This paper presents an improved nonlinear fivepoint model capable of analytically describing the electrical behaviors of a photovoltaic module for each generic operating condition of temperature and solar irradiance. The models used to replicate the electrical behaviors of operating PV modules are usually based on some simplified assumptions which provide convenient mathematical model which can be used in conventional simulation tools. Unfortunately, these assumptions cause some inaccuracies, and hence unrealistic economic returns are predicted. As an alternative, we used the advantages of a nonlinear analytical fivepoint model to take into account the nonideal diode effects and nonlinear effects generally ignored, which PV modules operation depends on. To verify the capability of our method to fit PV panel characteristics, the procedure was tested on three different panels. Results were compared with the data issued by manufacturers and with the results obtained using the fiveparameter model proposed by other authors.
Several methods have been suggested for predicting the behavior of operating photovoltaic (PV) modules. The basis of most of them is the equivalent electrical circuit represented in the simplest way by a current source in parallel with one or many diodes describing the PN junction. An improved version includes parasitic series and shunt resistances. In general, multidiode representations modeling PN junctions of PV devices offer accurate results at the expense of long computational time. For simplicity, the singlediode model is used in this paper. This model offers a good compromise between simplicity and accuracy [
Due to the transcendental nature of the
However, all these previously proposed models for PV modules pointed out the following assumptions.
All the connected cells are identical and work under the same conditions of illumination and temperature.
The shortcircuit current is equivalent to photocurrent and hence proportional to the level of solar irradiation.
The variation of opencircuit voltage with irradiance is known to follow a logarithmic function based on an ideal diode equation, and the effect of temperature is due to an exponential increase in the diode saturation current with an increase in temperature.
Voltage drops in the conductors connecting the cells are negligible.
The main purpose of this paper is to present an improved methodology for characterizing PV systems. Based on the classical fivepoint model, amendatory terms are introduced to take into account the effects of nonideal diode parameters and nonlinearity effects that PV module behaviors depend on. Furthermore, series resistance is evaluated using nonlinear fitting of experimental data. Results are compared to experimental data provided by PV modules manufacturers and an existing model.
An ideal PV module consists of a single diode connected in parallel with a light generated current source (
Ideal PV circuit model.
Equation (
PV circuit model with series and parallel resistances,
The fivepoint model is an analytical method to extract related device parameters from values of key operational quantities measured from welldefined points of
Analyses of outdoor tested PV module result in some deviations of shortcircuit current from its linearity with solar irradiance
The evaluation of the opencircuit voltage based on an ideal diode equation leads to difficulties in replicating the behaviors of tested PV modules. Additional terms or some correction coefficients must be introduced to account for the shunt resistance, series resistance, and the nonideality of the diode. Based on the model given by Van Dyk et al. [
Electric generators are generally classified as current or voltage sources. The practical PV device presents a hybrid behavior, which may be of current or voltage source depending on the operating point [
Nominal parasitic resistances
Beyond the core losses related to the selective absorption of light and recombination, there are significant energy degradations due to parasitic resistances. Resistive effects in solar cells reduce efficiency by dissipating power in the resistance. Making their evaluation based on operating conditions is extremely important for studying the electrical behaviors of photovoltaic devices.
The series resistance of solar cell is a parameter of particular interest because of its influence on the maximum available power and the fill factor. It is also a parameter that indicates in some way the quality of device and can be used as production test [
At shortcircuit point,
At the opencircuit point,
At maximum power point MPP,
Rearranging (
The constants
The variation of the opencircuit voltage is related to the variations of the solar radiation intensity and cells temperature. To calculate
The capabilities of the nonlinear fivepoint model to predict the electrical response of PV devices is validated by measured experimental data of selected PV modules. Three PV modules of different technologies are used for investigation; these include monocrystalline, multicrystalline and thinfilm types, namely, Shell SM55, Shell S75, and Shell ST40, respectively. The experimental data were extracted from manufacturer’s data sheet [
Specifications for the three modules used in the experiments.
Parameter  Monocrystalline (Si) SM55  Multicrystalline (Si) S75  Thinfilm (CIS) ST40 


3.45  4.7  2.68 

21.7  21.6  23.3 

3.15  4.26  2.41 

17.4  17.6  16.6 

1.4  2  0.35 

−76  −76  −100 

36  36  42 
By applying the nonlinear fivepoint model described in the previous subsection, the computed results of selected PV modules are obtained. The procedure was executed for various irradiance and temperature levels. To evaluate the accuracy of the proposed model, the results obtained are compared to the fiveparameter model described in [
The constants
Constants estimation for PV modules.
Constant 




Monocrystalline SM55  0.984  0.058  1.064 
Multicrystalline S75  0.996  0.052  1.155 
Thinfilm ST40  0.998  0.087  1.343 
In Figures
Calculated
Calculated
Table
Parameters for the proposed model.
Parameter  Monocrystalline SM55  Multicrystalline S75  Thinfilm ST40  

Proposed model  Fiveparameter model  Proposed model  Fiveparameter model  Proposed model  Fiveparameter model  
1000 W/m²  

3.453  3.457  4.715  4.715  2.702  2.694 








1.338  1.183  1.311  1.388  1.361  1.75 

0.3  0.3625  0.2  0.1281  1.3  0.7457 

350  186.5  179  127.4  250  140.8 
 
800 W/m²  

2.771  2.765  3.774  3.772  2.157  2.155 








1.486  1.183  1.432  1.388  1.571  1.75 

0.2371  0.3625  0.1283  0.1281  1.02  0.7457 

436  233.1  223.6  159.2  312.5  175.9 
 
600 W/m²  

2.087  2.074  2.832  2.829  1.616  1.617 








1.606  1.183  1.519  1.388  1.771  1.75 

0.1762  0.3625  0.117  0.1281  0.7465  0.7457 

578.7  310.8  297.8  212.3  416.7  234.6 
 
400 W/m²  

1.4  1.383  1.89  1.886  1.076  1.075 








1.698  1.183  1.512  1.388  1.95  1.75 

0.1155  0.3625  0.07654  0.1281  0.4813  0.7457 

862.5  466.1  446.1  318.5  625  351.9 
 
200 W/m²  

0.707  0.6913  0.9473  0.9429  0.5377  0.5388 








1.763  1.183  1.582  1.388  2.085  1.75 

0.05624  0.3625  0.03706  0.1281  0.2278  0.7457 

1706  932.3  890  636.9  1250  703.8 
The computed parameters using the proposed and the fiveparameter models for temperature variation are shown in Table
Parameters for the proposed model (
Parameter  Monocrystalline SM55  Multicrystalline S75  Thinfilm ST40  

Proposed model  Fiveparameter model  Proposed model  Fiveparameter model  Proposed model  Fiveparameter model  
60°C  

3.502  3.507  4.744  4.73  2.712  2.706 








1.067  1.183  1.042  1.388  1.064  1.614 

0.2625  0.3625  0.1747  0.1281  1.114  0.7457 

350  186.5  179  127.4  250  140.8 
 
40°C  

3.474  3.478  4.728  4.721  2.706  2.699 








1.211  1.183  1.185  1.388  1.221  1.614 

0.2828  0.3625  0.1884  0.1281  1.214  0.7457 

350  186.5  179  127.4  250  140.8 
 
20°C  

3.446  3449  4.711  4.712  2.7  2.692 








1.385  1.183  1.357  1.388  1.413  1.614 

0.3061  0.3625  0.2042  0.1281  1.331  0.7457 

350  186.5  179  127.4  250  140.8 
These related device parameters are strongly influenced by the irradiance and temperature. However, computed parameters using the fiveparameter model present an obsolete dependence to the variation of environmental conditions. It is obvious that the use of constant parameters determined under STC must bring deviations in replicating the observed behavior of PV module in other operating conditions [
For the thinfilm type PV module, particularly large values of ideality factor are obtained in low irradiance due to decreasing series resistance. Theoretical approaches predict diode ideality factors in a range
To provide a clear picture of the precision of the proposed model, the errors using the proposed and fiveparameter models are computed. The absolute error is defined as the absolute difference between the experimental and computed current values of the
Absolute errors for different irradiance levels of Shell SM55 (a), Shell S75 (b), and Shell ST40 (c).
Absolute errors for different temperature levels of Shell SM55 (a), Shell S75 (b), and Shell ST40 (c).
The proposed model globally shows fewer errors than the fiveparameter model for various environmental conditions analyzed. This is expected because values of many related device parameters computed using the fiveparameter model do not vary with variation of environmental conditions as shown in Tables
In most cases, exceptionally high errors occur near the vicinity of MPP. This is ascribable to the fact that the value of the series resistance plays a dominant role in determining the curvature of the
In this paper, modeling of electrical response of PV modules using an analytical nonlinear fivepoint model is described. Unlike the previous models suggested by other researchers, the proposed model computes the PV module parameters at any irradiance and temperature point, using only the datasheet information for a PV module. The accuracy of the proposed model is evaluated using experimental data from the manufacturers of three PV modules of different types. Its performance is compared to a popular fiveparameter model. The observed superior accuracy of the proposed model to describe these PV modules behaviors suggests that this proposed model might also represent an even better phenomenological description of the electrical mechanisms prevalent in these particular devices and the nonlinear effects that they depend on. In addition, research on analysis and replication of operation of these specific devices in terms of the proposed model is currently being carried out, but the interest and scope of the proposed nonlinear fivepoint model is noteworthy. Beyond its simplicity of implementation, the proposed model adequately describes the evolution of these specific devices physical phenomena when subjected to temperature and irradiance variations, and hence it is envisaged that the proposed model can be a valuable design tool for PV system during the production as well as during the use.
Ideality factor
Copper indium selenide material
Irradiance
Current
Maximum power point
Resistance
Standard test conditions
Voltage
Saturation current
Photocurrent
Silicon material
Thermal voltage
Number of cells in series
Opencircuit voltage
Shortcircuit current
Reference conditions
Maximum power point
Opencircuit
Series
Shortcircuit
Shunt.
Temperature coefficient
Constant
Constant
Constant.
There is no competing interests in the validity of this paper due to the choice of the Shell SM55 and Shell SP5 modules.
The authors are grateful to Dr. Obounou, Dr. Akana, and Miss Enoh for their efforts in the realization of this work.