Lambert W-function based exact representation for double diode model of solar cells: Comparison on fitness and parameter extraction

Abstract Accurate modeling and parameter extraction of solar cells play an important role in the simulation and optimization of PV systems. This paper presents a Lambert W -function based exact representation (LBER) for traditional double diode model (DDM) of solar cells, and then compares their fitness and parameter extraction performance. Unlike existing works, the proposed LBER is rigorously derived from DDM, and in LBER the coefficients of Lambert W -function are not extra parameters to be extracted or arbitrary scalars but the vectors of terminal voltage and current of solar cells. The fitness difference between LBER and DDM is objectively validated by the reported parameter values and experimental I – V data of a solar cell and four solar modules from different technologies. The comparison results indicate that under the same parameter values, the proposed LBER can better represent the I – V and P – V characteristics of solar cells and provide a closer representation to actual maximum power points of all module types. Two different algorithms are used to compare the parameter extraction performance of LBER and DDM. One is our restart-based bound constrained Nelder-Mead (rbcNM) algorithm implemented in Matlab, and the other is the reported R cr -IJADE algorithm executed in Visual Studio. The comparison results reveal that, the parameter values extracted from LBER using two algorithms are always more accurate and robust than those from DDM despite more time consuming. As an improved version of DDM, the proposed LBER is quite promising for PV simulation and thus deserves serious attention.

[1]  Li Zeng,et al.  Universal analytical solution to the optimum load of the solar cell , 2015 .

[2]  Efstratios I. Batzelis,et al.  Direct MPP Calculation in Terms of the Single-Diode PV Model Parameters , 2015, IEEE Transactions on Energy Conversion.

[3]  Xiangning Xiao,et al.  A modeling method for photovoltaic cells using explicit equations and optimization algorithm , 2014 .

[4]  Hassan Fathabadi,et al.  Two novel techniques for increasing energy efficiency of photovoltaic-battery systems , 2015 .

[5]  M. Wolf,et al.  Investigation of the double exponential in the current—Voltage characteristics of silicon solar cells , 1977, IEEE Transactions on Electron Devices.

[6]  Alireza Rezazadeh,et al.  Parameter identification for solar cell models using harmony search-based algorithms , 2012 .

[7]  Yuqing He,et al.  Parameter extraction of solar cell models using mutative-scale parallel chaos optimization algorithm , 2014 .

[8]  Marcelo Gradella Villalva,et al.  Comprehensive Approach to Modeling and Simulation of Photovoltaic Arrays , 2009, IEEE Transactions on Power Electronics.

[9]  M. F. AlHajri,et al.  Optimal extraction of solar cell parameters using pattern search , 2012 .

[10]  Alon Kuperman,et al.  An improved approach to extract the single-diode equivalent circuit parameters of a photovoltaic cell/panel , 2014 .

[11]  Wenyin Gong,et al.  Parameter extraction of solar cell models using repaired adaptive differential evolution , 2013 .

[12]  Wenxiang Zhao,et al.  Parameters identification of solar cell models using generalized oppositional teaching learning based optimization , 2016 .

[13]  Mohamed A. Awadallah,et al.  Variations of the bacterial foraging algorithm for the extraction of PV module parameters from nameplate data , 2016 .

[14]  Y. Errami,et al.  Parameter estimation of photovoltaic modules using iterative method and the Lambert W function: A comparative study , 2016 .

[15]  Youssef Errami,et al.  Validation of a multi-exponential alternative model of solar cell and comparison to conventional double exponential model , 2015, 2015 27th International Conference on Microelectronics (ICM).

[16]  Saad Mekhilef,et al.  Solar cell parameters extraction based on single and double-diode models: A review , 2016 .

[17]  Lixing Han,et al.  Implementing the Nelder-Mead simplex algorithm with adaptive parameters , 2010, Computational Optimization and Applications.

[18]  Jin-lei Ding,et al.  A new method to determine the optimum load of a real solar cell using the Lambert W-function , 2008 .

[19]  Zhuo Meng,et al.  An improved model and parameters extraction for photovoltaic cells using only three state points at standard test condition , 2014 .

[20]  T. Easwarakhanthan,et al.  Nonlinear Minimization Algorithm for Determining the Solar Cell Parameters with Microcomputers , 1986 .

[21]  Kashif Ishaque,et al.  Cell modelling and model parameters estimation techniques for photovoltaic simulator application: A review , 2015 .

[22]  Dalia Yousri,et al.  Flower Pollination Algorithm based solar PV parameter estimation , 2015 .

[23]  A. K. Al-Othman,et al.  Simulated Annealing algorithm for photovoltaic parameters identification , 2012 .

[24]  Z. Salam,et al.  An accurate modelling of the two-diode model of PV module using a hybrid solution based on differential evolution , 2016 .

[25]  Adelmo Ortiz-Conde,et al.  An Explicit Multiexponential Model as an Alternative to Traditional Solar Cell Models With Series and Shunt Resistances , 2012, IEEE Journal of Photovoltaics.

[26]  Toshio Fukushima,et al.  Precise and fast computation of Lambert W-functions without transcendental function evaluations , 2013, J. Comput. Appl. Math..

[27]  Dhiaa Halboot Muhsen,et al.  Parameters extraction of double diode photovoltaic module’s model based on hybrid evolutionary algorithm , 2015 .

[28]  Lei Guo,et al.  Parameter identification and sensitivity analysis of solar cell models with cat swarm optimization algorithm , 2016 .

[29]  Ying Zhang,et al.  A comparative study of the maximum power point tracking methods for PV systems , 2014 .

[30]  Shuxian Lun,et al.  A new explicit double-diode modeling method based on Lambert W-function for photovoltaic arrays , 2015 .

[31]  Saad Mekhilef,et al.  Parameter extraction of solar photovoltaic modules using penalty-based differential evolution , 2012 .

[32]  Efstratios I. Batzelis,et al.  An Explicit PV String Model Based on the Lambert $W$ Function and Simplified MPP Expressions for Operation Under Partial Shading , 2014, IEEE Transactions on Sustainable Energy.

[33]  M. Vitelli,et al.  Power Electronics and Control Techniques for Maximum Energy Harvesting in Photovoltaic Systems , 2012 .

[34]  Hassan Fathabadi,et al.  Lambert W function-based technique for tracking the maximum power point of PV modules connected in various configurations , 2015 .

[35]  D. Carroll,et al.  Evaluation of methods to extract parameters from current–voltage characteristics of solar cells , 2013 .

[36]  Yuqing He,et al.  Parameter extraction of solar cell models using chaotic asexual reproduction optimization , 2014, Neural Computing and Applications.

[37]  Lele Peng,et al.  A new method for determining the characteristics of solar cells , 2013 .

[38]  M. Moallem,et al.  Maximum power point tracking using boost converter input resistance control by means of Lambert W-Function , 2012, 2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG).

[39]  Gonzalo Pajares,et al.  Parameter identification of solar cells using artificial bee colony optimization , 2014 .

[40]  Teuku Meurah Indra Mahlia,et al.  Characterization of PV panel and global optimization of its model parameters using genetic algorithm , 2013 .

[41]  Dalia Yousri,et al.  Parameters extraction of the three diode model for the multi-crystalline solar cell/module using Moth-Flame Optimization Algorithm , 2016 .

[42]  Yue Hao,et al.  A simple and efficient solar cell parameter extraction method from a single current-voltage curve , 2011 .

[43]  Javier Cubas,et al.  Explicit Expressions for Solar Panel Equivalent Circuit Parameters Based on Analytical Formulation and the Lambert W-Function , 2014 .

[44]  W. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[45]  Kang Li,et al.  An improved TLBO with elite strategy for parameters identification of PEM fuel cell and solar cell models , 2014 .

[46]  N. Rajasekar,et al.  Solar PV Modelling and Parameter Extraction Using Artificial Immune System , 2015 .

[47]  A. Kapoor,et al.  Exact analytical solutions of the parameters of real solar cells using Lambert W-function , 2004 .

[48]  Mike Duke,et al.  The numerical calculation of single-diode solar-cell modelling parameters , 2014 .

[49]  Arno Krenzinger,et al.  Method for photovoltaic parameter extraction according to a modified double-diode model , 2013 .

[50]  Q. Niu,et al.  A biogeography-based optimization algorithm with mutation strategies for model parameter estimation of solar and fuel cells , 2014 .

[51]  Filippo Attivissimo,et al.  On the performance of the double-diode model in estimating the maximum power point for different photovoltaic technologies , 2013 .

[52]  A. Ortiz-Conde,et al.  New method to extract the model parameters of solar cells from the explicit analytic solutions of their illuminated I–V characteristics , 2006 .

[53]  Giuseppe Marco Tina,et al.  Comparison of different metaheuristic algorithms for parameter identification of photovoltaic cell/module , 2013 .

[54]  Darko Veberic,et al.  Lambert W Function for Applications in Physics , 2012, Comput. Phys. Commun..

[55]  S. L. Shimi,et al.  Modeling of solar PV module and maximum power point tracking using ANFIS , 2014 .

[56]  Alireza Rezazadeh,et al.  Artificial bee swarm optimization algorithm for parameters identification of solar cell models , 2013 .

[57]  R. Boukenoui,et al.  A new Golden Section method-based maximum power point tracking algorithm for photovoltaic systems , 2016 .

[58]  Kashif Ishaque,et al.  A review of maximum power point tracking techniques of PV system for uniform insolation and partial shading condition , 2013 .

[59]  Alireza Rezazadeh,et al.  Extraction of maximum power point in solar cells using bird mating optimizer-based parameters identification approach , 2013 .

[60]  Yifeng Chen,et al.  Parameters extraction from commercial solar cells I-V characteristics and shunt analysis , 2011 .

[61]  Hassan Fathabadi,et al.  Novel neural-analytical method for determining silicon/plastic solar cells and modules characteristics , 2013 .