Parameter Identification of Photovoltaic Models Using an Enhanced INFO Algorithm

Abstract

Photovoltaic (PV) systems are electrical systems designed to convert solar energy into electrical energy. As a crucial component of PV systems, harsh weather conditions, photovoltaic panel temperature and solar irradiance infiuence the power output of photovoltaic cells. Therefore, accurately identifying the parameters of PV models is essential for simulating, controlling and evaluating PV systems. In this study, we propose an enhanced weighted-mean-of-vectors optimisation (EINFO) for efficiently determining the unknown parameters in PV systems. EINFO introduces a Lambert W-based explicit objective function for the PV model, enhancing the computational accuracy of the algorithm's population fitness. This addresses the challenge of improving the metaheuristic algorithms' identification accuracy for unknown parameter identification in PV models. We experimentally apply EINFO to three types of PV models (single-diode, double-diode and PV-module models) to validate its accuracy and stability in parameter identification. The results demonstrate that EINFO achieves root mean square errors (RMSEs) of 7.7301E-04, 6.8553E-04 and 2.0608E-03 for the single-diode model, double-diode model and PV-module model, respectively, surpassing those obtained by using INFO algorithm as well as other methods in terms of convergence speed, accuracy and stability. Furthermore, comprehensive experimental findings on three commercial PV modules (ST40, SM55 and KC200GT) indicate that EINFO consistently maintains high accuracy across varying temperatures and irradiation levels. In conclusion, EINFO emerges as a highly competitive and practical approach for parameter identification in diverse types of PV models.

Keywords

Lambert W function / multi-objective optimisation / optimisation / parameteridentification / photovoltaic model / weighted-mean-of-vectorsalgorithm

References

[1] F. Yu, C. Lu, L. Yin, and J. Zhou, “Modeling and Optimization Al-gorithm for Energy-Efficient Distributed Assembly Hybrid Flowshop Scheduling Problem Considering Worker Resources,” Journal of In-dustrial Information Integration 40 (July 2024): 100620, https://doi.org/10.1016/j.jii.2024.100620.

[2] A. M. Beigi and A. Maroosi, “Parameter Identification for Solar Cells and Module Using a Hybrid Firefiy and Pattern Search Algorithms,” Solar Energy 171 (September 2018): 435-446, https://doi.org/10.1016/j.solener.2018.06.092.

[3] J. B. Wang, B. Yang, D. Y. Li, et al., “Photovoltaic Cell Parameter Estimation Based on Improved Equilibrium Optimizer Algorithm,” Energy Conversion and Management 236 (May 2021): 114051, https://doi.org/10.1016/j.enconman.2021.114051.

[4] Y. Kharchouf, R. Herbazi, and A. Chahboun, “Parameter’s Extraction of Solar Photovoltaic Models Using an Improved Differential Evolution Algorithm,” Energy Conversion and Management 251 (January 2022): 114972, https://doi.org/10.1016/j.enconman.2021.114972.

[5] T. L. Pushparaj, E. Raj, E. Rani, S. Darwin, and M. Appadurai, “Employing Novel Si-Over-Si Technology to Optimize PV Effect in Solar Array,” Silicon 14, no. 18 (December 2022): 12823-12835, https://doi.org/10.1007/s12633-022-01976-1.

[6] H. J. Loschi, Y. Iano, J. León, A. Moretti, F. D. Conte, and H. Braga, “A Review on Photovoltaic Systems: Mechanisms and Methods for Irradiation Tracking and Prediction,” Smart Grid and Renewable Energy 6, no. 7 (2015): 187-208, https://doi.org/10.4236/sgre.2015.67017.

[7] M. M. Rahman, M. Hasanuzzaman, and N. A. Rahim, “Effects of Operational Conditions on the Energy Efficiency of Photovoltaic Modules Operating in Malaysia,” Journal of Cleaner Production 143 (February 2017): 912-924, https://doi.org/10.1016/j.jclepro.2016.12.029.

[8] A. Fathy and H. Rezk, “Parameter Estimation of Photovoltaic System Using Imperialist Competitive Algorithm,” Renewable Energy 111 (October 2017): 307-320, https://doi.org/10.1016/j.renene.2017.04.014.

[9] M. Abd Elaziz, S. B. Thanikanti, I. A. Ibrahim, et al., “Enhanced Marine Predators Algorithm for Identifying Static and Dynamic Photovoltaic Models Parameters,” Energy Conversion and Management 236 (May 2021): 113971, https://doi.org/10.1016/j.enconman.2021.113971.

[10] F. Montalvo-Galicia, M. T. Sanz-Pascual, P. Rosales-Quintero, and M. Moreno-Moreno, “Solar Cell Parameter Extraction Method From Illumination and Dark I-V Characteristics,” Nanomaterials 12, no. 12 (January 2022): 1955, https://doi.org/10.3390/nano12121955.

[11] M. Premkumar, P. Jangir, C. Kumar, et al., “Constraint Estimation in Three-Diode Solar Photovoltaic Model Using Gaussian and Cauchy Mutation-Based Hunger Games Search Optimizer and Enhanced Newton-Raphson Method,” IET Renewable Power Generation 16, no. 8 (June 2022): 1733-1772, https://doi.org/10.1049/rpg2.12475.

[12] V. L. Brano, A. Orioli, and G. Ciulla, “On the Experimental Vali-dation of an Improved Five-Parameter Model for Silicon Photovoltaic Modules,” Solar Energy Materials and Solar Cells 105 (October 2012): 27-39, https://doi.org/10.1016/j.solmat.2012.05.028.

[13] R. Abbassi, A. Boudjemline, A. Abbassi, A. Torchani, H. Gasmi, and T. Guesmi, “A Numerical-Analytical Hybrid Approach for the Identifi-cation of SDM Solar Cell Unknown Parameters,” Engineering, Tech-nology & Applied Science Research 8, no. 3 (June 2018): 2907-2913, https://doi.org/10.48084/etasr.2027.

[14] M. M. Shebani, T. Iqbal, and J. E. Quaicoe, “Comparing Bisection Numerical Algorithm with Fractional Short Circuit Current and Open Circuit Voltage Methods for MPPT Photovoltaic Systems,” in 2016 IEEE Electrical Power and Energy Conference (EPEC) IEEE, 2016), 1-5.

[15] H. Moayedi and S. Hayati, “Modelling and Optimization of Ultimate Bearing Capacity of Strip Footing near a Slope by Soft Computing Methods,” Applied Soft Computing 66 (2018): 208-219, https://doi.org/10.1016/j.asoc.2018.02.027.

[16] Y. Duan,Y. Zhao, and J. Hu, “An Initialization-Free Distributed Algorithm for Dynamic Economic Dispatch Problems in Microgrid: Modeling, Optimization and Analysis,” Sustainable Energy, Grids and Networks 34 (June 2023): 101004, https://doi.org/10.1016/j.segan.2023.101004.

[17] B. Cao, J. Zhao, Z. Lv, Y. Gu, P. Yang, and S. K. Halgamuge, “Multiobjective Evolution of Fuzzy Rough Neural Network via Distributed Parallelism for Stock Prediction,” IEEE Transactions on Fuzzy Systems 28, no. 5 (May 2020): 939-952, https://doi.org/10.1109/tfuzz.2020.2972207.

[18] B. Cao, X. Wang, W. Zhang, H. Song, and Z. Lv, “A many-objective Optimization Model of Industrial Internet of Things Based on Private Blockchain,” IEEE Network 34, no. 5 (September 2020): 78-83, https://doi.org/10.1109/MNET.011.1900536.

[19] B. Cao, W. Zhang, X. Wang, J. Zhao, Y. Gu, and Y. Zhang, “A Memetic Algorithm Based on Two_Arch2 for Multi-Depot Heteroge-neous-Vehicle Capacitated Arc Routing Problem,” Swarm and Evolu-tionary Computation 63 (June 2021): 100864, https://doi.org/10.1016/j.swevo.2021.100864.

[20] X. Xu, Z. Lin, X. Li, C. Shang, and Q. Shen, “Multi-Objective Robust Optimisation Model for MDVRPLS in Refined Oil Distribution,” Inter-national Journal of Production Research 60, no. 22 (March 2022): 6772-6792, https://doi.org/10.1080/00207543.2021.1887534.

[21] C. Wang, Z. Wang, S. Zhang, X. Liu, and J. Tan, “Reinforced Quantum-Behaved Particle Swarm-Optimized Neural Network for Cross-Sectional Distortion Prediction of Novel Variable-Diameter-Die-Formed Metal Bent Tubes,” Journal of Computational Design and Engineering 10, no. 3 (April 2023): 1060-1079, https://doi.org/10.1093/jcde/qwad037.

[22] K. Yu, J. J. Liang, B. Y. Qu, X. Chen, and H. Wang, “Parameters Identification of Photovoltaic Models Using an Improved JAYA Opti-mization Algorithm,” Energy Conversion and Management 150 (October 2017): 742-753, https://doi.org/10.1016/j.enconman.2017.08.063.

[23] E. Demirci and A. R. Yıldız, “A New Hybrid Approach for Reliability-Based Design Optimization of Structural Components,” Materials Testing 61, no. 2 (April 2019): 111-119, https://doi.org/10.3139/120.111291.

[24] X. Chen, S. Wang, and K. X. He, “Parameter Estimation of Various PV Cells and Modules Using an Improved Simultaneous Heat Transfer Search Algorithm,” Journal of Computational Electronics 23, no. 3 (March 2024): 584-599, https://doi.org/10.1007/s10825-024-02153-w.

[25] C. Chermite and M. R. Douiri, “Hybrid Tiki Taka and Mean Differ-ential Evolution Based Weibull Distribution: A Comprehensive Approach for Solar PV Modules Parameter Extraction With Newton-Raphson Optimization,” Energy Conversion and Management 314 (August 2024): 118705, https://doi.org/10.1016/j.enconman.2024.118705.

[26] X. J. Ye, W. Liu, H. Li, et al., “Modified Whale Optimization Al-gorithm for Solar Cell and PV Module Parameter Identification,” Complexity 2021, no. 1 (February 2021): 8878686, https://doi.org/10.1155/2021/8878686.

[27] X. Weng, A. A. Heidari, G. Liang, H. Chen, and X. Ma, “An Evolu-tionary Nelder-Mead Slime Mould Algorithm with Random Learning for Efficient Design of Photovoltaic Models,” Energy Reports 7 (November 2021): 8784-8804, https://doi.org/10.1016/j.egyr.2021.11.019.

[28] B. Xu, A. A. Heidari, F. Kuang, S. Zhang, H. Chen, and Z. Cai, “Quantum Nelder-Mead Hunger Games Search for Optimizing Photo-voltaic Solar Cells,” International Journal of Energy Research 46, no. 9 (July 2022): 12417-12466, https://doi.org/10.1002/er.8011.

[29] H. P. Lin, I. Ahmadianfar, N. A. Golilarz, et al., “Adaptive Slime Mould Algorithm for Optimal Design of Photovoltaic Models,” Energy Science & Engineering 10, no. 7 (July 2022): 2035-2064, https://doi.org/10.1002/ese3.1115.

[30] C. Chermite and M. R. Douiri, “Differential Evolution Algorithm Featuring Novel Mutation Combined With Newton-Raphson Method for Enhanced Photovoltaic Parameter Extraction,” Energy Conversion and Management 326 (February 2025): 119468, https://doi.org/10.1016/j.enconman.2024.119468.

[31] Y. Liu, G. S. Chong, A. A. Heidari, et al., “Horizontal and Vertical Crossover of Harris Hawk Optimizer With Nelder-Mead Simplex for Parameter Estimation of Photovoltaic Models,” Energy Conversion and Management 223 (November 2020): 113211, https://doi.org/10.1016/j.enconman.2020.113211.

[32] I. Ahmadianfar, A. A. Heidari, S. Noshadian, H. Chen, and A. H. Gandomi, “INFO: An Efficient Optimization Algorithm Based on Weighted Mean of Vectors,” Expert Systems With Applications 195 (June 2022): 116516, https://doi.org/10.1016/j.eswa.2022.116516.

[33] Z. Q. Geng, W. K. Kong, X. T. Wang, L. Wang, and Y. M. Han, “Adaptive Search Based Grey Wolf Optimization Algorithm for multi-objective Optimization of Ethylene Cracking Furnace,” Swarm and Evolutionary Computation 92 (February 2025): 101810, https://doi.org/10.1016/j.swevo.2024.101810.

[34] C. Chermite and M. R. Douiri, “A Novel Hybrid Approach Combining Differentiated Creative Search With Adaptive Refinement for Photovoltaic Parameter Extraction,” Renewable Energy 245 (June 2025): 122764, https://doi.org/10.1016/j.renene.2025.122764.

[35] X. T. Wang, Z. Q. Geng, L. C. Chen, and Y. M. Han, “Improved Dragonfiy Optimization Algorithm Based on Quantum Behavior for Multi-Objective Optimization of Ethylene Cracking Furnace,” Swarm and Evolutionary Computation 88 (July 2024): 101607, https://doi.org/10.1016/j.swevo.2024.101607.

[36] M. Jiang, K. Ding, X. Chen, et al., “CGH-GTO Method for Model Parameter Identification Based on Improved Grey Wolf Optimizer, Honey Badger Algorithm, and Gorilla Troops Optimizer,” Energy 296 (June 2024): 131163, https://doi.org/10.1016/j.energy.2024.131163.

[37] X. Yu, Y. Duan, and Z. Cai, “Sub-Population Improved Grey Wolf Optimizer With Gaussian Mutation and Lévy Flight for Parameters Identification of Photovoltaic Models,” Expert Systems With Applications 232 (December 2023): 120827, https://doi.org/10.1016/j.eswa.2023.120827.

[38] M. A. El-Dabah, R. A. El-Sehiemy, H. M. Hasanien, and B. Saad, “Photovoltaic Model Parameters Identification Using Northern Goshawk Optimization Algorithm,” Energy 262 (January 2023): 125522, https://doi.org/10.1016/j.energy.2022.125522.

[39] L. Chaib, M. Tadj, A. Choucha, F. Z. Khemili, and A. El-Fergany, “Improved Crayfish Optimization Algorithm for Parameters Estimation of Photovoltaic Models,” Energy Conversion and Management 313 (August 2024): 118627, https://doi.org/10.1016/j.enconman.2024.118627.

[40] Y. Zhang, S. Li, Y. Wang, Y. Yan, J. Zhao, and Z. Gao, “Self-Adaptive Enhanced Learning Differential Evolution With Surprisingly Efficient Decomposition Approach for Parameter Identification of Photovoltaic Models,” Energy Conversion and Management 308 (May 2024): 118387, https://doi.org/10.1016/j.enconman.2024.118387.

[41] I. Choulli, M. Elyaqouti, E. hanafi Arjdal, et al., “DIWJAYA: JAYA Driven by Individual Weights for Enhanced Photovoltaic Model Parameter Estimation,” Energy Conversion and Management 305 (April 2024): 118258, https://doi.org/10.1016/j.enconman.2024.118258.

[42] C. Chermite and M. R. Douiri, “Harnessing Hybrid Intelligence: Four Vector Metaheuristic and Differential Evolution for Optimized Photovoltaic Parameter Extraction,” Computers & Electrical Engineering 123 (April 2025): 110276, https://doi.org/10.1016/j.compeleceng.2025.110276.

[43] F. Belabbes, D. T. Cotfas, P. A. Cotfas, and M. Medles, “Using the Snake Optimization Metaheuristic Algorithms to Extract the Photovol-taic Cells Parameters,” Energy Conversion and Management 292 (September 2023): 117373, https://doi.org/10.1016/j.enconman.2023.117373.

[44] M. Qaraad, S. Amjad, N. K. Hussein, M. A. Farag, S. Mirjalili, and M. A. Elhosseini, “Quadratic Interpolation and a New Local Search Approach to Improve Particle Swarm Optimization: Solar Photovoltaic Parameter Estimation,” Expert Systems With Applications 236 (February 2024): 121417, https://doi.org/10.1016/j.eswa.2023.121417.

[45] Z. Song, C. Ren, and Z. Meng, “An Adaptive Differential Evolution With Opposition-Learning Based Diversity Enhancement,” Expert Sys-tems With Applications 243 (June 2024): 122942, https://doi.org/10.1016/j.eswa.2023.122942.

[46] Y. Li, K. Yu, J. Liang, C. Yue, and K. Qiao, “A landscape-aware Particle Swarm Optimization for Parameter Identification of Photovol-taic Models,” Applied Soft Computing 131 (December 2022): 109793, https://doi.org/10.1016/j.asoc.2022.109793.

[47] H. M. Ridha, H. Hizam, S. Mirjalili, M. L. Othman, and M. E. Ya’acob, “Zero Root-Mean-Square Error for Single-and Double-Diode Photovoltaic Models Parameter Determination,” Neural Computing & Applications 34, no. 14 (2022): 1-22, https://doi.org/10.1007/s00521-022-07047-1.

[48] J. Cubas, S. Pindado, and C. De Manuel, “Explicit Expressions for Solar Panel Equivalent Circuit Parameters Based on Analytical Formulation and the Lambert W-function,” Energies 7, no. 7 (2014): 7-4115, https://doi.org/10.3390/en7074098.

[49] S. Lun, S. Wang, G. Yang, and T. Guo, “A New Explicit double-diode Modeling Method Based on Lambert W-function for Photovoltaic Ar-rays,” Solar Energy 116 (2015): 69-82, https://doi.org/10.1016/j.solener.2015.03.043.

[50] L. M. P. Archila, J. D. B. Rodríguez, and R. Correa, “Implicit Modelling of Series-Parallel Photovoltaic Arrays Using Double-Diode Model and Its Solution,” Solar Energy 214 (2021): 131-137, https://doi.org/10.1016/j.solener.2020.11.036.

[51] M. A. Alghamdi, M. F. Nadeem Khan, A. K. Khan, et al., “PV Model Parameter Estimation Using Modified FPA With Dynamic Switch Probability and Step Size Function,” IEEE Access 9 (2021): 42027-42044, https://doi.org/10.1109/access.2021.3064757.

[52] X. Weng, A. A. Heidari, G. Liang, et al., “Laplacian Nelder-Mead Spherical Evolution for Parameter Estimation of Photovoltaic Models,” Energy Conversion and Management 243 (September 2021): 114223, https://doi.org/10.1016/j.enconman.2021.114223.

[53] M. Premkumar, R. Sowmya,S. Umashankar, and P. Jangir, “Extraction of Uncertain Parameters of Single-Diode Photovoltaic Module Using Hybrid Particle Swarm Optimization and Grey Wolf Optimization Algorithm,” Materials Today: Proceedings 46 (January 2021): 5315-5321, https://doi.org/10.1016/j.matpr.2020.08.784.

[54] K. Yu, J. J. Liang, B. Y. Qu, Z. Cheng, and H. Wang, “Multiple Learning Backtracking Search Algorithm for Estimating Parameters of Photovoltaic Models,” Applied Energy 226 (2018): 408-422, https://doi.org/10.1016/j.apenergy.2018.06.010.

[55] Y. Zheng and Y. Meng, “Swarm Intelligence Based Dynamic Object Tracking,” in 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence June 2008), 405-412, https://doi.org/10.1109/CEC.2008.4630829.

[56] F. Yu, C. Lu, J. Zhou, L. Yin, and K. Wang, “A Knowledge-Guided Bi-Population Evolutionary Algorithm for Energy-Efficient Scheduling of Distributed Flexible Job Shop Problem,” Engineering Applications of Artificial Intelligence 128 (2024): 107458, https://doi.org/10.1016/j.engappai.2023.107458.

[57] A. Dehghanzadeh, G. Farahani, and M. Maboodi, “A Novel Approximate Explicit Double-Diode Model of Solar Cells for Use in Simulation Studies,” Renewable Energy 103 (2017): 468-477, https://doi.org/10.1016/j.renene.2016.11.051.

[58] Y. Chen, Y. Sun, and Z. Meng, “An Improved Explicit Double-Diode Model of Solar Cells: Fitness Verification and Parameter Extraction,” Energy Conversion and Management 169 (2018): 345-358, https://doi.org/10.1016/j.enconman.2018.05.035.

[59] G. Alefeld, “On the Convergence of Halley’s Method,” American Mathematical Monthly 88, no. 7 (1981): 530-536, https://doi.org/10.1080/00029890.1981.11995308.

[60] D. Veverič, “Lambert W Function for Applications in Physics,” Computer Physics Communications 183, no. 12 (2012): 2622-2628, https://doi.org/10.1016/j.cpc.2012.07.008.

[61] J. P. Ram, T. S. Babu, T. Dragicevic, and N. Rajasekar, “A New Hybrid Bee Pollinator Flower Pollination Algorithm for Solar PV Parameter Estimation,” Energy Conversion and Management 135 (March 2017): 463-476, https://doi.org/10.1016/j.enconman.2016.12.082.

[62] I. Ahmadianfar, A. A. Heidari, A. H. Gandomi, X. Chu, and H. Chen, “RUN Beyond the Metaphor: An Efficient Optimization Algo-rithm Based on Runge Kutta Method,” Expert Systems With Applications 181 (November 2021): 115079, https://doi.org/10.1016/j.eswa.2021.115079.

[63] F. Marini and B. Walczak, “Particle Swarm Optimization (PSO). A Tutorial,” Chemometrics and Intelligent Laboratory Systems 149 (December 2015): 153-165, https://doi.org/10.1016/j.chemolab.2015.08.020.

[64] R. Rao, “Review of Applications of TLBO Algorithm and a Tutorial for Beginners to Solve the Unconstrained and Constrained Optimization Problems,” Decision Science Letters 5, no. 1 (2016): 1-30, https://doi.org/10.5267/j.dsl.2015.9.003.

[65] B. Cao, J. Zhao, Y. Gu, S. Fan, and P. Yang, “Security-Aware In-dustrial Wireless Sensor Network Deployment Optimization,” IEEE Transactions on Industrial Informatics 16, no. 8 (2019): 5309-5316, https://doi.org/10.1109/tii.2019.2961340.

[66] B. Cao, J. Zhao, Y. Gu, Y. Ling, and X. Ma, “Applying Graph-Based Differential Grouping for Multiobjective Large-Scale Optimization,” Swarm and Evolutionary Computation 53 (2020): 100626, https://doi.org/10.1016/j.swevo.2019.100626.

Funding

MRC(MC_PC_17171)

Royal Society(RP202G0230)

BHF(AA/18/3/34220)

Hope Foundation for Cancer Research(RM60G0680)

GCRF(P202PF11)

Sino-UK Industrial Fund(RP202G0289)

Sino-UK Education Fund(OP202006)

LIAS(P202ED10)

LIAS(P202RE969)

Data Science Enhancement Fund(P202RE237)

Fight for Sight(24NN201)

BBSRC(RM32G0178B8)