DOI: https://doi.org/10.61435/ijred.2025.61489

Thermal analysis of bifacial photovoltaic modules with single-axis trackers in a large power plant: Modeling by symbolic equations in tropical climates

1Programa de Ingeniería Electrónica, Grupo de Investigación ITEM, Universidad Pontificia Bolivariana Seccional Montería, Montería, Colombia

2Institute for Energetic Engineering, Universitat Politècnica de València, 46022 Valencia, Spain

3Departamento de Eléctrica, Electrónica y Telecomunicaciones, Universidad de las Fuerzas Armadas ESPE, Sangolquí, Ecuador

4 Instituto de Energías Renovables,Universidad Nacional Autónoma de México, Temixco, Mexico

5 Atlantica Colombia SAS, Bogota, Colombia

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Received: 16 Jun 2025; Revised: 18 Sep 2025; Accepted: 30 Sep 2025; Available online: 5 Oct 2025; Published: 1 Nov 2025.
Editor(s): H Hadiyanto
Open Access Copyright (c) 2025 The Author(s). Published by Centre of Biomass and Renewable Energy (CBIORE)
Creative Commons License This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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Abstract

The thermal behavior of the single-axis tracked bifacial photovoltaic (PV) module is important for efficient energy extraction in large-scale power plants, especially in tropical regions under high irradiation and high ambient temperature. However, it is difficult to accurately predict their operating temperature due to the complex interaction between environmental variables and the characteristics of solar tracking. The available models, ranging from empirical correlations and computational fluid dynamics (CFD) simulations to machine learning methods, face challenges in terms of accuracy, interpretability, and computational load. This gap is addressed in this study, with the development of a modeling methodology based on symbolic regression (SR) utilizing genetic algorithms (GA) towards obtaining an explicit, interpretable Equation for the prediction of the PV module temperature in single-axis tracking systems. One year of data was collected at 5-minute intervals from a 19.9 MW PV plant located in San Marcos, Colombia, consisting of measurements for solar radiation, ambient temperature, wind speed, and module temperature. The constructed SR GA model achieved satisfactory prediction accuracy compared to classic models with the best root mean square error (RMSE = 4.14 °C) and R² (0.91) on the test data set. These results compare favorably with results from MLR (RMSE = 4.31 °C, R² = 0.90), the standard industry NOCT model (RMSE = 8.59 °C, R² = 0.60), and the empirical Skoplaki I model (RMSE = 5.92 °C, R² = 0.81). The resulting symbolic equation directly characterizes the effects of nonlinear solar radiation, ambient temperature, and wind speed, providing greater physical insight into the thermal dynamics of the system. An important finding is that the maximum temperature of the bifacial module is reached around 14:00h, probably due to the accumulation of temperature caused by solar tracking, which contrasts with what occurs in fixed-tilt monofacial technology. This study demonstrates that the symbolic regression technique with a genetic algorithm kernel can produce accurate, interpretable, and computationally economical models for advanced photovoltaic systems.


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Keywords: PV temperature prediction; Bifacial Photovoltaics; Single‐axis trackers; Genetic algorithms; symbolic regression

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Section: Original Research Article
Language : EN
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  1. Abe, J. Batista Dias, G. Notton, G. -A. Faggianelli, G. Pigelet and D. Ouvrard. (2023). Estimation of the Effective Irradiance and Bifacial Gain for PV Arrays Using the Maximum Power Current. IEEE J Photovolt 13:. https://doi.org/10.1109/JPHOTOV.2023.3242117
  2. Ali, M.M., Rokonuzzaman, M. D. Z,. Shuvo, A., Das, M., Islam, M., Rahman, M.M.(2021). Performance Investigation of Bifacial Module Based Time Varying Multilevel Solar Panel System. In: Conference Record of the IEEE Photovoltaic Specialists Conference. https://doi.org/10.1109/PVSC43889.2021.9518456
  3. Angelis, D., Sofos, F., Karakasidis, T.E. (2023). Artificial Intelligence in Physical Sciences: Symbolic Regression Trends and Perspectives. Archives of Computational Methods in Engineering 30. https://doi.org/10.1007/s11831-023-09922-z
  4. Aslam, M., Algarni, A. (2020). Analyzing the solar energy data using a new anderson-darling test under indeterminacy. International Journal of Photoenergy. https://doi.org/10.1155/2020/6662389
  5. Atlantica Colombia.(2023). Get to know our Plants. In: https://atlanticacolombia.com/en/nuestras-plantas/
  6. Ballina, J., Yun, L. (2025). Quantification and Comparative Analysis of Environmental Factors to Large-Scale Solar Plant’s Energy Performance via Regression and Linear Correlation Models. Journal of Energy and Power Technology; 7(1), 001; https://doi.org/doi: 10.21926/jept.2501001
  7. Becerra, V.G., Valdivia-Lefort, P., Barraza, R., García, J.G.(2024). Electrical Model Analysis for Bifacial PV Modules Using Real Performance Data in Laboratory. Energies (Basel), 17, 5868. https://doi.org/10.3390/en17235868
  8. Bera, C., Premachandra, K.W.R.S, Sujeewan, G., Rathwaththa, J.D.R.R, Abejeewa, P.A.I.S, Priyadarshana, H.V.V, Koswattage, K.R. (2024). A Comparative Experimental Performance Analysis for Fixed Solar PV Systems and Solar Tracker PV Systems in a Tropical Region. International Journal of Research and Innovation in Applied Science IX, 476–480. https://doi.org/10.51584/IJRIAS.2024.909041
  9. Bharti,. R, Kuitche, J,, Tamizhmani, M.G. (2009). Nominal Operating Cell Temperature (NOCT): Effects of module size, loading and solar spectrum. Conference Record of the IEEE Photovoltaic Specialists Conference. https://doi.org/10.1109/PVSC.2009.5411408
  10. Burnham, L., Riley, D., Walker, B., Pearce, J.M. (2019). Performance of Bifacial Photovoltaic Modules on a Dual-Axis Tracker in a High-Latitude, High-Albedo Environment. Conference Record of the IEEE Photovoltaic Specialists Conference
  11. Díaz-Bello, D., Vargas-Salgado, C., Alcázar-Ortega, M., Solar-Alfonso, D. (2024). Optimizing Photovoltaic Power Plant Forecasting with Dynamic Neural Network Structure Reenement Optimizing Photovoltaic Power Plant Forecasting with Dynamic Neural Network Structure Refinement. Scientific Reports, 15, 3337 https://doi.org/10.21203/rs.3.rs-3835055/v1
  12. Fan, X., Liu, W., Zhu, G. (2017). Scientific linkage and technological innovation capabilities: international comparisons of patenting in the solar energy industry. Scientometrics 111:. https://doi.org/10.1007/s11192-017-2274-5
  13. Haeberle, F., Dias, J.B., Cardoso Junior, J.T., Abe, C., Notton, G. (2022). Estimativa da temperatura do módulo fv a partir de um modelo de balanço de energia. Anais Congresso Brasileiro de Energia Solar - CBENS. https://doi.org/10.59627/cbens.2022.1122
  14. He, M., Zhang, L. (2021). Machine learning and symbolic regression investigation on stability of MXene materials. Comput Mater Sci 196:. https://doi.org/10.1016/j.commatsci.2021.110578
  15. Hodson, T.O. (2022). Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not. Geosci Model Dev 15. https://doi.org/10.5194/gmd-15-5481-2022
  16. Jiang, J. (2022). Multiple Linear Regression. Applied Medical Statistics. John Wiley & Sons, Ltd, 345–367. https://www.wiley.com/en-us/Applied+Medical+Statistics-p-9781119716822
  17. Johansson, F., Gustafsson, B.E., Stridh, B., Campana, P.E. (2022). 3D-thermal modelling of a bifacial agrivoltaic system: a photovoltaic module perspective. Energy Nexus, 5. https://doi.org/10.1016/j.nexus.2022.100052
  18. Kaplani, E., & Kaplanis, S. (2014). Thermal modelling and experimental assessment of the dependence of PV module temperature on wind velocity and direction, module orientation and inclination. Solar Energy 107. https://doi.org/10.1016/j.solener.2014.05.037
  19. Kaplani, E., & Kaplanis, S. (2020). PV Module Temperature Prediction at Any Environmental Conditions and Mounting Configurations. In: Sayigh, A. (eds) Renewable Energy and Sustainable Buildings. Innovative Renewable Energy. Springer, Cham. https://doi.org/10.1007/978-3-030-18488-9_77
  20. Kaushik, A.R., Padmavathi, S., Gurucharan, K.S., Raja, S.C. (2023). Performance Analysis of Regression Models in Solar PV Forecasting. 2023 3rd International Conference on Artificial Intelligence and Signal Processing, AISP 2023. https://doi.org/10.1109/AISP57993.2023.10134943
  21. Kayri, I., Aydin, H. (2022). ANN Based Prediction of Module Temperature in a Single Axis PV System. IEEE Global Energy Conference, GEC 2022. https://doi.org/10.1109/GEC55014.2022.9986829
  22. Kinaneva, D., Hristov, G., Kyuchukov, P., Georgiev, G., Zahariev, P., Daskalov, R.(2021). Machine Learning Algorithms for Regression Analysis and Predictions of Numerical Data. In: HORA 2021 - 3rd International Congress on Human-Computer Interaction, Optimization and Robotic Applications, Proceedings. https://doi.org/10.1109/HORA52670.2021.9461298
  23. Lara Vargas, FA, De la Ossa Rivera, J., Jaramillo Mira, S., Vargas Salgado, C. (2025a). Optimización del rendimiento de plantas solares en azotea mediante monitoreo IoT de bajo costo: Un estudio de caso en Montería, Colombia. Entre Ciencia e Ingeniería, 19, 71–78. https://doi.org/10.31908/19098367.3106
  24. Lara-Vargas, F.A., Vargas-Salgado, C., Águila-León, J., Díaz-Bello, D. (2025b). Optimizing Bifacial Solar Modules with Trackers: Advanced Temperature Prediction Through Symbolic Regression. Energies (Basel) 18. https://doi.org/10.3390/en18082019
  25. Mannino, G., Tina, G.M., Cacciato, M., Todaro, L., Bizzarri, F. (2022). Experimental assessment of temperature estimation models of bifacial photovoltaic modules. 2022 IEEE 49th Photovoltaics Specialists Conference (PVSC). IEEE, pp 0214–0216. https://doi.org/10.1109/PVSC48317.2022.9938792
  26. Masrur, H., Konneh, K.V., Ahmadi, M., Khan, K., Lutfi, M., Senjyu, T. (2021). Assessing the techno-economic impact of derating factors on optimally tilted grid-tied photovoltaic systems. Energies (Basel) 14. https://doi.org/10.3390/en14041044
  27. Mattei, M., Notton, G., Cristofari, C., Muselli, M., Poggi, P. (2006). Calculation of the polycrystalline PV module temperature using a simple method of energy balance. Renew Energy 31, 553–567. https://doi.org/10.1016/J.RENENE.2005.03.010
  28. Meflah, A., Aouchiche, I., Berkane, S., Chekired, F. (2023). Estimation models of photovoltaic module operating temperature under various climatic conditions. Indonesian Journal of Electrical Engineering and Computer Science 32. https://doi.org/10.11591/ijeecs.v32.i1.pp13-20
  29. Nolay, P. (1987). Developpement d’une methode generale d’analyse des systemes photovoltaiques. ENMP
  30. Obaideen, K., Olabi, A.G., Al Swailmeen, Y., Shehata, N., Ali, M., Hai, A., Rodriguez, C. E. (2023). Solar Energy: Applications, Trends Analysis, Bibliometric Analysis and Research Contribution to Sustainable Development Goals (SDGs). Sustainability (Switzerland) 15. https://doi.org/10.3390/su15021418
  31. Patel, M.T., Vijayan, R.A., Asadpour, R., Varadharajaperumal, M,,
  32. Khan, R., Alam, M.(2020). Temperature-dependent energy gain of bifacial PV farms: A global perspective. Appl Energy, 276. https://doi.org/10.1016/j.apenergy.2020.115405
  33. Ponnada, S., Kumari, I., Chinnam, S., Sadat, M., Lakshaman, A., Kumar, L., Bose, R.S.C., Gorle, D.B., Nowduri, A., Sharma, R.K. (2022). Renewable Energy: Introduction, Current Status, and Future Prospects. In: Green Energy Harvesting: Materials for Hydrogen Generation and Carbon Dioxide Reduction. https://doi.org/10.1002/9781119776086.ch1
  34. Radwan, Y.A., Kronberger, G., Winkler, S. (2024). A Comparison of Recent Algorithms for Symbolic Regression to Genetic Programming. Lecture Notes in Computer Science, 15172.. https://doi.org/10.1007/978-3-031-82949-9_15
  35. Raina, G., Sharma, S., Sinha, S. (2023). Dynamic Opto-Electric-Thermal Modelling for Performance Assessment of Bifacial PV Modules. 2023 IEEE 3rd International Conference on Sustainable Energy and Future Electric Transportation, SeFet 2023. https://doi.org/10.1109/SeFeT57834.2023.10245096
  36. República de Colombia (2005). Atlas de Radiación Solar de Colombia. Bogota
  37. Sanchís-Gómez, C., Aleix-Moreno, J., Vargas-Salgado, C., Alfonso-Solar, D. (2025). The novel evaluation method for PV module temperature and string size risk in utility-scale solar projects. Solar Energy 295:113520. https://doi.org/10.1016/J.SOLENER.2025.113520
  38. Sheta, A., Abdel-Raouf, A., Fraihat, K.M., Baareh, A. (2023). Evolutionary Design of a PSO-Tuned Multigene Symbolic Regression Genetic Programming Model for River Flow Forecasting. International Journal of Advanced Computer Science and Applications(IJACSA), 14 (4). http://dx.doi.org/10.14569/IJACSA.2023.0140489
  39. Shmuel, A., Glickman, O., Lazebnik, T. (2023). Symbolic Regression as Feature Engineering Method for Machine and Deep Learning Regression Tasks. Mach. Learn.: Sci. Technol. 5 025065. https://doi.org/10.1088/2632-2153/ad513a
  40. Singha, R. M., Roy, B., Gupta, R., Das Sharma, K. (2020) .On-Device Reliability Assessment and Prediction of Missing Photoplethysmographic Data Using Deep Neural Networks. IEEE Trans Biomed Circuits Syst 14. https://doi.org/10.1109/TBCAS.2020.3028935
  41. Skoplaki, E., Boudouvis, A.G., Palyvos, J.A. (2008). A simple correlation for the operating temperature of photovoltaic modules of arbitrary mounting. Solar Energy Materials and Solar Cells 92,1393–1402. https://doi.org/10.1016/j.solmat.2008.05.016
  42. Storlie, C.B., Therneau, T.M., Carter, R.E, Chia. N., Bergquist, J.(2020). Prediction and Inference With Missing Data in Patient Alert Systems. J Am Stat Assoc 115:. https://doi.org/10.1080/01621459.2019.1604359
  43. Sunday, V.E., Simeon, O., Anthony, U.M. (2017). Multiple Linear Regression Photovoltaic Cell Temperature Model for PVSyst Simulation Software. International Journal of Theoretical and Applied Mathematics 2, 140–143. https://doi.org/10.11648/j.ijtam.20160202.27
  44. Tarantola, S., Ferretti, F., Lo Piano, S., kaslova, M., Lachi, A., Rosati, R., Puy, A., Roy, P., Vannucci, G., Czarnecka, M., Saltelli, A. (2024). An annotated timeline of sensitivity analysis. Environmental Modelling and Software 174. https://doi.org/10.1016/j.envsoft.2024.105977
  45. Tina, G.M., Scavo, F.B., Gagliano, A. (2020). Multilayer Thermal Model for Evaluating the Performances of Monofacial and Bifacial Photovoltaic Modules. IEEE J Photovolt 10, 1035–1043. https://doi.org/10.1109/JPHOTOV.2020.2982117
  46. Tripathi, A.K., Ray, S., Aruna, M. (2021). Analysis on Photovoltaic Panel Temperature under the Influence of Solar Radiation and Ambient Temperature. 2021 International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT). IEEE, pp 1–5. https://doi.org/10.1109/ICAECT49130.2021.9392619
  47. Wang, S., Shen, Y., Zhou, J., Li, C., Ma, L. (2022). Efficiency Enhancement of Tilted Bifacial Photovoltaic Modules with Horizontal Single-Axis Tracker—The Bifacial Companion Method. Energies (Basel) 15:1262. https://doi.org/10.3390/en15041262
  48. Yakubu, R.O., Mensah, L.D., Quansah, D.A., Adaramola, M,S. (2022). Improving solar photovoltaic installation energy yield using bifacial modules and tracking systems: An analytical approach. Advances in Mechanical Engineering 14. https://doi.org/10.1177/16878132221139714
  49. Zaimi, M., El Achouby, H., Ibral, A., Assaid, E., Salaheddine, M., Saadani, R.(2019). Temporal monitoring of temperature and incident irradiance for predicting photovoltaic solar module peak power and efficiency using analytical expressions of model physical parameters. Proceedings of 2018 6th International Renewable and Sustainable Energy Conference, IRSEC 2018. https://doi.org/10.1109/IRSEC.2018.8702973
  50. Zand, M., Nasab, M.A., Padmanaban, S., Maroti, P., Muyeen, S.(2023). Sensitivity analysis index to determine the optimal location of multi-objective UPFC for improvement of power quality parameters. Energy Reports 10. https://doi.org/10.1016/j.egyr.2023.06.028

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