AbstractâIn this paper a modeling method is investigated that finds the non-linear equation parameters of a photovoltaic (PV) module in order to obtain the ...
MATLAB Modeling and Simulation of Photovoltaic Modules Soliman A. Mahmoud, Mejd M. Alsari, Esra I. Reda, and Ruqiya M. Alhammadi Electrical and Computer Engineering Department University of Sharjah Sharjah, UAE Email: {solimanm, U00010850, 20620300, 20720464} @sharjah.ac.ae Abstract—In this paper a modeling method is investigated that finds the non-linear equation parameters of a photovoltaic (PV) module in order to obtain the desired PV model using any circuit simulator. This modeling method adjusts the I-V curve at three remarkable points: the open circuit voltage, the short circuit current, and the maximum power point [1]. Three models are realized using this technique namely, the single-diode model, the two-diode model, and the three-diode model. The evaluation study of the accuracy of these three models showed relative errors ranging from 32% to 50%. Further, this technique is improved by adjusting the I-V curve at more than three points depending on the number of unknowns to be found for each model, which showed a reduction in the relative error ranging from 0.37% to 38%. Finally, a study of the parameters obtained from the modeling algorithm on the performance of the proposed single-diode model is presented.
I.
INTRODUCTION
The increasing demand for electrical power has created many challenges for the energy industry, which can play a vital role in the quality of the generated power in both short and long terms. The limited supply of fossil fuels had grabbed the international community attention towards the importance of renewable energy. Transforming the sun’s potential into clean non-polluted, efficient energy has become an alternative of many power sources creating a revolution in the energy industry. The direct conversion of sunlight into electricity can be done using PV systems. Lately, many researchers have investigated this topic showing how promising this field might be. Learning the basics of the PV system is stepping stone to carry out a PV model [2]-[3]. Manufacturers of PV modules provide only a few experimental data regarding the electrical and thermal characteristics of these modules. These parameters, which are obtained under nominal conditions of temperature and solar irradiation, are not enough to build an accurate PV circuit model with any circuit simulator using basic math blocks [1]. Therefore, a modeling method should be investigated that would find the rest of these parameters in order to obtain the
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desired PV model. Different techniques have been developed in the literature regarding this issue. One particular method finds the non-linear equation parameters by adjusting the I-V curve at three remarkable points: the open circuit voltage, the short circuit current, and the maximum power point [1]. Further, it is critical to consider the non-idealities of a solar cell by extending the modeling and simulation to three models namely, the single-diode model, the two-diode model, and the three-diode model. The developed models will be suitable to simulate several homogenous or/and heterogeneous PV cells or PV panels. This paper is organized as follows: Sec. 2 discusses the modeling of the PV module using three different models: the single-diode model, the two-diode model, and the three-diode model. Sec. 3 proposes an improvement of the modeling discussed in Sec. 2. The results of both modeling algorithms are discussed in Sec. 4. Sec. 5 studies the effect of the variations of the PV module parameters on the overall performance of the model. Finally, the paper is concluded in Sec. 6. II.
MODELING THE PV MODULE
A. The Single-Diode Model The I-V characteristics of the single-diode model of a solar cell shown in fig. 1 can be represented by Eq. 1 [1].
1 – Where
(1) (2)
The I-V curve that represents eq. 1 is shown in fig. 2 in which three significant points are highlighted: the open circuit voltage (Voc), the short circuit current (Isc), and the maximum power point (MPP).
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exp
,
1 (7)
,
/
V
Rs and Rsh can be obtained using an iterative method that assumes an initial value of Rs, namely, zero, and incrementing it until the maximum power of the model matches the experimental maximum power. The initial value of Rsh is given in eq. 9 [1]. ,
Figure 2. The I-V curve adjusted to three remarkable points In practical PV cells the generated light current depends upon the solar radiation and the temperature according to eq. 3 [1]. (3)
∆
where
(4)
The second parameter in the I-V equation is the diode saturation current that is represented by eq. 5. For simplification purposes eq. 5 can be improved to eq. 6 [1] showing the dependence of the saturation current on the temperature in a different manner. This alteration aims to match the open circuit voltage of the model with the available parameters in the datasheet, namely, KI and KV, for a wide range of temperatures.
,
(5)
exp ∆
,
∆
,
,
(9)
,
As for the fifth and last parameter, the diode ideality factor (n), a set of n values have been assumed ranging from 1 to 2 with an increment of 0.1. This represents the usual assumption for n [1]. The developed model can be further improved taking into consideration the effect of Rs and Rsh on the light current as shown in eq. 10 [1]. This shows a significant reliance where the light current has a different value from the short circuit current. ,
∆
(8)
,
Figure 1. The single-diode model of a solar cell
.
exp
(10)
,
The I-V curve can be obtained using Newton-Raphson method for solving non-linear systems by numerically solving g(V,I) = I-f(V,I)=0 for a set of V values obtaining the corresponding set of I values. The modeling algorithm computes these five unknowns using equations (1)-(10) for the sake of adjusting the I-V curve to the three remarkable points [1]. The simulation was based on several values of n for each module comparing the absolute error |I,m-I,e| for the purpose of matching the calculated current with the experimental value. The objective of this method, to fit the IV equation to the three distinct points, was successfully achieved. B. The Two-diode and Three-Diode Models The generalized model of a non-ideal solar cell comprises of two diodes as shown in fig. 3 and can be represented by Eq. 11 [4].
(6)
,
The third and fourth parameters to be considered are the series and parallel resistances. The modeling method used here chooses only one pair (Rs,Rsh) that makes the peak output power available in the datasheet equal to the peak output power of the proposed model. The relationship between Rs and Rsh can be obtained by setting Pmax,e = Pmax,m as shown in eq. 7 [1]. The resultant relationship is expressed in eq. 8 [1] that shows a great dependence between the two resistances.
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V
Figure 3. The two-diode model of a solar cell
algorithm. This evaluation aims at improving the accuracy of the obtained results [5]. 1 1 –
(12)
11
(13)
0 The second diode describes the "non-ideality" of the real p-n junction due to the recombination that occurs at the depletion region. The modeling procedure applied here is similar to that for the single-diode model. In addition, the saturation current of the second diode is set to be equal to the saturation current of the first diode [4]. As for the diode ideality factor (n), according to the Shockley’s diffusion theory, the value of n1 must be unity. In addition, the value of n2 should be greater than or equal to 1.2 (>=1.2) to obtain the best possible match between the proposed model and the experimental model as extensive simulations showed [4]. It is critical to take into consideration the non-idealities of a solar cell by means of modeling and simulation. Therefore, this analysis can be further extended by studying the three-diode model taking into consideration the effect of the leakage current. The equivalent circuit of this model is shown in fig. 4 and the same procedure was applied for modeling.
(14) (15) (16)
IV.
RESULTS
The modeling algorithm for the three proposed models was applied to the MSX60 PV module. The error curves of the three models based on the three remarkable points are shown in fig. 5. Fig. 6 shows the error curves of the three improved models. It can be noticed that the least error can be obtained from the single-diode model. The corresponding five-point adjusted I–V curve is shown in fig. 7 for the obtained parameters listed in table 1.
V
Figure 4. The three-diode model of a solar cell III.
Figure 5. The error curves of the 3-point adjusted models
ACCURACY IMPROVEMENT OF THE PROPOSED MODELS
The accuracy of the proposed models is evaluated by comparing the experimental data of any PV module with the measured data obtained from the modeling algorithm. The accuracy can be further improved by finding the unknown parameters that are not available in the typical PV datasheets using more than three points from the I-V curve instead of only the three remarkable points depending on the number of unknowns for each model. For the single-diode model, five points are needed to find the unknown parameters. For the two-diode model, seven points are extracted; and for the threediode model, nine points are required. The additional points in each model were selected according to where a large error occurs. The improvement process works as follows: the main five points in the I-V curve are extracted. Then, these points are used as input parameters for the five nonlinear equations 12, 13, 14, 15, 16 that are solved using the quasi-Newton method in the nominal condition. Finally, the five unknown parameters are determined and used in the modeling
Figure 6. The error curves of the 5-point adjusted models
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Figure 9. The I-V curve for different shunt resistance values
Figure 7. The I-V curve of the 5-point adjusted single-diode model TABLE 1 OBTAINED PARAMETERS FROM THE SINGLE-DIODE MODEL
I.
Parameter
Measured Value
IL [A]
3.799962
Io [A]
3.7278e-007
Rs [ohm]
0.194933
Rsh [ohm]
27067.846214
n
1.4138
Figure 10. The I-V curve for different saturation current values II.
PARAMETERS EFFECT ON PV MODULE PERFORMANCE
Variations in the parameters obtained from the modeling algorithm for any PV module affects the performance of the module. These variations might occur after a long period of time from its manufacturing. The effect of each parameter can be studied for variations ranging from 20% to 30%. The parameters to be studied are the series resistance, the shunt resistance, and the saturation current that are obtained from the modeling algorithm of the single-diode model. Fig. 8 shows the effect of changing the series resistance on the I-V curve of the proposed model. It can be seen that as the value of Rs changes the I-V curve is no longer adjusted to the three remarkable points. The same analysis can be done for the remaining two parameters as shown in fig. 9, and fig. 10.
CONCLUSION
This paper proposed a modeling algorithm that depends upon three remarkable points (Voc, Isc, and MPP). This algorithm was applied to develop three models namely, the single-diode model, the two-diode model, and the three-diode model. The accuracy of these models were improved taking into account the number of unknowns in each model using more than three points from the I-V curve. We concluded that the most accurate results are obtained using the single-diode model with a relative error of 0.37% compared to the other two models. Moreover, any alteration on the PV parameters slightly affects the overall performance depending on our choice of variation. REFERENCES [1]
[2] [3] [4]
[5]
Figure 8. The I-V curve for different series resistance values
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