Abstract

The mathematical modeling of solar cells and panels is critical in many photovoltaic applications. However, the standard single-diode solar cell model, commonly selected to model these devices, is implicit and difficult to integrate into simulation software. Therefore, exact explicit solutions of this model, more suitable for computing purposes, have been proposed based on the Lambert W-function. This work introduces an explicit single-diode, easy-to-use six-parameter solar cell model. The proposed model is formulated with elementary functions. The model is developed and tested over seven photovoltaic technologies as an alternative to traditional approaches. Results of the extensive comparison of the three models (implicit, explicit Lambert W, and explicit six-parameter) show that the proposed approach is more accurate (14.81% relative improvement on average compared to the traditional methods), almost as fast as the Lambert W approach and much faster than the implicit approach. Due to its simplicity and accuracy, the proposed model will become an alternative in photovoltaic applications such as energy prediction and maximum power point tracking.

References

1.
Khatibi
,
A.
,
Razi Astaraei
,
F.
, and
Ahmadi
,
M. H.
,
2019
, “
Generation and Combination of the Solar Cells: A Current Model Review
,”
Energy Sci. Eng.
,
7
(
2
), pp.
305
322
.
2.
Adeel
,
M.
,
Hassan
,
A. K.
,
Sher
,
H. A.
, and
Murtaza
,
A. F.
,
2021
, “
A Grade Point Average Assessment of Analytical and Numerical Methods for Parameter Extraction of a Practical PV Device
,”
Renew. Sustainable Energy Rev.
,
142
, p.
110826
.
3.
Hara
,
S.
,
2021
, “
Parameter Extraction of Single-Diode Model From Module Datasheet Information Using Temperature Coefficients
,”
IEEE J. Photovolt.
,
11
(
1
), pp.
213
218
.
4.
Ndi
,
F. E.
,
Perabi
,
S. N.
,
Ndjakomo
,
S. E.
,
Ondoua Abessolo
,
G.
, and
Mengounou Mengata
,
G.
,
2021
, “
Estimation of Single-Diode and Two Diode Solar Cell Parameters by Equilibrium Optimizer Method
,”
Energy Rep.
,
7
, pp.
4761
4768
.
5.
Ridha
,
H. M.
,
Hizam
,
H.
,
Mirjalili
,
S.
,
Othman
,
M. L.
,
Ya’acob
,
M. E.
, and
Ahmadipour
,
M.
,
2022
, “
Parameter Extraction of Single, Double, and Three Diodes Photovoltaic Model Based on Guaranteed Convergence Arithmetic Optimization Algorithm and Modified Third Order Newton Raphson Methods
,”
Renew. Sustainable Energy Rev.
,
162
, p.
112436
.
6.
Yahya-Khotbehsara
,
A.
, and
Shahhoseini
,
A.
,
2018
, “
A Fast Modeling of the Double-Diode Model for PV Modules Using Combined Analytical and Numerical Approach
,”
Sol. Energy
,
162
, pp.
403
409
.
7.
Li
,
C.
,
Yang
,
Y.
,
Spataru
,
S.
,
Zhang
,
K.
, and
Wei
,
H.
,
2021
, “
A Robust Parametrization Method of Photovoltaic Modules for Enhancing One-Diode Model Accuracy Under Varying Operating Conditions
,”
Renew. Energy
,
168
, pp.
764
778
.
8.
Li
,
S.
,
Gong
,
W.
, and
Gu
,
Q.
,
2021
, “
A Comprehensive Survey on Meta-Heuristic Algorithms for Parameter Extraction of Photovoltaic Models
,”
Renew. Sustainable Energy Rev.
,
141
, p.
110828
.
9.
Venkateswari
,
R.
, and
Rajasekar
,
N.
,
2021
, “
Review on Parameter Estimation Techniques of Solar Photovoltaic Systems
,”
Int. Trans. Electr. Energy Syst.
,
31
(
11
), p.
e13113
.
10.
Lambert
,
J. H.
,
1758
, “
Observationes Variae in Mathesin Puram
,”
Acta Helvetica
,
3
(
1
), pp.
128
168
.
11.
Gao
,
X.
,
Cui
,
Y.
,
Hu
,
J.
,
Tahir
,
N.
, and
Xu
,
G.
,
2018
, “
Performance Comparison of Exponential, Lambert W Function and Special Trans Function Based Single Diode Solar Cell Models
,”
Energy Convers. Manage.
,
171
, pp.
1822
1842
.
12.
de Castro
,
F.
,
Laudani
,
A.
,
Riganti Fulginei
,
F.
, and
Salvini
,
A.
,
2016
, “
An In-Depth Analysis of the Modelling of Organic Solar Cells Using Multiple-Diode Circuits
,”
Sol. Energy
,
135
, pp.
590
597
.
13.
Voswinckel
,
S.
,
Wesselak
,
V.
, and
Lustermann
,
B.
,
2013
, “
Behaviour of Amorphous Silicon Solar Modules: A Parameter Study
,”
Sol. Energy
,
92
, pp.
206
213
.
14.
Akbaba
,
M.
, and
Alattawi
,
M. A. A.
,
1995
, “
A New Model for I–V Characteristic of Solar Cell Generators and its Applications
,”
Sol. Energy Mater. Sol. Cells
,
37
(
2
), pp.
123
132
.
15.
Das
,
A. K.
,
2013
, “
An Explicit J–V Model of a Solar Cell Using Equivalent Rational Function Form for Simple Estimation of Maximum Power Point Voltage
,”
Sol. Energy
,
98
, pp.
400
403
.
16.
Lun
,
S.
,
Du
,
C.
,
Guo
,
T.
,
Wang
,
S.
,
Sang
,
J.
, and
Li
,
J.
,
2013
, “
A New Explicit I–V Model of a Solar Cell Based on Taylor’s Series Expansion
,”
Sol. Energy
,
94
, pp.
221
232
.
17.
Lun
,
S.
,
Du
,
C.
,
Sang
,
J.
,
Guo
,
T.
,
Wang
,
S.
, and
Yang
,
G.
,
2014
, “
An Improved Explicit I–V Model of a Solar Cell Based on Symbolic Function and Manufacturer’s Datasheet
,”
Sol. Energy
,
110
, pp.
603
614
.
18.
Lun
,
S.
,
Du
,
C.
,
Yang
,
G.
,
Wang
,
S.
,
Guo
,
T.
,
Sang
,
J.
, and
Li
,
J.
,
2013
, “
An Explicit Approximate I–V Characteristic Model of a Solar Cell Based on Padé Approximants
,”
Sol. Energy
,
92
, pp.
147
159
.
19.
Lun
,
S.
,
Du
,
C.
, and
Xu
,
C.
,
2016
, “
An Explicit I—V Model of Solar Cells Based on Padé Approximants
,”
Proceedings of the 2016 Chinese Control and Decision Conference (CCDC)
,
Yinchuan, China
,
May 28–30
, pp.
6169
6172
..
20.
Jordehi
,
A. R.
,
2016
, “
Parameter Estimation of Solar Photovoltaic (PV) Cells: A Review
,”
Renew. Sustainable Energy Rev.
,
61
, pp.
354
371
.
21.
Phang
,
J. C. H.
,
Chan
,
D. S. H.
, and
Phillips
,
J. R.
,
1984
, “
Accurate Analytical Method for the Extraction of Solar Cell Model Parameters
,”
Electron Lett
,
20
(
10
), pp.
406
408
.
22.
Saloux
,
E.
,
Teyssedou
,
A.
, and
Sorin
,
M.
,
2011
, “
Explicit Model of Photovoltaic Panels to Determine Voltages and Currents at the Maximum Power Point
,”
Sol. Energy
,
85
(
5
), pp.
713
722
.
23.
Aldwane
,
B.
,
2014
, “
Modeling, Simulation and Parameters Estimation for Photovoltaic Module
,”
Proceedings of the 2014 First International Conference on Green Energy ICGE 2014
,
Sfax, Tunisia
,
Mar. 25–27
, pp.
101
106
.
24.
Bai
,
J.
,
Liu
,
S.
,
Hao
,
Y.
,
Zhang
,
Z.
,
Jiang
,
M.
, and
Zhang
,
Y.
,
2014
, “
Development of a New Compound Method to Extract the Five Parameters of PV Modules
,”
Energy Convers. Manage.
,
79
, pp.
294
303
.
25.
Cubas
,
J.
,
Pindado
,
S.
, and
Victoria
,
M.
,
2014
, “
On the Analytical Approach for Modeling Photovoltaic Systems Behavior
,”
J. Power Sources
,
247
, pp.
467
474
.
26.
Batzelis
,
E. I.
, and
Papathanassiou
,
S. A.
,
2016
, “
A Method for the Analytical Extraction of the Single-Diode PV Model Parameters
,”
IEEE Trans. Sustain. Energy
,
7
(
2
), pp.
504
512
.
27.
Schumacher
,
J.
,
2023
, “INSEL”. https://www.insel.eu/en/home_en.html. Accessed August 17, 2023.
28.
Easwarakhanthan
,
T.
,
Bottin
,
J.
,
Bouhouch
,
I.
, and
Boutrit
,
C.
,
1986
, “
Nonlinear Minimization Algorithm for Determining the Solar Cell Parameters With Microcomputers
,”
Int. J. Sol. Energy
,
4
(
1
), pp.
1
12
.
29.
Elbaset
,
A. A.
,
Ali
,
H.
, and
Abd-El Sattar
,
M.
,
2014
, “
Novel Seven-Parameter Model for Photovoltaic Modules
,”
Sol. Energy Mater. Sol. Cells
,
130
, pp.
442
455
.
30.
Tchakpedeou
,
A.-B.
,
Lare
,
Y.
,
Napo
,
K.
, and
Fousseni
,
A.
,
2022
, “
An Improved Levenberg–Marquardt Approach With a New Reduced Form for the Identification of Parameters of the One-Diode Photovoltaic Model
,”
ASME J. Sol. Energy Eng
,
144
(
4
), p.
041005
.
31.
Kalliojärvi-Viljakainen
,
H.
,
Lappalainen
,
K.
, and
Valkealahti
,
S.
,
2022
, “
A Novel Procedure for Identifying the Parameters of the Single-Diode Model and the Operating Conditions of a Photovoltaic Module From Measured Current–Voltage Curves
,”
Energy Rep.
,
8
, pp.
4633
4640
.
32.
Chegaar
,
M.
,
Ouennoughi
,
Z.
, and
Hoffmann
,
A.
,
2001
, “
A New Method for Evaluating Illuminated Solar Cell Parameters
,”
Solid State Electron.
,
45
(
2
), pp.
293
296
.
33.
Ishaque
,
K.
,
Salam
,
Z.
,
Mekhilef
,
S.
, and
Shamsudin
,
A.
,
2012
, “
Parameter Extraction of Solar Photovoltaic Modules Using Penalty-Based Differential Evolution
,”
Appl. Energy
,
99
, pp.
297
308
.
34.
Dizqah
,
A. M.
,
Maheri
,
A.
, and
Busawon
,
K.
,
2014
, “
An Accurate Method for the PV Model Identification Based on a Genetic Algorithm and the Interior-Point Method
,”
Renew. Energy
,
72
, pp.
212
222
.
35.
Abdalla
,
O.
,
Rezk
,
H.
, and
Ahmed
,
E. M.
,
2019
, “
Wind Driven Optimization Algorithm Based Global MPPT for PV System Under Non-Uniform Solar Irradiance
,”
Sol. Energy
,
180
, pp.
429
444
.
36.
Alam
,
D. F.
,
Yousri
,
D. A.
, and
Eteiba
,
M. B.
,
2015
, “
Flower Pollination Algorithm Based Solar PV Parameter Estimation
,”
Energy Convers Manag
,
101
, pp.
410
422
.
37.
Kler
,
D.
,
Sharma
,
P.
,
Banerjee
,
A.
,
Rana
,
K. P. S.
, and
Kumar
,
V.
,
2017
, “
PV Cell and Module Efficient Parameters Estimation Using Evaporation Rate Based Water Cycle Algorithm
,”
Swarm Evol. Comput.
,
35
, pp.
93
110
.
38.
El-Naggar
,
K. M.
,
AlRashidi
,
M. R.
,
AlHajri
,
M. F.
, and
Al-Othman
,
A. K.
,
2012
, “
Simulated Annealing Algorithm for Photovoltaic Parameters Identification
,”
Sol. Energy
,
86
(
1
), pp.
266
274
.
39.
Sirjani
,
R.
, and
Shareef
,
H.
,
2016
, “
Parameter Extraction of Solar Cell Models Using the Lightning Search Algorithm in Different Weather Conditions
,”
ASME J. Sol. Energy Eng.
,
138
(
4
), p.
041007
.
40.
Beigi
,
A. M.
, and
Maroosi
,
A.
,
2018
, “
Parameter Identification for Solar Cells and Module Using a Hybrid Firefly and Pattern Search Algorithms
,”
Sol. Energy
,
171
, pp.
435
446
.
41.
Jacob
,
B.
,
Balasubramanian
,
K.
,
Babu
T, S.
,
Azharuddin
,
S. M.
, and
Rajasekar
,
N.
,
2015
, “
Solar PV Modelling and Parameter Extraction Using Artificial Immune System
,”
Energy Proc.
,
75
, pp.
331
336
.
42.
Fathy
,
A.
, and
Rezk
,
H.
,
2017
, “
Parameter Estimation of Photovoltaic System Using Imperialist Competitive Algorithm
,”
Renew. Energy
,
111
, pp.
307
320
.
43.
Li
,
S.
,
Gong
,
W.
,
Yan
,
X.
,
Hu
,
C.
,
Bai
,
D.
,
Wang
,
L.
, and
Gao
,
L.
,
2019
, “
Parameter Extraction of Photovoltaic Models Using an Improved Teaching-Learning-Based Optimization
,”
Energy Convers. Manage.
,
186
, pp.
293
305
.
44.
Liang
,
J.
,
Ge
,
S.
,
Qu
,
B.
,
Yu
,
K.
,
Liu
,
F.
,
Yang
,
H.
,
Wei
,
P.
, and
Li
,
Z.
,
2020
, “
Classified Perturbation Mutation Based Particle Swarm Optimization Algorithm for Parameters Extraction of Photovoltaic Models
,”
Energy Convers. Manage.
,
203
, p.
112138
.
45.
Oliva
,
D.
,
Ewees
,
A. A.
,
Aziz
,
M. A. e.
,
Hassanien
,
A. E.
, and
Peréz-Cisneros
,
M.
,
2017
, “
A Chaotic Improved Artificial Bee Colony for Parameter Estimation of Photovoltaic Cells
,”
Energies (Basel)
,
10
(
7
), p.
865
.
46.
Long
,
W.
,
Cai
,
S.
,
Jiao
,
J.
,
Xu
,
M.
, and
Wu
,
T.
,
2020
, “
A New Hybrid Algorithm Based on Grey Wolf Optimizer and Cuckoo Search for Parameter Extraction of Solar Photovoltaic Models
,”
Energy Convers. Manage.
,
203
, p.
112243
.
47.
Almonacid
,
F.
,
Rodrigo
,
P.
, and
Fernández
,
E. F.
,
2016
, “
Determination of the Current-Voltage Characteristics of Concentrator Systems by Using Different Adapted Conventional Techniques
,”
Energy
,
101
, pp.
146
160
.
48.
2022
, “
DSSC: Dye Sensitized Solar Cells
,” Gamry Instruments. https://www.gamry.com/application-notes/physechem/dssc-dye-sensitized-solar-cells/, Accessed August 2, 2022.
49.
Jošt
,
M.
,
Lipovšek
,
B.
,
Glažar
,
B.
,
Al-Ashouri
,
A.
,
Brecl
,
K.
,
Matič
,
G.
,
Magomedov
,
A.
,
Getautis
,
V.
,
Topič
,
M.
, and
Albrecht
,
S.
,
2020
, “
Perovskite Solar Cells Go Outdoors: Field Testing and Temperature Effects on Energy Yield
,”
Adv. Energy Mater.
,
10
(
25
), p.
2000454
.
50.
Jain
,
A.
, and
Kapoor
,
A.
,
2004
, “
Exact Analytical Solutions of the Parameters of Real Solar Cells Using Lambert W-Function
,”
Sol. Energy Mater. Sol. Cells
,
81
(
2
), pp.
269
277
.
51.
Levenberg
,
K.
,
1944
, “
A Method for the Solution of Certain Non-Linear Problems in Least Squares
,”
Q Appl. Math.
,
2
(
2
), pp.
164
168
.
52.
Marquardt
,
D. W.
,
1963
, “
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
,”
J. Soc. Ind. Appl. Math.
,
11
(
2
), pp.
431
441
.
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