# Electrical and Thermal Behaviour of Crystalline Photovoltaic Solar Modules in Shading Conditions
## 1 Introduction  
Photovoltaic (PV) installations can significantly affect their normal operation in shading conditions caused by vegetation or nearby architectural elements [1]. In addition, the accumulation of dirt on the front surface of the module can cause a situation of shading with equivalent effects [2]. This shading situation is common for urban environments in building integrated photovoltaics (BIPV) [3], but also for rural environments in photovoltaic greenhouses [4]. The effect of non-optimal operation by shading can occur in PV systems integrated with greenhouses, according to the orientation of the installation and the way of sharing the solar radiation with the crop [5]. The shading can be complete or partial depending on the location of the PV installation and on the elements that stand in relation to the solar position. Some references do not consider the shading conditions as failures although they may lead to power loss or safety issues [6]. PV modules affected by shadow or soiling conditions are subjected to non-homogeneous values of irradiance and temperature, making it work in non-optimal operation conditions, which can lead to hot spots or even burned cells [7]. In order to protect the PV modules from shading and soiling, bypass diodes are installed. A group of PV cells protected by one by-pass diode is normally known as a substring or sub-module. Normally, a PV module is split into several substrings. Therefore, in the presence of shading or soiling, the use of bypass diodes makes a distinctive I-V and P-V curve where different local maximum power points (LMPP) and one global maximum power point (GMPP) are obtained [8]. The operational values of current and voltage in a PV system depend on the maximum power point (MPP) tracked by the algorithm, which may be one of the local power peaks rather than the global one. Operating the PVsystems at the MPP, the algorithm will fix the operating voltage of the group of PV modules or array [9] and, depending of it, some of the bypass diodes can be turned on. The manufacturers of photovoltaic modules apply to their products tests of resistance to the formation of hot spots to determine their capacity to resist hot spots. This test is defined in the design and approval qualification standard: IEC-61215-2 [10]. It is broadly known that the output current of a PV system is directly related to the solar irradiation, while the output voltage is reduced slightly with an increase of temperature [1]. Furthermore, when a substring is covered by dirt or shadow, the temperature of PV cells increases considerably because it converts the solar energy into thermal instead of electric energy [11]. In some cases, electrical and thermal mathematical models of PV systems have been studied and coupled in [12], to determine the module temperature based on experimental data of weather conditions and the electrical operation point. Such a fact means that the correlation between temperature and performance of PV modules has been widely studied by different authors in the last decade, such as [11; 13]. To determine such a correlation, IR thermography has been used to determine thermal behaviour, while conventional electrical measure equipment has been employed to obtain the electric characteristics, such as the I-V curve tracer. IR thermography is a fast and contactless way to measure the back or front side temperature of the PV module, being useful to detect failures in PV modules or even in the junction box [14]. An explanation of some PV faults with their corresponding infrared (IR) image was proposed in [15; 16], proposing in some cases acceptance or rejection criteria of modules, depending on the measured hot spot temperatures [17]. The PV module degradation under operating conditions was also analysed through IR thermography [18]. Since IR thermography is gaining importance in such cases, some methods have been proposed to make an accurate temperature measurement through a predefined configuration of the thermographic equipment [19].