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Least square estimator and IEC-60891 procedure for parameters estimation of single-diode model of photovoltaic generator at standard test conditions (STC)

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Abstract

Like some previous works, it is shown that (I–V) curve analysis can be applied to photovoltaic (PV) modules and to PV plants. Generally, manufacturers give data at standard test conditions (STC); therefore, for performance analysis and diagnosis of PV modules it is useful to extrapolate data and parameters at STC according to the International Electrotechnical Commission (IEC)-60891 procedures. Review on modeling PV generator is first established in this paper; next, the combination of the optimization method of least squares estimator algorithm and Newton–Raphson (NR) resolution for identifying the unknown parameters of single diode photovoltaic generators at STC is proposed; if parameters and curves are not obtained at STC, they are then extrapolated at STC according to IEC-60891 procedures. For polycrystalline silicon MSX60 PV generators, the dynamic variations of parameter values are carried out by graphs and the (I–V) curves are superposed, justifying the accuracy of the proposed method. The method is then extended to a 500 kW PV generator, the obtained parameters are then extrapolated to STC according to IEC-60891. The (I–V) and (P–V) curves obtained by extrapolated parameters are then compared with those measured. After up to 222 iterations, the parameters converge to constant values. Simulation shows maximum error value of 0.06 between experimental curve and estimated curves.

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Abbreviations

\( {\text{PV}} \) :

Photovoltaic

\( I \) :

Current

\( V \) :

Voltage

\( P \) :

Power

\( I^{\text{m/p}} \) :

\( I^{\text{m}} \) or \( I^{\text{p}} \)

\( I^{\text{m}} \) :

Current of PV module

\( I^{\text{p}} \) :

Current of PV array

\( I_{{{\text{ph}}_{\text{p}} }} = N_{\text{p}} I_{{{\text{ph}}_{\text{m}} }} \) :

Photo current of PV array or PV generator

\( I_{{{\text{ph}}_{\text{m}} }} = n_{\text{p}} I_{\text{ph}} \) :

Photo current of PV module

\( I_{\text{ph}} \) :

Photo current of PV module/array

\( I_{{{\text{o}}_{\text{m/p}} }} \) :

\( I_{{{\text{o}}_{\text{m}} }} \) or \( I_{{{\text{o}}_{\text{p}} }} \)

\( I_{\text{o}} \) :

Saturation current of PV cell

\( I_{{{\text{o}}_{\text{m}} }} = n_{\text{p}} I_{\text{o}} \) :

Saturation current of PV module

\( I_{{{\text{o}}_{\text{p}} }} = N_{\text{p}} I_{{{\text{o}}_{\text{m}} }} \) :

Saturation current of PV array or PV generator

\( V^{\text{m/p}} \) :

\( V^{\text{m}} \) or \( V^{\text{p}} \)

\( V^{\text{c}} \) :

Voltage of PV cell

\( V^{\text{m}} = n_{\text{s}} V^{\text{c}} \) :

Voltage of PV module

\( V^{\text{p}} = N_{\text{s}} V^{\text{m}} \) :

Voltage of PV array or PV generator

\( R_{{{\text{s}}_{\text{c/m/p}} }} \) :

\( R_{{{\text{s}}_{\text{c}} }} \) or \( R_{{{\text{s}}_{\text{m}} }} \) or \( R_{{{\text{s}}_{\text{p}} }} \)

\( R_{{{\text{s}}_{\text{c}} }} \) :

A series resistance of a PV cell

\( R_{{{\text{s}}_{\text{m}} }} = \frac{{n_{\text{s}} }}{{n_{\text{p}} }}R_{\text{s}} \) :

A series resistance of a PV module

\( R_{{{\text{s}}_{\text{p}} }} = \frac{{N_{\text{s}} }}{{N_{\text{p}} }}R_{{{\text{s}}_{\text{m}} }} \) :

A series resistance of a PV array or PV generator

\( R_{{{\text{p}}_{\text{c/m/p}} }} \) :

\( R_{{{\text{p}}_{\text{c}} }} \) or \( R_{{{\text{p}}_{\text{m}} }} \) or \( R_{{{\text{p}}_{\text{p}} }} \)

\( R_{{{\text{p}}_{\text{c}} }} \) :

The parallel resistance of a PV cell

\( R_{{{\text{p}}_{\text{m}} }} = \frac{{n_{\text{s}} }}{{n_{\text{p}} }}R_{{{\text{p}}_{\text{c}} }} \) :

The parallel resistance of a PV module

\( R_{{{\text{P}}_{\text{p}} }} = \frac{{N_{\text{s}} }}{{N_{\text{p}} }}R_{{{\text{p}}_{\text{m}} }} \) :

The parallel resistance of a PV array or PV generator

\( V_{{{\text{T}}_{\text{p}} }} = N_{\text{s}} V_{{{\text{T}}_{\text{m}} }} \) :

Thermal voltage of a photovoltaic array

\( n_{\text{s}} \) :

Number of series cells placed in string

\( n_{\text{p}} \) :

Number of parallel strings of cells

\( N_{\text{s}} \) :

Number of series modules placed in string

\( N_{\text{p}} \) :

Number of parallel strings of module

\( V_{{{\text{T}}_{\text{c/m/p}} }} \) :

\( V_{{{\text{T}}_{\text{c}} }} \) or \( V_{{{\text{T}}_{\text{m}} }} \) or \( V_{{{\text{T}}_{\text{p}} }} \)

\( V_{{{\text{T}}_{\text{c}} }} = \frac{{k_{\text{B}} T_{\theta }^{\text{c}} }}{q} \) :

Thermal voltage of a photovoltaic cell

\( V_{{{\text{T}}_{\text{m}} }} = n_{\text{s}} \frac{{k_{\text{B}} T_{\theta }^{\text{c}} }}{q} \) :

Thermal voltage of a photovoltaic module

\( V_{{{\text{T}}_{\text{p}} }} = N_{\text{s}} V_{{{\text{T}}_{\text{m}} }} \) :

Thermal voltage of a photovoltaic array

\( n \) :

The diode ideality factor for a p–n junction in a cell

\( q \) :

The electron charge (\( 1.602 \times 10^{ - 19} \,{\text{C}} \))

\( k_{\text{B}} \) :

Boltzmann constant (\( 1.38 \times 10^{ - 23} \,{\text{J/K}} \))

\( T_{{_{\theta } }}^{\text{c}} \) :

The absolute temperature of the cell

\( I_{\text{mp}} \) :

Maximum current

\( V_{\text{mp}} \) :

Maximum voltage

\( P_{\hbox{max} ,e} \) :

Experimental maximum power

\( I_{\text{sc}} \) :

Short circuit current

\( V_{\text{oc}} \) :

Open circuit voltage

\( \alpha_{\text{v}} \) :

Temperature coefficient of voltage

\( \alpha_{\text{I}} \) :

Temperature coefficient of current

\( x_{\text{opt}} \) :

Optimal solution

\( \beta \left( {\Omega /^{ \circ } {\text{C}}} \right) \) :

Correction factor

STC:

Standard test conditions

NOCT:

Nominal condition test

A.M:

Air mass

LS:

Least square

IEC:

International Electrotechnical Commission

G m :

Measured irradiance

G ref :

Irradiance at reference point

References

  1. McHenry MP (2012) Are small-scale grid-connected photovoltaic systems a cost-effective policy for lowering electricity bills and reducing carbon emissions? Energy Policy 45:64–72

    Article  Google Scholar 

  2. Tivanov M, Patryn A, Drozdov N, Fedotov A, Mazanik A (2005) Determination of solar cell parameters from its current–voltage and spectral characteristics. Sol Energy Mater Sol Cells 87(1):457–465

    Article  Google Scholar 

  3. Macabebe EQ, Van Dyk EE (2008) Parameter extraction from dark current-voltage characteristics of solar cells. S Afr J Sci 104(9–10):401–404

    Google Scholar 

  4. Ayodele T, Ogunjuyigbe A, Ekoh E (2016) Evaluation of numerical algorithms used in extracting the parameters of a single-diode photovoltaic model. Sustain Energy Technol Assess 13:51–59

    Google Scholar 

  5. Bencherif M, Chermitti A (2012) New method to assess the loss parameters of the photovoltaic modules. J Renew Sustain Energy 4(6):063115

    Article  Google Scholar 

  6. Gow J, Manning C (1999) Development of a photovoltaic array model for use in power-electronics simulation studies. IEE Proc Electr Power Appl 146(2):193–200

    Article  Google Scholar 

  7. Di Piazza MC, Vitale G (2012) Photovoltaic sources: modeling and emulation. Springer, Berlin

    Google Scholar 

  8. Gottschalg R, Rommel M, Infield D, Kearney M (1999) The influence of the measurement environment on the accuracy of the extraction of the physical parameters of solar cells. Meas Sci Technol 10(9):796

    Article  Google Scholar 

  9. Aubry V, Meyer F (1994) Schottky diodes with high series resistance: limitations of forward I–V methods. J Appl Phys 76(12):7973–7984

    Article  Google Scholar 

  10. De Soto W, Klein S, Beckman W (2006) Improvement and validation of a model for photovoltaic array performance. Sol Energy 80(1):78–88

    Article  Google Scholar 

  11. Boyd MT, Klein SA, Reindl DT, Dougherty BP (2011) Evaluation and validation of equivalent circuit photovoltaic solar cell performance models. J Sol Energy Eng 133(2):021005

    Article  Google Scholar 

  12. Jain A, Kapoor A (2004) Exact analytical solutions of the parameters of real solar cells using Lambert W-function. Sol Energy Mater Sol Cells 81(2):269–277

    Article  Google Scholar 

  13. Jain A, Sharma S, Kapoor A (2006) Solar cell array parameters using Lambert W-function. Sol Energy Mater Sol Cells 90(1):25–31

    Article  Google Scholar 

  14. Jain A, Kapoor A (2005) A new approach to study organic solar cell using Lambert W-function. Sol Energy Mater Sol Cells 86(2):197–205

    Article  Google Scholar 

  15. Wolf P, Benda V (2013) Identification of PV solar cells and modules parameters by combining statistical and analytical methods. Sol Energy 93:151–157

    Article  Google Scholar 

  16. Villalva MG, Gazoli JR, Ruppert Filho E (2009) Comprehensive approach to modeling and simulation of photovoltaic arrays. IEEE Trans Power Electron 24(5):1198–1208

    Article  Google Scholar 

  17. Townsend TU (1989) The long-term performance of direct-coupled photovoltaic systems. University of Wisconsin-Madison, Madison

    Google Scholar 

  18. Carrero C, Ramírez D, Rodríguez J, Platero C (2011) Accurate and fast convergence method for parameter estimation of PV generators based on three main points of the I–V curve. Renew Energy 36(11):2972–2977

    Article  Google Scholar 

  19. Karatepe E, Boztepe M, Çolak M (2003) Estimation of equivalent circuit parameters of PV module using neural network. In: IJCI proceedings of international XII. Turkish symposium on artificial intelligence and neural networks, vol 1, no 1

  20. Siddiqui M (2011) Multiphysics modeling of photovoltaic panels and arrays with auxiliary thermal collectors. King Fahd University of Petroleum and Minerals, Dhahran

    Google Scholar 

  21. Zagrouba M, Sellami A, Bouaïcha M, Ksouri M (2010) Identification of PV solar cells and modules parameters using the genetic algorithms: application to maximum power extraction. Sol Energy 84(5):860–866

    Article  Google Scholar 

  22. Jervase JA, Bourdoucen H, Al-Lawati A (2001) Solar cell parameter extraction using genetic algorithms. Meas Sci Technol 12(11):1922

    Article  Google Scholar 

  23. Ye M, Wang X, Xu Y (2009) Parameter extraction of solar cells using particle swarm optimization. J Appl Phys 105(9):094502

    Article  Google Scholar 

  24. Soon JJ, Low K-S (2012) Photovoltaic model identification using particle swarm optimization with inverse barrier constraint. IEEE Trans Power Electron 27(9):3975–3983

    Article  Google Scholar 

  25. AlHajri M, El-Naggar K, AlRashidi M, Al-Othman A (2012) Optimal extraction of solar cell parameters using pattern search. Renew Energy 44:238–245

    Article  Google Scholar 

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

    Article  Google Scholar 

  27. Askarzadeh A, Rezazadeh A (2013) Artificial bee swarm optimization algorithm for parameters identification of solar cell models. Appl Energy 102:943–949

    Article  Google Scholar 

  28. Askarzadeh A, Rezazadeh A (2012) Parameter identification for solar cell models using harmony search-based algorithms. Sol Energy 86(11):3241–3249

    Article  Google Scholar 

  29. Azab M (2015) Identification of one-diode model parameters of PV devices from nameplate information using particle swarm and least square methods. In: 2015 First workshop on smart grid and renewable energy (SGRE). IEEE, pp 1–6

  30. Nayak B, Mohapatra A, Mohanty K (2013) Parameters estimation of photovoltaic module using nonlinear least square algorithm: a comparative study. In: 2013 Annual IEEE India conference (INDICON). IEEE, pp 1–6

  31. Mohapatra A, Nayak B, Mohanty K (2013) Comparative study on single diode photovoltaic module parameter extraction methods. In: 2013 International conference on power, energy and control (ICPEC). IEEE, pp 30–34

  32. Ayang A et al (2019) Maximum likelihood parameters estimation of single-diode model of photovoltaic generator. Renew Energy 130:111–121

    Article  Google Scholar 

  33. Ayang A, Wamkeue R, Ouhrouche M, Essiane Salomé N, Djongyang N (2018) Parameters estimation of single-diode photovoltaic module/array using least square estimator: a comparative study

  34. Brano VL, Orioli A, Ciulla G, Di Gangi A (2010) An improved five-parameter model for photovoltaic modules. Sol Energy Mater Sol Cells 94(8):1358–1370

    Article  Google Scholar 

  35. Ishaque K, Salam Z, Taheri H (2011) Simple, fast and accurate two-diode model for photovoltaic modules. Sol Energy Mater Sol Cells 95(2):586–594

    Article  Google Scholar 

  36. Carrero C, Amador J, Arnaltes S (2007) A single procedure for helping PV designers to select silicon PV modules and evaluate the loss resistances. Renew Energy 32(15):2579–2589

    Article  Google Scholar 

  37. Koutroulis E, Kalaitzakis K, Tzitzilonis V (2009) Development of an FPGA-based system for real-time simulation of photovoltaic modules. Microelectron J 40(7):1094–1102

    Article  Google Scholar 

  38. Yi-Bo W, Chun-Sheng W, Hua L, Hong-Hua X (2008) Steady-state model and power flow analysis of grid-connected photovoltaic power system. In: IEEE international conference on industrial technology, 2008. ICIT 2008. IEEE, pp1–6

  39. Hansen AD, Sørensen PE, Hansen LH, Bindner HW (2001) Models for a stand-alone PV system

  40. Chi H (2015) A discussions on the least-square method in the course of error theory and data processing. In: 2015 International conference on computational intelligence and communication networks (CICN), 2015. IEEE, pp 486–489

  41. Coleman T, Branch MA, Grace A, (1999) Optimization toolbox. For use with MATLAB. User’s guide for MATLAB 5, Version 2, Relaese II

  42. Devices P (2010) Procedures for temperature and irradiance corrections to measured IV characteristics. IEC

  43. Hansen CW, King BH (2018) Determining series resistance for equivalent circuit models of a PV module. IEEE J Photovolt 9(2):538–543

    Article  Google Scholar 

  44. Trentadue G, Pavanello D, Salis E, Field M, Müllejans H (2016) Determination of internal series resistance of PV devices: repeatability and uncertainty. Meas Sci Technol 27(5):055005

    Article  Google Scholar 

  45. I. E. Commission (2006) Photovoltaic devices-part 1: measurement of photovoltaic current–voltage characteristics. IEC 60904-1

  46. Moretón R, Lorenzo E, Muñoz J (2014) A 500-kW PV generator I–V curve. Prog Photovolt Res Appl 22(12):1280–1284

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Sciences, University of Québec in Chicoutimi, 555 Boulevard de l’Université, Chicoutimi, QC, G7H 2B1, Canada

    Albert Ayang, René Wamkeue, Mohand Ouhrouche, Tommy Andy Tameghe & Pierre Tchakoua Takoutsing

  2. School of Engineering, University of Québec in Abitibi-Témiscamingue (UQAT), 445 Boulevard de l’Université, Rouyn-Noranda, QC, J9X 5E4, Canada

    Albert Ayang, René Wamkeue, Mohamad Saad, Tommy Andy Tameghe & Pierre Tchakoua Takoutsing

  3. National Advanced Polytechnic School, Department of Renewable Energy, University of Maroua, P.O. Box 46, Maroua, Cameroon

    Albert Ayang & Kodji Deli

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Contributions

AA is the main author of this work. This paper further elaborates on some of the results from his Ph.D. dissertation. RW, MO and MS supervised and supported AA scientific and technical expertise research. TAT, PTT, KD assisted in the results analysis and interpretations.

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Correspondence to Albert Ayang.

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Ayang, A., Wamkeue, R., Ouhrouche, M. et al. Least square estimator and IEC-60891 procedure for parameters estimation of single-diode model of photovoltaic generator at standard test conditions (STC). Electr Eng 103, 1253–1264 (2021). https://doi.org/10.1007/s00202-020-01131-2

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