Bulletin of the Transilvania University of Brasov • Vol 3(52) - 2010

Series III: Mathematics, Informatics, Physics, 213-222

A PORTABLE DEVICE FOR PHOTOVOLTAIC CELLS ANDPANELS

D.T. COTFAS1, P.A. COTFAS2, L. POPESCU3, D. URSUTIU4, C. SAMOILA5

Abstract

This paper introduces a mobile system for the characterization of solar cells andpanels, presented from the early stage of a research idea to the final stage of a scientificdevice. The main advantage of the system lies in the fact that measurements canbe performed in situ - in the very place where the solar panels are mounted. Themethods implemented to determine the parameters of the solar cells and panels arealso presented.

2010 PACS:84.60.JtKey words: solar cells and panels, MOSFET, parameters, mobile system.

1 Introduction

The determination of solar cells and panels’ parameters is important for manufacturersand users as well as for stand alone or on grid solar panels designers. Whereas for cellsor for solar panels production the parameters determination is usually performed in labsor at the production site, for the checking and repairing of the photovoltaic systems it isdesirable that the parameters determination is performed in the very place where they aremounted and used.

The checking and repairing in case of need are more conveniently realized and moreefficient financially at the mounting place of the photovoltaic systems. The development offlexible and mobile systems for the solar cells and panels characterization has the purposeof realizing these desiderates.

Most characterization systems of solar cells are developed for lab conditions [1-4].The advantage of these systems is the possibility to reproduce the standard measurementconditions: the irradiance of 1000W/m2, the temperature of 25C and the air mass 1.5,these being the standard measurement conditions. The cost of such a system is a majordisadvantage. The reproducing of natural illumination conditions in the lab is realizedby using the solar simulators including filters, with extremely high costs implied. Solarsimulators based on halogen lamps can be used to reduce the costs.

1Dept. of Physics, Transilvania University of Brasov, e-mail: dtcotfas@unitbv.ro2Dept. of Physics, Transilvania University of Brasov3Master Student, Transilvania University of Brasov4Dept. of Physics, Transilvania University of Brasov5Dept. of UTSM, Transilvania University of Brasov

214 D.T. Cotfas, P.A. Cotfas, L. Popescu, D. Ursutiu, C. Samoila

The performance of measurements in natural illumination conditions eliminates the useof the solar simulator, the costs being thus reduced. The disadvantage of this measurementmethod is its dependence on the atmosphere conditions. The measurements have to beperformed at solar noon and in clear sky conditions, as the measurement conditions arereproducible for a sufficient period of time.

Taking into account all these considerations, a flexible and cheap mobile system wasdeveloped, designed to allow the measurements performance at the mounting place of thepanels. The realization of such a system prevents the systems from being demounted andtransported to labs for the necessary check up. The system, together with a pyranometerallows the solar cells’ calibration in natural light conditions.

2 Theoretical considerations

There are several methods to characterize and determine the parameters of solar cellsand panels. Most of these are based on using the current-voltage characteristic I-V. Theparameters that can be determined using one or more I-V characteristics are: Isc - shortcircuit current, Voc - open circuit voltage, Pmax - maximum power, Rs - series resistance,Rsh - shunt resistance, m - ideality factor of diode, Io - reverse saturation current, FF -fill factor and η - efficiency.

A simple and quick method to characterize the solar cells and panels is the plotting ofthe I-V characteristic and its non linear fitting using the one diode model, which mathe-matically describes the behavior of photovoltaic cells [5]. The approximation used for thefitting is Imax · Rs << Vmax, thus the equation describing the one diode model becom-ing explicit (1). The fitting ensured the determination of the following parameters:Isc,Io, m, Rsh, Pmax and implicitly FF and η can be determined using the power- voltagecharacteristic P-V.

I = Isc − Io

(e

qVmkT − 1

)− V

Rsh(1)

The method called “The Analytical Five Point Method” allows the determination of allthe interest parameters of the solar cell [6]. The method is based on the use of the onediode model and on the plotting of the I-V and P-V characteristics for the photovoltaiccells. The first step is the determination of Isc and Voc as intersection points betweenthe I-V characteristic and the coordinates’ axis, Pmax and implicitly Imax and Vmax usingthe P-V characteristic. The next step is the determination of the shunt resistance by thelinear fitting of the I-V characteristic around the point (0, Isc), see formula (2):

Rsh = Rsho = −(

dV

dI

)I=Isc

(2)

The determination of the series resistance is performed in two stages. The first consistsof the linear fitting around the point (Voc, 0), see relation(3), a primary value that needscorrection being obtained:

Rso = −(

dV

dI

)V =Voc

(3)

A portable device for photovoltaic cells and panels 215

The coefficients A, B, C and m′ are calculated using relations (4-7), in order to obtainthe other parameters:

A = Vmax + RsoImax − Voc (4)

B = ln(

Isc −Vmax

Rsho− Imax

)− ln

(Isc −

Voc

Rsh

)(5)

C =Imax

Isc − VocRsh

(6)

m′ =A

VT (B + C)(7)

The reverse saturation current is calculated using equation (8):

Io =(

Isc −Voc

Rsh

)exp

(− Voc

m′VT

)(8)

The value of the series resistance is obtained using the value Rso obtained with relation(3) and the correction formula (9).

Rs = Rso −m′VT

Ioexp

(− Voc

m′VT

)(9)

The current photo-generated by the cell and the ideality factor of the diode are obtainedusing relations (10-11).

Iph = Isc

(I +

Rs

Rsh

)+ Io

(exp

(IscRs

m′VT

)− 1

)(10)

m = 10m′ (11)

Two methods were implemented to determine only the series resistance of the solar cellsand panels, namely the “two characteristics method” and “the area method” [7]. The twocharacteristics method uses two I-V characteristics raised at the same temperature fortwo illumination levels. The two characteristics are translated one from the other with thequantities ∆Isc and ∆Isc ·Rs = ∆V . Two correspondent points from the characteristics aremoved away from each other with a distance equaling the translations of the coordinatessystem. The series resistance will be thus determined from the ratio (12):

Rs =∆V

∆Isc(12)

Rs can be calculated by the area method, using equation (13):

Rs = 2(

Voc

Isc− A

I2sc

− mkT

qIsc

)(13)

where: A is the area between the I-V characteristic, the V axe and the I axe, T is thetemperature measured in Kelvin, q the electrical charge of 1.6 · 10−19C, k the Boltzmannconstant of 1.38 · 10−23JK−1. The effect of the shunt resistance is neglected, being con-sidered infinite and m can be considered as 1.

216 D.T. Cotfas, P.A. Cotfas, L. Popescu, D. Ursutiu, C. Samoila

3 Experimental system

The idea of creating a mobile and flexible system that allows the characterization ofsolar cells and photovoltaic panels was the starting point for the realization of the charac-terization system. To fulfill these conditions the following configuration of the system wasused: Laptop, acquisition board and the circuit for the plotting of the I-V characteristics.The first two components of the system don’t need to be dedicated, so that the priceof the system can be greatly reduced. Function of the accuracy desired, the acquisitionboard is chosen. For the system described a National Instruments NI 6009 acquisitionboard was chosen, with 8/4 analog input (AI) chanels in the configuration Single-EndedChannels/Differential Channels with a sampling rate of 48kS/s and a resolution of 14 bits,two analog input channels AO of a 12 bits resolution, 12 Digital Input/Output (DIO) anda counter . The connection of the board to a laptop is realized by a USB connection.

The plotting of the I-V characteristic can be realized by using an electronic load,a MOSFET transistor or a capacitor used as variable charge [8]. The method usinga MOSFET transistor was used for the mobile characterization system because of itsflexibility but also for the reduction of the costs.

The realization of the circuit consisted of the following stages:- conceiving the circuit;- realizing and checking the circuit on the rapid prototyping board of the educational

platform NI ELVIS, see fig. 1;

Figure 1: Testing the circuit for the raising of the I-V characteristic on the NI ELVISplatform

- simulating the electronic circuit with the NI Multisim soft;- exporting the circuit in NI Ultiboard - the platform that allows the optimum realiza-

tion of the circuit, visualization 3D, see fig.2, and its preparing for the printing;The miniaturization of the device for the plotting of the I-V characteristic is possible

with the soft dedicated to the design and optimization of the circuits. Due to the reduceddimensions, to the mass under half a kilogram and to the autonomy offered by the batteriesused and by the acquisition board with a USB connection, the system becomes portableand can be used in any location.

A portable device for photovoltaic cells and panels 217

Figure 2: The circuit simulated in Ultibord for the raising of the I-V characteristic

Figure 3: Automatic system for the plotting of the I-V characteristic with a MOSFETtransistor

218 D.T. Cotfas, P.A. Cotfas, L. Popescu, D. Ursutiu, C. Samoila

Software applications were created in the graphical programming language LabVIEWto control the circuit, to automatically raise the I-V characteristic and to determine theparameters. The applications were then compiled into one complex application. Theapplication is created on tabs, see fig.4. The first tab “Ridicarea caracteristicii I-V”permits the control of the acquisition board, the control of the transistor, the plotting ofthe I-V characteristic and the saving of the data. The tab “Determinarea parametrilor”permits the import of the processing file, the determination of the interest parameters ofthe cell using the method of the nonlinear fitting. The other methods to determine theparameters of the solar cells and panels described in the theoretical considerations wereimplemented as sub-tabs in the tab “Aplicatii”.

Figure 4: The interface for the application built on tabs

4 Results

To check the system for reliability and flexibility, for the repeatability of the measure-ments, it was tested for various types of cells and solar panels, at different illuminationlevels and at different cells temperatures. In case of the typical photovoltaic panels with36 cells bound in series a voltage divisor is used to permit the voltage measurements. Theacquisition board used can measure only between -10V and 10V, and a photovoltaic panelwith 36 cells bound in series debits an open circuit voltage of over 21V.

The determination of the parameters of a polycrystalline silicon solar cell with an areaof 6 cm2 by the method of simple nonlinear fitting is presented in fig.5. The method usedis based on the algorithm developed by Levenberg - Marquardt. The initial parameters

A portable device for photovoltaic cells and panels 219

have to be introduced to realize the fitting. This implies that the user has basic knowledgeof the type of cell that he intends to characterize. The method permits the determinationof the parameters Isc, Io, m, Rsh and Voc. Using the characteristic P-V, Pmax can bedetermined by finding the maximum of this curve. With these parameters determined,the factor fill can also be calculated.

Figure 5: The interface for the nonlinear fitting method

The methods: the analytical five point method, the area method and the two charac-teristics method, are used to determine the parameters of the solar cells also taking intoconsideration the series resistance.

Figure 6 presents the interface of the application that permits the determination of theseries resistance by using the two characteristics method. The series resistance of the cellcan be determined using relation (12) with the requirement to determine ∆V precisely.To realize this, the facilities offered by the graphical programming language LabVIEWwere used, namely the simultaneous and independent use of two or more cursors. Thefirst cursor, which is placed on the characteristic plotted at lower illumination, is set sothat the value on the current axis is half the short circuit current. The two voltage valuesare thus determined and ∆V is calculated.

220 D.T. Cotfas, P.A. Cotfas, L. Popescu, D. Ursutiu, C. Samoila

Figure 6: The two characteristics method

Figure 7: The area method

A portable device for photovoltaic cells and panels 221

The application realized to determine the series resistance using the area method ispresented in figure 7. In the application relation (13) is implemented. The area neededfor the calculations is determined by the numerical integral for the function that describesthe characteristic I-V.

The values of the parameters of the cells and panel obtained by the two methods arepresented in Table 1.

Table 1:Cell/ Photo-voltaic Panel

Method Iph[A] Isc[A] Voc[V ] Io[A] m Rs[Ω] Rsh[Ω]

PollycrystallineSi cell (6cm2)

Nonlinearfitting

− 0.0981 ±0.003

0.539 ±0.0002

2.34E −5 ±4.1E − 6

2.51 ±0.02

− 438.5 ±0.67

PollycrystallineSi cell (6cm2)

Five pa-rameters

0.102 ±0.007

0.0982 ±0.001

0.540 ±0.0003

2.41E −5 ±1.1E − 6

2.49 ±0.016

0.5419 ±0.011

445.5 ±0.45

MonocrystallineSi cell (6cm2)

Nonlinearfitting

− 0.123 ±0.005

0.559 ±0.0012

7.211E−6 ±7.4E − 7

1.71 ±0.034

− 771.3 ±0.99

MonocrystallineSi cell (6cm2)

Five pa-rameters

0.128 ±0.001

0.122 ±0.002

0.561 ±0.002

7.24E −6 ±2.1E − 7

1.73 ±0.017

0.342 ±0.009

768.1 ±0.78

3 cells panelbound in series

Nonlinearfitting

− 0.154 ±0.001

1.678 ±0.004

4.362E−6 ±5.9E − 7

2.13 ±0.023

− 871.5 ±0.85

3 cells panelbound in series

Five pa-rameters

0.160 ±0.002

0.1536 ±0.004

1.6767 ±0.001

4.366E−6 ±3.4E − 7

2.112 ±0.009

1.23 ±0.019

872.33 ±0.56

5 Conclusions

A portable, flexible, reliable and cheap system for the characterization of the solar cellsand photovoltaic panels was created.

By the multiple facilities offered, the system becomes an important tool for the usersas well as for the educational environment. The students can gain theoretical knowledgeas well as practical abilities in the domain of photovoltaics by using the mobile character-ization system.

By implementing several methods to determine the parameters of the solar cells andphotovoltaic panels, the system ensures, by comparison, the authenticity of the valuesdetermined.

From Table1 and from the interfaces presented, there are small differences to be ob-served between the values of the determined parameters.

222 D.T. Cotfas, P.A. Cotfas, L. Popescu, D. Ursutiu, C. Samoila

References

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[2] http://www.keithley.com/solar cell.

[3] http://www.home.agilent.com/agilent/product.jspx?cc=US&lc=eng&ckey=582565&nid=-33786.536905585.00&id=582565&pselect=SR.General.

[4] Atia Y., Zahran M., Al-Hossain A.: Solar Cell Curves Measurement Based on Lab-VIEW Microcontroller Interfacing, Proceedings of the 12th WSEAS InternationalConference on AUTOMATIC CONTROL, MODELLING & SIMULATION, Cata-nia, Sicily, Italy May 29-31, 2010.

[5] Cotfas D.T.: Investigation on parameters affecting the photoconversion efficiency inPV-cells based on Si and Cd/Te, PhD thesis, 2007

[6] Chan D. S. H., Phillips J. R., PHANG J. C. H.: A comparative study of extractionmethods for solar cell model parameters, Solid-State Electronics, vol. 29, no. 3. p.329-337, 1986.

[7] Cotfas D.T., Cotfas P.A., Kaplanis S., Ursutiu D.: Results on series and shunt resis-tances in a c-Si PV cell. Comparison using existing methods and a new one, Journalof optoelectronics and advanced materials, vol. 10, no. 11, p. 3124 - 3130, November2008;

[8] Cotfas D. T., Cotfas P., Ursuiu D., Samoila C.: Current-Voltage Characteristic Rais-ing Techniques for Solar Cells. Comparisons and Applications, 12th Internationalconference on optimization of electrical and electronic equipaments, Brasov, IEEEXplore Digital Library, 2010.