Influence of Shading on Solar Cell Parameters and Modelling Accuracy Improvement of PV Modules with Reverse Biased Solar Cells
Round 1
Reviewer 1 Report
The authors employed the well-built models in the community, adding the improvement in varying parameters, to analyze the precision of a model in fitting a single Si solar cell and a Si PV model containing two series and total 36 cells. The whole manuscript provides a clear and well-organized structure and presents both experimental data and fitted results using different varied PV parameters. The authors concluded the fitting precision of the models to a single cell and a PV model with different shaded cells, which came from solid evidence. I agree to publish with minor changes.
In Line 177 and 184, there are "three days" and "two day's". Do they mean the same sets of experiments?
Author Response
Reviewer 1:
1.1. In Line 177 and 184, there are "three days" and "two day's". Do they mean the same sets of experiments?
Response 1.1:
Thanks for raising this point. They are two different sets of experiments. We have revised the manuscript and hope it is clearer (see lines 185-186 on page 5 and line 200 on page 6). Please see below for explanation.
The description associated with Line 177 (old version) explains a specific experiment carried out to determine the probable error of I-V measurements using the equipment of this study. The error bars shown in Figures 5 and 6 were determined from this experiment.
The description associated with Line 184 (old version) explains the additional efforts that have been taken to ensure the repeatability of the shading experiments and the results were used to determine the average values only.
Reviewer 2 Report
1. It is necessary to finalize the review in the Introduction . Lines 85 and 86 simply list similar works. It is necessary to cite the differences and advantages of the presented study from similar studies, to compare results.
2. Was the experiment carried out under real conditions, when the shading of the module changes over time? Has it been investigated how the power generation of the module will change during the day under partial dynamic shading?
Author Response
Reviewer 2:
2.1. It is necessary to finalize the review in the Introduction. Lines 85 and 86 simply list similar works. It is necessary to cite the differences and advantages of the presented study from similar studies, to compare results.
Response 2.1:
Thank the reviewer for good suggestion. We have revised this part in accordance with the reviewer’s suggestions (see lines 86-98 on pages 2-3).
2.2. Was the experiment carried out under real conditions, when the shading of the module changes over time? Has it been investigated how the power generation of the module will change during the day under partial dynamic shading?
Response 2.2:
The experiments were performed under a solar simulator as described in Section 2.3 (see lines 147-151 and Figure 4 on page 5). This is because the experiments must be carried out under a well-defined steady state light irradiation in order to draw valid conclusions. The experiment under real conditions is outside the scope of this investigation.
Reviewer 3 Report
The manuscript contains interesting results on the influence of shading on solar cell parameters.
However, there are some comments to improve the manuscript:
Fig. 1 - Currents ID and Ish must be marked on the scheme.
Fig. 1 - Voltage arrow incorrectly marked - there should be only one arrowhead.
line 59: Equation (1), should be: I = Iph - ID - Ish = ....
line 112: shoud be: W/m∙K
Fig. 2 - Should be: "Insolated water tubes", small letter "w"
lines: 123, 130, 135, 136, 289, 321, 327, 343: Unify the nomenclature of bypass diode (sometimes is by-pass diode, sometimes bypass diode)
line 145: Present the power density distribution on the module (in the form of a table). How spatial non-uniformity was determined? Present the equation.
Such spatial non-uniformity may mean that individual solar cells could be irradited with different intensities by up to 40% or even more. This will have a significant impact on the results of the research. The research for the PV module must be repeated for the system ensuring greater spatial uniformity of irradiation. The spatial non-uniformity of irradiation equal to 18.9% is unacceptable.
line 147: What mean: "noticeable distortion to the I-V curves ...." ? How it was checked?
Lines 145-151: The current flowing through a chain of series connected cells is determined by the current generated by the least efficient solar cell in that chain (i.e. the lowest current solar cell or the shaded solar cell). Therefore, no difference was noticed in the shading of the different solar cells in the chain. Results of the research confirming the conclusions presented in lines 145-151 should be presented.
lines 174-175: Should be "solar cell temperature".
Line 180: Present shadings in the figure. Lack of information how shading cases of solar cell (25%, 50%, 75%) was verified? How were the exact shading levels obtained for a small size solar cell?
Lines 196-197: "...was investigated under reduced irradiance (instead of shading)." It is not the same, please refer to work [40], which presents the convergence of the influence of shading and irradiance on the solar cell parameters.
Fig. 5 and 6: Polynomial functions have not been plotted in the graphs: 5a-5d, 6c, 6d, 6f.
Fig. 5c: The results of the parameter n>2 must be commented.
Table 1: The data in the table are not consistent with the measurement data presented in Figures 5a-5d. Should be respectively: 0.39, 0.62, 1.85, 0.13, 23.92!
Fig. 7: Curves were drawn based on incorrect data, because data in table 1 are incorrect.
Fig. 7: Present the coefficient of compliance of the measured and calculated data.
Lines 261-266: Provide conclusions after recalculation curves in figure 7.
Fig. 8: The electrical sheme shown in figure 8 is incorrect and meaningless! String-1 does not transfer energy to the output. Cells in PV modules are not connected like that!
Lines 337-338: The values are not in good agreement - currents differ by 18% and voltages by 8%. Additionally in opposite directions - the measured current is lower and the measured voltage is higher than the datasheet parameters.
Table 2: Ipho is the same as Isc ? What with ID and Ish ?
Table 4. Present shading cases 1-6 in the figure. How was it verified?
Fig. 9-11: The measurement results of figures 8-11 do not correspond to the electrical scheme of figure 8.
Fig. 9-11: The measurement results of figures 8-11 do not correspond to the electrical scheme of figure 8.
Lines 428-430: Present the coefficient of compliance of the measured and calculated data in figures 9-11.
Fig 9-11: Fig. 7: Present the coefficient of compliance of measured and calculated data.
Lines 475-594: Year of publication of a book, article, or references sometimes written in plain font (e.g. 1,2,14) and sometimes in bold (3, 4,5). It should be unify.
Author Response
Reviewer 3:
3.1. Fig. 1 - Currents ID and Ish must be marked on the scheme.
Response 3.1:
The currents ID and Ish have now been included (see Figure 1 on page 2).
3.2. Fig. 1 - Voltage arrow incorrectly marked - there should be only one arrowhead.
Response 3.2:
The voltage arrow has been corrected as suggested (see Figure 1 on page 2).
3.3. Line 59: Equation (1), should be: I = Iph - ID - Ish =
Response 3.3:
The equation (1) has been modified as suggestion and the corresponding description was provided (see lines 59-62 on page 2).
3.4. line 112: shoud be: W/m∙K
Response 3.4:
The correction has been made as suggested (see line 119 on page 3).
3.5. Fig. 2 - Should be: "Insolated water tubes", small letter "w"
Response 3.5:
The correction has been made as suggested (see Figure 2 on page 4).
3.6. lines: 123, 130, 135, 136, 289, 321, 327, 343: Unify the nomenclature of bypass diode (sometimes is by-pass diode, sometimes bypass diode).
Response 3.6:
The “by-pass” in line 123 (old version) has been changed to “bypass” (see line 131 on page 4 in this revised version) to ensure the consistency.
3.7. line 145: Present the power density distribution on the module (in the form of a table). How spatial non-uniformity was determined? Present the equation.
Response 3.7:
An explanation has been added as Appendix A to describe how the spatial non-uniformity was determined (see lines 499-514 on pages 16-17). An in-text pointer is also provided (see line 153 on page 5).
3.8. Such spatial non-uniformity may mean that individual solar cells could be irradited with different intensities by up to 40% or even more. This will have a significant impact on the results of the research. The research for the PV module must be repeated for the system ensuring greater spatial uniformity of irradiation. The spatial non-uniformity of irradiation equal to 18.9% is unacceptable.
Response 3.8:
An explanation has been added as Appendix B (see lines 516-536 on pages 17-18). The description in the relevant part has also been revised (see lines 155-161 on page 5).
In short, the experimental results provided in Appendix B demonstrate that the non-uniformity of the light source can result in a shift in the I-V curves but has no significant effect on their slopes. Since the modelling improvement investigated in this work is associated with the change in the slope of the I-V curves, this result implies that the non-uniformity of the light source has no influence on the validity of the conclusions drawn from this work.
3.9. line 147: What mean: "noticeable distortion to the I-V curves ...." ? How it was checked?
Response 3.9:
The sentence has been revised to make clear that “… did not cause any noticeable distortion to the shape of the I-V curves …” (see lines 155-161 on page 5).
3.10. Lines 145-151: The current flowing through a chain of series connected cells is determined by the current generated by the least efficient solar cell in that chain (i.e. the lowest current solar cell or the shaded solar cell). Therefore, no difference was noticed in the shading of the different solar cells in the chain. Results of the research confirming the conclusions presented in lines 145-151 should be presented
Response 3.10:
We believe that the explanation in Appendix B and in Response 3.8 has provided satisfactory answer to this question.
3.11. lines 174-175: Should be "solar cell temperature".
Response 3.11:
The correction has been made as suggested (see lines 184-185 on page 6).
3.12. Line 180: Present shadings in the figure. Lack of information how shading cases of solar cell (25%, 50%, 75%) was verified? How were the exact shading levels obtained for a small size solar cell?
Response 3.12:
A brief description has been added to provide necessary information regarding the reliability of the shading position (see lines 191-197 on page 6).
3.13. Lines 196-197: "...was investigated under reduced irradiance (instead of shading)." It is not the same, please refer to work [40], which presents the convergence of the influence of shading and irradiance on the solar cell parameters.
Response 3.13:
We have added a sentence (see lines 213-215 on page 6) and a new reference [44] (see lines 645-647 on page 21) to clarify this point. Our recent work [44] has shown that the shading on a part of a solar cell is equivalent to irradiance reduction on the whole cell if the total light power is the same for both cases.
3.14. Fig. 5 and 6: Polynomial functions have not been plotted in the graphs: 5a-5d, 6c, 6d, 6f.
Response 3.14:
We have increased the data points of the polynomial functions. The smooth graphs of polynomial fitting have now been obtained and added in Figures 5 and 6 as requested (see pages 7-8).
3.15. Fig. 5c: The results of the parameter n>2 must be commented.
Response 3.15:
Thanks for good suggestion. We have added a sentence to discuss the change of n with shading and commented on the cases of n>2 for shading of > 30% (see lines 218-221 on page 6).
3.16. Table 1: The data in the table are not consistent with the measurement data presented in Figures 5a-5d. Should be respectively: 0.39, 0.62, 1.85, 0.13, 23.92!
Response 3.16:
The data in Table 1 was extracted from a solar cell that is different from the one used to extract the data for Figures 5a-5d. Therefore, they must be different. The purpose of this part of the work is to demonstrate the derived trend of change (polynomial equations) can be used as a general trend for the same type but different individual solar cells. Please see the sentence (lines 267-270 on page 9), which should have provided a clear explanation.
3.17. Fig. 7: Curves were drawn based on incorrect data, because data in table 1 are incorrect.
Response 3.17:
We believe that the data in Table 1 is correct as explained in Response 3.16. Therefore, we have no reason to doubt the validity of the curves in Figure 7.
3.18. Fig. 7: Present the coefficient of compliance of the measured and calculated data.
Response 3.18:
We are not familiar with the definition of the “coefficient of compliance”. We tried to find out from literatures and textbooks without success. We shall be happy to consider if the reviewer can provide further information on this.
3.19. Lines 261-266: Provide conclusions after recalculation curves in figure 7.
Response 3.19:
We believe that recalculation is not needed (see Response 3.16 and 3.17).
3.20. Fig. 8: The electrical sheme shown in figure 8 is incorrect and meaningless! String-1 does not transfer energy to the output. Cells in PV modules are not connected like that!
Response 3.20:
Sorry for the mistake and thanks for pointing out. Figure 8 has now been corrected and updated (see page 11).
3.21. Lines 337-338: The values are not in good agreement - currents differ by 18% and voltages by 8%. Additionally in opposite directions - the measured current is lower and the measured voltage is higher than the datasheet parameters.
Response 3.21:
Thanks for raising this issue. On the second thought, we agree with the reviewer. The sentence has now been revised (see lines 358-359 on page 12).
3.22. Table 2: Ipho is the same as Isc ? What with ID and Ish ?
Response 3.22:
They are equal but only to the 3rd decimal place. The reason for using only the 3rd decimal place is to reflect experimental error of the solar cell parameters derived from I-V measurements. According to our record, the measured value of Isc is 0.515587 A, whereas the calculated value of Ipho is 0.51593 A. It is well-known that ID and Ish are much smaller than the difference between Ipho and Isc, for crystalline silicon solar cells, indicating the validity of our data and justify the presented data in Table 2.
3.23. Table 4. Present shading cases 1-6 in the figure. How was it verified?
Response 3.23:
We don’t understand the exact meaning of the comments here. We try to address this point based on our interpretation. We are confident that these shading cases were implemented appropriately by:
- A blocking test has proved that the black adhesive foam tape employed for the shading experiments blocks all light from reaching the solar cell.
- The tapes were carefully positioned on the solar cell surface with the help of high-quality ruler and magnifying glass. Since the solar cells have an area of 3cm x 5cm, an acceptable shading accuracy can be readily achieved.
- The solar cells have a central busbar, which has been used as a reference for 50% shading.
3.24. Fig. 9-11: The measurement results of figures 8-11 do not correspond to the electrical scheme of figure 8.
Response 3.24:
The reviewer had pointed out in comment 3.20 that there is a mistake in Figure 8, which has now been corrected and updated. We believe that this inconsistency has been resolved.
3.25. Fig. 9-11: The measurement results of figures 8-11 do not correspond to the electrical scheme of figure 8.
Response 3.25:
Is this a duplicate comment by mistake? If not, please see Response 3.24.
3.26. Lines 428-430: Present the coefficient of compliance of the measured and calculated data in figures 9-11.
Response 3.26:
As explained in Response 3.18, we are not familiar with the definition of the “coefficient of compliance”. We shall be happy to consider if the reviewer can provide further information on this.
3.27. Fig 9-11: Fig. 7: Present the coefficient of compliance of measured and calculated data.
Response 3.27:
Please see Response 3.18 and Response 3.26 above.
3.28. Lines 475-594: Year of publication of a book, article, or references sometimes written in plain font (e.g. 1,2,14) and sometimes in bold (3, 4,5). It should be unify.
Response 3.28:
The use of bold and non-bold font is required by this journal. The detailed guideline is available on “Instructions for Authors” page. In this case of the Year of publication, we are required to use bold if the reference is a journal article and use non-bold if it is a book, or conference paper, or website.
Round 2
Reviewer 2 Report
Overall Recommendation is to accept in present form.
Author Response
There appears to be no comments or suggestions from this reviewer for further revision.
Reviewer 3 Report
3.2. Fig. 1 - Voltage arrow incorrectly marked - there should be only one arrowhead.
Response 3.2:
The voltage arrow has been corrected as suggested (see Figure 1 on page 2).
Response 3.2.1:
The voltage arrow should be directed in the opposite direction (from „-” to „+”).
3.4. line 112: shoud be: W/m∙K
Response 3.4:
The correction has been made as suggested (see line 119 on page 3).
Response 3.4.1:
Unit of thermal conductivity was’t corrected (still is W/m.K). Shoud be: [W/(m∙K)]
3.18. Fig. 7: Present the coefficient of compliance of the measured and calculated data.
Response 3.18:
We are not familiar with the definition of the “coefficient of compliance”. We tried to find out from literatures and textbooks without success. We shall be happy to consider if the reviewer can provide further information on this.
Response 3.18.1:
For example: R-Squared, MSE.
3.22. Table 2: Ipho is the same as Isc ? What with ID and Ish ?
Response 3.22:
They are equal but only to the 3rd decimal place. The reason for using only the 3rd decimal place is to reflect experimental error of the solar cell parameters derived from I-V measurements. According to our record, the measured value of Isc is 0.515587 A, whereas the calculated value of Ipho is 0.51593 A. It is well-known that ID and Ish are much smaller than the difference between Ipho and Isc, for crystalline silicon solar cells, indicating the validity of our data and justify the presented data in Table 2.
Response 3.22.1:
Please provide a short information about the non-significance of ID and Ish.
3.26. Lines 428-430: Present the coefficient of compliance of the measured and calculated data in figures 9-11.
Response 3.26:
As explained in Response 3.18, we are not familiar with the definition of the “coefficient of compliance”. We shall be happy to consider if the reviewer can provide further information on this.
Response 3.26.1:
For example: R-Squared, MSE.
3.27. Fig 9-11: Fig. 7: Present the coefficient of compliance of measured and calculated data.
Response 3.27:
Please see Response 3.18 and Response 3.26 above.
Response 3.27.1:
For example: R-Squared, MSE.
3.29. Line 366 and Table 2: The measurements of V-I were made not in STC conditions but with irradiance equal to 860 W/m2 (average irradiance of 40cm x 40cm area). The average irradiance of the PV module should be measured (34cm x 24cm area), not the 40cm x 40cm area.
3.30. Appendix A, line 499: Please specify the location of the PV module on the irradiated area of 40 cm x 40 cm or specify the irradiance distribution on the module area of 34 cm x 24 cm. Only then Authors could define the average irradiance of the PV module. Are You sure these were exactly STC conditions? The average irradiance of area of 40cm x 40cm is 860 W/m2.
Other responses and corrections are accepted.
Author Response
Reviewer 3:
3.2.1. The voltage arrow should be directed in the opposite direction (from „-” to „+”).
Response 3.2.1:
The positive and negative signs have now been added to Figure 1. We also delete the arrow. We believe that this is sufficient and clearer.
3.4.1. Unit of thermal conductivity was’t corrected (still is W/m.K). Shoud be: [W/(m∙K)].
Response 3.4.1:
The correction has been made as suggested (see line 119 on page 3).
3.18.1. For example: R-Squared, MSE.
Response 3.18.1:
Thanks for clarification. Unfortunately, our available data is not suitable for R-Squared or MSE calculation here. To facilitate this calculation, it is necessary for both the experimental data and simulation data to have the same voltage value for each corresponding point. However, the simulation was carried out using data points that are different from experiments. There are no matching points available for this calculation.
Although this is not perfect, we believe that the differences are shown clearly in the figures, providing clear demonstration of the effect of different modelling approaches.
3.22.1. Please provide a short information about the non-significance of ID and Ish.
Response 3.22.1:
A sentence has been added to provide information on this as required (see lines 364-366 in page 12).
3.26.1. For example: R-Squared, MSE.
Response 3.26.1:
The same as Response 3.18.1.
3.27.1. For example: R-Squared, MSE.
Response 3.27.1:
The same as Response 3.18.1.
3.29. Line 366 and Table 2: The measurements of V-I were made not in STC conditions but with irradiance equal to 860 W/m2 (average irradiance of 40cm x 40cm area). The average irradiance of the PV module should be measured (34cm x 24cm area), not the 40cm x 40cm area.
Response 3.29:
Many thanks for pointing out an inaccurate description. We have revised the relevant parts to ensure accurate description of measurement condition (see lines 173-174 on page 5, 361-363 and 373-374 on page 12, 412 and 420-41 on page 13, 449-450 on page 15, 469 on page 16, 547-548 on page 18).
3.30. Appendix A, line 499: Please specify the location of the PV module on the irradiated area of 40 cm x 40 cm or specify the irradiance distribution on the module area of 34 cm x 24 cm. Only then Authors could define the average irradiance of the PV module. Are You sure these were exactly STC conditions? The average irradiance of area of 40cm x 40cm is 860 W/m2.
Response 3.30:
Thanks again for good suggestion. We have revised Figure A1 to show the position of the PV module in relation to the calibrated area and added description (see Figure A1, the lines 136-137 on page 4 and 522-523 on page 17).
