International Journal of Mechanical Engineering and Technology (IJMET) olume 9, Issue 11, November 2018, pp. 1251 1261, rticle ID: IJMET_09_11_129 vailable online at http://www.iaeme me.com/ijmet/issues.asp?jtype=ijmet&type=9&ity Type=11 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 IEME Publication Scopus Indexed STUDY OF MTHEMTICL METHOD FOR PRMETERS CLCULTION OF CURRENT- OLTGE CHRCTERISTIC OF PHOTOOLTIC MODULES EbtsamKadhum li Central Technical University / Institute of Technology / Departmentt of Electrical Techniques, Baghdad, Iraq BSTRCT The high efficiency of P solar module under sun radiation is necessary to describe the electrical parameters of the cell. Solar module analyzer is used for the professional testing of four solar panels at Baghdad climate conditions. oltage- solar current characteristics of various area of solar modules worked under irradiation for testing their quality and determining the optimal operational parameters for maximum electrical output were gained. The photovoltaic module is typically represented by an equivalent circuit whose parameters are calculated using the experimental current voltage characteristic I-. The precise determination of these parameters remains a challenge for researchers, which led to a diversification in models and numerical methods used for their characterizations. For the four solar module types,b,c and D, the parallel resistance R sh is generally high, and its contribution has a little influence in the model, so for that the model with four parameters is one of the mainly used in literature. Parametric characterization of the four parameters model is the objective of this work. Keywords: Solar Module, Four Parameters, oltage, Current, Power. Cite this rticle: EbtsamKadhum li, Study of Mathematical Method for Parameters Calculation of Current-oltage Characteristic of Photovoltaic Modules, International Journal of Mechanical Engineering and Technology, 9(11), 2018, pp. 1251 1261. http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&type=9&itype= =11 1. INTRODUCTION Solar power is one of the basic sources of energy replacing fossil fuels due to its abundance. Its versatility, abundance and environmental friendly have made it one of the renewable sources of power. Solar modules convert solar power into electrical power that is used to drive various appliances. Many works that had been made to improve the efficiency of these solar modules and the reduction of their costs. Modeling and simulation of various structures
Study of Mathematical Method For Parameters Calculation of Current-oltage Characteristic of Photovoltaic Modules of solar cells provides an insight into the physics involved in its operation and best understanding of the ways to improve their efficiency. Using of fossil fuels for power supply is the main threat for the stability of the global climate system and our natural living conditions. The scientific community gave evidence that mankind has to decrease the greenhouse gases emissions, mainly CO 2 and methane, by 60-70% as a minimum until the year 2050 [1]. In order not to harm our natural living spaces and threaten their resilience, a renewed compatibility would require a suitable form of energy alternatives sources that should be independent, easily accessible, and low in cost and should be environmentally clean. Renewable energy, and in particular power generation from solar energy using Photovoltaic (P) has emerged in last decades since it has the aforesaid benefit and less maintenance, no wear and tear. Photovoltaic system are in either stand-alone systems such as water pumping, domestic and street lighting, electric vehicles, military and space applications [2-3] or grid-connected configurations like hybrid systems and power plants [4]. The main aim of this work is to obtain solar parameters values of the selected solar modules by simplified explicit method. To study the actual system behavior we need an authenticated simulation model. Many photovoltaic MTLB models are available in the literature. Many researchers are working to develop a sophisticated model to reduce the computational time and to get accurate information with less number of parameters. In literature [5]showed that the five parameter model accurate with experimental data under out door weather conditions in three days at different radiation and the error between the maximum power declared by manufacturer and simulation at standard test conditions (STC) is 5.63%. The value of ideality factor obtained at maximum power 250.1W is equal 1.58. Soto et al. [6]calculated the panel internal parameters photocurrent,saturation current, series resistance, shunt resistance and ideality factor (I ph,ref, I o,ref, R s,ref, R sh,ref and ref ) respectively of five parameter model at reference condition (G=1000W/m² and T=25 o C) to predict the (current voltage) curve for four different cell(single crystalline,poly crystalline,silicon thin film,and triple-junction amorphous). The five parameter model agree with both experimental measurements of the National Institute of Standards and Technology (NIST) and the king model for all four panel types at different working conditions. Dongue et al. [7] studied modeling of two different solar modules (mono-crystalline and multi-crystalline) for various working operation by using two models, four parameter model which assume shunt resistance of infinity value and five parameter model which takes into account series and shunt resistance. They concluded that both four and five parameter models accurately fit experimental data of both P panels and the five parameter model is more accurate than four parameter model in power and current.the double exponential model is the most accurate model, which contains seven unknown parameters. In general, this model is more accurate for polycrystalline silicon cells [8]. Bellia et al. [9] developed an empirical model to produce the current and voltage curve using five located points at the current-voltage curve. However, the method needs empirically determined parameters which are typically not available from the manufacturers datasheet. The coefficients are provided by the Sandia National Laboratory. There are many researchers [10-13]thatstudied the effect of operating temperature upon the performance of free-standing P panel and simple semi-empirical explicit correlation that was used included the environmental conditions. s a result, the power depends linearly on panel temperature. This paper presents the study of experimental testing results for the performance of solar four solar module types under natural sun and outdoor exposure in Baghdad for four consecutive months. lso, the aim of the paper is to investigate validation of I- and P- output curves of the five parameter model of P module (using Matlab/Simulink) and http://www.iaeme.com/ijmet/index.asp 1252 editor@iaeme.com
EbtsamKadhum li compare them with the corresponding experimental results. These comparisons were made at different solar irradiance values 100 to 1000 W/m 2, and also and took into account environmental factors on module temperature. The precise determination of these parameters remains a challenge for researchers, which led to a diversification in models and numerical methods used for their characterizations. For the four solar module types, B, C and D the parallel resistance R sh is generally high, and its contribution has a little influence in the model, so for that the model with four parameters is one of the mainly used in literature. Parametric characterization of the four parameters model is the objective of this work. 2. EXPERIMENTL MESUREMENTS The Prova 200 solar module analyzer is used for the testing and maintenance of solar panels and modules. The solar panel analyzer also provides the user with current and voltage (I-) test curves, maximum solar power as well as current and voltage. Figure 1 represent the four module types and Table 1 summarized the four solar module characteristic properties. = 0.03m 2 B=0.036m 2 C= 0.842m 2 D=1m 2 Type rea, oc, m 2 Figure 1 Solar modules tested, B, C, and D Table 1 Solar module specifications I sc, Peak power, W Peak voltage, Peak current, Production date 0.03 11 0.33 1.8 6.6 0.28 2013 B 0.36 18 3 38 16 2.4 2010 C 0.84 20 6.0 100 16.8 4.8 2013 D 1.00 22 8.1 130 18.5 6.0 2013
Study of Mathematical Method For Parameters Calculation of Current-oltage Characteristic of Photovoltaic Modules 3. FOUR PRMETERS MODEL FOR PRMETERS CLCULTION OF CURRENT-OLTGE CHRCTERISTIC OF PHOTOOLTIC MODULE The equivalent one-diode model is a four-parameter empirical model to predict the electrical performance of monocrystalline and polycrystalline) P modules. The model simulates a P module with an equivalent circuit consisting of a direct-current source, diode, and one or two resistors. The strength of the current source is dependent on incident solar radiation. The current-voltage characteristics of the diode depend on the temperature of the solar cells: the hotter the module, the lower its electrical output. The model determines current as a function of load voltage. The performance of an array of identical modules is assumed to be linear with the number of modules in series and parallel [14, 15]. The model with four parameters as its name indicates has four unknown parameters namely: I L (the photocurrent), I 0 (the saturation current), (ideality factor) and R s (the series resistance). These parameters are not usually measurable or included in the manufacturing data. The present model is one of the mainly used for modeling solar cells, from which one can describe the cell current-voltage curve [14-16] = exp + 1 The four unknown parameters in this model are I L (the photocurrent), I 0 (the saturation current), (ideality factor) and R s (the series resistance). These parameters are determined from measurements of the I- characteristic at reference values of irradiance and temperature (E ref =1000 W/m 2, T ref =25 C) Three remarkable couples of points from the I- curve (0, I sc ), ( oc, 0) and ( m, I m ), can be employed in order to determinate the unknown parameters, as = exp 1 0= exp 1 1 2 3! = exp! +! 1 4 3.1. Simplified explicit method This method considers as a first approximation I L = I sc, after simplification of Eq.2, Eq.3 and Eq.4 we obtain: = 5 0= exp! = exp! +! 1 7 From Eq.5 and Eq.6 one can deduce the saturation current & = exp 8 nd from that Eq.1becomes = 1 exp + 9 The equation at the point of maximum power at is turn becomes 6 http://www.iaeme.com/ijmet/index.asp 1254 editor@iaeme.com
EbtsamKadhum li! = 1 exp! +! 10 From this equation, we can deduce the value of series resistance ) * +,- ln11 2 3 5+. 2! = *4 11! The last parameter to be determined is the ideality factor, by exploiting the fact that the derivative of the maximum power is zero: 67 Ә = 0= 6 Ә +Ә Ә nd using Eq.1 one can find 12 2! = 2 [ *4 +ln11 2 13 3 5] 2 *4 :2 3 2 *4 The substitution of different parameters with their respective formulas in Eq.1 gives a simple equation linking the current I to the voltage for different temperatures and irradiances. Table 2 tabulated the results of extracting solar module () parameters. Tables 3, Table 4 and Table 5 are represented the corresponding modules B,C and D respectively. The experimental results of the solar cells from different manufacturers are presented. Cell samples have been investigated regarding their I-characteristics at different solar intensities in a range 100-1000 W/m 2 and the ambient temperature between (40-45 o C). ll the measurements and the characteristics of these solar modules have been made within the date of Sep. and Oct. 2013. Table 2Solar module () parameters at irradiances rate 100-1000 W/m 2 G, I sc, oc, I m, m, R s, Ω I o, I ph, FF Ƞ, % 100 0.0347 8.545 0.0286 6.425 2.34 7.87916 1.37E-05 0.03 0.619 6.1 200 0.0439 9.058 0.0362 6.921 2.59 0.95089 2.43E-05 0.04 0.630 4.2 300 0.0682 9.309 0.0591 6.985 1.82 10.3377 1.20E-06 0.07 0.650 4.6 400 0.0791 9.359 0.0674 7.182 2.21 3.0359 9.12E-06 0.08 0.653 4.0 500 0.1192 9.606 0.1041 7.158 1.73 7.47569 8.21E-07 0.12 0.650 5.0 600 0.1341 9.618 0.1126 7.238 2.37 3.21481 2.18E-05 0.13 0.631 4.5 700 0.1607 9.656 0.1371 7.047 1.95 6.33398 3.84E-06 0.16 0.622 4.6 800 0.1656 9.619 0.1446 6.78 1.45 9.96413 1.12E-07 0.17 0.615 4.1 900 0.1905 9.674 0.165 6.902 1.62 7.58043 5.32E-07 0.19 0.617 4.2 1000 0.2153 9.995 0.1822 6.883 1.75 8.71336 1.00E-06 0.22 0.582 4.2 http://www.iaeme.com/ijmet/index.asp 1255 editor@iaeme.com
Study of Mathematical Method For Parameters Calculation of Current-oltage Characteristic of Photovoltaic Modules Table 3 Solar module (B) parameters at irradiances rate 100-1000 W/m 2 G, I sc, oc, I m, m, R s, I o, I ph, FF Ƞ, % Ω 100 0.339 15.55 0.2508 11.94 3.90-3.514 3.20E-03 0.34 0.568 8.3 200 0.4672 15.7 0.3737 12.31 3.08-2.263 1.20E-03 0.47 0.627 6.4 300 0.5002 15.97 0.403 12.59 3.07-2.286 1.14E-03 0.50 0.635 4.7 400 0.764 16.61 0.6264 13.18 2.97-1.4761 1.11E-03 0.76 0.650 5.7 500 1.028 16.69 0.8707 13.34 2.51-0.7764 4.29E-04 1.03 0.676 6.4 600 1.127 16.83 0.9545 13.52 2.57-0.8439 5.23E-04 1.13 0.680 6.0 700 1.342 17.02 1.154 13.51 2.26-0.251 2.01E-04 1.34 0.682 6.2 800 1.439 17.08 1.238 13.61 2.29-0.3031 2.30E-04 1.44 0.685 5.9 900 1.658 17.13 1.426 13.67 2.31-0.292 2.79E-04 1.66 0.686 6.0 1000 1.928 17.16 1.684 13.51 1.98 0.09311 7.50E-05 1.93 0.687 6.3 G, I sc, Table 4 Solar module (C) parameters at irradiances rate 100-1000 W/m 2 oc, I m, m, R s, Ω I o, I ph, FF Ƞ, % 100 0.4442 37.03 0.3464 31.2 4.49-19.767 5.34E-03 0.44 0.657 12.8 200 0.5969 37.71 0.5173 31.12 2.40-4.6819 1.30E-04 0.60 0.715 9.6 300 0.9617 37.4 0.8206 31.06 2.71-4.0815 5.83E-04 0.96 0.708 10.1 400 1.128 37.71 0.9927 30.99 2.09-1.5712 7.20E-05 1.13 0.723 9.1 500 1.347 38.02 1.194 31.03 1.95-0.7526 3.77E-05 1.35 0.723 8.8 600 1.542 37.75 1.367 31.01 1.96-0.8919 5.08E-05 1.54 0.728 8.4 700 1.832 37.97 1.637 31.03 1.81-0.3682 2.32E-05 1.83 0.730 8.6 800 2.175 38.05 1.943 30.96 1.79-0.2034 2.49E-05 2.18 0.726 8.9 900 2.41 37.91 2.169 30.7 1.64 0.08449 9.70E-06 2.41 0.728 8.8 1000 2.65 37.8 2.367 30.38 1.73 0.09037 2.13E-05 2.65 0.717 8.5 Table 5 Solar module (D) parameters at irradiances rate 100-1000 G, I sc, oc, I m, m, R s, Ω I o, I ph, FF Ƞ, % 100 1.05 18.69 0.9313 15.98 1.92-1.7499 8.79E-05 1.05 0.758 14.9 200 1.27 18.91 1.135 16.23 1.83-1.3731 5.76E-05 1.27 0.767 9.2 300 1.905 19.23 1.752 16.21 1.28-0.1883 9.84E-07 1.91 0.775 9.5 400 2.513 19.42 2.295 16.28 1.40-0.1729 3.72E-06 2.51 0.765 9.4 500 2.965 19.46 2.569 16.77 2.48-0.9685 1.54E-03 2.97 0.746 8.6 600 4.043 19.67 3.72 16.22 1.23 0.05905 8.39E-07 4.04 0.758 10.1 700 4.332 19.63 3.956 16.26 1.37-0.0255 4.30E-06 4.33 0.756 9.2 800 5.332 19.65 4.906 16.06 1.21 0.08875 6.73E-06 8.59 0.752 9.9 900 5.719 19.59 5.262 16.04 1.21 0.07411 9.00E-07 5.72 0.753 9.4 1000 6.276 19.65 5.774 15.95 1.19 0.10363 7.05E-07 6.28 0.746 9.2 http://www.iaeme.com/ijmet/index.asp 1256 editor@iaeme.com
EbtsamKadhum li Figure 2 oltage-current (I) and power-voltage (P) curves of solar module at irradiance 100 Figure 3 oltage-current (I) and power-voltage (P) curves of solar module at irradiance 200 Figure 4 oltage-current (I) and power-voltage (P) curves of solar module at irradiance 300
Study of Mathematical Method For Parameters Calculation of Current-oltage Characteristic of Photovoltaic Modules Figure 5 oltage-current (I) and power-voltage (P) curves of solar module at irradiance 400 Figure 6 oltage-current (I) and power-voltage (P) curves of solar module at irradiance 500 Figure 7 oltage-current (I) and power-voltage (P) curves of solar module at irradiance 600
EbtsamKadhum li Figure 8 oltage-current (I) and power-voltage (P) curves of solar module at irradiance 700 Figure 9 oltage-current (I) and power-voltage (P) curves of solar module at irradiance 800 Figure 10 oltage-current (I) and power-voltage (P) curves of solar module at irradiance 900
Study of Mathematical Method For Parameters Calculation of Current-oltage Characteristic of Photovoltaic Modules Figure 11 oltage-current (I) and power-voltage (P) curves of solar module at irradiance 1000 4. CONCLUSION The objective of the solar panels modeling is of the estimation of their behavior under different meteorological conditions. The simplified explicit method has been presented in order to estimate the parameters of the four parameters model and to simulate its currentvoltage and power voltage characteristics. List of Symbols Diode factor. FF Fill factor G Solar radiation, I D I 0 I L I m I P I sc current is related to the diffusion current, Diode saturation current, Photocurrent, Maximum Current atp max, m Operating current, Current at short circuit, m J sc Photocurrent density, m/cm 2 J diff Diffusion current, K, k B Boltzmann constant,1.3806488(13) 10 23 J/K N s P P m R L R sh R s T T Number of cells in series. Photovoltaic Maximum solar power, w Load resistance, Ω shunt resistances, Ω series resistances, Ω cell temperature,k temperature, k maxp, mp Maximum voltage at P max, oc oltage at open circuit, < Efficiency, %
EbtsamKadhum li REFERENCES [1] M.. Green, Solar Cells. (rtech House, Boston, 1992). [2] BP, 2011. Statistical Review of World Energy 2011. [3] E.L. Meyer, E.E. van Dyk, ssessing the reliability and degradation of P module performance parameters, (IEEE Transactions on Reliability, 53, No.1, March 2004. [4] J. Decker, Performance of 170 grid connected P plants in northern Germany-analysis of yields and optimization potentials. (Solar Energy 59 1997) 127-133.Panels Using Only Reference Data, Energy and [5] oun, N.,Chenni R., Nahman B., Bouchouicha K.:Evaluation and alidation of Equivalent Five Parameter Model Performance for Photovoltaic Power Engineering, ol. 6, No. 9, pp.235-245, 2014. [6] De Soto, W., Klein S.., Beckman W..: Improvement and alidation of Model ForPhotovoltaic rray Performance, Solar Energy, ol. 80, No. 1, pp.78-88, 2006. [7] Dongue, S. D., Njomo D., Tamba J. G., Ebengai L.:Modelling of Electrical Response of IlluminatedCrystalline Photovoltaic Modules Using Four-nd Five-Parameter Models, International Journal ofemerging Technology and dvanced Engineering, ol. 2, No. 11, pp. 612-619, 2012. [8] bdulwahhad, O. M.: Improvement of the MTLB /Simulink Photovoltaic System Simulator Based on a Two-Diode Model, International Journal of Soft Computing and Engineering, ol.4, No.1, 2014. [9] Bellia, H., Youcef R., Fatima M.: detailed modeling of photovoltaic module using MTLB,NRIG Journal of stronomy and Geophysics, ol. 3, No. 1, pp.53-61, 2014. [10] Skoplaki, E.,Boudouvis. G.,Palyvos J..: Simple Correlation for the Operating Temperature of Photovoltaic Modules of rbitrary Mounting, Solar Energy Material and Solar Cells, ol. 92, No.11, pp.1393-1402, 2008. [11] Elias, B. H., lsadoon S. H. M., bdulgafar S..:Modeling and Simulation of Photovoltaic Module Considering an Ideal Solar Cell, International Journal of dvanced Research in Physical Science, ol. 1, No. 3, pp. 9-18, 2014. [12] Fesharaki,. J. et al.: The Effect of Temperature on Photovoltaic Cell Efficiency, Proceedings of the1st International Conference on Emerging Trends in Energy Conservation ETEC, (2011). [13] Ferry, R., Monoian E.: field guide to renewable energy technologies, Project of society for cultural Exchange and land rt Generator Initiative, 2012. [14] T. U. Townsend, method for estimating the long term performance of direct-coupled photovoltaic systems. MS Thesis, Solar Energy Laboratory, University of Wisconsin, Madison, 1989. [15] Widalys De Soto. Improvement and alidation of a Model for Photovoltaic rray Performance.MS Thesis, Solar Energy Laboratory University of Wisconsin-Madison, 2004. [16] Bryan F. Simulation of grid-tied building integrated photovoltaic systems. MS thesis, Solar Energy Laboratory, University of Wisconsin, Madison, 1999. http://www.iaeme.com/ijmet/index.asp 1261 editor@iaeme.com