A Parameter Estimation of Photovoltaic Models Using a Boosting Flower Pollination Algorithm
Abstract
:1. Introduction
- A Boosting Flower Pollination Algorithm (BFPA) combining three novel strategies is designed to estimate unknown parameters of different photovoltaic cell/module models.
- The proposed method is used to identify unknown parameters of three PV cell/module models and the manufacturer’s PV module model.
- Compared to existing popular methods, comprehensive experiments on BFPA were conducted in a variety of different environments. The research results verified that BFPA can provide more excellent results, indicating the significant competitive advantage of the proposed method in PV systems.
2. Materials and Methods
2.1. Mathematical Models of Photovoltaic Systems
2.1.1. Single Diode Model (SDM)
2.1.2. Double Diode Model (DDM)
2.1.3. PV Module Model (PMM)
2.2. Problem Formulation
2.3. Boosting Flower Pollination Algorithm (BFPA)
2.3.1. Summary of FPA
- (1)
- Biological pollination and cross-pollination carry out the global pollination processes through the Lévy flight behavior.
- (2)
- Abiotic and self-pollination perform local pollination process via their own characteristics.
- (3)
- Flower constancy, also known as reproductive rate, can be considered to be related to the similarity between two flowers.
- (4)
- Local pollination and global pollination can be switched freely and controlled by probability p ∈ [0, 1].
2.3.2. The Proposed Algorithm of BFPA
Gaussian Distribution Global Pollination Strategy
The Clustering Strategy of Population
Algorithm 1: Pseudo code of clustering strategy of population. |
|
The Chaotic Elite-Guided Learning Strategy
Algorithm 2: Pseudo code of chaotic elite-guided learning strategy |
|
Adaptive Boundary Handling Strategy
Algorithm 3: Pseudo code of adaptive boundary handling strategy |
|
The Framework of BFPA
3. Simulation Results
3.1. Results of PV Cell and Module Model
3.1.1. Statistical Results Analysis on Different PV Models
3.1.2. Result on Single Diode Model
3.1.3. Result on Double Diode Model
3.1.4. Result on Photovoltaic Module Model
3.2. The Result of Datasheets from Different Manufacturers
4. Discussions
5. Conclusions and Future Works
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
BFPA | Boosting flower pollination algorithm | Rsh | Shunt resistor |
FPA | Flower Pollination Algorithm | Np/Ns | Number of solar cells in parallel/series |
PV | Photovoltaic | X | Unknown variable of the problem |
I-V | Current-voltage | K | Number of the observed current-voltage data |
SDM | Single diode model | RMSE | Root mean square error |
DDM | Double diode model | Γ(λ) | Gamma function |
PMM | Photovoltaic module model | sin(·) | Sine function |
Iph | Photocurrent | Gauss(0, α) | Gaussian distribution function |
Id | Current through the diode | Levy(s, λ) | Step size of Lévy flight |
Ish | Current through the shunt resistor | N | Number of pollens |
Isd, Isd1, Isd2 | Currents of diode | D | Number of variables |
q | Elementary charge | B, C | Subpopulation |
VL | Output voltage | KC200GT | Multi-crystalline PV module |
Rs | Series resistor | SM55 | Mono-crystalline PV module |
n, n1, n2 | Diode ideality factors | ST40 | Thin-film PV module |
k | Boltzmann constant | IAe | Absolute error |
T | Kelvin temperature | IRe | Relative error |
References
- Chang, J.; Leung, D.Y.C.; Wu, C.Z.; Yuan, Z.H. A review on the energy production, consumption, and prospect of renewable energy in China. Renew. Sustain. Energy Rev. 2003, 7, 453–468. [Google Scholar] [CrossRef]
- Alam, D.F.; Yousri, D.A.; Eteiba, M.B. Flower Pollination Algorithm based solar PV parameter estimation. Energy Convers. Manag. 2015, 101, 410–422. [Google Scholar] [CrossRef]
- Kumari, P.A.; Geethanjali, P. Parameter estimation for photovoltaic system under normal and partial shading conditions: A survey. Renew. Sustain. Energy Rev. 2018, 84, 1–11. [Google Scholar]
- Zagrouba, M.; Sellami, A.; Bouaïcha, M.; Ksouri, M. Identification of PV solar cells and modules parameters using the genetic algorithms: Application to maximum power extraction. Sol. Energy 2010, 84, 860–866. [Google Scholar] [CrossRef]
- Prince Winston, D.; Kumaravel, S.; Praveen Kumar, B.; Devakirubakaran, S. Performance improvement of solar PV array topologies during various partial shading conditions. Sol. Energy 2020, 196, 228–242. [Google Scholar] [CrossRef]
- Peng, L.; He, C.; Heidari, A.A.; Zhang, Q.; Chen, H.; Liang, G.; Aljehane, N.O.; Mansour, R.F. Information sharing search boosted whale optimizer with Nelder-Mead simplex for parameter estimation of photovoltaic models. Energy Convers. Manag. 2022, 270, 116246. [Google Scholar]
- Rawat, N.; Thakur, P.; Singh, A.K.; Bhatt, A.; Sangwan, V.; Manivannan, A. A new grey wolf optimization-based parameter estimation technique of solar photovoltaic. Sustain. Energy Technol. Assess. 2023, 57, 103240. [Google Scholar] [CrossRef]
- Bo, Q.; Cheng, W.; Khishe, M.; Mohammadi, M.; Mohammed, A.H. Solar photovoltaic model parameter identification using robust niching chimp optimization. Sol. Energy 2022, 239, 179–197. [Google Scholar] [CrossRef]
- Pan, J.; Tian, A.; Snášel, V.; Kong, L.; Chu, S. Maximum power point tracking and parameter estimation for multiple-photovoltaic arrays based on enhanced pigeon-inspired optimization with Taguchi method. Energy 2022, 251, 123863. [Google Scholar] [CrossRef]
- Song, S.; Wang, P.; Heidari, A.A.; Zhao, X.; Chen, H. Adaptive Harris hawks optimization with persistent trigonometric differences for photovoltaic model parameter extraction. Eng. Appl. Artif. Intell. 2022, 109, 104608. [Google Scholar]
- Dastgeer, G.; Shahzad, Z.M.; Chae, H.; Kim, Y.H.; Ko, B.M.; Eom, J. Bipolar Junction Transistor Exhibiting Excellent Output Characteristics with a Prompt Response against the Selective Protein. Adv. Funct. Mater. 2022, 32, 2204781. [Google Scholar] [CrossRef]
- Dastgeer, G.; Nisar, S.; Shahzad, Z.M.; Rasheed, A.; Kim, D.K.; Jaffery, S.H.A.; Wang, L.; Usman, M.; Eom, J. Low-Power Negative-Differential-Resistance Device for Sensing the Selective Protein via Supporter Molecule Engineering. Adv. Sci. 2023, 10, e2204779. [Google Scholar] [CrossRef] [PubMed]
- Xu, B.; Heidari, A.A.; Kuang, F.; Zhang, S.; Chen, H.; Cai, Z. Performance optimization of photovoltaic systems: Reassessment of political optimization with a quantum Nelder-mead functionality. Sol. Energy 2022, 234, 39–63. [Google Scholar]
- 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. 2017, 150, 742–753. [Google Scholar] [CrossRef]
- Doerr, C. Complexity Theory for Discrete Black-Box Optimization Heuristics. In Theory of Evolutionary Computation: Recent Developments in Discrete Optimization; Doerr, B., Neumann, F., Eds.; Springer International Publishing: Cham, Switzerland, 2020; pp. 133–212. [Google Scholar]
- Abd El-Mageed, A.A.; Abohany, A.A.; Saad, H.M.H.; Sallam, K.M. Parameter extraction of solar photovoltaic models using queuing search optimization and differential evolution. Appl. Soft Comput. 2023, 134, 110032. [Google Scholar] [CrossRef]
- Kharchouf, Y.; Herbazi, R.; Chahboun, A. Parameter’s extraction of solar photovoltaic models using an improved differential evolution algorithm. Energy Convers. Manag. 2022, 251, 114972. [Google Scholar] [CrossRef]
- Ali, F.; Sarwar, A.; Ilahi Bakhsh, F.; Ahmad, S.; Ali Shah, A.; Ahmed, H. Parameter extraction of photovoltaic models using atomic orbital search algorithm on a decent basis for novel accurate RMSE calculation. Energy Convers. Manag. 2023, 277, 116613. [Google Scholar] [CrossRef]
- Ganesh Pardhu, B.S.S.; Kota, V.R. Radial movement optimization based parameter extraction of double diode model of solar photovoltaic cell. Sol. Energy 2021, 213, 312–327. [Google Scholar] [CrossRef]
- Beşkirli, A.; Dağ, İ. Parameter extraction for photovoltaic models with tree seed algorithm. Energy Rep. 2023, 9, 174–185. [Google Scholar] [CrossRef]
- Li, S.; Gong, W.; Gu, Q. A comprehensive survey on meta-heuristic algorithms for parameter extraction of photovoltaic models. Renew. Sustain. Energy Rev. 2021, 141, 110828. [Google Scholar]
- Yu, S.; Heidari, A.A.; He, C.; Cai, Z.; Althobaiti, M.M.; Mansour, R.F.; Liang, G.; Chen, H. Parameter estimation of static solar photovoltaic models using Laplacian Nelder-Mead hunger games search. Sol. Energy 2022, 242, 79–104. [Google Scholar]
- Madhiarasan, M.; Cotfas, D.T.; Cotfas, P.A. Barnacles Mating Optimizer Algorithm to Extract the Parameters of the Photovoltaic Cells and Panels. Sensors 2022, 22, 6989. [Google Scholar]
- Wang, M.; Chen, L.; Chen, H. Multi-Strategy Learning Boosted Colony Predation Algorithm for Photovoltaic Model Parameter Identification. Sensors 2022, 22, 8281. [Google Scholar]
- Yu, X.; Duan, Y.; Cai, Z. Sub-population improved grey wolf optimizer with Gaussian mutation and Lévy flight for parameters identification of photovoltaic models. Expert Syst. Appl. 2023, 232, 120827. [Google Scholar]
- Abdel-Basset, M.; Shawky, L.A. Flower pollination algorithm: A comprehensive review. Artif. Intell. Rev. 2019, 52, 2533–2557. [Google Scholar]
- Mirjalili, S.; Mirjalili, S.M.; Lewis, A. Grey Wolf Optimizer. Adv. Eng. Softw. 2014, 69, 46–61. [Google Scholar]
- Hemalatha, S.; Albert, J.R.; Banu, G.; Indirajith, K. Design and investigation of PV string/central architecture for bayesian fusion technique using grey wolf optimization and flower pollination optimized algorithm. Energy Convers. Manag. 2023, 286, 117078. [Google Scholar]
- Wang, Z.; Luo, Q.; Zhou, Y. Hybrid metaheuristic algorithm using butterfly and flower pollination base on mutualism mechanism for global optimization problems. Eng. Comput. 2021, 37, 3665–3698. [Google Scholar]
- Chen, Y.; Pi, D.; Xu, Y. Neighborhood global learning based flower pollination algorithm and its application to unmanned aerial vehicle path planning. Expert Syst. Appl. 2021, 170, 114505. [Google Scholar]
- Liang, J.; Qiao, K.; Yu, K.; Ge, S.; Qu, B.; Xu, R.; Li, K. Parameters estimation of solar photovoltaic models via a self-adaptive ensemble-based differential evolution. Sol. Energy 2020, 207, 336–346. [Google Scholar]
- Kler, D.; Sharma, P.; Banerjee, A.; Rana, K.P.S.; Kumar, V. PV cell and module efficient parameters estimation using Evaporation Rate based Water Cycle Algorithm. Swarm Evol. Comput. 2017, 35, 93–110. [Google Scholar] [CrossRef]
- Gong, W.; Cai, Z. Parameter extraction of solar cell models using repaired adaptive differential evolution. Sol. Energy 2013, 94, 209–220. [Google Scholar]
- Oliva, D.; Abd El Aziz, M.; Ella Hassanien, A. Parameter estimation of photovoltaic cells using an improved chaotic whale optimization algorithm. Appl. Energy 2017, 200, 141–154. [Google Scholar]
- 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. 2020, 225, 113474. [Google Scholar]
- Yang, X. Flower Pollination Algorithm for Global Optimization; Durand-Lose, J., Jonoska, N., Eds.; Springer: Berlin/Heidelberg, Germany, 2012; pp. 240–249. [Google Scholar]
- Krohling, R.A. Gaussian swarm: A novel particle swarm optimization algorithm. In Proceedings of the IEEE Conference on Cybernetics and Intelligent Systems, Singapore, 1–3 December 2004; Volume 1, pp. 372–376. [Google Scholar]
- Maulik, U.; Bandyopadhyay, S. Genetic algorithm-based clustering technique. Pattern Recognit. 2000, 33, 1455–1465. [Google Scholar] [CrossRef]
- May, R.M. Simple mathematical models with very complicated dynamics. Nature 1976, 261, 459–467. [Google Scholar] [CrossRef]
- Gandomi, A.H.; Yang, X. Evolutionary boundary constraint handling scheme. Neural Comput. Appl. 2012, 21, 1449–1462. [Google Scholar] [CrossRef]
- Li, Y.; Yu, K.; Liang, J.; Yue, C.; Qiao, K. A landscape-aware particle swarm optimization for parameter identification of photovoltaic models. Appl. Soft Comput. 2022, 131, 109793. [Google Scholar]
- Easwarakhanthan, T.; Bottin, J.; Bouhouch, I.; Boutrit, C. Nonlinear Minimization Algorithm for Determining the Solar Cell Parameters with Microcomputers. Int. J. Sol. Energy 1986, 4, 1–12. [Google Scholar] [CrossRef]
- Feng, Z.; Niu, W.; Liu, S. Cooperation search algorithm: A novel metaheuristic evolutionary intelligence algorithm for numerical optimization and engineering optimization problems. Appl. Soft Comput. 2021, 98, 106734. [Google Scholar]
- Faramarzi, A.; Heidarinejad, M.; Mirjalili, S.; Gandomi, A.H. Marine Predators Algorithm: A nature-inspired metaheuristic. Expert Syst. Appl. 2020, 152, 113377. [Google Scholar] [CrossRef]
- Su, H.; Zhao, D.; Heidari, A.A.; Liu, L.; Zhang, X.; Mafarja, M.; Chen, H. RIME: A physics-based optimization. Neurocomputing 2023, 532, 183–214. [Google Scholar]
- Civicioglu, P. Backtracking Search Optimization Algorithm for numerical optimization problems. Appl. Math. Comput. 2013, 219, 8121–8144. [Google Scholar] [CrossRef]
- Chen, X.; Yu, K.; Du, W.; Zhao, W.; Liu, G. Parameters identification of solar cell models using generalized oppositional teaching learning based optimization. Energy 2016, 99, 170–180. [Google Scholar]
- Zhang, J.; Sanderson, A.C. JADE: Adaptive Differential Evolution with Optional External Archive. IEEE Trans. Evol. Comput. 2009, 13, 945–958. [Google Scholar] [CrossRef]
- 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 2019, 237, 241–257. [Google Scholar]
- Feng, Z.; Liu, S.; Niu, W.; Li, B.; Wang, W.; Luo, B.; Miao, S. A modified sine cosine algorithm for accurate global optimization of numerical functions and multiple hydropower reservoirs operation. Knowl.-Based Syst. 2020, 208, 106461. [Google Scholar]
- Xu, S.; Wang, Y. Parameter estimation of photovoltaic modules using a hybrid flower pollination algorithm. Energy Convers. Manag. 2017, 144, 53–68. [Google Scholar]
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Liu, S.; Yang, Y.; Qin, H.; Liu, G.; Qu, Y.; Deng, S.; Gao, Y.; Li, J.; Guo, J. A Parameter Estimation of Photovoltaic Models Using a Boosting Flower Pollination Algorithm. Sensors 2023, 23, 8324. https://doi.org/10.3390/s23198324
Liu S, Yang Y, Qin H, Liu G, Qu Y, Deng S, Gao Y, Li J, Guo J. A Parameter Estimation of Photovoltaic Models Using a Boosting Flower Pollination Algorithm. Sensors. 2023; 23(19):8324. https://doi.org/10.3390/s23198324
Chicago/Turabian StyleLiu, Shuai, Yuqi Yang, Hui Qin, Guanjun Liu, Yuhua Qu, Shan Deng, Yuan Gao, Jiangqiao Li, and Jun Guo. 2023. "A Parameter Estimation of Photovoltaic Models Using a Boosting Flower Pollination Algorithm" Sensors 23, no. 19: 8324. https://doi.org/10.3390/s23198324
APA StyleLiu, S., Yang, Y., Qin, H., Liu, G., Qu, Y., Deng, S., Gao, Y., Li, J., & Guo, J. (2023). A Parameter Estimation of Photovoltaic Models Using a Boosting Flower Pollination Algorithm. Sensors, 23(19), 8324. https://doi.org/10.3390/s23198324