The accuracy of unknown parameters determines the accuracy of photovoltaic (PV) models that occupy an important position in the PV power generation system. Due to the complexity of the equation equivalent of PV models, estimating the parameters of the PV model is still an arduous task. In order to accurately and reliably estimate the unknown parameters in PV models, in this paper, an enhanced Rao-1 algorithm is proposed. The main point of enhancement lies in i) a repaired evolution operator is presented; ii) to prevent the Rao-1 algorithm from falling into a local optimum, a new evolution operator is developed; iii) in order to enable population size to change adaptively with the evolutionary process, the population size linear reduction strategy is employed. To verify the validity of ERao-1 algorithm, we embark a study on parameter estimation of three different PV models. Experimental results show that the proposed ERao-1 algorithm performs better than existing parameter estimation algorithms in terms of the accuracy and reliability, especially for the double diode model with RMSE 9.8248E-04, three diode model with RMSE 9.8257E-04 for the R.T.C France silicon cell, and 2.4251E-03 for the three diode model of Photowatt- PWP201 cell. In addition, the fitting curve of the simulated data and the measured data also shows the accuracy of the estimated parameters.
Citation: Junhua Ku, Shuijia Li, Wenyin Gong. Photovoltaic models parameter estimation via an enhanced Rao-1 algorithm[J]. Mathematical Biosciences and Engineering, 2022, 19(2): 1128-1153. doi: 10.3934/mbe.2022052
The accuracy of unknown parameters determines the accuracy of photovoltaic (PV) models that occupy an important position in the PV power generation system. Due to the complexity of the equation equivalent of PV models, estimating the parameters of the PV model is still an arduous task. In order to accurately and reliably estimate the unknown parameters in PV models, in this paper, an enhanced Rao-1 algorithm is proposed. The main point of enhancement lies in i) a repaired evolution operator is presented; ii) to prevent the Rao-1 algorithm from falling into a local optimum, a new evolution operator is developed; iii) in order to enable population size to change adaptively with the evolutionary process, the population size linear reduction strategy is employed. To verify the validity of ERao-1 algorithm, we embark a study on parameter estimation of three different PV models. Experimental results show that the proposed ERao-1 algorithm performs better than existing parameter estimation algorithms in terms of the accuracy and reliability, especially for the double diode model with RMSE 9.8248E-04, three diode model with RMSE 9.8257E-04 for the R.T.C France silicon cell, and 2.4251E-03 for the three diode model of Photowatt- PWP201 cell. In addition, the fitting curve of the simulated data and the measured data also shows the accuracy of the estimated parameters.
| [1] |
S. Li, W. Gong, Q. Gu, A comprehensive survey on meta-heuristic algorithms for parameter extraction of photovoltaic models, Renew. Sustain. Energy Rev., 141 (2021), 110828. doi: 10.1016/j.rser.2021.110828. doi: 10.1016/j.rser.2021.110828
|
| [2] |
G. Xiong, J. Zhang, D. Shi, Y. He, Parameter extraction of solar photovoltaic models using an improved whale optimization algorithm, Energy Convers. Manage., 174 (2018), 388–405. doi: 10.1016/j.enconman.2018.08.053. doi: 10.1016/j.enconman.2018.08.053
|
| [3] |
T. Ayodele, A. Ogunjuyigbe, E. Ekoh, Evaluation of numerical algorithms used in extracting the parameters of a single-diode photovoltaic model, Sustain. Energy Technol. Assess, 13 (2016), 51–59. doi: 10.1016/j.seta.2015.11.003. doi: 10.1016/j.seta.2015.11.003
|
| [4] |
T. Babu, J. Ram, K. Sangeetha, A. Laudani, N. Rajasekar, Parameter extraction of two diode solar pv model using fireworks algorithm, Sol. Energy, 140 (2016), 265–276. doi: 10.1016/j.solener.2016.10.044. doi: 10.1016/j.solener.2016.10.044
|
| [5] |
S. Li, W. Gong, X. Yan, C. Hu, D. Bai, L. Wang, Parameter estimation of photovoltaic models with memetic adaptive differential evolution, Sol. Energy, 190 (2019), 465–474. doi: 10.1016/j.solener.2019.08.022. doi: 10.1016/j.solener.2019.08.022
|
| [6] |
T. Easwarakhanthan, J. Bottin, I. Bouhouch, C. Boutrit, Nonlinear minimization algorithm for determining the solar cell parameters with microcomputers, Int. J. Sol. Energy, 4 (1986), 1–12. doi: 10.1080/01425918608909835. doi: 10.1080/01425918608909835
|
| [7] |
A. Conde, F. S $ \acute{a} $ nchez, J. Muci, New method to extract the model parameters of solar cells from the explicit analytic solutions of their illuminated characteristics, Sol. Energy Mater. Sol. Cells, 90 (2006), 352–361. doi: 10.1016/j.solmat.2005.04.023. doi: 10.1016/j.solmat.2005.04.023
|
| [8] |
R. Messaoud, Extraction of uncertain parameters of single-diode model of a photovoltaic panel using simulated annealing optimization, Energy Rep., 6 (2020), 350–357. doi: 10.1016/j.egyr.2020.01.016. doi: 10.1016/j.egyr.2020.01.016
|
| [9] |
M. AlHajri, K. Naggar, M. AlRashidi, A. Othman, Optimal extraction of solar cell parameters using pattern search, Renew. Energy, 44 (2012), 238–245. doi: 10.1016/j.renene.2012.01.082. doi: 10.1016/j.renene.2012.01.082
|
| [10] |
S. Ebrahimi, E. Salahshour, M. Malekzadeh, F. Gordillo, Parameters identification of pv solar cells and modules using flexible particle swarm optimization algorithm, Energy, 179 (2019), 358–372. doi: 10.1016/j.energy.2019.04.218. doi: 10.1016/j.energy.2019.04.218
|
| [11] |
S. Li, Q. Gu, W. Gong, B. Ning, An enhanced adaptive differential evolution algorithm for parameter extraction of photovoltaic models, Energy Convers. Manage., 205 (2020), 112443. doi: 10.1016/j.enconman.2019.112443. doi: 10.1016/j.enconman.2019.112443
|
| [12] |
Z. Yan, S. Li, W. Gong, An adaptive differential evolution with decomposition for photovoltaic parameter extraction, Math. Biosci. Eng., 18 (2021), 7363–7388. doi: 10.3934/mbe.2021364. doi: 10.3934/mbe.2021364
|
| [13] |
S. Li, W. Gong, L. Wang, X. Yan, C. Hu, A hybrid adaptive teaching-learning-based optimization and differential evolution for parameter identification of photovoltaic models, Energy Convers. Manage., 225 (2020), 113474. doi: 10.1016/j.enconman.2020.113474. doi: 10.1016/j.enconman.2020.113474
|
| [14] |
D. Oliva, M. Aziz, A. Hassanien, Parameter estimation of photovoltaic cells using an improved chaotic whale optimization algorithm, Appl. Energy, 200 (2017), 141–154. doi: 10.1016/j.apenergy.2017.05.029. doi: 10.1016/j.apenergy.2017.05.029
|
| [15] |
X. Chen, K. Yu, W. Du, W. Zhao, G. Liu, Parameters identification of solar cell models using generalized oppositional teaching learning based optimization, Energy, 99 (2016), 170–180. doi: 10.1016/j.energy.2016.01.052. doi: 10.1016/j.energy.2016.01.052
|
| [16] |
K. Yu, J. Liang, B. Qu, X. Chen, H. Wang, Parameters identification of photovoltaic models using an improved jaya optimization algorithm, Energy Convers. Manage., 150 (2017), 742–753. doi: 10.1016/j.enconman.2017.08.063. doi: 10.1016/j.enconman.2017.08.063
|
| [17] |
K. Yu, J. Liang, B. Qu, Z. Cheng, H. Wang, Multiple learning backtracking search algorithm for estimating parameters of photovoltaic models, Appl. Energy, 226 (2018), 408–422. doi: 10.1016/j.apenergy.2018.06.010. doi: 10.1016/j.apenergy.2018.06.010
|
| [18] |
X. Chen, B. Xu, C. Mei, Y. Ding, K. Li, Teaching-learning-based artificial bee colony for solar photovoltaic parameter estimation, Appl. Energy, 212 (2018), 1578–1588. doi: 10.1016/j.apenergy.2017.12.115. doi: 10.1016/j.apenergy.2017.12.115
|
| [19] |
K. Yu, B. Qu, C. Yue, S. Ge, X. Chen, J. Liang, A performance-guided jaya algorithm for parameters identification of photovoltaic cell and module, Appl. Energy, 237 (2019), 241–257. doi: 10.1016/j.apenergy.2019.01.008. doi: 10.1016/j.apenergy.2019.01.008
|
| [20] |
S. Li, W. Gong, X. Yan, C. Hu, D. Bai, L. Wang, et al., Parameter extraction of photovoltaic models using an improved teaching-learning-based optimization, Energy Convers. Manage., 186 (2019), 293–305. doi: 10.1016/j.enconman.2019.02.048. doi: 10.1016/j.enconman.2019.02.048
|
| [21] |
R. Rao, Rao algorithms: three metaphor-less simple algorithms for solving optimization problems, Int. J. Ind. Eng. Comput., 11 (2020), 107–130. doi: 10.5267/j.ijiec.2019.6.002. doi: 10.5267/j.ijiec.2019.6.002
|
| [22] |
R. Rao, R. Pawar, Constrained design optimization of selected mechanical system components using rao algorithms, Appl. Soft Comput., 89 (2020), 106141. doi: 10.1016/j.asoc.2020.106141. doi: 10.1016/j.asoc.2020.106141
|
| [23] |
M. Srikanth, N. Yadaiah, Analytical tuning rules for reduced-order active disturbance rejection control with fopdt models through multi-objective optimization and multi-criteria decision-making, ISA Trans., 114 (2021), 370–398. doi: 10.1016/j.isatra.2020.12.035. doi: 10.1016/j.isatra.2020.12.035
|
| [24] |
L. Wang, Z. Wang, H. Liang, C. Huang, Parameter estimation of photovoltaic cell model with rao-1 algorithm, Optik, 210 (2020), 163846. doi: 10.1016/j.ijleo.2019.163846. doi: 10.1016/j.ijleo.2019.163846
|
| [25] |
X. Jian, Y. Zhu, Parameters identification of photovoltaic models using modified rao-1 optimization algorithm, Optik, 231 (2021), 166439. doi: 10.1016/j.ijleo.2021.166439. doi: 10.1016/j.ijleo.2021.166439
|
| [26] |
M. Alrashidi, M. Alhajri, K. Elnaggar, A. Alothman, A new estimation approach for determining the i-v characteristics of solar cells, Sol. Energy, 85 (2011), 1543–1550. doi: 10.1016/j.solener.2011.04.013. doi: 10.1016/j.solener.2011.04.013
|
| [27] |
K. Naggar, M. AlRashidi, M. AlHajri, A. Othman, Simulated annealing algorithm for photovoltaic parameters identification, Sol. Energy, 86 (2012), 266–274. doi: 10.1016/j.solener.2011.09.032. doi: 10.1016/j.solener.2011.09.032
|
| [28] |
A. Askarzadeh, A. Rezazadeh, Parameter identification for solar cell models using harmony search-based algorithms, Sol. Energy, 86 (2012), 3241–3249. doi: 10.1016/j.solener.2012.08.018. doi: 10.1016/j.solener.2012.08.018
|
| [29] | W. Huang, C. Jiang, L. Xue, D. Song, Extracting solar cell model parameters based on chaos particle swarm algorithm, In 2011 International Conference on Electric Information and Control Engineering, pages 398–402, April 2011. doi: 10.1109/ICEICE.2011.5777246. |
| [30] |
K. Ishaque, Z. Salam, S. Mekhilef, A. Shamsudin, Parameter extraction of solar photovoltaic modules using penalty-based differential evolution, Appl. Energy, 99 (2012), 297–308. doi: 10.1016/j.apenergy.2012.05.017. doi: 10.1016/j.apenergy.2012.05.017
|
| [31] |
H. Hasanien, Shuffled frog leaping algorithm for photovoltaic model identification, IEEE Trans. Sustain. Energy, 6 (2015), 509–515. doi: 10.1109/TSTE.2015.2389858. doi: 10.1109/TSTE.2015.2389858
|
| [32] |
J. Ram, T. Babu, T. Dragicevic, N. Rajasekar, A new hybrid bee pollinator flower pollination algorithm for solar pv parameter estimation, Energy Convers. Manage., 135 (2017), 463–476. doi: 10.1016/j.enconman.2016.12.082. doi: 10.1016/j.enconman.2016.12.082
|
| [33] |
K. Yu, X. Chen, X. Wang, Z. Wang, Parameters identification of photovoltaic models using self-adaptive teaching-learning-based optimization, Energy Convers. Manage., 145 (2017), 233–246. doi: 10.1016/j.enconman.2017.04.054. doi: 10.1016/j.enconman.2017.04.054
|
| [34] |
F. Zeng, H. Shu, J. Wang, Y. Chen, B. Yang, Parameter identification of pv cell via adaptive compass search algorithm, Energy Rep., 7 (2021), 275–282. doi: 10.1016/j.egyr.2021.01.069. doi: 10.1016/j.egyr.2021.01.069
|
| [35] |
G. Xiong, L. Li, A. Mohamed, X. Yuan, J. Zhang, A new method for parameter extraction of solar photovoltaic models using gaining sharing knowledge based algorithm, Energy Rep., 7 (2021), 3286–3301. doi: 10.1016/j.egyr.2021.05.030. doi: 10.1016/j.egyr.2021.05.030
|
| [36] |
W. Li, W. Gong, Differential evolution with quasi-reflection-based mutation, Math. Biosci. Eng., 18 (2021), 2425–2441. doi: 10.3934/MBE.2021123. doi: 10.3934/MBE.2021123
|
| [37] |
Q. Pang, X. Mi, J. Sun, H. Qin, Solving nonlinear equation systems via clustering-based adaptive speciation differential evolution, Math. Biosci. Eng., 18 (2021), 6034–6065. doi: 10.3934/MBE.2021302. doi: 10.3934/MBE.2021302
|
| [38] |
S. García, D. Molina, M. Lozano, F. Herrera, A study on the use of non-parametric tests for analyzing the evolutionary algorithms behaviour: a case study on the cec 2005 special session on real parameter optimization, J. Heurist., 15 (2009), 617–644. doi: 10.1007/s10732-008-9080-4. doi: 10.1007/s10732-008-9080-4
|
| [39] |
L. Deotti, J. Pereira, I. J $ \acute{e} $ nior, Parameter extraction of photovoltaic models using an enhanced l $ \acute{e} $ vy flight bat algorithm, Energy Convers. Manage., 221 (2020), 113114. doi: 10.1016/j.enconman.2020.113114. doi: 10.1016/j.enconman.2020.113114
|
| [40] |
J. Liang, S. Ge, B. Qu, K. Yu, F. Liu, H. Yang, et al., Classified perturbation mutation based particle swarm optimization algorithm for parameters extraction of photovoltaic models, Energy Convers. Manage., 203 (2020), 112138. doi: 10.1016/j.enconman.2019.112138. doi: 10.1016/j.enconman.2019.112138
|
| [41] |
X. Lin, Y. Wu, Parameters identification of photovoltaic models using niche-based particle swarm optimization in parallel computing architecture, Energy, 196 (2020), 117054. doi: 10.1016/j.energy.2020.117054. doi: 10.1016/j.energy.2020.117054
|
| [42] |
M. Basset, R. Mohamed, S. Mirjalili, R. Chakrabortty, M. Ryan, Solar photovoltaic parameter estimation using an improved equilibrium optimizer, Sol. Energy, 209 (2020), 694–708. doi: 10.1016/j.solener.2020.09.032. doi: 10.1016/j.solener.2020.09.032
|
| [43] |
X. Yang, W. Gong, Opposition-based jaya with population reduction for parameter estimation of photovoltaic solar cells and modules, Appl. Soft Comput., 104 (2021), 107218. doi: 10.1016/j.asoc.2021.107218. doi: 10.1016/j.asoc.2021.107218
|
| [44] |
W. Long, T. Wu, M. Xu, M. Tang, S. Cai, Parameters identification of photovoltaic models by using an enhanced adaptive butterfly optimization algorithm, Energy, 229 (2021), 120750. doi: 10.1016/j.energy.2021.120750. doi: 10.1016/j.energy.2021.120750
|
| [45] |
Y. Liu, A. Heidari, X. Ye, C. Chi, X. Zhao, C. Ma, et al., Evolutionary shuffled frog leaping with memory pool for parameter optimization, Energy Rep., 7 (2021), 584–606. doi: 10.1016/j.egyr.2021.01.001. doi: 10.1016/j.egyr.2021.01.001
|
| [46] |
M. Basset, R. Mohamed, R. Chakrabortty, K. Sallam, M. Ryan, An efficient teaching-learning-based optimization algorithm for parameters identification of photovoltaic models: Analysis and validations, Energy Convers. Manage., 227 (2021), 113614. doi: 10.1016/j.enconman.2020.113614. doi: 10.1016/j.enconman.2020.113614
|
| [47] |
O. Hachana, B. Aoufi, G. Tina, M. Sid, Photovoltaic mono and bifacial module/string electrical model parameters identification and validation based on a new differential evolution bee colony optimizer, Energy Convers. Manage., 248 (2021), 114667. doi: 10.1016/j.enconman.2021.114667. doi: 10.1016/j.enconman.2021.114667
|
| [48] |
Y. Zhang, M. Ma, Z. Jin, Comprehensive learning jaya algorithm for parameter extraction of photovoltaic models, Energy, 211 (2020), 118644. doi: 10.1016/j.energy.2020.118644. doi: 10.1016/j.energy.2020.118644
|
| [49] |
Y. Zhang, M. Ma, Z. Jin, Backtracking search algorithm with competitive learning for identification of unknown parameters of photovoltaic systems, Expert Syst. Appl., 160 (2020), 113750. doi: 10.1016/j.eswa.2020.113750. doi: 10.1016/j.eswa.2020.113750
|
| [50] |
L. Tang, X. Wang, W. Xu, C. Mu, B. Zhao, Maximum power point tracking strategy for photovoltaic system based on fuzzy information diffusion under partial shading conditions, Sol. Energy, 220 (2021), 523–534. doi: 10.1016/j.solener.2021.03.047. doi: 10.1016/j.solener.2021.03.047
|
| [51] |
S. Li, W. Gong, L. Wang, X. Yan, C. Hu, Optimal power flow by means of improved adaptive differential evolution, Energy, 198 (2020), 117314. doi: 10.1016/j.energy.2020.117314. doi: 10.1016/j.energy.2020.117314
|
| [52] |
S. Li, W. Gong, C. Hu, X. Yan, L. Wang, Q. Gu, Adaptive constraint differential evolution for optimal power flow, Energy, 235 (2021), 121362. doi: 10.1016/j.energy.2021.121362. doi: 10.1016/j.energy.2021.121362
|
| [53] |
W. Gong, Z. Liao, X. Mi, L. Wang, Y. Guo, Nonlinear equations solving with intelligent optimization algorithms: a survey, Complex Syst. Model. Simul., 1 (2021), 15–32. doi: 10.23919/CSMS.2021.0002. doi: 10.23919/CSMS.2021.0002
|
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Junhua Ku, Shuijia Li, Wenyin Gong. Photovoltaic models parameter estimation via an enhanced Rao-1 algorithm[J]. Mathematical Biosciences and Engineering, 2022, 19(2): 1128-1153. doi: 10.3934/mbe.2022052
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