Parameter Extraction of Photovoltaic Cell and Module with Four Diode Model Using Flood Algorithm

Abstract

Photovoltaic (PV) cells exhibit a nonlinear characteristic. Before modeling these cells, obtaining accurate parameters is essential. During the modeling phase, using these parameters is crucial for accurately characterizing and reflecting the behavior of PV structures. Therefore, this article focuses on PV parameter extraction. A PV cell and module were selected and modeled using the four-diode model (FDM). This problem, consisting of eleven unknown parameters related to the FDM, was solved with the flood algorithm (FLA). To compare the algorithm’s performance on the same problem, the polar lights optimizer (PLO), moss growth optimization (MGO), walrus optimizer (WO), and educational competition optimizer (ECO) were also employed. These five metaheuristic algorithms were used for the first time in this study, both for solving the PV parameter extraction problem and with the FDM. The objective function aimed at obtaining the smallest root mean square error (RMSE) was evaluated and compared through assessment metrics, computational accuracy, computational time, and statistical methods. The smallest minimum RMSE was obtained with FLA, calculated as 9.8251385E-04 with FDM-C and 1.6884311E-03 with FDM-M. To statistically demonstrate and reinforce FLA’s success over other algorithms, the Friedman test and Wilcoxon signed-rank test were utilized. According to these tests, FLA produced significantly better results than the other algorithms and outperformed them in pairwise comparisons. In conclusion, FLA has proven to be a successful and promising algorithm for PV parameter extraction, with its success statistically validated.

Keywords

• Flood algorithm
• four diode model
• friedman test
• parameter extraction
• photovoltaic
• wilcoxon signed-rank

References

1. [1] International Energy Agency: IEA, “Solar and wind global,” 2024.
2. [2] IEA, “Solar PV,” International Energy Agency. [Online]. Available: https://www.iea.org/energy-system/renewables/solar-pv. [Accessed: 30-Oct-2024].
3. [3] Çi̇ni̇ci̇ OK, Acir A. Optimization of array design in photovoltaic power plants using the taguchi and ANOVA analysis. Gazi University Journal of Science Part C: Design and Technology. 2023; 11(4), 1195-1208, 2023.
4. [4] Bayyi̇ği̇t A, Çi̇ni̇ci̇ OK, Acir A. Tek yüzeyli ve çift yüzeyli fotovoltaik panellerin performans analizi. Gazi University Journal of Science Part C: Design and Technology. 2023; 11(2), 407-420.
5. [5] Abd-Elhady MM, Elhendawy MA, Abd-Elmajeed MS, Rizk RB. Enhancing photovoltaic systems: a comprehensive review of cooling, concentration, spectral splitting, and tracking techniques. Next Energy, 2025; 6, 100185.
6. [6] Rehman T-U, Qaisrani MA, Shafiq MB, Baba YF, Aslfattahi N, Shahsavar A, Cheema TA, Park CW. Global perspectives on advancing photovoltaic system performance—a state-of-the-art review. Renewable and Sustainable Energy Reviews. 2025; 207, 114889.
7. [7] Emi̇noğlu U, Atay BK. PV modüller/hücrelerin tek-diyot eşdeğer devre parametrelerinin kestirimi için yeni bir analitik model. Gazi University Journal of Science Part C: Design and Technology, 2023; 11(2), 524-533.
8. [8] Pedroza-Díaz A, Rodrigo PM, Dávalos-Orozco Ó, De-la-Vega E, Valera-Albacete Á. Review of explicit models for photovoltaic cell electrical characterization. Renewable and Sustainable Energy Reviews. 2025, 207, 114979.

9. [9] Choulli I, Elyaqouti M, Arjdal EH, Saadaoui D, Ben Hmamou D, Lidaighbi S, Elhammoudy A, Abazine I, Ydir B. Mitigating local minima in extracting optimal parameters for photovoltaic models: an optimizer leveraging multiple initial populations (OLMIP). International Journal Of Hydrogen Energy. 2024; 92, 367-391.
10. [10] Lidaighbi S, Elyaqouti M, Assalaou K, Ben Hmamou D, Saadaoui D, H’roura J. Parameter estimation of photovoltaic modules using analytical and numerical/iterative approaches: a comparative study. Materials Today. 2022; 52, 1–6.
11. [11] Ben Hmamou D, Elyaqouti M, Arjdal E, Ibrahim A, Abdul-Ghaffar HI, Aboelsaud R, Obukhov S, Diab AAZ. Parameters identification and optimization of photovoltaic panels under real conditions using lambert W-function. Energy Reports. 2021; 7, 9035–9045.
12. [12] Mlazi NJ, Mayengo M, Lyakurwa G, Kichonge B. Mathematical modeling and extraction of parameters of solar photovoltaic module based on modified Newton–Raphson method. Results in Physics. 2024; 57, 107364.
13. [13] Nassar-eddine I, Obbadi A, Errami Y, El Fajri A, Agunaou M. Parameter estimation of photovoltaic modules using iterative method and the lambert W function: a comparative study. Energy Conversion and Management. 2016; 119, 37–48.
14. [14] Çetinbaş İ. Parameter extraction of single, double, and triple-diode photovoltaic models using the weighted leader search algorithm. Global Challenges. 2024; 8(5), 2300355.
15. [15] Demirtas M, Koc K. Parameter extraction of photovoltaic cells and modules by INFO algorithm. IEEE Access, 2022; 10, 87022-87052.
16. [16] Navarro MA, Oliva D, Ramos-Michel A, Haro EH. An analysis on the performance of metaheuristic algorithms for the estimation of parameters in solar cell models. Energy Conversion and Management. 2023; 276, 116523.
17. [17] Singla mk, Gupta J, Parag N, Ekta T, Tella TG, Mosaad MI, Murodbek S. Improving photovoltaic cell parameter calculations through a puffer fish inspired optimization technique. Heliyon. 2024; 10(13), e33952.
18. [18] Yu X, Hu Z, Wang X, Luo W. Ranking teaching-learning-based optimization algorithm to estimate the parameters of solar models. Engineering Applications of Artificial Intelligence. 2023; 123, 106225.
19. [19] Ren C, Song Z, Meng Z. Photovoltaic model parameters identification using diversity improvement-oriented differential evolution. Swarm and Evolutionary Computation. 2024; 90, 101689.
20. [20] Xiong G, Gu Z, Mohamed AW. Bouchekara HREH, Suganthan PN. Accurate parameters extraction of photovoltaic models with multi-strategy gaining-sharing knowledge-based algorithm. Information Sciences. 2024; 670, 120627.
21. [21] El Marghichi M, Dangoury S. Electrical parameters identification for three diode photovoltaic based on the manta ray foraging optimization with dynamic fitness distance balance. Optik. 2024; 296, 171548.
22. [22] Choulli I, Elyaqouti M, Arjdal EH, Ben Hmamou D, Saadaoui D, Lidaighbi S, Elhammoudy A, Abazine I, El Aidi Idrissi Y. DIWJAYA: JAYA driven by individual weights for enhanced photovoltaic model parameter estimation. Energy Conversion and Management. 2024; 305, 118258.
23. [23] Beşkirli A, Dağ İ, Kiran MS. A tree seed algorithm with multi-strategy for parameter estimation of solar photovoltaic models. Applied Soft Computing. 2024; 167, 112220.
24. [24] Mai C, Zhang L, Hu X. An adaptive snake optimization algorithm incorporating subtraction-average-based optimizer for photovoltaic cell parameter identification. Heliyon. 2024; 10(15), e35382.
25. [25] Hassan Hakmi S, Alnami H, Ginidi A, Shaheen A, Alghamdi TAH. A fractional order-kepler optimization algorithm (FO-KOA) for single and double-diode parameters PV cell extraction. Heliyon. 2024; 10(16), e35771.
26. [26] Çetinbaş İ, Tamyurek B, Demirtaş M. Parameter extraction of photovoltaic cells and modules by hybrid white shark optimizer and artificial rabbits optimization. Energy Conversion and Management. 2023; 296, 117621.
27. [27] Singh B, Singla MK, Nijhawan P. Parameter estimation of four diode solar photovoltaic cell using hybrid algorithm. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects. 2022; 44(2), 4597-4613.
28. [28] Premkumar M, Jangir p, Sowmya R, Elavarasan RM, Kumar BS. Enhanced chaotic JAYA algorithm for parameter estimation of photovoltaic cell/modules. ISA Transactions. 2021; 116, 139-166.
29. [29] Choulli I, Elyaqouti M, Ben Hmamou D, Arjdal EH, Saadaoui D, Lidaighbi S, Elhammoudy A, Obukhov S, Ibrahim A. A novel hybrid analytical/iterative method to extract the single-diode model’s parameters using lambert’s W-function. Energy Conversion and Management: X. 2023; 18, 100362.
30. [30] Słowik A, Cpałka K, Xue Y, Hapka A. An efficient approach to parameter extraction of photovoltaic cell models using a new population-based algorithm. Applied Energy. 2024; 364, 123208.
31. [31] Celtek SA, Kul S, Singla MK, Gupta J, Safaraliev M, Zeinoddini-Meymand H. Grey wolf‐based heuristic methods for accurate parameter extraction to optimize the performance of PV modules. IET Renewable Power Generation. 2024; 18(14), 2248-2260.
32. [32] Premkumar M, Ravichandran S, Hashim TJT, Sin TC, Abbassi R. Fitness-guided particle swarm optimization with adaptive newton-raphson for photovoltaic model parameter estimation. Applied Soft Computing. 2024; 167, 112295.
33. [33] Gude S Jana KC. A multiagent system based cuckoo search optimization for parameter identification of photovoltaic cell using lambert W-function. Applied Soft Computing. 2022; 120, 108678.
34. [34] Abdel-Basset M, Mohamed R, Hezam IM, Sallam KM, Hameed IA. Parameters identification of photovoltaic models using lambert W-function and newton-raphson method collaborated with AI-based optimization techniques: a comparative study. Expert Systems with Applications. vol. 2024; 255, 124777.
35. [35] Wolpert DH, Macready WG. No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation. 1997; 1(1), 67-82.
36. [36] Talbi EG. Metaheuristics: from design to ımplementation, 1st ed. Nashville, TN: John Wiley & Sons, 2009.
37. [37] Yang X, Zeng G, Cao Z, Huang X, Zhao J. Parameters estimation of complex solar photovoltaic models using bi-parameter coordinated updating L-SHADE with parameter decomposition method. Case Studies in Thermal Engineering. 2024; 61, 104917.
38. [38] Yang X, Zeng G, Cao Z, Huang X, Zhao J. Novel parameter identification for complex solar photovoltaic models via dynamic L-SHADE with parameter decomposition. Case Studies in Thermal Engineering. 2024; 61, 104938.
39. [39] Ghasemi M, Golalipour K, Zare M, Mirjalili S, Trojovský P, Abualigah L, Hemmati R. Flood algorithm (FLA): an efficient inspired meta-heuristic for engineering optimization. The Journal of Supercomputing. 2024; 80(15), 22913-23017.
40. [40] Yuan C, Zhao D, Heidari AA, Liu L, Chen Y, Chen H. Polar lights optimizer: algorithm and applications in image segmentation and feature selection. Neurocomputing. 2024; 607, 128427.
41. [41] Zheng B, Chen Y, Wang C, Heidari AA, Liu L, Chen H. The moss growth optimization (MGO): concepts and performance. Journal of Computational Design and Engineering. 2024; 11(5), 184–221.
42. [42] Han M, Du Z, Yuen KF, Zhu H, Li Y, Yuan Q. Walrus optimizer: a novel nature-inspired metaheuristic algorithm. Expert Systems with Applications. 2024; 239, 122413.
43. [43] Lian J, Zhu T, Ma L, Wu X, Heidari AA, Chen Y, Hui G. The educational competition optimizer. International Journal of Systems Science, 2024, 55(15), 3185-3222.
44. [44] Easwarakhanthan T, Bottin J, Bouhouch I, Boutrit C. Nonlinear minimization algorithm for determining the solar cell parameters with microcomputers. International Journal of Solar Energy. 1986; 4(1), 1-12.
45. [45] Tong NT, Pora W. A parameter extraction technique exploiting intrinsic properties of solar cells. Applied Energy. 2016; 176, 104-115.