Skip to main content
Log in

Parameter estimation of solar PV models with quantum-based avian navigation optimizer and Newton–Raphson method

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

A mathematical model with precise parameters is required to analyze the performance of a solar photovoltaic generating system. This technical note presents a unique scheme for accurately estimating the parameters of a solar PV system. The proposed method is a combination of quantum-based avian navigation optimizer (QANO) and Newton–Raphson (NR) method. QANO algorithm, a novel metaheuristic algorithm, is employed for identifying a global optimum solution with optimal parameters which suit well the given experimental solar cell/module. The NR method, on the other hand, is used to solve nonlinear equations during the objective function calculation process. Most of the algorithms estimate the parameters based on the conventional objective function, which do not consider the nonlinearities of the I–V characteristics. Such inaccurate models may not be reliable for real-time applications. In this work, an objective function is formulated which offers a more accurate parameters of the equivalent PV models without neglecting nonlinearities. The proposed method is applied to estimate parameters for a single diode model (SDM), a double diode model (DDM), and a PV module. The efficacy of the proposed QANO algorithm is compared to the results of other state-of-the-art algorithms reported in the literature. The proposed algorithm achieves an RMSE of 7.7300630E−04 for SDM and 7.5248E−04 for DDM, which are lower than most of the existing algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Ayyarao, T.S.L.V., Kumar, P.P.: Parameter estimation of solar <scp>PV</scp> models with a new proposed war strategy optimization algorithm. Int. J. Energy Res. 46(6), 7215–7238 (2022). https://doi.org/10.1002/er.7629

    Article  Google Scholar 

  2. Ridha, H.M., Gomes, C., Hizam, H.: Estimation of photovoltaic module model’s parameters using an improved electromagnetic-like algorithm. Neural Comput. Appl. 32(16), 12627–12642 (2020). https://doi.org/10.1007/s00521-020-04714-z

    Article  Google Scholar 

  3. Et-torabi, K., et al.: Parameters estimation of the single and double diode photovoltaic models using a Gauss-Seidel algorithm and analytical method: a comparative study. Energy Convers. Manag. 148, 1041–1054 (2017). https://doi.org/10.1016/j.enconman.2017.06.064

    Article  Google Scholar 

  4. Wang, D., Ding, F.: Parameter estimation algorithms for multivariable Hammerstein CARMA systems. Inf. Sci. (Ny) 355–356, 237–248 (2016). https://doi.org/10.1016/j.ins.2016.03.037

    Article  MATH  Google Scholar 

  5. Abdel-Basset, M., El-Shahat, D., Chakrabortty, R.K., Ryan, M.: Parameter estimation of photovoltaic models using an improved marine predators algorithm. Energy Convers. Manag. 227, 113491 (2021). https://doi.org/10.1016/j.enconman.2020.113491

    Article  Google Scholar 

  6. Ye, M., Wang, X., Xu, Y.: Parameter extraction of solar cells using particle swarm optimization. J. Appl. Phys. 105(9), 094502 (2009). https://doi.org/10.1063/1.3122082

    Article  Google Scholar 

  7. Ishaque, K., Salam, Z., Mekhilef, S., Shamsudin, A.: Parameter extraction of solar photovoltaic modules using penalty-based differential evolution. Appl. Energy 99, 297–308 (2012). https://doi.org/10.1016/j.apenergy.2012.05.017

    Article  Google Scholar 

  8. Askarzadeh, A., Rezazadeh, A.: Parameter identification for solar cell models using harmony search-based algorithms. Sol. Energy 86(11), 3241–3249 (2012). https://doi.org/10.1016/j.solener.2012.08.018

    Article  Google Scholar 

  9. Rajasekar, N., Krishna Kumar, N., Venugopalan, R.: Bacterial foraging algorithm based solar PV parameter estimation. Sol. Energy 97, 255–265 (2013). https://doi.org/10.1016/j.solener.2013.08.019

    Article  Google Scholar 

  10. El-Naggar, K.M., AlRashidi, M.R., AlHajri, M.F., Al-Othman, A.K.: Simulated Annealing algorithm for photovoltaic parameters identification. Sol. Energy 86(1), 266–274 (2012). https://doi.org/10.1016/j.solener.2011.09.032

    Article  Google Scholar 

  11. Alam, D.F., Yousri, D.A., Eteiba, M.B.: Flower pollination algorithm based solar PV parameter estimation. Energy Convers. Manag. 101, 410–422 (2015). https://doi.org/10.1016/j.enconman.2015.05.074

    Article  Google Scholar 

  12. Xiong, G., Zhang, J., Shi, D., He, Y.: Parameter extraction of solar photovoltaic models using an improved whale optimization algorithm. Energy Convers. Manag. 174, 388–405 (2018). https://doi.org/10.1016/j.enconman.2018.08.053

    Article  Google Scholar 

  13. Chen, X., Xu, B., Mei, C., Ding, Y., Li, K.: Teaching–learning–based artificial bee colony for solar photovoltaic parameter estimation. Appl. Energy 212, 1578–1588 (2018). https://doi.org/10.1016/j.apenergy.2017.12.115

    Article  Google Scholar 

  14. Gao, X., et al.: Parameter extraction of solar cell models using improved shuffled complex evolution algorithm. Energy Convers. Manag. 157, 460–479 (2018). https://doi.org/10.1016/j.enconman.2017.12.033

    Article  Google Scholar 

  15. Gao, X., Cui, Y., Hu, J., Xu, G., Yu, Y.: Lambert W-function based exact representation for double diode model of solar cells: Comparison on fitness and parameter extraction. Energy Convers. Manag. 127, 443–460 (2016). https://doi.org/10.1016/j.enconman.2016.09.005

    Article  Google Scholar 

  16. Allam, D., Yousri, D.A., Eteiba, M.B.: Parameters extraction of the three diode model for the multi-crystalline solar cell/module using Moth-Flame Optimization Algorithm. Energy Convers. Manag. 123, 535–548 (2016). https://doi.org/10.1016/j.enconman.2016.06.052

    Article  Google Scholar 

  17. Oliva, D., Abd El Aziz, M., Ella Hassanien, A.: Parameter estimation of photovoltaic cells using an improved chaotic whale optimization algorithm. Appl. Energy 200, 141–154 (2017). https://doi.org/10.1016/j.apenergy.2017.05.029

    Article  Google Scholar 

  18. Xu, S., Wang, Y.: Parameter estimation of photovoltaic modules using a hybrid flower pollination algorithm. Energy Convers. Manag. 144, 53–68 (2017). https://doi.org/10.1016/j.enconman.2017.04.042

    Article  Google Scholar 

  19. Kanimozhi, G., Kumar, H., Satyanarayana, N.: A novel hybrid approach for the optimization of <scp>double-diode</scp> model parameters of solar cell. Int. J. Energy Res. (2022). https://doi.org/10.1002/er.8180

    Article  Google Scholar 

  20. Singla, M.K., Nijhawan, P.: Triple diode parameter estimation of solar PV cell using hybrid algorithm. Int. J. Environ. Sci. Technol. 19(5), 4265–4288 (2022). https://doi.org/10.1007/s13762-021-03286-2

    Article  Google Scholar 

  21. Gafar, M., El-Sehiemy, R.A., Hasanien, H.M., Abaza, A.: Optimal parameter estimation of three solar cell models using modified spotted hyena optimization. J. Ambient Intell. Humaniz. Comput. (2022). https://doi.org/10.1007/s12652-022-03896-9

    Article  Google Scholar 

  22. Oliva, D., Cuevas, E., Pajares, G.: Parameter identification of solar cells using artificial bee colony optimization. Energy 72, 93–102 (2014). https://doi.org/10.1016/j.energy.2014.05.011

    Article  Google Scholar 

  23. Agwa, A.M., El-Fergany, A.A., Maksoud, H.A.: Electrical characterization of photovoltaic modules using farmland fertility optimizer. Energy Convers. Manag. 217, 112990 (2020). https://doi.org/10.1016/j.enconman.2020.112990

    Article  Google Scholar 

  24. Qais, M.H., Hasanien, H.M., Alghuwainem, S.: Identification of electrical parameters for three-diode photovoltaic model using analytical and sunflower optimization algorithm. Appl. Energy 250, 109–117 (2019). https://doi.org/10.1016/j.apenergy.2019.05.013

    Article  Google Scholar 

  25. Ma, J., Ting, T.O., Man, K.L., Zhang, N., Guan, S.-U., Wong, P.W.H.: Parameter estimation of photovoltaic models via cuckoo search. J. Appl. Math. 1–8, 2013 (2013). https://doi.org/10.1155/2013/362619

    Article  MathSciNet  Google Scholar 

  26. Chen, S., Gholami-Farkoush, S., Leto, S.: Photovoltaic cells parameters extraction using variables reduction and improved shark optimization technique. Int. J. Hydrogen Energy 45(16), 10059–10069 (2020). https://doi.org/10.1016/j.ijhydene.2020.01.236

    Article  Google Scholar 

  27. Sudhakar Babu, T., Prasanth Ram, J., Sangeetha, K., Laudani, A., Rajasekar, N.: Parameter extraction of two diode solar PV model using Fireworks algorithm. Sol. Energy 140, 265–276 (2016). https://doi.org/10.1016/j.solener.2016.10.044

    Article  Google Scholar 

  28. Zamani, H., Nadimi-Shahraki, M.H., Gandomi, A.H.: CCSA: conscious neighborhood-based crow search algorithm for solving global optimization problems. Appl. Soft Comput. 85, 105583 (2019). https://doi.org/10.1016/j.asoc.2019.105583

    Article  Google Scholar 

  29. Zamani, H., Nadimi-Shahraki, M.H., Gandomi, A.H.: Starling murmuration optimizer: a novel bio-inspired algorithm for global and engineering optimization. Comput. Methods Appl. Mech. Eng. 392, 114616 (2022). https://doi.org/10.1016/j.cma.2022.114616

    Article  MathSciNet  MATH  Google Scholar 

  30. Lin, P., Cheng, S., Yeh, W., Chen, Z., Wu, L.: Parameters extraction of solar cell models using a modified simplified swarm optimization algorithm. Sol. Energy 144, 594–603 (2017). https://doi.org/10.1016/j.solener.2017.01.064

    Article  Google Scholar 

  31. Yousri, D., Thanikanti, S.B., Allam, D., Ramachandaramurthy, V.K., Eteiba, M.B.: Fractional chaotic ensemble particle swarm optimizer for identifying the single, double, and three diode photovoltaic models’ parameters. Energy 195, 116979 (2020). https://doi.org/10.1016/j.energy.2020.116979

    Article  Google Scholar 

  32. Ibrahim, I.A., Hossain, M.J., Duck, B.C., Fell, C.J.: An adaptive wind-driven optimization algorithm for extracting the parameters of a single-diode PV cell model. IEEE Trans. Sustain. Energy 11(2), 1054–1066 (2020). https://doi.org/10.1109/TSTE.2019.2917513

    Article  Google Scholar 

  33. Yu, K., Chen, X., Wang, X., Wang, Z.: Parameters identification of photovoltaic models using self-adaptive teaching-learning-based optimization. Energy Convers. Manag. 145, 233–246 (2017). https://doi.org/10.1016/j.enconman.2017.04.054

    Article  Google Scholar 

  34. Shaheen, A.M., El-Seheimy, R.A., Xiong, G., Elattar, E., Ginidi, A.R.: Parameter identification of solar photovoltaic cell and module models via supply demand optimizer. Ain Shams Eng. J. 13(4), 101705 (2022). https://doi.org/10.1016/j.asej.2022.101705

    Article  Google Scholar 

  35. Beigi, A.M., Maroosi, A.: Parameter identification for solar cells and module using a Hybrid Firefly and Pattern Search Algorithms. Sol. Energy 171, 435–446 (2018). https://doi.org/10.1016/j.solener.2018.06.092

    Article  Google Scholar 

  36. Abdel-Basset, M., Mohamed, R., El-Fergany, A., Askar, S., Abouhawwash, M.: Efficient ranking-based whale optimizer for parameter extraction of three-diode photovoltaic model: analysis and validations. Energies 14(13), 3729 (2021). https://doi.org/10.3390/en14133729

    Article  Google Scholar 

  37. Liang, J., et al.: Parameters estimation of solar photovoltaic models via a self-adaptive ensemble-based differential evolution. Sol. Energy 207, 336–346 (2020). https://doi.org/10.1016/j.solener.2020.06.100

    Article  Google Scholar 

  38. Nadimi-Shahraki, M.H., Zamani, H.: DMDE: Diversity-maintained multi-trial vector differential evolution algorithm for non-decomposition large-scale global optimization. Expert Syst. Appl. 198L, 116895 (2022). https://doi.org/10.1016/j.eswa.2022.116895

    Article  Google Scholar 

  39. Zamani, H., Nadimi-Shahraki, M.H., Gandomi, A.H.: QANA: Quantum-based avian navigation optimizer algorithm. Eng. Appl. Artif. Intell. 104, 104314 (2021). https://doi.org/10.1016/j.engappai.2021.104314

    Article  Google Scholar 

  40. Ridha, H.M., Hizam, H., Mirjalili, S., Othman, M.L., Ya’acob, M.E.: Zero root-mean-square error for single- and double-diode photovoltaic models parameter determination. Neural Comput. Appl. (2022). https://doi.org/10.1007/s00521-022-07047-1

    Article  Google Scholar 

  41. Easwarakhanthan, T., Bottin, J., Bouhouch, I., Boutrit, C.: Nonlinear minimization algorithm for determining the solar cell parameters with microcomputers. Int. J. Sol. Energy 4(1), 1–12 (1986). https://doi.org/10.1080/01425918608909835

    Article  Google Scholar 

  42. 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 

  43. Yang, X., Gong, W.: Opposition-based JAYA with population reduction for parameter estimation of photovoltaic solar cells and modules. Appl. Soft Comput. 104, 107218 (2021). https://doi.org/10.1016/j.asoc.2021.107218

    Article  Google Scholar 

  44. Kumar, C., Raj, T.D., Premkumar, M., Raj, T.D.: A new stochastic slime mould optimization algorithm for the estimation of solar photovoltaic cell parameters. Optik 223, 165277 (2020). https://doi.org/10.1016/j.ijleo.2020.165277

    Article  Google Scholar 

  45. Xiong, G., Zhang, J., Shi, D., Zhu, L., Yuan, X., Tan, Z.: Winner-leading competitive swarm optimizer with dynamic Gaussian mutation for parameter extraction of solar photovoltaic models. Energy Convers. Manag. 206, 112450 (2020). https://doi.org/10.1016/j.enconman.2019.112450

    Article  Google Scholar 

  46. Yu, K., Liang, J.J., Qu, B.Y., Chen, X., Wang, H.: Parameters identification of photovoltaic models using an improved JAYA optimization algorithm. Energy Convers. Manag. 150, 742–753 (2017). https://doi.org/10.1016/j.enconman.2017.08.063

    Article  Google Scholar 

  47. Naeijian, M., Rahimnejad, A., Ebrahimi, S.M., Pourmousa, N., Gadsden, S.A.: Parameter estimation of PV solar cells and modules using Whippy Harris Hawks Optimization Algorithm. Energy Rep. 7, 4047–4063 (2021). https://doi.org/10.1016/j.egyr.2021.06.085

    Article  Google Scholar 

  48. Zhou, W., et al.: Metaphor-free dynamic spherical evolution for parameter estimation of photovoltaic modules. Energy Rep. 7, 5175–5202 (2021). https://doi.org/10.1016/j.egyr.2021.07.041

    Article  Google Scholar 

  49. Yeh, W., Lin, P., Huang, C.: Simplified swarm optimisation for the solar cell models parameter estimation problem. IET Renew. Power Gener. 11(8), 1166–1173 (2017). https://doi.org/10.1049/iet-rpg.2016.0473

    Article  Google Scholar 

  50. Chen, X., Yu, K., Du, W., Zhao, W., Liu, G.: Parameters identification of solar cell models using generalized oppositional teaching learning based optimization. Energy 99, 170–180 (2016). https://doi.org/10.1016/j.energy.2016.01.052

    Article  Google Scholar 

  51. Xiong, G., Zhang, J., Shi, D., Zhu, L., Yuan, X.: Parameter extraction of solar photovoltaic models with an either-or teaching learning based algorithm. Energy Convers. Manag. 224, 113395 (2020). https://doi.org/10.1016/j.enconman.2020.113395

    Article  Google Scholar 

  52. Liang, J.J., Qin, A.K., Suganthan, P.N., Baskar, S.: Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans. Evol. Comput. 10(3), 281–295 (2006). https://doi.org/10.1109/TEVC.2005.857610

    Article  Google Scholar 

  53. Lekouaghet, B., Boukabou, A., Boubakir, C.: Estimation of the photovoltaic cells/modules parameters using an improved Rao-based chaotic optimization technique. Energy Convers. Manag. 229, 113722 (2021). https://doi.org/10.1016/j.enconman.2020.113722

    Article  Google Scholar 

  54. Shell SM55 Solar PV Module Datasheet, “Shell SM55,” 2002.

  55. 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 Br. 26, 104527 (2019). https://doi.org/10.1016/j.dib.2019.104527

    Article  Google Scholar 

Download references

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. The authors have no relevant financial or non-financial interests to disclose.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tummala S. L. V. Ayyarao.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

I–V and P–V characteristics of solar PV cell

See Figs. 14 and 15.

Fig. 14
figure 14

I–V characteristics for solar PV cell

Fig. 15
figure 15

P–V characteristics for solar PV cell

I–V and P–V characteristics of solar PV module STM6-40/36

See Figs.

Fig. 16
figure 16

I–V characteristics for solar PV cell

16 and

Fig. 17
figure 17

P–V characteristics for solar PV cell

17.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ayyarao, T.S.L.V. Parameter estimation of solar PV models with quantum-based avian navigation optimizer and Newton–Raphson method. J Comput Electron 21, 1338–1356 (2022). https://doi.org/10.1007/s10825-022-01931-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-022-01931-8

Keywords

Navigation