This paper compares a single-diode model (SDM) parameter extraction method based on differential evolution (DE) with the analytical Villalva method, using a selected set of current-voltage (I-V) curves from the publicly available Sandia flash test dataset. The paper examines the methods’ applicability to experimentally measured curves from commercial photovoltaic (PV) modules. The SDM DE method analytically eliminates parameters from five to three, uses a Newton-Raphson solver for the implicit I-V characteristic, and minimises an objective function based on the error at the maximum power point. The results show that the proposed method achieves a lower root mean square error (RMSE) and normalized root mean square error (NRMSE) than the Villalva method across all tested curves, though at a higher computational cost.

Solar photovoltaic power, Photovoltaic parameter extraction, Single-diode model, Differential evolution

[1] Renewable Capacity Statistics 2026. International Renewable Energy Agency, 2026. https://www.irena.org/Publications/2026/Mar/Renewable-capacity-statistics-2026 (Accessed: 4 June 2026).
[2] Renewable Power Generation Costs in 2025. International Renewable Energy Agency. 2026. https://www.irena.org/Publications/2026/Jul/Renewable-Power-Generation-Costs-in-2025 (Accessed: 29 July 2026).
[3] W. Shockley, The Theory of p-n Junctions in Semiconductors and p-n Junction Transistors. Bell System Technical Journal, 28(3), 1949: 435-489. https://doi.org/10.1002/j.1538-7305.1949.tb03645.x
[4] D.C. Jordan, S.R. Kurtz, Photovoltaic Degradation Rates—an Analytical Review. Progress in Photovoltaics: Research and Applications, 21(1), 2011: 12-29. https://doi.org/10.1002/pip.1182
[5] V.J. Chin, Z. Salam, K. Ishaque, Cell Modelling and Model Parameters Estimation Techniques for Photovoltaic Simulator Application: A Review. Applied Energy, 154, 2015: 500-519.
https://doi.org/10.1016/j.apenergy.2015.05.035
[6] A.M. Humada, M. Hojabri, S. Mekhilef, H.M. Hamada, Solar Cell Parameters Extraction Based on Single and Double-Diode Models: A Review. Renewable and Sustainable Energy Reviews, 56, 2016: 494-509. https://doi.org/10.1016/j.rser.2015.11.051
[7] A.R. Jordehi, Parameter Estimation of Solar Photovoltaic (PV) Cells: A Review. Renewable and Sustainable Energy Reviews, 61, 2016: 354-371. https://doi.org/10.1016/j.rser.2016.03.049
[8] M.G. Villalva, J.R. Gazoli, E.R. Filho, Comprehensive Approach to Modeling and Simulation of Photovoltaic Arrays. IEEE Transactions on Power Electronics, 24(5), 2009: 1198-1208.
https://doi.org/10.1109/TPEL.2009.2013862
[9] W. De Soto, S.A. Klein, W.A. Beckman, Improvement and Validation of a Model for Photovoltaic Array Performance. Solar Energy, 80(1), 2006: 78-88. https://doi.org/10.1016/j.solener.2005.06.010
[10] W. Xiao, W.G. Dunford, A. Capel, A Novel Modeling Method for Photovoltaic Cells. 2004 IEEE 35^th Annual Power Electronics Specialists Conference, Aachen, Germany, 20–25 June 2004. pp.1950- 1956.
[11] Y. Mahmoud, W. Xiao, H.H. Zeineldin, A Simple Approach to Modeling and Simulation of Photovoltaic Modules. IEEE Transactions on Sustainable Energy, 3(1), 2012: 185-186.
https://doi.org/10.1109/TSTE.2011.2170776
[12] V. Stornelli, M. Muttillo, T. de Rubeis, I. Nardi, A New Simplified Five-Parameter Estimation Method for Single-Diode Model of Photovoltaic Panels. Energies, 12(22), 2019: 4271.
https://doi.org/10.3390/en12224271
[13] E.A. Silva, F. Bradaschia, M.C. Cavalcanti, A.J. Nascimento, Parameter Estimation Method to Improve the Accuracy of Photovoltaic Electrical Model. IEEE Journal of Photovoltaics, 6(1), 2016: 278-285.
https://doi.org/10.1109/JPHOTOV.2015.2483369
[14] R. Storn, K. Price, Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization, 11(4), 1997: 341-359.
https://doi.org/10.1023/A:1008202821328
[15] K. Ishaque, Z. Salam, S. Mekhilef, A. Shamsudin, Parameter Extraction of Solar Photovoltaic Modules Using Penalty-Based Differential Evolution. Applied Energy, 99, 2012: 297-308.
https://doi.org/10.1016/j.apenergy.2012.05.017
[16] M. Ye, X. Wang, Y. Xu, Parameter Extraction of Solar Cells Using Particle Swarm Optimization. Journal of Applied Physics, 105(9), 2009: 094502. https://doi.org/10.1063/1.3122082
[17] J.A. Jervase, H. Bourdoucen, A. Al-Lawati, Solar Cell Parameter Extraction Using Genetic Algorithms. Measurement Science and Technology, 12(11), 2001: 1922-1925. https://doi.org/10.1088/0957-0233/12/11/322
[18] Y. Kharchouf, R. Herbazi, A. Chahboun, Parameter’s Extraction of Solar Photovoltaic Models Using an Improved Differential Evolution Algorithm. Energy Conversion and Management, 251, 2022: 114972. https://doi.org/10.1016/j.enconman.2021.114972
[19] C. Chermite, M.R. Douiri, Differential Evolution Algorithm Featuring Novel Mutation Combined with Newton-Raphson Method for Enhanced Photovoltaic Parameter Extraction. Energy Conversion and Management, 326, 2025: 119468. https://doi.org/10.1016/j.enconman.2024.119468
[20] S.Z. Almutairi, A.M. Shaheen, A Novel Kangaroo Escape Optimizer for Parameter Estimation of Solar Photovoltaic Cells/Modules via One, Two and Three-Diode Equivalent Circuit Modeling. Scientific Reports, 15, 2025: 32669. https://doi.org/10.1038/s41598-025-19917-4
[21] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd Edition. Cambridge University Press, Cambridge, 2007.
[22] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, et al., SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17, 2020: 261-272. https://doi.org/10.1038/s41592-019-0686-2
[23] T. Easwarakhanthan, J. Bottin, I. Bouhouch, C. Boutrit, Nonlinear Minimization Algorithm for Determining the Solar Cell Parameters with Microcomputers. International Journal of Solar Energy, 4(1), 1986: 1-12. https://doi.org/10.1080/01425918608909835
[24] M.R. AlRashidi, M.F. AlHajri, K.M. El-Naggar, A.K. Al-Othman, A New Estimation Approach for Determining the I–V Characteristics of Solar Cells. Solar Energy, 85(7), 2011: 1543-1550.
https://doi.org/10.1016/j.solener.2011.04.013
[25] K.M. El-Naggar, M.R. AlRashidi, M.F. AlHajri, A.K. Al-Othman, Simulated Annealing Algorithm for Photovoltaic Parameters Identification. Solar Energy, 86(1), 2012: 266-274.
https://doi.org/10.1016/j.solener.2011.09.032
[26] D. Oliva, E. Cuevas, G. Pajares, Parameter Identification of Solar Cells Using Artificial Bee Colony Optimization. Energy, 72, 2014: 93-102. https://doi.org/10.1016/j.energy.2014.05.011
[27] Z. Chen, L. Wu, P. Lin, Y. Wu, S. Cheng, Parameters Identification of Photovoltaic Models Using Hybrid Adaptive Nelder-Mead Simplex Algorithm Based on Eagle Strategy. Applied Energy, 182, 2016: 47-57. https://doi.org/10.1016/j.apenergy.2016.08.083
[28] Y. Bouali, B. Alamri, Parameter Extraction for Photovoltaic Models with Flood-Algorithm-Based Optimization. Mathematics, 13(1), 2025: 19. https://doi.org/10.3390/math13010019
[29] A. Bennagi, O. AlHousrya, D.T. Cotfas, P.A. Cotfas, Parameter Extraction of Photovoltaic Cells and Panels Using a PID-Based Metaheuristic Algorithm. Applied Sciences, 15(13), 2025: 7403.
https://doi.org/10.3390/app15137403
[30] Y. Bouali, B. Alamri, Parameter Extraction of Photovoltaic Cell/Module Models Using Starfish Optimization Algorithm with a Secant-Based Objective Function Modification. Scientific Reports, 16, 2026: 4467. https://doi.org/10.1038/s41598-025-34584-1
[31] B. Byford,  J. Braid, M. Theristis, C. Robinson, W. Snyder, K. Santistevan, N. Jost, N. B. King,  Photovoltaic Module Current-Voltage and Electroluminescence Image Data (PV-IV-EL). [Data set]. Open Energy Data Initiative (OEDI). Sandia National Laboratories, 2015.
https://data.openei.org/submissions/8378 (Accessed: 17 July 2026).
[32] J.A. Gow, C.D. Manning, Development of a Photovoltaic Arraymodel for Use in Power-Electronics Simulation Studies. IEE Proceedings – Electric Power Applications, 146(2), 1999: 193-200.
https://doi.org/10.1049/ip-epa:19990116
[33] A. Savitzky, M.J.E. Golay, Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 36(8), 1964: 1627-1639. https://doi.org/10.1021/ac60214a047
[34] G.M. Tina, C. Ventura, Evaluation and Validation of an Electrical Model of Photovoltaic Module Based on Manufacturer Measurement. In: A. Hakansson, M. Höjer, R.J. Howlett, L.C. Jain, (Eds.). Sustainability in Energy and Buildings. Springer Berlin Heidelberg, Berlin, Heidelberg, 2013: pp.15-24. https://doi.org/10.1007/978-3-642-36645-1_2
[35] M. Ćalasan, S.H.E. Abdel Aleem, A.F. Zobaa, On the Root Mean Square Error (RMSE) Calculation for Parameter Estimation of Photovoltaic Models: A Novel Exact Analytical Solution Based on Lambert W Function. Energy Conversion and Management, 210, 2020: 112716.
https://doi.org/10.1016/j.enconman.2020.112716