A mathematical modeling framework to evaluate the performance of single diode and double diode based SPV systems

Bana, Sangram; Saini, R. P. Article A mathematical modeling framework to evaluate the performance of single diode and double diode based SPV systems Energy Reports Provided in Cooperation with: Elsevier Suggested Citation: Bana, Sangram; Saini, R. P. (2016) : A mathematical modeling framework to evaluate the performance of single diode and double diode based SPV systems, Energy Reports, ISSN 2352-4847, Elsevier, Amsterdam, Vol. 2, pp. 171-187, https://doi.org/10.1016/j.egyr.2016.06.004 This Version is available at: https://hdl.handle.net/10419/187859 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ Energy Reports 2 (2016) 171–187 Contents lists available at ScienceDirect Energy Reports journal homepage: www.elsevier.com/locate/egyr A mathematical modeling framework to evaluate the performance of single diode and double diode based SPV systems Sangram Bana∗, R.P. Saini Alternate Hydro Energy Centre, Indian Institute of Technology, Roorkee 247667, India article info Article history: Received 30 November 2015 Received in revised form 2 June 2016 Accepted 26 June 2016 Available online 19 July 2016 Keywords: Photovoltaic (PV) Single diode model Double diode model STC (Standard test condition) Modeling abstract In order to predict the performance of a PV system, a reliable and accurate simulation design of PV systems before being installed is a necessity. The present study concerns the development of single and double diode model of solar PV system and ensures the best suited model under specific environmental condition for accurate performance prediction. The information provided in the manufacturers’ data sheet is not sufficient for developing a Simulink based single and double diode models of PV module. These parameters are crucial to predict accurate performance of a PV module. These parameters of the proposed solar PV models have been calculated using an efficient iterative technique. This paper compares the simulation results of both the models with manufacturer’s data sheet to investigate the accuracy and validity. A MATLAB/Simulink based comparative performance analysis of these models under inconsistent atmospheric conditions and the effect of variations in model parameters has been carried out. Despite the simplicity, these models are highly sensitive and respond to a slight variation in temperature and insolation. It is observed that double diode PV model is more accurate under low intensity insolation or shading condition. The performance evaluation of the models under present study will be helpful to understand the I-V curves, which will enable us in predicting the solar PV system power production under variable input conditions. ©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/). 1. Introduction Solar PV systems are environmentally friendly and assist in minimizing GHG emissions that would have otherwise arisen due to the use of fossil fuels for power generation. Feeding electricity into the grid by solar PV plants can help in to transmit equal amounts of electricity as would have been generated from the GHG intensive grid (most power grids receive electricity from coal based power plants). However, the high cost of photovoltaic power system modules inhibits optimum and utmost utilization of available solar energy. Thus, before actually installing the system, it is necessary that reliability and accuracy of the system is ensured in simulated environments. Solar PV systems are environmentally friendly and assist in minimizing GHG emissions that would have otherwise arisen due to the use of fossil fuels for power generation. Feeding electricity into the grid by solar PV plants can help in to transmit equal amounts of electricity as would have been generated from the ∗Corresponding author. Fax: +91 1332 286125. E-mail address: [email protected] (S. Bana). GHG intensive grid (most power grids receive electricity from coal based power plants). However, the high cost of photovoltaic power system modules inhibits optimum and utmost utilization of available solar energy. Thus, before actually installing the system, it is necessary that reliability and accuracy of the system is ensured in simulated environments. A PV system converts light into electricity. More precisely, a PV cell converts incoming solar radiation into direct current (DC). A PV cell is the heart of the solar power system, and sunlight being free of cost and available in abundance, can be used as an alternative energy source. The word ‘‘photovoltaic’’ originates from the word ‘‘light’’ pronounced as ‘‘photo’’ in Greek, and ‘‘voltaic’’ from Alessandro Volta—an electricity pioneer. The ability of photovoltaic material to convert light energy into electrical energy was discovered by Edmond Becquerel—a French physicist, in 1839. Although the use of sunlight to produce electric current in solid materials was also recognized by Becquerel, it took a century to understand this procedure of conversion. Nonetheless, scientists have identified materials that exhibit photovoltaic properties of converting light energy into electrical energy at the atomic level (Tossa et al.,2014;Alsayid,2012). A number of solar cells are attached in series or parallel (depending upon the necessity) in a single support system known as a ‘‘PV module’’. Depending http://dx.doi.org/10.1016/j.egyr.2016.06.004 2352-4847/©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/). 172 S. Bana, R.P. Saini / Energy Reports 2 (2016) 171–187 Fig. 1. Solar PV cell and its equivalent electrical circuits: (a) SPV Cell; (b) Ideal model; (c) single diode model; (d) double diode model. upon the requirement of current and voltage combinations, these modules can further be connected in series or parallel arrangements known as ‘‘array’’ of PV modules (Anne and Michel, 2006;Bourdoucen and Gastli, 2007). Performance of solar PV cell is evaluated under standard test conditions i.e. cell temperature at 25 °C; insolation of 1000 W/m2; and solar spectrum at A.M 1.5. Thus, it is important to accurately predict the power output of PV module under real weather conditions before installing solar PV systems. Various solar PV models have been proposed by researchers and each model comes with certain advantages of its own (Phang et al.,1984;Townsend, 1989;Glass,1996;Dongue et al.,2012;Karamirad et al.,2013). Townsend (Townsend, 1989). Further, researchers in the past have considered constant parameters (ideality factor, series and shunt resistance) for solar PV cell modeling. Results thus obtained were inaccurate as these parameters vary with change in temperature and insolation. Various studies have been carried out on the model development of the PV modules. However the modeling of these models has different level of complexity of their own. These models may be differentiated on the basis of number of employed diodes, finite or infinite shunt resistance, fixed or variable ideality factor and the techniques used to determine the unknown parameters (Saloux et al.,2011;Lun et al.,2013;Kulaksiz,2013;Siddiqui and Abido, 2013;Ma et al.,2014). The result of comparative studies does not provide that ‘‘which model will provide better results under real environmental exposure conditions and which model should be considered to study the effect of shading and nonshading conditions?’’ The present study is a comparative study of single diode and double diode solar PV models. Development of these models is done by evaluating their respective equivalent circuits. The performance characteristic of PV components is estimated on the basis of electrical parameters of the equivalent circuits. The effect of variation in environmental factors (insolation and temperature) and internal parameters (ideality factor and series resistance) on both models has been evaluated and extensively discussed in this study. This performance assessment will help in understanding I–Vcurves for forecasting PV system output power under inconsistent input conditions. Parameters such as ideality factor (n), series resistance (Rs) and shunt resistance (Rsh) are unfortunately not provided in manufacturer data sheets. (These parameters are termed as unknown parameters.) These unknown parameters have been determined by an iterative method. This study evaluates the performance of presented SPV models under variable operating conditions and analyzes their power deviation with respect to the ideal solar PV model. The modeling process is divided into three parts: First, mathematical modeling of single and double diode models and unknown parameters are determined. Second, simulation models of these solar PV models in Matlab/Simulink environment are presented. Finally, the accuracy of the proposed models is validated by comparing simulation results against manufacturer data sheets. The experimental data is measured at National institute of Solar Energy (NISE), Gawalpahari, Gurgaon-Faridabad road, Haryana, India. This data has been considered for comparing I–Vcurves of the proposed models with the measured I–Vcurves obtained under controlled operating conditions in this study (latitude = 28.4700°Nand longitude =77.0300°E). A commercial PV module MSX60 (Polycrystalline silicon), manufactured by Solarex has been considered as reference module for this study. 2. Simulation models of solar PV device In order to determine the electrical characteristics of solar photovoltaic cell accurately, mathematical modeling of single and double diode models is presented in the following subsections. 2.1. Solar PV cells, modules and arrays A cell is a fundamental unit of PV system. A group of cells are encapsulated to form a module. In order to increase the voltage level, modules are connected in series and to increase current levels, modules are connected in parallel depending on load requirements. 2.2. Equivalent circuits of solar PV device and their mathematical models A solar PV cell is conventionally represented by an equivalent circuit comprising a current source and one or two forward biased diodes without the correlation of internal series resistance and shunt resistance in case of an ideal cell, and with internal series resistance (Rs) and shunt resistance (Rsh) in case of single diode and double diode models. The equivalent circuits of an ideal cell, a single diode and a double diode SPV cell model are represented in Fig. 1 (Tossa et al.,2014;Patel and Agarwal, 2008;Villalva et al., S. Bana, R.P. Saini / Energy Reports 2 (2016) 171–187 173 Fig. 2. I–Vcharacteristics curve of a PV cell. 2009;Rauschenbach,1980;Jain and Kapoor, 2004). These models exhibit voltage and current data as output. These data outputs provide the I–Vcharacteristic curve as shown in Fig. 2. 2.3. Modeling of solar PV system Modeling of solar PV cell can be achieved by extensively analyzing the mathematical equations based on the respective equivalent circuits of solar PV models presented in following subsections (Bellia et al.,2014;Benlarbi et al.,2004;Gow and Manning, 1999;Hadj Arab et al.,2004;Sera et al.,2007). 2.3.1. Ideal PV cell modeling Ideal solar PV cell is represented by photo-generated current Iphc , which diverges from ideal outcome due to electrical and optical losses. The ideal PV cell model presented in Fig. 1(b) is the simplest PV model as the effect of series and parallel resistance are not considered. Output current of the cell is represented by I–V characteristics and mathematically expressed as: I=IPhc −Id.(1) The diode current Id, signifies diffusion and recombination currents in quasi steady state regions of emitter and excess concentration regions of PN junction. This diode current is represented by Shockley equation as: Id=IseVd/nVT−1(2) where ‘Vd’ is the diode Voltage, VTis termed asthermal voltage (VT=kT/q) due to its substantial temperature dependence, q is the charge of an electron (=1.6×10−19 C), nis the ideality factor (1.7), Kis the Boltzmann constant (=1.3805 ×10 −23 J/K) and Tis the cell temperature (K) (Anne and Michel, 2006;Sheik Mohammed,2011). I=Iphc −IseqVd/nKT −1.(3) Ideal solar PV cell does not consider the effects of internal resistance, thus fails to establish an accurate relationship between cell current and voltage. 2.3.2. Single diode PV cell modeling Generally, a series resistance (Rs), is introduced to the ideal cell model in order to get precise results.Although this model is simple, it reveals deficiencies when subjected to temperature variations. This model has been extended by considering a shunt resistance (Rsh). This single diode or five parameter model consists of current producer and diode with series and shunt resistances as shown in Fig. 2(c). The series resistance represents the resistance (ohmic loss) offered to the current flow due to ohmic contact (metal–semiconductor contact) and resistance due to impurity concentrations along with junction depth. Leakage current across the junction signifies shunt resistance, Rsh, connected parallel to the diode. The mathematical representation of the output current in Eq. (1) is modified as: I=IPhc −Id−Vd/RSh (4) where Vd, is the diode voltage which is represented as: Vd=V+IRS(5) where V, is the input voltage and I, is the current output. It is recognized that I–Vcharacteristic curve of a PV device is affected by series and shunt resistance, output voltage is affected by series resistance, and shunt resistance is responsible for reduction in available current (Jain and Kapoor, 2004;Tsai et al.,2008). Eq. (3) is further modified to obtain the single diode model equation. The single diode model of SPV cell is represented as: I=IPhc −IseqVd/nKT −1−V+IRS RSh .(6) 2.3.3. Double diode PV cell modeling Although the single diode model carries some improvement, yet its accuracy is questionable. To overcome this problem, a two diode model is introduced considering two diodes connected in parallel to the current source, shown in Fig. 1(d). The current Id1, through the first diode is the current component same as Idin case of single diode model. The current through the second diode Id2, is the recombination current in space charge region. This suggests that two Shockley terms contribute to the saturation currents of a solar PV cell. Series resistance Rs, and shunt resistance Rsh, are same as defined for single diode model. The double diode model of a SPV cell is highly accurate at low insolation levels. The double diode model can be represented by the following equation (Ma et al., 2014;Tsai et al.,2008;Ishaque and Salam, 2011): I=IPhc −Is1eqVd/n1KT −1−Is2eqVd/n2KT −1 −V+IRS RSh (7) where Is1and Is2are saturation currents of corresponding diodes. 2.3.4. Other equations involved in PV cell modeling The dependency of saturation current (Is) and photo generated current (Iphc ) in a PV cell on temperature and insolation is shown by the following equations: (i) Saturation current of a solar PV cell varies with the cubic function of temperature shown in Fig. 3, which is represented by the following equation: Is=Irs (T/Tr)3eq∗Ebg nK {1/Tr−1/T}(8) where Irs,Tr, and Ebg are reverse saturation current, ambient temperature and energy band gap (1.1 eV) respectively. (ii) Reverse saturation current at a reference temperature T, can be given by the following equation: Irs =Isc /e(qVoc /knT)−1 (9) where Isc ,Voc are short circuit current and open circuit voltage. The saturation current depends on current density and effective area of the cell. The intrinsic characteristic determines current density. 174 S. Bana, R.P. Saini / Energy Reports 2 (2016) 171–187 Fig. 3. Detailed Isimplementation. Fig. 4. Detailed Iph implementation. (iii) Photo generated current shares a linear relationship with insolation and depends on temperature (see Fig. 4). It is represented by the following equation: IPhc ={Isc +Ki(T−Tr)}HT 1000 (10) where Ki, is temperature coefficient of cell’s short circuit current and HTis the insolation on the solar cell. IPhc ,Is,n,Rs, and Rsh are five unknown parameters for single diode model and IPhc ,Is1,Is2,n1,n2,Rs,and Rsh are seven unknown parameters for double diode model of solar PV cell. The photocurrent generated by incident solar radiation varies with change in temperature and solar radiation. By determining the above parameters, modeling of solar PV arrays can be achieved. Table 1 represents the series/parallel connected modules (Jain and Kapoor, 2004;Ishaque, 2011;Chouder et al.,2012). This series–parallel topology is represented by Fig. 5. Based on Fig. 5, the output current for series–parallel configuration for single diode and double diode model can be written as: I=Np   Iphc −Is1 exp   V+IRsNs Np VTNs  −1    −   V+IRsNs Np Rsh Ns Np   (11) I=Np   Iphc −Is1 exp   V+IRsNs Np VT1Ns  −1  −Is2 exp   V+IRsNs Np VT2Ns  −1    −   V+IRsNs Np RpNs Np   (12) where VTis the thermal voltage (VT=nkT/q,VT1=n1kT/q and VT2=n2kT/q). In order to increase voltage levels, the number of modules is to be connected in series while to increase current levels, they are connected in parallel depending on the load requirements. 3. Determination of model parameters Greater accuracy can be achieved by computing the unknown parameters, namely Ipv,Is1, (Is2in case of two diode model), Rp,Rsh,n1and (n2in case of two diode model). The photo generated current as a function of insolation and temperature is represented by Eq. (10). The saturation current for a single diode model considering temperature variation is given in Eq. (16). In case of double diode model, several researchers (Ishaque,2011;Ishaque and Salam, 2011;Sheik Mohammed,2011;Kulaksiz,2013) have S. Bana, R.P. Saini / Energy Reports 2 (2016) 171–187 175 Table 1 Transformed parameters for series and parallel connected modules. Parameters of SPV cell Parameters of series arrays of NScells Parameters of parallel arrays of NPcells IPhc IPhc NpIPhc Irsc Irsc NpIrsc VtNsVtVt RsNsRsRs/Np Rsh NsRsh Rsh/Np Fig. 5. Equivalent circuit model of PV array. computed the values of Is1and Is2through iterative techniques. These techniques are responsible for increase in computation time and complexity. Therefore, both saturation currents were derived analytically, and can be determined by Eq. (17). Is=Ipv +Ki(T−Tr) exp [(Voc +Kv(T−Tr)) /nVT]−1(13) Is1=Is2=Is =Ipv +Ki(T−Tr) exp [(Voc +Kv(T−Tr)) /{(n1+n2)/p}VT]−1.(14) As computation turns out to be easy due to equalization, iterations are eliminated and an analytical solution is obtained. According to Shockley’s theory of diffusion, ideality factor n1must be unity. Ideality factor n2should be less than or equal to 1.2 as determined through simulation. This estimation provides the best match between the I–Vcurves of practical model and proposed models. As (n1+n2)/p=1 and n1=1, it shows that variable pis preferred to be less than or equal to 2.2. This uncertainty in determining the values of n1and n2can be eliminated and Eq. (7) is re-arranged in terms of pas shown by Eq. (18). I=IPhc −Is1eqVd/KT −1−Is2eqVd/(P−1)KT −1 −V+IRS RSh .(15) The expression for Rsh at Pmax can be arranged as follows: Rsh=Vmp+ImpRs IPhc −IoexpVmp+ImpRs VT+expVmp+ImpRs (p−1)VT−2−Pmax,E Vmp  .(16) Considering a simple iterative method, the value of Rsis iteratively increased while Rsh is calculated simultaneously. For initializing the iteration process, the appropriate values of Rsh and Rsare considered (Lun et al., 2013). Value of Rsis taken as zero and the value of Rsh is obtained using the following equation: Rsh0=Vmp Isc −Imp −Voc −Vmp Imp .(17) The proposed SPV Simulink models represent a generalized SPV model. The input parameters for both models are insolation and temperature while I–Vand P–Vcharacteristics are obtained as output parameters under different input conditions. The characteristic curves of both models are exhibited by highly nonlinear radiation and temperature which are being simulated for the parameters given in Table 1. 4. Basic parameters (i) Short-circuit current: In case of electrodes of the SPV cell is short-circuited, the current that flows through the circuit is termed short-circuit current (Isc ). It is the maximum current that flows through the SPV cell. The short-circuit current of a solar cell depends on the insolation incident on SPV cell, which is determined by the spectrum of the incident light, i.e. AM 1.5 spectrum. Isc depends on the cell area and its ability to absorb incident solar radiation (Bourdoucen and Gastli, 2007). (ii) Open circuit voltage: It is the maximum voltage that can be delivered by a cell. The Voc corresponds to the forward bias voltage, at which the dark current compensates the photocurrent. The Voc depends on photo-generated current density and can be expressed as: Voc =n∗K∗T qln Ipv I0 ;Ipv>Is.(18) (iii) Maximum voltage (Vmp) and current (Imp): It is the power at a point on I–Vcurve, the product of maximum current and voltage is the maximum power point. (iv) Temperature: Solar cells work best at low temperature as determined by their material properties. As the temperature exceeds operating temperature, cell efficiency decreases. A substantial part of the incident insolation is lost in the form of heat resulting in high temperature of cells. (v) Resistance: Large electrical contacts can minimize electrical resistance, but covering a cell with large, opaque metallic contact would block too much incident light. Therefore, a tradeoff must be made between loss due to resistance and loss due to shading effects (Chan and Phang, 1987a,b). (vi) Standard test condition (STC): The standard test conditions for a cell are specified as follows: solar radiation—1000 W/m2, cell temperature—25 °C and spectral distribution—AM 1.5. (vii) Incoming solar radiation: In order to analyze the proposed model, the input solar radiation data considered to perform the experiment is measured at National institute of Solar Energy (NISE), Gurgaon (a city in Haryana, India). The considered solar radiation (total solar radiation considering beam, diffused and reflected solar radiation incident on the surface of a PV module), module temperature and ambient temperature along with date and time under the present study are given in Table 4. Developers and engineers also require an accurate model to evaluate the energy yield of the PV system. However, the information provided by the manufacturers is not enough to determine the energy yield of the PV power system. Also the specifications provided by the manufacturer are under STC. To make these specifications effective under other environmental conditions an accurate and reliable PV model is needed inevitably. 176 S. Bana, R.P. Saini / Energy Reports 2 (2016) 171–187 Fig. 6. Simulink model of single diode SPV system model. Fig. 7. Simulink model of two diode SPV system model. 5. Modeling of single diode SPV model This study offers a simple, reliable and accurate model with a current source, series resistance, parallel correlation of forward biased diode and shunt resistance, and is presented in Fig. 6 using the mathematical equations discussed in Section 2. The output current (I) of an ideal diode is represented in subsystem 5 (excluding subsystems 2 and 3). Here, subsystem 1 determines the photo-generated current (Iphc ), subsystem 3 determines the reverse saturation current and subsystem 2 determines the temperature dependency of reverse saturation current. Values of Rsand Rsh are calculated through iterations. After finding the values of Rsand Rsh,Isand ncan be calculated easily. Modeling of single diode model provides values of current, voltage and power as output in workspace of MATLAB. S. Bana, R.P. Saini / Energy Reports 2 (2016) 171–187 177 Fig. 8. ENDEAS QUICKSUN 700A solar simulator. Table 2 Key specifications of Solarex MSX 60 (Polycrystalline silicon) PV module. COMPANY : Solarex MODEL: MSX 60 Parameters Values Peak power (Pmax) (W) 60 Max peak voltage (V) 17.1 Max peak current (A) 3.5 Open circuit voltage (V) 21.1 Short circuit current (A) 3.8 Kv(V/°C) −80 ×10−3 Ki(A/°C) 3 ×10−3 Np1 Ns36 Table 3 Estimated parameters of Solarex MSX-60 (Polycrystalline silicon) PV module. Solarex MSX-60 Parameters Calculated by Newton method Iph (A) 3.8084 Is1(Is)(A) 4.8723 Is2(A) 6.1528 Rs0.3692 Rsh 169.0471 n1(n) 1.0003 n21.9997 6. Modeling of two diode SPV model Following a procedure similar to that of single diode modeling which has been discussed earlier, modeling of two diode solar PV model along with Rsand Rsh is accomplished. The first diode represents charge diffusion in quasi steady state along with recombination current in high concentration region of PN junction and the second diode considered here represents recombination current in space charge region. The two diodes connected in parallel to the current source are represented by subsystems 5 and 6 as shown in Fig. 7. The current outputs Id1and Id2are calculated accordingly. Values of current, voltage and power are obtained as output in workspace of MATLAB. 7. Results and discussions The present study presents and analyzes modeling of single and double diode models of solar PV module. These models are obtained by implementing equations in MATLAB/Simulink environment based on their respective equivalent circuits as discussed in Section 2. 7.1. Model verification The outdoor measurement for poly-crystalline technology based PV module was carried out at National institute of Solar Energy (NISE), 19th milestone Gawalphari, Gurgaon-Faridabad Road, Haryana (India). This site has specific composite climate type environment distinguished by high insolation and temperature levels. The geographical location of NISE is: latitude 28.4700°N and longitude 77.0300°E with an elevation of 216 m from sea level. In order to carry out measurements of I–Vand P–Vunder STC in accordance with manufacturer data sheet, a calibrated ENDEAS QUICKSUN 700A solar simulator shown in Fig. 8 has been used. The main parameters such as Isc ,Voc ,Imp,Vmp and Pmp at STC are obtained according to International Standards for Crystalline silicon modules (IEC 61215 Ed. 2 - 2005,Xiao et al., 2004). A commercial PV module MSX 60 (Polycrystalline silicon), manufactured by Solarex has been considered as reference module to investigate the effect of varying insolation, temperature, ideality factor, series and shunt resistance on the output of both the Simulink models for this study. The key specifications of Solarex MSX 60 module as provided by the manufacturer are presented in Table 2 (http://www.solarelectricsupply.com/media/ custom/upload/Solarex-MSX64.pdf). Table 3 shows the computed unknown parameters discussed in Section 4. Although two diode solar PV model has more unknown parameters, the specific unknown parameters to be determined are four since Is1=Is2whereas n1and n2can be randomly chosen from Eq. (3). Further, the unknown parameters determined by numerical iteration method (Table 3) are compared with the data sheet at STC (Table 2) for both the models. Fig. 9a,9b shows an excellent match between manufacturer curves and computed results at STC. Fig. 9a shows computed curves of MSX-60 module for single and double diode models, and the curves are compared with manufacturer data sheets at different insolation and constant temperature (=25 °C). Fig. 9b shows computed curves of MSX60 module for single and double diode models as compared with manufacturer data sheets at different temperatures and constant insolation (1000 W/m2). From these figures, the inaccuracies and inefficiencies of single diode model as compared with two diode model at different irradiances and temperatures can be observed. Fig. 9a indicates a good agreement between provided and calculated data at different irradiances especially at low irradiance in case of two diode model or seven parameter model. 178 S. Bana, R.P. Saini / Energy Reports 2 (2016) 171–187 Fig. 9a. I–Vcurves of single and double-diode model of the Solarex MSX 60 SPV module for several irradiation levels. Fig. 9b. I–Vcurves of single and double-diode model of the Solarex MSX 60 SPV module for several temperature levels. From Fig. 9a it can be observed that single diode PV model provides accurate results for high solar insolation whereas double diode PV model is more accurate under low intensity insolation or shading condition. 7.2. Model verification under real operating conditions: The measurements of the I–Vand P–Vcharacteristic curve of the considered technology module were performed with data acquisition system PVPM-2540 C, Solar radiation sensor SOZ-03, Personal computer—hp 4th generation Intel i-3 processor as shown in Fig. 10. PVPM device measures the I–Vcurves of PV modules. It also measures and calculates the peak power at the place of installed PV system. Peak power is the power measured under STC. As mentioned previously, in order to validate both the Simulation models for PV module, the characteristic I–Vcurves of the considered module was determined under real operating conditions and compared with the computed simulated curves presented. The result thus obtained is presented in Table 4. Using the identified parameters presented in Table 5, the characteristic I–Vand P–Vcurves for the selected module was computed under real operating conditions and are demonstrated in Fig. 11 along with the simulated I–Vcurves. 7.3. Simulation results: For easy implementation, the solar radiation intensity for a sample day is anticipated to be a function of Gaussian function distribution expressed as (Messenger and Ventre, 2000) λ(t)=λmax exp −(t−tc)2 2σ2 where λmax is the utmost sunlight intensity at a particular time, tcis the center time, and σis the standard deviation of Gaussian function. Fig. 12 illustrates a plot of the Gaussian function distribution for the solar radiation intensity for a sample day with the conditions: λmax =1 kW/m2,tc=12, and σ=0.5. The peak of sunlight intensity occurs at noon. In addition, the ambient temperature for such a sample day is assumed to be a Gaussian function distribution. For deviations in solar irradiance and ambient temperature, the cell temperature can be predicted by Eq. (9). Both ambient and cell temperature are also presented in Fig. 12. For an insolation-oriented model of PV module, the cell temperature is affected by sunlight irradiance. For different output voltage, the output current and power are obtained in Figs. 13a and 13b for a sample day. The insolation values specified above and temperature value of 25 °C are taken as inputs for the proposed models. The output of single and double diode SPV models is given in Table 6. Based on the output of single and double diode SPV models, the I–Vcharacteristic curves for these models are obtained as shown in Fig. 14. This figure illustrates that the power output of both single and two diode SPV models is same up to a voltage of 7.03 V (Psingle = Pdouble =26.64 W). Beyond this voltage,power output of double diode SPV model starts decreasing as compared to single diode SPV model (Pdouble =37.70 W and Psingle =37.80 W) due to decrease ingenerated current (Idouble =3.77 A, Isingle =3.78 A at V=10 V). This variation in power output of double diode SPV model may be due to consideration of recombination losses in space charge region represented by subsystem 6 in Fig. 7. These Recombination losses effect both the current collection (therefore the short-circuit current) as well as the forward bias injection current (and therefore the open-circuit voltage). The decrease in current of double diode SPV model is continuous. The value of current is nearly zero at 19.81 V for double diode SPV model and in case of single diode SPV model the value of current is approximately zero at 21.07 V. Therefore, it is observedthat both short circuit current and open circuit voltage is affected by consideration of second diode in case of double diode SPV model as compared to single diode SPV model under specified operating conditions. The effect of environmental factors such as insolation level, temperature (provided as inputs from Matlab workspace) and effect of internal parameters such as ideality factor, series and shunt resistance are analyzed in this study to match the parameters (Isc ,Voc ,Imp,Vmp,Pmax) as given by manufactures for both the models. Considering the output of an ideal PV cell as a reference power,a comparison between both the presented Simulink models in terms of power difference has also been carried out. This comparison illustrates that less the difference, more is the power output of the model. S. Bana, R.P. Saini / Energy Reports 2 (2016) 171–187 185 Fig. 21. Effect of Rs(a) Single diode I–Vcharacteristic curve, (b) single diode P–Vcharacteristic curve, (c) two diode I–Vcharacteristic curve, (d) two diode P–Vcharacteristic curve. Fig. 22. Comparison of power output of presented models with a standard output power with varying series resistance. power output of double diode model is less than single diode model as the value of shunt resistance (Rsh) is increased. 8. Conclusions The proposed modeling of single and double diode models is done on the basis of their equivalent circuits. The study is carried out under the real operating conditionsas well asunder controlled atmospheric conditions in order to investigate the effect of varying atmospheric conditions. Also the effect of parameters such as varying ideality factor (n) series resistance (Rs) and shunt resistance (Rsh) are investigated to determine the difference in power generated for both the models with respect to ideal PV module. The fill factor and efficiency of a solar cell decreases due to both shunt and series resistance losses. The utilization of iterative method guides us to definite values of photo-generated current (Iph), ideality factor (n), series resistance (Rs) and shunt resistance (Rsh). It is found that the output power of PV module is extensively affected even with a small variation in series resistance (Rs), thus this value is kept very small.This comparison empowers the outcome of this study. The final outcomes establish the accuracy of double diode model over the single diode model under low intensity insolation (or shading). On the other hand, single diode confirms the effectiveness under high insolation levels. Findings of this study could be very helpful in selecting the appropriate model under given operating conditions. Acknowledgments This work was supported by Grant of Ministry of New and Renewable Energy (MNRE), Government of India (8793-38-061/429), Indian Institute of Technology (IIT) Roorkee, Uttarakhand, India 186 S. Bana, R.P. Saini / Energy Reports 2 (2016) 171–187 Fig. 23. Effect of Rsh (a) Single diode I–Vcharacteristic curve, (b) single diode P–Vcharacteristic curve, (c) two diode I–Vcharacteristic curve, (d) two diode P–Vcharacteristic curve. Fig. 24. Comparison of power output of presented models with a standard output power with varying series resistance. and National Institute of Solar Energy (NISE, Gurgaon under MNRE, Government of India), India. References Tossa, Alain K., Soro, Y.M., Azoumah, Y., Yamegueu, D., 2014. A new approach to estimate the performance and energy productivity of photovoltaic modules in real operating conditions. Sol. Energy 110, 543–560. Alsayid, B., 2012. Modeling and simulation of photovoltaic cell-module-array with two-diode model. Int. J. Comput. Technol. Electron. Eng. (IJCTEE) 1 (3), June. Anne, Labouret, Michel, Villoz, 2006. Energiephotovoltaïque. (Dunod3ème édition). Bourdoucen, H., Gastli, A., 2007. Analytical modeling and simulation ofphotovoltaic panels and array. J. Eng. Res. 4 (1), 75–81. Benlarbi, K., Mokrani, L., Nait-Said, M.S., 2004. A fuzzy global efficiency optimization of a photovoltaic water pumping system. Sol. Energy 77, 203–216. Chan, D.S., Phang, J.C.H., 1987a. Analytical methods for the extraction of solarcell singleand double-diode model parameters from I–Vcharacteristics. IEEE Trans. Electron. Dev. 34, 286–293. Chouder, A., Rahmani, L., Sadaoui, N., Silvestre, S., 2012. Modelingand simulation of a grid connected PV system based on the evaluation of main PV module parameters. Simul. Modell. Pract. Theory 20, 46–58. Chan, Daniel S.H., Phang, Jacob C.H., 1987b. IEEE, analytical methods for the extraction of solar-cell singleand double-diode model parameters from IV characteristic. IEEE Trans. Electron. Dev. ED-34 (2), February. Dongue, S.B., Njomo, D., Tamba, J.G., Ebengai, L., 2012. Modeling of electrical response of illuminated crystalline photovoltaic modules using four and fiveparameter models. Int. J. Emerg. Technol. Adv. Eng. 2 (11), 612–619. Glass, M.C., 1996. Improved solar array power point model with SPICE realization. In: Proc. IECEC, Vol. 1, Aug, pp. 286–291. Gow, J.A., Manning, C.D., 1999. Development of a photovoltaic array model for use in power-electronics simulation studies. IEEE Proc. Power Appl. 146, 193–200. Bellia, Habbati, Youcef, Ramdani, Fatima, Moulay, 2014. A detailed modeling of photovoltaic module using MATLAB. NRIAG J. Astron. Geophys. 3, 53–61. Hadj Arab, A., Chenlo, F., Benghanem, M., 2004. Loss-of-load probability of photovoltaic water pumping systems. Sol. Energy 76, 713–723. IEC 61215, 2005. Crystalline silicon terrestrial photovoltaic (PV) modules-design qualification and type approval. Ishaque, K., 2011. A comprehensive Matlabsimulink PV system Simulator with partial shading capability based on two-diode model. Solar energy 85, 2217–2227. Ishaque, K., Salam, Z., 2011. An improved modeling method to determine the model parameters of photovoltaic (PV) modules using differential evaluation (DE). Sol. Energy 85, 2349–2359. Jain, A., Kapoor, A., 2004. Exact analytical solution of the parameters of real solar cells∥using Lambert W-fonction. Sol. Energy Mater. Sol. Cells 81, 269–277. Karamirad, M., Omid, M., Alimardani, R., Mousazadeh, H., Heidari, S.N., 2013. ANN based simulation and experimental verification of analytical fourand fiveparameters models of PV modules. Simul. Modell. Pract. Theory 34 (May), 86–98. Kulaksiz, A.A., 2013. ANFIS-based estimation of PV module equivalent parameters: application to a stand-alone PV system with MPPT controller. Turk. J. Electr. Eng. Comput. Sci. 21, 2127–2140. Lun, S., Du, C., Guo, T., Wang, S., Sang, J., Li, J., 2013. A new explicit I– V model of a solar cell based on Taylor’s series expansion. Sol. Energy 94 (August), 221–232. Ma, T., Yang, H., Lu, L., 2014. Development of a model to simulate the performance characteristics of crystalline silicon photovoltaic modules/strings/arrays. Sol. Energy 100 (February), 31–41. Messenger, R., Ventre, J., 2000. Photovoltaic Systems Engineering. CRC Press, Boca Raton, pp. 11–12 and 41–51. Patel, H., Agarwal, V., 2008. MATLAB-based modeling to study the effects of partial shading on PV array characteristics. IEEE Trans. Energy Convers. 23 (1), 302–310. Phang, J.C.H., Chan, D.S.H., Philips, J.R., 1984. Accurate analytical method for the extraction of solar cell model parameters. Electron. Lett. 20 (10), 406–408. Rauschenbach, H.S., 1980. Solar Cell Array Design Handbook. Van Nostrand Reinhold. Saloux, E., Teyssedou, A., Sorin, M., 2011. Explicit model of photovoltaic panels to determine voltages and currents at the maximum power point. Sol. Energy 85 (5), 713–722. Sera, D., Teodorescu, R., Rodriguez, P., 2007. PV panel model based on datasheet values. In: IEEE International Symposium on Industrial Electronics ISIE 2007. pp. 2392–2396. S. Bana, R.P. Saini / Energy Reports 2 (2016) 171–187 187 Sheik Mohammed, S., 2011. Modeling and simulation of photovoltaicmodule using MATLAB/Simulink. Int. J. Chem. Environ. Eng. 2 (5). Siddiqui, M.U., Abido, M., 2013. Parameter estimation for fiveand sevenparameter photovoltaic electrical models using evolutionary algorithms. Appl. Soft Comput. 13 (12), 4608–4621. Townsend, T.U.. Townsend, T.U., 1989. A Method for Estimating the Long-term Performance of Direct-coupled Photovoltaic Systems. University of Wisconsin. Tsai, H.L., Tu, C.S., Sui, Y.J., 2008. Development of Generalized photovoltaic. In: WCECS 2008, October 22-24, San Francisco, USA. Villalva, M.G., Gazoli, J.R., Filho, E.R., 2009. Modeling and Circuit-based Simulation of photovoltaic arrays 10th Brazilian Power Electronics Conference, COBEP. Xiao, W., Dunford, W.G., Capel, A., 2004. A novel modeling method for photovoltaic cells. In: Proc. PESC, Vol. 3, pp. 1950–1956.