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A Simple and Efficient Determination of the Ideality Factor of Solar Cells and Modules from the Knee Point of the Shunt Resistance Curve

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Abstract

In this work, a simple and efficient method is proposed to determine the ideality factor of solar cells and modules using the knee point of the shunt resistance curve. The method was implemented by deriving a nonlinear empirical equation, which is a function of the shunt resistance and ideality factor, from which a peak value of the function is obtained that corresponds to the knee point of the shunt resistance. Researchers can use this simple approach to efficiently determine the ideality factor by either having the datasheet information or experimental current–voltage (I–V) data. Also, the determined ideality factor can be utilized to extract the other parameters of solar cells/modules, thereby modelling the I–V curve of these devices at different conditions. The method was validated on four different PV modules that are available on the market, namely Poly-Si, Mono-Si, thin film and multijunction (hybrid). It was found that the determination of the ideality factor by applying the proposed approach is easier and more efficient than the methods reported in the literature.

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References

  1. Luque, A.; Hegedus, S.: Handbook of Photovoltaic Science and Engineering. Wiley, New York (2011)

    Google Scholar 

  2. Zurita, A.; Castillejo-Cuberos, A.; García, M.; Mata-Torres, C.; Simsek, Y.; García, R.; Antonanzas-Torres, F.; Escobar, R.A.: State of the art and future prospects for solar PV development in Chile. Renew. Sustain. Energy Rev. 92, 701–727 (2018). https://doi.org/10.1016/j.rser.2018.04.096

    Article  Google Scholar 

  3. Thopil, G.A.; Sachse, C.E.; Lalk, J.; Thopil, M.S.: Techno-economic performance comparison of crystalline and thin film PV panels under varying meteorological conditions: A high solar resource southern hemisphere case. Appl. Energy. 275, 115041 (2020). https://doi.org/10.1016/j.apenergy.2020.115041

    Article  Google Scholar 

  4. Ghaleb, B.; Asif, M.: Assessment of solar PV potential in commercial buildings. Renew. Energy. 187, 618–630 (2022). https://doi.org/10.1016/j.renene.2022.01.013

    Article  Google Scholar 

  5. Xiao, W.; Edwin, F.F.; Spagnuolo, G.; Jatskevich, J.: Efficient approaches for modeling and simulating photovoltaic power systems. IEEE J. Photovolt. 3, 500–508 (2013). https://doi.org/10.1109/JPHOTOV.2012.2226435

    Article  Google Scholar 

  6. Banik, A.; Shrivastava, A.; Manohar Potdar, R.; Kumar Jain, S.; Gopal Nagpure, S.; Soni, M.: Design, modelling, and analysis of novel solar PV system using MATLAB. Mater. Today Proc. 51, 756–763 (2022). https://doi.org/10.1016/j.matpr.2021.06.226

    Article  Google Scholar 

  7. Pendem, S.R.; Mikkili, S.: Modelling and performance assessment of PV array topologies under partial shading conditions to mitigate the mismatching power losses. Sol. Energy. 160, 303–321 (2018). https://doi.org/10.1016/j.solener.2017.12.010

    Article  Google Scholar 

  8. Gholami, A.; Ameri, M.; Zandi, M.; Gavagsaz Ghoachani, R.: A single-diode model for photovoltaic panels in variable environmental conditions: investigating dust impacts with experimental evaluation. Sustain. Energy Technol. Assess. 47, 101392 (2021). https://doi.org/10.1016/j.seta.2021.101392

    Article  Google Scholar 

  9. Chen, Z.; Chen, Y.; Wu, L.; Cheng, S.; Lin, P.; You, L.: Accurate modeling of photovoltaic modules using a 1-D deep residual network based on I-V characteristics. Energy Convers. Manag. 186, 168–187 (2019). https://doi.org/10.1016/j.enconman.2019.02.032

    Article  Google Scholar 

  10. Patel, H.; Agarwal, V.: MATLAB-based modeling to study the effects of partial shading on PV array characteristics. IEEE Trans. Energy Convers. 23, 302–310 (2008). https://doi.org/10.1109/TEC.2007.914308

    Article  Google Scholar 

  11. Abdulrazzaq, A.K.; Bognár, G.; Plesz, B.: Evaluation of different methods for solar cells/modules parameters extraction. Sol. Energy. 196, 183–195 (2020). https://doi.org/10.1016/j.solener.2019.12.010

    Article  Google Scholar 

  12. Caprioglio, P.; Wolff, C.M.; Sandberg, O.J.; Armin, A.; Rech, B.; Albrecht, S.; Neher, D.; Stolterfoht, M.: On the origin of the ideality factor in perovskite solar cells. Adv. Energy Mater. 10, 2000502 (2020). https://doi.org/10.1002/aenm.202000502

    Article  Google Scholar 

  13. Hu, Z.; Nomoto, K.; Song, B.; Zhu, M.; Qi, M.; Pan, M.; Gao, X.; Protasenko, V.; Jena, D.; Xing, H.G.: Near unity ideality factor and Shockley–Read–Hall lifetime in GaN-on-GaN p-n diodes with avalanche breakdown. Appl. Phys. Lett. 107, 243501 (2015). https://doi.org/10.1063/1.4937436

    Article  Google Scholar 

  14. Almora, O.; Cho, K.T.; Aghazada, S.; Zimmermann, I.; Matt, G.J.; Brabec, C.J.; Nazeeruddin, M.K.; Garcia-Belmonte, G.: Discerning recombination mechanisms and ideality factors through impedance analysis of high-efficiency perovskite solar cells. Nano Energy 48, 63–72 (2018). https://doi.org/10.1016/j.nanoen.2018.03.042

    Article  Google Scholar 

  15. Hameiri, Z.; McIntosh, K.; Xu, G.: Evaluation of recombination processes using the local ideality factor of carrier lifetime measurements. Sol. Energy Mater. Sol. Cells. 117, 251–258 (2013). https://doi.org/10.1016/j.solmat.2013.05.040

    Article  Google Scholar 

  16. Calado, P.; Burkitt, D.; Yao, J.; Troughton, J.; Watson, T.M.; Carnie, M.J.; Telford, A.M.; O’Regan, B.C.; Nelson, J.; Barnes, P.R.F.: Identifying dominant recombination mechanisms in perovskite solar cells by measuring the transient ideality factor. Phys. Rev. Appl. 11, 044005 (2019). https://doi.org/10.1103/PhysRevApplied.11.044005

    Article  Google Scholar 

  17. Duan, L.; Yi, H.; Xu, C.; Upama, M.B.; Mahmud, M.A.; Wang, D.; Shabab, F.H.; Uddin, A.: Relationship between the diode ideality factor and the carrier recombination resistance in organic solar cells. IEEE J. Photovolt. 8, 1701–1709 (2018). https://doi.org/10.1109/JPHOTOV.2018.2870722

    Article  Google Scholar 

  18. Ahmed, D.R.; Abdullah, H.M.; Muhammadsharif, F.F.: Utilization of device parameters to assess the performance of a monocrystalline solar module under varied temperature and irradiance. Energy Syst. (2021). https://doi.org/10.1007/s12667-021-00472-6

    Article  Google Scholar 

  19. Babbe, F.; Choubrac, L.; Siebentritt, S.: The optical diode ideality factor enables fast screening of semiconductors for solar cells. Sol. RRL 2, 1800248 (2018). https://doi.org/10.1002/solr.201800248

    Article  Google Scholar 

  20. Ahmed, D.R.; Mohammed, I.R.; Abdullah, H.M.; Muhammadsharif, F.F.; Sulaiman, K.; Alsoufi, M.S.; Bawazeer, T.M.: The correlation of device parameters with illumination energy to explore the performance of a monocrystalline silicon solar module. SILICON 14, 1439–1445 (2022). https://doi.org/10.1007/s12633-021-00966-z

    Article  Google Scholar 

  21. Yordanov, G.H.; Midtgård, O.-M.; Saetre, T.O.: PV modules with variable ideality factors. In: 2012 38th IEEE Photovoltaic Specialists Conference, pp. 002362–002367 (2012)

  22. Velilla, E.; Jaramillo, F.; Mora-Seró, I.: High-throughput analysis of the ideality factor to evaluate the outdoor performance of perovskite solar minimodules. Nat. Energy. 6, 54–62 (2021). https://doi.org/10.1038/s41560-020-00747-9

    Article  Google Scholar 

  23. Olikh, O.; Lozitsky, O.; Zavhorodnii, O.: Estimation for iron contamination in Si solar cell by ideality factor: deep neural network approach. Prog. Photovolt. Res. Appl. 30, 648–660 (2022)

    Article  Google Scholar 

  24. Williams, B.; Daiber, B.; Case, C.: Importance of ideality factors in perovskite/Si tandem solar cell design. In: 2022 IEEE 49th Photovoltaics Specialists Conference (PVSC). pp. 0328–0328. IEEE (2022)

  25. Shin, D.-S.; Shim, J.-I.: Understanding microscopic properties of light-emitting diodes from macroscopic characterization: ideality factor, S-parameter, and internal quantum efficiency. Phys. Status Solidi A. 219, 2200042 (2022)

    Article  Google Scholar 

  26. Myeong, G.; Shin, W.; Sung, K.; Kim, S.; Lim, H.; Kim, B.; Jin, T.; Park, J.; Lee, T.; Fuhrer, M.S.: Dirac-source diode with sub-unity ideality factor. Nat. Commun. 13, 1–6 (2022)

    Article  Google Scholar 

  27. Muhammadsharif, F.F.: A new simplified method for efficient extraction of solar cells and modules parameters from datasheet information. SILICON 14, 3059–3067 (2022). https://doi.org/10.1007/s12633-021-01097-1

    Article  Google Scholar 

  28. Muhammadsharif, F.F.; Hashim, S.; Hameed, S.S.; Ghoshal, S.K.; Abdullah, I.K.; Macdonald, J.E.; Yahya, M.Y.: Brent’s algorithm based new computational approach for accurate determination of single-diode model parameters to simulate solar cells and modules. Sol. Energy. 193, 782–798 (2019). https://doi.org/10.1016/j.solener.2019.09.096

    Article  Google Scholar 

  29. Muhammad, F.F.; Sangawi, A.W.K.; Hashim, S.; Ghoshal, S.K.; Abdullah, I.K.; Hameed, S.S.: Simple and efficient estimation of photovoltaic cells and modules parameters using approximation and correction technique. PLoS ONE 14, e0216201 (2019). https://doi.org/10.1371/journal.pone.0216201

    Article  Google Scholar 

  30. Chen, Z.; Yu, H.; Luo, L.; Wu, L.; Zheng, Q.; Wu, Z.; Cheng, S.; Lin, P.: Rapid and accurate modeling of PV modules based on extreme learning machine and large datasets of I-V curves. Appl. Energy. 292, 116929 (2021). https://doi.org/10.1016/j.apenergy.2021.116929

    Article  Google Scholar 

  31. Boutana, N.; Mellit, A.; Haddad, S.; Rabhi, A.; Pavan, A.M.: An explicit I-V model for photovoltaic module technologies. Energy Convers. Manag. 138, 400–412 (2017). https://doi.org/10.1016/j.enconman.2017.02.016

    Article  Google Scholar 

  32. Pandiarajan, N.; Muthu, R.: Mathematical modeling of photovoltaic module with Simulink. In: 2011 1st International Conference on Electrical Energy Systems. pp. 258–263 (2011)

  33. Khatib, T.; Ghareeb, A.; Tamimi, M.; Jaber, M.; Jaradat, S.: A new offline method for extracting I-V characteristic curve for photovoltaic modules using artificial neural networks. Sol. Energy. 173, 462–469 (2018). https://doi.org/10.1016/j.solener.2018.07.092

    Article  Google Scholar 

  34. Ma, X.; Huang, W.-H.; Schnabel, E.; Köhl, M.; Brynjarsdóttir, J.; Braid, J.L.; French, R.H.: Data-driven $I$–$V$ feature extraction for photovoltaic modules. IEEE J. Photovolt. 9, 1405–1412 (2019). https://doi.org/10.1109/JPHOTOV.2019.2928477

    Article  Google Scholar 

  35. Tao, Y.; Bai, J.; Pachauri, R.K.; Sharma, A.: Parameter extraction of photovoltaic modules using a heuristic iterative algorithm. Energy Convers. Manag. 224, 113386 (2020). https://doi.org/10.1016/j.enconman.2020.113386

    Article  Google Scholar 

  36. Ben Hmamou, D.; Elyaqouti, M.; Hanafi, A.E.; Saadaoui, D.; Lidaighbi, S.; Chaoufi, J.; Ibrahim, A.; Aqel, R.; El Fatmi, D.; Obukhov, S.: A novel hybrid numerical with analytical approach for parameter extraction of photovoltaic modules. Energy Convers. Manag. X. 14, 100219 (2022). https://doi.org/10.1016/j.ecmx.2022.100219

    Article  Google Scholar 

  37. Ibrahim, H.; Anani, N.: Evaluation of analytical methods for parameter extraction of PV modules. Energy Procedia. 134, 69–78 (2017). https://doi.org/10.1016/j.egypro.2017.09.601

    Article  Google Scholar 

  38. Abdulrazzaq, A.K.; Bognár, G.; Plesz, B.: Accurate method for PV solar cells and modules parameters extraction using I-V curves. J. King Saud Univ. Eng. Sci. 34, 46–56 (2022). https://doi.org/10.1016/j.jksues.2020.07.008

    Article  Google Scholar 

  39. Oulcaid, M.; El Fadil, H.; Ammeh, L.; Yahya, A.; Giri, F.: Parameter extraction of photovoltaic cell and module: analysis and discussion of various combinations and test cases. Sustain. Energy Technol. Assess. 40, 100736 (2020). https://doi.org/10.1016/j.seta.2020.100736

    Article  Google Scholar 

  40. Elkholy, A.; Abou El-Ela, A.A.: Optimal parameters estimation and modelling of photovoltaic modules using analytical method. Heliyon 5, e02137 (2019). https://doi.org/10.1016/j.heliyon.2019.e02137

    Article  Google Scholar 

  41. Li, S.; Gong, W.; Gu, Q.: A comprehensive survey on meta-heuristic algorithms for parameter extraction of photovoltaic models. Renew. Sustain. Energy Rev. 141, 110828 (2021). https://doi.org/10.1016/j.rser.2021.110828

    Article  Google Scholar 

  42. Merchaoui, M.; Sakly, A.; Mimouni, M.F.: Particle swarm optimisation with adaptive mutation strategy for photovoltaic solar cell/module parameter extraction. Energy Convers. Manag. 175, 151–163 (2018). https://doi.org/10.1016/j.enconman.2018.08.081

    Article  Google Scholar 

  43. Hachana, O.; Hemsas, K.E.; Tina, G.M.; Ventura, C.: Comparison of different metaheuristic algorithms for parameter identification of photovoltaic cell/module. J. Renew. Sustain. Energy. 5, 053122 (2013). https://doi.org/10.1063/1.4822054

    Article  Google Scholar 

  44. Nguyen, T.T.; Nguyen, T.T.; Tran, T.N.: Parameter estimation of photovoltaic cell and module models relied on metaheuristic algorithms including artificial ecosystem optimization. Neural Comput. Appl. (2022). https://doi.org/10.1007/s00521-022-07142-3

    Article  Google Scholar 

  45. Bashahu, M.; Nkundabakura, P.: Review and tests of methods for the determination of the solar cell junction ideality factors. Sol. Energy. 81, 856–863 (2007). https://doi.org/10.1016/j.solener.2006.11.002

    Article  Google Scholar 

  46. Cotfas, D.T.; Cotfas, P.A.; Ursutiu, D.; Samoila, C.: The methods to determine the series resistance and the ideality factor of diode for solar cells-review. In: 2012 13th International Conference on Optimization of Electrical and Electronic Equipment (OPTIM). pp. 966–972 (2012)

  47. Santakrus Singh, N.; Jain, A.; Kapoor, A.: Determination of the solar cell junction ideality factor using special trans function theory (STFT). Sol. Energy Mater. Sol. Cells. 93, 1423–1426 (2009). https://doi.org/10.1016/j.solmat.2009.03.013

    Article  Google Scholar 

  48. Perovich, S.M.; Djukanovic, M.D.J.; Dlabac, T.; Nikolic, D.; Calasan, M.P.: Concerning a novel mathematical approach to the solar cell junction ideality factor estimation. Appl. Math. Model. 39, 3248–3264 (2015). https://doi.org/10.1016/j.apm.2014.11.026

    Article  MATH  Google Scholar 

  49. Bayhan, H.; Bayhan, M.: A simple approach to determine the solar cell diode ideality factor under illumination. Sol. Energy. 85, 769–775 (2011). https://doi.org/10.1016/j.solener.2011.01.009

    Article  Google Scholar 

  50. Cuce, E.; Cuce, P.M.; Karakas, I.H.; Bali, T.: An accurate model for photovoltaic (PV) modules to determine electrical characteristics and thermodynamic performance parameters. Energy Convers. Manag. 146, 205–216 (2017). https://doi.org/10.1016/j.enconman.2017.05.022

    Article  Google Scholar 

  51. Gulkowski, S.; Muñoz Diez, J.V.; Aguilera Tejero, J.; Nofuentes, G.: Computational modeling and experimental analysis of heterojunction with intrinsic thin-layer photovoltaic module under different environmental conditions. Energy 172, 380–390 (2019). https://doi.org/10.1016/j.energy.2019.01.107

    Article  Google Scholar 

  52. Shinong, W.; Qianlong, M.; Jie, X.; Yuan, G.; Shilin, L.: An improved mathematical model of photovoltaic cells based on datasheet information. Sol. Energy. 199, 437–446 (2020). https://doi.org/10.1016/j.solener.2020.02.046

    Article  Google Scholar 

  53. Maouhoub, N.: Photovoltaic module parameter estimation using an analytical approach and least squares method. J. Comput. Electron. 17, 784–790 (2018). https://doi.org/10.1007/s10825-017-1121-5

    Article  Google Scholar 

  54. 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 Convers. Manag. 119, 37–48 (2016). https://doi.org/10.1016/j.enconman.2016.04.030

    Article  Google Scholar 

  55. Lineykin, S.; Averbukh, M.; Kuperman, A.: An improved approach to extract the single-diode equivalent circuit parameters of a photovoltaic cell/panel. Renew. Sustain. Energy Rev. 30, 282–289 (2014). https://doi.org/10.1016/j.rser.2013.10.015

    Article  Google Scholar 

  56. Zhang, C.; Zhang, J.; Hao, Y.; Lin, Z.; Zhu, C.: A simple and efficient solar cell parameter extraction method from a single current-voltage curve. J. Appl. Phys. 110, 064504 (2011). https://doi.org/10.1063/1.3632971

    Article  Google Scholar 

  57. Tong, N.T.; Pora, W.: A parameter extraction technique exploiting intrinsic properties of solar cells. Appl. Energy. 176, 104–115 (2016). https://doi.org/10.1016/j.apenergy.2016.05.064

    Article  Google Scholar 

  58. Chaibi, Y.; Allouhi, A.; Malvoni, M.; Salhi, M.; Saadani, R.: Solar irradiance and temperature influence on the photovoltaic cell equivalent-circuit models. Sol. Energy. 188, 1102–1110 (2019). https://doi.org/10.1016/j.solener.2019.07.005

    Article  Google Scholar 

  59. Chaibi, Y.; Malvoni, M.; Allouhi, A.; Mohamed, S.: Data on the I-V characteristics related to the SM55 monocrystalline PV module at various solar irradiance and temperatures. Data Brief. 26, 104527 (2019). https://doi.org/10.1016/j.dib.2019.104527

    Article  Google Scholar 

  60. Zaimi, M.; El Achouby, H.; Ibral, A.; Assaid, E.M.: Determining combined effects of solar radiation and panel junction temperature on all model-parameters to forecast peak power and photovoltaic yield of solar panel under non-standard conditions. Sol. Energy. 191, 341–359 (2019). https://doi.org/10.1016/j.solener.2019.09.007

    Article  Google Scholar 

  61. El Achouby, H.; Zaimi, M.; Ibral, A.; Assaid, E.M.: New analytical approach for modelling effects of temperature and irradiance on physical parameters of photovoltaic solar module. Energy Convers. Manag. 177, 258–271 (2018). https://doi.org/10.1016/j.enconman.2018.09.054

    Article  Google Scholar 

  62. Villalva, M.G.; Gazoli, J.R.; Filho, E.R.: Comprehensive approach to modeling and simulation of photovoltaic arrays. IEEE Trans. Power Electron. 24, 1198–1208 (2009). https://doi.org/10.1109/TPEL.2009.2013862

    Article  Google Scholar 

  63. Chaibi, Y.; Allouhi, A.; Salhi, M.: A simple iterative method to determine the electrical parameters of photovoltaic cell. J. Clean. Prod. 269, 122363 (2020). https://doi.org/10.1016/j.jclepro.2020.122363

    Article  Google Scholar 

  64. Fébba, D.M.; Rubinger, R.M.; Oliveira, A.F.; Bortoni, E.C.: Impacts of temperature and irradiance on polycrystalline silicon solar cells parameters. Sol. Energy. 174, 628–639 (2018). https://doi.org/10.1016/j.solener.2018.09.051

    Article  Google Scholar 

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Acknowledgements

Fahmi F. Muhammadsharif is thankful to the Islamic Development Bank for their support under IDB Merit Scholarship Program. The authors thank Assoc. Prof. Dr. Yassine Chaibi at Moroccan School of Engineering Sciences for providing some datasets used to validate this work.

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Muhammadsharif, F.F., Hashim, S. A Simple and Efficient Determination of the Ideality Factor of Solar Cells and Modules from the Knee Point of the Shunt Resistance Curve. Arab J Sci Eng 48, 8217–8225 (2023). https://doi.org/10.1007/s13369-023-07860-3

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