 4(b). The intensity of the condensing spot is even more than 1000 times that of other places of the solar cell. The high energy of sunlight will damage the solar cell. Figure 5 is the light field diagram with ±23.5° declination angle and zenith angles of 0°, 40°, and 85° on the focal plane. We can find the phenomenon of the very uneven light field in Figs. 4 and 5. Therefore, it is necessary to use the additional waveguides to improve the uneven light field distribution problem.
Fig. 4. Light field diagram at the focal plane with a declination angle of 0° at different zenith angles (a) side structure, (b) 0°, (c) 40°, and (d) 85°.
Fig. 5. Light field diagram at the focal plane with a declination angle of ±23.5° at different zenith angles. (a) top structure, (b) 0°, (c) 40°, and (d) 85°.
Then, the third optical element––a movable long waveguide consisting a reflective wedge, with a length of 76 mm, width of 2.5 mm, and height of 2.5 mm––was added. The length is the same with the diameter of the concentrating lens, 76 mm. The cross section is the same with the commercial concentrating solar cell, 2.5 mm×2.5 mm. As exhibited in Fig. 6, the wedge angle θp increased, the light propagating in the waveguide decreased and the conversion efficiency decreased. On the contrary, a decrease in the wedge angle θp of the reflector caused the reflected light to exit the waveguide without reaching the total reflection angle, which also reduced the conversion efficiency, indicating the existence of a reflective wedge angle θp capable of maximizing the conversion efficiency. The maximum efficiency of short-wavelength light was taken as the main consideration. When the reflective wedge angle θp reached 46.62°, the receiver on the waveguide side exhibited maximum efficiency. Figure 7 shows the light tracking path of the short-wavelength sunlight. The incident solar light was focused on the concentrating lens and the optical reflector with compensated dispersion. A large amount of short-wavelength light was successfully coupled into the waveguide in this design. The incident sunlight was focused on the reflective wedge of the movable waveguide and propagated through the waveguide to be absorbed by the solar cell.
Fig. 6. Relation between the reflective wedge angle θp and conversion efficiency of the short-wavelength light source.
Figure 8(a) shows the relation between the 0° declination angle and efficiency of the three absorption junctions. When the movable waveguide was added to the optical system, some losses were caused in the transmission process, because the chromatic dispersion of the material refractive index was large in short wavelength. To optimize the waveguide, the efficiency of the short wavelength in each zenith angle has to be higher than that of the medium and long wavelengths. The efficiency of the long-wavelength light was considerably lowered to reduce the formation of excessive electron–hole pairs. Figure 8(b) displays the relation between the ±23.5° declination angle and efficiency of the three wavelength junctions. Due to the aberration, the amount of light coupled into the waveguide is reduced. Overall, the short-wavelength efficiency is reduced by ∼5%–10%. Especially when the sun zenith angle is ±85°, the short-wavelength efficiency is slightly improved. Figure 9 is the displacement of the waveguide on the plane when the 0° and ±23.5° declination angle are at different zenith angles. When the declination angle starts to move to ±23.5°, the aberration in the two dimensions of the declination angle and the zenith angle causes the waveguide to show a curve tracking the sun.
Fig. 8. Relations among light sources of three junctions at different zenith angle and efficiencies (a) 0° declination angle and (b) ±23.5° declination angle.
To prevent the total energy from being focused at one point on the solar cell, it is important that uniformity of light energy distribution should be maintained. Figures 10 and 11 exhibit light energy distribution at the end of the waveguide under the illumination of the AM1.5G continuous solar spectrum at 0° declination angle and ±23.5° declination angle, suggesting that using the waveguide has the advantage of evenly distributing light, which enables the solar cell to produce carriers uniformly so as to evenly disperse the generated heat energy. This can extend the life of solar cells and ensure their safety.
Fig. 10. Energy distribution of light illuminated at 0° declination angle and different zenith angle at the end of the waveguide: (a) top structure, (b) 0°, (c) 40°, and (d) 85°.
Fig. 11. Energy distribution of light illuminated at ±23.5° declination angle and different zenith angle at the end of the waveguide: (a) top structure, (b) 0°, (c) 40°, and (d) 85°.
The photon number corresponding to each absorption junction, the overall conversion efficiency, and the quantum efficiency of the solar cell were multiplied to calculate the ideal number of electron–hole pairs generated by each junction per square centimeter per second. Figure 12 shows that the electron–hole pairs formed by the long-wavelength light have a rapid and substantial decline as the zenith angle increases. Electron–hole pairs formed by short-wavelength light only slightly decrease, which proves to have successfully improved the current matching, thereby avoiding excessive heat generation. Finally, the number of electron–hole pairs was multiplied by the area of the incident light source to calculate the current and output power, as shown in Table 3. When the 0° declination angle and zenith angle of the light source were 0°, 40°, and 85°, the output currents were 0.578 A, 0.395 A, and 0.039 A, respectively. The open-circuit voltage of the III-V multijunction solar cell was related to the energy gap of the material. With the open-circuit voltage of the multijunction solar cell being 3.555 V [28], the corresponding maximum output powers were 2.055 W, 1.404 W, and 0.139 W. The total input optical powers at each angle were calculated as 4.536 W, 3.475 W, and 0.396 W, representing the conversion efficiency of 45.3%, 40.4%, and 35.1%, respectively. When the ±23.5° declination angle and zenith angle of the light source were 0°, 40°, and 85°, the conversion efficiency of 43.4%, 36.9%, and 39.1%, respectively.
Fig. 12. Number of electron–hole pairs versus zenith angle of three junctions (a) 0° declination angle and (b) ±23.5° declination angle.
Table 3. Module current and conversion efficiency
4. Conclusion
In this research, the design of the planar-displacement waveguide tracker has been confirmed to be able to reduce the optical module thickness to 6.16 cm and to increase the current efficiency in the short-wavelength top junction at 0° declination angle. Simultaneously, 890–1900-nm long-wavelength light was reduced successfully. Moreover, the overall condensing magnification reaches 725 times, and the sun tracking angle is more than 170°, which is equivalent to 11.3 hours per day. The waveguide-based illumination optical field was very uniform, and the overall maximum output power was calculated at 2.055 W. When the 0° declination angle and the zenith angle is 0°, 40°, and 85°, the conversion efficiency is 45.3%, 40.4%, and 35.1%, respectively. When the ±23.5° declination angle and the zenith angle is 0°, 40°, and 85°, the conversion efficiency is 43.4%, 36.9%, and 39.1%, respectively. Overall, the planar-displacement waveguide tracker has been demonstrated to be far superior to the traditional two-axis tracking system for solar concentrators in terms of module thickness, optical field uniformity, current matching, and mechanical strength for modularization.
Funding
Ministry of Science and Technology, Taiwan (MOST 109-2221-E-008 -077 -MY3).
Acknowledgments
We acknowledge Dr. Ray Lin at Taicrystal International Technology Co., Ltd. for the support of quantum efficiency of the III-V multijunction solar cell.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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