Comparison of the Analytical Model and the Data-Driven Long Short-Term Memory Model for the Digital Twin of a Photovoltaic Panel

Abstract

The importance of digital twin methods in system monitoring, energy management, fault detection, and assessment of system health is increasing day by day. Due to environmental pollution and global warming, photovoltaic (PV) panels have become an essential part of energy systems because of the widespread adoption of renewable energy systems. Factors such as variability in weather conditions and non-linearity of PV systems necessitate close monitoring. Digital twin methods emerge as a novel solution to this problem. Digital twin modeling methods are classified in the literature as analytical methods and neural methods. Analytical methods provide rapid results and straightforward approaches; however, the complexity and non-linearity of systems complicate the modeling of PV systems. Although neural methods achieve success in system-specific results, they pose challenges such as the necessity of individual training for each system, difficulty in obtaining sufficient training data, and complexities involved in data processing. In this study, a performance comparison was conducted between the neural digital twin and the analytical digital twin for PV systems. Data-driven Long Short-Term Memory (LSTM) was used as the neural method, whereas the Single-Diode Model (TDM-SDM) was utilized as the analytical method. Experimental studies indicated that the TDM-based PV digital twin method achieved a performance with a coefficient of determination R² greater than 0.95.

Keywords

• Digital twin
• Long Short-Term Memory (LSTM)
• Photovoltaic systems
• Analytical modeling
• Single-diode model

Fotovoltaik Panel Dijital İkizi için Analitik Model ile Veri Odaklı Uzun Kısa Süreli Bellek Modelin Karşılaştırılması

Öz

Sistem izleme, enerji yönetimi, arıza tespiti ve sistem sağlığının değerlendirilmesi durumlarında dijital ikiz yöntemlerinin önemi her geçen gün artmaktadır. Çevre kirliliği ve küresel ısınma ile yenilenebilir enerji sistemlerinin yaygınlaşmasından dolayı fotovoltaik (FV) paneller, enerji sistemlerinin vazgeçilmez bir parçası haline gelmiştir. Hava şartlarının değişkenliği ve FV’lerin doğrusal olmaması gibi sebepler, FV sistemlerinin sıkı takip edilmesi zorunluluğunu doğurmaktadır. Dijital ikiz yöntemleri bu soruna yeni bir çözüm olarak ortaya çıkmaktadır. Dijital ikiz modelleme yöntemleri literatürde analitik yöntemler ve veri odaklı yöntemler olarak yer almaktadır. Analitik yöntemler, hızlı sonuç üretme ve doğrudan yaklaşımlar sunsa da sistem karmaşıklığı ve sistemlerin doğrusal olmaması, FV sistemlerinin modellenmesini zorlaştırmaktadır. Veri odaklı yöntemler, sistemlere özel sonuçlarda başarı sağlamasına karşın, her farklı sistem için ayrı eğitim gerekliliği, eğitim için yeterli veri elde etme ve verilerin işlenme zorluğu gibi sebeplerden dolayı sorunlar oluşturmaktadır. Bu çalışmada FV sistemleri için veri odaklı dijital ikiz ile analitik dijital ikiz arasında performans karşılaştırması yapılmıştır. Veri odaklı yöntem için uzun-kısa süreli bellek (LSTM), analitik yöntem için tek diyot modeli (SDM) kullanılmıştır. Yapılan deneysel çalışmalarda SDM tabanlı FV dijital ikiz yönteminin performansının R2=0,95’in üzerinde olduğu görülmüştür.

Anahtar Kelimeler

• Dijital İkiz
• Uzun Kısa Süreli Bellek
• Fotovoltaik Sistem
• Analitik Model
• Tek diyot Model

Kaynakça

1. [1] E. Demirci and M. Karaatli, “Comparison Of Classification Algorithms Used For Estimatıon Of Development Levels Of Countries,” 2019. [Online]. Available: https://orcid.org/0000-0002-7403-9587.
2. [2] X. Zhang, W. Xu, A. Rauf, and I. Ozturk, “Transitioning from conventional energy to clean renewable energy in G7 countries: A signed network approach,” Energy, vol. 307, Oct. 2024, doi: 10.1016/j.energy.2024.132655.
3. [3] M. D. Bauer, D. Huber, G. D. Rudebusch, and O. Wilms, “Where is the carbon premium? Global performance of green and brown stocks,” Journal of Climate Finance, vol. 1, p. 100006, Dec. 2022, doi: 10.1016/j.jclimf.2023.100006.
4. [4] D. Nong, P. Simshauser, and D. B. Nguyen, “Greenhouse gas emissions vs CO2 emissions: Comparative analysis of a global carbon tax,” Appl Energy, vol. 298, Sep. 2021, doi: 10.1016/j.apenergy.2021.117223.
5. [5] O. Bamisile, C. Acen, D. Cai, Q. Huang, and I. Staffell, “The environmental factors affecting solar photovoltaic output,” Feb. 01, 2025, Elsevier Ltd. doi: 10.1016/j.rser.2024.115073.
6. [6] Gaëtan Masson, Elina Bosch, and Adrien Van Rechem, “Snapshot of Global PV Markets 2024,” 2024. [Online]. Available: www.iea-pvps.org
7. [7] D. Cohen and D. Elmakis, “Reliability of photo-voltaic power plants,” Electric Power Systems Research, vol. 224, Nov. 2023, doi: 10.1016/j.epsr.2023.109736.
8. [8] J. Antonanzas, N. Osorio, R. Escobar, R. Urraca, F. J. Martinez-de-Pison, and F. Antonanzas-Torres, “Review of photovoltaic power forecasting,” Oct. 15, 2016, Elsevier Ltd. doi: 10.1016/j.solener.2016.06.069.

9. [9] L. Abad, S. Tamalouzt, K. Djermouni, S. Mekhilef, and Y. Belkhier, “Analytical Modeling of Photovoltaic Systems Under Partial Shading Conditions Incorporating Bypass and Blocking Diodes Influence,” Int J Energy Res, vol. 2025, no. 1, 2025, doi: 10.1155/er/3384091.
10. [10] K. Çelik, M. Demirtas, and N. Öztürk, “Analytical MPPT Control and Comparative Analysis for PV Panel Connected to DC Microgrid,” Electric Power Components and Systems, vol. 51, no. 11, pp. 1075–1088, 2023, doi: 10.1080/15325008.2023.2189759.
11. [11] Manju, Rajendra Kumar, Soma Rajwade, P. K. Yadaw, Akash ingle, and Mukendra Kumar Sahu, “Advancements in Modeling, Estimation Techniques, and Fault Analysis in Solar Photovoltaic Systems: A Comprehensive Review,” Journal of Technology Innovations and Energy, vol. 3, no. 2, pp. 23–48, Jun. 2024, doi: 10.56556/jtie.v3i2.917.
12. [12] L. Abad, S. Tamalouzt, K. Djermouni, S. Mekhilef, and Y. Belkhier, “Analytical Modeling of Photovoltaic Systems Under Partial Shading Conditions Incorporating Bypass and Blocking Diodes Influence,” Int J Energy Res, vol. 2025, no. 1, 2025, doi: 10.1155/er/3384091.
13. [13] R. Castro and M. Silva, “Experimental and theoretical validation of one diode and three parameters–based pv models,” Energies (Basel), vol. 14, no. 8, Apr. 2021, doi: 10.3390/en14082140.
14. [14] L. de O. Santos, T. AlSkaif, G. C. Barroso, and P. C. M. de Carvalho, “Photovoltaic power estimation and forecast models integrating physics and machine learning: A review on hybrid techniques,” Dec. 01, 2024, Elsevier Ltd. doi: 10.1016/j.solener.2024.113044.
15. [15] M. Kolahi, S. M. Esmailifar, A. M. Moradi Sizkouhi, and M. Aghaei, “Digital-PV: A digital twin-based platform for autonomous aerial monitoring of large-scale photovoltaic power plants,” Energy Convers Manag, vol. 321, Dec. 2024, doi: 10.1016/j.enconman.2024.118963.
16. [16] C. Xiang, B. Li, P. Shi, T. Yang, and B. Han, “Short-Term Photovoltaic Power Prediction Based on a Digital Twin Model,” J Mar Sci Eng, vol. 12, no. 7, Jul. 2024, doi: 10.3390/jmse12071219.
17. [17] J. Yuan, J. Ma, Z. Tian, and K. L. Man, “Digital Twin Integration With Data Fusion for Enhanced Photovoltaic System Management: A Systematic Literature Review,” IEEE Open Journal of Power Electronics, vol. 5, pp. 1045–1058, 2024, doi: 10.1109/OJPEL.2024.3422021.
18. [18] D. D. Angelova, D. C. Fernández, M. C. Godoy, J. A. Á. Moreno, and J. F. G. González, “A Review on Digital Twins and Its Application in the Modeling of Photovoltaic Installations,” Mar. 01, 2024, Multidisciplinary Digital Publishing Institute (MDPI). doi: 10.3390/en17051227.
19. [19] X. Zhao, “A novel digital-twin approach based on transformer for photovoltaic power prediction,” Sci Rep, vol. 14, no. 1, p. 26661, Dec. 2024, doi: 10.1038/s41598-024-76711-4.
20. [20] M. YILMAZ and A. A. MARTİNEZ-MORALES, “Fault Detection in Photovoltaic Panels Using Digital Twin Technology: A Comprehensive Study,” The Journal of Cognitive Systems, Jun. 2023, doi: 10.52876/jcs.1407133.
21. [21] M. Kolahi, S. M. Esmailifar, A. M. Moradi Sizkouhi, and M. Aghaei, “Digital-PV: A digital twin-based platform for autonomous aerial monitoring of large-scale photovoltaic power plants,” Energy Convers Manag, vol. 321, Dec. 2024, doi: 10.1016/j.enconman.2024.118963.
22. [22] D. Hong, J. Ma, K. Wang, K. L. Man, H. Wen, and P. Wong, “Real-Time Power Prediction for Bifacial PV Systems in Varied Shading Conditions: A Circuit-LSTM Approach Within a Digital Twin Framework,” IEEE J Photovolt, vol. 14, no. 4, pp. 652–660, Jul. 2024, doi: 10.1109/JPHOTOV.2024.3393001.
23. [23] A. KARA, “Uzun-Kısa Süreli Bellek Ağı Kullanarak Global Güneş Işınımı Zaman Serileri Tahmini,” Gazi Üniversitesi Fen Bilimleri Dergisi Part C: Tasarım ve Teknoloji, vol. 7, no. 4, pp. 882–892, Dec. 2019, doi: 10.29109/gujsc.571831.
24. [24] A. H. Eşlik, O. Şen, and F. Serttaş, “CNN-LSTM model for solar radiation prediction: performance analysis,” Journal of the Faculty of Engineering and Architecture of Gazi University, vol. 39, no. 4, pp. 2155–2162, 2024, doi: 10.17341/gazimmfd.1243823.
25. [25] C. Xiang, B. Li, P. Shi, T. Yang, and B. Han, “Short-Term Photovoltaic Power Prediction Based on a Digital Twin Model,” J Mar Sci Eng, vol. 12, no. 7, Jul. 2024, doi: 10.3390/jmse12071219.
26. [26] H. Ertaş, U. Fesli, Ş. Demirbaş, and K. Çelik, “Proposed Solution to Infinite Loop Issues in the Digital Twin of a PV Array Based on the Single-Diode Model A Case Study,” Institute of Electrical and Electronics Engineers (IEEE), Jun. 2025, pp. 1–7. doi: 10.1109/cpe-powereng63314.2025.11027201.
27. [27] TommaTech, “TommaTech 240Wp 48PM M12,”https://tommatech.de/tr/urun/tommatech-240wp-48pm-m12-hc-mb-gunes-paneli-1043.html. Accessed: Oct. 09, 2025. [Online]. Available:https://tommatech.de/tr/urun/tommatech-240wp-48pm-m12-hc-mb-gunes-paneli-1043.html
28. [28] K. Çelik, M. Demirtaş, İ. Çetinbaş, and H. Ertaş, “Modeling, Parameter Optimization, and Experimental Comparison of a PV Array with Daily Data in Outdoor Conditions,” Institute of Electrical and Electronics Engineers (IEEE), Jun. 2025, pp. 1–5. doi: 10.1109/cpe-powereng63314.2025.11027312.
29. [29] H. Ertaş, U. Fesli, Ş. Demirbaş, and K. Çelik, “Proposed Solution to Infinite Loop Issues in the Digital Twin of a PV Array Based on the Single-Diode Model A Case Study,” Institute of Electrical and Electronics Engineers (IEEE), Jun. 2025, pp. 1–7. doi: 10.1109/cpe-powereng63314.2025.11027201.t