Comparison between the different numerical models ...

IPASJ International Journal of Electrical Engineering (IIJEE) Web Site: http://www.ipasj.org/IIJEE/IIJEE.htm Email:[email protected] ISSN 2321-600X

A Publisher for Research Motivation ........

Volume 5, Issue 6, June 2017

Comparison between the different numerical models and determination of parameters characteristics of photovoltaic module of LRAER M. M. MENOU1,3,*, A. YAHFDHOU1,2, A. K. MAHMOUD1 and I. YOUM2,3 1

Applied Research Laboratory for Renewable Energies ' LRAER ' University of Science and Technology and Medicine, Nouakchott, Mauritania

2

Laboratory of Semiconductor and Solar Energy, ' LASES ‘, Faculty of Science and Technology, University Cheikh Anta Diop, Dakar, Senegal 3

Studies and Research Center of Renewable Energies ' CERER ‘, Dakar, Senegal

ABSTRACT The objective of this paper is to establish a systematic approach to the comparison of the performance of mathematical modeling models of photovoltaic systems most used in the literature. This desired performance is normally evaluated under the standard test conditions (STC), where an average solar spectrum of AM 1.5 is employed, the sunshine is normalized to 1000W / m², and the cell temperature is set equal to 25 ° C. In this paper, two methods of modeling the cell or the panel are presented. These two methods are based on the data provided by the manufacturers of solar cells or panels, which will be presented. A comparison of the traditional modeling method for an electrical circuit that is equivalent to a photovoltaic cell or panel is called the Madison Model (MM), with the Cenerg Model, under the term (MC). The mathematical modeling process is realized with the two models (MM and MC) for the cases, a diode, two diodes and for the grouping of the photovoltaic panels of the LRAER. Thus, we try to determine the parameters of the mathematical models (MM and MC) that are used. This is done with the aim of comparing their precisions by comparing the results of simulations obtained and then by comparing them with the data of the experimental data acquisition system for the ATERSA 75 W modules of the LRAER, of UNAA. It is important to note at the end of this summary that the main objective of this paper is to compare the mathematical models (MM and MC) and the comparison of the different technologies of crystalline silicon, amorphous silicon, CIS and Of CdTe does not fit into these objectives, although sometimes there is a shift in this direction. However, they are modules that can easily be found in the trade.

Keywords: Photovoltaic generator model (GPV); Comparison of MM and MC calculation methods; Characteristics I (V); Characteristics P (V).

1. INTRODUCTION In the bibliographic study [1,2,3], two physical approaches have been identified, the first one requiring measurements on the photovoltaic sensor once installed, as in the 'Sandia' and 'Cenerg' models, the second approach prioritizes the use only of the data provided by the manufacturers, as in the case of the 'Madison' model. The Sandia model was developed by Sandia National Laboratory (Albuquerque, USA) and is based on a photovoltaic sensor, enabling both to test and estimate its productivity [4]. About the Cenerg model is a model developed by the Energy Center that is based on the one-diode model. This model has been experimentally validated by the Center Energy in Sophia Antipolis [5]. As for the Madison model, it was developed by the University of Madison (Wisconsin, USA) for the programming of a module simulating PV sensors called 'PHANTASM' chained to the building thermal simulation program 'TRNSYS' [6]. Like the model 'Cenerg', it is based on the electrical model of the cells in the form of 'model with a diode'. The most important thing to remember for this model is the fact that it proposes a method which makes it possible to calculate the performances of the PV module from the data provided by the manufacturers. It then fails to emphasize that these equations represent the variation of the current of the cell or of the panel with the output voltage, and they show the


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IPASJ International Journal of Electrical Engineering (IIJEE) A Publisher for Research Motivation ........


Web Site: http://www.ipasj.org/IIJEE/IIJEE.htm Email:[email protected] ISSN 2321-600X

influence of several terms which may influence the determination of the characteristic I (V). In this work perspective, it is important to make a comparison between the MC and MM models: By simulations through the Matlab software for these two models, similarly, by obtaining the simulation results, in search of the best Models of representations of the characteristics I (V) and P (V), by the comparison in terms of errors between the models and at the end, by the setting in motion of a methodology of validation of the results of simulations. *Corresponding Author: Tel. +22236303457, E-mail address: [email protected] (Mohamed M. MENOU). In order to achieve our objective, we chose two reliable electric models with an acceptable precision to compare the performance of the two modeling methods (MC and MM) in the climatic conditions of our countries.

2. EXPERIMENTAL DEVICE OF LRAER The experimental design is designed to provide electrical energy from both renewable sources (wind and solar) and a backup generator to charge the storage system and meet the load demand (CA). The system is optional, it is possible to stop the operation of the wind, to let only the solar power, or to stop the solar power to let only the wind. 2.2 Constituents of the experimental device This is achieved by the photovoltaic generator of LRAER which consists of 16 modules (Atersa). Its configuration gives four panels (Figure 1), which are connected in series to have (48V) and then they are paralleled with the other groups. The total peak power of the system is 1.2 Kwp. The surface area of the generator system is 8.6 m². It is important to note that the storage system capacity (1200 Ah). The energy storage device implanted in this hybrid system is connected directly to the DC bus. There are 24 accumulator elements of 2 V. The elements are connected in series. The DC bus is connected to AC network via 5 Kw reversible power converter, Trace Engineering, SW. It will be necessary to add that the converter should be able to deliver a power higher than the peaks of the load. This configuration is proposed in Fig.1.

Figure 1 PV / wind / diesel hybrid system (LRAER) 2.2 Data of the monocrystalline GPV (silicon) The advantages of silicon: This semiconductor is easily doped with boron and phosphorus; Silicon is the second most common element in the Earth's crust: 02 (46%), Si (28%), Al (8%); It possesses a natural Si O2 oxide with excellent electronic properties; Production technologies are now matured and their industrialization is not difficult; The panels offer high conversion efficiency; The lifespan and aging of the GPV panels are under control. On the other hand, the disadvantages of crystalline silicon are: a cost of manufacture which is still high for the countries of the south; A performance that decreases sharply as the modulus temperature increases (which will allow both models (MM and MC) to be tested for changes in site temperatures); A performance which decreases strongly at low illumination (which will allow to test the two models (MM and MC) to the changes of the insolation on the site) and lack of flexibility of use (rigid surface ...). Above, the data of the monocrystalline photovoltaic panel (silicon) manufacturer is given in Table 1.


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Table 1: GPV characteristic Specification ATERSA 1000 W/m2 25°C AM 1.5 Number of series 98090135 Number of panels 16 Model AP-7105/A-75 Maximum power 75 W Short circuit current Icc 4.8 A Open circuit voltage Vco 21 V Maximum current Imp 4.4 V Maximum voltage Vmp 17 V Dimensions 1,206 × 0,53 × 0,034m Weight 8,2kg Mode de connexion 4 panels (//) of 4 en séries Area used by the modules 8.6 m2

3. ELECTRIC CONFIGURATION AND MATHEMATICAL MODELING OF MODELS (MM AND MC) 3.1 Electric models of the GPV The literature [10, 11, 12, 13] also proposes several electrical models for the GPV (Fig. 2 and Fig. 3), which are also called GPV equivalent circuits, in order to reproduce the behavior of the cell using electronic components. The circuits which have been proposed in this paper are those which have been used most frequently in the literature to model the crystalline cells constituted by a p-n junction. They are single and dual diode circuits. The recombination losses are proportional to the concentration of carriers and consequently to the photocurrent. Therefore, in the literature, a 1 to 2 diode is added to the electric model to account for these losses in layer i, proportional to the luminous intensity. In this context, the 1-diode model of the GPV (Fig. 2) and the 2-diode model of the GPV (Fig. 3) proposed in this paper are considered to be among the most accurate. Proposed by other authors.

Figure 2 1 diode model of GPV

Figure 3 2 diode model of GPV

3.2 Mathematical models MM and MC Several models of photovoltaic cells are proposed for the configurations (Fig. 2 and Fig. 3) in the literature [14, 15], among these mathematical models, 1 and 2 diode models are generally retained as the most Adapted to model a cell or a photovoltaic panel in normal operation. It is sought through the electrical modeling of photovoltaic generators which is proposed to be able to show the following main advantages: ease of use through mastering the equivalent circuits of equivalent photovoltaic generators, better popularization of photovoltaic generator properties and Better understanding of the complex phenomena that occur in photovoltaic generators. Thus, if the literature proposes several electrical models for the GPV, it also proposes in parallel several mathematical models for example the Madison Model (MM), with the Cenerg Model, under the term (MC) which interests us in the framework of this work. In sum, it is still considered mathematically difficult to determine the model parameters on a diode and the dual diode model due to the presence of exponential term of the junction equation (PN) of the diode. In the case of the extraction of the parameters which is proposed later, it is important to note that the equations in (3.2.1 and 3.2.2) are nonlinear, programs are then proposed to optimally adjust the parameters so that the modeled curves correspond to the experimental values. Once these parameters are known, it is subsequently possible to reproduce, with the aid of the equivalent circuit (Fig. 2 and Fig 3), the behavior of a panel. As a result, just vary Iph. It should be noted that this is not the case for amorphous


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silicon panels for which one or more additional terms must be added if one wishes to model their behavior correctly (this is not the case in this study). 3.2.1 Model 1 diode of GPV

3.2.2

Model 2 diode of GPV

MM model


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To conclude this section, it is important to note that the models that have been proposed are those most used in the literature, these two models treat cell or photovoltaic panel as current source, dependent on sunshine, connected in parallel with 1 diode or 2 diodes, in parallel with resistor Rsh and in series with series resistance Rs. Both models have been developed and take into account the multi physical process related to the conversion of photovoltaic energy. Similarly, the two modeling methods have been chosen by their presence in the literature. They are considered the most adapted by the authors [16, 17, 18] to solve the equation models with one or two exponential equations. The approaches used in these two methods are also based on the data of the manufacturers of the solar panels that have been presented.


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The aim of the proposed modeling process is to determine the constant parameters in the equations chosen with the determination of the precision that will follow, for the two modeling methods (comparison of simulation results between models at the beginning and to the experimental data, thereafter).

4. EXTRACTION OF PARAMETERS FOR ATERSA 75W These parameters are not measurable quantities and are not generally included in manufacturers' data. Consequently, they must be determined from the systems of equations I (V) already given, for different operating points (given by the manufacturers). Thus, for the extraction of the parameters of ATERSA 75 W, several cases are recorded: Extraction of the parameters for the model MC to a diode, parameters of the model MC with double diodes and parameters of the model MC with double diodes. 4.1 Seven parameters of MC model with 1 diode (ATERSA 75) Table 2: Seven parameters of MC model with 1 diode (ATERSA 75) Parameters Value P1 0.0048 P2 0.0001 P3 -0.0005 P4 202.5 A 1 Rs 0.28 Rsh 115.9

4.2 Eight parameters of MC model with 2 diodes (ATERSA 75) Table 3: Eight parameters of MC model with 2 diodes (ATERSA 75) Parameters P1 P2 P3 P4 P5 A Rs Rsh

Value 0.0048 0.0025 -0.0027 200.7 0.00019 1 0.27 112.42

4.3 Parameters of the dual-diode MC model (ATERSA 75) Since the manufacturers have provided a part of the parameters, these are in particular the no load voltage (VOC), the short-circuit current (ISC), not to mention the maximum power and voltage, respectively, (VMP) and (IMP). This is why, subsequently, it will be necessary to determine the sequence of these parameters. It is necessary to find three other parameters (I0, IL and g) by forcing the passage of curve I (V) through the points retained. This is obtained by solving the system of equations in which these. Therefore, in this part of extraction of parameters photovoltaic panel, one should not forget to note the nonlinear nature of the system of equations which is solved through the use of the Newton method. It should also be noted that the solution by Newton's method is very sensitive to the initial conditions. Therefore, initial conditions that are not well chosen and do not always correspond to correct values. This can introduce errors, as it can distort the solution. Nevertheless, if the approach is precise, Newton's method is considered to be efficient and yields coherent results.


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5 SIMULATION I(V) AND P(V) OF MM ET MC MODELS In the previous section, we presented the basics of the mathematical modeling of the PV generator. This model will be presented under the Matlab environment in which the different levels of programming language will be used, above, to carry out the various simulations in accordance with the objectives of this work. 5.1 Simulation I(V) and P(V): 1 diode model (G=1000W/m2, T=298.2 K) This simulation allows to characterize the cell or the panel and at the same time to compare the performances of the two models used, depending on the influence of different climatic and other parameters on the I (V), P (V) That are addressed.

For Fig. 3, I (V); Before comparing, we noticed that in Fig. 4, simulated for a sunshine of G = 1000 w / m², the current Isc = 4.8 A for an open circuit voltage close to 21V. We also have, for the comparison between the two curves of the two models of 1 diode (MM-red and MC-blue) which shows a voltage difference of 0.02v. We can say that the first model (MM-red) is closely followed by the second model (MC-blue). For Fig. 4, P (V): The two curves (Fig. 5), above, show a power difference of the order of 0.23w for the two models of 1diode (MM-red and MC-blue). The first model (MM-red) is closely followed by the second model (MC-blue).

5.2 Simulation I(V) and P(V): 2 diodes model (G=1000W/m2, T=298.2K)


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For Fig. 6, I (V): We have the comparison between the two curves, for the two models of 2 diodes (MM-red and MC-blue) shows a voltage difference of 0.02v, this is the same value we found in the simulated model for 1 diode. The first model (MMred) is closely followed by the second model (MC-blue). For Fig. 7, P (V): As regards the two curves, P (V) above, show a power difference of the order of 0.23w, for the two models of 2 diode (MM-red and MC-blue), this Value is similar to the 1 model. The difference in behavior is very minimal, the first model (MM-red) is closely followed by the second model (MC-blue). 5.3 Influence of resistances Rs and Rsh of MM et MC models (G=1000W/m2, T=298.2 K) The simulations are carried out for: - The constants that are retained: G = 1000W / m2 and T = 298.2 K, - The two models (MM and MC) for different values of Rs = [0.23, 0.28 and 0.32] Ohm. 5.3.1 Influence of resistance Rs: MM and MC models (G=1000W/m2, T=298.2K)

For I (V), see Fig. 8: The series resistance acts on the slope of the characteristic, Fig. 8, in the area where the cell behaves as voltage generator, and when it is raised it decreases the short-circuit current value. The performance of photovoltaic cell is all the more degraded when Rs is large or Rs is low. We note that the series resistance is varied, in one of the models, the second model follows. Thus, we can signal the perfect harmony between the simulations of our two models, the two curves (MM-blue and MC-red) are superimposed. For P (V), see Fig. 9: As soon as the series resistance is varied, in one of the models, the second model follows. The comparison between the curves of the model (MM-blue) and that of the model (MC-red) gives no appreciable difference even under the influence of the variation of the value of Rs. (V), is noted to the right of the characteristic, substantially, the red color gives the line. It has been found that there is a very good correlation between the simulation result and the experimental data delivered by the manufacturer. Regarding the difference between the model MM and MC, it is not quantifiable, given the almost superimposition of their curves. The remark that we have drawn is that the two models arrive at the same results, in this configuration. 5.3.2

Influence of resistance Rsh: MM and MC models


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For I (V), Fig. 10: The shunt resistance is directly linked to the manufacturing process, and its influence is only felt for very low values of the current (close to the short-circuit current). Fig. 10 shows that this influence results in an increase in the slope of the curve I-V of the panel in the zone corresponding to an operation as a current source. This is due to the fact that an additional current varying linearly with the developed voltage must be subtracted from the photocurrent, in addition to the diode direct current. As for the comparison between the curves given by the model MM and MC, as soon as the shunt resistance is varied, in one of the models, the second model follows. There are no marked differences between the curves of the two models. Both models give almost the same result. The effect of the series resistance is very low and is only noticeable for a value of the parallel resistance. For P-V, Fig. 11: In this case the variation of Rsh, leads to a very small variation of the curves, but identical for both models. We observe a superposition of the curves of the two models. 5.4 Simulation I(V) and P(V): 1 diode model of GPV (MM and MC) The simulations are carried out for the LRAER site: - The constants that are retained: G = 1000W / m2 and T = 298.2 K, - The two models (MM and MC) for a group of panels For the LRAER, we have Ns = 4 (number of panels in series) and Np = 4 (number of panels in parallel)

For Fig. 12, I (V): We note for the two curves, of the two models of a diode (MM-red and MC-blue) shows a voltage difference of 0.2v. This value was found in the simulated model for a panel. The first model (MM-red) is followed closely by the second model (MC-blue) in the case of the grouping. For Fig. 13, P (V):


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The curves, P (V) above, show a power difference of the order of 3W, for the two models of a diode (MM-red and MCblue). The difference in behavior is very minimal. The first model (MM-red) is closely followed by the second model (MC-blue). 5.5 Influence of sunshine I(V) and P(V), 1 diode model The results of simulation of the GPV characteristics I (V) and P (V) are done to visualize the influence of the sunshine, this is obtained by fixing the ambient temperature (T = 25 ° C) and varying Sunshine in a sufficient range.

We note for the two curves (Fig. 14), of two models of a diode (MM-red and MC-blue) show, for the first curves, counting from the bottom up: • For a sunshine of 600 W / m², we have a current difference of 0.115A and voltage of 0.120V, • For a sunshine of 800 W / m², we have a current difference of 0.077A and voltage of 0.050v, • For a sunshine of 1000 W / m², we have a current difference of 0.001A and voltage of 0, 020 v. In Fig. 14, the first observation is related to the fact that increase in the luminous flux causes the short-circuit current (ICC) to increase, as well as the open-circuit voltage (VOC). The second observation in (Fig. 14) shows that for sunshine G = 1000 w / m², we have current ICC = 4.8A and for G = 800w / m2, we have another current Isc = 3.8A. See that the current undergoes an important variation, when the sunshine increases. This implies that the short-circuit current also increases. But on the other hand, the tension varies slightly what makes it possible to write, that the more one rises in value in current, the difference, between our models decreases in current in a way and in tension. Indeed, the difference in behavior is very minimal between these two models and can be zero, if one increases in sunshine. This implies that the ideal sunshine for simulation through these two models is 1000 W / m². This value (1000 W / m²) gives two curves that are almost confused. For Fig. 15, P (V): On the other hand, the curve (Fig. 15) shows that the power delivered by PV generator (Atersa module 75) depends on the irradiation it receives. The greater the amount of sunshine, the greater the power generated by the panel. Thus, for the two models of a diode (MM-red and MC-blue) shows, for the first two curves (Fig. 15), counting from bottom to top: - For a sunshine of 600 W / m², we have a difference of power 2.01 w and voltage of 0, 120 v, - For a sunshine of 800 W / m², we have a power difference of 1.4 w and voltage of 0.05v, - For a sunshine of 1000 W / m², we have a power difference of 0.23 w and voltage of 0.020 v. In figure 15, we find that increasing the luminous flux causes the circuit voltage to increase. We note that the power delivered by the PV generator (module Atersa75) rises, when the sunshine increases.


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Similarly, Fig. 11 shows that for the sunshine of two models increase in power, according to the increase of the sunshine in the interval [600w / m², 1000w / m²]. 5.6 Influence of temperature I(V) et P(V): 1 diode model

Before, any discussion, we retain the constant values for T = 298.2K and G = 1000W / m2. Moreover, under these conditions, it can be seen (Fig. 16) that the temperature has a negligible influence on the value of the short-circuit current. On the other hand, the open circuit voltage drops rather sharply as the temperature increases. It is thus deduced that the panel can continue to provide a correct voltage, with a decrease in the sunshine, therefore the extractable power decreases. Similarly, it is important to note that the power of the panel (Fig. 17) decreases by about 1.96 w on average. So, let's go back to our comparisons with the different models. For Fig. 16, I (V): The two curves (Fig. 16), of the two models of a diode (MM-red and MC-blue) show, for the first curves, counting from bottom to top: - For a temperature of 25 ° C, we have a current difference almost zero, on the other hand a voltage difference of 0, 020v, - For a temperature of 50 ° C, we have a current difference of almost zero, and a voltage difference of 0, 61 v. - For a temperature of 75 ° C, we have a near zero current difference and a voltage difference of 1.25 v. If, in Fig. 16, the first observation is related to the fact that the increase in temperature affects the open-circuit voltage (VOC) without initiating a noticeable change in the current for both models. On the other hand, the curve (Fig. 17) shows that the power delivered by the PV generator (Atersa module 75) depends on the temperature it receives. The power decreases, with the temperature increasing, for both models. Then, with regard to the second observation in (Fig. 16), it can be seen that for the 25 ° C sunshine the two curves recorded the least possible differences for both models. In this particular case, both models have almost the same, behavior. This temperature (25 ° C) is the most suitable for the module. For Fig. 17, P (V): The two models of a diode (MM-red and MC-blue) show, for the first two curves (Fig. 17), counting from bottom to top: - For a temperature of 25 ° C, we have a voltage difference of 0, 020 v, with a power difference of 0.2W, - For a temperature of 50 ° C, we have a voltage difference of 0, 61 v and a power of 4.4W, - For a temperature 0 ° C, we have a voltage difference of 1.25 v and a power difference of 8.4 w. But again, in Fig. 17, we find that the higher the temperature, the lower the generation power. Similarly, both models record a lower power difference, for temperature 25 ° C. 5.7 Discussions In this work, we have presented two close electrical models that best describe the physical phenomena in the GPV and among the most used ones. Then we proposed for these electric models, two numerical modeling approaches that lead


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to the establishment of mathematical equations that also govern the dynamics of the GPV. Thus, we have obtained, electric models and mathematical approaches to describe a real entity and its operation. We have subsequently, thanks to the real entity existing at the LRAER of the FST of Nouakchott, adopted an approach to the research of the parameters of electrical circuits, considered complex in the literature which will subsequently be validated in the course of the work. Thus, the modeling process was given as follows through, the determination of constant parameter parameters, determination of the remaining parameters, characterizing the GPV, comparison of models (MM and MC) to determine the degree of accuracy of Two methods of modeling by simulation and finally by comparison with experimental data recorded at LRAER. Therefore, modeling for the design of a module or GPV depends largely on the choice of electrical circuits (without a diode, with a diode, with two diodes, without Rs, with Rs, without Rsh, With Rsh) to approximate the actual functioning of the GPV, it also depends on the numerical modeling and the type of numerical model developed to make the simulation, not forgetting the influence of different factors on the modulus, Sunshine and temperature. It is observed that the photovoltaic panel comprises parasitic resistances in series (Rs) and in parallel (Rsh). These two types of resistances have the effect of reducing the shape factor and consequently the power delivered by the cell. Finally, after a comparison between the simulation results obtained by these two models (MM and MC) and the experimental results, we draw the following conclusions: The shunt resistance in the two models does not affect the characteristic I (V ), As well as, the choice of electric models must lean on the parameter of the series resistance that we have noticed influential. It should be noted that the two models MM and MC, are performing and do not translate a great difference in precision. In the same way, the characteristics developed in the work, translate the physical phenomena in the GPV in a precise way.

6. COMPARISON BETWEEN THE POWERS GENERATED AND SIMULATED BY THE MM, MC MODELS AND THE EXPERIMENTAL POWER FOR 3 DAYS Before proposing the experimental part, it is important to give the standards for the application and operation of meteorological measurements. One of the standards that is more in line with this paper is IEC 61724, which provides procedures for monitoring the performance of photovoltaic systems, recommendations for measurement, transfer and analysis of data for PV systems. The objective is to be able to compare the performance results of the mathematical models that have been used, which leads to a background to a comparison of the electrical models of the GPV that are given in this work. This comparison by means of the actual measurements on the LRAER site requires a methodology for the measurement of system-specific data. First, the parameters to be considered are cited. The luminous intensity in the plane of the module, the ambient temperature and the wind speed for meteorology. For PV modules the current, voltage and output power, its operating temperature, inclination angle and orientation. For the measurement of illumination: The illumination shall be measured in the plane and as close as possible to the PV modules. The illumination probe must have a measuring accuracy of 5% or more. These conditions are given for the parameters that are the most retained in the literature: 1. For ambient temperature measurement: The ambient temperature measurement must be carried out near the platform and the uncertainty must not exceed 1 ° C, 2. For the measurement of wind speed: The wind speed must be measured close to the platform and at a height corresponding to that of the PV modules. 3. For measuring instrument accuracy better than 0.5 m s-1 for wind speeds of less than 5 m s-1 and better than 10% for values greater than 5 m s-1. Not forgetting to note for all the standard test conditions that have been set to characterize the modules of the GPV. This makes it possible to compare the performance of the PV modules independently of the dies, the manufacturers, the commercial PV modules. LRAER solar sensor system: The LRAER has its own measuring equipment, there are two types of illumination sensors that allow acquisition of the intensity of the global light radiation. Pyranometer on a horizontal plane: According to the International ISO 9060 standard and the World Meteorological Organization, a pyranometer is a heat flux sensor used to measure the amount of solar energy in natural light. It allows the measurement of the power of the global solar radiation, in W.m-2. It is sensitive in a spectral range from 300 μm to 3000 μm. Reference panel: The reference panels use a crystalline silicon solar cell, which has a low impedance resistance, exploited at the limit of the short circuit, that is to say in the part of the characteristic where the current is exactly proportional to irradiance.


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Pyrheliometer: This instrument is permanently oriented towards the sun and measures only the radiation coming from the solar disk alone. A black surface captures the light radiation and the temperature difference between this surface and the body of the instrument is proportional to the irradiance of the direct radiation. It should also be added that there is an anemometer installed at the level of the panels.

Figure 18 LRAER solar sensor system Then, the results of measurements made it possible to propose the power for the two models which is given by the equation P = V (I), on the other hand the experimental power is given by the data acquisition system of the LRAER. 800

MM model

Experimental Data

MC model

700

Power [W]

600 500 400 300 200 100 0

0

10

20

30

40

50

60

70

Hours

Figure 19 Comparison between the simulated powers of the MM and MC models and the experimental power for 3 days

4 MM model

MC model

Error [%]

3 2 1 0

0

10

20

30

40

50

60

70

Hours

Figure 20 Comparison of the relative error of the MM and MC models


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Fig. 19 and 20 were obtained by means of horizontal illumination measurements taken at the level of the LRAER. The equipment used which has been described shows that one rarely finds oneself in the standard illumination condition at 1000 W m-2 (not to mention the distribution of the solar spectrum). Thus, there is a real difference between the STC conditions in which the modules and the actual conditions of the LRAER site are characterized. It is then normal to ask how the modules work under conditions other than standard and how the weather conditions of the site influence the mathematical models and electrical models of the GPV. In addition, our final objective was to verify whether the models (MM and MC) were able to predict the performance of monocrystalline (silicon) GPV. To validate the model, we chose three typical days (Fig. 19 and 20): a sunny day (maximum 720 w, a slightly less sunny day (below 700 w) and a cloudy day with short periods of the output power of the GPV for both MM and MC models (Fig. 19) visually shows a negligible difference, while a slight difference is recorded (Fig. 20). The experimental data. 6.1 Absolute error comparison for the two models at STC Table 4: Absolute error comparison for both models at ST Parameters

Manufactures data

MM model

Relative error MM

MC model

4.8 21 4.4 17 75

4.7926 20.98 4.4 17.1 75.24

0.73 0.02 0 0.1 0.24

4.7885 20.93 4.3891 17.09 75.09

Short-circuit current (A) Open circuit voltage (V) Maximum current (A) Maximum voltage (V) Maximum power (W)

Relative error MC 0.011 0.07 0.011 0.09 0.09

Subsequently, Table 4 gives a comparison, for the parameters of the constructor of the photovoltaic panel and those of the MM and MC models. With regard to the example of the short-circuit current, the relative errors between the manufacturer's data and the MM and MC models are respectively 0.73 (for MM) and 0.011 (for MC). The MC model appears to be more precise than that of the MM, to approach the parameters of the manufacturer. The total error recorded is less than 0.24 (except for the value 0.73). 6.2 Errors between simulated power and actual power (three days) Table 5: Comparison of error between simulated power and real power (three days) Relatives errors Date in hours 8 :00 9 :00 10 :00 11 :00 12 :00 13 :00 14 :00 15 :00 16 :00 17 :00 18 :00 19 :00

First day MM model 0.9869 2.218 0.3026 0.5166 0.4942 0.4601 0.5524 0.3933 0.0932 2.84 1.327 0.1394

MC model

Second day MM model

0.8092 2.307 0.2778 0.6899 0.6358 0.5862 0.6785 0.4904 0.2847 0.55 1.1119 0.1072

2.285 0.3281 0.3637 0.5332 0.4014 0.3638 0.1819 0.054 2.315 1.044 0.053 0.01


MC model

Third day MM model

MC model

1.991 0.6603 0.5654 0.6792 0.6467 0.63 0.5249 0.47 0.1461 2.481 0.8662 0.0378

2.086 0.2815 0.2544 0.5355 0.5095 0.4285 0.4358 0.2164 2.045 2.112 0.553 0.0471

1.808 0.75 0.4715 0.7606 0.6932 0.595 0.6479 0.45 1.727 1.795 0.4458 0.0339

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On the other hand, in Table 5, a comparison was made for the parameters recorded experimentally on the LRAER site and the MM and MC model data of the photovoltaic panel. Regarding, these relative error values, shows the degree of accuracy of the results, thanks to the comparison of the models with the experimental data.

7. CONCLUSION It is recalled in this section the principle of photovoltaic conversion, the fundamental electrical characteristics to be taken into account which are illustrated from measurements carried out in laboratories using crystalline silicon modules. It was at the outset exposed two electrical diagrams which make it possible to model the GPV. Then, it was presented the bases of the mathematical modeling of the GPV. Two models (MM and MC) are presented under the Matlab environment in which the different levels of programming language are used, above, to carry out the various simulations in accordance with the objectives that were originally set. From this point of view, it should be noted that the curves produced for the two models (MM and MC) follow one another and take the form dictated by the physical phenomena and the constitution of the GPV materials. The differences recorded in the simulations which call for the variation of Rs, sunshine and temperature are acceptable and do not greatly influence the physical analysis of the studied systems. These differences are explained by the fact that the photovoltaic modules are strongly influenced by the Rs resistance and the climatic conditions, particularly the solar irradiation and the temperature of the module. Moreover, we have carried out simulations for two circuits of models with one diode and two diodes. The differences recorded between these two circuits through the MM and MC model are not felt, and not influencing the results obtained. It should also be noted in this conclusion that the GPV modules are characterized under STC conditions. However, these conditions correspond to a clear sky without pollution for a sun high enough in the sky, a modulus in the normal plane to the rays of the sun (optimum) and a cell temperature of 25 ° C (which is never the case For a module that operates at 1000 W m-2). It must be said that it is observed through the results that STC conditions almost never occur. It should not be forgotten to mention that the models that have been proposed are those most used in the literature. But, it must be said that the most difficult of the two mathematical models is that of MC. This difficulty is related to the search for the parameters. (For an electrical circuit with a diode equivalent to a panel, it is necessary to look for seven parameters, but against two diodes, eight parameters have to be found). These modeling difficulties are perhaps at the source that the classic model (MM) is the most used in the literature compared to the model MC. Finally, the modeling proposed by the model MM uses directly the parameters of the constructor. NOMENCLATURE STC: standard test conditions, I: current supplied by the cell, IPV: photon-current of the cell, VT: Thermal voltage, K: the Boltzmann constant (1.38.10-23 Joules / Kelvin), T: the temperature of the cell in Kelvin, Q: the charge of an electron (1.6.10-19C), V: the voltage at the terminals of the cell RS: The series resistor characterizing the various resistances of contacts and connections, Ns: Number of cells, A1: Ideality factor of diode 1, A2: Ideality factor of diode 2, I01: reverse saturation current of diode 1, I02: reverse saturation current of diode 2, Id: The polarization current of the junction PN of the diode, Id1: The polarization current of the junction PN of the diode 1, Id2: The polarization current of the PN junction of diode 2, GPV: Photovoltaic generator, Es: the sunshine in the plane of the panels (W / m2), IPh: photon-current of the cell, Tj: Cell junction temperature (° C), IG: current supplied by the panel (A), VG: voltage at the generator terminal (V),


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ISat: saturation current of the diode, ISat1: saturation current of diode 1, ISat2: saturation current of diode 2, K: constant of Boltzmann, A: ideality factor of the junction of the diode, Eg: Energy of gaps, Eref: Reference sunshine 1000W / m2, Tref: Reference sunshine 25 ° C, Q: Elemental charge (1.6.10-19C), VT1: Thermal voltage of diode 1, VT2: Thermal voltage of diode 2, P1, P2, P3, P4, P5, are constant parameters

REFERENCES [1]Zadeh and A. Rezazadeh, Artificial bee swarm optimization algorithm for parameters identifications of solar cell modules, Applied Energy 102, 943-949, 2013. [2] M. Yahya, I. Youm, A. Kader, Behavior and performance of a photovoltaic generator in real time, International Journal of the Physical Science 6(18), pp. 4361-4367, 2011. [3] R.Khazzar, M.Zereg ‘Comparaison entre les différents modèles électriques et détermination des paramètres de la caractéristique I-V d’un module photovoltaïque’, Revue des Energies Renouvelables Vol. 13 N°3 (2010) 379 – 388. [4] Chenni R, Makhlouf M, Kerbache T and Bouzid A, ‘A Detailed Modelling Method for Photovoltaic Cells’, Energy, Vol. 32, N°9, pp. 1724 – 1730, 2007. [5] A. Yahfdhou, A.Mahmoud, I.Youm, Modeling and optimization of photovoltaic generator with Matlab/Simulink, International Journal of I Tech and E Engineering 3(4), pp. 108-111, 2013. [6] M. R. Alrashidi, M. F. Alhajri, K.M. El-naggar, A. K. Al-othman, A new estimation approach for determining the I-V characteristics of solar cells, Solar Energy 85, pp. 1543-1550, 2011. [7] D. Bonkoungou, Z. Koalaga, D. Njomo, Modeling and simulation of photovoltaic module considerin single-diode equivalent circuit model in Matlab, International Journal of Emerging Technology and Advanced Engineering 3(3), pp. 493-502, 2013. [8] Basim Alsayid Modeling and Simulation of Photovoltaic Cell/Module/Array with Two-Diode Model International Journal of Computer Technology and Electronics Engineering (IJCTEE) Volume 1, Issue 3, June 2012. [9] El Ouariachi M, Mrabti T, Tidhaf B, Kassmi K (2009b). “Regulation of the electric power provided by the panels of the photovoltaic systems”, Int. J. Phys. Sci., 4 (5): 294-309. [10] Vilalva MG, Gazoli JR, and Filho ER, ―Comprehensive approach to modeling and simulation of photovoltaic arrays, IEEE Transactions on Power Electronics, Vol.24, No. 5, pp. 1198-1208, May 2009. [11] Zhou W, Yang H, Fang Z (2007). “A novel model for photovoltaic array performance prediction”. Appl. Ener., 84 : 1187-1198. [12] King D. L., Kratochvil J. A. and Boyson W. E: 'Temperature coefficients for PV modules and arrays: measurement methods, difficulties, and results’; 26th IEEE Photovoltaic Specialists Conference, Anaheim, California, 1997. [13] King D. L., Kratochvil J. A., Boyson W. E., and Bower W. I: ‘Field experience with a new performance characterization procedure for photovoltaic arrays’; 2nd World conference on photovoltaic solar energy conversion, Vienna, Austria, 1998. [14] Olivier Gergaud, Bernard Multon, Hamid Ben Ahmed. Analysis and Experimental Validation of Various Photovoltaic System Models. ELECTRIMACS, Aug 2002, MONTREAL, Canada.6p., 2002. [15] K. Ishaque, Z. Salam, H. Thateri, Simple, fast and accurate two diode models for photovoltaic. modules. Solar Energy Materials & solar Cells 95, 586-594, 2011. [16] Belhadj R, Benouaz, Cheknane A et Bekkouche SMA Revue des Energies Renouvelables Vol. 13 N°2 (2010) 257 – 264_257 ; Estimation de la puissance maximale produite par un générateur photovoltaïque. [17] M. M. Menou, A. Yahfdhou, A. K. Mahmoud, A. M. Yahya, and I. Youm, "Numerical modeling and determination of parameters characteristic of a photovoltaic module LRAER (FST Nouakchott)." International Journal of Physical Sciences 11, no. 24 (2016): 326-335. [18] Yahfdhou, A., Menou, M.M., Yahya, A.M., Eida, Ne.D.,Mahmoud, A.K. and Youm, I. (2016) Valuation and Determination of Seven and Five Parameters of Photovoltaic Generator by Iterative Method. Smart Grid and Renewable


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AUTHOR Mohamed Mahmoud Menou: Received his Master degree in Electromechanical Engineering, from Department of Sciences and Technics, University of tebessa, Algeria in 2014. He is working on his doctorate thesis at University of Nouakchott, Mauritania.

Ahmed Yahfhou: He received his Master degree in Solar Energy, Materials and Systems from College of Sciences and Technics, Dakar, Senegal, Cheikh Anta DIOP University in the year 2010. He is working on his doctorate thesis at Cheikh Anta DIOP, University Dakar, Senegal.

Abdel Kader Mahmoud: Received his Master degree of Sciences in power stations in 1988 and his PhD degree in electrical engineering from the Technical University of Tashkent in Uzbekistan, in 1991. Then he received his second doctorate degree in renewable energy from the University of Cheikh anta diop, Dakar, Senegal, in 2008. From 1992 until now he works as professor at the University of Nouakchott, Mauritania. Currently he is in charge of the Applied Research Laboratory of Renewable Energy (LRAER). He participated in several national and international meetings relative to the renewables energies. He is the author and co-author of more than 30 scientific papers. Issaka Youm: Studied at the university Cheikh Anta Diop of Dakar, Senegal where obtained BSc in physical sciences in 1978, post-graduate diploma and PhD degree in scholar energy in 1981 and 1983 respectively, He re received a scholarship from the French government from 1986 to 1990 to prepare a doctoral Thetis at the University of Monpelier II, France, and the, he received a DSc degree in solid state physics from University of Anta Diop of Dakar, Senegal in 1991. From 1983 till now, he was professor of physic in the University of Dakar. He is currently the director of the Centre of Studies and Research in Renewable Energy. He is the author and co-author of more than 50 scientific papers.


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