At present, photovoltaic energy is one of the most important renewable energy sources. The demand for solar panels has been continuously growing, both in the industrial electric sector and in the private sector. In both cases the analysis of the solar panel efficiency is extremely important in order to maximize the energy production. In order to have a more efficient photovoltaic system, the most accurate understanding of this system is required. However, in most of the cases the only information available in this matter is reduced, the experimental testing of the photovoltaic device being out of consideration, normally for budget reasons. Several methods, normally based on an equivalent circuit model, have been developed to extract the I-V curve of a photovoltaic device from the small amount of data provided by the manufacturer. The aim of this paper is to present a fast, easy, and accurate analytical method, developed to calculate the equivalent circuit parameters of a solar panel from the only data that manufacturers usually provide. The calculated circuit accurately reproduces the solar panel behavior, that is, the I-V curve. This fact being extremely important for practical reasons such as selecting the best solar panel in the market for a particular purpose, or maximize the energy extraction with MPPT (Maximum Peak Power Tracking) methods

A Askarzadeh

J Cubas

JCH Phang

MG Villalva

T Easwarakhanthan

W Gong

Javier Cubas

Santiago Pindado

Carlos de Manuel

Crossref

New Method for Analytical Photovoltaic Parameters Identification: Meeting Manufacturer’s Datasheet for Different Ambient Conditions

Cubas Cano, Javier

Pindado Carrion, Santiago

Manuel Navío, Carlos de

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

Chapter 21 
New Method for Analytical Photovoltaic 
Parameters Identification: Meeting 
Manufacturer's Datasheet for Different 
Ambient Conditions 
Javier Cubas, Santiago Pindado and Carlos de Manuel 
Abstract At present, photovoltaic energy is one of the most important renewable 
energy sources. The demand for solar panels has been continuously growing, both 
in the industrial electric sector and in the private sector. In both cases the analysis 
of the solar panel efficiency is extremely important in order to maximize the 
energy production. In order to have a more efficient photovoltaic system, the most 
accurate understanding of this system is required. However, in most of the cases 
the only information available in this matter is reduced, the experimental testing of 
the photovoltaic device being out of consideration, normally for budget reasons. 
Several methods, normally based on an equivalent circuit model, have been 
developed to extract the I-V curve of a photovoltaic device from the small amount 
of data provided by the manufacturer. The aim of this paper is to present a fast, 
easy, and accurate analytical method, developed to calculate the equivalent circuit 
parameters of a solar panel from the only data that manufacturers usually provide. 
The calculated circuit accurately reproduces the solar panel behavior, that is, the 
I-V curve. This fact being extremely important for practical reasons such as 
selecting the best solar panel in the market for a particular purpose, or maximize 
the energy extraction with MPPT (Maximum Peak Power Tracking) methods. 
21.1 Introduction 
It is a fact that energy efficiency of electric systems requires a good understanding 
of each one of its parts. In case of systems that involve photovoltaic panels, the 
analysis of the system must take into account the behavior of the mentioned panels 
depending on, at least, sun radiation levels, temperature, and connected loads. In 
the case of space applications, the cumulative ionizing radiation is another 
important factor. The optimization of the system requires then a mathematical 
modeling of the photovoltaic devices (solar panels or solar cells). One of the most 
popular photovoltaic systems models is based on an equivalent circuit. In the 
present work the mentioned equivalent circuit model is analyzed in order to get the 
best approximation to the solar panel/cells behavior. This work was carried out in 
the framework of the UPMSat-2 satellite project at the IDR/UPM Institute 
(Madrid, Spain), nevertheless, the calculation process can be applied to every 
photovoltaic system no matter if it is designed for space or terrestrial applications. 
21.2 Solar Cell/Panel Modeling 
The simpler equivalent circuit of a solar cell/panel involves a current source and 
one or several diodes connected in parallel. A series resistance and a shunt 
resistance, Rs, and Rsu, are normally added to the circuit to take respectively into 
account losses in cell solder bonds, interconnection, junction box, etc., and the 
current leakage through the high conductivity shunts across the p-n junction. The 
most popular equivalent circuit is shown in Fig. 21.1, it includes a current source, 
one diode and the mentioned resistances. It reproduces quite well the behavior of 
the solar cell/panel, that is, the I-V curve, see Fig. 21.2. In Fig. 21.2 open circuit, 
maximum power, and short circuit points are indicated. These points together with 
their variation as a function of the temperature and the radiation exposure (also 
known as fluence) are the normal information included in manufacturers' data-
sheets see Table 21.1. 
The circuit model of Fig. 21.1 is defined by the following expression [1]: 
i i i\ fV + IR>\ i / = / p v - / o ^ e x p ( ^ - ) - l 
where Ipv is the photocurrent delivered by the constant current source, I0 is the 
reverse saturation current corresponding to the diode, N is the number of cells in 
series, and a is the ideality factor that takes into account the deviation of the diodes 
from the Shockley diffusion theory (the value of this factor, is assumed to be 
constant and between 1 and 1.5 [2] for one-junction cells. VVis the thermal voltage 
of the diode and depends of the charge of the electron, q, the Boltzmann constant, 
k, and the temperature, T, with (21.2). 
V + IR, 
R sh 
(21.1) 
Fig. 21.1 Equivalent circuit 
for a solar cell u 0 M 
-AAA/ o 
Fig. 21.2 Example of the I-
V curve of a solar cell 
i ' 
CA l x 
0 3 
CS 
0.1 
0 ) 0.5 1.5 
\ J 
K\ 
2 25 3 
f ( V ) 
Table 21.1 Characteristic points and its variation with temperature and fiuence of Emcore ZTJ 
photovoltaic cell from manufacturer datasheet 
Fiuence (e/cm2) 
0 
3.00 x 1013 
1.00 x 1014 
5.00 x 1014 
1.00 x 1015 
3.00 x 1015 
1.00 x 1016 
V„c 
(V) 
2.726 
2.617 
2.590 
2.481 
2.426 
2.344 
2.235 
he 
(A) 
0.463 
0.458 
0.454 
0.449 
0.435 
0.412 
0.380 
v 
' nip (V) 
2.410 
2.362 
2.338 
2.241 
2.193 
2.097 
2.000 
*mp 
(A) 
0.439 
0.435 
0.435 
0.421 
0.413 
0.377 
0.325 
AVoc 
(mV/°C) 
-6 .3 
-
-6 .6 
-
-6 .9 
-
-7 .4 
A/sc 
(mA/°C) 
0.31 
-
0.30 
-
0.30 
-
0.31 
AVmp 
(mV/°C) 
-6 .7 
-
-7 .0 
-
-7 .3 
-
-6 .6 
A/mp 
(mA/°C) 
0.24 
-
0.24 
-
0.28 
-
0.36 
AM0 (1,353 W irT2 ) Tr = 28 °C [3] 
Vr JL kT' (21.2) 
These parameters, together with Rs and Rsh, are adjusted to fit the circuit 
behavior to the solar cell/panel testing results. As testing results depend on the 
mentioned temperature, radiation and fiuence, the aforementioned parameters will 
change from one case to another. 
21.3 Parameter Calculation 
The parameters of the equivalent electric circuit, Ipv, I0, a, Rs, and Rsh, can be 
numerically [4] or analytically [5] extracted from I-V curves experimentally 
measured, or can be calculated from the data included by the manufacturer in the 
datasheet (normally, the mentioned three characteristic points: open circuit, 
maximum power, and short circuit). In this second case the procedure use to be 
numerical [2, 6]. In the present work, an analytical procedure [7] has been selected 
to extract the circuit parameters based on the characteristic points. This method is 
direct, simple, non-iterative, and has been proved to be as accurate as other more 
sophisticated numerical methods [8, 9]. The first step consists in the estimation of 
parameter a, whose value will be in the bracket 1-1.5. This first estimation of one 
of the 5 parameters of the circuit is necessary, as the number of equations resulting 
from the characteristic points is only 4. The other 4 parameters can be derived, for 
specific temperature, irradiation and fluence conditions from equations: 
&*T*mp\^mp *-sc) 
\*mp'-sc i Voc\lmp *sc J J \ * mp ^mp^sj ^ *T \ *mp'-sc *oc'-mpj 
'V + / R — V 
,
 v
 mp i 1mp1Ys v "< 
= exp | — — aV, T 
u \ *mp l-mpK-s J yV mp Ks\*sc *-mp) ClVfJ 
sh=
 (V -I R)(I -I ) - aVrl ' ( 2 L 3 ) 
y v mp 1mplvs) y-sc 1mpJ "- v 11m 
h = 
-mp 
(Rsh + Rs)ISc — Voc 
Rsh ex-P aV] 
j _ Rsh +RS j 
Lnv „ ls< 
Ksh 
*pv 
As said, temperature variations will modify the behavior of the photovoltaic 
device, that is, its I-V curve. More specifically, the characteristic points of the 
curve will also be modified, the variations being lineal with the temperature as it 
can be appreciated in the example of Table 21.1. An increase of temperature will 
increase the current level but decrease the voltage level, and as a result the 
maximum power point will also decrease. The variations of current and voltage 
levels of open circuit, maximum power, and short circuit points as a function of the 
temperature can be expressed as: 
VOC,T = Voc,Tr + AVoc(T - TV); VmPiT = VmPiTr + AVmp(T - TV); 
*sc,T *sc,Tr i L\1SC\1 *-r)> lmp,T ^mp,Tr > {\lmp\l *-r)> 
where TV is the reference temperature. There are several methods in the existing 
literature that relates directly the equivalent circuit parameters with the tempera-
ture [2, 10]. Nevertheless, a different procedure has been followed in the present 
work: (21.3) were solved for a specific temperature with the characteristic points 
values calculated previously with (21.4). This procedure implies much more 
precision than other methods that estimate parameter variation with temperature, 
as the calculated circuits are directly forced to meet the manufacturers' data. 
Usually, manufacturers do not include in the datasheets any information 
regarding the behavior of the solar cell/panel at different irradiation levels. 
However, it is known that the I-V curve is essentially invariant with intensity in 
ranges around one solar constant. On the other hand, temperature affects Isc lin-
early and Voc exponentially, whereas Rs remains not affected for temperature 
variations [11]. Those conditions, once simulated using an equivalent circuit, lead 
to the following expression [2]: 
Ipv,G = Ipv,Gr 7 T , (21.5) 
where G is the irradiance on the cell/solar panel, Ipv G is the photocurrent delivered 
by the current source of the equivalent circuit, and Gr and IpVrar are the reference 
values. 
The radiation exposure or fluence radiation is translated into a degradation of 
the photovoltaic system performances. Obviously, the fluence modifies the char-
acteristic points of the I-V curve, as it can be observed in the example of 
Table 21.1. However, in this case the variation is not linear, and normally is not 
easy to interpolate using the manufacturers' data. Additionally, fluence radiation 
degradation is a slow process that will take months or years to affect visibly the 
operation of the cell. For this reason it seems reasonable to calculate separately the 
circuit parameters for each one of the fluence levels specified in the manufacturers' 
datasheets (see Table 21.1), and apply the proper one for each stage of the mission. 
21.4 Example of Application, LTSpice Model 
In this Section, the method explained above is applied in the performance analysis 
of a commercial solar cell, Emcore ZTJ, for every irradiance and temperature 
condition, using LTSpice models fitted to the experimental data from the manu-
facturer (see Table 21.1). Although, the mentioned analysis is carried out for zero 
fluence, it can be easily reproduced for different levels of radiation exposure (see 
other fluence levels in Table 21.1). 
As said in Sect. 21.1, the value of parameter a is firstly estimated as a = 1.1. 
Taking also into account that the studied cell is triple junction N = 3. Solving 
(21.3) at AMO (1,353 W m"2) and Tr = 28 °C, it is possible to calculate the rest of 
the equivalent circuit parameters, see Table 21.2. Repeating this process for 
temperatures in the bracket 0-100 °C, the variation of the mentioned parameters as 
a function of the temperature can be obtained, see Figs. 21.3, 21.4, 21.5, and 21.6. 
Taking into account that, with the exception of Ipv, all parameters are not 
dependent of the irradiance, and fitting the temperature using the least squares 
method, the following 21.6 can be then derived. 
Table 21.2 Parameters of equivalent circuit of Emcore ZTJ 
N 
3 
a 
1.1 
Ipv (A) 
0.463 
/o(A) 
6.80 x 10~15 
RS(Q) 
6.09 x 10~2 
Rsh 
284.4 
AMO (1,353 W irT2 ) Tr = 28 °C 
Fig. 21.3 Calculated 
RS(T) and polynomial 
regression 
0.075 
0.07 • 
~ 0.065 
[ ] 5 
u.:55 
R5m 
Calculated Values ofRs 
-Polynomial regression ? 
20 40 50 
/ 
7 
, / 
fin i[..] 
Fig. 21.4 Calculated 
RSh(T) and polynomial 
regression 
550 r 
500 • 
450 • 
400 • 
350 
300 
250 
%, m 
• 
• Calculated Values of J ^ * 
~J 
/ 
• • 
?' ta 60 
TTO 
f..l 100 
Fig. 21.5 Calculated 
Ipv(T) and polynomial 
regression 
0.49 
n . ; = 
< 0.47 
0 46 
0.45 
: • ] 
Um 
Calculated Va lues I 
- Polynomial regression 
4 0 SO E: i [ ] 
X if: L 
2£ 
2 
ten 
• Calculaled Values cf L 
Polynomial regression 
Fig. 21.6 Calculated IQ(T) and polynomial regression 
op 
Step Param Pot 0 3.23 0.001 
.TEMP 28 .Param TR 28 .Param DT=TEMP-TR 
.Param G 13S3 .Param GR 1353 
.Param a 1.1*8 
.Param Ipv (0.463+3 11E-4-DT)-G<GR 
.Param Rs 6.09E-2-1.42E-4*OT+3.77E-«*DT"2+2,68E-9'DT"3 
.Param Rsh 1/(3.51E-3J!.5GE-6*OT-1.51E-7*DT**2-1.45E-9*DT**3) 
.Param 10 eip(-32 62+0.18*DT-5 92E -4*DT"2+1.53E-6*DT"3) 
MODEL DIODE D (IS= 10 TNOM=TEMP N=a) 
Fig. 21.7 LTSpice model for Emcore ZTJ solar cell 
a= 1.1 
( r , G) = (0.463 3.11 x W^AT) 
Gr' 
RS(T) = 6.09 x 10~2 - 1.42 x 10"4Ar + 3.77 x lO^Ar2 + 2.68 x 10~9Ar3, 
Rsh{T) = 1/(3.51 x 10"3 -4.56 x W'6AT-1.51 x l (T7Ar2- 1.45 x 10"9Ar3), 
I0{T) = exp(-32.62 + 0.18A7/-5.92 x 10"4Ar2+ 1.53 x 10"6Ar3). 
(21.6) 
Finally, programming (21.6) in a LTSpice model (see Fig. 21.7), it is possible 
to obtain a quiet accurate estimation of the studied photovoltaic device behavior 
for every irradiation, temperature and fluence condition, see Figs. 21.8 and 21.9. 
Fig. 21.8 Curves IV for 
Emcore ZTJ solar cell, 
G = 1,353 W/rrT2; 
r(0:100 °C) 
Fig. 21.9 Curves IV for 
Emcore ZTJ solar cell, 
T = 28 °C; G(500:l,800 W/ 
m-2) 
a./ 
[(A; 
[15-
u.-i-
[1.3-
(1,1-
[) 
r 
: 
^ v \ 
— ^ A W V 
D 0,1 o.n 
,...,... 
: 
: i 
! 
0,9 
"" T " 
: 
: 
: 
! 
i_? 1.F l 1,0 
; 
I 
?-1 2 A 2.7 
-TV) 
21.5 Conclusions 
In the present work a simple but accurate method to analyze the performances of a 
photovoltaic device for different working conditions is described. This method is 
based on manufacturers' data. The present work is part the research framework 
associated to the design and construction of the UPMSat-2 satellite at the Uni-
versidad Politecnica de Madrid (Polytechnic University of Madrid). 
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T. Easwarakhanthan, J. Bottin, I. Bouhouch, C. Boutrit, Nonlinear minimization algorithm 
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4. J.C.H. Phang, D.S.H. Chan, J.R. Phillips, Accurate analytical method for the extraction of 
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New method for analytical photovoltaic parameters identification: meeting manufacturer’s datasheet for different ambient conditions

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New method for analytical photovoltaic parameters identification: meeting manufacturer’s datasheet for different ambient conditions

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