5708 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013

A Parameterization Approach forEnhancing PV Model Accuracy

Yousef A. Mahmoud, Weidong Xiao, Member, IEEE, and Hatem H. Zeineldin, Member, IEEE

AbstractReliable and accurate photovoltaic (PV) models areessential for simulation of PV power systems. A solar cell is typi-cally represented by a single diode equivalent circuit. The circuitparameters need to be estimated accurately to get an accuratemodel. However, one circuit parameter was assumed because ofthe limited information provided by commercial manufacturingdatasheets, and thus the model accuracy is affected. This paperproposes a parameterization approach for PV models to improvemodeling accuracy and reduce implementation complexity. It de-velops a method to accurately estimate circuit parameters, andthus improving the overall accuracy, relying only on the pointsprovided by all commercial modules datasheet. The proposedmodeling approach results in two simplified models demonstrat-ing the advantage of fast simulation. The effectiveness of themodeling approach is thoroughly evaluated by comparing thesimulation results with experimental data of solar modules madeof mono-crystalline, multi-crystalline, and thin film.

Index TermsEquivalent circuit, modeling, parameterization,photovoltaic (PV), solar cell.

I. INTRODUCTION

PHOTOVOLTAIC (PV) system studies need a reliable andaccurate mathematical model to predict energy productionfrom the PV resource under various irradiance and temperatureconditions [1], [2]. PV models can be categorized into two maintypes, double diode models and single diode models, which areillustrated in Fig. 1. The double diode model is characterizedby its high accuracy [3][12]; however, it is relatively complexand suffers from low computational speed [13]. The secondtype, single-diode model, is the most commonly used modelin power electronics simulation studies, because it offers areasonable tradeoff between simplicity and accuracy [6], [14][19]. Another advantage of using the single diode model is thepossibility to parameterize it based only on provided informa-tion by datasheet as presented in [1], [2], [14], [16], [20], [21].Modeling PV partial shading has been investiaged in [22], [23].

Manuscript received August 18, 2012; revised October 17, 2012; acceptedNovember 23, 2012. Date of publication November 30, 2012; date of currentversion June 21, 2013.

Y. A. Mahmoud is with the Department of Electrical and Computer En-gineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail:ymahmoud@uwaterloo.ca).

W. Xiao is with the Electrical Power Engineering Program, Masdar Instituteof Science and Technology, Abu Dhabi, UAE (e-mail: mwxiao@masdar.ac.ae).

H. H. Zeineldin is with the Masdar Institute of Science and Technology,Masdar City, UAE, and also with the Electrical Power and Machines Depart-ment, Cairo University, 12613 Giza, Egypt (e-mail: hzainaldin@masdar.ac.ae).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2012.2230606

Fig. 1. Equivalent circuit of double-diode and single-diode model.

There are various methods presented in literature, for extract-ing parameters of single diode PV models. One approach wouldbe to use the device physics to develop expressions for the IVcurve parameters, but such parameters would be in terms ofsemiconductor material constants and manufacturing variablessuch as doping densities [5], [13], [24]. Most semiconductorconstants vary considerably with production spread and are notprovided in a manufacturers data sheet [5], [13], [24]. A look-up table-based model to approximately represent the IV curveof the PV cell is presented in [25], but it is highly simplified andresults in a high modeling error. Another approach is to use er-ror minimization optimization analytical techniques [26], [27]or numerical techniques [13], [21], [28] to estimate parametersof the PV equation from a measured IV curve. Such approach,in spite of its high accuracy, requires a measured curve whichmay not be available for users. A common approach, which isfollowed in this paper, is to parameterize the PV model basedonly on information provided by product datasheets [1], [2], [8],[14], [16], [29][34]. Although the extracted parameters do notnecessarily correspond to the PV module physical parameters(for example, negative values for the series resistance might beresulted) as explained in [6], [12], [35], [36], the simulated IVand PV curves can highly match the real curves.

PV manufacturing datasheets provide only four informationabout the output electrical characteristics of their PV modules atstandard test conditions (STC), which are short-circuit currentIsc, open circuit voltage Voc, operating voltage and current atmax power point (Vm, Im), and the implicit information that thepeak of PV curve occurs at the voltage point (Vm). Thus, onlyfour equations can be written accurately relying on datasheetinformation. However, single diode PV models have five un-known parameters which need to be estimated. To compensate,the parameterization in [6] starts with one predefined parameter,the ideality factor, and then derives the rest four parameters ac-cordingly. Similarly, the parameterization in [2] approximatesthat one parameter, the shunt resistance Rsh, equals to inverseof the slope at short-circuit point, and then derives the restfour parameters accordingly. As a result, the accuracy of themodeled curves is affected, although they exactly pass throughthe four points provided by datasheets. Furthermore, they mightlead to a singular solution, if the approximated parameter issignificantly different from the exact value.

0278-0046/$31.00 2012 IEEE

MAHMOUD et al.: PARAMETERIZATION APPROACH FOR ENHANCING PV MODEL ACCURACY 5709

This paper proposes a parameterization approach that doesnot presume parameters and thus enhances modeling accuracy.It develops a method to determine the best estimation of oneparameter Rsh independently in order to solve the set of fourequations accurately without any approximation or assumption.In addition to improving the model accuracy, the proposedmodeling approach reduces the model complexity demonstrat-ing the advantage of fast simulation. The parameterizationapproach utilizes measured IV curves to deduce a systematicapproach for estimating the PV parameters. However, users arenot required to have a measured IV curve to implement theproposed parameterization approach.

The developed method is derived as follows: an optimizationmodel is formulated to find the upper and lower bounds of Rshwhich produce a non-singular system of equations. By usingeach Rsh value, in the determined range, the remaining PVparameters are determined and the root mean square deviation(RMSD) of the resulted modeled curves is plotted against thecorresponding Rsh values, and a relation between both of themis found. This relation will provide a rule of thumb to choosingthe best value of Rsh and Rs without the need from users toperform the optimization or acquire measured IV curves.

The paper is organized as follows: Section II reviews thelimitations in current PV parameterization approaches anddescribes how the proposed parameterization approach meetsthem. Then, it estimates the parameters of the PV model at STCwhich includes photon current, diode saturation current, diodeideality factor, shunt, and series resistances. Section III includesthe effect of atmospheric conditions variation, temperature, andirradiance, on the profound STC parameters. A comprehen-sive experimental evaluation is conducted in Section IV todemonstrate the improvement and verify the effectiveness ofthe proposed approach over the existing approaches based onthree different solar cell materials in terms of mono-crystalline,poly-crystalline, and thin film.

II. PV MODELINGA single diode model consists of a current source, diode,

series, and shunt resistances, as shown in Fig. 1. Thecurrentvoltage (IV ) characteristic can be expressed as fol-lows [37], [38]:

I = Iph Is[e

(q(V +IRs)NsKTA

) 1

] (V + IRs)

Rsh(1)

where q, K, T , and Ns are the electron charge, Boltzmannconstant, module temperature, and number of series connectedcells, respectively. The values of the electron charge q andBoltzman constant are 1.6 1019 C and 1.38 1023 J/K,respectively. The parameters Iph, Is, A, Rs, and Rsh are thephoton current, diode saturation current, ideality factor, seriesresistance, and shunt resistance, respectively. Therefore, fiveunknown parameters need to be estimated from the availableinformation given in product datasheets or from experimentalmeasurements. PV manufacturers typically provide values ofopen-circuit voltage (Voc), short-circuit current (Isc), and themaximum power point (Vm, Im) at STC. Temperature coeffi-cients are also given with respect to voltage and current.

A. Model Parameters

As shown in (1), there are five unknown parameters whichare A, Rs and Rsh, Iph, and Is. Estimating these parameterswill be based completely on datasheet information to avoidthe need of measurements which are not always available.Substituting short-circuit point (0, Isc) at STC into (1) gives

Isc = Ipho Irs[e(

qIscRsNsKToA

) 1] IscRs

Rsh(2)

where Ipho and Irs are the specific values of the photon currentand saturation current at STC. To is the STC temperature. Thesecond and third terms of (2) can be neglected resulting in thefollowing estimation of the photon current at STC:

Ipho = Isc. (3)

Substituting open circuit voltage point (Voc, 0) in (1) gives

Irs =Ipho Voc/Rshe(

qVocNsKToA

) 1. (4)

Substituting the operating voltage and current at maximumpower point (Vm, Im) in (1) at STC produces

Im = Ipho Irs[e

(q(Vm+ImRs)

NsKToA

) 1

] (Vm + ImRs)

Rsh.

(5)Implicit information is also available at the max power point

because the power equation derivative is equal to zero at maxpower point. Therefore, substituting the max power point to thederivative of the power equation (dP/dV = 0) gives

dP

dV=

[Isc Irs

[e

(q(Vm+ImRs)

NsKToA

) 1

] (Vm + ImRs)

Rsh

]

+Vm

[ qNsKToA

Irs

[e

(q(Vm+ImRs)

NsKToA

)] 1

Rsh

]=0. (6)

Substituting the variables Ipho from (3) and Irs from (4) into(5) and (6) produces (7) and (8)

0 =

[IscRsh Vm ImRs ImRsh

IscRsh Voc

]e(

qVocNsKToA

)

e(

q(Vm+ImRs)NsKToA

)[Voc Vm ImRs ImRsh

IscRsh Voc

](7)

0 = Isc Ipho VocRsh

e(qVoc

NsKToA) 1

[[

NsKToA qVmNsKToA

]e

(q(Vm+ImRs)

NsKToA

) 1

]

[2Vm + ImRs

Rsh

]. (8)

The information provided in the PV datasheet has beenutilized to derive the four (3), (4), (7) and (8) as in [6], [13].However, there are five unknowns which include Ipho, Rsh, Rs,A, and Irs. These parameters cannot be calculated from the fourderived (3), (4), (7), and (8). An approach would be to assume

5710 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013

the value of one parameter (for example, the ideality factor asin [6], or the shunt resistance as in [2]) and find the remainingparameters accordingly. Although the IV curve passes exactlythrough the datasheet points, intermediate points on the IVand PV curves (the curvatures) can exhibit inaccuracies aswill be shown in later sections. Therefore, this paper providesa method to determine the best estimation of one parameterRsh independently in order to solve the set of four equationsaccurately without any approximation or assumption, and henceimproving the modeling accuracy in the intermediate points ofthe IV curve.

B. Modeling Performance IndicesThe RMSD of the PV current will be used to evaluate the

modeling accuracy. The current RMSD is a measure of thedifferences between values predicted by a model and the valuesactually measured from real systems. For this specific study, theRMSD of the model-generated PV current array I with respectto the measured values I is defined as the square root of themean square error and can be expressed as follows:

RMSD(I) =

nj=1(ij ij)2

n(9)

where, I =

i1i2.

.

.

in

and I =

i1i2.

.

.

in

.

The normalized RMSD (NRMSD) of the PV current is theRMSD divided by the range of PV current values which can beexpressed as

NRMSD =RMSD

Isc(10)

where Isc is the short-circuit current at STC and represents thereference base of the PV current. In this paper, the RMSD andNRMSD results will be used to verify and deduce the proposedparameterization approach.

C. Shunt Resistance Evaluation

The process of shunt resistance estimation involves determin-ing its upper and lower bounds within which a solution to theset of equations provided in Section II can be found as wellas utilizing IV curves to determine the best Rsh value. First,an optimization problem is formulated to determine Rsh upperand lower bounds. Then, the corresponding PV parameters foreach Rsh value in the determined range are calculated, andthe IV curves are utilized to determine the model accuracyat each value of Rsh. As will be seen latter, the results of thisprocedure will be used only to deduce a systematic approach forestimating the PV parameters which will not rely on acquiringIV curves.

As mentioned earlier, the set of four equations provided in(3), (4), (7), and (8) are not sufficient to estimate the five PVparameters. Thus, one parameter needs to be estimated inde-pendently in order to solve the set of equations. An approach

TABLE ISHUNT RESISTANCE BOUNDARY OF DIFFERENT PV MODULES

would be to assume the value of one parameter (ideality factor)and calculate the rest as in [6]. Another approach approximatesthat the shunt resistance Rsh equals to the inverse of the slopeat short-circuit point [2]. Unfortunately, these approximationsaffect the accuracy of the modeled curve, although it exactlypasses through the points provided by datasheets. To improvethe accuracy, this paper proposes a method to determine thebest estimation of shunt resistance Rsh. The proposed methodis derived as follows: first, (7) and (8) are utilized to find theentire range of Rsh which produce a non-singular solutionwhen solving (7) with (8). Then, each value of Rsh in thedetermined range is substituted in the equation set (3), (4), (7),and (8) to find rest of parameters at each point of Rsh. Finally,the RMSD of the resulted modeled curves, at each value of Rshinside the range, are plotted against corresponding Rsh values,and a relation between the Rsh and resulted modeling RMSD isfound. The relation will provide a rule of thumb to choosing thebest value of Rsh which results in minimum RMSD. Followingparagraphs in this section presents the method explicitly.

There exists an upper and lower bound on the shunt resis-tance for which the solution of (7) and (8) is non-singular. Theupper bound is determined by maximizing the value of Rshsubject to (7) and (8). The problem can be formulated in anoptimization framework where the main objective J is

J = Maximize Rsh. (11)The constraints involved in the optimization include (7) and

(8). The same constraints will apply to determine the lowerbound on Rsh but with an objective of minimizing Rsh. Theoptimization problem is solved using the reduced gradientapproach. Table I summarizes the lower and upper boundsof Rsh for the various solar modules under study. Withinthe determined range of Rsh, the other parameters can bederived accordingly from (3), (4), (7) and (8). As a result, amodel can be constructed with the known values of Rsh, Rs,A, Iph, and Is. The modeling accuracy can be evaluated interms of the RMSD, defined in (9). The RMSD samples aredemonstrated in Table II for the various values of Rsh withinthe predetermined range. The analysis has been conducted onfour mono-crystalline, six poly-crystalline, and two thin filmsolar panels. Fig. 2 shows the characteristics of the NRMSDversus normalized values of Rsh based on four solar panels.

MAHMOUD et al.: PARAMETERIZATION APPROACH FOR ENHANCING PV MODEL ACCURACY 5711

TABLE IIROOT MEAN SQUARE DEVIATION VERSUS VARIATION

OF SHUNT RESISTANCE

Fig. 2. Characteristics of the normalized root-mean-square deviation(NRMSD) and the normalized Rsh.

The Rsh values are normalized to the value of a referencecurrent. The results show that setting Rsh equal to the upperbound gives relatively low NRMSD values. Thus, the first stepin the proposed modeling approach is calculating Rsh upperbound and setting Rsh to its maximum value.

One important observation, resulting from the optimizationmodel, is that for cases where the upper bound on Rsh is notinfinity (as for JAM and PS-M36S models), the optimal valuefor Rs is zero. On the contrary, for cases where the upper boundof Rsh is infinity, the optimal value of Rs is non-zero. Using theabove, a simple procedure can be implemented to determinethe best parameters for PV models. This will be explainedin the next subsection. That means the solution of (7) and (8)always results either for zero series resistant or infinite shuntresistant.

To demonstrate the result graphically, the range of Rsh isplotted against its corresponding Rs values for four differentPV modules as shown in Fig. 3. Two characteristics can bedistinguished from Fig. 3(a) and (b). There is no finite upper

Fig. 3. Characteristics of the series resistance and the shunt resistance fordifferent PV modules.

bound on Rsh for the case of E19/320 and PS_P36, and thus themaximum value of Rsh is equal to infinity which correspondsto a non-zero Rs value. On the other hand, for the case of JAM5and JAP6, Rsh has a finite upper bound which corresponds toRs equal to zero.

Thus, the solution of (7) and (8) either results in a solutionwhere Rs is equal to zero or Rsh is equal to infinity. The findingis verified for the different types of commercial PV panels understudy: single crystalline, multi-crystalline, and thin film. Usingthe above, a simple procedure can be implemented to determinethe best parameters for PV models.

Finally, it is worth to mention that it is not required, fromusers, to utilize measured IV curves to estimate the valueof Rsh. Measured curves are used in this paper only for thepurpose of showing that Rsh results in the lowest RMSD at itsmaximum value.

D. Modeling Parameterization

A simple and general approach is proposed to estimatethe best parameters for various PV models. Fig. 4 presentsa flowchart highlighting the procedure for extracting the fiveparameters in a single diode model. The modeling process startswith the approximation of the photon current Ipho accordingto (3), where the short-circuit current is given in the productdatasheets. Then, to find the max value of Rsh, the methodstarts by assigning Rsh = infinity( 107) and attempting tosolve (7) and (8) simultaneously. If a solution for Rs and A,within the feasible region, is reached, then the next step wouldbe to calculate Irs using (4). Therefore, all five unknowns areestimated, and these parameters are determined at STC.

For cases where a solution is not reached, this signifies thatRsh has finite upper bound which needs to be calculated. Ashighlighted in the previous subsection, the upper bound on Rshcan be determined simply by setting Rs = 0. Thus, Rs is setto zero, and (7) and (8) are solved to estimate A and Rsh.Similarly, the last step would be to calculate Irs using (4).Fig. 5 shows the simplified single diode model. Fig. 5(a) wouldbe used for models, such as JAP6-60/240, where the value ofRsh is finite and Rs is zero. On the other hand, Fig. 5(b) isconsidered the best representation for PV models such as PS-P60, where Rsh is infinity and Rs has a non-zero value. Thus,the PV equivalent circuit representation will depend on the PVmodel type.

5712 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013

Fig. 4. Proposed parameterization flowchart to estimate the five parameters ina single-diode equivalent circuit.

Fig. 5. Simplified single-diode models resulting from the proposed parame-terization: (a) with Rsh only; (b) with Rs only.

III. PARAMETER VARIATIONS AND SIMULATIONMODEL CONSTRUCTION

A PV simulation model is ready for construction when allparameters at STC are derived. All the profound parametersvary with meteorological conditions, majorly, temperature andirradiance. The photon current Iph is proportional to the irradi-ance and affected slightly by temperature. It can be expressed in(12), where T is the temperature deviation from the tempera-ture at STC, and is temperature coefficient, which is given bymanufacturer datasheet

Iph = G(Ipho + T ). (12)

The saturation current Is depends on the temperature and isusually shown as [39]

Is = Irs

(T

To

)3e

qEgKA (

1To

1T ). (13)

As shown in (13), Is depends on the value of Eg , which isnot given in the product datasheet. The symbol To refers tothe cell temperature equal to 298 K. An alternative approach

Fig. 6. Block diagram of simulation model implementation: (a) Rs = 0;(b) Rsh =.

is described to evaluate Is according to the meteorologicalfeatures. The open-circuit voltage varies with temperature andcan be represented by (14) [40]

VOC(G,To) VOC(G,T ) = ||T (14)

where Voc(G,To) and Voc(G,T ) are the open circuit voltagesat a certain temperature (T ) and the STC temperature (To),respectively, for a specific irradiance level. || is the absolutevalue of the voltage temperature coefficient given by the prod-uct datasheets. T is the temperature deviation from the STC,which is calculated as T = T To. Assigning I = 0 into (1),the open circuit formula is approximated as in (15)

Voc NsKTAq

ln

[IphIs

+ 1

]. (15)

By substituting (14) into (15), Is can be expressed as

Is =e

||TqNsKTAG(Isc + T )

(GIsc/Irs + 1)ToT e ||TqNsKTA

. (16)

In (16), it is shown that the saturation current, Is, is a functionof the solar irradiance and the variation of cell temperature fromthe STC. The effect of meteorological conditions on the rest ofparameters is slight and can be neglected [35]. The simulationmodel can be constructed using the estimated parameters ofRsh, A, Rs, Ipho, and Irs as well as the impact of irradianceand temperature, which are expressed in (12) and (16). ThePV module can be modeled by a dependent current source andmathematic blocks as shown in Fig. 6. In the case of Rs = 0,the PV circuit model is implemented using a controlled currentsource and a simple computational block shown in Fig. 6(a),where I = f(V ). This model avoids the use of a nonlinearsolver, and thus simple mathematical blocks are required. Incase of Rsh = , the implementation requires a numericalsolver, which is illustrated in Fig. 6(b), since I = f(V, I). Bothmodels are simpler than the practical model shown in Fig. 1.The modeling accuracy and simulation speed will be presentedin the next section.

MAHMOUD et al.: PARAMETERIZATION APPROACH FOR ENHANCING PV MODEL ACCURACY 5713

Fig. 7. Comparison plots between model output and measured data ofKC200GT with (a) variation of temperature and (b) variation of irradiance.

IV. EVALUATION

Fig. 7 demonstrates the modeled IV curves with respectto the experimental data for the KC200GT poly-crystalline PVmodel, for various temperatures and irradiance levels. It canbe seen that simulation results of the proposed model coin-cides closely with the experimental measurements. In addition,the accuracy of the proposed approach was evaluated exper-imentally and compared against previous approaches. Fig. 8presents the IV curves, PV curves, and absolute error fortwo modeling approaches with respect to the experimental dataof the JAM5(L)-72/165 mono-crystalline PV module. By com-paring with the modeling approach in [6], the proposed methoddemonstrates small modeling errors in the span of the PV volt-age. Similar evaluation is conducted for poly-crystalline andthin film modules. Fig. 9 illustrates the smaller modeling errorof the proposed approach in comparison with the modeling ap-proach in [6]. Fig. 10 demonstrates the modeling performanceof a thin film solar module with respect to the IV and PVcurves. The results show that the proposed modeling approach,for all cases, outperforms the method presented in [6].

The modeling accuracy is compared with respect to theNRMSD, which is defined in (8). The comparison includes ninesolar panels from different manufacturers, built with differentmaterials in term of mono-crystalline, poly-crystalline, and thin

Fig. 8. Modeling performance comparison between the proposed parameter-ization and the modeling process in [6] regarding (a) IV curves, (b) P-Vcurves, and (c) absolute modeling errors; based on the JAM5(L)-72/165 mono-crystalline PV module at STC.

film. Table III summarizes the modeling accuracy comparisonfor four mono-crystalline, three poly-crystalline, and two thinfilm modules. With regard to the NRMSD, the proposed mod-eling approach shows on average a 1.8% error reduction incomparison with the method proposed in [6]. The extractedmodel parameters are also listed in Table III for comparison.The results show that the ideality factor varies with moduletype and model. Assigning a constant ideality factor limits themodeling accuracy and results in potential mismatched valuesof Rsh and Rs.

5714 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013

Fig. 9. Modeling performance comparison between the proposed param-eterization and the modeling process in [6] regarding (a) IV curves,(b) P-V curves, and (c) absolute modeling errors; based on the JAP6-60/240poly-crystalline PV module at STC.

In addition to the modeling accuracy, the proposed parame-terization approach provides benefits, which include simplifiedstructure and fast simulation. As described in Section II, theparameterization leads to the equivalent circuits without eitherRsh or Rs, as shown in Fig. 5(a) and (b) respectively. Thesimulation study shows that the simplified models contributeless computation time compared to the practical model per-

Fig. 10. Modeling performance comparison between the proposed parame-terization and the modeling process in [6] regarding (a) IV curves, (b) P-Vcurves, and (c) absolute modeling errors; based on the MPT3.6-75 thin film PVmodule at STC.

taining to both Rsh and Rs, which is presented in [6]. Forthe simplified model shown in Fig. 4(a), the simulation timeis reduced by 34.72% in favor of the direct computationalform, I = f(V ). For another model (Fig. 5(b)), the simulationtime is also 8.89% faster than the practical model becauseof the ignored value of Rsh. The simulation shows that themodel configuration (refer to Fig. 6(a)) reduces the computersimulation time thanks to the absence of numerical solver. Al-though the proposed method was tested on nine PV samples, weenvisage that the method would be applicable to the majority ofPV samples.

MAHMOUD et al.: PARAMETERIZATION APPROACH FOR ENHANCING PV MODEL ACCURACY 5715

TABLE IIIPARAMETERIZATION RESULT AND MODELING DEVIATION COMPARISON

V. CONCLUSION

This paper has proposed an effective approach to improve theaccuracy of the single diode PV model. The model parametersare extracted according to the output electrical characteristicsgiven by manufacturing datasheets, which include the short-circuit current, the open circuit voltage, and the maximumpower point. Although the manufacturer datasheets providefour information about the electrical characteristics, while themodel has five unknowns, the proposed approach provides amethod to accurately estimate the values of five parameterswithout any approximations. This achieves the best accuracy ofPV model as well as avoiding reliability problems involved inPV parameter identification. It ensures high accuracy throughthe three characteristic points in the PV datasheet (the open-circuit voltage, short-circuit current, and the maximum powerpoint), guarantees that the maximum point generated by themathematical model coincides with the datasheet, and achievesthe best curvature. The proposed modeling approach resultsin two simplified models demonstrating the advantage of fastsimulation. The method is also easier to be implemented invarious simulation platforms for solar power systems studies.Experimental measurements validated and proved the effec-tiveness of the generalized modeling approach for three typesof PV materials, made of mono-crystalline, multi-crystalline,and thin film.

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Yousef A. Mahmoud received the B.Sc. degree inelectrical power engineering from Albalqaa Ap-plied University, Amman, Jordan, in 2009, and theM.Sc. degree from Masdar Institute of Science andTechnology, Abu Dhabi, UAE, in 2012. Currently,he is working toward the Ph.D. degree in electricalengineering at the University of Waterloo, Waterloo,ON, Canada.

His research interests are mainly in control andoperation of grid-connected photovoltaic power sys-tems including photovoltaic modeling, maximum

power point tracking, inverter control, and partial shading impact.

Weidong Xiao (M07) received the M.Sc. and Ph.D.degrees from the University of British Columbia,Vancouver, BC, Canada, in 2003 and 2007,respectively.

He is a Faculty Member with the electric powerengineering program at the Masdar Institute ofScience and Technology, Abu Dhabi, UAE. In2010, he spent eight months working as a visitingscholar at the Massachusetts Institute of Technology,Cambridge, MA, USA. Prior to his academic career,he was with MSR Innovations Inc. in Canada as

an R&D Engineering Manager focusing on projects related to integration,research, optimization, and design of photovoltaic power systems. His researchinterests include photovoltaic power systems, dynamic systems and control,power electronics, and industry applications.

Hatem H. Zeineldin (M06) received the B.Sc. andM.Sc.degrees in electrical engineering from CairoUniversity, Cairo, Egypt, in 1999 and 2002, respec-tively. In 2006, he received the Ph.D. degree in elec-trical and computer engineering from the Universityof Waterloo, Waterloo, ON, Canada.

He worked for Smith and Andersen Electrical En-gineering Inc. where he was involved with projectsinvolving distribution system design, protection, anddistributed generation. He then worked as a VisitingProfessor at the Massachusetts Institute of Technol-

ogy, Cambridge, MA, USA. He is currently an Associate Professor with MasdarInstitute of Science and Technology, Masdar City, UAE, and a Faculty Memberat Cairo University, Cairo, Egypt. His research interests include power systemprotection, distributed generation, and deregulation.

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