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Thermal and electrical performance analysis of silicon vertical multi-junction solar cell under non-uniform illumination
Renewable Energy 90 (2016) 77e82
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Thermal and electrical performance analysis of silicon vertical multijunction solar cell under non-uniform illumination Yupeng Xing a, *, Kailiang Zhang a, c, *, Jinshi Zhao a, Peide Han b a Tianjin Key Laboratory of Film Electronic and Communication Devices, School of Electronics Information Engineering, Tianjin University of Technology, Tianjin 300384, China b State Key Lab on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China c State Key Laboratory of Functional Materials for Informatic, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050 China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 April 2015 Received in revised form 13 December 2015 Accepted 16 December 2015 Available online xxx
The silicon vertical multi-junction (VMJ) solar cell has low costs and low series resistance, thus it has a good potential in concentration photovoltaics. However, there were few discussions about the thermal and electrical performance of silicon VMJ cell under non-uniform illumination. In this work, the thermal performance of silicon VMJ cell under 1D non-uniform illumination of 500 suns was calculated using finite element method first, and then the electrical performance of the cell was calculated using SPICE software based on the thermal simulation results. It was found that the mean temperature of the cell increased with the degree of non-uniform illumination when the area ratio of the sink to the cell was 500X, and the mean temperature changed few when the area ratio was 2500X. The efficiency of the cell did not decrease with the increase of the degree of non-uniform illumination when the area ratio was 500X, and the efficiency increased with the degree of non-uniform illumination when the area ratio was 2500X. Thus, the silicon VMJ cell had better performance than silicon planar junction cell under 1D nonuniform illumination of 500 suns. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Vertical multi-junction Non-uniform illumination Electrical performance Concentration
1. Introduction Photovoltaics (PV) is being paid more and more attention as a kind of renewable energy, lots of work is being done to decrease the costs of solar cells, the concentration photovoltaics (CPV) is becoming more and more competitive as a kind of third generation photovoltaics [1e5]. The silicon vertical multi-junction (VMJ) solar cell which has low series resistance and low costs has a good potential in CPV [6], the efficiency of the cell has reached 19.19% under 2480 suns [7], simulation results showed that the efficiency of the cell would reach close to 30% under 1000 suns after optimizing the device parameters of the cell [8e10]. However, above simulation work on VMJ cell was all based on the assumption that the VMJ cell was under uniform illumination, and non-uniform illumination
* Corresponding authors. Tianjin Key Laboratory of Film Electronic and Communication Devices, School of Electronics Information Engineering, Tianjin University of Technology, 391 West Binshui Road, Xiqing District, Tianjin City 300384, China. E-mail addresses: [email protected] (Y. Xing), [email protected] (K. Zhang). http://dx.doi.org/10.1016/j.renene.2015.12.045 0960-1481/© 2015 Elsevier Ltd. All rights reserved.
was inevitable in realistic CPV systems, the non-uniform illumination was caused by many factors, such as concentrator optics, improper tracking and so on [11]. Lots of experiment and simulation work has been done to analyze the effect of non-uniform illumination on the electrical and thermal performance of other solar cells [11]. The non-uniform illumination profiles on the cells were complex in realistic CPV systems, the Gaussian function was always used to characterize the profiles in theory. Vishnoi et al. studied the effect of non-uniform illumination on the electrical performance of silicon planar junction cell by simulation and experiment, they found that the short circuit current density (Jsc), open circuit voltage (Voc) and efficiency of the cell decreased with the area of the illuminated region of the cell, because the dark region of the cell worked as a load [12]. Luque et al. calculated and tested the thermal and electrical performance of silicon planar junction cell under 1D non-uniform illumination, they found that the temperature of the center of the cell increased, the Voc of the cell decreased a few, the fill factor (FF) and efficiency of the cell decreased badly under non-uniform illumination, because the electrical losses of the center of the cell caused by series resistance increased. They also found that the edge of the cell became less
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active under non-uniform illumination, because the illumination intensity of the edge decreased. The quality of the edge of the realistic cells was always poor, thus the non-uniform illumination also had positive effect [13]. Mellor et al. calculated the electrical performance of silicon planar junction cell under 1D non-uniform illumination using finite element method [14], Herrero et al. tested the electrical performance of III-V multi-junction cell under 2D non-uniform illumination, they also found that the Voc, FF and efficiency of the cell decreased with the increase of the degree of non-uniform illumination [15]. Araki et al. calculated the electrical performance of III-IV multi-junction cell under 1D non-uniform illumination using a distributed circuit model, they found that the Jsc of the cell decreased with the increase of the chromatic aberration of non-uniform illumination [16]. Sater et al. have made a 500X CPV system which used the VMJ cells as the receivers, they focused the sunlight reflected by many mirrors to two receivers. The final illumination patterns on the VMJ cells were line-focused although the system was point concentration, thus the illumination on the VMJ cells was non-uniform along one direction and nearly uniform along another vertical direction [17]. Segev et al. calculated the electrical performance of the module made of silicon VMJ cells under 2D non-uniform illumination, they found that the module made of silicon VMJ cells had an obvious advantage over the module made of silicon planar junction cells [18]. However, Segev et al. didn't discuss the electrical performance of a single VMJ cell under non-uniform illumination, and they didn't consider the heat generated in the cells [18]. The heat was also inevitable in realistic CPV systems [17], but there was very few simulation and experiment work about the effect of non-uniform illumination on the thermal and electrical performance of the VMJ cell. Thus the thermal and electrical performance of the VMJ cell under 1D non-uniform illumination of 500 suns was calculated and analyzed based on Segev et al.’s device parameters [18], and the performance of the cell under uniform illumination was also calculated to compare in this work. The temperature profiles of the VMJ cell under uniform and 1D non-uniform illumination were calculated using finite element method first, and then the electrical performance of the cell was calculated based on the temperature profiles using SPICE software, and the performance of the cell under 300 K room temperature was also calculated to compare. 2. Structure and models The passive cooling was used in this work as Sater et al. did [17], the VMJ cell was mounted on the center of an aluminum flat sink to simplify the simulation, as shown in Fig. 1 (a). The volume of the sink could be made smaller by using more complicated structure,
the insulating layer between the cell and sink in realistic CPV systems was ignored here. The sizes of the cell and sink varied freely in our simulation although the area ratio of the sink to the cell was always set close to the concentration ratio of the system, the thickness of the sink was set to 4 mm which was close to the thickness of the sinks in realistic CPV systems [19,20]. The cell and sink were assumed to be square to simplify the discussion, thus we used their side lengths to represent their sizes, and a quarter of the cell and sink was simulated in this work according to the symmetry of the cell and sink. The illumination on the cell was set to be uniform along X direction, which was the direction of current flowing in the cell, and the illumination was set to be only nonuniform along Y direction, which was perpendicular to X direction, thus the illumination intensity of each sub-cell of the VMJ cell was equal [17]. The Gaussian function was used to characterize the 1D non-uniform illumination profile as follows [14,21]:
3 2 y 5 ¼ Pm Am exp4 2S20 2
Pillumination
(1)
which indicated that the illumination intensity of the center of the cell was the highest and that of the edge was the lowest. The S0 in formula (1) was the shape factor, Am was the normalization factor, Pm was the average illumination intensity. The degree of nonuniform illumination increased with the decrease of S0, Am was adjusted with S0 to ensure that the total illumination intensity of the cell was not changed with S0 [14]. The Pm was determined by concentration ratio C as follows:
Pm ¼ P1sun C
(2)
where P1sun was 1000 W/m2 (1 sun), C was fixed to 500X which was close to the realistic concentration ratio of Sater et al.’s system [17]. The single diode model was used to characterize the basic electrical character of the VMJ cell under illumination as follows [18,22]:
J ¼ Jsc;1 C Jd
ðV þ IRs Þ 1 exp ðnkT=qÞ
(3)
where Jsc,1 was the Jsc normalized by concentration ratio, Jd was the dark current density, Rs was the series resistance, n was the ideality factor, k was the Boltzmann's constant, T was the absolute temperature and q was the charge of an electron. The device parameters of VMJ cell which were used by Segev et al. were used here, these parameters were introduced in detail in Segev et al.’s paper, the thickness and width of the sub-cell of the VMJ cell were set to
Fig. 1. The schematic of the VMJ cell mounted on the center of an aluminum flat sink (a), the circuit simulation model of the VMJ cell (b), D represents the diode character of the unit cell, Jsc represents the photocurrent of the unit cell and R represents the series resistance of the unit cell.
Y. Xing et al. / Renewable Energy 90 (2016) 77e82
79
Table 1 The thermal conductivities and heat capacities of the silicon VMJ cell and aluminum sink. Material
Thermal conductivity [W/(m$K)]
Heat capacity [J/(kg$K)]
Solar Cell-Silicon Sink-Aluminum Plate
163 201
703 900
50 mm and 40 mm respectively, the Jsc,1, Jd, Rs and n of the cell varied with illumination intensity [18]. The bulk power density of the heat generated in the cell was calculated as follows [23]:
Pheat ¼ Pillumination
ð1 hÞ t
(4)
where h was the efficiency and was obtained by calculating the JV curve of the cell using equation (3), T was set to 300 K when calculating the efficiency, t was the thickness of the cell, the incident light was assumed to be absorbed by the cell totally. The finite element method was used to solve the 3D equations of heat transmission and dissipation in the cell and sink to get the temperature profiles of the cell [23]. The thermal conductivities and heat capacities of the silicon VMJ cell and aluminum sink were listed in Table 1, the heat generated in the cell diffused to the sink, and then the heat was dissipated through thermal radiation of the front and back surfaces of the sink, the surface emissivity was set to 0.9 [23,24]. The surrounding temperature of the cell and sink was
set to 300 K, and the convection caused by wind in realistic CPV systems was ignored to simplify the discussion. Based on above temperature and illumination profiles, the SPICE software was used to calculate the electrical performance of VMJ cell. The VMJ cell was divided into sub-cells, and the sub-cells were divided into unit cells, as shown in Fig. 1 (b), formula (3) was also used to model the unit cells, the illumination of each unit cell was assumed to be uniform because the area of the unit cell was very small. Jd had the following relationship with temperature [25]:
Eg Jd fT ð3þg=2Þ exp kT
where g was constant, Eg was the bandgap of silicon and was fixed to 1.12 eV. The second exponential term played a major role compared to the first term in formula (5), thus the first term was ignored and the Jd was assumed to have a linear relationship with the second exponential term as follows:
Temperature [K]
380
Y direction [mm]
Mean temperature [K]
361.1 2.0
361.8 362.4
1.5
363.1 1.0
363.7
0.5 0.0 0.0
375 370 365 360 355
0.5
1.0
1.5
(5)
2
2.0
4 6 8 Cell length [mm]
X direction [mm]
(a)
10
(b) Mean temperature [K]
400 380 360 340 320 300 0.0
3
5.0x10
4
1.0x10
4
1.5x10
4
2.0x10
Area ratio of the sink to the cell
(c) Fig. 2. The temperature profile of the 4.8 mm long VMJ cell with 500X sink under uniform illumination of 500 suns (a), the mean temperatures of the cells with different sizes (b), the mean temperatures of the cell with the change of the area ratio of the sink to the cell (c). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Y. Xing et al. / Renewable Energy 90 (2016) 77e82
Temperature [K]
Temperature [K]
362.8 365.7 368.7
1.5
371.7 1.0
374.7
0.5 0.0 0.0
0.5
1.0
1.5
361.0 2.0
Y direction [mm]
Y direction [mm]
2.0
361.8 362.6
1.5
363.4 1.0
364.1
0.5 0.0 0.0
2.0
X direction [mm]
0.5
1.0
1.5
2.0
X direction [mm]
(a)
(b)
Mean temperature [K]
370 360 350
500X 2500X
340 330 320 0.0
0.5
1.0
1.5 2.0 S0 [mm]
2.5
3.0
(c) Fig. 3. The temperature profiles of the VMJ cell with 500X sink under non-uniform illumination with shape factors of 0.1 mm (a) and 2.4 mm (b), the mean temperatures of the cell with the change of S0 (c) (0.1 mm < S0 < 2.4 mm, the points of S0 ¼ 2.8 mm represented uniform illumination), the circular points represented the case of the cell with 500X sink and the triangular points represented the case of the cell with 2500X sink. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
exp Eg kT Jd ðT0 Þ
Jd ðTÞ ¼ exp Eg kT0
(6)
where T0 was 300 K, Segev et al.’s Jd(T0) parameters were used here [18]. The Jsc changed with temperature very few, thus the effect of temperature on Jsc was not considered in our simulation [22]. The decrease of efficiency caused by the increase of temperature was not very large compared to the original value of efficiency in our calculation range, thus we did not couple the thermal and electrical simulation together to simplify the calculation. 3. Results and discussions The temperature profiles of the VMJ cells with different sizes under uniform illumination of 500 suns were calculated first, the side length of the VMJ cell was between 1.2 mm and 9.6 mm, and the side length of the sink was changed with that of the cell to ensure that the area ratio of the sink to the cell was fixed to 500X, which was the concentration ratio of the system. The temperature profile of the 4.8 mm long cell was shown in Fig. 2 (a), it was centrosymmetric, the highest temperature of the center of the cell was 363.7 K and the lowest temperature of the edge was 361.1 K. The mean temperatures of the cells were calculated, the results were shown in Fig. 2 (b), it could be seen that the mean temperature decreased from 376.9 K to 357.3 K with the decrease of the length of the cell from 9.6 mm to 1.2 mm. The decrease magnitude of mean temperature also decreased with the length, the mean
temperature only decreased 2.2 K when the length decreased from 4.8 mm to 3.6 mm. The mean temperature of the cell was still as high as 357.3 K even when the length of the cell decreased to 1.2 mm if the area ratio was fixed to 500X. Thus, the temperature profiles of the cell with the change of sink size under uniform illumination of 500 suns were calculated, and the mean temperatures of the cell were calculated, as shown in Fig. 2 (c), the length of the cell was fixed to 4.8 mm, and the area ratio of the sink to the cell was between 250X and 20000X. The mean temperature of the cell decreased from 399.7 K to 311.7 K with the increase of area ratio from 250X to 20000X, the decrease magnitude of mean temperature also decreased with the increase of area ratio, the mean temperature only decreased 6.3 K when the area ratio increased from 2500X to 5000X. Above simulation results indicated that the mean temperature of the cell could be decreased to rather low value when the area of the sink was large enough. Based on above simulation results, the temperature profiles of the cell under 1D non-uniform illumination of 500 suns were calculated, the length of the cell was 4.8 mm, two area ratios of 500X and 2500X were considered, and the shape factor S0 was between 0.1 mm and 2.4 mm (the half of the length of the cell). The temperature profiles of the VMJ cell with 500 X sink were shown in Fig. 3 (a) and (b), the shape factors were 0.1 mm and 2.4 mm, respectively. The temperature profiles were not centrosymmetric, the variation magnitude of temperature along the direction of nonuniform illumination (Y direction) was larger than that along the direction of uniform illumination (X direction). The highest and lowest temperatures of the cell were 372.7 K and 362.8 K when S0
Y. Xing et al. / Renewable Energy 90 (2016) 77e82
was 0.1 mm, the highest and lowest temperatures were 364.1 K and 361 K when S0 was 2.4 mm, and the temperature profile of the cell with shape factor of 2.4 mm was close to that of the cell under uniform illumination, which was shown in Fig. 2 (a). The mean temperatures of the cell with the change of S0 were shown in Fig. 3 (c), the mean temperature of the cell with 500X sink decreased from 367 K to 362.7 K with the increase of S0 from 0.1 mm to 2.4 mm, and the decrease magnitude of mean temperature also decreased with the increase of S0, the mean temperature changed few and was close to that of the cell under uniform illumination when S0 was larger than 0.8 mm. The reason was that the illumination intensity of the center of the cell increased with the decrease of S0, the heat generated in the center of the cell increased although the total heat generated in the cell was not changed, it mean that the heat centralized to the center of the cell with the decrease of S0, and the sink was not large enough to dissipate the centralized heat sufficiently. The mean temperature of the cell with 2500X sink decreased a few from 323.5 K to 322 K with the increase of S0 from 0.1 mm to 2.4 mm, the mean temperature was much smaller than that of the cell with 500X sink. The reason was that the area of the sink was much larger, which made the centralized heat in the cell could be dissipated by the surface of the sink more sufficiently. Based on above temperature profiles, the Jsc, Voc, FF and efficiency of the VMJ cell under uniform and 1D non-uniform illumination of 500 suns were calculated using SPICE software, the electrical performance of the cell under 300 K room temperature was also calculated to compare. The results were shown in Fig. 4, the Jsc of the cell was multiplied by the sub-cell number of the cell
81
and was normalized by concentration ratio, the Voc of the cell was divided by the sub-cell number. The Jsc increased a few from 28.1 mA/cm2 to 28.4 mA/cm2 with the decrease of S0 from 2.4 mm to 0.1 mm although the total illumination intensity of the cell was not changed. The reason was that the illumination intensity of the center of the cell increased and that of the edge decreased with the decrease of S0, the Jsc normalized by concentration ratio increased a few with illumination intensity [26], and the Jsc increase of the center of the cell was larger than the Jsc decrease of the edge. The mean temperature of the cell with 500X sink was larger than that of the cell with 2500X sink, and they were both larger than 300 K in our calculation range as mentioned above. The Voc of the cell decreased with the increase of mean temperature, because Jd increased with the increase of temperature. The Voc of the cell under 300 K room temperature increased from 0.8 V to 0.828 V and the Voc of the cell with 2500X sink increased from 0.752 V to 0.77 V with the decrease of S0 from 2.4 mm to 0.1 mm, the Voc changed few when S0 was larger than 0.8 mm for the two cases. The illumination intensity of the center of the cell increased and that of the edge decreased with the decrease of S0, thus the Jsc and Voc of the unit cells near the center increased with illumination intensity linearly and logarithmically, and those near the edge decreased. The Jsc increase of the unit cells near the center was larger than the Jsc decrease of the unit cells near the edge with the decrease of S0, the unit cells of a sub-cell were connected in parallel, and the sub-cells were connected in series as shown in Fig. 1 (b), thus the Voc of the cell increased for above two cases. But the Voc of the cell with 500X sink only increased from 0.663 V to 0.667 V, the increase magnitude
0.84 0.81 0.78
28.3 Voc [V]
2
Jsc [mA/cm ]
28.4
28.2 28.1 28.0 0.0
0.75
300 K 500X 2500X
0.72 0.69
0.5
1.0
1.5 2.0 S0 [mm]
2.5
0.66 0.0
3.0
0.5
1.0
(a)
3.0
2.5
3.0
(b) 19 Efficiency [%]
0.82 0.81 FF
2.5
20
0.83
0.80 0.79 0.78
18 17 16 15
0.77 0.76 0.0
1.5 2.0 S0 [mm]
0.5
1.0
1.5 2.0 S0 [mm]
(c)
2.5
3.0
14 0.0
0.5
1.0
1.5 2.0 S0 [mm]
(d)
Fig. 4. The Jsc (a), Voc (b), FF (c) and efficiency (d) of the VMJ cell with the change of S0 (0.1 mm < S0 < 2.4 mm, the points of S0 ¼ 2.8 mm represented uniform illumination), the circular points represented the case of the cell with 500X sink, the triangular points represented the case of the cell with 2500X sink and the square points represented the case of the cell under 300 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Y. Xing et al. / Renewable Energy 90 (2016) 77e82
was much smaller than that of the cell with 2500X sink, because the mean temperature of the cell with 500X sink increased with the decrease of S0 as mentioned above, Jd increased with temperature, which decreased the increase magnitude of Voc. The FF of the cell increased with the decrease of mean temperature, because the Voc increased with the decrease of mean temperature. The FF of the cell increased a few with the increase of S0 although the Voc decreased with the increase of S0 for the three cases. The reason was that the illumination intensity of the center of the cell decreased and that of the edge increased with the increase of S0, the power losses caused by series resistance decreased with illumination intensity, and the decrease magnitude of the power losses of the center of the cell was larger than the increase magnitude of the power losses of the edge. The series resistance of the VMJ cell was very small, thus the power losses caused by series resistance was very small and the change magnitude of FF was small. The FF was still as high as 0.767 even when S0 decreased to 0.1 mm and the area ratio of the sink to the cell decreased to 500X. The variation magnitudes of Jsc and FF were very small, thus the change trend of efficiency was very similar to that of Voc. The efficiency of the cell under 300 K increased from 18.6% to 19.5% and that of the cell with 2500X sink increased from 17.2% to 17.7% with the decrease of S0 from 2.4 mm to 0.1 mm. The efficiency of the cell with 500X sink increased from 14.5% to 14.6% when S0 decreased from 2.4 mm to 0.2 mm, and the efficiency decreased from 14.6% to 14.5% when S0 decreased from 0.2 mm to 0.1 mm. The FF, Voc and efficiency of silicon planar junction cell decreased with the increase of the degree of non-uniform illumination as mentioned in the introduction [14], thus silicon VMJ cell had better performance than silicon planar junction cell under 1D non-uniform illumination, and this advantage was mainly attributed to the low series resistance of VMJ cell. We only discussed the effect of 1D non-uniform illumination on the thermal and electrical performance of VMJ cell in this work, the Jsc and efficiency of the VMJ cell would decrease badly under 2D non-uniform illumination, because the sub-cells of the VMJ cell were series connected, the Jsc of the VMJ cell would be reduced to that of the sub-cell whose illumination intensity was the lowest. 4. Conclusions The thermal and electrical performance of silicon VMJ cell under 1D non-uniform illumination of 500 suns was calculated and analyzed in this work. It was found that the mean temperature of the cell increased with the degree of non-uniform illumination when the area ratio of the sink to the cell was 500X, and the mean temperature changed few when the area ratio was 2500X. The efficiency of the cell did not decrease with the increase of the degree of non-uniform illumination when the area ratio was 500X, and the efficiency increased with the degree of non-uniform illumination when the area ratio was 2500X. Thus, the silicon VMJ cell had better performance than silicon planar junction cell under 1D nonuniform illumination of 500 suns. Acknowledgement This work was supported by the National Natural Science Foundation of China (Grant Nos 61275040, 61274113, 11204212 and 61404091), and Program for New Century Excellent Talents in University (Grant No NCET-11-1064), and Tianjin Natural Science Foundation (Grant Nos 13JCYBJC15700, 13JCZDJC26100, 14JCZDJC31500 and 14JCQNJC00800), and Tianjin Science and Technology Developmental Funds of Universities and Colleges
(Grant Nos 20130701 and 20130702), and the State Key Laboratory of Functional Materials for Informatics (SKL201504).
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Thermal and electrical performance analysis of silicon vertical multijunction solar cell under non-uniform illumination Yupeng Xing a, *, Kailiang Zhang a, c, *, Jinshi Zhao a, Peide Han b a Tianjin Key Laboratory of Film Electronic and Communication Devices, School of Electronics Information Engineering, Tianjin University of Technology, Tianjin 300384, China b State Key Lab on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China c State Key Laboratory of Functional Materials for Informatic, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050 China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 April 2015 Received in revised form 13 December 2015 Accepted 16 December 2015 Available online xxx
The silicon vertical multi-junction (VMJ) solar cell has low costs and low series resistance, thus it has a good potential in concentration photovoltaics. However, there were few discussions about the thermal and electrical performance of silicon VMJ cell under non-uniform illumination. In this work, the thermal performance of silicon VMJ cell under 1D non-uniform illumination of 500 suns was calculated using finite element method first, and then the electrical performance of the cell was calculated using SPICE software based on the thermal simulation results. It was found that the mean temperature of the cell increased with the degree of non-uniform illumination when the area ratio of the sink to the cell was 500X, and the mean temperature changed few when the area ratio was 2500X. The efficiency of the cell did not decrease with the increase of the degree of non-uniform illumination when the area ratio was 500X, and the efficiency increased with the degree of non-uniform illumination when the area ratio was 2500X. Thus, the silicon VMJ cell had better performance than silicon planar junction cell under 1D nonuniform illumination of 500 suns. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Vertical multi-junction Non-uniform illumination Electrical performance Concentration
1. Introduction Photovoltaics (PV) is being paid more and more attention as a kind of renewable energy, lots of work is being done to decrease the costs of solar cells, the concentration photovoltaics (CPV) is becoming more and more competitive as a kind of third generation photovoltaics [1e5]. The silicon vertical multi-junction (VMJ) solar cell which has low series resistance and low costs has a good potential in CPV [6], the efficiency of the cell has reached 19.19% under 2480 suns [7], simulation results showed that the efficiency of the cell would reach close to 30% under 1000 suns after optimizing the device parameters of the cell [8e10]. However, above simulation work on VMJ cell was all based on the assumption that the VMJ cell was under uniform illumination, and non-uniform illumination
* Corresponding authors. Tianjin Key Laboratory of Film Electronic and Communication Devices, School of Electronics Information Engineering, Tianjin University of Technology, 391 West Binshui Road, Xiqing District, Tianjin City 300384, China. E-mail addresses: [email protected] (Y. Xing), [email protected] (K. Zhang). http://dx.doi.org/10.1016/j.renene.2015.12.045 0960-1481/© 2015 Elsevier Ltd. All rights reserved.
was inevitable in realistic CPV systems, the non-uniform illumination was caused by many factors, such as concentrator optics, improper tracking and so on [11]. Lots of experiment and simulation work has been done to analyze the effect of non-uniform illumination on the electrical and thermal performance of other solar cells [11]. The non-uniform illumination profiles on the cells were complex in realistic CPV systems, the Gaussian function was always used to characterize the profiles in theory. Vishnoi et al. studied the effect of non-uniform illumination on the electrical performance of silicon planar junction cell by simulation and experiment, they found that the short circuit current density (Jsc), open circuit voltage (Voc) and efficiency of the cell decreased with the area of the illuminated region of the cell, because the dark region of the cell worked as a load [12]. Luque et al. calculated and tested the thermal and electrical performance of silicon planar junction cell under 1D non-uniform illumination, they found that the temperature of the center of the cell increased, the Voc of the cell decreased a few, the fill factor (FF) and efficiency of the cell decreased badly under non-uniform illumination, because the electrical losses of the center of the cell caused by series resistance increased. They also found that the edge of the cell became less
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active under non-uniform illumination, because the illumination intensity of the edge decreased. The quality of the edge of the realistic cells was always poor, thus the non-uniform illumination also had positive effect [13]. Mellor et al. calculated the electrical performance of silicon planar junction cell under 1D non-uniform illumination using finite element method [14], Herrero et al. tested the electrical performance of III-V multi-junction cell under 2D non-uniform illumination, they also found that the Voc, FF and efficiency of the cell decreased with the increase of the degree of non-uniform illumination [15]. Araki et al. calculated the electrical performance of III-IV multi-junction cell under 1D non-uniform illumination using a distributed circuit model, they found that the Jsc of the cell decreased with the increase of the chromatic aberration of non-uniform illumination [16]. Sater et al. have made a 500X CPV system which used the VMJ cells as the receivers, they focused the sunlight reflected by many mirrors to two receivers. The final illumination patterns on the VMJ cells were line-focused although the system was point concentration, thus the illumination on the VMJ cells was non-uniform along one direction and nearly uniform along another vertical direction [17]. Segev et al. calculated the electrical performance of the module made of silicon VMJ cells under 2D non-uniform illumination, they found that the module made of silicon VMJ cells had an obvious advantage over the module made of silicon planar junction cells [18]. However, Segev et al. didn't discuss the electrical performance of a single VMJ cell under non-uniform illumination, and they didn't consider the heat generated in the cells [18]. The heat was also inevitable in realistic CPV systems [17], but there was very few simulation and experiment work about the effect of non-uniform illumination on the thermal and electrical performance of the VMJ cell. Thus the thermal and electrical performance of the VMJ cell under 1D non-uniform illumination of 500 suns was calculated and analyzed based on Segev et al.’s device parameters [18], and the performance of the cell under uniform illumination was also calculated to compare in this work. The temperature profiles of the VMJ cell under uniform and 1D non-uniform illumination were calculated using finite element method first, and then the electrical performance of the cell was calculated based on the temperature profiles using SPICE software, and the performance of the cell under 300 K room temperature was also calculated to compare. 2. Structure and models The passive cooling was used in this work as Sater et al. did [17], the VMJ cell was mounted on the center of an aluminum flat sink to simplify the simulation, as shown in Fig. 1 (a). The volume of the sink could be made smaller by using more complicated structure,
the insulating layer between the cell and sink in realistic CPV systems was ignored here. The sizes of the cell and sink varied freely in our simulation although the area ratio of the sink to the cell was always set close to the concentration ratio of the system, the thickness of the sink was set to 4 mm which was close to the thickness of the sinks in realistic CPV systems [19,20]. The cell and sink were assumed to be square to simplify the discussion, thus we used their side lengths to represent their sizes, and a quarter of the cell and sink was simulated in this work according to the symmetry of the cell and sink. The illumination on the cell was set to be uniform along X direction, which was the direction of current flowing in the cell, and the illumination was set to be only nonuniform along Y direction, which was perpendicular to X direction, thus the illumination intensity of each sub-cell of the VMJ cell was equal [17]. The Gaussian function was used to characterize the 1D non-uniform illumination profile as follows [14,21]:
3 2 y 5 ¼ Pm Am exp4 2S20 2
Pillumination
(1)
which indicated that the illumination intensity of the center of the cell was the highest and that of the edge was the lowest. The S0 in formula (1) was the shape factor, Am was the normalization factor, Pm was the average illumination intensity. The degree of nonuniform illumination increased with the decrease of S0, Am was adjusted with S0 to ensure that the total illumination intensity of the cell was not changed with S0 [14]. The Pm was determined by concentration ratio C as follows:
Pm ¼ P1sun C
(2)
where P1sun was 1000 W/m2 (1 sun), C was fixed to 500X which was close to the realistic concentration ratio of Sater et al.’s system [17]. The single diode model was used to characterize the basic electrical character of the VMJ cell under illumination as follows [18,22]:
J ¼ Jsc;1 C Jd
ðV þ IRs Þ 1 exp ðnkT=qÞ
(3)
where Jsc,1 was the Jsc normalized by concentration ratio, Jd was the dark current density, Rs was the series resistance, n was the ideality factor, k was the Boltzmann's constant, T was the absolute temperature and q was the charge of an electron. The device parameters of VMJ cell which were used by Segev et al. were used here, these parameters were introduced in detail in Segev et al.’s paper, the thickness and width of the sub-cell of the VMJ cell were set to
Fig. 1. The schematic of the VMJ cell mounted on the center of an aluminum flat sink (a), the circuit simulation model of the VMJ cell (b), D represents the diode character of the unit cell, Jsc represents the photocurrent of the unit cell and R represents the series resistance of the unit cell.
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79
Table 1 The thermal conductivities and heat capacities of the silicon VMJ cell and aluminum sink. Material
Thermal conductivity [W/(m$K)]
Heat capacity [J/(kg$K)]
Solar Cell-Silicon Sink-Aluminum Plate
163 201
703 900
50 mm and 40 mm respectively, the Jsc,1, Jd, Rs and n of the cell varied with illumination intensity [18]. The bulk power density of the heat generated in the cell was calculated as follows [23]:
Pheat ¼ Pillumination
ð1 hÞ t
(4)
where h was the efficiency and was obtained by calculating the JV curve of the cell using equation (3), T was set to 300 K when calculating the efficiency, t was the thickness of the cell, the incident light was assumed to be absorbed by the cell totally. The finite element method was used to solve the 3D equations of heat transmission and dissipation in the cell and sink to get the temperature profiles of the cell [23]. The thermal conductivities and heat capacities of the silicon VMJ cell and aluminum sink were listed in Table 1, the heat generated in the cell diffused to the sink, and then the heat was dissipated through thermal radiation of the front and back surfaces of the sink, the surface emissivity was set to 0.9 [23,24]. The surrounding temperature of the cell and sink was
set to 300 K, and the convection caused by wind in realistic CPV systems was ignored to simplify the discussion. Based on above temperature and illumination profiles, the SPICE software was used to calculate the electrical performance of VMJ cell. The VMJ cell was divided into sub-cells, and the sub-cells were divided into unit cells, as shown in Fig. 1 (b), formula (3) was also used to model the unit cells, the illumination of each unit cell was assumed to be uniform because the area of the unit cell was very small. Jd had the following relationship with temperature [25]:
Eg Jd fT ð3þg=2Þ exp kT
where g was constant, Eg was the bandgap of silicon and was fixed to 1.12 eV. The second exponential term played a major role compared to the first term in formula (5), thus the first term was ignored and the Jd was assumed to have a linear relationship with the second exponential term as follows:
Temperature [K]
380
Y direction [mm]
Mean temperature [K]
361.1 2.0
361.8 362.4
1.5
363.1 1.0
363.7
0.5 0.0 0.0
375 370 365 360 355
0.5
1.0
1.5
(5)
2
2.0
4 6 8 Cell length [mm]
X direction [mm]
(a)
10
(b) Mean temperature [K]
400 380 360 340 320 300 0.0
3
5.0x10
4
1.0x10
4
1.5x10
4
2.0x10
Area ratio of the sink to the cell
(c) Fig. 2. The temperature profile of the 4.8 mm long VMJ cell with 500X sink under uniform illumination of 500 suns (a), the mean temperatures of the cells with different sizes (b), the mean temperatures of the cell with the change of the area ratio of the sink to the cell (c). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Y. Xing et al. / Renewable Energy 90 (2016) 77e82
Temperature [K]
Temperature [K]
362.8 365.7 368.7
1.5
371.7 1.0
374.7
0.5 0.0 0.0
0.5
1.0
1.5
361.0 2.0
Y direction [mm]
Y direction [mm]
2.0
361.8 362.6
1.5
363.4 1.0
364.1
0.5 0.0 0.0
2.0
X direction [mm]
0.5
1.0
1.5
2.0
X direction [mm]
(a)
(b)
Mean temperature [K]
370 360 350
500X 2500X
340 330 320 0.0
0.5
1.0
1.5 2.0 S0 [mm]
2.5
3.0
(c) Fig. 3. The temperature profiles of the VMJ cell with 500X sink under non-uniform illumination with shape factors of 0.1 mm (a) and 2.4 mm (b), the mean temperatures of the cell with the change of S0 (c) (0.1 mm < S0 < 2.4 mm, the points of S0 ¼ 2.8 mm represented uniform illumination), the circular points represented the case of the cell with 500X sink and the triangular points represented the case of the cell with 2500X sink. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
exp Eg kT Jd ðT0 Þ
Jd ðTÞ ¼ exp Eg kT0
(6)
where T0 was 300 K, Segev et al.’s Jd(T0) parameters were used here [18]. The Jsc changed with temperature very few, thus the effect of temperature on Jsc was not considered in our simulation [22]. The decrease of efficiency caused by the increase of temperature was not very large compared to the original value of efficiency in our calculation range, thus we did not couple the thermal and electrical simulation together to simplify the calculation. 3. Results and discussions The temperature profiles of the VMJ cells with different sizes under uniform illumination of 500 suns were calculated first, the side length of the VMJ cell was between 1.2 mm and 9.6 mm, and the side length of the sink was changed with that of the cell to ensure that the area ratio of the sink to the cell was fixed to 500X, which was the concentration ratio of the system. The temperature profile of the 4.8 mm long cell was shown in Fig. 2 (a), it was centrosymmetric, the highest temperature of the center of the cell was 363.7 K and the lowest temperature of the edge was 361.1 K. The mean temperatures of the cells were calculated, the results were shown in Fig. 2 (b), it could be seen that the mean temperature decreased from 376.9 K to 357.3 K with the decrease of the length of the cell from 9.6 mm to 1.2 mm. The decrease magnitude of mean temperature also decreased with the length, the mean
temperature only decreased 2.2 K when the length decreased from 4.8 mm to 3.6 mm. The mean temperature of the cell was still as high as 357.3 K even when the length of the cell decreased to 1.2 mm if the area ratio was fixed to 500X. Thus, the temperature profiles of the cell with the change of sink size under uniform illumination of 500 suns were calculated, and the mean temperatures of the cell were calculated, as shown in Fig. 2 (c), the length of the cell was fixed to 4.8 mm, and the area ratio of the sink to the cell was between 250X and 20000X. The mean temperature of the cell decreased from 399.7 K to 311.7 K with the increase of area ratio from 250X to 20000X, the decrease magnitude of mean temperature also decreased with the increase of area ratio, the mean temperature only decreased 6.3 K when the area ratio increased from 2500X to 5000X. Above simulation results indicated that the mean temperature of the cell could be decreased to rather low value when the area of the sink was large enough. Based on above simulation results, the temperature profiles of the cell under 1D non-uniform illumination of 500 suns were calculated, the length of the cell was 4.8 mm, two area ratios of 500X and 2500X were considered, and the shape factor S0 was between 0.1 mm and 2.4 mm (the half of the length of the cell). The temperature profiles of the VMJ cell with 500 X sink were shown in Fig. 3 (a) and (b), the shape factors were 0.1 mm and 2.4 mm, respectively. The temperature profiles were not centrosymmetric, the variation magnitude of temperature along the direction of nonuniform illumination (Y direction) was larger than that along the direction of uniform illumination (X direction). The highest and lowest temperatures of the cell were 372.7 K and 362.8 K when S0
Y. Xing et al. / Renewable Energy 90 (2016) 77e82
was 0.1 mm, the highest and lowest temperatures were 364.1 K and 361 K when S0 was 2.4 mm, and the temperature profile of the cell with shape factor of 2.4 mm was close to that of the cell under uniform illumination, which was shown in Fig. 2 (a). The mean temperatures of the cell with the change of S0 were shown in Fig. 3 (c), the mean temperature of the cell with 500X sink decreased from 367 K to 362.7 K with the increase of S0 from 0.1 mm to 2.4 mm, and the decrease magnitude of mean temperature also decreased with the increase of S0, the mean temperature changed few and was close to that of the cell under uniform illumination when S0 was larger than 0.8 mm. The reason was that the illumination intensity of the center of the cell increased with the decrease of S0, the heat generated in the center of the cell increased although the total heat generated in the cell was not changed, it mean that the heat centralized to the center of the cell with the decrease of S0, and the sink was not large enough to dissipate the centralized heat sufficiently. The mean temperature of the cell with 2500X sink decreased a few from 323.5 K to 322 K with the increase of S0 from 0.1 mm to 2.4 mm, the mean temperature was much smaller than that of the cell with 500X sink. The reason was that the area of the sink was much larger, which made the centralized heat in the cell could be dissipated by the surface of the sink more sufficiently. Based on above temperature profiles, the Jsc, Voc, FF and efficiency of the VMJ cell under uniform and 1D non-uniform illumination of 500 suns were calculated using SPICE software, the electrical performance of the cell under 300 K room temperature was also calculated to compare. The results were shown in Fig. 4, the Jsc of the cell was multiplied by the sub-cell number of the cell
81
and was normalized by concentration ratio, the Voc of the cell was divided by the sub-cell number. The Jsc increased a few from 28.1 mA/cm2 to 28.4 mA/cm2 with the decrease of S0 from 2.4 mm to 0.1 mm although the total illumination intensity of the cell was not changed. The reason was that the illumination intensity of the center of the cell increased and that of the edge decreased with the decrease of S0, the Jsc normalized by concentration ratio increased a few with illumination intensity [26], and the Jsc increase of the center of the cell was larger than the Jsc decrease of the edge. The mean temperature of the cell with 500X sink was larger than that of the cell with 2500X sink, and they were both larger than 300 K in our calculation range as mentioned above. The Voc of the cell decreased with the increase of mean temperature, because Jd increased with the increase of temperature. The Voc of the cell under 300 K room temperature increased from 0.8 V to 0.828 V and the Voc of the cell with 2500X sink increased from 0.752 V to 0.77 V with the decrease of S0 from 2.4 mm to 0.1 mm, the Voc changed few when S0 was larger than 0.8 mm for the two cases. The illumination intensity of the center of the cell increased and that of the edge decreased with the decrease of S0, thus the Jsc and Voc of the unit cells near the center increased with illumination intensity linearly and logarithmically, and those near the edge decreased. The Jsc increase of the unit cells near the center was larger than the Jsc decrease of the unit cells near the edge with the decrease of S0, the unit cells of a sub-cell were connected in parallel, and the sub-cells were connected in series as shown in Fig. 1 (b), thus the Voc of the cell increased for above two cases. But the Voc of the cell with 500X sink only increased from 0.663 V to 0.667 V, the increase magnitude
0.84 0.81 0.78
28.3 Voc [V]
2
Jsc [mA/cm ]
28.4
28.2 28.1 28.0 0.0
0.75
300 K 500X 2500X
0.72 0.69
0.5
1.0
1.5 2.0 S0 [mm]
2.5
0.66 0.0
3.0
0.5
1.0
(a)
3.0
2.5
3.0
(b) 19 Efficiency [%]
0.82 0.81 FF
2.5
20
0.83
0.80 0.79 0.78
18 17 16 15
0.77 0.76 0.0
1.5 2.0 S0 [mm]
0.5
1.0
1.5 2.0 S0 [mm]
(c)
2.5
3.0
14 0.0
0.5
1.0
1.5 2.0 S0 [mm]
(d)
Fig. 4. The Jsc (a), Voc (b), FF (c) and efficiency (d) of the VMJ cell with the change of S0 (0.1 mm < S0 < 2.4 mm, the points of S0 ¼ 2.8 mm represented uniform illumination), the circular points represented the case of the cell with 500X sink, the triangular points represented the case of the cell with 2500X sink and the square points represented the case of the cell under 300 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Y. Xing et al. / Renewable Energy 90 (2016) 77e82
was much smaller than that of the cell with 2500X sink, because the mean temperature of the cell with 500X sink increased with the decrease of S0 as mentioned above, Jd increased with temperature, which decreased the increase magnitude of Voc. The FF of the cell increased with the decrease of mean temperature, because the Voc increased with the decrease of mean temperature. The FF of the cell increased a few with the increase of S0 although the Voc decreased with the increase of S0 for the three cases. The reason was that the illumination intensity of the center of the cell decreased and that of the edge increased with the increase of S0, the power losses caused by series resistance decreased with illumination intensity, and the decrease magnitude of the power losses of the center of the cell was larger than the increase magnitude of the power losses of the edge. The series resistance of the VMJ cell was very small, thus the power losses caused by series resistance was very small and the change magnitude of FF was small. The FF was still as high as 0.767 even when S0 decreased to 0.1 mm and the area ratio of the sink to the cell decreased to 500X. The variation magnitudes of Jsc and FF were very small, thus the change trend of efficiency was very similar to that of Voc. The efficiency of the cell under 300 K increased from 18.6% to 19.5% and that of the cell with 2500X sink increased from 17.2% to 17.7% with the decrease of S0 from 2.4 mm to 0.1 mm. The efficiency of the cell with 500X sink increased from 14.5% to 14.6% when S0 decreased from 2.4 mm to 0.2 mm, and the efficiency decreased from 14.6% to 14.5% when S0 decreased from 0.2 mm to 0.1 mm. The FF, Voc and efficiency of silicon planar junction cell decreased with the increase of the degree of non-uniform illumination as mentioned in the introduction [14], thus silicon VMJ cell had better performance than silicon planar junction cell under 1D non-uniform illumination, and this advantage was mainly attributed to the low series resistance of VMJ cell. We only discussed the effect of 1D non-uniform illumination on the thermal and electrical performance of VMJ cell in this work, the Jsc and efficiency of the VMJ cell would decrease badly under 2D non-uniform illumination, because the sub-cells of the VMJ cell were series connected, the Jsc of the VMJ cell would be reduced to that of the sub-cell whose illumination intensity was the lowest. 4. Conclusions The thermal and electrical performance of silicon VMJ cell under 1D non-uniform illumination of 500 suns was calculated and analyzed in this work. It was found that the mean temperature of the cell increased with the degree of non-uniform illumination when the area ratio of the sink to the cell was 500X, and the mean temperature changed few when the area ratio was 2500X. The efficiency of the cell did not decrease with the increase of the degree of non-uniform illumination when the area ratio was 500X, and the efficiency increased with the degree of non-uniform illumination when the area ratio was 2500X. Thus, the silicon VMJ cell had better performance than silicon planar junction cell under 1D nonuniform illumination of 500 suns. Acknowledgement This work was supported by the National Natural Science Foundation of China (Grant Nos 61275040, 61274113, 11204212 and 61404091), and Program for New Century Excellent Talents in University (Grant No NCET-11-1064), and Tianjin Natural Science Foundation (Grant Nos 13JCYBJC15700, 13JCZDJC26100, 14JCZDJC31500 and 14JCQNJC00800), and Tianjin Science and Technology Developmental Funds of Universities and Colleges
(Grant Nos 20130701 and 20130702), and the State Key Laboratory of Functional Materials for Informatics (SKL201504).
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