Abstract: This paper has as main goal to evaluate the quality of a model to describe the behavior of the thermal conditions of photovoltaic (PV) modules. The methodology consists in compare measured and calculated PV modules temperature values. As result, the maximal deviations are in a range of 12%

Cristiano Augusto

Marques De Carvalho

Paulo César

S Freire

Sanderson Emanuel Uchôa De Lima

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RIO 3 - World Climate & Energy Event, 1-5 December 2003, Rio de Janeiro, Brazil 81 
 
A STATIC LINEAR SIMULATION FOR THE THERMAL BEHAVIOR OF 
PHOTOVOLTAIC MODULES 
 
Cristiano Augusto da S. Freire 
ARCE - Agência Reguladora de Serviços Públicos Delegados do Estado do Ceará 
Fortaleza - CE - Brazil 
Phone: ++55- 85-4331283, cristiano@arce.ce.gov.br 
 
Paulo César Marques de Carvalho, Sanderson Emanuel Uchôa de Lima 
Departamento de Engenharia Elétrica, Universidade Federal do Ceará 
Fortaleza - CE - Brazil 
Phone/Fax: ++55-85- 2889585 / 2889580 
carvalho@dee.ufc.br, sanderson@dee.ufc.br 
 
Abstract: This paper has as main goal to evaluate the quality of a model to describe the 
behavior of the thermal conditions of photovoltaic (PV) modules. The methodology consists 
in compare measured and calculated PV modules temperature values. As result, the maximal 
deviations are in a range of 12%. 
Keywords: Photovoltaic modules; thermal behavior. 
 
1. Introduction 
The data used in this paper were collected in a PV powered reverse osmosis (RO) plant, 
installed in the community of Coité – Pedreiras, state of Ceará, Northeast Region of Brazil, 
where one finds yearly average temperature of 28ºC and a solar potential of about 2,000 
kWh/m2year. The main components of the plant are: 8 batteries (12V, 100Ah) with charge 
control, 1 RO unity (nominal drinking water product flow of 250 l/h) and 20 PV modules (55 
Wp each). The plant is equipped with sensors for global radiation, ambient temperature, 
module temperature, wind speed, water flow and direct voltage and current for the PV 
modules and batteries. Figure 1 shows a view of the PV modules and figure 2 shows the basic 
configuration of the plant.  
For this first project only power for the RO 
plant is supplied by the PV modules; power for 
the feed water pump is supplied by the electric 
grid (Carvalho et al., 2002). By a temperature 
increase of 2.7 K the PV-power output decrease 
on average 1% (Tegethoff, 1995). An important 
consequence of the influences of temperature is 
the variation of the MPP (Maximum Power 
Point). 
 
 
Figure 1: View of the photovoltaic modules     . 
82   C.A. da S. Freire, P.C.M. de Carvalho, S. E.U. de Lima: A static linear simulation for the thermal… 
 
Figure 2: Basic configuration of a photovoltaic powered reverse osmosis plant 
2. Collected data 
The data collection was accomplished during the year of 2001 and includes data of ambient 
temperature, module temperature, solar radiation and wind speed. For the present calculation, 
data come from the dry and rainy season of the state of Ceará: March 30th, June 30th, 
September 28th, November 15th. Figure 3 shows data of ambient and module temperature for 
these days. Only data collected between the sunrise and the sunset were used and during 
operation of the PV-system. 
 
Figure 3: Data of ambient temperature and module temperature. 
3. Results  
The quality of simulation is evaluated with a static linear model of temperature (Duffie, 
1991). The calculation of the relaxation time (Tr) for the modules results in simulation 
intervals of 8 min. After this time the system can be deemed to be static. For the simulation 
was used a higher value, with intervals of 10min and only the values during operation of the 
PV system in 2001. For the module temperature calculation it was used a static linear model: 
RIO 3 - World Climate & Energy Event, 1-5 December 2003, Rio de Janeiro, Brazil 83 
 
)(tGmTT ac ⋅+=         (1) 
where: 
 Tc – Module Temperature; 
 Ta – Ambient Temperature; 
 G – Solar Radiation; 
 m – linear coefficient. 
 
For the Equation (1) it is used a linear regression to evaluate the value of m. Figure 4 shows 
this linear regression. 
Figure 4: Determination of m through linear regression 
Using the result of the linear regression, the calculated value is m = 0.022 m²K/W. In this 
way, the temperature of the module can be calculated as: 
GTT ac ⋅+= 022.0        (2) 
To compare, a similar study gives a value of m = 0.021 m²K/W. for a PV system in Lagoa das 
Pedras, Ceará (Tegethoff, 1995). By comparing measured and calculated values, the maximal 
deviation obtained was about ±12%. Figure 5 shows curves of measured and calculated by the 
static linear model temperatures, together with the deviation D (%) for each time interval.  
 
4. Conclusion  
This paper compares measured and calculated PV modules temperature values. The calculated 
values are found by the use of a static linear thermal model. Maximal deviation from both 
values are in a range of 12%. In this way, the linear model is acceptable and can used in MPP-
Tracker programs or in PV systems simulations. 
 
5. Acknowledgments 
The authors thank Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) 
and Banco do Nordeste for the financial support of this project. 
 
84   C.A. da S. Freire, P.C.M. de Carvalho, S. E.U. de Lima: A static linear simulation for the thermal… 
 
Figure 5: Measured and calculated temperature of the module. 
REFERENCES 
Carvalho, P.; Oliveira, R.; Freire, C., 2002. Dimensionamento de uma instalação de osmose 
reversa acionada por painéis fotovoltaicos: a experiência de Coité-Pedreiras; IX Congresso 
Brasileiro de Energia – Rio de Janeiro. 
Duffie, J.A., Beckman, W.A., 1991. Solar Engineering of Thermal Processes, second ed. 
Wiley Interscience, New York, pp. 158-161. 
Tegethoff, W., 1995. Experimentelle und theoretische Analyse eines photovoltaisch 
betriebenen Pumpsystems unter besonderer Berücksichtigung der Aquiferdynamik, 
Diplomarbeit. Philipps-Universität Marburg, Fachbereich Physik, pp. 26-29.


A STATIC LINEAR SIMULATION FOR THE THERMAL BEHAVIOR OF PHOTOVOLTAIC MODULES

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A STATIC LINEAR SIMULATION FOR THE THERMAL BEHAVIOR OF PHOTOVOLTAIC MODULES

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