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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: josean.ramos@ehu.es, jj.campayo@ehu.es

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: ekaitz.zulueta@ehu.es, oscar.barambones@ehu.es

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: pablo.eguia@ehu.es, inmaculada.zamora@ehu.es

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

needed.

Key words

Photovoltaic Cells, PV-IV Curves, Modeling, Simulation,

Matlab/Simulink.

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

centers.

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:

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44 344 21

P

D

S

I

P

S

I

aKT RIVq

LRRIV

eIII )(

)1(. )(.

0+

−−−= + (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

complicated.

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

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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

another.

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 Ω) and RP

(1000 Ω) 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

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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

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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.

Acknowledgement

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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