investigation of performance parameters of different photovoltaic cell materials using the lambert w function

Available online at www.sciencedirect.com ScienceDirect Energy Procedia 90 (2016) 566 – 573 5th International Conference on Advances in Energy Research, ICAER 2015, 15-17 December 2015, Mumbai, India Investigation of Performance Parameters of Different Photovoltaic Cell Materials using the Lambert-W Function a b c Dhass A D a*, Lakshmi.P b, Natarajan.E c Research Scholar, Institute for Energy Studies, College of Engineering, Guindy, Anna University, Chennai-600025, India Professor, Department of EEE, College of Engineering, Guindy, Anna University, Chennai-600025, India Professor, Institute for Energy Studies, College of Engineering, Guindy, Anna University, Chennai-600025, India Abstract A photovoltaic (PV) system can generate electrical energy and maintain sustainability in the environment In the future, these energy-generating systems that not alter the environment will play a major role in building a nation A PV system, a sustainable energy source, acts as a vital system in reducing environmental pollution and is called a clean energy source In this study, we analysed the performance of various PV cell materials such as mono crystalline (m-Si), polycrystalline (p-Si), and black solar cells The operating parameters of a solar PV cell, such as parasitic series and shunt resistances and photo-generated current, are affected by temperature A m-Si module of 250 W shunt resistance, polycrystalline module of a 3-kW (Yingli’s manufactured) system in a series resistance, and black m-Si type of 250 W and kW of photo-generated current were highly influenced and changed their output with the effect of temperature Theoretical parasitic resistances were calculated using the Lambert W function These theoretical investigation results were compared with the experimental results of 3-kW polycrystalline solar PV modules Moreover, the influence of this resistance on system performance was analysed Keywords: parasitic resistances; photovoltaic (PV) modules; photo-generated current; lambert-W function Introduction Parasitic shunt and series resistances influence the degradation of performance parameters by reducing the energy from a system [1-2] Wrong shunting of a p-Si silicon solar cell reduces the performance of solar cells This issue may be rectified and the overall output performance may be improved using a laser isolation process on the wrongly shunted solar cell [3] The five-parameter model of a single diode photovoltaic (PV) cell equivalent delivers accurate results of performance characteristics In particular, shunt and series resistances play a vital role in determining the progress of the performance process These resistances affect the slope of the I-V characteristic curve Similarly, a photo-generator is not a constant current or voltage source, and it describes the relationship between current and voltage in the equivalent circuit [4] A solar PV cell is a function of temperature and solar irradiation The effect of temperature on a PV module changes the performance and output electrical parameters of a PV cell [5] 1876-6102 © 2016 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of ICAER 2015 doi:10.1016/j.egypro.2016.11.225 A.D Dhass et al / Energy Procedia 90 (2016) 566 – 573 567 Nomenclature A Black Mono Ipv Imp Isc Mono Rs Rsh Vt Vmp Voc A,B,C,D Ideality factor of the diode Black monocrystalline Photovoltaic current (A) Current at the maximum power point (A) Short circuit current (A) Monocrystalline Series resistance (Ω) Shunt resistance (Ω) Thermal voltage of the cell (V) Voltage at the maximum power point (V) Open circuit voltage (V) Notations for simplifying the equations A series resistance was evaluated using different methods, and the values differed This deviation occurred because of the number of diodes in the solar cell model, values such as ideality factor, shunt resistance, and estimation of other relevant parameters Thus, a series resistance may not estimate accurately within the range of values in a solar PV cell [6] Increasing the series resistance by 0.1 Ω reduces the corresponding fill factor value by 2.5% [7] The effect of temperature on the parasitic resistances of a polycrystalline solar cell was identified A series resistance exhibited a positive temperature coefficient, whereas a shunt resistance produced a negative temperature coefficient at a solar radiance of 100 mW/cm2[8] Various connection configurations of PV cells in a module, such as simple series, series–parallel, total cross-tied, bridge-linked, and honey comb, changed their parasitic resistance values based on the temperature variation [9] At low radiation level (400 W/m2) on a PV module, its shunt resistance increased; when the radiation level increased (above 400 W/m2), its shunt resistance decreased correspondingly in a PV cell or module The value of the series resistance decreased at an increasing level of irradiation intensity [10] This study analysed the effect of temperature on parasitic resistances and photo-generated current on the same type of m-Si module having different manufacturing categories, and the results were compared with the experimental values Basics of different PV cell materials 2.1 Yingli’s PV modules We used Yingli’s PV module, a type of m-Si PV module, having 250 W capacity and a 3-kW PV system for the experimental analysis This module was installed for experiments, and the output values were measured for calculating parasitic resistances and photo-generated current in a PV module The details of the electrical parameters are provided in Table 2.2 Monocrystalline (m-Si) PV module This m-Si PV module is considered for analytical objectives only and was used as a typical PV module to compare with the experimental results A 250 W and 3-kW PV system was used for evaluating the parasitic resistance and output current The ratings of PV modules are listed in Table 2.3 Black monocrystalline(m-Si) PV module A black m-Si PV module was laminated with a black back sheet This PV module exhibited a high efficiency 568 A.D Dhass et al / Energy Procedia 90 (2016) 566 – 573 level, long service, and superior operational performance under low levels of irradiation The electrical ratings of this PV module are presented in Table [11] Table 1: Electrical parameter specifications of different PV modules Sr No Electrical parameters specifications Monocrystalline PV module Yingli’s monocrystalline PV Black (ESP 250 6M) module module Rated maximum power 250 W 250 W 250 W Rated voltage 30.62 V 30.2 V 29.9 V Rated current 8.16 A 8.11 A 8.36 A Open circuit voltage 37.44 V 37.8 V 37.6 V Short circuit current 8.73 A 8.63 A 8.9 A monocrystalline PV Methodology The concept of this study is used to estimate the parasitic resistance and photo-generated current of different types of PV modules by using the Lambert W function The estimated values and the experimental output values of Yingli’s 3-kW PV modules were compared Typically, parasitic resistances are calculated using complex equations To overcome this problem, the Lambert W function can be used to estimate the parasitic resistances using the current– voltage exponential equation relationship in a PV module The Lambert W function converts a complex equation in to a simple equation by using the exponential concept By using this technique, the current is related to the explicit function of the voltage; this provides high accuracy of the given modules [12-14] 3.1 PV cell equivalent circuit Fig Solar cell equivalent circuit [15] The current-generating source, diode, and shunt resistance are connected in parallel The illustrative equivalent circuit of a single diode PV cell is shown in fig.1 A series resistance is connected through the load terminal in a series connection In an ideal scenario a large shunt resistance (in the range of mega ohms) is considered to reduce the leakage current A low-value series resistance (in the range of ohms) and large amount of photo-generated current flow through the resistance and generate electric power across the PV module The calculation of shunt and series resistances requires complex equations and depends on several parameters such as internal parameters, manufacturing technique, and external atmospheric conditions Mitigating this problem by using the Lambert W function helps to reduce the complexity, and it is easy to obtain the resistance values The Lambert W function is used to estimate parasitic series and shunt resistances and photo-generated current 569 A.D Dhass et al / Energy Procedia 90 (2016) 566 – 573 3.2 Series resistance The simplified expression for series resistance is as follows: ( aVtVmp I mp − I sc (V mp I sc + Voc (I mp − I sc ))(Vmp ) ⎛ Vmp + I mp Rs − Voc = exp⎜⎜ aVt − I mp Rs ) − aVt (Vmp I sc − Voc I mp ) ⎝ ⎞ ⎟⎟ (1) ⎠ Using the Lambert W function Rs = A(W−1 (B exp(C )) − (D + C )) (2) where, A= D= Vmp (2 I mp − I sc ) aVt , B=− , (Vmp I sc + Voc (I mp − I sc )) I mp (Vmp I sc − Voc I mp ) , ⎛ 2Vmp − Voc ⎞ ⎟⎟ + C = −⎜⎜ ⎝ aVt ⎠ (Vmp I sc + Voc (I mp − I sc )) Vmp − Voc aVt 3.3 Shunt resistance By implementing the Lambert W function in the shunt resistance equation, we obtain the following simplified expression: Rsh = (V mp − I mp Rs )(Vmp − Rs (I sc − I mp ) − aVT ) (V mp − I mp Rs )(I sc − I mp ) − aVT I mp (3) 3.4 PV current The photo-generated current is interrelated with the shunt and series resistances of a PV cell/module The simplified expression is as follows: I pv = Rsh + Rs I sc Rsh (4) The Lambert W function simplifies the complexity to determine the parasitic resistance and photo-generated current This method has provided the best fit with experimentally measured values Moreover, the accuracy level is within the range [16] This Lambert W function is derived using Maple This function provides the expression of current– voltage characteristics, including the shunt and series resistances of a solar PV cell [17] The voltage and current are related to explicit equations in the Lambert W function and has considerably reduced the calculation time for the analytical values of electrical parameters Lastly, this technique is simple for estimating and relating the current and voltage of solar PV modules [18] 570 A.D Dhass et al / Energy Procedia 90 (2016) 566 – 573 Experimental setup The experimental setup for a 3-kW solar PV system is a combination of × module configurations is shown in fig.2 The PV modules are assembled as four numbers in series and three numbers in parallel, and each PV module has a capacity of 250 W The output parameters, voltage and current, are measured using a voltmeter and ammeter, respectively The interconnections of cables in a PV module are connected to a common junction box, which is placed at the bottom of the PV module system The temperature on the PV modules was measured using a thermometer The values measured by the Yingli’s m-Si PV modules are compared with other PV modules of the same m-Si materials This setup was installed and the readings were measured at the Centre for Nanoscience and Technology (CNST), Anna University, Chennai The temperatures were measured using a digital thermometer, and simultaneously, the electrical parameters of voltage and current were measured using the voltmeter and ammeter, respectively Fig Photographic view of 3-kW Yingli’s m-Si PV system Results and Discussion 5.1 Temperature effects on shunt resistance Fig Effect of temperature on shunt resistance of PV modules A.D Dhass et al / Energy Procedia 90 (2016) 566 – 573 571 The effect of temperature on the shunt resistance in a PV module changes exponentially on decreasing the corresponding values A low temperature of the PV module was maintained, which increased the corresponding shunt resistance By contrast, for a high temperature of the PV module, the shunt resistance decreased For the same rating of various PV materials, the same m-Si module exhibited different performance curves, which are based on material properties The shunt resistance measured practically deviated initially at 272 Ω and then at 156 Ω from the analytical value for considering a 3-kW PV system The decrease of shunt resistance against the increase of thermal effect may increase the leakage current, thereby reducing the lifespan of PV modules An increase in the shunt resistance reduced the voltage level Both the shunt resistance and voltage are directly proportional and are affected by temperature changes The effects of temperature on the shunt resistance in the PV module are mainly classified on the basis of ratings of the PV module We used 250 W and 3-kW PV panels for analysis and a 3-kW m-Si module for the experimental study Mono 250 W exhibited a maximum amount of shunt resistance against a minimum temperature in the PV module Similarly, the shunt resistances of Yingli 250 W, black mono 250 W, Yingli kW (practical), mono kW, Yingli kW, and black mono 3-kW PV modules reduced against the change in the temperature of the PV module Figure shows the effect of temperature on the shunt resistance of the PV module This effect is observed due to material properties, the PV cell connected in series or parallel in a string, and the amount of solar radiation incident on the PV module The shunt resistance of Yingli’s 3kW (practical) PV module was estimated through an experimentally measured value, and the remaining types of PV modules were estimated using Lambert W functions For a single-type m-Si PV module under different ranges of specification, a comparison between the analytical and practical values of the shunt resistance is plotted in Fig The shunt resistance values for black mono kW, Yingli kW, and mono kW modules decreased when the temperature changed from 20°C to 35°C Then, the shunt resistance value maintained the nearby constant value, and the temperature of PV modules increased For the remaining modules, the shunt resistance may not be attained with the nearby constant or within the range for the increasing level of temperature in the PV modules 5.2 Temperature effects on series resistance Fig Effect of temperature on series resistance of PV modules The series resistance, connected in series with the electric load, linearly changes its value with a change in the temperature For all different types of PV modules, an increase in the temperature level gradually increased the 572 A.D Dhass et al / Energy Procedia 90 (2016) 566 – 573 corresponding series resistance because of the decreased mobility in the PV cell material Although the voltage drop decreased because of the current, the effect of temperature on series resistance increased the power loss The impact of series resistance on the performance of PV modules reduced the fill factor and short circuit current, but did not affect the open circuit voltage The PV module’s power output was inversely proportional to the series resistance parameter; both varied with the effect of another parameter In general, the series resistance value is low Under particular conditions such as rise in the temperature on PV modules, these values increase The Yingli kW (practical) only exhibits a maximum level of the series resistance compared with the other conditions and specifications of the PV module ratings is shown in fig.4 In addition to these PV modules, the resistances of the remaining modules were estimated using Lambert W functions All theoretically estimated series resistance values were within the range only 5.3 Temperature effects on PV current Under all working conditions, the effects of temperature on solar PV modules increase the photo-generated current linearly; the same phenomenon was exhibited in this study, but with a different range of photo-generated output current Both the 250 W and kW PV modules and the black solar PV module generated a maximum output PV current against with the same PV ratings of other modules Figures (a) and (b) show the output current for Yingli’s m-Si type and black solar PV modules These modules exhibited parasitic resistance values against the thermal effect, which may not exhibit the most amount of the PV output current value These modules had a rating of 250 W and kW specifications The black mono type of 250 W and kW produced a maximum solar PV current compared with the other two categories (Figs (a) and (b)) These PV modules had a maximum level of PV current generated compared with the two types of PV modules of the same materials These results were influenced by the parasitic resistance because the PV output current increased with an increase in the shunt resistance, decrease in the series resistance, and the overall effect of temperature In Fig 5(a), the 250-W black solar cell produces the output current 8.93–9 A when the temperature ranges from 20°C to 50°C, and similarly, the other two categories were affected by the output current against the thermal effect (as shown in the same graph) Figure 5(b) plots the 3-kW PV module output current with variation in temperature; the black solar PV module exhibited a maximum output current from 36.04 A to 37 A In this process, the effect of temperature exhibited more control on the PV cell than the PV module a b Fig ( a, b) Effect of temperature on PV current of PV modules A.D Dhass et al / Energy Procedia 90 (2016) 566 – 573 Conclusion This study analysed the effect of temperature on parasitic resistances and photo-generated current in a solar PV module, and the values were estimated using the Lambert W function Similar modules of m-Si types manufactured by different companies were used for analysis The different m-Si PV modules, such as Yingli-manufactured m-Si, m-Si, black solar PV module, and practically measured values of Yingli m-Si PV module’s parasitic resistance and photo-generated current were compared to analyse the effect of temperature The results showed that the m-Si 250W module was highly sensitive to temperature for measuring the shunt resistance These changes exponentially decreased with an increase in temperature A gradual increase in temperature increased the corresponding series resistance This analysis can be used for PV material selection under high temperature applications This process confirms that for similar types of PV materials, such as m-Si of different manufacturing types, PV modules may not deliver the same output results under the same working conditions Hence, modules must be carefully assembled in the same system Acknowledgements We thank the Centre for Nanoscience and Technology (CNST), Anna University, Chennai, for allowing us to conduct this study in their solar photovoltaic system References [1] K Bouzidi, M.Chegaar, A.Bouhemaduu, Solar cells parameters evaluation considering the series and shunt resistance, 2007, 91: 1647-51 [2] Je Ranuarez, A Ortiz-cond Sanchez fjg, A new method to extract diode parameters under the presence of 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modules, International Journal of Photoenergy, Vol.2014, Article ID 346704, pp: 1-9 573 ... Methodology The concept of this study is used to estimate the parasitic resistance and photo-generated current of different types of PV modules by using the Lambert W function The estimated values and the. .. 250 W, Yingli kW (practical), mono kW, Yingli kW, and black mono 3-kW PV modules reduced against the change in the temperature of the PV module Figure shows the effect of temperature on the shunt... compared with the two types of PV modules of the same materials These results were influenced by the parasitic resistance because the PV output current increased with an increase in the shunt