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International Conference on Renewable Energies and Power Quality (ICREPQ’13)
Bilbao (Spain), 20th to 22th March, 2013
exÇxãtuÄx XÇxÜzç tÇw cÉãxÜ dâtÄ|àç ]ÉâÜÇtÄ (RE&PQJ)
ISSN 2172-038 X, No.11, March 2013
Obtaining the characteristics curves of a photocell by different methods
JA. Ramos-Hernanz1, JJ. Campayo1, E. Zulueta2, O. Barambones2, P. Eguía3 and I. Zamora3
1 Department of Electrical Engineering
E.U.I., Vitoria-Gasteiz, University of the Basque Country
Nieves Cano, 12, 01005 Vitoria-Gasteiz (Spain)
Phone/Fax number: 0034 945 014147/0034 945 013270, e-mail:,
2 Department of Systems Engineering and Automatic
E.U.I., Vitoria-Gasteiz, University of the Basque Country
Nieves Cano, 12, 01005 Vitoria-Gasteiz (Spain)
Phone/Fax number: 0034 945 014160/0034 945 013270, e-mail:,
3 Department of Electrical Engineering
E. T. S. de Ingeniería de Bilbao, University of the Basque Country
Alameda Urquijo s/n. 48013 – Bilbao (Spain)
Phone/Fax number: 0034 946 014063/0034 946 014200, e-mail:,
Abstract. The objective of this paper is to show different
models that simulate the behavior of a photovoltaic cell. The
study of photovoltaic systems, in an effective way, requires a
precise knowledge of the IV and PV characteristic curves of
those photovoltaic elements. This paper shows the results of the
implementation of various methods of simulation of a
photovoltaic cell, the representation of their IV and PV
characteristic curves. The knowledge of the curves allows to
know the functioning of the cell and the adequacy of the model.
The models are implemented in Matlab/Simulink and in Excel.
To carry out mathematical models or experimental data will be
Key words
Photovoltaic Cells, PV-IV Curves, Modeling, Simulation,
1. Introduction
The high interest aroused by distributed generation due to
the opening of electricity markets and the need for
alternatives to conventional electric power generation,
fossil fuel based, has fostered a renewed interest in
renewable systems. Among these renewable systems,
photovoltaic systems are expected to play an important
role in the generation of electrical energy in the future.
Photovoltaic energy is a clean energy, with a long service
life and high reliability. Thus, it can be considered as one
of the most sustainable renewable energies. These systems
may be located at the points of consumption or near them,
avoiding transmission losses. And, in addition,
contributing to the reduction of CO2 emissions in urban
An ideal solar cell, theoretically, can be modeled as a
current source in anti-parallel with a diode (Fig. 1). The
direct current generated, when the cell is exposed to light,
varies linearly with solar radiation. An improvement of
the model includes the effects of a series resistor and
other one in shunt. [1]
Fig. 1. Equivalent circuit of a photovoltaic cell
The equation describing the relationship between voltage
(V) and current (I) provided by a module is as follows:
I = IL – ID – IP (1)
Being the net current of the cell, the difference of the
photocurrent IL, (the current generated by the incident
light, directly proportional to the sun irradiation), ID (the
normal diode current) and IP the current through the shunt
resistor. If each term is replaced by its value is obtained:
RE&PQJ, Vol.1, No.11, March 2013
44 344 21
eIII )(
)1(. )(.
= + (2)
Where, I0 is a saturation current of the diode (A), V is a
cell voltage (V), q is the charge of an electron, equal to
1’6.10-19 (C), a is the diode ideality constant, K is the
Boltzan’s constant, 1’38.10-23 (j/K) and T is the cell
temperature. [2-7]
The typical representation of the output characteristic of a
photovoltaic device (cell, module, or photovoltaic system)
is called characteristic curve, and indicates their behaviour.
The IV curve indicates the relationship between the current
and voltage according to the level of incident radiation
and temperature. The PV curve indicates the same
relationship but for power and voltage. These curves can
be obtained in several ways. Mainly, they can be
calculated from (2) or can be obtained experimentally from
the photovoltaic system. This way could be expensive and
It is, therefore, extremely interesting to have computer
models that simulate the behavior of the solar cell. The
validity of these models will depend on the similarity of
the relationship between the current and voltage, compared
to the physical model. The result of this simulation has to
be a graph or curve similar to that provided by the
manufacturer. (Fig. 2)
Fig. 2. Characteristic curves provided by the manufacturer
In this case the graphics provided by the manufacturer are
at constant temperature and for different values of
irradiance (1000 W/m2, 900 W/m2, 800 W/m2 y 700
W/m2). Graphs can also be obtained at constant irradiance
and different temperature values.
2. Characteristic Curves
The current-voltage curve (IV) shows the possible
combinations of pairs of current-voltage of the
photovoltaic device. Conceptually, the curve represents
the combinations of current and voltage at which the cell
can operate, if the irradiance and cell temperature could
be kept constant. The evaluation of the performance of
solar cells and the design of photovoltaic systems must
be based on the electrical characteristics, that is, in the
current-voltage relationships of the cells subjected to
various levels of irradiation and temperature.
Fig. 3. Characteristic curves of a solar cell
Figure 3 shows the IV characteristic curves (red) and PV
(blue), for a cell working at temperature and radiation
will be obtained known; depending on these factors a
curve or another. The horizontal axis represents the
working cell voltage (V) and the vertical axis the current
(A). It shows the energy produced by the cell or
photovoltaic module at a point, called operating point, in
any part of the IV curve. The coordinates of the point of
operation are the operating voltage and current.
Analyzing the graph, there are several characteristic
points. The cell will produce the maximum intensity
when the resistance between the terminals of the output
circuit is minimal; this is when there is short circuit. The
operating voltage is zero and this value is called "Short
Circuit Current" (ISC). The maximum voltage is reached
in the case that the resistance is infinite and then the
current is zero, the circuit is open, that is, there is "Open
Circuit Voltage" (VOC). Another point to consider is the
maximum of the PV curve, called maximum power point
(MPP), which corresponds to the point on the IV curve,
wherein the area of the rectangle formed by the points
(V,I) is maximum. This is the point at which the module
operates with maximum efficiency and produces the
maximum output power. It is the point of maximum
power (Vmpp, Impp). In a photovoltaic system operating,
one of the functions of the inverter is to constantly adjust
the load. The available power of a photovoltaic device at
any point along the curve is simply the product of current
and voltage at that point and is expressed in Watts.
3. Simulation Types
The models presented in this paper are the result of the
search for different computer simulation models of solar
cells or photovoltaic panels. The models differ depending
RE&PQJ, Vol.1, No.11, March 2013
on whether they were modeled with Excel, Matlab,
Simulink, or with the support of some of their toolbox.
Following is a brief overview of each of the types of
simulation discussed in this paper.
A. Matlab Programming
This model is made only in Matlab, based on mathematical
equations that define the photovoltaic cell. From the work
of Walker [6], Gonzalez [7] and Ahikiro [8] a function in
Matlab [2] has been developed which calculates the
current module from data of voltage, solar radiation and
temperature. Setting the constant temperature or radiation,
curves IV and PV will be obtained. From another script
also calculates the maximum power point.
B. Matlab Tools
This section has taken into account two ways to represent
the IV and PV curves. In the first form of representation,
the graphic interface for curve fitting Cftool (Curve Fitting
Toolbox) has been used. The starting point of this model is
the manufacturer's datasheet, in which the IV and PV
curves of the panel are represented. In this curve at least
three coordinates (V, I) are known, (0, ISC), (Vmpp, Impp)
and (VOC, 0). Manually more coordinates can be
approximated to facilitate the representation. With these
coordinates, the tool will provide an equation of a similar
curve to the original one.
In the second form, the model consists of two Matlab
programs. The first serves for the presentation and data
capture and calculations are made in the second one. These
calculations are based on three functions of MATLAB:
fsolve, fzero and lsqnonlin. In this case the data used were
obtained experimentally from the panels analyzed. Data
can be exchanged from one form of representation to
C. Basic model in Simulink
Fig. 4. Basic model in Simulink
This model is made based on [5] and [9]. It is a model like
the one shown in section D, also based on mathematical
equations (1) but made with elements of Simulink. It is a
basic model in which the values of RS (0.001 ) and RP
(1000 ) are assumed to be known
D. Simulink model with tags
This is the usual way to model a PV cell that has been
developed among other authors, by Villava [3]. It starts
from the same equations as in section A, but it is
developed in Simulink. Based on this kind of
programming could also simulate the basic model of the
previous section in this way.
E. Model of physical component
This model is made from physical elements using
Simscape. With those elements, electrical equivalent
circuit diagram of the cell is performed.
Fig. 5. Model of physical component in Simulink
F. Model of advanced component library
This is the simplest model. It works with an element of
SimElectronics, that is a toolbox dependent of Simscape.
The element to model, Solar Cell, appears in the Source
Library. Only, it is needed to enter the parameters that
define the cell, provided by the manufacturer's data sheet.
Fig. 6. Characteristic curves obtained with the A-model
4. Results
One can say that, fotocurrent depends on the irradiation
of the moment, for a fixed temperature (in these cases,
25° C). The higher the irradiation, the greater the current.
On the other hand, voltage is going to maintain almost
RE&PQJ, Vol.1, No.11, March 2013
constant and it is not going to vary much, although
increases or diminishes the irradiation.
Below are the graphs (Fig. 7-13) showing the results of
this study:
Fig. 7. Characteristic curves obtained with the A-model
Fig. 8. Characteristic curves obtained with the B1-model
Fig. 9. Characteristic curves obtained with the B2-model
Fig. 10. Characteristic curves obtained with the C-model
Fig. 11. Characteristic curves obtained with the D-model
Fig. 12. Characteristic curves obtained with the E-model
RE&PQJ, Vol.1, No.11, March 2013
Fig. 13. Characteristic curves obtained with the F-model
5. Conclusions
As already mentioned, to get experimental data can be
expensive and will depend primarily on weather
conditions, so it is very useful to have simulation models
to be able to work at any time. For this reason, in this
paper, several methods of modeling photovoltaic panels
have been developed.
The objective of the models is to achieve similar IV and
PV characteristics curves to the graphs that are in the data
sheet of the manufacturer of the different solar panels.
The most similar will be the best model, or the one that
behaves more like the physical model. In the made models,
the results are similar and they resemble the desired
results, although they are simple models, and it is possible
to study the behavior and performance of photovoltaic
cells in the time domain.
The developed model A, with electrics main parameters, is
valid for I-V characteristics measured and can work with
few parameters of input demonstrate to graph and
numerically the operation of a solar model. Unfortunately,
the manufacturers do not provide the values of the
resistance in series nor in parallel of the cell. That would
make easier the simulation.
The set of experiments with different models designed in
Matlab/Simulink (model B) provide the ability to analyze
easily the study of the photovoltaic cell, based on few data
pairs (V, I) that are known. It can be said that the results
obtained with those models are quite similar. The models
made in this section "Matlab Tools" are models for a fixed
irradiance and cannot be generalized for any irradiance.
For each irradiance must be, recalculated the pairs (V, I)
for the corresponding curve.
The models C and D are more likely to work than those
developed in model A. These three models are very
similar, because they start from the same equation, but the
Simulink models, being in a graphical environment, are
easier to see and to analyze the performance of the model.
Models C and D are almost the same model. Because, they
are the result of the same equation. But defined with
different elements.
In the models A, C, D and F, it is easier to make
adjustments than in the model E. Because in the first
models are used data supplied by the manufacturer. And
in the model E, you need to know the values of RS and RP
that are not normally provided by the manufacturer.
The easiest model to work with and to configure is the
model E. This model is provided and developed by
Matlab, Solar Cell Block. The block represents a single
solar cell as a resistance RS that is connected in series
with a parallel combination of the following elements:
Current source, two exponential diodes and parallel
resistor RP.
The authors are grateful to the Basque Government by
the support of this work through the project DYNBLADE
(SAIOTEK 2011-12).
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RE&PQJ, Vol.1, No.11, March 2013
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