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Effect of concentration distribution on cell performance for low-concentrators with a three-dimensional lens
Solar Energy Matmials and Solar Cells
ELSEVIER
Solar Energy Materials and Solar Cells 47 (1997) 339-344
Effect of concentration distribution on cell performance for low-concentrators with a three-dimensional lens S. Goma*, K. Yoshioka, T. Saitoh Tokyo A&T University. 2-24-16 Nakamachi, Koganei,Tokyo 184, Japan
Abstract The effect of concentration distribution on the performance of a static concentrator cell with a new three-dimensional lens was investigated to design an optimum cell structure. A concentration distribution of this lens was simulated using a ray-tracing method, Based on these results, fill factors were calculated as a function of series resistance and irradiance to clarify the effect of concentration distribution. The effect of concentration distribution appeared when series resistance is larger than 0.2 f~ cm z and irradiance is higher than 30 mW/cm 2. Keywords: Three-dimensional lens; Half acceptance angle; Low-concentration; Concentration
distribution
1. Introduction Recently, conversion efficiency of c-Si solar cells has greatly been improved, but m o r e cost reduction is to be achieved. A shortage of Si feedstock is also pointed out. O n e of the ideas to solve these issues is the development of c o n c e n t r a t o r modules, which enables low-cost P V modules by less use of costly solar cells. Especially, since global solar radiation in J a p a n includes m u c h diffuse sunlight, a low-concentration static module is more a d v a n t a g e o u s than a high-concentration, tracking one. F r o m the above b a c k g r o u n d , the authors have studied static c o n c e n t r a t o r modules with two-dimensional (2D) and three-dimensional (3D) lenses [1, 2]. But the 3D lens
* Corresponding author. 0927-0248/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S 0 9 2 7 - 0 2 4 8 ( 9 7 ) 0 0 0 6 0 - 3
340
S. Goma et al./Solar Energy Materials and Solar Cells 47 (1997) 339-344
had much optical loss around the four corners of the entry aperture for normal incidence rays. So, an improved 3D lens was devised by rounding the four corners of the 3D lens mentioned above [3]. In addition to development of the lens design, it is also important to design an optimum cell structure suitable for the concentrator module. In this paper, concentration distribution of irradiance was calculated using a raytracing method and compared with measured data. Using the results, fill factors were calculated under non-uniform and uniform light intensity distributions as a function of series resistance and irradiance to compare with measured fill factors.
2. Concentration distribution of a new 3 D lens
The 3D lens was designed using the cross sections of the 2D lenses designed at half acceptance angles of 30 ° and 45' in the north south and east-west directions. Furthermore, the new 3D lens was devised by rounding the four corners of the 3D lens [2, 3]. Concentration distribution on an exit aperture of the new 3D lens was calculated at various incident light angles by computer simulation using the raytracing method. For the new 3D lens, the ray-tracing was carried out for each cross section cut with a constant interval along an east-west direction. As an example, Fig. 1 shows ray trace illustrations for normal incident rays. Measurement was also carried out under a solar simulator for an experimental model fabricated by attaching the 3D lens to a photodiode array using silicone resin. In Fig. 2, calculated and measured concentration distributions are drawn for normal incident rays. A good agreement was obtained between the calculated and measured results. As seen from the figure, the collected rays were distributed non-uniformly like "X". The highest light intensity was about 8 suns along middle positions of the X pattern.
3. Determination of cell parameters to calculate fill factor
To investigate the effect of concentration distribution, two kinds of 20 x 30 m m 2 solar cells with different series resistance (R~) were prepared. The finger pitches of cells # 1 and # 2 were 1 and 3 mm. The parameters of the solar cells were determined based on results obtained from I - V curve fitting using Eq. (1). Saturation current density (Jo) could be calculated by Eq. (2):
J = JL -- Jo
exp (
J~ + exp
NakT
J - 1J
R f l s ¢ - Vo¢ Rsh - exP~N--~)
Rsh
(1)
S. Goma et al./Solar Energy Materials and Solar Cells 47 (1997) 339-344
I
341
Incidentlight
View angle
Section 1
Section 1
Fig. 1. Ray traces inside the lens at normal incidence.
Calculation
E E r. ._o
~"
Measurement 8
7 s
4
13 c-
3
"t~
7
8 ~
~
2
o
Z
--,I o CO
2
6 10 14 18'22-'26-~-30 (Sun) West-East direction (mm)
~::::3 O
o0
10T14'18'22
26
-
6 5 4 3 2 1 0
30 (Sun)
West-East direction (mm)
Fig. 2. Calculated and measured light intensity distribution for the new 3D lens at normal incidence.
where J L is the photocurrent density, Nd is the diode factor and Rsh is the shunt resistance. Short circuit current density (J~c) and open circuit voltage (Voc) were obtained by measurement of cell performance. Mean squared error (MSE) was defined by
MSE= ~N~__, 1 : [(J _ J(N))sin{tan_ 1 ( - ddJJJ] V~'(T '
(3)
where L is the number of I-V data. The parameters of N d , Rs and Rsh were obtained at minimum MSE [4]. Fitted Rs agreed well with values calculated by Meier's method [5]. Based on the above results, parameters of an equivalent circuit were determined by fitting and Meier's method. As shown in Fig. 3, fill factors (FF) of the concentrator cell were calculated using the equivalent circuit model including cell segments, Ns connected in parallel. So values of resistances must be multiplied by Ns and current values must be divided by Ns. Furthermore, they must be normalized at 1 segment size. N~ is the number of segments defined as cell size (600 mm2)/segment size (a number of
342
S. Goma et al./Solar Energy. Materials and Solar Cells 47 (1997) 339 344
•
R0
1 segment~,
4 --
lout l
',
72~7c~iR
r;';-::"!i::?: "
,7
....
,,: }"
....
Vout
LS.>qmm
finger pitch - - -
"[ Rf= 1.34xl0 2 ~2, Rb= 1.61x10 3 for cell //1 and//2
Fig. 3. Equivalent circuit to calculate the fill factor values of the concentrator cells.
Table 1 The parameters to calculate the fill factor of the I segment (/ell #1
Cell # 2
Finger pitch
1 mm
3 mm
N, Na R~ R~h! Io
600 1.28 35.38 ~1 2250 kf2 1.359xl0
200 1.28 26.58 fl 750 kfl 4.348X10
IIA
11A
fingers x 1 mm2). Thus, Rsh and I'o used in the equivalent circuit are obtained by N~ R;h = R~h x cellsize'
(4)
cellsize Ii~ = Jo x - N~
(5)
All segments are connected each other through fingers or busbars. R~ used in the equivalent circuit is a series resistance for a 1 segment except for finger and busbar losses. From Meier's method, R'~ was given by
(1
R~= ~b2ps+pbl
)
×N~,
(6)
where b is the half finger pitch, Ps is the sheet resistance (70 D/C])and Pb is the resistivity of base (10 D cm). Furthermore, finger and busbar resistances (Rf, Rb) were obtained by a four-point probe measurement. The parameters of 1 segment for cell # 1 and # 2 used in equivalent circuit were shown in Table 1.
S. Goma et al./Solar Energy Materials and Solar Cells 47 (1997) 339 344
343
4. Effect of concentration distribution on cell performance The F F values of the concentrator cells can be obtained from simulated I - V curves using equivalent circuit as seen Fig. 3 and cell parameters as seen in Table 1 by Simulation Program with Integrated Circuit Emphasis (SPICE). In this research, F F values were calculated as a function of Rs under real, non-uniform and uniform conditions to investigate the effect of non-uniform concentration distribution. Then, p h o t o c u r r e n t (/ph) obtained as Is¢ from the measurement was allotted to each segment cell proportionally based on calculated concentration distribution. For comparison, measurements were carried out for cells # 1 and # 2 under a solar simulator at 100 mW/cm 2, AM 1.5. As seen from Fig. 4, good agreement was obtained between the calculated and measured results at the non-uniform condition. Calculated F F of the cell # 1 under the uniform condition did not make a much difference from the uniform condition. But F F of cell # 2 was very different from the non-uniform condition. As a result, the effect of concentration distribution appeared for Rs larger than 0.2 ~ c m 2. Similarly, the F F of the cell # 2 with a wider finger pitch was calculated and measured under various incident light intensities. As seen from Fig. 5, the measured results agreed well with the values obtained by calculation. Furthermore, the effect of non-uniform distribution tended to be smaller with the decrease in irradiance and disappeared under 30 mW/cm 2.
5. Summary Concentration distribution of incident light for a new 3D lens was calculated using a ray-tracing method. G o o d agreement was obtained between simulation and measurement. Based on the above results, F F was calculated as a function of Rs and irradiance under the real, non-uniform and uniform conditions. The calculated FF under non-uniform condition agreed well with measured one. As a result, the effect of concentration distribution appeared for the Rs larger than 0.2 ~2 cm z and irradiance
0.85
Uniform
0.80 0.75 LL 14.
0.70 0.65 0.60 0.55 0.50
Non-uniformo Measured
T~,\ ,'~
0.1
1 Rs (Q.em2)
Fig. 4. FF vs. Rs for concentrator modules with non-uniform and uniform light distribution with an irradiance of 100 mW/cm 2.
344
S. Goma et al./'Solar Energy. Materials and Solar Cells 47 (1997) 339-.344 0.85 Uniform
0.80 0.75 i.i.
0.70 0.65 0.60
Non-uniform o Measured
0,55 0.50
I
20
I
I
I
40
60
80
1O0
Incident light intensity (mW/cm 2)
Fig. 5. FF vs. incident light intensity for cell #2 with a finger pitch of 3 mm and R~ of 0.89 ~ cm 2.
higher than 30 m W / c m 2. To reduce the effect of c o n c e n t r a t i o n distribution, it is necessary to design a solar cell with 8~ less than 0.2 ~ cm 2.
Acknowledgements This work was supported by the New Energy a n d I n d u s t r i a l T e c h n o l o g y Development O r g a n i z a t i o n as a part of the New S u n s h i n e Project of the Ministry of I n t e r n a t i o n a l T r a d e a n d Industry. The a u t h o r s also would like to express our t h a n k s to Mr. T. N u n o i a n d T. M a c h i d a of S H A R P Corp. for supplying Si solar cells for our experiments.
References [1] K. Yoshioka, S. Goma, T. Saitoh, The J. Japan Solar Energy Soc. 22 (5) (1996) 47. [2] K. Yoshioka, K. Endoh, A. Suzuki, N. Ohe, T. Saitoh, Proc. 13th European PV Solar Energy Conf., II, 1995, pp. 2373-2376. [3] K. Yoshioka, K. Nakamura, S. Goma, T. Saitoh, Tech. Digest of9th PVSEC, 1996, A-V-12. [4] J.P. Charles, I. Mekkaoui-Alaoui, G. Bordure, Solid-State Electron. 28 (8) (1985) 807. [5] D.L. Meier, D.K. Schroder, IEEE Trans. Electron Devices ED- 31 (5) (1984) 647.
ELSEVIER
Solar Energy Materials and Solar Cells 47 (1997) 339-344
Effect of concentration distribution on cell performance for low-concentrators with a three-dimensional lens S. Goma*, K. Yoshioka, T. Saitoh Tokyo A&T University. 2-24-16 Nakamachi, Koganei,Tokyo 184, Japan
Abstract The effect of concentration distribution on the performance of a static concentrator cell with a new three-dimensional lens was investigated to design an optimum cell structure. A concentration distribution of this lens was simulated using a ray-tracing method, Based on these results, fill factors were calculated as a function of series resistance and irradiance to clarify the effect of concentration distribution. The effect of concentration distribution appeared when series resistance is larger than 0.2 f~ cm z and irradiance is higher than 30 mW/cm 2. Keywords: Three-dimensional lens; Half acceptance angle; Low-concentration; Concentration
distribution
1. Introduction Recently, conversion efficiency of c-Si solar cells has greatly been improved, but m o r e cost reduction is to be achieved. A shortage of Si feedstock is also pointed out. O n e of the ideas to solve these issues is the development of c o n c e n t r a t o r modules, which enables low-cost P V modules by less use of costly solar cells. Especially, since global solar radiation in J a p a n includes m u c h diffuse sunlight, a low-concentration static module is more a d v a n t a g e o u s than a high-concentration, tracking one. F r o m the above b a c k g r o u n d , the authors have studied static c o n c e n t r a t o r modules with two-dimensional (2D) and three-dimensional (3D) lenses [1, 2]. But the 3D lens
* Corresponding author. 0927-0248/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S 0 9 2 7 - 0 2 4 8 ( 9 7 ) 0 0 0 6 0 - 3
340
S. Goma et al./Solar Energy Materials and Solar Cells 47 (1997) 339-344
had much optical loss around the four corners of the entry aperture for normal incidence rays. So, an improved 3D lens was devised by rounding the four corners of the 3D lens mentioned above [3]. In addition to development of the lens design, it is also important to design an optimum cell structure suitable for the concentrator module. In this paper, concentration distribution of irradiance was calculated using a raytracing method and compared with measured data. Using the results, fill factors were calculated under non-uniform and uniform light intensity distributions as a function of series resistance and irradiance to compare with measured fill factors.
2. Concentration distribution of a new 3 D lens
The 3D lens was designed using the cross sections of the 2D lenses designed at half acceptance angles of 30 ° and 45' in the north south and east-west directions. Furthermore, the new 3D lens was devised by rounding the four corners of the 3D lens [2, 3]. Concentration distribution on an exit aperture of the new 3D lens was calculated at various incident light angles by computer simulation using the raytracing method. For the new 3D lens, the ray-tracing was carried out for each cross section cut with a constant interval along an east-west direction. As an example, Fig. 1 shows ray trace illustrations for normal incident rays. Measurement was also carried out under a solar simulator for an experimental model fabricated by attaching the 3D lens to a photodiode array using silicone resin. In Fig. 2, calculated and measured concentration distributions are drawn for normal incident rays. A good agreement was obtained between the calculated and measured results. As seen from the figure, the collected rays were distributed non-uniformly like "X". The highest light intensity was about 8 suns along middle positions of the X pattern.
3. Determination of cell parameters to calculate fill factor
To investigate the effect of concentration distribution, two kinds of 20 x 30 m m 2 solar cells with different series resistance (R~) were prepared. The finger pitches of cells # 1 and # 2 were 1 and 3 mm. The parameters of the solar cells were determined based on results obtained from I - V curve fitting using Eq. (1). Saturation current density (Jo) could be calculated by Eq. (2):
J = JL -- Jo
exp (
J~ + exp
NakT
J - 1J
R f l s ¢ - Vo¢ Rsh - exP~N--~)
Rsh
(1)
S. Goma et al./Solar Energy Materials and Solar Cells 47 (1997) 339-344
I
341
Incidentlight
View angle
Section 1
Section 1
Fig. 1. Ray traces inside the lens at normal incidence.
Calculation
E E r. ._o
~"
Measurement 8
7 s
4
13 c-
3
"t~
7
8 ~
~
2
o
Z
--,I o CO
2
6 10 14 18'22-'26-~-30 (Sun) West-East direction (mm)
~::::3 O
o0
10T14'18'22
26
-
6 5 4 3 2 1 0
30 (Sun)
West-East direction (mm)
Fig. 2. Calculated and measured light intensity distribution for the new 3D lens at normal incidence.
where J L is the photocurrent density, Nd is the diode factor and Rsh is the shunt resistance. Short circuit current density (J~c) and open circuit voltage (Voc) were obtained by measurement of cell performance. Mean squared error (MSE) was defined by
MSE= ~N~__, 1 : [(J _ J(N))sin{tan_ 1 ( - ddJJJ] V~'(T '
(3)
where L is the number of I-V data. The parameters of N d , Rs and Rsh were obtained at minimum MSE [4]. Fitted Rs agreed well with values calculated by Meier's method [5]. Based on the above results, parameters of an equivalent circuit were determined by fitting and Meier's method. As shown in Fig. 3, fill factors (FF) of the concentrator cell were calculated using the equivalent circuit model including cell segments, Ns connected in parallel. So values of resistances must be multiplied by Ns and current values must be divided by Ns. Furthermore, they must be normalized at 1 segment size. N~ is the number of segments defined as cell size (600 mm2)/segment size (a number of
342
S. Goma et al./Solar Energy. Materials and Solar Cells 47 (1997) 339 344
•
R0
1 segment~,
4 --
lout l
',
72~7c~iR
r;';-::"!i::?: "
,7
....
,,: }"
....
Vout
LS.>qmm
finger pitch - - -
"[ Rf= 1.34xl0 2 ~2, Rb= 1.61x10 3 for cell //1 and//2
Fig. 3. Equivalent circuit to calculate the fill factor values of the concentrator cells.
Table 1 The parameters to calculate the fill factor of the I segment (/ell #1
Cell # 2
Finger pitch
1 mm
3 mm
N, Na R~ R~h! Io
600 1.28 35.38 ~1 2250 kf2 1.359xl0
200 1.28 26.58 fl 750 kfl 4.348X10
IIA
11A
fingers x 1 mm2). Thus, Rsh and I'o used in the equivalent circuit are obtained by N~ R;h = R~h x cellsize'
(4)
cellsize Ii~ = Jo x - N~
(5)
All segments are connected each other through fingers or busbars. R~ used in the equivalent circuit is a series resistance for a 1 segment except for finger and busbar losses. From Meier's method, R'~ was given by
(1
R~= ~b2ps+pbl
)
×N~,
(6)
where b is the half finger pitch, Ps is the sheet resistance (70 D/C])and Pb is the resistivity of base (10 D cm). Furthermore, finger and busbar resistances (Rf, Rb) were obtained by a four-point probe measurement. The parameters of 1 segment for cell # 1 and # 2 used in equivalent circuit were shown in Table 1.
S. Goma et al./Solar Energy Materials and Solar Cells 47 (1997) 339 344
343
4. Effect of concentration distribution on cell performance The F F values of the concentrator cells can be obtained from simulated I - V curves using equivalent circuit as seen Fig. 3 and cell parameters as seen in Table 1 by Simulation Program with Integrated Circuit Emphasis (SPICE). In this research, F F values were calculated as a function of Rs under real, non-uniform and uniform conditions to investigate the effect of non-uniform concentration distribution. Then, p h o t o c u r r e n t (/ph) obtained as Is¢ from the measurement was allotted to each segment cell proportionally based on calculated concentration distribution. For comparison, measurements were carried out for cells # 1 and # 2 under a solar simulator at 100 mW/cm 2, AM 1.5. As seen from Fig. 4, good agreement was obtained between the calculated and measured results at the non-uniform condition. Calculated F F of the cell # 1 under the uniform condition did not make a much difference from the uniform condition. But F F of cell # 2 was very different from the non-uniform condition. As a result, the effect of concentration distribution appeared for Rs larger than 0.2 ~ c m 2. Similarly, the F F of the cell # 2 with a wider finger pitch was calculated and measured under various incident light intensities. As seen from Fig. 5, the measured results agreed well with the values obtained by calculation. Furthermore, the effect of non-uniform distribution tended to be smaller with the decrease in irradiance and disappeared under 30 mW/cm 2.
5. Summary Concentration distribution of incident light for a new 3D lens was calculated using a ray-tracing method. G o o d agreement was obtained between simulation and measurement. Based on the above results, F F was calculated as a function of Rs and irradiance under the real, non-uniform and uniform conditions. The calculated FF under non-uniform condition agreed well with measured one. As a result, the effect of concentration distribution appeared for the Rs larger than 0.2 ~2 cm z and irradiance
0.85
Uniform
0.80 0.75 LL 14.
0.70 0.65 0.60 0.55 0.50
Non-uniformo Measured
T~,\ ,'~
0.1
1 Rs (Q.em2)
Fig. 4. FF vs. Rs for concentrator modules with non-uniform and uniform light distribution with an irradiance of 100 mW/cm 2.
344
S. Goma et al./'Solar Energy. Materials and Solar Cells 47 (1997) 339-.344 0.85 Uniform
0.80 0.75 i.i.
0.70 0.65 0.60
Non-uniform o Measured
0,55 0.50
I
20
I
I
I
40
60
80
1O0
Incident light intensity (mW/cm 2)
Fig. 5. FF vs. incident light intensity for cell #2 with a finger pitch of 3 mm and R~ of 0.89 ~ cm 2.
higher than 30 m W / c m 2. To reduce the effect of c o n c e n t r a t i o n distribution, it is necessary to design a solar cell with 8~ less than 0.2 ~ cm 2.
Acknowledgements This work was supported by the New Energy a n d I n d u s t r i a l T e c h n o l o g y Development O r g a n i z a t i o n as a part of the New S u n s h i n e Project of the Ministry of I n t e r n a t i o n a l T r a d e a n d Industry. The a u t h o r s also would like to express our t h a n k s to Mr. T. N u n o i a n d T. M a c h i d a of S H A R P Corp. for supplying Si solar cells for our experiments.
References [1] K. Yoshioka, S. Goma, T. Saitoh, The J. Japan Solar Energy Soc. 22 (5) (1996) 47. [2] K. Yoshioka, K. Endoh, A. Suzuki, N. Ohe, T. Saitoh, Proc. 13th European PV Solar Energy Conf., II, 1995, pp. 2373-2376. [3] K. Yoshioka, K. Nakamura, S. Goma, T. Saitoh, Tech. Digest of9th PVSEC, 1996, A-V-12. [4] J.P. Charles, I. Mekkaoui-Alaoui, G. Bordure, Solid-State Electron. 28 (8) (1985) 807. [5] D.L. Meier, D.K. Schroder, IEEE Trans. Electron Devices ED- 31 (5) (1984) 647.