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Adjusting the Single-Diode Model Parameters of a Photovoltaic Module with Irradiance and Temperature

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Adjusting the Single-Diode Model Parameters of a Photovoltaic Module with Irradiance and Temperature energies Article Adjusting the Single-Diode Model Parameters of a Photovoltaic Module with Irradiance and Temperature Nader Anani 1,* and Haider Ibrahim 2 1 School of Engineering, University of Wolverhampton, Telford TF2 9NT, UK 2 Department of Electrical Technique, Southern Technical University, Technical Institute-Qurna, Basra, Iraq; [email protected] * Correspondence: [email protected] Received: 30 May 2020; Accepted: 17 June 2020; Published: 22 June 2020 Abstract: This paper presents a concise discussion and an investigation of the most literature-reported methods for modifying the lumped-circuit parameters of the single-diode model (SDM) of a photovoltaic (PV) module, to suit the prevailing climatic conditions of irradiance and temperature. These parameters provide the designer of a PV system with an essential design and simulation tool to maximize the efficiency of the system. The parameter modification methods were tested using three commercially available PV modules of different PV technologies, namely monocrystalline, multicrystalline, and thin film types. The SDM parameters of the three test modules were extracted under standard test conditions (STC) using a well-established numerical technique. Using these STC parameters as reference values, the parameter adjustment methods were subsequently deployed to calculate the modified parameters of the SDM under various operating conditions of temperature and irradiance using MATLAB-based software. The accuracy and effectiveness of these methods were evaluated by a comparison between the calculated and measured values of the modified parameters. Keywords: ideality factor; irradiance; photocurrent; saturation current; series resistance; shunt resistance; single-diode model; temperature effects 1. Introduction Photovoltaic systems offer the most direct conversion of the electromagnetic energy in the sunlight into electricity. At the heart of any PV power plant is the PV generator, which typically consists of an array of PV modules connected in series-parallel combinations to deliver the rated power at the required levels of terminal current and voltage. Each PV module consists of several PV cells, which are almost always connected in series to provide a specific terminal voltage. The terminal I-V (current-voltage) and P-V (power-voltage) characteristics of a typical PV generator, whether it is a cell, a module, or an array, are shown in Figure1. Three salient points can be identified on the I-V curve: The short circuit (SC), the open circuit (OC), and the maximum power point (MPP). The design of a PV power system requires a lumped-circuit parameters’ model of the PV generator. This is used for purposes, such as to properly size the power switching devices used in the power processing converters, designing the maximum power point tracking system, and for efficient sizing of the PV array. In addition, such an equivalent circuit model can be readily embedded in circuit simulation programs. The widely accepted circuit model of a PV generator is the single-diode model (SDM), which is also included in Figure1[ 1–3]. This model can be easily adapted to model a cell, a module, or an array and offers a compromise between accuracy and complexity [4–6]. An extensive study on the measurement uncertainty using different lumped-circuit parameters models of a PV module can be found in [7]. However, this paper was based on the single-diode model. Energies 2020, 13, 3226; doi:10.3390/en13123226 www.mdpi.com/journal/energies Energies 2020, 13, 3226 2 of 17 Energiesextensive2020, study13, 3226 on the measurement uncertainty using different lumped-circuit parameters models2 of 17 of a PV module can be found in [7]. However, this paper was based on the single-diode model. Figure 1. The normalized I-V and P-V curves of a typical PV module (left) and the single-diode Figure 1. The normalized I-V and P-V curves of a typical PV module (left) and the single-diode model model (right). (right). The SDM involves five parameters: The photocurrent Iph, the saturation current Isat, and the The SDM involves five parameters: The photocurrent , the saturation current , and the ideality factor n of the diode, the parallel resistance Rsh, and the series resistance Rs. These parameters areideality not provided factor in of manufacturers’ the diode, the datasheets parallel ofresistance PV modules. , However,and the series they can resistance be extracted . fromThese dataparameters given in are a datasheet, not provided which in almost manufacturers’ always includes datasheets thethree of PV salient modules. points However, (SC, OC, they and MPP),can be extracted from data given in a datasheet, which almost always includes the three salient points (SC, the number of series-connected cells NS, and the temperature coefficients of the short-circuit current µOC,( Aand/°C MPP),) and the open-circuit number of voltage series-connectedµ (V/°C cells) [8]. However,, and the these temperature parameters coefficients are always of specifiedthe short- ISC VOC circuit current (A/℃) and open-circuit voltage (V/℃) [8]. However, these2 parameters are at only one operating condition, namely the STC (STC: Irradiance G = 1000 W.m− , air mass ratio = AMalways= 1.5, specified and temperature at onlyT =one25 °Coperating). Since the condition, characteristics namely of a PVthe generator STC (STC: can vary Irradiance significantly 1000 (W. m) =25 ℃) with the ambient, air temperature mass ratio andAM irradiance,=1.5, and temperature parameters estimated from. Since information the characteristics in a datasheet of a PV aregenerator only valid can at vary standard significantly test conditions. with the For ambient any other temperature arbitrary valuesand irradiance, of temperature parameters and irradiance, estimated thesefrom parameters information must in a be datasheet adjusted, are i.e., only re-estimated, valid at standard accordingly test [9 conditions.,10]. It is worth For notingany other at this arbitrary point thatvalues the problemof temperature of variations and in irradiance, module parameters these para is furthermeters complicatedmust be adjusted, due to the i.e., eff ectsre-estimated, of partial shadingaccordingly (PS) [[9,10].11,12], It which is worth can noting have adverseat this point consequences that the problem on the performanceof variations andin module energy parameters yield of a PVis plant.further Alleviation complicated of thedue e fftoects the of effects PS requires of partial the use shading of bypass (PS) diodes. [11,12], However, which can these have diodes adverse can varyconsequences the parameters on the of performance the PV generator and andenergy also yield give of rise a toPV complicated plant. Alleviation P-V curves of the with effects multiple of PS powerrequires peaks the [use13, 14of]. bypass However, diodes. the However, focus of this these paper diodes was can on exploringvary the parameters the performance of the PV of methodsgenerator forand varying also give the parametersrise to complicated of the SDM P-V with curves variations with multiple in irradiance power and peaks temperature [13,14]. However, without including the focus theof ethisffects paper of bypass was on diodes. exploring the performance of methods for varying the parameters of the SDM withTwo variations different in approaches irradiance and have temperature been reported without in the literatureincluding for the considering effects of bypass the variations diodes. of the SDM parametersTwo different with approaches fluctuations have in been ambient reported climatic in the conditions literature [15 for]. Theconsidering first approach the variations assumes of thatthe SDM the photocurrent parameters with depends fluctuations only on in irradiance,ambient climatic while conditions the saturation [15]. The current first dependsapproach only assumes on temperature,that the photocurrent while all other depends parameters only on remain irradiance constant, while [16 ,the17]. saturation The second current approach depends assumes only that on thetemperature, saturation currentwhile all and other the resistancesparameters vary remain with constant both conditions [16,17]. The of irradiance second approach and temperature assumes [ 18that]. Thethe idealitysaturation factor current is, however, and the assumed resistances to remainvary with constant both conditions in both approaches. of irradiance The contributionsand temperature of this[18]. paper The are:ideality Review factor the major is, however, methods ofassumed modifying to theremain parameters constant of thein SDMboth withapproaches. due account The takencontributions of their variationsof this paper with are: temperature Review the and majo irradiance,r methods provideof modifying the mathematical the parameters derivation of the SDM of thesewith methods,due account which taken is not generallyof their providedvariations in thewith literature, temperature apply theseand methodsirradiance, to PVprovide modules the ofmathematical different technologies, derivation and of these compare methods, their results. which is not generally provided in the literature, apply theseFollowing methods thisto PV introduction, modules of Section different2 presents technologies, the mathematical and compare background their results. that underpins the rest ofFollowing the work discussedthis introduction, in this paper. Section The 2 presents most reported the mathematical methods of modifyingbackground the that STC underpins parameters the ofrest the of SDM the work according discussed to changes
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