112 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 5, NO. 1, JANUARY 2015 Modeling the Effects of Inhomogeneous Irradiation and Temperature Proﬁle on CPV Solar Cell Behavior F. Reis, C. Guerreiro, F. Batista, T. Pimentel, M. Pravettoni, J. Wemans, G. Sorasio, and M. C. Brito Abstract—Solar cells that integrate concentration photovoltaic systems are usually exposed to inhomogeneous illumination and temperature proﬁles which inﬂuence their performance. Under such conditions, the solar cell behavior is only accurately modeled if the diode and resistive losses are considered to be distributed across the solar cell instead of being gathered, as in the conventional lumped model. This paper presents a distributed diode model and its experimental validation, which was carried out for standard test conditions and a range of temperature and concentration lev- els going from 25 to 70 °C and 1 to 30 suns, respectively, for both homogeneous and a set of inhomogeneous proﬁles. Modeled and experimental results showed good agreement, thus validating the model. The results of traditional and distributed model approaches are compared with homogeneous and inhomogeneous proﬁles of irradiation and temperature. Finally, we analyze the effect of dif- ferent proﬁles on cell performance. Index Terms—Concentration photovoltaic (CPV), nonuniform illumination, nonuniform temperature, PV solar cell model. I. INTRODUCTION C ONCENTRATION photovoltaic (CPV) systems generally exhibit a nonuniform illumination proﬁle along the solar cells they integrate [1]–[4]. The light distribution in such pro- ﬁles is deﬁned by the design of the concentrator optics and is inﬂuenced by structure, optics, and tracking misalignments, which possibly occur during manufacturing/mounting processes or even during its lifetime [2]. The resulting illumination pro- ﬁle on the CPV cells will inﬂuence the distribution of current in these devices, thus modifying its ohmic losses and, conse- quently, its I–V curve [2]–[5]. On the other hand, the illumination proﬁle will also dictate the temperature proﬁle on those cells since the highly illu- minated cell regions are susceptible to become warmer than the ones poorly illuminated [5]. Furthermore, in the CPV solar cells, the amount of radiation that reaches the cell is Manuscript received May 10, 2013; revised December 30, 2013, May 20, 2014, and August 27, 2014; accepted September 8, 2014. Date of publication October 20, 2014; date of current version December 18, 2014. This work was supported by the Massachusetts Institute of Technology (MIT) Portugal Program on Sustainable Energy Systems under FCT Grant SFRH/BD/45328/2008. F. Reis, C. Guerreiro, F. Batista, T. Pimentel, and M. C. Brito are with the Departamente de Engenharia Geogr´ aﬁca, Geofsica e Energia (DEGGE), Faculty of Sciences, University of Lisbon, Lisbon 1749-016, Portugal (e-mail: fareis@fc.ul.pt; catarina_cguerreiro@hotmail.com; fabiobta_8@hotmail.com; pimentel_tomas@hotmail.com; mcbrito@fc.ul.pt). M. Pravettoni is with the Institute of Applied Sustainability to the Built Environment, University of Applied Sciences and Arts of Southern Switzerland, Canobbio, Switzerland (e-mail: mauro.pravettoni@supsi.ch). J. Wemans and G. Sorasio are with the WS Energia S.A., Porto Salvo 2740- 257, Portugal (e-mail: wemans@ws-energia.com; sorasio@ws-energia.com). Color versions of one or more of the ﬁgures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identiﬁer 10.1109/JPHOTOV.2014.2358080 considerably high, which is why most CPV systems usually integrate active or passive cooling mechanisms to dissipate the heat of the solar cell, thus warranting higher operating perfor- mances and preventing premature damage. Depending on the cooling system, the solar cells may present different tempera- ture distributions which also affect the I–V curve differently [6]. The behavior of CPV solar cells operating under both il- lumination and temperature inhomogeneous proﬁles are only carelessly reproduced by traditional solar cell models which in- clude an equivalent-lumped series resistance [2]–[4], as shown in Fig. 1(a). In the lumped resistance model, all the series resistance com- ponents (sheet, contact, metal grid resistances) are joined in one single resistance. The light-generated current corresponds to the total light and passes through the total series resistance of the cell [1]. This traditional model overestimates the power losses on the cell under nonuniform illumination. For an accurate es- timation of the CPV solar cells output in these conditions, it is thus crucial that the solar cell model takes into account the “distributed diode effect” [1], [4]. In this distributed model, the cell is divided into small units whose electric circuit lies on a diode in parallel with a shunt resistor, as well as a series resistor component, which depends on the region of the cell where the unit is located [1], [4]. Previous works [1]–[4], [6]–[9], [11], [12], [14] have been performed to better understand the effect of inhomogeneous illumination and temperature on the solar cell’s performance. Some authors have explored this issue only through experimen- tal work [8], [9], [11], [12], while others have developed solar cell distributed models and even validated them, but only by ad- dressing the effects of illumination inhomogeneity [1]–[4], [7]. More recently, Domenech-Garret [14] have gone further and ex- tended a previous model [4] to combined proﬁles of uniform and nonuniform Gaussian temperature and radiation. Following this model framework, Chemisana and Rosell [6] have experimen- tally validated the model but only up to 5 suns of concentration. This paper presents a 1-D solar cell model that takes into ac- count the distributed diode effect to predict the output of a solar cell for nonuniform illumination and temperature distribution. The model was developed in a MATLAB/Simulink application based on a modular structure whose features are easily modiﬁed, thus allowing suitability for application in any cell design. We have experimentally validated the model for homogeneous illu- mination distributions, within a range of 1–30 suns, and homo- geneous temperature distributions, within a range of 25–70 °C. Model validity was also thoroughly explored through an exten- sive quantitative and qualitative analysis for a set of inhomo- geneous illumination proﬁles and inhomogeneous temperature 2156-3381 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.