Plane Thermoelastic Waves in Infinite Half-Space Caused FACTA UNIVERSITATIS Series: Electronics and Energetics Vol. 31, N o 1, March 2018, pp. 63 - 74 https://doi.org/10.2298/FUEE1801063F PREDICTION OF ANNUAL ENERGY PRODUCTION FROM PV STRING UNDER MISMATCH CONDITION DUE TO LONG-TERM DEGRADATION * Miodrag Forcan University of East Sarajevo, Faculty of Electrical Engineering, East Sarajevo, Bosnia and Herzegovina University of Belgrade, Faculty of Electrical Engineering, Belgrade, Serbia Abstract. Reduction of long-term degradation effects represents a long-time challenge in photovoltaic (PV) manufacturing industry. Modelling of long-term degradation types and their impact on maximum power of PV systems have been analysed in this article. Brief guidelines for PV cell-based modelling of PV systems have been illustrated. Special study case, PV string consisting of 12 PV modules, has been modelled in order to determine degradation and mismatch power losses. Modified methodology for prediction of annual energy production from PV string, based on horizontal irradiation and ambient temperature experimental measurements at the location of Belgrade, has been developed. Coefficient named “degradation factor” has been introduced to include and validate degradation power losses. Economic considerations have indicated evident money income reduction, as a consequence of lower annual energy production related to long-term degradation. Key words: PV string, energy production, long-term degradation, degradation factor, mismatch losses 1. INTRODUCTION Precise determination of annual energy production from PV systems is very difficult to achieve, mostly due to variable operating conditions (irradiation and ambient temperature) [1]. Electricity production is closely related to conversion efficiency, which represents one of the most important parameters when discussing PV systems [2]. The new materials are being constantly developed with purpose of increasing conversion efficiency and mitigating degradation effects. According to research, presented in [3], organic materials with PV properties have proved to be one of the most promising solutions. Meanwhile, conventional silicon materials remain the most widely used in field applications. Received January 31, 2017; received in revised form September 18, 2017 Corresponding author: Miodrag Forcan University of East Sarajevo, Faculty of Electrical Engineering, Vuka Karadzica 30, 71126 Lukavica, 71123 East Sarajevo, Republic of Srpska, Bosnia and Herzegovina (E-mail: miodrag.forcan@live.com, miodrag.forcan@etf.unssa.rs.ba) * An earlier version of this paper was presented at the 2 nd Virtual International Conference on Science, Technology and Management in Energy (eNergetics 2016), 22-23 September, 2016, in Niš, Serbia [1]. 64 M. FORCAN Conventional methods for prediction of energy production from PV systems usually use hourly-averaged horizontal irradiation and ambient temperature measurements for specific locations [4-6]. One of their main shortcomings is neglecting of long-term degradations related to encapsulating material, e.g. delamination, discoloration and corrosion. According to various research results [7-12], it has been found that long-term degradation effects can often reduce PV system’s power up to 15-20% during lifetime exploitation period. This article is organized as follows. The second chapter covers basic facts related to most common types of long-term degradation. In the third chapter, modelling guidelines for PV systems and degradation types are presented. PV module degradation effects, under variable irradiation and temperature condition, have been analysed with results presented in the fourth chapter. The fifth chapter presents study case dedicated to PV string power reduction due to long-term degradation. Modified methodology for prediction of annual energy production from PV string and financial income, based on introduction of degradation factor, has been investigated in sixth chapter. Valuable conclusions are pointed out in final chapter. 2. LONG-TERM DEGRADATION OF PV SYSTEMS Degradation represents a gradual deterioration of PV system components caused by real operating conditions in the field. Affected PV modules can continue to generate electricity, although produced energy can be significantly reduced. According to manufacturers, it is common practise to identify PV module as degraded when its maximum power reduces below 80% of the initial value. Long-term degradation of PV systems is related to encapsulation material deterioration and its effects could be observed on the surfaces of PV cells during exploitation period. Ethylene vinyl acetate (EVA) is recognized, over the decades, as one of the best encapsulation materials for PV cells. As a consequence, nearly 80% of PV modules, produced around the world, are encapsulated by EVA [7]. Typical long-term degradation types of PV cells, related to EVA, are: delamination, discoloration and corrosion. Characteristic field examples of PV cells affected by long-term degradation types are shown in Fig.1 [8]. (a) (b) (c) Fig. 1 Typical long-term degradations of PV cells [8]: (a) Delamination; (b) Discoloration; (c) Corrosion Prediction of Annual Energy Production from PV String under Mismatch Condition due to Long-term Degradation 65 2.1. Delamination Glass, EVA and PV material are tightly affixed (laminated) in normal PV cells. If some of the mentioned layers is damaged it could lead to delamination development. Delamination represents separation between the different layers within the PV cells and it is usually followed by the penetration of moisture and corrosion. The most common PV cell’s surface area affected is located around busbars, as can be seen in Fig.1.a. This type of degradation is observed in more than 50% of installed PV modules according to research [9]. 2.2. Discoloration Ultra-violet radiation, followed by high degree of humidity and environment temperature, is recognized as the main cause of discoloration. Discoloration is the most common type of long-term degradation represented by electro-chemical process in which PV material changes colour, usually from light yellow to brown (Fig. 1.b). According to research papers [10] and [11], discoloration can reduce PV cell’s short-circuit current up to 15%. 2.3. Corrosion The main reason for corrosion occurrence in PV cells is moisture penetration. Corrosion damages metal parts and contacts of PV cells (Fig.1.c), which leads to PV cell’s series resistance increase. Based on the results of accelerated corrosion tests, it has been found that probability of corrosion occurrence is related to oxygen presence in silicon layers of PV cell [12]. 3. PV SYSTEM MODELLING In order to precisely determine degradation and mismatch power losses in PV systems, it is essential to use PV cell-based modelling [1]. For proper calculation of degradation effects on PV systems it is necessary to model functionality between generated power and specific ambient conditions. It is a common practice to model I-V curve with irradiation and temperature as controllable primary input variables. One-diode MATLAB-based model of PV cell has been created by using recommendations from [13]. Corresponding PV module and cell models are used throughout previous research and series of related publications [14-16]. Future PV modelling research will include the cooling effect of wind on PV cell temperature [17]. Regarding mismatch effect due to long-term degradation it can be assumed that wind conditions are uniform at the relatively small surface of PV string. Low irradiation effects have been included in modelling process by threatening of PV cell’s series resistance, parallel resistance and diode ideality factor, as functions of irradiation and operating temperature, with corresponding analytical expressions recommended in literature [18-20]. PV module modelling has been realized by using MATLAB/Simulink software [21]. The chosen PV module ZDNY -250P60 250Wp [22] consists of 60 polycrystalline Suntellite 156M PV cells with electrical data for Standard Test Conditions (STC) presented in Table 1. PV string model consists of 12 PV modules with maximum installed power of 2.995 kW. Similar types of PV systems are often used on the roofs of households in urban environments. PV system modelling procedure is presented in Fig.2. PV modules within PV string are enumerated with numbers 1-12. 66 M. FORCAN Table 1 STC electrical data of Suntellite 156M PV cell and PV module Suntellite PV PV cell PV module Efficiency [%] 17.00-17.19 17.00 PMPP [W] 4.16 249.61 VMPP [V] 0.531 31.84 IMPP [A] 7.834 7.84 VOC [V] 0.63 37.78 ISC [A] 8.35 8.35 FF [%] 79.08 79.12 Fig. 2 PV system modelling procedure: (a) One-diode PV cell model; (b) 60-cell PV module model; (c) 12-module PV string model 3.1. Long-term degradation modelling In order to analyse long-term degradation effects on reduction of PV string power, it is mandatory to establish relation between degradation mechanisms and PV cell’s parameters. As delamination, discoloration and corrosion are impossible to predict precisely, their modelling is limited on approximate relations resulting from field observations and statistical analysis of experimentally obtained data. According to experimental research results [8], delamination reduces PV module’s short-circuit current ISC, while its effects on open-circuit voltage VOC can be neglected. Based on experimentally obtained data for characteristic PV module, several modelling cases are defined: 1. Case 0 - Del 0 - no delamination - ISC = ISC-(STC). 2. Case 1 - Del 1 - limited area around PV cells’ busbars affected - ISC = 0.95 × ISC-(STC) (5% decrease). 3. Case 2 - Del 2 - limited area around small cracks in PV module’s surface - ISC = 0.92 × ISC-(STC) (8% decrease). Based on statistical analyses and experimental field data obtained in temperate climate zone [23], it has been found that discoloration also can be modelled as reduction of ISC, the following cases are defined: 1. Case 0 - Dis 0 - no discoloration - ISC = ISC-(STC). 2. Case 1 - Dis 1 - bright colours present on less than 50% of PV module’s surface - ISC = 0.9473 × ISC-(STC) (5.27% decrease). 3. Case 2 - Dis 2 - bright colours present on more than 50% of PV module’s surface - ISC = 0.9137 × ISC-(STC) (8.63% decrease). 4. Case 3 - Dis 3 - dark colours present on less than 50% of PV module’s surface - ISC = 0.9088 × ISC-(STC) (9.12% decrease). Prediction of Annual Energy Production from PV String under Mismatch Condition due to Long-term Degradation 67 Regarding corrosion modelling of PV modules, according to same experimental results, as in the case of discoloration [23], PV module’s series resistance RS has been identified as key parameter. Corrosion manifests as increase of RS. The following modelling cases are defined: 1. Case 0 - Cor 0 - no corrosion. 2. Case 1- Cor 1 - bright colour corrosion on metal parts of PV module - RS = 1.65 × RS-(STC) (65% increase). 3. Case 2 - Cor 2 - bright colour corrosion on metal parts and terminals of PV module - RS = 2.2 × RS-(STC) (120% increase). 4. Case 3 - Cor 3 - dark colour corrosion on metal parts and terminals of PV module - RS = 4.3 × RS-(STC) (330% increase). 4. PV MODULE DEGRADATION EFFECTS UNDER VARIABLE IRRADIATION AND TEMPERATURE CONDITION In real-time field conditions PV systems are operating under hourly-based irradiation and temperature variations. It is of mandatory importance to determine long-term degradation effects under variable irradiation and temperature conditions. By using earlier defined long- term degradation modelling cases, PV module maximum power is observed for ambient temperature and irradiation ranges: -5°C - 35°C; 200 W/m 2 - 1000 W/m 2 , respectively. Ambient temperature values have been varied with constant irradiation condition 800 W/m 2 . Similarly, irradiation values have been varied with constant ambient temperature condition - 8.75°C (PV cells’ operating temperature 25°C). Corresponding results are presented in Fig.3. By analysing graphs from Fig.3, the several observations can be made:  Delamination and discoloration preserve approximate linear correlation between PV module’s maximum power (Pm) and both ambient temperature (T) and irradiation (I), while corrosion inserts slightly nonlinear components.  In the case of T variations, Pm curve slopes remain approximately constant in delamination and discoloration analysis. As a consequence, differences between Pm for all modelling cases (del0, del1, del2 and dis0, dis1, dis2, dis3) remain approximately constant.  In the case of I variations, Pm curve slopes slightly change in delamination and discoloration analysis, which leads to important conclusion: for higher irradiation values, differences between Pm for all considered modelling cases (del0, del1, del2 and dis0, dis1, dis2, dis3) are also higher.  Regarding the corrosion effects, it can be seen from Fig.3.c that modelling case cor3 significantly differ from other cases in terms of Pm curve slope for variable T condition. For variable I condition, Pm value differences between different modelling cases of corrosion are lower than the corresponding cases of delamination and discoloration.  Degradation losses related to delamination and discoloration maintain approximately equal values in whole analysed T and I ranges, while corrosion losses nonlinearly increase with T and I values increasing (Fig.3.d). It can be concluded that delamination and discoloration losses are approximately unaffected by variation of T and I. 68 M. FORCAN Fig. 3 PV module maximum power and degradation losses under variable temperature and irradiation condition: (a) delamination; (b) discoloration; (c) corrosion; (d) power losses due to long-term degradation Prediction of Annual Energy Production from PV String under Mismatch Condition due to Long-term Degradation 69 5. PV STRING POWER REDUCTION DUE TO LONG-TERM DEGRADATION - STUDY CASE Determination of PV string power losses due to degradation is a complex task, because of the mismatch condition occurrence. The term “mismatch condition” refers to differences in current-voltage (I-V) curves of individual PV modules in PV string due to different degradation rates. In the field conditions, during long exploitation periods, it is very common that PV modules degrade differently. In order to investigate PV string’s degradation and degradation mismatch power losses, the special study case, consisting of adopted PV module’s degradation modelling cases, is defined in Table 2. Table 2 PV string under long-term degradation study case Period of PV string exploitation 10 years 15 years 20 years 25 years Type of long-term degradation Del. Disc. Corr. Del. Disc. Corr. Del. Disc. Corr. Del. Disc. Corr. PV1 del 0 dis 1 cor 1 del 1 dis 2 cor 2 del 2 dis 2 cor 2 del 2 dis 2 cor 3 PV2 del 0 dis 0 cor 1 del 1 dis 0 cor 2 del 1 dis 1 cor 2 del 2 dis 1 cor 3 PV3 del 0 dis 1 cor 0 del 0 dis 3 cor 1 del 1 dis 3 cor 2 del 2 dis 3 cor 2 PV4 del 0 dis 0 cor 0 del 0 dis 1 cor 1 del 1 dis 2 cor 2 del 1 dis 2 cor 2 PV5 del 0 dis 0 cor 0 del 0 dis 1 cor 1 del 0 dis 2 cor 2 del 1 dis 2 cor 2 PV6 del 0 dis 0 cor 0 del 0 dis 0 cor 1 del 0 dis 1 cor 2 del 1 dis 2 cor 2 PV7 del 0 dis 0 cor 0 del 0 dis 1 cor 0 del 0 dis 3 cor 1 del 1 dis 3 cor 2 PV8 del 0 dis 0 cor 0 del 0 dis 1 cor 0 del 0 dis 3 cor 1 del 1 dis 3 cor 2 PV9 del 0 dis 0 cor 0 del 0 dis 0 cor 0 del 0 dis 1 cor 1 del 0 dis 3 cor 2 PV10 del 0 dis 0 cor 0 del 0 dis 0 cor 0 del 0 dis 1 cor 1 del 0 dis 1 cor 2 PV11 del 0 dis 0 cor 0 del 0 dis 0 cor 0 del 0 dis 1 cor 0 del 0 dis 1 cor 1 PV12 del 0 dis 0 cor 0 del 0 dis 0 cor 0 del 0 dis 0 cor 0 del 0 dis 1 cor 1 According to data in Table 2 it can be observed that several key time points are defined during 25 years long exploitation period of PV string. Long-term degradation modelling cases are assumed to take place after 10, 15, 20 and 25 years of exploitation period. The highest combined degradation rate is set for PV modules with starting indexes (1, 2, 3 …). It is assumed that degradation rate is negligible in the first 10 years of exploitation. In order to determine PV string degradation losses and mismatch losses separately, it is necessary to identify total maximum power of individual PV modules (12 PV modules operate separately), beside the maximum power of the entire PV string (12 PV modules operate in series connection). For defined study case (Table 2), under constant ambient temperature T = 20°C and irradiation I = 600 W/m 2 conditions, maximum power points of individual PV modules PMPP-IM and PV string PMPP-String have been determined and presented in Table 3. 70 M. FORCAN Table 3 Maximum power points of individual PV modules and PV string for study case defined in Tab.5.1 under constant ambient temperature and irradiation values (T = 20°C and I = 600 W/m 2 ) Maximum power point PV modules / string (PMPP-IM / PMPP-String) Period of PV string exploitation 10 years 15 years 20 years 25 years PPV1-MPP [W] 126.773 115.478 111.637 109.500 PPV2-MPP [W] 133.563 126.533 119.793 113.653 PPV3-MPP [W] 127.631 121.935 114.847 111.005 PPV4-MPP [W] 134.518 126.918 115.478 115.478 PPV5-MPP [W] 134.518 126.918 121.895 115.478 PPV6-MPP [W] 134.518 133.702 126.189 115.478 PPV7-MPP [W] 134.518 127.773 121.935 114.847 PPV8-MPP [W] 134.518 127.773 121.935 114.847 PPV9-MPP [W] 134.518 134.518 126.914 121.268 PPV10-MPP [W] 134.518 134.518 126.914 126.189 PPV11-MPP [W] 134.518 134.518 127.773 126.194 PPV12-MPP [W] 134.518 134.518 134.518 126.194 PMPP-IM = ΣPPVi-MPP (i=1…12) 1598.6 W 1561.1 W 1475.2 W 1418.5 W PMPP-String 1591.7 W 1511 W 1440.4 W 1392.7 W Power losses due to long-term degradation PMPP-New string* - PMPP-String 22.52 W 1.4 % 103.2 W 6.4 % 173.82 W 10.8 % 221.52 W 13.7 % Mismatch losses due to long-term degradation PMPP-IM - PMPP-String 6.9 W 0.43 % 50.1 W 3.1 % 34.8 W 2.16 % 25.8 W 1.6 % *New PV string maximum power - 1614.22 W According to results presented in Table 3 it can be concluded that power losses due to long-term degradation are increasing from 1.4% to 13.7% over the 25 years exploitation period. On the other hand, mismatch losses have the highest value after just 15 years of exploitation (3.1%), because the degradation rates of individual PV modules differ the most in that time period. It is important to notice that mismatch losses are very difficult to predict and they certainly depend on particular study cases. Their values could reach up to 50% of power losses due to long-term degradation itself. 6. PV STRING ANNUAL ENERGY PRODUCTION Statistical prediction of energy production from PV string is based on horizontal irradiation and ambient temperature measurements. Acquisition system provided measurements of horizontal irradiation and ambient temperature for every 10 minutes between July 15 th , 2013 and July 15 th , 2014, at location of Belgrade, Serbia, with WGS coordinates: 44.8 0 ; 20.47 0 ; 120 m. The obtained irradiation and ambient temperature values have been averaged for every three hours and in the next step monthly-averaged. Based on the procedure given in [24], horizontal irradiation can be divided into direct and diffuse component. In addition, reflected component can be determined by using corresponding reflection coefficient. Prediction of Annual Energy Production from PV String under Mismatch Condition due to Long-term Degradation 71 In order to determine irradiation components on PV string surface, position angles need to be defined. Corresponding assumed tilt and azimuth angles are Σ=30 0 and S=0 0 , respectively. In the process of determining ambient reflection coefficient, it is assumed that household with PV string on its roof is located on a grassy surface. The adopted reflection coefficient value is ρ=0.15. Total irradiation on the surface of PV string has been calculated by usage of following relation: , PV Dir Dif Ref I I I I   (1) where: IDir, IDif and IRef are direct, diffused and reflected irradiation components, respectively. By using calculated irradiation and measured ambient temperature data, it is possible to determine operating temperature of PV string, according to following relation: 20( ) , 0.8 PV amb PV NOCT T T I     (2) where: TPV is operating temperature of PV string; Tamb is ambient temperature; NOCT is nominal operating temperature of PV cell (47 °C for considered PV cells); IPV is irradiation value on the surface of PV string. Based on the calculated and averaged IPV and TPV values, PV string DC power values are obtained (PDC). Conventional relation for calculation of PV systems’ DC power in the field conditions, expanded with insertion of degradation factor, is defined as follows: (field) ( , ) (1 ) (1 ) (1 ), DC DC PV PV N Z D P P I T          (3) where: μN is efficiency reduction factor due to resulting unequal I-V curves in the manufacturing process of PV modules; μZ is efficiency reduction factor resulting from soiling of PV modules in the field; μD (DF) is newly defined efficiency reduction factor as a consequence of long-term degradation (degradation factor). Assumed values of efficiency reduction factors in the analysed study case are μN = 0.03 (3%) and μZ = 0.04 (4%). Degradation factor has been calculated on the hour basis according to relation (4) and initially averaged for every three hours, and in the next step also monthly-averaged. _ _ _string _ . new string long term d D new string P P DF P      (4) Monthly averaged PV string maximum power and degradation factor have been presented in Fig.4 for analysed exploitation period of one year and considered study case. Daily time intervals with irradiation values below 30 W/m 2 have been neglected in the analysis. 72 M. FORCAN Fig. 4 Monthly averaged PV string maximum power and degradation factor during the considered year of exploitation in different hourly-based time intervals: (a) 8:30h - 11:30h; (b) 11:30h - 14:30h; (c) 14:30h - 17:30h According to results from Fig.4, the following observations can be obtained:  Degradation factor has higher values in the summer time (up to 14%), with the exception of January in time interval 11:30h - 14:30h.  The highest values of degradation factor are present in the period with maximum irradiation (11:30h - 14:30h).  Degradation factor monthly-based differences are most expressed after 25 years of PV string exploitation. Prediction of annual energy production exhibits PV string AC power calculation by using the following relation: (field) (field) , AC DC I P P  (5) where μI is inverter efficiency. After determination of PAC-(field) values, annual energy production can be easily calculated. Purchase price of electricity produced from small capacity PV systems, installed on the households in Serbia, can be calculated by using relation (6).  0.01 (20.941 – 9.383 ) / ,P EUR kWh  (6) where P is installed power of PV system in MW units. Prediction of Annual Energy Production from PV String under Mismatch Condition due to Long-term Degradation 73 With assumed inverter efficiency of μI = 97%, PV string annual energy production has been predicted, together with annual money income and losses due to long-term degradation. Corresponding results are presented in Table 4. Table 4 PV string annual energy production, money income and losses due to long-term degradation PV string annual energy production and income Period of PV string exploitation New string 10 years 15 years 20 years 25 years Annual energy production [kWh] 3422 3374 3204 3058 2962 Annual money income [EUR] 715.6 705.6 670.1 639.5 619.4 Loss of money due to degradation [EUR] 0 10 45.5 76.1 96.2 With assumption that loss of money due to long-term degradation is approximately equal in consecutive time periods of 5 years (e.g. loss of money in time period 7.5 - 12.5 years is equal to 5 × loss of money in the 10th year of exploitation) it is possible to roughly estimate total loss of money in time period 0 - 27.5 years (very close to lifetime of PV string): 5 × (10 + 45.5 + 76.1 + 96.2) = 1139 EUR. It can be concluded that predicted amount of money loss due to long-term degradation is enough to buy several new PV modules during considered exploitation period. Even rough estimation of degradation factor could be of significant interest for economic predictions, especially for larger installed PV capacities (> 20 kW) where money income could be reduced for more than 10 000 EUR in lifetime exploitation period due to long-term degradation. 7. CONCLUSIONS Modelling of PV system degradation in terms of statistical prediction of annual energy production proved to be a very complex task, mainly because of many uncertainties related to long exploitation period and field conditions. Several useful guidelines and study case results have been presented in this article. The most common long-term degradation types have been modelled by using approximate relations, adopted on the basis of experimental observations. It has been shown that power losses of individual PV modules due to delamination and discoloration remain approximately constant under wide range of irradiation and ambient temperature values, while power losses due to corrosion proved to be temperature-dependent. Mismatch power losses, caused by different degradation rates of individual PV modules in PV string, have been identified as potentially significant part of total degradation losses. Methodology for prediction of annual energy production from PV string, based on horizontal irradiation and ambient temperature field measurements, has been modified in order to include long-term degradation effects. Degradation factor has been introduced as useful tool for validating power losses due to long-term degradation. Analysis of PV string consisting of 12 PV modules, located in Belgrade, study case, showed that money losses during lifetime exploitation period, caused by long-term degradation could overcome price of several new PV modules. Acknowledgement: The author would like to thank to Professors Jovan Mikulović and Željko Đurišić for their advices and support during research period. Special acknowledgement belongs to my best friend Slobodan Elez, who contributed with useful results related to his master thesis. 74 M. FORCAN REFERENCES [1] M. Forcan, “Prediction of Energy Production from String PV System under Mismatch Condition”, In Proceedings of the 2 nd Virtual International Conference on Science, Technology and Management in Energy - eNergetics, 2016, pp. 3-9. [2] M. Jošt and M. Topič, “Efficiency limits in photovoltaics – case of single junction solar cells”, Facta Universitatis, Series: Electronics and Energetics, vol. 27, no 4, pp. 631 - 638, December 2014. [3] Y. Georgiev, G. Angelov, T. Takov, I. Zhivkov and M. Hristov, “The photovoltaic behavior of vacuum deposited diphenyl-diketo-pyrrolopyrrole polymer”, Facta Universitatis, Series: Electronics and Energetics, vol. 27, no 4, pp. 639 - 648, December 2014. [4] O. Perpinan, E. Lorenzo and M.A. Castro, “On the calculation of energy produced by PV grid-connected system”, Progress in Photovoltaics Research and Applications, vol. 15, issue: 3, pp. 265-274, 2007. [5] M. Brabec, E. Pelikán, P. Krč, K. Eben and P. Musilek, “Statistical modeling of energy production by photovoltaic farms”, In Proceedings of the IEEE Elect. Power Energy Conf. (EPEC), Aug. 2010, pp. 1-6. [6] O. Perpinan, “Statistical analysis of performance and simulation of two axis tracking PV system”, Solar Energy, vol. 83, issue 11, pp. 2074-2085, Nov. 2009. [7] S. Jiang, K. Wang, H. Zhang, Y. Ding and Q. Yu “Encapsulation of PV Modules Using Ethylene Vinyl Acetate Copolymer as the Encapsulant”, Macromol. React. Eng., 9, pp. 522–529, 2015. [8] T. Shioda, “Delamination failures in long-term field-aged PV modules from point of view of encapsulant”, Lecture presented at 2013 NREL PV Module Reliability Workshop, Denver. [9] D. C. Jordan, J. H. Wohlgemuth, and S. R. Kurtz, “Technology and Climate Trends in PV Module Degradation”, in Proceedings of the 27th European Photovoltaic Solar Energy Conference and Exhibition, 2012, pp. 3118-3124. [10] M. Kempe, “Modelling of rates of moisture ingress into photovoltaic modules”, Solar Energy Materials & Solar Cells, vol. 90, issue: 16, pp. 2720–2738, 2006. [11] M. Kempe, “Ultraviolet test and evaluation methods for encapsulants of photovoltaic modules”, Solar Energy Materials & Solar Cells, vol. 94, issue: 2, pp. 246–253, 2010. [12] A. Ndiaye, A. Charki, A. Kobi, C.M.F. Kébé, P.A. Ndiaye and V. Sambou, “Degradations of silicon photovoltaic modules: A literature review”, Solar Energy, vol. 96, pp. 140–151, 2013. [13] D. Sera, R. Teodorescu and P. Rodriguez, “PV panel model based on datasheet values”, In Proceedings of the IEEE International Symposium on Industrial Electronics, Vigo, Spain, 2007, pp. 2392–2396. [14] M. Forcan, Ţ. Đurišić, and J. Mikulović, “An algorithm for elimination of partial shading effect based on a Theory of Reference PV String,” Solar Energy, vol. 132, pp. 51–63, 2016. [15] M. Forcan, J. Tuševljak, S. Lubura and M. Šoja, “Analyzing and modeling the power optimizer for boosting efficiency of PV panel,” IX Symposium Industrial Electronics INDEL, Banja Luka, November 2012, pp. 193-198. [16] M. Forcan and Ţ. Đurišić, “The analysis of PV string efficiency under mismatch conditions,” in 4th International Symposium on Environment Friendly Energies and Applications - EFEA, 2016, pp. 1-6. [17] C. Schwingshackl, M. Petitta, J.E. Wagner, G. Belluardo, D. Moser, M. Castelli, M. Zebisch and A. Tetzlaff, “Wind effect on PV module temperature: Analysis of different techniques for an accurate estimation”, Energy Procedia, vol. 40, pp. 77–86, 2013. [18] S. Bensalem and M. Chegaar, “Thermal behavior of parasitic resistances of polycrystalline silicon solar cells”, Revue des Energies Renouvelables, vol. 15, pp. 171-176, 2013. [19] M.L. Priyanka and S.N. Singh, “A new method of determination of series and shunt resistances of silicon solar cells”, Solar Energy Materials & Solar Cells, vol. 91, pp. 137–142, Jan. 2007. [20] D. Macdonald and A. Cuevas, “Reduced fill factors in multicrystalline silicon solar cells due to injection- level dependent bulk recombination lifetimes”, Progress in Photovoltaics: Research and Applications, vol. 8, pp. 363–375, 2000. [21] MATLAB/Simulink. MathWorks, Inc. Natick. Massachusetts. United States. [22] PV module data sheet, available online at http://www.suntellite.cn/en/product/suntellite-module- polycrystalline-20.html [23] R. Dubey, S. Chattopadhyay, V. Kuthanazhi, J. J. John, B. M. Arora, A. Kottantharayil, K. L. Narasimhan, C. S. Solanki, V. Kuber, J. Vasi, A. Kumar and O. S. Sastry “All India Survey of Photovoltaic Module Degradation 2013”, National Centre for Photovoltaic Research and Education, Mumbai, India, 2014, available online at http://www.ncpre.iitb.ac.in/pages/publications_reports.html [24] G. M. Masters, Renewable and Efficient Electric Power Systems. Hoboken, NJ: John Wiley & Sons, 2004, Chapters 7-8. http://www.suntellite.cn/en/product/suntellite-module-polycrystalline-20.html http://www.suntellite.cn/en/product/suntellite-module-polycrystalline-20.html http://www.ncpre.iitb.ac.in/pages/publications_reports.html