Direct MPP Calculation in Terms of the Single-Diode PV Model Parameters

In this paper, new expressions are introduced for the determination of the maximum power point (MPP) of photovoltaic (PV) systems as explicit functions of the five parameters of the single-diode model employing the Lambert W function. These equations provide the voltage and current at MPP in a direct and straightforward manner, thus dispensing with any need for iterative solution. They are initially derived for a PV system operating under uniform conditions, and subsequently extended for mismatched conditions at the PV string level. The novelty of these formulae lies in their solid theoretical foundation, which supports their validity in the general case and offers a well-founded symbolic formulation for the MPP evaluation problem. Extended simulations and experimental validation are performed to verify the accuracy and computational efficiency of the proposed equations compared with other methods available in the literature.

[1]  F.Z. Peng,et al.  Analytical Model for a Photovoltaic Module using the Electrical Characteristics provided by the Manufacturer Data Sheet , 2005, 2005 IEEE 36th Power Electronics Specialists Conference.

[2]  A. Das.  An explicit J–V model of a solar cell using equivalent rational function form for simple estimation of maximum power point voltage , 2013 .

[3]  Josie Close,et al.  Efficiency model for photovoltaic modules and demonstration of its application to energy yield estimation , 2007 .

[4]  K. Naito,et al.  Simulation of I–V characteristics of a PV module with shaded PV cells , 2003 .

[5]  Jin Jiang,et al.  Modeling, Prediction, and Experimental Validations of Power Peaks of PV Arrays Under Partial Shading Conditions , 2014, IEEE Transactions on Sustainable Energy.

[6]  William E. Boyson,et al.  Photovoltaic array performance model. , 2004 .

[7]  Avinashi Kapoor,et al.  An Exact Analytical Method for Calculating the Parameters of a Real Solar Cell Using Special Trans Function Theory (STFT) , 2013 .

[8]  A. Das.  Analytical derivation of explicit J–V model of a solar cell from physics based implicit model , 2012 .

[9]  V. Agarwal,et al.  MATLAB-Based Modeling to Study the Effects of Partial Shading on PV Array Characteristics , 2008, IEEE Transactions on Energy Conversion.

[10]  Shu-xian Lun,et al.  An explicit approximate I–V characteristic model of a solar cell based on padé approximants , 2013 .

[11]  H. H. Zeineldin,et al.  A Simple Approach to Modeling and Simulation of Photovoltaic Modules , 2012, IEEE Transactions on Sustainable Energy.

[12]  Gaston H. Gonnet,et al.  On the LambertW function , 1996, Adv. Comput. Math..

[13]  Mikhail Sorin,et al.  Explicit model of photovoltaic panels to determine voltages and currents at the maximum power point , 2011 .

[14]  S. Karmalkar,et al.  A Physically Based Explicit $J$ – $V$ Model of a Solar Cell for Simple Design Calculations , 2008, IEEE Electron Device Letters.

[15]  G. Kumar,et al.  Geometrical prediction of maximum power point for photovoltaics , 2014 .

[16]  J. M. Ruíz,et al.  Analysis and modelling the reverse characteristic of photovoltaic cells , 2006 .

[17]  J. W. Bishop.  Computer simulation of the effects of electrical mismatches in photovoltaic cell interconnection circuits , 1988 .

[18]  Robert M. Corless,et al.  A sequence of series for the Lambert W function , 1997, ISSAC.

[19]  N. H. Helwa,et al.  Estimation of the maximum power and normal operating power of a photovoltaic module by neural networks , 2004 .

[20]  S. L. Miller.  Ionization Rates for Holes and Electrons in Silicon , 1957 .

[21]  Felix A. Farret,et al.  Improved analytical solution to obtain the MPP of PV modules , 2013, IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society.

[22]  E. Karatepe,et al.  Development of a suitable model for characterizing photovoltaic arrays with shaded solar cells , 2007 .

[23]  Shu-xian Lun,et al.  A new explicit I–V model of a solar cell based on Taylor’s series expansion , 2013 .

[24]  Gehan A. J. Amaratunga,et al.  Analytic Solution to the Photovoltaic Maximum Power Point Problem , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[25]  S. Karmalkar,et al.  The power law J―V model of an illuminated solar cell , 2011 .

[26]  K. Woodbury,et al.  Optimization of a cooling system based on Peltier effect for photovoltaic cells , 2013 .

[27]  Seddik Bacha,et al.  Forecasting photovoltaic array power production subject to mismatch losses , 2010 .

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

[29]  D. Chan,et al.  Analytical methods for the extraction of solar-cell single- and double-diode model parameters from I-V characteristics , 1987, IEEE Transactions on Electron Devices.

[30]  Ioulia T. Papaioannou,et al.  Mathematical and graphical approach for maximum power point modelling , 2012 .

[31]  K. Ebihara,et al.  Estimation of equivalent circuit parameters of PV module and its application to optimal operation of PV system , 2001 .

[32]  Slobodan K. Simic,et al.  On the analytical solution of some families of transcendental equations , 2007, Appl. Math. Lett..

[33]  Marcello Artioli,et al.  Numerical method for the extraction of photovoltaic module double-diode model parameters through cluster analysis , 2010 .

[34]  Avinashi Kapoor,et al.  A New Method to Determine the Optimum Load of a Real Solar Cell Using Special Trans Function Theory (STFT) , 2013 .

[35]  William A. Beckman,et al.  Improvement and validation of a model for photovoltaic array performance , 2006 .

[36]  Ding Kun,et al.  A simplified model for photovoltaic modules based on improved translation equations , 2014 .

[37]  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.

[38]  A. Massi Pavan,et al.  Explicit empirical model for general photovoltaic devices: Experimental validation at maximum power point , 2014 .

[39]  A. Das.  An explicit J–V model of a solar cell for simple fill factor calculation , 2011 .

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

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

[42]  E. V. Paraskevadaki,et al.  Evaluation of MPP Voltage and Power of mc-Si PV Modules in Partial Shading Conditions , 2011, IEEE Transactions on Energy Conversion.

[43]  A model based on artificial neuronal network for the prediction of the maximum power of a low concentration photovoltaic module for building integration , 2014 .

[44]  S. M. Perovich,et al.  On the Exact Analytical Solutions of Certain Lambert Transcendental Equations , 2011 .

[45]  Wei Zhou,et al.  A novel model for photovoltaic array performance prediction , 2007 .

[46]  A. Sellami,et al.  Identification of PV solar cells and modules parameters using the genetic algorithms: Application to maximum power extraction , 2010 .

[47]  M. Vitelli,et al.  Analytical model of mismatched photovoltaic fields by means of Lambert W-function , 2007 .