Journal of Solar Energy

Volume 2015 (2015), Article ID 169015, 9 pages

http://dx.doi.org/10.1155/2015/169015

## Simulations Based on Experimental Data of the Behaviour of a Monocrystalline Silicon Photovoltaic Module

^{1}Department of Electrical and Power Engineering, Higher Technical Teachers’ Training College (HTTTC), University of Buea, Kumba, Cameroon^{2}Department of Electrical, Energetic and Automatic Engineering, ENSAI, University of Ngaoundere, Ngaoundere, Cameroon^{3}Laboratory of Modeling, Intelligence, Process and Systems (MIPS), University of Haute Alsace, 61 Road Albert Camus, 68093 Mulhouse Cedex, France

Received 26 June 2015; Accepted 12 August 2015

Academic Editor: Santanu Bandyopadhyay

Copyright © 2015 Abraham Dandoussou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The performance of monocrystalline silicon cells depends widely on the parameters like the series and shunt resistances, the diode reverse saturation current, and the ideality factor. Many authors consider these parameters as constant while others determine their values based on the characteristic when the module is under illumination or in the dark. This paper presents a new method for extracting the series resistance, the diode reverse saturation current, and the ideality factor. The proposed extraction method using the least square method is based on the fitting of experimental data recorded in 2014 in Ngaoundere, Cameroon. The results show that the ideality factor can be considered as constant and equal to 1.2 for the monocrystalline silicon module. The diode reverse saturation current depends only on the temperature. And the series resistance decreases when the irradiance increases. The extracted values of these parameters contribute to the best modeling of a photovoltaic module which can help in the accurate extraction of the maximum power.

#### 1. Introduction

The world energetic consumption is still dominated by the use of nonconventional sources like fossil sources, natural gases, and nuclear sources. The main drawback of the use of these sources is that they are exhaustible and they contribute to the pollution of the environment. Hence, it is useful to use renewable energy sources such as biomass, wind energy, hydroelectricity, and solar energy. Solar energy occupies an important place because it is available everywhere. Photovoltaic energy which is based on the conversion of direct sunlight into electricity is the most promising one. There are different technologies of photovoltaic (PV) cells which are found on the market: monocrystalline silicon (efficiency of %), polycrystalline silicon (efficiency of %), amorphous silicon (efficiency of %), and organic solar cells (laboratory efficiency of %) [1, 2].

However, the performance of a photovoltaic cell is influenced by the climatic and meteorological conditions such as the irradiance and the temperature. It is known in the literature that when the irradiance decreases, the current also decreases and consequently, the output power decreases. When the temperature increases, the voltage decreases and the output power also decreases [3, 4]. Some authors [4, 5] stated that the photovoltaic parameters like the series resistance, the diode ideality factor, and the diode reverse saturation current influence the performance of the PV cell. The diode reverse saturation current has been modeled by an equation showing its dependence on the temperature [5]. But the other parameters have not been in the center of a particular study for a mathematical model. Nevertheless, these parameters and the diode reverse saturation current have been determined by some authors [3–8]. These authors measured the - characteristic of a PV module using a solar simulator instead of the normal operating conditions. Under the real weather conditions, it is difficult to have a constant irradiance and a constant temperature, particularly in the tropical climate. So, it is not evident to get the - characteristic of the PV module under the normal weather conditions. That is why this paper proposes a new method of the determination of photovoltaic parameters under the normal operating conditions. The irradiance, the temperature, the load current, and the load voltage have been recorded during a whole day. Then, the PV parameters have been calculated from these experimental data using a least square method in the PV parameters extraction algorithm. The results confirm that the diode reverse saturation current effectively depends on the temperature and the mathematical expression obtained in the literature has been validated [6–9]. The diode ideality factor, , changes less with the weather conditions. The series resistance depends essentially on the irradiance. The mathematical expression of the series resistance has been obtained.

In order to verify the effectiveness of these results, the PV module has been modeled with MATLAB/SIMULINK. The input parameters for the simulations are the recorded irradiance and surface temperature, the determined PV parameters (, , and ). The recorded load current has been also loaded in the SIMULINK model for comparison. For the comparison with the literature results, the same PV module model has been simulated as inputs: the recorded irradiance and temperature, a constant diode ideality factor (), a constant series resistor ( Ω), and the diode reverse saturation current expression. The results show that the PV module modeled with the variable PV parameters is more accurate than the one modeled with the constant series resistance and the constant diode ideality factor. These simulation results show the real behaviour of the PV module under the normal operating conditions. Consequently, the obtained model can be used for the extraction of the maximum power of the PV module, under the normal weather conditions.

This paper is divided into the following sections: the first section presents research method including the modeling of a photovoltaic cell, the experiment, and the extraction algorithm of PV module parameters and the second section presents the results and analysis.

#### 2. Research Method

##### 2.1. Modeling of a Photovoltaic Cell

Two electrical models are used for modeling a photovoltaic cell:(i)A two-diode model (TDM) with the second diode which represents the recombination phenomenon in the bulk cell. However, this model is generally used for a polycrystalline silicon cell [10–12].(ii)A one diode model (ODM) which is simple and represents precisely the operation of a monocrystalline solar cell [5–13]. This model which is used in this work is presented in Figure 1 with , a diode which represents the - junction; and are the series and shunt resistances. By applying Kirchhoff’s laws, the following equation is obtained:Due to the fact that is higher than () and its influence on the performance of the PV cell is insignificant [5–13], (1) becomeswhere(i) is the diode ideality factor;(ii) is the thermal voltage;(iii) C is the electrical charge;(iv) J/K is the Boltzmann constant;(v) is the surface PV cell temperature (K);(vi) is the diode reverse saturation current (A).Equation (2) is a nonlinear expression of because it expresses in function of and . In order to obtain a linear expression of , the Lambert function can be used. In fact, the Lambert function is used to solve nonlinear equation as .