Development of the Real-time Algorithm for Intra-string Photovoltaic Modules Faults Detection and Classification
DOI:
https://doi.org/10.24160/1993-6982-2024-4-36-48Keywords:
short circuit, photovoltaic installation, photovoltaic array, photovoltaic module, circuit current, faultAbstract
The purpose of this work was to develop and verify an algorithm for detecting, classification and localization short circuits that occur within one string of photovoltaic modules of solar power plants.
The paper provides a comparative analysis of the proposed algorithm with current methods for detecting short circuits in arrays of photovoltaic modules. A computational model of a photovoltaic installation is described.
An algorithm for detecting short circuits within one string of an PV array in real time has been developed.
In the future, the obtained results will be used in the development of an algorithm for detecting short circuits between different PV strings.
Based on the results of the study, a conclusion was made about the correct operation of the developed algorithm in a wide range of insolation, the accepted assumptions are described, and the sequence of implementation of the algorithm for photovoltaic batteries with an arbitrary number of chains and the number of modules in one chain is given.
References
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2. IEA. Renewables [Электрон. ресурс] https://iea.blob.core.windows.net/assets/bda6e589-33a6-4120-b9c8-3b78c8348743/LaunchPresentation.pdf (дата обращения 02.08.2023).
3. Firth S.K., Lomas K.J., Rees S.J. A Simple Model of PV System Performance and Its Use in Fault Detection // Solar Energy. 2010. V. 84. Pp. 624—635.
4. Triki-Lahiani A. e. a. Fault Detection and Monitoring Systems for Photovoltaic Installations: a Review // Renewable and Sustainable Energy Reviews.2017. V. 82(11). Pp. 2680—2692.
5. Gallardo-Saavedra S., Hernández-Callejo L., Duque O. Quantitative Failure Rates and Modes Analysis in Photovoltaic Plants // Energy. 2019. V. 183. Pp. 825—836.
6. Klise G.T., Lavrova O.A., Gooding R.L. PV System Component Fault and Failure Compilation and Analysis [Электрон. ресурс] https://sunspec.org/wp-content/uploads/2016/12/PVSystemComponentFaultandFailureCompilationandAnalysis.pdf (дата обращения 02.08.2023).
7. Монаков Ю.В., Шарапов С.А., Середкин Д.Ю. Эффективность гетероструктурных фотоэлектрических модулей на территории России и корректность методики выбора защитных аппаратов в их цепях // Вестник МЭИ. 2021. № 6. С. 49—57.
8. Aghaei M. Line-line Fault Detection and Classification for Photovoltaic Systems Using Ensemble Learning Model Based on I-V Characteristics // Solar Energy. 2020. V. 211. Pp. 354—365.
9. Pei T., Hao X. A Fault Detection Method for Photovoltaic Systems Based on Voltage and Current Observation and Evaluation // Energies 2019. V. 12(9). P. 1712.
10. Ding K., Zhang J., Ding H., Liu Y., Chen F., Li Y. Fault Detection of Photovoltaic Array Based on Grubbs Criterion and Local Outlier Factor // IET Renewable Power Generation. 2020. V. 14. Pp. 551—559.
11. Guerriero P., Piegari L., Rizzo R., Daliento S. Mismatch Based Diagnosis of PV Fields Relying on Monitored String Currents // Intern. J. Photoenergy. 2017. Pp. 1—10.
12. Hariharan R. e. a. A Method to Detect Photovoltaic Array Faults and Partial Shading in PV Systems // IEEE J. Photovoltaics. 2016. V. 6(5). Pp. 1278—1285.
13. Середкин Д.Ю., Монаков Ю.В., Шарапов С.А. Реализация двухдиодной расчетной модели фотоэлектрического модуля для исследования переходных процессов в сети постоянного тока солнечных электростанций // Вестник МЭИ. 2023. № 2. С. 98—107.
14. Spataru S., Sera D., Kerekes T., Teodorescu R. Photovoltaic Array Condition Monitoring Based on Online Regression of Performance Model // Proc. 39th Photovoltaic Specialists Conf. 2013. Pp. 0815—0820.
15. Ando B. e. a. Sentinella: Smart Monitoring of Photovoltaic Systems at Panel Level // IEEE Instrumentation and Measurement Trans. 2015. V. 64(8). Pp. 2188—2199.
16. Takashima T., Yamaguchi J., Otani K., Kato K., Ishida M. Experimental Studies of Failure Detection Methods in PV Module Strings // Proc. IEEE IV World Conf. Photovoltaic Energy Conversion. 2006. Pp. 2227—2230.
17. Kolantla D. e. a. Critical Review on Various Inverter Topologies for PV System Architectures // IET Renewable Power Generation. 2021. V. 14(17). Pp. 3418—3438.
18. Nedumgatt J. e. a. Perturb and Observe MPPT Algorithm for Solar PV Systems-modeling and Simulation // Proc. Annual IEEE India Conf. Hyderabad. 2011. Pp. 1—6.
19. Suryavanshi R. e. a. PSO and P & O based MPPT Technique for SPV Panel Under Varying Atmospheric Conditions // Proc. Intern. Conf. Power, Signals, Controls and Computation. Thrissur, 2012. Pp. 1—6.
20. Femia N., Petrone G., Spagnuolo G., Vitelli M. Optimization of Perturb and Observe Maximum Power Point Tracking Method // IEEE Trans. Power Electronics 2005. V. 20(4). Pp. 963—973.
21. Oubbati B.K., Boutoubat M., Belkheiri M., Rabhi A. Global Maximum Power Point Tracking of a PV System MPPT Control Under Partial Shading // Proc. 2018 Intern. Conf. Electrical Sci. and Technol. in Maghreb (CISTEM). Algiers, 2018. Pp. 1—6.
22. Arjyadhara P., Bhagabat P. A Simplified Design and Modeling of Boost Converter for Photovoltaic System // Intern. J. Electrical and Computer Eng. 2018. V. 8. Pp. 141—149.
23. Ayop R., Tan C.W. Design of Boost Converter Based on Maximum Power Point Resistance for Photovoltaic Applications // Solar Energy. 2018. V. 160. Pp. 322—335.
24. Güler N., Irmak E. MPPT Based Model Predictive Control of Grid Connected Inverter for PV Systems // Proc. VIII Intern. Conf. Renewable Energy Research and Appl. Brasov, 2019. Pp. 982—986.
25. Skiera B., Reiner J., Albers S. Regression Analysis // Handbook of Market Research. N.-Y.: Springer, 2022. Pp. 299—327.
26. Gasparin F.P., Bühler A.J., Rampinelli G.A., Krenzinger A. Statistical Analysis of I–V Curve Parameters from Photovoltaic Modules // Solar Energy. 2016. V. 131. Pp. 30—38.
---
Для цитирования: Середкин Д.Ю., Монаков Ю.В. Разработка алгоритма обнаружения и классификации замыкания внутри цепочки фотоэлектрических модулей в режиме реального времени // Вестник МЭИ. 2024. № 4. С. 36—48. DOI: 10.24160/1993-6982-2024-4-36-48
---
Конфликт интересов: авторы заявляют об отсутствии конфликта интересов
#
1. IEA. Trends in Photovoltaic Applications [Elektron. Resurs] https://iea-pvps.org/wp-content/uploads/2023/02/PVPS_Trend_Report_2022.pdf (Data Obrashcheniya 03.09.2023).
2. IEA. Renewables [Elektron. Resurs] https://iea.blob.core.windows.net/assets/bda6e589-33a6-4120-b9c8-3b78c8348743/LaunchPresentation.pdf (Data Obrashcheniya 02.08.2023).
3. Firth S.K., Lomas K.J., Rees S.J. A Simple Model of PV System Performance and Its Use in Fault Detection. Solar Energy. 2010;84:624—635.
4. Triki-Lahiani A. e. a. Fault Detection and Monitoring Systems for Photovoltaic Installations: a Review. Renewable and Sustainable Energy Reviews.2017;82(11):2680—2692.
5. Gallardo-Saavedra S., Hernández-Callejo L., Duque O. Quantitative Failure Rates and Modes Analysis in Photovoltaic Plants. Energy. 2019;183:825—836.
6. Klise G.T., Lavrova O.A., Gooding R.L. PV System Component Fault and Failure Compilation and Analysis [Elektron. Resurs] https://sunspec.org/wp-content/uploads/2016/12/PVSystemComponentFaultandFailureCompilationandAnalysis.pdf (Data Obrashcheniya 02.08.2023).
7. Monakov Yu.V., Sharapov S.A., Seredkin D.Yu. Effektivnost' Geterostrukturnykh Fotoelektricheskikh Moduley na Territorii Rossii i Korrektnost' Metodiki Vybora Zashchitnykh Apparatov v Ikh Tsepyakh. Vestnik MEI. 2021;6:49—57. (in Russian).
8. Aghaei M. Line-line Fault Detection and Classification for Photovoltaic Systems Using Ensemble Learning Model Based on I-V Characteristics. Solar Energy. 2020;211:354—365.
9. Pei T., Hao X. A Fault Detection Method for Photovoltaic Systems Based on Voltage and Current Observation and Evaluation. Energies 2019;12(9):1712.
10. Ding K., Zhang J., Ding H., Liu Y., Chen F., Li Y. Fault Detection of Photovoltaic Array Based on Grubbs Criterion and Local Outlier Factor. IET Renewable Power Generation. 2020;14:551—559.
11. Guerriero P., Piegari L., Rizzo R., Daliento S. Mismatch Based Diagnosis of PV Fields Relying on Monitored String Currents. Intern. J. Photoenergy. 2017:1—10.
12. Hariharan R. e. a. A Method to Detect Photovoltaic Array Faults and Partial Shading in PV Systems. IEEE J. Photovoltaics. 2016;6(5):1278—1285.
13. Seredkin D.Yu., Monakov Yu.V., Sharapov S.A. Realizatsiya Dvukhdiodnoy Raschetnoy Modeli Fotoelektricheskogo Modulya dlya Issledovaniya Perekhodnykh Protsessov v Seti Postoyannogo Toka Solnechnykh Elektrostantsiy. Vestnik MEI. 2023;2:98—107. (in Russian).
14. Spataru S., Sera D., Kerekes T., Teodorescu R. Photovoltaic Array Condition Monitoring Based on Online Regression of Performance Model. Proc. 39th Photovoltaic Specialists Conf. 2013:0815—0820.
15. Ando B. e. a. Sentinella: Smart Monitoring of Photovoltaic Systems at Panel Level. IEEE Instrumentation and Measurement Trans. 2015;64(8):2188—2199.
16. Takashima T., Yamaguchi J., Otani K., Kato K., Ishida M. Experimental Studies of Failure Detection Methods in PV Module Strings. Proc. IEEE IV World Conf. Photovoltaic Energy Conversion. 2006:2227—2230.
17. Kolantla D. e. a. Critical Review on Various Inverter Topologies for PV System Architectures. IET Renewable Power Generation. 2021;14(17):3418—3438.
18. Nedumgatt J. e. a. Perturb and Observe MPPT Algorithm for Solar PV Systems-modeling and Simulation. Proc. Annual IEEE India Conf. Hyderabad. 2011:1—6.
19. Suryavanshi R. e. a. PSO and P & O based MPPT Technique for SPV Panel Under Varying Atmospheric Conditions. Proc. Intern. Conf. Power, Signals, Controls and Computation. Thrissur, 2012:1—6.
20. Femia N., Petrone G., Spagnuolo G., Vitelli M. Optimization of Perturb and Observe Maximum Power Point Tracking Method. IEEE Trans. Power Electronics 2005;20(4):963—973.
21. Oubbati B.K., Boutoubat M., Belkheiri M., Rabhi A. Global Maximum Power Point Tracking of a PV System MPPT Control Under Partial Shading. Proc. 2018 Intern. Conf. Electrical Sci. and Technol. in Maghreb (CISTEM). Algiers, 2018:1—6.
22. Arjyadhara P., Bhagabat P. A Simplified Design and Modeling of Boost Converter for Photovoltaic System. Intern. J. Electrical and Computer Eng. 2018;8:141—149.
23. Ayop R., Tan C.W. Design of Boost Converter Based on Maximum Power Point Resistance for Photovoltaic Applications. Solar Energy. 2018;160:322—335.
24. Güler N., Irmak E. MPPT Based Model Predictive Control of Grid Connected Inverter for PV Systems. Proc. VIII Intern. Conf. Renewable Energy Research and Appl. Brasov, 2019:982—986.
25. Skiera B., Reiner J., Albers S. Regression Analysis. Handbook of Market Research. N.-Y.: Springer, 2022:299—327.
26. Gasparin F.P., Bühler A.J., Rampinelli G.A., Krenzinger A. Statistical Analysis of I–V Curve Parameters from Photovoltaic Modules. Solar Energy. 2016;131:30—38
---
For citation: Seredkin D.Yu., Monakov Yu.V. Development of the Real-time Algorithm for Intra-Sstring Photovoltaic Modules Faults Detection and Classification. Bulletin of MPEI. 2024;4:36—48. (in Russian). DOI: 10.24160/1993-6982-2024-4-36-48
---
Conflict of interests: the authors declare no conflict of interest
2. IEA. Renewables [Электрон. ресурс] https://iea.blob.core.windows.net/assets/bda6e589-33a6-4120-b9c8-3b78c8348743/LaunchPresentation.pdf (дата обращения 02.08.2023).
3. Firth S.K., Lomas K.J., Rees S.J. A Simple Model of PV System Performance and Its Use in Fault Detection // Solar Energy. 2010. V. 84. Pp. 624—635.
4. Triki-Lahiani A. e. a. Fault Detection and Monitoring Systems for Photovoltaic Installations: a Review // Renewable and Sustainable Energy Reviews.2017. V. 82(11). Pp. 2680—2692.
5. Gallardo-Saavedra S., Hernández-Callejo L., Duque O. Quantitative Failure Rates and Modes Analysis in Photovoltaic Plants // Energy. 2019. V. 183. Pp. 825—836.
6. Klise G.T., Lavrova O.A., Gooding R.L. PV System Component Fault and Failure Compilation and Analysis [Электрон. ресурс] https://sunspec.org/wp-content/uploads/2016/12/PVSystemComponentFaultandFailureCompilationandAnalysis.pdf (дата обращения 02.08.2023).
7. Монаков Ю.В., Шарапов С.А., Середкин Д.Ю. Эффективность гетероструктурных фотоэлектрических модулей на территории России и корректность методики выбора защитных аппаратов в их цепях // Вестник МЭИ. 2021. № 6. С. 49—57.
8. Aghaei M. Line-line Fault Detection and Classification for Photovoltaic Systems Using Ensemble Learning Model Based on I-V Characteristics // Solar Energy. 2020. V. 211. Pp. 354—365.
9. Pei T., Hao X. A Fault Detection Method for Photovoltaic Systems Based on Voltage and Current Observation and Evaluation // Energies 2019. V. 12(9). P. 1712.
10. Ding K., Zhang J., Ding H., Liu Y., Chen F., Li Y. Fault Detection of Photovoltaic Array Based on Grubbs Criterion and Local Outlier Factor // IET Renewable Power Generation. 2020. V. 14. Pp. 551—559.
11. Guerriero P., Piegari L., Rizzo R., Daliento S. Mismatch Based Diagnosis of PV Fields Relying on Monitored String Currents // Intern. J. Photoenergy. 2017. Pp. 1—10.
12. Hariharan R. e. a. A Method to Detect Photovoltaic Array Faults and Partial Shading in PV Systems // IEEE J. Photovoltaics. 2016. V. 6(5). Pp. 1278—1285.
13. Середкин Д.Ю., Монаков Ю.В., Шарапов С.А. Реализация двухдиодной расчетной модели фотоэлектрического модуля для исследования переходных процессов в сети постоянного тока солнечных электростанций // Вестник МЭИ. 2023. № 2. С. 98—107.
14. Spataru S., Sera D., Kerekes T., Teodorescu R. Photovoltaic Array Condition Monitoring Based on Online Regression of Performance Model // Proc. 39th Photovoltaic Specialists Conf. 2013. Pp. 0815—0820.
15. Ando B. e. a. Sentinella: Smart Monitoring of Photovoltaic Systems at Panel Level // IEEE Instrumentation and Measurement Trans. 2015. V. 64(8). Pp. 2188—2199.
16. Takashima T., Yamaguchi J., Otani K., Kato K., Ishida M. Experimental Studies of Failure Detection Methods in PV Module Strings // Proc. IEEE IV World Conf. Photovoltaic Energy Conversion. 2006. Pp. 2227—2230.
17. Kolantla D. e. a. Critical Review on Various Inverter Topologies for PV System Architectures // IET Renewable Power Generation. 2021. V. 14(17). Pp. 3418—3438.
18. Nedumgatt J. e. a. Perturb and Observe MPPT Algorithm for Solar PV Systems-modeling and Simulation // Proc. Annual IEEE India Conf. Hyderabad. 2011. Pp. 1—6.
19. Suryavanshi R. e. a. PSO and P & O based MPPT Technique for SPV Panel Under Varying Atmospheric Conditions // Proc. Intern. Conf. Power, Signals, Controls and Computation. Thrissur, 2012. Pp. 1—6.
20. Femia N., Petrone G., Spagnuolo G., Vitelli M. Optimization of Perturb and Observe Maximum Power Point Tracking Method // IEEE Trans. Power Electronics 2005. V. 20(4). Pp. 963—973.
21. Oubbati B.K., Boutoubat M., Belkheiri M., Rabhi A. Global Maximum Power Point Tracking of a PV System MPPT Control Under Partial Shading // Proc. 2018 Intern. Conf. Electrical Sci. and Technol. in Maghreb (CISTEM). Algiers, 2018. Pp. 1—6.
22. Arjyadhara P., Bhagabat P. A Simplified Design and Modeling of Boost Converter for Photovoltaic System // Intern. J. Electrical and Computer Eng. 2018. V. 8. Pp. 141—149.
23. Ayop R., Tan C.W. Design of Boost Converter Based on Maximum Power Point Resistance for Photovoltaic Applications // Solar Energy. 2018. V. 160. Pp. 322—335.
24. Güler N., Irmak E. MPPT Based Model Predictive Control of Grid Connected Inverter for PV Systems // Proc. VIII Intern. Conf. Renewable Energy Research and Appl. Brasov, 2019. Pp. 982—986.
25. Skiera B., Reiner J., Albers S. Regression Analysis // Handbook of Market Research. N.-Y.: Springer, 2022. Pp. 299—327.
26. Gasparin F.P., Bühler A.J., Rampinelli G.A., Krenzinger A. Statistical Analysis of I–V Curve Parameters from Photovoltaic Modules // Solar Energy. 2016. V. 131. Pp. 30—38.
---
Для цитирования: Середкин Д.Ю., Монаков Ю.В. Разработка алгоритма обнаружения и классификации замыкания внутри цепочки фотоэлектрических модулей в режиме реального времени // Вестник МЭИ. 2024. № 4. С. 36—48. DOI: 10.24160/1993-6982-2024-4-36-48
---
Конфликт интересов: авторы заявляют об отсутствии конфликта интересов
#
1. IEA. Trends in Photovoltaic Applications [Elektron. Resurs] https://iea-pvps.org/wp-content/uploads/2023/02/PVPS_Trend_Report_2022.pdf (Data Obrashcheniya 03.09.2023).
2. IEA. Renewables [Elektron. Resurs] https://iea.blob.core.windows.net/assets/bda6e589-33a6-4120-b9c8-3b78c8348743/LaunchPresentation.pdf (Data Obrashcheniya 02.08.2023).
3. Firth S.K., Lomas K.J., Rees S.J. A Simple Model of PV System Performance and Its Use in Fault Detection. Solar Energy. 2010;84:624—635.
4. Triki-Lahiani A. e. a. Fault Detection and Monitoring Systems for Photovoltaic Installations: a Review. Renewable and Sustainable Energy Reviews.2017;82(11):2680—2692.
5. Gallardo-Saavedra S., Hernández-Callejo L., Duque O. Quantitative Failure Rates and Modes Analysis in Photovoltaic Plants. Energy. 2019;183:825—836.
6. Klise G.T., Lavrova O.A., Gooding R.L. PV System Component Fault and Failure Compilation and Analysis [Elektron. Resurs] https://sunspec.org/wp-content/uploads/2016/12/PVSystemComponentFaultandFailureCompilationandAnalysis.pdf (Data Obrashcheniya 02.08.2023).
7. Monakov Yu.V., Sharapov S.A., Seredkin D.Yu. Effektivnost' Geterostrukturnykh Fotoelektricheskikh Moduley na Territorii Rossii i Korrektnost' Metodiki Vybora Zashchitnykh Apparatov v Ikh Tsepyakh. Vestnik MEI. 2021;6:49—57. (in Russian).
8. Aghaei M. Line-line Fault Detection and Classification for Photovoltaic Systems Using Ensemble Learning Model Based on I-V Characteristics. Solar Energy. 2020;211:354—365.
9. Pei T., Hao X. A Fault Detection Method for Photovoltaic Systems Based on Voltage and Current Observation and Evaluation. Energies 2019;12(9):1712.
10. Ding K., Zhang J., Ding H., Liu Y., Chen F., Li Y. Fault Detection of Photovoltaic Array Based on Grubbs Criterion and Local Outlier Factor. IET Renewable Power Generation. 2020;14:551—559.
11. Guerriero P., Piegari L., Rizzo R., Daliento S. Mismatch Based Diagnosis of PV Fields Relying on Monitored String Currents. Intern. J. Photoenergy. 2017:1—10.
12. Hariharan R. e. a. A Method to Detect Photovoltaic Array Faults and Partial Shading in PV Systems. IEEE J. Photovoltaics. 2016;6(5):1278—1285.
13. Seredkin D.Yu., Monakov Yu.V., Sharapov S.A. Realizatsiya Dvukhdiodnoy Raschetnoy Modeli Fotoelektricheskogo Modulya dlya Issledovaniya Perekhodnykh Protsessov v Seti Postoyannogo Toka Solnechnykh Elektrostantsiy. Vestnik MEI. 2023;2:98—107. (in Russian).
14. Spataru S., Sera D., Kerekes T., Teodorescu R. Photovoltaic Array Condition Monitoring Based on Online Regression of Performance Model. Proc. 39th Photovoltaic Specialists Conf. 2013:0815—0820.
15. Ando B. e. a. Sentinella: Smart Monitoring of Photovoltaic Systems at Panel Level. IEEE Instrumentation and Measurement Trans. 2015;64(8):2188—2199.
16. Takashima T., Yamaguchi J., Otani K., Kato K., Ishida M. Experimental Studies of Failure Detection Methods in PV Module Strings. Proc. IEEE IV World Conf. Photovoltaic Energy Conversion. 2006:2227—2230.
17. Kolantla D. e. a. Critical Review on Various Inverter Topologies for PV System Architectures. IET Renewable Power Generation. 2021;14(17):3418—3438.
18. Nedumgatt J. e. a. Perturb and Observe MPPT Algorithm for Solar PV Systems-modeling and Simulation. Proc. Annual IEEE India Conf. Hyderabad. 2011:1—6.
19. Suryavanshi R. e. a. PSO and P & O based MPPT Technique for SPV Panel Under Varying Atmospheric Conditions. Proc. Intern. Conf. Power, Signals, Controls and Computation. Thrissur, 2012:1—6.
20. Femia N., Petrone G., Spagnuolo G., Vitelli M. Optimization of Perturb and Observe Maximum Power Point Tracking Method. IEEE Trans. Power Electronics 2005;20(4):963—973.
21. Oubbati B.K., Boutoubat M., Belkheiri M., Rabhi A. Global Maximum Power Point Tracking of a PV System MPPT Control Under Partial Shading. Proc. 2018 Intern. Conf. Electrical Sci. and Technol. in Maghreb (CISTEM). Algiers, 2018:1—6.
22. Arjyadhara P., Bhagabat P. A Simplified Design and Modeling of Boost Converter for Photovoltaic System. Intern. J. Electrical and Computer Eng. 2018;8:141—149.
23. Ayop R., Tan C.W. Design of Boost Converter Based on Maximum Power Point Resistance for Photovoltaic Applications. Solar Energy. 2018;160:322—335.
24. Güler N., Irmak E. MPPT Based Model Predictive Control of Grid Connected Inverter for PV Systems. Proc. VIII Intern. Conf. Renewable Energy Research and Appl. Brasov, 2019:982—986.
25. Skiera B., Reiner J., Albers S. Regression Analysis. Handbook of Market Research. N.-Y.: Springer, 2022:299—327.
26. Gasparin F.P., Bühler A.J., Rampinelli G.A., Krenzinger A. Statistical Analysis of I–V Curve Parameters from Photovoltaic Modules. Solar Energy. 2016;131:30—38
---
For citation: Seredkin D.Yu., Monakov Yu.V. Development of the Real-time Algorithm for Intra-Sstring Photovoltaic Modules Faults Detection and Classification. Bulletin of MPEI. 2024;4:36—48. (in Russian). DOI: 10.24160/1993-6982-2024-4-36-48
---
Conflict of interests: the authors declare no conflict of interest
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Published
2024-08-28
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Electric Power Industry (Technical Sciences) (2.4.3)
