International Journal of Photoenergy

Volume 2018, Article ID 5945602, 12 pages

https://doi.org/10.1155/2018/5945602

## Study of Temperature Coefficients for Parameters of Photovoltaic Cells

Electronics and Computers Department, Transilvania University of Brasov, Brasov, Romania

Correspondence should be addressed to Daniel Tudor Cotfas; or.vbtinu@saftoctd

Received 11 September 2017; Revised 19 November 2017; Accepted 22 January 2018; Published 1 April 2018

Academic Editor: Leonardo Sandrolini

Copyright © 2018 Daniel Tudor Cotfas 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 temperature is one of the most important factors which affect the performance of the photovoltaic cells and panels along with the irradiance. The current voltage characteristics, *I-V*, are measured at different temperatures from 25°C to 87°C and at different illumination levels from 400 to 1000 W/m^{2}, because there are locations where the upper limit of the photovoltaic cells working temperature exceeds 80°C. This study reports the influence of the temperature and the irradiance on the important parameters of four commercial photovoltaic cell types: monocrystalline silicon—mSi, polycrystalline silicon—pSi, amorphous silicon—aSi, and multijunction InGaP/InGaAs/Ge (Emcore). The absolute and normalized temperature coefficients are determined and compared with their values from the related literature. The variation of the absolute temperature coefficient function of the irradiance and its significance to accurately determine the important parameters of the photovoltaic cells are also presented. The analysis is made on different types of photovoltaics cells in order to understand the effects of technology on temperature coefficients. The comparison between the open-circuit voltage and short-circuit current was also performed, calculated using the temperature coefficients, determined, and measured, in various conditions. The measurements are realized using the SolarLab system, and the photovoltaic cell parameters are determined and compared using the LabVIEW software created for SolarLab system.

#### 1. Introduction

An increasing number of countries have introduced renewable energy policies to reduce the greenhouse gas emissions and to avoid an energetic crisis created by the exhaustion of the fossil fuels. Most of them have fixed targets for using different types of renewable energy, and for this, they offer financial support [1]. The ways to improve the renewable energy domain are to develop hybrid renewable energy systems [2, 3], to solve the problems created when the renewable energy is inserted in the electrical power system [3], to achieve a very good integration of the renewable energy in buildings [4], to solve the storage problem, and to increase the efficiency of the existing ones.

The important role that the photovoltaic technology plays in the renewable energy domain is demonstrated by the dynamics, by the photovoltaic capacity installed worldwide (which is over 40 GW each year over the last years), and by the growth in the number of jobs created, which is over 2.8 million and represents 30% from the total new jobs created in the renewable energy domain [1].

Due to the major interest for photovoltaic technology, the researchers have developed various types of photovoltaic cells, such as multijunction, perovskite, and quantum well [5–9]. Although these types of photovoltaic cells are very promising, the monocrystalline, polycrystalline, and the amorphous silicon photovoltaic cells and panels are still more widely used in terrestrial applications. The multijunction photovoltaic cells are highly efficient, but because of their rather high price, they are generally used in space applications and in concentrated light applications.

The photovoltaic cells and panels can be characterized using their important dc parameters: the photogenerated current, ; the short-circuit current, ; the open-circuit voltage, ; the maximum power, ; the fill factor, ; the efficiency, ; the series resistance, ; the shunt resistance, ; the ideality factor of diode, *m*; and the reverse saturation current, [10]. Using the *I-V* characteristic, the equivalent circuit and one or more of the methods developed by researchers in the last 40 years, [10], the important parameters of the photovoltaic cells can be determined.

All the photovoltaic cell parameters are influenced by the temperature variation. If the temperature of the photovoltaic cells increases, most of them being influenced negatively—they decrease. The others increase with temperature, such as the short-circuit current, which slightly increases, and the reverse saturation current which increases exponentially [11–14].

The temperature of the photovoltaic cells in most of the locations varies from 0°C to 60°C. There are locations where the lower limit of the working temperature can be below −20°C and the upper limit can be over 80°C in semiarid areas [15]. These limits can be exceeded in other applications such as the spatial applications and concentrated light applications or extreme locations [16, 17].

The behavior of the photovoltaic cell parameter function of the temperature is very well described by the temperature coefficients [11–21]. The temperature coefficients, , can be absolute and normalized as in the following [13, 18, 21]: where represents the parameter of the photovoltaic cell and is the temperature.

The dependence of the photovoltaic cell parameter function of the temperature is approximately linear [21], and thus, the temperature coefficients of the parameters can be determined experimentally using the linear regression method [22]. The mechanisms which influence the performance of the photovoltaic cell can be better studied if the normalized temperature coefficient of the is considered as a sum of the normalized temperature coefficients of the , , and [12, 21].

Four types of commercial photovoltaic cells are taken into consideration for this study: three from the silicon family—the monocrystalline, polycrystalline, and the amorphous silicon photovoltaic cells—and one from the multijunction family—InGaP/InGaAs/Ge photovoltaic cell. The important parameters of these photovoltaic cells, like , , , , , , and *m* were studied related to the temperature, which was varied from 25°C to 87°C. The temperature coefficients of the photovoltaic cell parameters are determined and compared with the reference ones found in the related literature. The dependence of the temperature coefficients for , , , , and upon the irradiance was also studied.

#### 2. Theoretical Considerations

The *I-V* characteristic and the equivalent circuit with the suitable mathematical model are important tools to study and to determine the parameters of the photovoltaic cells in different conditions. There are three models: one-, two-, and three-diode model function of the electric current conduction mechanism from the photovoltaic cell as the diffusion mechanism, the generation-recombination mechanism, and the thermionic mechanism [10]. The generally accepted model is the one-diode model [10, 23]. The equivalent circuit for this model can be seen in Figure 1, and the model is described mathematically by the following equation:
where is the thermal voltage, is the temperature, is the Boltzmann constant, and represents the elementary charge.