Skip to main content
SpringerLink
Log in

Chaos Game Optimization-Least Squares Algorithm for Photovoltaic Parameter Estimation

  • Research Article-Electrical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Estimating the parameters of photovoltaic (PV) models accurately is vital to increase the effectiveness of PV systems. During the past few years, many approaches have been developed to solve this problem. However, due to the presence of nonlinearity and multi-modality in the problem, the estimated parameters are usually not very accurate and reliable. Therefore, this paper proposes a novel hybrid algorithm called chaos game optimization-least squares (CGO-LS) algorithm. The novelty of CGO-LS is that it adopts a cascade estimation strategy based on parameter decomposition. By the aid of this decomposition, CGO-LS combines a sophisticated nonlinear optimization capability of chaos game optimization (CGO) and the power of the optimal linear least squares (LS) estimator. LS focuses directly on estimating linear parameters, thus reducing the workload of CGO and helping to increase its convergence speed. To validate the performance of CGO-LS, it is employed to estimate the parameters of four PV models, including single-diode, double-diode, three-diode models, and PV module model. The results obtained by CGO-LS are compared with those of CGO, six state-of-the-art metaheuristics, their hybridized versions with LS, as well as some reported results in the literature. The overall results show that CGO-LS possesses superior estimation performance and excellent robustness in emulating experimental datasets.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. 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)

    Google Scholar 

  2. Zhang, Y.: Neural network algorithm with reinforcement learning for parameters extraction of photovoltaic models. IEEE Trans. Neural Netw. Learn. Syst. (2021)

  3. Parida, B.; Iniyan, S.; Goic, R.: A review of solar photovoltaic technologies. Renew. Sustain. Energy Rev. 15(3), 1625–1636 (2011)

    Google Scholar 

  4. Abbassi, R.; Abbassi, A.; Jemli, M.; Chebbi, S.: Identification of unknown parameters of solar cell models: a comprehensive overview of available approaches. Renew. Sustain. Energy Rev. 90, 453–474 (2018)

    Google Scholar 

  5. 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)

    Google Scholar 

  6. Askarzadeh, A.; Rezazadeh, A.: Artificial bee swarm optimization algorithm for parameters identification of solar cell models. Applied Energy 102, 943–949 (2013). Special Issue on Advances in sustainable biofuel production and use—XIX International Symposium on Alcohol Fuels - ISAF

  7. Jordehi, A.R.: Parameter estimation of solar photovoltaic (PV) cells: a review. Renew. Sustain. Energy Rev. 61, 354–371 (2016)

    Google Scholar 

  8. Huang, C.; Li, Y.; Yao, X.: A survey of automatic parameter tuning methods for metaheuristics. IEEE Trans. Evolut. Comput. 24(2), 201–216 (2020)

    Google Scholar 

  9. 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)

    Google Scholar 

  10. Li, S.; Gong, W.; Yan, X.; Hu, C.; Bai, D.; Wang, L.; Gao, L.: Parameter extraction of photovoltaic models using an improved teaching-learning-based optimization. Energy Convers. Manag. 186, 293–305 (2019)

    Google Scholar 

  11. 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)

    Google Scholar 

  12. Wang, L.; Huang, C.: A novel elite opposition-based JAYA algorithm for parameter estimation of photovoltaic cell models. Optik 155, 351–356 (2018)

    Google Scholar 

  13. Yu, K.; Qu, B.; Yue, C.; Ge, S.; Chen, X.; Liang, J.: A performance-guided JAYA algorithm for parameters identification of photovoltaic cell and module. Appl. Energy 237, 241–257 (2019)

    Google Scholar 

  14. Wu, L.; Chen, Z.; Long, C.; Cheng, S.; Lin, P.; Chen, Y.; Chen, H.: Parameter extraction of photovoltaic models from measured i–v characteristics curves using a hybrid trust-region reflective algorithm. Appl. Energy 232, 36–53 (2018)

    Google Scholar 

  15. Dkhichi, F.; Oukarfi, B.; Fakkar, A.; Belbounaguia, N.: Parameter identification of solar cell model using Levenberg–Marquardt algorithm combined with simulated annealing. Solar Energy 110, 781–788 (2014)

    Google Scholar 

  16. Gan, M.; Chen, C.L.P.; Chen, G.-Y.; Chen, L.: On some separated algorithms for separable nonlinear least squares problems. IEEE Trans. Cybern. 48(10), 2866–2874 (2018)

    Google Scholar 

  17. McLoone, S.; Brown, M.D.; Irwin, G.; Lightbody, A.: A hybrid linear/nonlinear training algorithm for feedforward neural networks. IEEE Trans. Neural Netw. 9(4), 669–684 (1998)

    Google Scholar 

  18. Peng, H.; Ozaki, T.; Haggan-Ozaki, V.; Toyoda, Y.: A parameter optimization method for radial basis function type models. IEEE Trans. Neural Netw. 14(2), 432–438 (2003)

    MATH  Google Scholar 

  19. Talatahari, S.; Azizi, M.: Optimization of constrained mathematical and engineering design problems using chaos game optimization. Comput. Ind. Eng. 145, 106560 (2020)

    Google Scholar 

  20. Talatahari, S.; Azizi, M.: Chaos game optimization: a novel metaheuristic algorithm. Artif. Intell. Rev. 54(2), 917–1004 (2021)

    Google Scholar 

  21. Wang, G.; Zhao, K.; Shi, J.; Chen, W.; Zhang, H.; Yang, X.; Zhao, Y.: An iterative approach for modeling photovoltaic modules without implicit equations. Appl. Energy 202, 189–198 (2017)

    Google Scholar 

  22. Tong, N.T.; Pora, W.: A parameter extraction technique exploiting intrinsic properties of solar cells. Appl. Energy 176, 104–115 (2016)

    Google Scholar 

  23. Guo, L.; Meng, Z.; Sun, Y.; Wang, L.: Parameter identification and sensitivity analysis of solar cell models with cat swarm optimization algorithm. Energy Convers. Manag. 108, 520–528 (2016)

    Google Scholar 

  24. Li, S.; Gong, W.; Wang, L.; Yan, X.; Hu, C.: A hybrid adaptive teaching-learning-based optimization and differential evolution for parameter identification of photovoltaic models. Energy Convers. Manag. 225, 113474 (2020)

    Google Scholar 

  25. Easwarakhanthan, T.; Bottin, J.; Bouhouch, I.; Boutrit, C.: Nonlinear minimization algorithm for determining the solar cell parameters with microcomputers. Int. J. Solar Energy 4(1), 1–12 (1986)

    Google Scholar 

  26. Tossa, A.K.; Soro, Y.M.; Azoumah, Y.; Yamegueu, D.: A new approach to estimate the performance and energy productivity of photovoltaic modules in real operating conditions. Solar Energy 110, 543–560 (2014)

    Google Scholar 

  27. Mirjalili, S.; Mirjalili, S.M.; Lewis, A.: Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61 (2014)

    Google Scholar 

  28. Bogar, E.; Beyhan, S.: Adolescent identity search algorithm (AISA): a novel metaheuristic approach for solving optimization problems. Appl. Soft Comput. 95, 106503 (2020)

    Google Scholar 

  29. El-Naggar, K.M.; AlRashidi, M.R.; AlHajri, M.F.; Al-Othman, A.K.: Simulated annealing algorithm for photovoltaic parameters identification. Solar Energy 86(1), 266–274 (2012)

    Google Scholar 

  30. Oliva, D.; Cuevas, E.; Pajares, G.: Parameter identification of solar cells using artificial bee colony optimization. Energy 72, 93–102 (2014)

    Google Scholar 

  31. Alam, D.F.; Yousri, D.A.; Eteiba, M.B.: Flower pollination algorithm based solar PV parameter estimation. Energy Convers. Manag. 101, 410–422 (2015)

    Google Scholar 

  32. 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)

    Google Scholar 

  33. Subudhi, B.; Pradhan, R.: Bacterial foraging optimization approach to parameter extraction of a photovoltaic module. IEEE Trans. Sustain. Energy 9(1), 381–389 (2018)

    Google Scholar 

  34. Messaoud, R.B.: Extraction of uncertain parameters of single and double diode model of a photovoltaic panel using Salp swarm algorithm. Measurement 154, 107446 (2020)

    Google Scholar 

  35. 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)

    Google Scholar 

  36. Ismaeel, A.A.K.; Houssein, E.H.; Oliva, D.; Said, M.: Gradient-based optimizer for parameter extraction in photovoltaic models. IEEE Access 9, 13403–13416 (2021)

    Google Scholar 

  37. Jiang, L.L.; Maskell, D.L.; Patra, J.C.: Parameter estimation of solar cells and modules using an improved adaptive differential evolution algorithm. Appl. Energy 112, 185–193 (2013)

    Google Scholar 

  38. 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)

    Google Scholar 

  39. Wu, Z.; Yu, D.; Kang, X.: Parameter identification of photovoltaic cell model based on improved ant lion optimizer. Energy Convers. Manag. 151, 107–115 (2017)

    Google Scholar 

  40. 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)

    Google Scholar 

  41. Yu, K.; Liang, J.J.; Qu, B.Y.; Cheng, Z.; Wang, H.: Multiple learning backtracking search algorithm for estimating parameters of photovoltaic models. Appl. Energy 226, 408–422 (2018)

    Google Scholar 

  42. 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)

    Google Scholar 

  43. Jiao, S.; Chong, G.; Huang, C.; Hu, H.; Wang, M.; Heidari, A.A.; Chen, H.; Zhao, X.: Orthogonally adapted Harris hawks optimization for parameter estimation of photovoltaic models. Energy 203, 117804 (2020)

    Google Scholar 

  44. Yu, S.; Heidari, A.A.; Liang, G.; Chen, C.; Chen, H.; Shao, Q.: Solar photovoltaic model parameter estimation based on orthogonally-adapted gradient-based optimization. Optik 252, 168513 (2022)

    Google Scholar 

  45. 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)

    Google Scholar 

  46. El-Fergany, A.A.: Parameters identification of PV model using improved slime mould optimizer and lambert w-function. Energy Rep. 7, 875–887 (2021)

    Google Scholar 

  47. Long, W.; Cai, S.; Jiao, J.; Xu, M.; Wu, T.: A new hybrid algorithm based on grey wolf optimizer and cuckoo search for parameter extraction of solar photovoltaic models. Energy Convers. Manag. 203, 112243 (2020)

    Google Scholar 

  48. Chen, X.; Yu, K.: Hybridizing cuckoo search algorithm with biogeography-based optimization for estimating photovoltaic model parameters. Solar Energy 180, 192–206 (2019)

    Google Scholar 

  49. AlRashidi, M.R.; AlHajri, M.F.; El-Naggar, K.M.; Al-Othman, A.K.: A new estimation approach for determining the i–v characteristics of solar cells. Solar Energy 85(7), 1543–1550 (2011)

    Google Scholar 

  50. Chin, V.J.; Salam, Z.; Ishaque, K.: Cell modelling and model parameters estimation techniques for photovoltaic simulator application: a review. Appl. Energy 154, 500–519 (2015)

    Google Scholar 

  51. Nishioka, K.; Sakitani, N.; Uraoka, Y.; Fuyuki, T.: Analysis of multicrystalline silicon solar cells by modified 3-diode equivalent circuit model taking leakage current through periphery into consideration. Solar Energy Mater. Solar Cells 91(13), 1222–1227 (2007)

    Google Scholar 

  52. Abbassi, R.; Abbassi, A.; Heidari, A.A.; Mirjalili, S.: An efficient Salp swarm-inspired algorithm for parameters identification of photovoltaic cell models. Energy Convers. Manag. 179, 362–372 (2019)

    Google Scholar 

  53. Chen, G.-Y.; Wang, S.-Q.; Wang, D.-Q.; Gan, M.: Regularization methods for separable nonlinear models. Nonlinear Dyn. 98(2), 1287–1298 (2019)

    Google Scholar 

  54. Chenouard, R.; El-Sehiemy, R.A.: An interval branch and bound global optimization algorithm for parameter estimation of three photovoltaic models. Energy Convers. Manag. 205, 112400 (2020)

    Google Scholar 

  55. Rao, R.V.; Savsani, V.J.; Vakharia, D.P.: Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems. Comput. Aided Des. 43(3), 303–315 (2011)

    Google Scholar 

  56. Kiran, M.S.: Tsa: tree-seed algorithm for continuous optimization. Expert Syst. Appl. 42(19), 6686–6698 (2015)

    Google Scholar 

  57. Rao, R.: Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int. J. Ind. Eng. Comput. 7(1), 19–34 (2016)

    MathSciNet  Google Scholar 

  58. Mirjalili, S.; Lewis, A.: The whale optimization algorithm. Adv. Eng. Softw. 95, 51–67 (2016)

    Google Scholar 

  59. Liang, J.; Qiao, K.; Yuan, M.; Yu, K.; Qu, B.; Ge, S.; Li, Y.; Chen, G.: Evolutionary multi-task optimization for parameters extraction of photovoltaic models. Energy Convers. Manag. 207, 112509 (2020)

    Google Scholar 

  60. Long, W.; Wu, T.; Xu, M.; Tang, M.; Cai, S.: Parameters identification of photovoltaic models by using an enhanced adaptive butterfly optimization algorithm. Energy 229, 120750 (2021)

    Google Scholar 

  61. Xiong, G.; Zhang, J.; Yuan, X.; Shi, D.; He, Y.: Application of symbiotic organisms search algorithm for parameter extraction of solar cell models. Appl. Sci. 8(11), 2155 (2018)

    Google Scholar 

  62. Zhang, Y.; Jin, Z.; Mirjalili, S.: Generalized normal distribution optimization and its applications in parameter extraction of photovoltaic models. Energy Convers. Manag. 224, 113301 (2020)

    Google Scholar 

  63. Xiong, G.; Li, L.; Mohamed, A.W.; Yuan, X.; Zhang, J.: A new method for parameter extraction of solar photovoltaic models using gaining sharing knowledge based algorithm. Energy Rep. 7, 3286–3301 (2021)

    Google Scholar 

  64. Fan, Y.; Wang, P.; Heidari, A.A.; Chen, H.; HamzaTurabieh; Mafarja, M.: Random reselection particle swarm optimization for optimal design of solar photovoltaic modules. Energy 239, 121865 (2022)

    Google Scholar 

  65. Zhou, W.; Wang, P.; Heidari, A.A.; Zhao, X.; Turabieh, H.; Chen, H.: Random learning gradient based optimization for efficient design of photovoltaic models. Energy Convers. Manag. 230, 113751 (2021)

    Google Scholar 

  66. Said, M.; Shaheen, A.M.; Ginidi, A.R.; El-Sehiemy, R.A.; Mahmoud, K.; Lehtonen, M.; Darwish, M.M.F.: Estimating parameters of photovoltaic models using accurate turbulent flow of water optimizer. Processes 9(4), 627 (2021)

    Google Scholar 

  67. Gao, S.; Wang, K.; Tao, S.; Jin, T.; Dai, H.; Cheng, J.: A state-of-the-art differential evolution algorithm for parameter estimation of solar photovoltaic models. Energy Convers. Manag. 230, 113784 (2021)

    Google Scholar 

  68. Ku, J.; Li, S.; Gong, W.: Photovoltaic models parameter estimation via an enhanced Rao-1 algorithm. Math. Biosci. Eng. 19(2), 1128–1153 (2022)

  69. Zhou, W.; Wang, P.; Heidari, A.A.; Zhao, X.; Turabieh, H.; Mafarja, M.; Chen, H.: Metaphor-free dynamic spherical evolution for parameter estimation of photovoltaic modules. Energy Rep. 7, 5175–5202 (2021)

    Google Scholar 

  70. Ramadan, A.; Kamel, S.; Hussein, M.M.; Hassan, M.H.: A new application of chaos game optimization algorithm for parameters extraction of three diode photovoltaic model. IEEE Access 9, 51582–51594 (2021)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronic and Automation, Denizli Vocational School of Technical Sciences, Pamukkale University, 20070, Denizli, Turkey

    Esref Bogar

Authors
  1. Esref Bogar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Esref Bogar.

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

Bogar, E. Chaos Game Optimization-Least Squares Algorithm for Photovoltaic Parameter Estimation. Arab J Sci Eng 48, 6321–6340 (2023). https://doi.org/10.1007/s13369-022-07364-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-022-07364-6

Keywords

Search

Navigation