afastandaccurateanalyticalmethodforparameter … · 2020. 5. 15. · comparative study of the two...

Research ArticleA Fast and Accurate Analytical Method for ParameterDetermination of a Photovoltaic System Based onManufacturerrsquos Data

Robinson Ndegwa 1 Justus Simiyu1 Elijah Ayieta1 and Nicodemus Odero 2

1Department of Physics University of Nairobi PO Box 30197-00100 Nairobi Kenya2Department of Electrical and Electronic Engineering Machakos University PO Box 136 90100 Machakos Kenya

Correspondence should be addressed to Robinson Ndegwa ndegwarguonbiacke

Received 3 January 2020 Accepted 24 April 2020 Published 15 May 2020

Academic Editor Shuhui Li

Copyright copy 2020 Robinson Ndegwa et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Modeling and simulation of a photovoltaic solar system play a significant role in understanding its behavior in various envi-ronmental conditions Utilization of the datasheet information in modeling and simulation of the PV system correlates theexperimental data and the theory that instigate the mathematical predictions of an actual system A single-diode model gives asimple fast and straightforward way of depicting the PV system performanceWe have developed a new approach of determiningthe five unknown parameters of a single-diode model using manufacturerrsquos data at three main points the open circuit point(OCP) short circuit point (SCP) and the maximum power point (MPP) of the IV and PV curves e ideality factor (A) and thediode saturation current (Io) are the key unknown parameters that greatly affect the reduplication of the three main points epurpose of this study is to evaluate the ideality factor using simple calculation procedure starting from its optimal value (Ao) andother values within the proximity of Ao e optimal value is obtained by assumptions of negligible series resistance (Rs) and verylarge shunt resistance (Rsh) erefore the choice of the other ideality factors in the neighborhood of its optimal value gives rise todifferent values of Rs Rsh and Iph that are more realistic in an experimental setup Positive values of Rsh and Rs have been iterativelyobtained by utilizing data at maximum power point combined with open and short circuit data e five unknown parametershave been determined in the proximity ofAo and have been used to plot the PV curve with accuracy and precision of less than 05error of maximum power and less than 01 error of Voc of manufacturerrsquos data e proposed method has been implementedusing fast simple and accurate procedures using GNU Octave programming software to calculate Ao Io Rs Rsh and Iph and toexecute both Rs-Rsh and PV characteristic equations of BP3235T KC200GT BP-SX 150 and MSX60 PV modules e reducedsteps employed in the algorithm improve execution speed thereby reducing the computation time

1 Introduction

Single- and double-diode PV models have been widely usedfor evaluation and analysis of electrical characteristics forphotovoltaic (PV) solar modules [1ndash3] Several authors [4ndash8]have reviewed the advantages and drawbacks of both modelsand compared their accuracy in replicating the experimentalIV and PV curves Comparative study of the two modelsshowed a trade-off between accuracy and computation time[9] e double-diode model gives better profiling of the PVmodules but requires complex computation procedure in

order to extract its seven unknown parameters [10 11]However improved approaches for calculating unknownparameters using seven [12] six [13] five [14] and fourparameters [15] for the double-diode models have also beenstudied ese methods utilize numerical algorithms such asparticle swarm optimization or the NewtonndashRaphsonmethodthat requires large amount of data and several mathematicalmanipulations to evaluate the unknown parameters ere-fore the single-diode model remains a method of choicewhere quick and simplified analyses are required for design ofmaximum power point tracking (MPPT)

HindawiJournal of Renewable EnergyVolume 2020 Article ID 7580279 18 pageshttpsdoiorg10115520207580279

A single-diode model has five unknown parameters (AIo Iph Rs and Rsh) that must be determined to obtain thebest solution of the current-voltage equation [16] Severalapproaches have been discussed in the literature for de-termination of the correct values of these five parameters[17 18] e simplest model that reduces the number ofunknown parameters to three (A Io and Iph) is a single-exponential diode equivalent circuit without any resistance[19ndash21] Ignoring the series and shunt resistances givesinaccurate evaluation of the PV module and fails to accountfor the loss of power due to electrical contacts base regionand the front layer [22] A better approach based on fourparameters incorporates a series resistance and omits theshunt resistance [23ndash25]e five-parameter model gives thebest solutions since it accounts for the effect of power lossesdue to parasitic series and shunt resistances that are em-bedded in the solar module as a result of fabrication defects[26 27]

e five-parameter single-diode model is based on aShockley diode equivalent circuit with series and parallelresistances and is defined by a transcendental equation thatcannot be solved explicitly Several procedures have beendeveloped for evaluation and determination of the lumpedparameters namely ideality factor (A) saturation current(Io) photocurrent (Iph) and shunt (Rsh) and series (Rs)resistances using IV characteristic [8] Experimental data orinformation available from manufacturerrsquos datasheet isusually utilized in order to derive the necessary nonlinearequations for extraction of the unknown parameters byconsidering three crucial points at short circuit currentopen circuit voltage and maximum power point of an IVcurve [28] Experimental procedures are expensive andrequire more time for setup data collection and analysis[29] Nevertheless evaluation of the five parameters usingmanufacturerrsquos data has become more popular since theinformation about the three critical points is readily availableat STC and NOCT for module with IEC standards [30ndash32]Different approaches have been proposed for extraction ofthese unknown parameters depending on which parameteris perturbed first either Rs or A Traditionally thestraightforward way of getting the five parameters has beenbased on five nonlinear equations selected from the threecritical points and determining the RS and Rsh from thereciprocal of IV slopes at these points [33 34] Computersoftware has been exploited to solve these equations usingLambert W function [35 36] nonlinear least square (NLS)[37] and NewtonndashRaphson algorithms [38 39] esetechniques are comprehensive methods with good accuracyand fast convergence but their main drawbacks are compleximplementation procedures and relatively low calculationspeed that require more computing power

Recent advances in computing technology has led toapplication of evolutionary computation techniques in-spired by biological evolution and chemistryphysics-basedswarming-based and hybridization-based algorithms forextraction of the unknown parameters for single- double-or triple-diode models [40] ese soft-computing tech-niques are problem solvers using trial and error meta-heuristic or stochastic optimization procedures such as

pattern search (PS) [41] genetic algorithm (GA) [42]simulated annealing (SA) [43 44] particle swarm optimi-zation [45 46] artificial fish swarm algorithm (AFSA) [47]fuzzy logic [48] and artificial neural networks (ANNs)[49ndash51] ese methods have disadvantages either in termsof sophistication and accuracy or in terms of convergenceand speed of execution

Fast and simplified approaches that calculate all modelparameters for the single-diode model of the photovoltaicsystem directly rely on careful evaluation of the under-lying analytical and numerical algorithms [52 53]Straightforward analytical methods for describing theparameters of PV models are heavily dependent onnonlinear explicit formulas using Isc Impp Vmpp and Vocdata in the PV panel datasheet [54] e simplest andcomprehensive approach assumes arbitrary value ofideality factor and determines other parameters byadjusting the curve at Isc Pmpp and Voc points [55] Anideal diode has an ideality factor of unity However anappropriate and actual diode for modeling PV system hasideality factor values ranging from one to two [56] Anaccurate and fast convergence method of extracting theunknown parameters by first analyzing the ideality factorand setting it as the primary parameter and obtaining theloss resistance through a repetitive process was reportedin [57] e authors used a protracted method to arrive ata control signal that was based on the series resistancevalue In this paper we present a novel analytical methodfor determining the single-diode model parameters di-rectly from the manufacturerrsquos datasheet using explicitequations

2 A Single-Diode Equivalent Circuit

A single-diode equivalent circuit shown in Figure 1 can bemathematically modeled using equation (1) [16] AShockleyrsquos diode is connected in parallel to the currentsource and shunt resistor and in series to Rs and the load

I Iph + Io minus Io expq V + IRs( 1113857

ANskTminus

V

Rshminus

IRs

Rsh (1)

where I is module output current in amperes (A) V is moduleoutput voltage in volts (V) q is charge of anelectron 1602176634times10minus19C k is Boltzmannrsquos constant

1380649times10minus23middotm2sminus2middotkgKminus1 and TSTC is standard temper-ature 29815K at STC

3 MathematicalModeling of a PVSystemUsingThree Critical Points and Their RespectiveSlopes of an IV Curve

Equation (1) can be evaluated by analyzing the open circuitshort circuit and the maximum power points whose data areusually available from datasheets

At short circuit I Isc VOIn Figure 1 a short circuit without the load gives zero

voltage and current Iasymp Isc that depend on IphA Io T Rs andRsh [16 58] erefore we can rewrite equation (1) as

2 Journal of Renewable Energy

Isc Iph + Io minus Io expIscRs

ANsVt

1113888 1113889 minusIscRs

Rsh (2)

where Vt kTq 00256796347 is the thermal voltageAt open circuit IO VVoc likewise at open circuit

we can also rearrange equation (1) to get

Iph Io

Voc

ANsVt

1113888 1113889 minus Io +Voc

Rsh (3)

For fast convergence equation (3) can be expressedlogarithmically as

ln Iph + Io minusVoc

Rsh1113888 1113889 minus ln Io( 1113857

Voc

ANsVt

(4)

At maximum power point I Impp VVmpp we cansimilarly replace I Impp VVmpp in equation (1) to obtain

Impp Iph + Io minus Io expVmpp + ImppRs

ANsVt

1113888 1113889 minusVmpp + ImppRs

Rsh

(5)

is can also be evaluated as

ln Iph + Io minus Impp minusVmpp + ImppRs

Rsh1113888 1113889 minus ln Io( 1113857

Vmpp + ImppRs

ANsVt

(6)

Subtracting equations (4) and (6) yields

lnIph + Io minus VocRsh

Iph + Io minus Impp minus Vmpp + ImppRs1113872 1113873Rsh

⎛⎝ ⎞⎠ Voc minus Vmpp minus ImppRs

ANsVt

(7)

is reduces to the five-parameter mathematical modelthat can be written as

A Voc minus Vmpp minus ImppRs

NsVt ln Iph + Io minus VocRshIph + Io minus Impp minus Vmpp + ImppRs1113872 1113873Rsh1113872 11138731113960 1113961 (8)

31 Photocurrent (Iph) Analysis e photocurrent can bededuced by rearranging equation (2) in order to obtainequation (9) in terms of A Io Rs and Rsh to get

Iph Isc minus Io + Io expIscRs

ANsVt

1113888 1113889 +IscRs

Rsh (9)

e light-generated current of the PV cell is linearly de-pendent on the solar irradiance and also varies with thetemperatureerefore the relationship between photocurrenttemperature and irradiance can be evaluated using tempera-ture coefficient of Isc (KI) as reported in [38 59 60] us

Iph s

sSTCIphSTC + KI T minus TSTC( 11138571113960 1113961 (10)

where T is the actual temperature in Kelvin TSTC is thetemperature at STC usually 29815K s is the irradiance on thePV surface sSTC is the irradiance at STC usually 1000Wm2and IphSTC is the light-generated current at STC

32 Ideality Factor (A) Analysis One of the simplest ways ofdetermining the ideality factor is to evaluate its value atstandard test conditions (STCs) using data provided inmanufacturerrsquos datasheet Using the information obtainablefrom the datasheet for Isc Impp Vmpp and Voc the optimalvalue of ideality factor can be easily deduced from equation

(8) by letting the photocurrent (Iph) to be equivalent to shortcircuit current (Isc) We can also assume that Rs has minimalresistance value (Rsasymp 0) and Rsh has large resistance value(Rshasympinfin) whose effects can initially be ignored in theequation ese assumptions will be reevaluated later in thefollowing sections to consider the nominal operation pa-rameters in which Rs and Rsh have other more practicalvalues us we can evaluate ideality factor as

A Voc minus Vmpp

NsVt

lnIsc + Io

Isc + Io minus Impp1113888 11138891113890 1113891

minus1

(11)

A closer look at its denominator infers that the logarithmterm is greatly influenced by the short circuit currenterefore small values of saturation current in microam-peres range can be ignored is gives rise to the optimumvalue of ideality factor (Ao) that can be expressed as

Ao Voc minus Vmpp

NsVt

lnIsc

Isc minus Impp1113888 11138891113890 1113891

minus1

(12)

Figure 2 illustrates the variation of ideality factor (A)with respect to saturation current for BP3235T KC200GTBP-SX 150 andMSX60 PVmodules respectivelye valuesof Io have been arbitrarily chosen within an acceptable rangefrom 0 to 1A According to Figure 2 the ideality factor

Iph IRs Rs

ID IRsh I

Rsh Load

Figure 1 A single-diode equivalent circuit

Journal of Renewable Energy 3

increases as saturation current (Io) increases and vice versae intercept on the y-axis represents the values of optimalideality factor (Ao) and optimal saturation current (Ioopt) foreach respective PV modules provided in Table 1

e optimum value of the ideality factor (Ao) has beendeduced from very low series and high shunt resistances Inorder to consider other Rs and Rsh resistances that are morerealistic and achievable in a practical setup it is important toconsider the ideality factor in the neighborhood of Ao suchthat 1leAleAo at a constant Io In this work we haveevaluated the effect of ideality factor on Iph Rs and Rsh byarbitrarily selecting different values of A in the neighbor-hood of A0 as discussed in Sections 33 and 34

33 Saturation Current (Io) Analysis e saturation currentappears as a constant at STC in equation (1) and can becalculated by merging two of the three equations that havebeen derived at the crucial points Substituting Iphappearing in equation 2 with Iph defined in equation 3 asdiscussed by the authors in [52 61] the saturation current(Io) at Isc and Voc can be derived as follows

Io1113858 1113859Isc Voc

IscRsh + IscRs minus Voc

Rsh exp VocANsVt( 1113857 minus exp IscRsANsVt( 11138571113858 1113859

(13)

Since Io depends on temperature we can first determineits optimal value at STC by assuming the boundary pa-rameter values for Rsasymp 0 and Rshasympinfin Consequently we canrewrite equation (13) as

Ioopt1113876 1113877

Isc Voc

Isc

exp VocANsVt( 11138571113858 1113859 (14)

Similarly equation (2) can be merged with equation (5)at Isc and Pmpp to obtain

Io1113858 1113859Isc Pmpp

Vmpp + ImppRsh + ImppRs minus IscRs minus IscRsh

Rsh exp IscRsANsVt( 1113857 minus exp Vmpp + Impp1113872 1113873RsANsVt1113872 11138731113960 1113961 (15)

Returning to Rsasymp 0 and Rshasympinfin equation (15) reduces to

Ioopt1113876 1113877

Isc Pmpp

Isc minus Impp

exp VmppANsVt1113872 1113873 (16)

Finally considering equation (3) and (5) atVoc and Pmppwe can deduce the saturation current as

Io1113858 1113859Voc Pmpp

Vmpp minus Voc + ImppRsh + ImppRs

Rsh exp VocANsVt( 1113857 minus exp Vmpp + Impp1113872 1113873RsANsVt1113872 11138731113960 1113961 (17)

Again assuming Rsasymp 0 and Rshasympinfin we can rewriteequation (17) as

Ioopt1113876 1113877

VocPmpp

Impp

exp VocANsVt( 1113857 minus exp VmppANsVt1113872 11138731113960 1113961

(18)

331 Dependence of the Saturation Current on Irradianceand Temperature e saturation current is not explicitlydependent on the irradiance so in the absence of irradiationthe term dark saturation current is used interchangeablywith saturation current [62 63] In contrast the dark sat-uration current strongly depends on temperature geo-

4

3

2

10 02 04 06 08 1

Saturation current (Io) in amperes (A)

BP3235TKC200GT

BP SX150MSX60

Idea

lity

fact

or (A

)

Figure 2 A graph of A vs Io for BP3235T KC200GT BP-SX 150and MSX60 PV modules

Table 1 PVmodule data (Pmpp Isc Impp Voc Vmpp andNs) at STC

ParametersPV module

SolarexMSX60

BP-SX150

KyoceraKC200GT BP3235T

Pmpp (W) 60 150 200 235Isc (A) 38 475 821 848Impp (A) 35 435 761 789Voc (V) 211 435 329 372Vmpp (V) 171 345 263 298Ns 36 72 54 60


metrical or transport semiconductor parameters and theintrinsic carrier concentration [63 64] In addition theintrinsic carrier concentration number depends on theconduction and valence band density of states and on theenergy band gap (Eg) of the semiconductor [64]

erefore saturation current density for a Schottkyjunction diode can be expressed using the derivation given in[63] as

Jo DT3 exp

minusqEg

kT1113888 1113889 (19)

where Jo is the dark saturation current density T is the actualtemperature D is the diode diffusion factor which is in-dependent of temperature k is Boltzmannrsquos constant and Eg

is the semiconductorrsquos band gap energy (Eg 112 eV for Siand 135 eV for GaGs)

Applying equation (19) to a solar system the saturationcurrent can be determined using similar approach presentedin [65] to get

Io IoSTC

T

TSTC1113890 1113891

3

expqEg

ANsk

1TSTC

minus1T

1113890 1113891 (20)

where IoSTCis the saturation current at standard test

conditione saturation current at STC (IoSTC

) can be calculatedusing either equation (13) (15) or (17) However theseequations depend on Rs Rsh and A which are also unknownparameters that must be determined us since this newapproach takes into account the upper boundary value of theideality factor (Ao) by assuming minimal series resistance(Rsasymp 0) and large shunt resistance (Rshasympinfin) same as-sumptions can be used to calculate the optimal saturationcurrent (Ioopt

) at STC using either equation (14) (16) or (18)erefore equation (20) can be written as

Io Ioopt STC

T

TSTC1113890 1113891

3

expqEg

ANsk

1TSTC

minus1T

1113890 1113891 (21)

34 Series Resistance (Rs) and Shunt Resistance (Rsh) Analysise shunt and series resistances have been neglected incalculating the optimal ideality factor in the previous sectionHowever the maximum power of a solar module can beestimated as the optimal power in the absence of Rs and Rshand the power losses in them e shunt and series can beevaluated using the combinations of equations derived usingthe three crucial points and the slopes at either output powerat maximum power point or at short circuit point efollowing section discusses these different ways of derivingthe relationship between Rsh and Rs

(i) At maximum power point only the relationshipbetween Rsh and Rs can be evaluated by rearrangingequation (5) to get

Rsh Vmpp + ImppRs

Iph minus Impp minus Io exp Vmpp + ImppRs1113872 1113873 ANsVt( 11138571113872 1113873 minus 11113872 1113873

(22)

(ii) Combining the equations defining the short circuitpoint at (Isc) and open circuit point at (Voc) equating(3) and (4) correlates Rsh and Rs with Isc and Voc asfollows

Rsh Voc minus IscRs

Isc + Io exp IscRsANsVt( 1113857 minus Io exp expVocANsVt( 1113857

(23)

(iii) Combining the equations defining short circuitpoint at (Isc) and maximum power point at (Pmpp)this can be done by substituting equation (3) intoequation (5) to obtain

Rsh Vmpp + ImppRs minus IscRs

Isc minus Impp minus Io exp Vmpp + ImppRs1113872 1113873ANsVt1113872 1113873 + Io exp exp IscRsANsVt( 1113857 (24)

Equations (22) and (24) give similar positive Rs andRsh values for ideality factors above Ao since theydepend on Pmpp and Isc Equation (23) has unrea-sonable outcome of Rsh and Rs pairs

(iv) Combining the equations defining open circuitpoint at (Voc) and maximum power point at (Pmpp)

e dependence of Rsh on Rs Voc and Pmpp can beexpressed by rearranging equations (4) and (5) toobtain

Rsh Voc minus Vmpp minus ImppRs

Impp + Io exp Vmpp + ImppRs1113872 1113873ANsVt1113872 1113873 minus exp expVocANsVt( 1113857 (25)


(v) Using the derivatives of equation (1) with respect toV at short circuit and open circuit points along withthe derivative of P IV with respect to V or I atmaximum power point [16 38 58 66]Differentiating equation (1) with respect to V gives

zI

zV minus

Io

ANsVt

1 +zI

zVRs1113888 1113889exp

V + IRs

ANsVt

1113888 1113889 minus1

Rsh1 +

zI

zV1113888 1113889Rs1113896 1113897

(26)

It has been shown in [67] that the derivative at shortcircuit point can be approximated as

zI

zV1113890 1113891

IIsc

minus1

Rsh (27)

and at open circuit point the derivative can be approximatedas

zI

zV1113890 1113891

VVoc

minus1Rs

(28)

At maximum power point the power derivative withrespect to voltage can be evaluated as

zP

zV

zI

zV1113888 1113889V + I O (29)

Taking into consideration that VVmpp and I Impp atmaximum power point we can rewrite equation (29) as

minusImpp

Vmpp minus

Io

ANsVt

1 minusImpp

VmppRs1113888 1113889exp

Vmpp + ImppRs

ANsVt

1113888 11138891113896 1113897

minus1

Rsh1 minus

Impp

VmppRs1113888 1113889

(30)

Rearranging equation (30) we can obtain

Rsh Vmpp minus ImppRs

Impp minus IoANsVt Vmpp minus ImppRs1113872 1113873exp Vmpp + ImppRs1113872 1113873ANsVt1113872 1113873 (31)

e four independent equations (22) (24) (25) and (31)that depend on Voc Impp and Vmpp have four unknownparameters (Rs Rsh A and Io) that can be resolved usingeither NewtonndashRaphson algorithm [38 39 68 69] non-linear least square (NLS) algorithm [37] or Lambert Wfunction [35 36 70] algorithm to analytically determine thevalues of unknown PV model parameters ese methodshave different levels of computational complexity accuracyconvergence and execution speed [8] A simplified approachis presented in this work using an iterative algorithm thatconsiders the boundary values of ideality factor and satu-ration current as discussed in the following section

341 Evaluation of Rsh and Rs Based on A below Ao (Method1) is paper proposes a robust method of obtaining theunknown parameters of equation (1) by first obtaining theoptimal values of the ideality factor using equation (12) andconsequently obtaining Ioasymp Ioopt

based on either equation(14) (16) or (18) e actual ideality factor (A) is arbitrarily

chosen in the neighborhood of Ao and applied in eitherequation (25) or (31) which leaves Rs and Rsh as the onlyunknown parameters Utilization of equations (25) and (31)can be done separately when the values of A are selectedabove or below (Ao) When applied in equation (25) thevalues of ideality factor below Ao give positive and negativevalues of Rsh but give negative and unrealistic values for Asabove Ao e best choice of Rs and Rsh pairs should be atpositive peak values of Rsh A choice of Rs values in steps of+00001Ω above Rs of a positive peak gives Rs and Rsh pairsthat are more pragmatic is approach is a departure fromthe conventional analytical methods reported in[52 55 58 61] that assumes arbitrary values of ideality factorbetween 1 and 15 e optimal saturation current is keptconstant when arbitrarily selecting the ideality factor nearAo To ensure a fast and an easy way of evaluating Rs and RshIo in equation (25) can be replaced by Ioopt

of equation (14) toget


Impp + Isc exp minusVocAoNsVt( 1113857exp Vmpp + ImppRs1113872 1113873ANsVt1113872 1113873 minus Isc exp minusVocAoNsVt( 1113857exp VocANsVt( 1113857 (32)

Equation (32) can be analyzed using a similar approachused in [55] in which an iterative method is employed toobtain the [Rs Rsh] pair that satisfies equation (33) in which

Pmpp relationship has been derived by replacing I Impp andVVmpp in (1) to yield


Pmpp ImppVmpp Vmpp Iph + Io minus Io expVmpp + ImppRs

ANsVt

1113888 11138891113888

minusVmpp + ImppRs

Rsh1113889

(33)

Unlike in ref [55] where Rs is arbitrarily selected thisiterative process involves determining the Rs and Rsh pairusing equation (32) by selecting the values of A that are lessthan Ao and subsequently obtaining Pmpp without neces-sarily plotting the PV curve Moreover the ideality factor isadjusted in order to get an Rs and Rsh pair that guaranteesPmpp VmppImpp that matches Pmpp in the datasheet isprocess is repeated until the value of simulated Pmpp matches

the maximum power value in the datasheet or has an errormargin of less than 05 [22]

e value of Iph in equation (33) can be calculated usingequation (9) e percentage error in power can be deter-mined by calculating the simulated maximum power minusmaximum power using Impp and Vmpp from datasheet asexpressed in the following equation

PmppError ΔPmpp Pmpp minus ImppVmpp

ImppVmpptimes 100 (34)

342 Evaluation of Rsh and Rs Based on A above Ao (Method2) Similar derivation has been used in equation (31) byreplacing Io with Ioopt

of equation (14) to obtain


Impp minus IscANsVt exp minusVocAoNsVt( 1113857 Vmpp minus ImppRs1113872 1113873exp Vmpp + ImppRs1113872 1113873ANsVt1113872 1113873 (35)

Equation (35) gives realistic and viable [Rs Rsh] pairs ifand only if the values of ideality factor are above Ao

343 Characterization of Rsh and Rs e simplest and mostconvenient way of displaying the relationship between Rshand Rs is through a graphical method using Rsh against Rsplots of equation (32) as illustrated in Figure 3 for BP3235TKyocera KC200GT BP-SX 150 and Solarex MSX60 solarmodules

e values of Rs have been chosen between 0 and 10ohms to obtain a positive value of Rsh using simple code inGNUOctave software For any choice of ideality factor thereare Rs and Rsh pairs with nonzero value of Rs Further asillustrated in Figure 3 Rsh has positive and negative valuesfor various Rs

4 Parameter Calculation Procedure

e flowchart shown in Figure 4 gives step by step proceduresthat have been used to determine all the desired parameterse immediate action is to obtain the Isc Impp Vmpp and Vocfrom the datasheet followed by direct calculation of the optimalideality factor (Ao) using equation (12) and Ioopt

using equation(14) Rs and Rsh are evaluated using equation (32) for differentvalues of As in the neighborhood of Ao such that 1leAleAoConsequently Iph is calculated using equation (9) e actualsaturation current (Io) corresponding to each ideality factor isrecalculated using equation (14)

emaximum power (Pmpp) is calculated using equation(33) using a simple code in GNU Octave software FurtherVoc error is calculated by comparing the simulated Voc ofequation (3) values with the datasheet values ese pro-cedures are repeated several times as shown in Figure 4However the process is stopped if a maximum power erroris less than 05 andor the short circuit voltage is greaterthan 01 Calculated values of Io Rsh Rs and Iph and

simulated values of Voc and Pmpp and errors for differentideality factors near Ao are summarized in Tables 2ndash5Eminently the instantaneous value of Rs increases as theideality factor (As) decreases us the most suitable idealityfactor should be chosen near Ao provided the errors in PmppandVoc arewithin the acceptable limits of less than 05 and01 respectively [22]e same procedure is repeated whenimplementing the second approach e only changeseffected are replacement of equation (32) with (35) andideality factors (As) are selected above Ao

5 Analysis of Extracted Parameters andSimulated Data

Table 2 gives a summary of extracted parameters andsimulated data for Pmpp and Voc and their respective errorsfor BP3235T PV solar module As depicted in equations (32)and (33) and verified in Figure 3 the shunt resistance variesgreatly within a small range of series resistance Henceforththe series resistance has been used as the lead parameter thatcontrols the interactive process that stops when appropriateRs is reached which guarantees simulated data match theexperimental data In this work the experimental data areobtained from the information available in the manufac-turerrsquos datasheet

For BP3235T PV solar module the value of idealityfactor has been kept constant at A 1792 since it providedsatisfactory [Rs Rsh] pair that resulted to a small error at bothmaximum power point and Voc Rs3 0242Ω presented theleast ∆Voc and ∆Pmpp errors of 0 and 0001 respectivelye values of Rs have been varied and checked withinplusmn1mΩ which are presented in Table 2 as Rs1 to Rs4 andoffer satisfactory results as compared to other data publishedin [25 71] as discussed later in Section 7

Tables 3ndash5 give similar summary for KC200GT BP-SX150 and MSX60 PV modules For KC200GT BP-SX 150and MSX60 PV the values corresponding to Rs4 02188Ω


Rs4 03301Ω and Rs5 015Ω respectively present theleast errors of less than 01 based on the first methodesemodules have been chosen to ensure that the tests cover awide variety of systems with different output power isshows how valid the proposed approach is for various PVsystems

In the second procedure where ideality factors (As) areselected above Ao the same Rs values of Rs4 02188ΩRs4 03301Ω and Rs5 015Ω have been set as the targetfor determining the [Rs Rsh] pair As illustrated inTables 3ndash5 the second approach unlike the first methodresults in unsatisfactory data with ∆Voc and ∆Pmpp errorsreaching and exceeding 05 percent is makes the firstapproach superior over the second one

Table 6 gives a summary of appropriate parameters forMSX60 BP-SX 150 KC200GT and BP3235T

6 PV Characteristics at StandardTest Conditions

is proposed technique is a straightforward way ofevaluating the desired unknown parameters of a single-

diode PV model e extracted parameters presented inthis work can be characterized using IV andor PV plotse output power of the solar cellmodule can be cal-culated and evaluated using equation (1) multiplied by theoutput voltage to obtain

P VI V Iph + Io minus Io expV + IRs

ANsVt

1113888 1113889 minusV

Rshminus

IRs

Rsh1113888 1113889

(36)

For simplified and clear description of the distinctivevariation of PV output power we have chosen to verify itsbehavior with respect to identified parameter through PVplots e PV characteristics are plotted as shown inFigures 5ndash8 by using the extracted parameters in equation(36) and using a powerful toolsoftware with built-inplotting and visualization capability such as MATLAB andOctave

As shown in Figures 5(a) 6(a) 7(a) and 8(a) forideality factors below Ao the output power plots arecloser to the expected result closer to the datasheetvalues is is in conformity with the data presented inTables 2ndash5

1

0

022 023 024 025 026Rs (Ω)

R sh (

Ω)

A = 1792 (BP3235T)

middot105

(a)

6

4

2

R sh (

Ω)

Rs (Ω)

0

minus2

minus402 022 023

A = 1809 (KC200GT)

middot104

02

(b)

R sh (

Ω)

Rs (Ω)

2

0

minus2

minus4

minus6

03 031 032 033 034 035

A = 196 (BPSX150)

middot105

(c)

R sh (

Ω)

Rs (Ω)

4

2

0

7 75 8 85 9middot10minus2

middot105

A = 1702 (MSX60)

(d)

Figure 3 A graph of Rsh vs Rs at STC for (a) BP3235T (b) Kyocera KC200GT (c) BP-SX 150 and (d) Solarex MSX60


e zoomed parts represent the maximum power pointsand the open circuit voltages respectively e curvesdemonstrate validity of simulated values where the criticalpoints of open circuit voltage and maximum power pointhave very minimal and acceptable deviation of less than01

e plots for Figures 5(b) 6(b) 7(b) and 8(b) whoseideality factors have been selected above Ao clearly show asignificant deviation at maximum power point is is alsoshown in Tables 2ndash5 where the errors in maximum power andshort circuit voltage surpass 05 percent e data also showerrors above 05 percent for high-output power modules like

Start

DatasheetIsc Impp

Vmpp Voc

Ao equation (12)

Ioopt equation (14)

Is ∆Pmpp le 05 amp∆Voc le 01

No

Yes

Pmpp error equation (34)

Pmpp equation (33)

Select A lt A0

Rsh Rs equation (32)

Io equation (14)

Iph equation (9)

Stop

PV curve equation (36)

Figure 4 An algorithm for evaluating the Ao A Ioopt Io Rsh and Rs using manufacturerrsquos datasheet

Table 2 Extracted parameters and data from simulations for BP3235T

Rs (Ω) AltAo Io (A) Rsh (Ω) Iph (A) Voc (V) ∆Voc () Pmpp (W) ∆Pmpp ()Method 1Rs1 0002 1801956 (Ao) 1286446Eminus 5 219578 84800 37194 minus0016 23417 minus0405Rs2 02419 1792 1194159Eminus 5 114606 84818 37201 0003 23517 0020Rs3 0242 1792 1194159Eminus 5 106637 84819 372 0 23512 minus0001Rs4 02421 1792 1194159Eminus 5 99702 84821 37199 minus0003 23506 minus0026Rs4 02422 1792 1194159Eminus 5 93610 84822 37198 minus0005 235 minus0052Method 2Rs1 00852 1801956 (Ao) 1286446Eminus 5 659576 84801 372 0 23542 0127Rs2 02419 18626 1989991Eminus 5 99272 84821 37199 minus0003 23296 minus0920Rs3 0242 18626 1989991Eminus 5 106630 84819 37199 minus0003 23303 minus0890Rs4 02421 18626 1989991Eminus 5 115168 84818 372 0 23309 minus0864Rs5 02422 18626 1989991Eminus 5 125195 84817 37201 0003 23314 minus0843


Table 3 Extracted parameters and data from simulations for Kyocera KC200GT

Rs (Ω) AltAo Io (A) Rsh (Ω) Iph (A) Voc (V) ∆Voc () Pmpp (W) ∆Pmpp ()Method 1Rs1 0001 181928 (Ao) 17807Eminus 5 3636875 82100 32897 minus00091 20024 0048Rs2 02186 1809 165353Eminus 5 1219678 82115 32902 00061 20022 0038Rs3 02187 1809 165353Eminus 5 1116104 82116 32901 00030 20017 0013Rs4 02188 1809 165353Eminus 5 1028696 82118 329 0 20012 minus0011Rs5 02189 1809 165353Eminus 5 953941 82119 329 0 20007 minus0036Method 2Rs1 00718 181928 (Ao) 178074Eminus 5 702018 82101 329 0 20066 026Rs2 02186 1882 275010Eminus 5 61269 82130 32893 minus0021 19784 minus115Rs3 02187 1882 275010Eminus 5 64429 82128 32894 minus0018 19789 minus113Rs4 02188 1882 275010Eminus 5 67935 82127 32894 minus0018 19797 minus109Rs5 02189 1882 275010Eminus 5 71845 82125 32895 minus0015 19806 minus104

Table 4 Extracted parameters and data from simulations for BP-SX 150

Rs (Ω) AltAo Io (A) Rsh (Ω) Iph (A) Voc (V) ∆Voc () Pmpp (W) ∆Pmpp ()Method 1Rs1 0004 196721 (Ao) 303832Eminus 5 9404501 47500 435 0 15018 0070Rs2 03295 196 290755Eminus 5 500102 47503 43509 00207 15016 0057Rs3 03297 196 290755Eminus 5 455572 47504 43508 00184 15014 0043Rs4 03299 196 290755Eminus 5 418307 47504 43507 00161 15012 0030Rs5 03301 196 290755Eminus 5 386664 47504 43507 00161 15009 0010Method 2Rs1 01272 196721 (Ao) 303832Eminus 5 1027775 47501 43499 minus00023 15009 00100Rs2 03295 2007 385129Eminus 5 786056 47502 43510 00230 14938 minus04631Rs3 03297 2007 385129Eminus 5 1001381 47502 43511 0025 14942 minus04364Rs4 03299 2007 385129Eminus 5 1379317 47501 43512 0028 14943 minus04298Rs5 03301 2007 385129Eminus 5 2215812 47501 43513 003 14947 minus04031

Table 5 Extracted parameters and data from simulations for Solarex MSX60

Rs (Ω) AltAo Io (A) Rsh (Ω) Iph (A) Voc (V) ∆Voc () Pmpp (W) ∆Pmpp ()Method 1Rs1 0001 170418 (Ao) 579749Eminus 06 598976 38000 211 0 5986 00184Rs2 0147 17 560956Eminus 06 2175959 38000 21106 00284 5991 00986Rs3 0148 17 560956Eminus 06 312783 38002 21104 00190 5983 minus00284Rs4 0149 17 560956Eminus 06 168173 38003 21102 00095 5976 minus01487Rs5 0150 17 560956Eminus 06 114849 38005 21100 00000 5968 minus02840Method 2Rs1 00351 170418 (Ao) 579749Eminus 06 340980 38000 211 0 5987 00251Rs2 0147 1737 746677Eminus 06 7338600 38008 21095 minus00237 5922 minus10560Rs3 0148 1737 746677Eminus 06 10529594 38005 21098 minus00095 5939 minus07686Rs4 0149 1737 746677Eminus 06 18664501 38003 21102 00095 5947 minus06383Rs5 0150 1737 746677Eminus 06 82735534 38001 21106 00284 5958 minus04478

Table 6 A summary of appropriate parameters for MSX60 BP-SX 150 KC200GT and BP3235T

MSX60 BP-SX 150 KC200GT BP3235TMethod 1 Method 2 Method 1 Method 2 Method 1 Method 2 Method 1 Method 2

Rs (Ω) 0150 0150 03301 03301 02188 02188 02420 02420Rsh (Ω) 114849 82735533 386664 2215812 1028695 67935 106637 106630A 17 1737 196 2007 1809 1882 17920 18626Io (A) 56096Eminus 6 74668Eminus 06 29076Eminus 5 38513Eminus 5 16535Eminus 5 27501Eminus 5 11942Eminus 5 199Eminus 5Iph (A) 3800013 38001 47504 47501 82119 82127 8481938 84819


Kyocera 200GT and BP2235T In order to overcome thisdrawback the ideality factor can be selected very close to Aoand consequently other parameters can be changed which willresult in small errors However this reduces the values of Rsand care must be taken not to get nonviable values

7 Comparison of the Proposed AnalyticalMethod with Other Related Works

In this paper the ideality factor the saturation current andthe series resistance are the three key parameters that have

been carefully evaluated and considered to have a majorimpact on the PV relationship compared to the shunt re-sistance and Iph Since the ideality factor has been consideredas the immediate parameter to be calculated the nextcritically analyzed parameter is the saturation current usingequations (13) to (18) Furthermore due to the nonlinearityof the equations that relate to these parameters it has beenimportant to use iterative solutions for series and shuntresistances

As shown in Tables 7ndash9 ideality factors between 1 and15 have lower Io values than ideal factors closer to Ao

Ao =1801956

A = 1792 Rsh = 10663747A = 1792 Rsh = 11460561

A = 1792 Rsh = 9970158A = 1792 Rsh = 9360957

2351

235

2349

2348299 301 303 305 307

00008000060000400002

037194 37196 37198 372

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

(a)

Ao = 1801956

A = 18626 Rsh = 10663A = 18626 Rsh = 99272

A = 18626 Rsh = 115168A = 18626 Rsh = 125195

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

2355235

2345234

2335233

2325232

296

00008000060000400002

037198

30 304 308

372

(b)

Figure 5 PV curves for BP3235T showing different (Rsh) values for (a) AltAo and (b) AgtAo

Ao = 181928

A = 1809 Rsh = 11161044 A = 1809 Rsh = 12196776

A = 1809 Rsh = 10286957A = 1809 Rsh = 9539412

200252002

200152001

20005200

264 266 268 27

00008000060000400002

032897 32899 32901

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

(a)

Ao = 181928

A = 1882 Rsh = 64429A = 1882 Rsh = 61269

A = 1882 Rsh = 67935A = 1882 Rsh = 71845

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

2001995

1991985

1981975

197256 264 272

00008000060000400002

032891 32895 32899

(b)

Figure 6 PV curves for KC200GT showing different (Rsh) values for (a) AltAo and (b) AgtAo


Depending on which parameters are calculated first dif-ferent approaches result to different values of Io For in-stance if A Rs and Rsh are calculated first then equations(13) and (15) can be used to calculate Io otherwise simplifiedapproaches found in [6 19] that first assume Rsasymp 0 andRshasympinfin to obtain Io have been applied here using equations(14) (16) and (18) Equation (17) gives negative values of Ioand has not been considered here is accounts for thediverse findings published in previous works such as works

of [25 71] for BP32235T findings in [52 55 58 61 66] forKyocera 200GT reports in [61 72 73] for BP-SX 150 andstudies in [25 61 70 72] for MSX60 e studies in[52 55 57ndash59 61 71] used equation (13) to calculate Iowhich provided reliable results that are consistent with theresults obtained in this study

For BP32235Tgiven in Table 7 consistent findings in theworks of [25 71] recorded appropriate values for Rs Rsh andIph within the same range as the values obtained in this work

15015

1501

15005

00008000060000400002

043498 43502 43506 4351

Pow

er in

wat

ts

150

100

50

00 10 20 30 40

3462 3482 3502

Ao = 196721

A = 196 Rsh = 45557158 A = 196 Rsh = 50010224

A = 196 Rsh = 41830674A = 196 Rsh = 38666358

Voltage in volts

(a)

150

100

50

Pow

er in

wat

ts

00 10 20 30 40

1501498149614941492

342 35 358

00008000060000400002

043498 43503 43508 43513

Ao = 196721

A = 2007 Rsh = 1001381 A = 2007 Rsh = 786056

A = 2007 Rsh = 1379317A = 2007 Rsh = 2215812

Voltage in volts

(b)

Figure 7 PV curves for BP-SX 150 showing different (Rsh) values for (a) AltAo and (b) AgtAo

60599598597596595594

00008000060000400002

021099 21103 21107

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

168 17 172 174 176

Ao = 170418

A = 17 Rsh = 3127832 A = 17 Rsh = 2603693

A = 17 Rsh= 168173 A = 17 Rsh = 114849

Voltage in volts

(a)

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

60

598

596

594

592

00008000060000400002

0

168 17 172 174 176

21094 21098 21102 21106

Ao = 170418

A = 1737 Rsh = 10529594 A = 1737 Rsh = 73386

A = 1737 Rsh = 18664501A = 1737 Rsh = 82735534

Voltage in volts

(b)

Figure 8 PV curves for MSX60 showing different (Rsh) values for (a) AltAo and (b) AgtAo


Table 7 Calculated parameters and data from simulations for BP3235T

Parameters Method 1 Method 2 Ref [25] Ref [71]Rs (Ω) 02420 02420 0336 02371Rsh (Ω) 10663747 106630 65209 43938A 17920 18626 101 134Io (A) 1194159Eminus 05 1989991Eminus 5 4610Eminus 10 129Eminus 07Iph (A) 8481938 84819 84929 84805Io (A) equation (3) [55] 119416Eminus 05 199000Eminus 05 352066Eminus 10 126861Eminus 07Io equation (3) 118925Eminus 05 198181Eminus 05 349697Eminus 10 126735Eminus 07Io equation (13) [61] 118952Eminus 05 198227Eminus 05 349879Eminus 10 126741Eminus 07Io equation (14) 119416Eminus 05 198999Eminus 05 352066Eminus 10 126861Eminus 07Io equation (15) 578361Eminus 06 893832Eminus 06 478243Eminus 10 127022Eminus 07Io equation (16) 121197Eminus 05 182458Eminus 05 284624Eminus 09 317969Eminus 07Io equation (18) 119285Eminus 05 200357Eminus 05 330414Eminus 10 317969Eminus 07

Table 8 Calculated parameters and data from simulations for KC200GT

Parameters Method 1 Method 2 Ref [52] Ref [55] Ref [58] Ref [61] Ref [66] Ref [59]Rs (Ω) 02188 02188 0217 0221 0231 0217 02108 021095Rsh (Ω) 953941 67935 951927 415405 594851 95192 145083 192757A 1809 1882 134 13 13 1342 11578 11482Io (A) 16535Eminus 5 27501Eminus 5 17100Eminus 7 9825Eminus 8 96990Eminus 8 171Eminus 7 101Eminus 8 86369Eminus 9Iph (A) 82119 82127 8212 8214 8213 8211 8226 8218985Io [55] 16535Eminus 5 27501Eminus 5 16782Eminus 7 97328Eminus 8 97328Eminus 8 17230Eminus 7 10340Eminus 8 3665Eminus 9Io equation (3) 16466Eminus 5 27339Eminus 5 16711Eminus 7 96389Eminus 8 96672Eminus 8 17158Eminus 7 10054Eminus 8 3568Eminus 9Io equation (13) 16470Eminus 5 27348Eminus 5 16715Eminus 7 96440Eminus 8 96710Eminus 8 17162Eminus 7 10069Eminus 8 3578Eminus 9Io equation (14) 16535Eminus 5 27501Eminus 5 16782Eminus 7 97327Eminus 8 97327Eminus 8 17230Eminus 7 10340Eminus 8 3665Eminus 9Io equation (15) 82468Eminus 6 12462Eminus 5 16784Eminus 7 97440Eminus 8 96720Eminus 8 17164Eminus 7 11867Eminus 8 1835Eminus 9Io equation (16) 16783Eminus 5 25205Eminus 5 42778Eminus 7 27675Eminus 7 27675Eminus 7 43690Eminus 7 46099Eminus 8 2012Eminus 8Io equation (18) 16516Eminus 5 27700Eminus 5 16014Eminus 7 92594Eminus 8 92594Eminus 8 16445Eminus 7 97438Eminus 9 3443Eminus 9

Table 9 Calculated parameters and data from simulations for BP-SX 150

Parameters Method 1 Method 2 Ref [61] Ref ([72]) Ref ([73])Rs (Ω) 03301 03301 04543 0312557 0331466Rsh (Ω) 386664 2215812 96006 1799371625 436759648A 196 2007 14851 164 1642Io (A) 290755Eminus 05 3851289Eminus 05 6166Eminus 07 28016100Eminus 06 28419820Eminus 06Iph (A) 47504 47501 47522 4750827 475Io equation (3) [55] 2907545Eminus 05 3851320Eminus 05 6258569Eminus 07 2794604Eminus 06 2843865Eminus 06Io equation (3) 2900659Eminus 05 3849728Eminus 05 6198869Eminus 07 2780381Eminus 06 2837902Eminus 06Io equation (13) [61] 2900917Eminus 05 3849802Eminus 05 6201831Eminus 07 2780867Eminus 06 2838119Eminus 06Io equation (14) 2907528Eminus 05 3851289Eminus 05 6258568Eminus 07 2794602Eminus 06 2843864Eminus 06Io equation (15) 1930475Eminus 05 2480836Eminus 05 6196016Eminus 07 2784494Eminus 06 2830482Eminus 06Io equation (16) 2934115Eminus 05 3666915Eminus 05 1397445Eminus 06 4578563Eminus 06 4642457Eminus 06Io equation (18) 2905107Eminus 05 3869178Eminus 05 5956163Eminus 07 2697940Eminus 06 2746036Eminus 06

Table 10 Calculated parameters and data from simulations for Solarex MSX60

Parameters Method 1 Method 2 Ref [25] Ref [61] Ref [70] Ref [72]Rs (Ω) 0150 0150 0234 0169 02165 0223427Rsh (Ω) 114849 82735534 929 6375 274937 406346152A 17 1737 127 1404 1277 1387Io (A) 560956Eminus 6 746677Eminus 6 595Eminus 8 329Eminus 07 64500Eminus 8 297156Eminus 6Iph (A) 3800013 38001 38 3801 3813 3872128Io equation (3) [55] 560957Eminus 06 746678Eminus 06 595254Eminus 08 330851Eminus 07 656881Eminus 08 271080Eminus 07Io equation (3) 558245Eminus 06 746177Eminus 06 239471Eminus 08 327969Eminus 07 643615Eminus 08 267376Eminus 07Io equation (13) [61] 558319Eminus 06 746191Eminus 06 254464Eminus 08 328057Eminus 07 644132Eminus 08 267525Eminus 07Io equation (14) 560956Eminus 06 746677Eminus 06 595254Eminus 08 330851Eminus 07 656881Eminus 08 271080Eminus 07Io equation (15) 384169Eminus 06 509713Eminus 06 minus360728Eminus 07 328789Eminus 07 641383Eminus 08 226480Eminus 07Io equation (16) 564471Eminus 06 711705Eminus 06 141800Eminus 07 569360Eminus 07 153585Eminus 07 484460Eminus 07Io equation (18) 560657Eminus 06 749835Eminus 06 567053Eminus 08 319383Eminus 07 626165Eminus 08 261219Eminus 07


Nevertheless no consistency exists between A and Io valueswhere higher values of ideality factors (As) give large Io valuesand lower values of ideality factors (As) give smaller values of Io

Consistent results have also been reported for KyoceraKC200GT as shown in Table 8 where the works of [55 58]gave closer results for Rs 0221(Ω) and Rs 0231(Ω) whilethe findings reported in [52 61 66] gave Rs 0217(Ω)Rs 0217(Ω) and Rs 02108(Ω) respectively which agreeswith Rs 02188(Ω) reported here e Rsh values differ witha higher margin since a minor adjustment in Rs in mΩs issignificant enough to shift Rsh exponentially according toequations (32) and (35) e results of [55 58] are higherthan those of methods 1 and 2 and those published in[52 61 66] due to the fact that the solutions were obtainedfor a fixed value of the ideality factor A 13 In addition thedifferent choice of ideality factor gives diverse values of Io

For BP-SX 150 data results shown in Table 9 similar andalmost matching results were obtained in [73] ofRs 0331466(Ω) compared with the proposed method inthis article of Rs 03301(Ω) e works of [61 72] reportedhigher and lower values of Rs 04543(Ω) and

Rs 0312557(Ω) respectively Other parameters do nothave satisfactory agreements with the parameters extractedhere

For MSX60 data given in Table 10 it is possible tocompare the result of Rs 015(Ω) using methods 1 and 2with the results given in [61] of Rs 0169(Ω) which shows aslight difference Nevertheless the results in [25 70 72] havemuch larger Rs values depending on the techniques appliedto achieve them while diverse results are given for otherparameters

8 Evaluation of the Proposed Method atDifferent Irradiance Levels and NominalOperating Cell Temperature

e proposed technique has also been tested for variousirradiance levels and nominal cell operation temperature(NOCT) Table 11 gives a summary of Kyocera KC200GTnominal operation cell temperature data that have beenprovided in manufacturerrsquos datasheet Figures 9 and 10 show


Datasheet valuesIsc (A) Impp (A) Voc (V) Vmpp (V) KI (AdegC) KV (VdegC) NOCT (degC)662 613 299 232 000328 (minus0123) 47

Simulated parameter valuesParameters Rs (Ω) Rsh (Ω) A Io (A) Iph (A) T (K)T 25degC 02188 1028685 1809 16535Eminus 05 65695 29815T 47degC 0233 67935 1808 10752Eminus 04 66257 32015Ref [59] 023901 21840213 111933 494422Eminus 09 657518 29815

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

10

8

6

4

2

00 10 20 30 40

Voltage in volts

Curr

ent i

n am

pere

s

(a)

Pow

er in

wat

ts

200

150

100

50

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

00 10 20 30 40

(b)

Figure 9 IV and PV curves for KC200GTshowing different irradiance values at 1000Wm2 800Wm2 600Wm2 400Wm2 and 200Wm2 forT 25degC (a) KC200GT IV curve for T 25degC (b) KC200GT PV curve for T 25degC


the IV and PV curves at both STC and NOCTfor KC200GTIt is clear from the figures that the IV and PV characteristicscoincide at a satisfactory level with the experimental dataprovided in the datasheet

9 Conclusion

A new method has been developed and tested to de-termine the unknown parameters of a single-diodemodel for PV modules based on the datasheet valuesis new algorithm provides a simplified and robust wayof extracting A Io Rsh Rs and Iph from the transcen-dental single-diode PV model equation using IV curvecrucial points from the manufacturerrsquos data Furtherthese parameters have been used to plot the PV char-acteristics for the solar modules whose three criticalpoints Isc Pmpp and Voc match the datasheet values ordata obtained through an experimental procedureVarious values of ideality factors near the optimumideality factor offer different options of selecting theseries and shunt resistance pairs that match the exper-imental data

Data Availability

e simulation data used to support the findings of thisstudy are included within the article and are available fromthe corresponding author upon request via ndegwarguonbiacke

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to thank the Department of Physicsand the Board of Graduate School Nairobi University(Kenya) for providing all the facilities and financial supportrespectively for this research

References

[1] A Orioli and A Di Gangi ldquoA criterion for rating the usabilityand accuracy of the one-diode models for photovoltaicmodulesrdquo Energies vol 9 no 6 p 427 2016

[2] V Franzitta A Orioli and A Di Gangi ldquoAssessment of theusability and accuracy of the simplified one-diode models forphotovoltaic modulesrdquo Energies vol 9 no 12 p 1019 2016

[3] V Franzitta A Orioli and A D Gangi ldquoAssessment of theusability and accuracy of two-diode models for photovoltaicmodulesrdquo Energies vol 10 no 4 p 564 2017

[4] D T Cotfas P A Cotfas and S Kaplanis ldquoMethods todetermine the dc parameters of solar cells a critical reviewrdquoRenewable and Sustainable Energy Reviews vol 28 pp 588ndash596 2013

[5] V J Chin Z Salam and K Ishaque ldquoCell modelling andmodel parameters estimation techniques for photovoltaicsimulator application a reviewrdquo Applied Energy vol 154pp 500ndash519 2015

[6] A M Humada M Hojabri S Mekhilef and H M HamadaldquoSolar cell parameters extraction based on single and double-diode models a reviewrdquo Renewable and Sustainable EnergyReviews vol 56 pp 494ndash509 2016

[7] A R Jordehi ldquoParameter estimation of solar photovoltaic(PV) cells a reviewrdquo Renewable and Sustainable Energy Re-views vol 61 pp 354ndash371 2016

[8] R Abbassi A Abbassi M Jemli and S Chebbi ldquoIdentifi-cation of unknown parameters of solar cell models a

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)

Figure 10 IV and PV curves for KC200GTshowing different irradiance values at 1000Wm2 800Wm2 600Wm2 400Wm2 and 200Wm2for NOCT 47degC (a) KC200GT IV curve for NOCT 47degC (b) KC200GT PV curve for NOCT 47degC


comprehensive overview of available approachesrdquo Renewableand Sustainable Energy Reviews vol 90 pp 453ndash474 2018

[9] N M A A Shannan N Z Yahaya and B Singh ldquoSingle-diode model and two-diode model of PV modules a com-parisonrdquo in Proceedings of the 2013 IEEE InternationalConference on Control System Computing and EngineeringIEEE Penang Malaysia pp 210ndash214 November 2013

[10] A Hovinen ldquoFitting of the solar cell IV-curve to the two diodemodelrdquo Physica Scripta vol T54 pp 175-176 1994

[11] J Gow and C Manning ldquoDevelopment of a model forphotovoltaic arrays suitable for use in simulation studies ofsolar energy conversion systemsrdquo in Proceedings of the 6thInternational Conference on Power Electronics and VariableSpeed Drives pp 69ndash74 Nottingham UK September 1996

[12] L Sandrolini M Artioli and U Reggiani ldquoNumericalmethod for the extraction of photovoltaic module double-diode model parameters through cluster analysisrdquo AppliedEnergy vol 87 no 2 pp 442ndash451 2010

[13] C Garrido-Alzar ldquoAlgorithm for extraction of solar cellparameters from IndashV curve using double exponential modelrdquoRenewable Energy vol 10 no 2-3 pp 125ndash128 1997

[14] M Hejri H Mokhtari M R Azizian M Ghandhari andL Soder ldquoOn the parameter extraction of a five-parameterdouble-diode model of photovoltaic cells and modulesrdquo IEEEJournal of Photovoltaics vol 4 no 3 pp 915ndash923 2014

[15] K Ishaque Z Salam and H Taheri ldquoSimple fast and accuratetwo-diode model for photovoltaic modulesrdquo Solar EnergyMaterials and Solar Cells vol 95 no 2 pp 586ndash594 2011

[16] K Kennerud ldquoAnalysis of performance degradation in CdSsolar cellsrdquo IEEE Transactions on Aerospace and ElectronicSystems vol AES-5 no 6 pp 912ndash917 1969

[17] S Shongwe and M Hanif ldquoComparative analysis of differentsingle-diode PV modeling methodsrdquo IEEE Journal of Pho-tovoltaics vol 5 no 3 pp 938ndash946 2015

[18] A Ortiz-Conde F Garcıa-Sanchez J Muci and A Sucre-Gonzalez ldquoA review of diode and solar cell equivalent circuitmodel lumped parameter extraction proceduresrdquo FactaUniversitatis-Series Electronics and Energetics vol 27 no 1pp 57ndash102 2014

[19] W Xiao W G Dunford and A Capel ldquoA novel modelingmethod for photovoltaic cellsrdquo in Proceedings of the 2004IEEE 35th Annual Power Electronics Specialists Conference(IEEE Cat No 04CH37551) vol 3 IEEE Aachen Germanypp 1950ndash1956 June 2004

[20] E Saloux A Teyssedou and M Sorin ldquoExplicit model ofphotovoltaic panels to determine voltages and currents at themaximum power pointrdquo Solar Energy vol 85 no 5pp 713ndash722 2011

[21] Y Mahmoud W Xiao and H Zeineldin ldquoA simple approachto modeling and simulation of photovoltaic modulesrdquo IEEETransactions on Sustainable Energy vol 3 no 1 pp 185-1862011

[22] C Carrero J Rodrıguez D Ramırez and C Platero ldquoSimpleestimation of PV modules loss resistances for low errormodellingrdquo Renewable Energy vol 35 no 5 pp 1103ndash11082010

[23] E Kiran and D Inan ldquoTechnical note an approximation tosolar cell equation for determination of solar cell parametersrdquoRenewable Energy vol 17 no 2 pp 235ndash241 1999

[24] R Khezzar M Zereg and A Khezzar ldquoModeling improve-ment of the four parameter model for photovoltaic modulesrdquoSolar Energy vol 110 pp 452ndash462 2014

[25] N Aoun and N Bailek ldquoEvaluation of mathematical methodsto characterize the electrical parameters of photovoltaic

modulesrdquo Energy Conversion and Management vol 193pp 25ndash38 2019

[26] E E Van Dyk and E L Meyer ldquoAnalysis of the effect ofparasitic resistances on the performance of photovoltaicmodulesrdquo Renewable Energy vol 29 no 3 pp 333ndash344 2004

[27] N Dieme and M Sane ldquoImpact of parasitic resistances on theoutput power of a parallel vertical junction silicon solar cellrdquoEnergy and Power Engineering vol 8 no 3 pp 130ndash136 2016

[28] S Lineykin M Averbukh and A Kuperman ldquoIssues inmodeling amorphous silicon photovoltaic modules by single-diode equivalent circuitrdquo IEEE Transactions on IndustrialElectronics vol 61 no 12 pp 6785ndash6793 2014

[29] S Kabir Basic Guidelines for Research An Introductory Ap-proach for All Disciplines Book Zone Publication Chawk-bazar India 2016

[30] E I Ortiz-Rivera and F Z Peng ldquoAnalytical model for aphotovoltaic module using the electrical characteristics pro-vided by the manufacturer data sheetrdquo in Proceedings of the2005 IEEE 36th Power Electronics Specialists Conference IEEERecife Brazil pp 2087ndash2091 June 2005

[31] S R Wenham M A Green M E Watt R Corkish andA Sproul Applied Photovoltaics Routledge Abingdon UK2013

[32] S Manda P Chaubey S Yelisetti S K Kuralla N k Yadavand N K Meena ldquoExact parameter identification of photo-voltaic panel by using datasheet detailsrdquo Energy Procediavol 158 pp 972ndash977 2019

[33] T Easwarakhanthan J Bottin I Bouhouch and C BoutritldquoNonlinear minimization algorithm for determining the solarcell parameters with microcomputersrdquo International Journalof Solar Energy vol 4 no 1 pp 1ndash12 1986

[34] W De Soto S A Klein and W A Beckman ldquoImprovementand validation of a model for photovoltaic array perfor-mancerdquo Solar Energy vol 80 no 1 pp 78ndash88 2006

[35] Z Z Zhang X F Cheng and J L Liu ldquoAn improvementmethod for extracting five parameters of a solar cell based onLambert W-function with the current-voltage datardquo in Ap-plied Mechanics and Materials vol 291 pp 38ndash42 Trans TechPublications Stafa-Zurich Switzerland 2013

[36] E I Batzelis and S A Papathanassiou ldquoA method for theanalytical extraction of the single-diode PV model parame-tersrdquo IEEE Transactions on Sustainable Energy vol 7 no 2pp 504ndash512 2015

[37] X Feng X Qing C Chung H Qiao X Wang and X ZhaoldquoA simple parameter estimation approach to modeling ofphotovoltaic modules based on datasheet valuesrdquo Journal ofSolar Energy Engineering vol 138 no 5 Article ID 0510102016

[38] D Sera R Teodorescu and P Rodriguez ldquoPV panel modelbased on datasheet valuesrdquo in Proceedings of the 2007 IEEEInternational Symposium on Industrial Electronics IEEEVigo Spain pp 2392ndash2396 June 2007

[39] A Yahfdhou A K Mahmoud and I Youm ldquoEvaluation anddetermination of seven and five parameters of a photovoltaicgenerator by an iterative methodrdquo 2016 httpsarxivorgftparxivpapers1601160103257pdf

[40] C Saha N Agbu and R Jinks ldquoReview article of the solar PVparameters estimation using evolutionary algorithmsrdquo MOJSolar and Photoenergy Systems vol 2 no 2 pp 66ndash78 2018

[41] M R AlRashidi M F AlHajri K M El-Naggar and A K Al-Othman ldquoA new estimation approach for determining the I-Vcharacteristics of solar cellsrdquo Solar Energy vol 85 no 7pp 1543ndash1550 2011


[42] M Zagrouba A Sellami M Bouaıcha and M KsourildquoIdentification of PV solar cells andmodules parameters usingthe genetic algorithms application to maximum power ex-tractionrdquo Solar Energy vol 84 no 5 pp 860ndash866 2010

[43] K M El-Naggar M R AlRashidi M F AlHajri and A K Al-Othman ldquoSimulated annealing algorithm for photovoltaicparameters identificationrdquo Solar Energy vol 86 no 1pp 266ndash274 2012

[44] F Dkhichi B Oukarfi A Fakkar and N BelbounaguialdquoParameter identification of solar cell model using Levenberg-Marquardt algorithm combined with simulated annealingrdquoSolar Energy vol 110 pp 781ndash788 2014

[45] M Ye X Wang and Y Xu ldquoParameter extraction of solarcells using particle swarm optimizationrdquo Journal of AppliedPhysics vol 105 no 9 Article ID 094502 2009

[46] M Azab ldquoParameters estimation of PV modules withoutexperimental measurements using particle swarm optimiza-tionrdquo in Proceedings of the IEEE Industrial Electronics Con-ference IECONrsquo13 pp 7004ndash7008 Vienna AustriaNovember 2013

[47] W Han H-HWang and L Chen ldquoParameters identificationfor photovoltaic module based on an improved artificial fishswarm algorithmrdquo gte Scientific World Journal vol 2014Article ID 859239 12 pages 2014

[48] H Al-Hamadi ldquoFuzzy estimation analysis of photovoltaicmodel parametersrdquo Journal of Power and Energy Engineeringvol 3 no 7 pp 39ndash43 2015

[49] A Kulaksız ldquoANFIS-based parameter estimation of one-di-ode equivalent circuit model of PV modulesrdquo in Proceedingsof the 2011 IEEE 12th International Symposium on Compu-tational Intelligence and Informatics (CINTI) IEEE BudapestHungary pp 415ndash420 November 2011

[50] M Karamirad M Omid R Alimardani H Mousazadeh andS N Heidari ldquoANN based simulation and experimentalverification of analytical four- and five-parameters models ofPV modulesrdquo Simulation Modelling Practice and gteoryvol 34 pp 86ndash98 2013

[51] F Salem and M A Awadallah ldquoParameters estimation ofphotovoltaic modules comparison of ANN and ANFISrdquoInternational Journal of Industrial Electronics and Drivesvol 1 no 2 pp 121ndash129 2014

[52] M Hejri H Mokhtari M R Azizian and L Soder ldquoAnanalytical-numerical approach for parameter determinationof a five-parameter single-diode model of photovoltaic cellsand modulesrdquo International Journal of Sustainable Energyvol 35 no 4 pp 396ndash410 2013

[53] T R Ayodele A S O Ogunjuyigbe and E E EkohldquoEvaluation of numerical algorithms used in extracting theparameters of a single-diode photovoltaic modelrdquo SustainableEnergy Technologies and Assessments vol 13 pp 51ndash59 2016

[54] R A P Franco and F H T Vieira ldquoAnalytical method forextraction of the single-diode model parameters for photo-voltaic panels from datasheet datardquo Electronics Letters vol 54no 8 pp 519ndash521 2018

[55] M G Villalva J R Gazoli and E R Filho ldquoComprehensiveapproach to modeling and simulation of photovoltaic arraysrdquoIEEE Transactions on Power Electronics vol 24 no 5pp 1198ndash1208 2009

[56] M Bashahu and P Nkundabakura ldquoReview and tests ofmethods for the determination of the solar cell junctionideality factorsrdquo Solar Energy vol 81 no 7 pp 856ndash8632007

[57] C Carrero D Ramırez J Rodrıguez and C A PlateroldquoAccurate and fast convergence method for parameter

estimation of PV generators based on three main points of theI-V curverdquo Renewable Energy vol 36 no 11 pp 2972ndash29772011

[58] J Cubas S Pindado and A Farrahi ldquoNew method for an-alytical photovoltaic parameter extractionrdquo in Proceedings ofthe 2013 International Conference On Renewable Energy Re-search And Applications (ICRERA) IEEE Madrid Spainpp 873ndash877 October 2013

[59] M Zaimi H El Achouby A Ibral and E M Assaid ldquoDe-termining combined effects of solar radiation and paneljunction temperature on all model-parameters to forecastpeak power and photovoltaic yield of solar panel under non-standard conditionsrdquo Solar Energy vol 191 pp 341ndash3592019

[60] W Shen Y Ding F H Choo P Wang P C Loh andK K Tan ldquoMathematical model of a solar module forenergy yield simulation in photovoltaic systemsrdquo in Pro-ceedings of the International Conference on Power Elec-tronics and Drive Systems (PEDS) IEEE Taipei Taiwanpp 336ndash341 November 2009

[61] B K Atay and U Eminoglu ldquoA new approach for parameterestimation of the single-diode model for photovoltaic cellsmodulesrdquo Turkish Journal of Electrical Engineering amp Com-puter Sciences vol 27 no 4 pp 3026ndash3039 2019

[62] H S Rauschenbach ldquoElectrical output of shadowed solararraysrdquo IEEE Transactions on Electron Devices vol 18 no 8pp 483ndash490 1971

[63] L Castaner and S Silvestre Modelling Photovoltaic SystemsUsing PSpice John Wiley amp Sons Hoboken NJ USA 2002

[64] R C Neville Solar Energy Conversiongte Solar Cell ElsevierAmsterdam Netherlands 1995

[65] R Chenni M Makhlouf T Kerbache and A Bouzid ldquoAdetailed modeling method for photovoltaic cellsrdquo Energyvol 32 no 9 pp 1724ndash1730 2007

[66] H El Achouby M Zaimi A Ibral and E M Assaid ldquoNewanalytical approach for modelling effects of temperature andirradiance on physical parameters of photovoltaic solarmodulerdquo Energy Conversion and Management vol 177pp 258ndash271 2018

[67] J C H Phang D S H Chan and J R Phillips ldquoAccurateanalytical method for the extraction of solar cell model pa-rametersrdquo Electronics Letters vol 20 no 10 pp 406ndash4081984

[68] L Reis J Camacho and D Novacki ldquoe Newton raphsonmethod in the extraction of parameters of PV modulesrdquo inProceedings of the International Conference on RenewableEnergies and Power Quality (ICREPQrsquo17) pp 4ndash6 MalagaSpain 2017

[69] D S H Chan and J C H Phang ldquoAnalytical methods for theextraction of solar-cell single- and double-diode model pa-rameters from I-V characteristicsrdquo IEEE Transactions onElectron Devices vol 34 no 2 pp 286ndash293 1987

[70] A A El Tayyan ldquoAn approach to extract the parameters ofsolar cells from their illuminated I-V curves using theLambertW functionrdquo Turkish Journal of Physics vol 39 no 1pp 1ndash15 2015

[71] A Laudani F Riganti Fulginei and A Salvini ldquoIdentificationof the one-diode model for photovoltaic modules fromdatasheet valuesrdquo Solar Energy vol 108 pp 432ndash446 2014

[72] A Hussein and A Hussein ldquoA simple approach to extract theunknown parameters of PV modulesrdquo Turkish Journal ofElectrical Engineering amp Computer Sciences vol 25 no 5pp 4431ndash4444 2017


[73] V Jha and U S Triar ldquoA novel approach for evaluation ofparameters of photovoltaic modulesrdquo International Journal ofApplied Engineering Research vol 12 no 21 pp 11167ndash11178 2017


A single-diode model has five unknown parameters (AIo Iph Rs and Rsh) that must be determined to obtain thebest solution of the current-voltage equation [16] Severalapproaches have been discussed in the literature for de-termination of the correct values of these five parameters[17 18] e simplest model that reduces the number ofunknown parameters to three (A Io and Iph) is a single-exponential diode equivalent circuit without any resistance[19ndash21] Ignoring the series and shunt resistances givesinaccurate evaluation of the PV module and fails to accountfor the loss of power due to electrical contacts base regionand the front layer [22] A better approach based on fourparameters incorporates a series resistance and omits theshunt resistance [23ndash25]e five-parameter model gives thebest solutions since it accounts for the effect of power lossesdue to parasitic series and shunt resistances that are em-bedded in the solar module as a result of fabrication defects[26 27]

e five-parameter single-diode model is based on aShockley diode equivalent circuit with series and parallelresistances and is defined by a transcendental equation thatcannot be solved explicitly Several procedures have beendeveloped for evaluation and determination of the lumpedparameters namely ideality factor (A) saturation current(Io) photocurrent (Iph) and shunt (Rsh) and series (Rs)resistances using IV characteristic [8] Experimental data orinformation available from manufacturerrsquos datasheet isusually utilized in order to derive the necessary nonlinearequations for extraction of the unknown parameters byconsidering three crucial points at short circuit currentopen circuit voltage and maximum power point of an IVcurve [28] Experimental procedures are expensive andrequire more time for setup data collection and analysis[29] Nevertheless evaluation of the five parameters usingmanufacturerrsquos data has become more popular since theinformation about the three critical points is readily availableat STC and NOCT for module with IEC standards [30ndash32]Different approaches have been proposed for extraction ofthese unknown parameters depending on which parameteris perturbed first either Rs or A Traditionally thestraightforward way of getting the five parameters has beenbased on five nonlinear equations selected from the threecritical points and determining the RS and Rsh from thereciprocal of IV slopes at these points [33 34] Computersoftware has been exploited to solve these equations usingLambert W function [35 36] nonlinear least square (NLS)[37] and NewtonndashRaphson algorithms [38 39] esetechniques are comprehensive methods with good accuracyand fast convergence but their main drawbacks are compleximplementation procedures and relatively low calculationspeed that require more computing power

Recent advances in computing technology has led toapplication of evolutionary computation techniques in-spired by biological evolution and chemistryphysics-basedswarming-based and hybridization-based algorithms forextraction of the unknown parameters for single- double-or triple-diode models [40] ese soft-computing tech-niques are problem solvers using trial and error meta-heuristic or stochastic optimization procedures such as

pattern search (PS) [41] genetic algorithm (GA) [42]simulated annealing (SA) [43 44] particle swarm optimi-zation [45 46] artificial fish swarm algorithm (AFSA) [47]fuzzy logic [48] and artificial neural networks (ANNs)[49ndash51] ese methods have disadvantages either in termsof sophistication and accuracy or in terms of convergenceand speed of execution

Fast and simplified approaches that calculate all modelparameters for the single-diode model of the photovoltaicsystem directly rely on careful evaluation of the under-lying analytical and numerical algorithms [52 53]Straightforward analytical methods for describing theparameters of PV models are heavily dependent onnonlinear explicit formulas using Isc Impp Vmpp and Vocdata in the PV panel datasheet [54] e simplest andcomprehensive approach assumes arbitrary value ofideality factor and determines other parameters byadjusting the curve at Isc Pmpp and Voc points [55] Anideal diode has an ideality factor of unity However anappropriate and actual diode for modeling PV system hasideality factor values ranging from one to two [56] Anaccurate and fast convergence method of extracting theunknown parameters by first analyzing the ideality factorand setting it as the primary parameter and obtaining theloss resistance through a repetitive process was reportedin [57] e authors used a protracted method to arrive ata control signal that was based on the series resistancevalue In this paper we present a novel analytical methodfor determining the single-diode model parameters di-rectly from the manufacturerrsquos datasheet using explicitequations

2 A Single-Diode Equivalent Circuit

A single-diode equivalent circuit shown in Figure 1 can bemathematically modeled using equation (1) [16] AShockleyrsquos diode is connected in parallel to the currentsource and shunt resistor and in series to Rs and the load

I Iph + Io minus Io expq V + IRs( 1113857

ANskTminus

V

Rshminus

IRs

Rsh (1)

where I is module output current in amperes (A) V is moduleoutput voltage in volts (V) q is charge of anelectron 1602176634times10minus19C k is Boltzmannrsquos constant

1380649times10minus23middotm2sminus2middotkgKminus1 and TSTC is standard temper-ature 29815K at STC

3 MathematicalModeling of a PVSystemUsingThree Critical Points and Their RespectiveSlopes of an IV Curve

Equation (1) can be evaluated by analyzing the open circuitshort circuit and the maximum power points whose data areusually available from datasheets

At short circuit I Isc VOIn Figure 1 a short circuit without the load gives zero

voltage and current Iasymp Isc that depend on IphA Io T Rs andRsh [16 58] erefore we can rewrite equation (1) as



ANsVt

1113888 1113889 minusIscRs

Rsh (2)



Iph Io

Voc

ANsVt

1113888 1113889 minus Io +Voc

Rsh (3)



Rsh1113888 1113889 minus ln Io( 1113857

Voc

ANsVt

(4)



ANsVt


Rsh

(5)



Rsh1113888 1113889 minus ln Io( 1113857

Vmpp + ImppRs

ANsVt

(6)





ANsVt

(7)






ANsVt

1113888 1113889 +IscRs

Rsh (9)


Iph s





A Voc minus Vmpp

NsVt

lnIsc + Io

Isc + Io minus Impp1113888 11138891113890 1113891

minus1

(11)


Ao Voc minus Vmpp

NsVt

lnIsc

Isc minus Impp1113888 11138891113890 1113891

minus1

(12)


Iph IRs Rs

ID IRsh I

Rsh Load






Io1113858 1113859Isc Voc



(13)


Ioopt1113876 1113877

Isc Voc

Isc

exp VocANsVt( 11138571113858 1113859 (14)


Io1113858 1113859Isc Pmpp




Ioopt1113876 1113877

Isc Pmpp

Isc minus Impp

exp VmppANsVt1113872 1113873 (16)


Io1113858 1113859Voc Pmpp




Ioopt1113876 1113877

VocPmpp

Impp


(18)


4

3

2

10 02 04 06 08 1


BP3235TKC200GT

BP SX150MSX60

Idea

lity

fact

or (A

)



ParametersPV module

SolarexMSX60

BP-SX150






Jo DT3 exp

minusqEg

kT1113888 1113889 (19)




Io IoSTC

T

TSTC1113890 1113891

3

expqEg

ANsk

1TSTC

minus1T

1113890 1113891 (20)





Io Ioopt STC

T

TSTC1113890 1113891

3

expqEg

ANsk

1TSTC

minus1T

1113890 1113891 (21)



Rsh Vmpp + ImppRs


(22)


Rsh Voc minus IscRs


(23)











zI

zV minus

Io

ANsVt

1 +zI

zVRs1113888 1113889exp

V + IRs

ANsVt

1113888 1113889 minus1

Rsh1 +

zI

zV1113888 1113889Rs1113896 1113897

(26)


zI

zV1113890 1113891

IIsc

minus1

Rsh (27)


zI

zV1113890 1113891

VVoc

minus1Rs

(28)


zP

zV

zI

zV1113888 1113889V + I O (29)


minusImpp

Vmpp minus

Io

ANsVt

1 minusImpp

VmppRs1113888 1113889exp

Vmpp + ImppRs

ANsVt

1113888 11138891113896 1113897

minus1

Rsh1 minus

Impp

VmppRs1113888 1113889

(30)















ANsVt

1113888 11138891113888

minusVmpp + ImppRs

Rsh1113889

(33)






























ANsVt

1113888 1113889 minusV

Rshminus

IRs

Rsh1113888 1113889

(36)



1

0

022 023 024 025 026Rs (Ω)

R sh (

Ω)

A = 1792 (BP3235T)

middot105

(a)

6

4

2

R sh (

Ω)

Rs (Ω)

0

minus2

minus402 022 023

A = 1809 (KC200GT)

middot104

02

(b)

R sh (

Ω)

Rs (Ω)

2

0

minus2

minus4

minus6

03 031 032 033 034 035

A = 196 (BPSX150)

middot105

(c)

R sh (

Ω)

Rs (Ω)

4

2

0


middot105

A = 1702 (MSX60)

(d)





Start

DatasheetIsc Impp

Vmpp Voc

Ao equation (12)

Ioopt equation (14)


No

Yes


Pmpp equation (33)

Select A lt A0


Io equation (14)

Iph equation (9)

Stop





















Ao =1801956

A = 1792 Rsh = 10663747A = 1792 Rsh = 11460561

A = 1792 Rsh = 9970158A = 1792 Rsh = 9360957

2351

235

2349

2348299 301 303 305 307

00008000060000400002

037194 37196 37198 372

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

(a)

Ao = 1801956

A = 18626 Rsh = 10663A = 18626 Rsh = 99272

A = 18626 Rsh = 115168A = 18626 Rsh = 125195

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

2355235

2345234

2335233

2325232

296

00008000060000400002

037198

30 304 308

372

(b)


Ao = 181928

A = 1809 Rsh = 11161044 A = 1809 Rsh = 12196776

A = 1809 Rsh = 10286957A = 1809 Rsh = 9539412

200252002

200152001

20005200

264 266 268 27

00008000060000400002

032897 32899 32901

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

(a)

Ao = 181928

A = 1882 Rsh = 64429A = 1882 Rsh = 61269

A = 1882 Rsh = 67935A = 1882 Rsh = 71845

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

2001995

1991985

1981975

197256 264 272

00008000060000400002

032891 32895 32899

(b)






15015

1501

15005

00008000060000400002

043498 43502 43506 4351

Pow

er in

wat

ts

150

100

50

00 10 20 30 40

3462 3482 3502

Ao = 196721

A = 196 Rsh = 45557158 A = 196 Rsh = 50010224

A = 196 Rsh = 41830674A = 196 Rsh = 38666358

Voltage in volts

(a)

150

100

50

Pow

er in

wat

ts

00 10 20 30 40

1501498149614941492

342 35 358

00008000060000400002

043498 43503 43508 43513

Ao = 196721

A = 2007 Rsh = 1001381 A = 2007 Rsh = 786056

A = 2007 Rsh = 1379317A = 2007 Rsh = 2215812

Voltage in volts

(b)


60599598597596595594

00008000060000400002

021099 21103 21107

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

168 17 172 174 176

Ao = 170418

A = 17 Rsh = 3127832 A = 17 Rsh = 2603693

A = 17 Rsh= 168173 A = 17 Rsh = 114849

Voltage in volts

(a)

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

60

598

596

594

592

00008000060000400002

0

168 17 172 174 176

21094 21098 21102 21106

Ao = 170418

A = 1737 Rsh = 10529594 A = 1737 Rsh = 73386

A = 1737 Rsh = 18664501A = 1737 Rsh = 82735534

Voltage in volts

(b)






















1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

10

8

6

4

2

00 10 20 30 40

Voltage in volts

Curr

ent i

n am

pere

s

(a)

Pow

er in

wat

ts

200

150

100

50

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

00 10 20 30 40

(b)




9 Conclusion


Data Availability




Acknowledgments


References









1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)











































































ANsVt

1113888 1113889 minusIscRs

Rsh (2)



Iph Io

Voc

ANsVt

1113888 1113889 minus Io +Voc

Rsh (3)



Rsh1113888 1113889 minus ln Io( 1113857

Voc

ANsVt

(4)



ANsVt


Rsh

(5)



Rsh1113888 1113889 minus ln Io( 1113857

Vmpp + ImppRs

ANsVt

(6)





ANsVt

(7)






ANsVt

1113888 1113889 +IscRs

Rsh (9)


Iph s





A Voc minus Vmpp

NsVt

lnIsc + Io

Isc + Io minus Impp1113888 11138891113890 1113891

minus1

(11)


Ao Voc minus Vmpp

NsVt

lnIsc

Isc minus Impp1113888 11138891113890 1113891

minus1

(12)


Iph IRs Rs

ID IRsh I

Rsh Load






Io1113858 1113859Isc Voc



(13)


Ioopt1113876 1113877

Isc Voc

Isc

exp VocANsVt( 11138571113858 1113859 (14)


Io1113858 1113859Isc Pmpp




Ioopt1113876 1113877

Isc Pmpp

Isc minus Impp

exp VmppANsVt1113872 1113873 (16)


Io1113858 1113859Voc Pmpp




Ioopt1113876 1113877

VocPmpp

Impp


(18)


4

3

2

10 02 04 06 08 1


BP3235TKC200GT

BP SX150MSX60

Idea

lity

fact

or (A

)



ParametersPV module

SolarexMSX60

BP-SX150






Jo DT3 exp

minusqEg

kT1113888 1113889 (19)




Io IoSTC

T

TSTC1113890 1113891

3

expqEg

ANsk

1TSTC

minus1T

1113890 1113891 (20)





Io Ioopt STC

T

TSTC1113890 1113891

3

expqEg

ANsk

1TSTC

minus1T

1113890 1113891 (21)



Rsh Vmpp + ImppRs


(22)


Rsh Voc minus IscRs


(23)











zI

zV minus

Io

ANsVt

1 +zI

zVRs1113888 1113889exp

V + IRs

ANsVt

1113888 1113889 minus1

Rsh1 +

zI

zV1113888 1113889Rs1113896 1113897

(26)


zI

zV1113890 1113891

IIsc

minus1

Rsh (27)


zI

zV1113890 1113891

VVoc

minus1Rs

(28)


zP

zV

zI

zV1113888 1113889V + I O (29)


minusImpp

Vmpp minus

Io

ANsVt

1 minusImpp

VmppRs1113888 1113889exp

Vmpp + ImppRs

ANsVt

1113888 11138891113896 1113897

minus1

Rsh1 minus

Impp

VmppRs1113888 1113889

(30)















ANsVt

1113888 11138891113888

minusVmpp + ImppRs

Rsh1113889

(33)






























ANsVt

1113888 1113889 minusV

Rshminus

IRs

Rsh1113888 1113889

(36)



1

0

022 023 024 025 026Rs (Ω)

R sh (

Ω)

A = 1792 (BP3235T)

middot105

(a)

6

4

2

R sh (

Ω)

Rs (Ω)

0

minus2

minus402 022 023

A = 1809 (KC200GT)

middot104

02

(b)

R sh (

Ω)

Rs (Ω)

2

0

minus2

minus4

minus6

03 031 032 033 034 035

A = 196 (BPSX150)

middot105

(c)

R sh (

Ω)

Rs (Ω)

4

2

0


middot105

A = 1702 (MSX60)

(d)





Start

DatasheetIsc Impp

Vmpp Voc

Ao equation (12)

Ioopt equation (14)


No

Yes


Pmpp equation (33)

Select A lt A0


Io equation (14)

Iph equation (9)

Stop





















Ao =1801956

A = 1792 Rsh = 10663747A = 1792 Rsh = 11460561

A = 1792 Rsh = 9970158A = 1792 Rsh = 9360957

2351

235

2349

2348299 301 303 305 307

00008000060000400002

037194 37196 37198 372

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

(a)

Ao = 1801956

A = 18626 Rsh = 10663A = 18626 Rsh = 99272

A = 18626 Rsh = 115168A = 18626 Rsh = 125195

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

2355235

2345234

2335233

2325232

296

00008000060000400002

037198

30 304 308

372

(b)


Ao = 181928

A = 1809 Rsh = 11161044 A = 1809 Rsh = 12196776

A = 1809 Rsh = 10286957A = 1809 Rsh = 9539412

200252002

200152001

20005200

264 266 268 27

00008000060000400002

032897 32899 32901

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

(a)

Ao = 181928

A = 1882 Rsh = 64429A = 1882 Rsh = 61269

A = 1882 Rsh = 67935A = 1882 Rsh = 71845

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

2001995

1991985

1981975

197256 264 272

00008000060000400002

032891 32895 32899

(b)






15015

1501

15005

00008000060000400002

043498 43502 43506 4351

Pow

er in

wat

ts

150

100

50

00 10 20 30 40

3462 3482 3502

Ao = 196721

A = 196 Rsh = 45557158 A = 196 Rsh = 50010224

A = 196 Rsh = 41830674A = 196 Rsh = 38666358

Voltage in volts

(a)

150

100

50

Pow

er in

wat

ts

00 10 20 30 40

1501498149614941492

342 35 358

00008000060000400002

043498 43503 43508 43513

Ao = 196721

A = 2007 Rsh = 1001381 A = 2007 Rsh = 786056

A = 2007 Rsh = 1379317A = 2007 Rsh = 2215812

Voltage in volts

(b)


60599598597596595594

00008000060000400002

021099 21103 21107

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

168 17 172 174 176

Ao = 170418

A = 17 Rsh = 3127832 A = 17 Rsh = 2603693

A = 17 Rsh= 168173 A = 17 Rsh = 114849

Voltage in volts

(a)

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

60

598

596

594

592

00008000060000400002

0

168 17 172 174 176

21094 21098 21102 21106

Ao = 170418

A = 1737 Rsh = 10529594 A = 1737 Rsh = 73386

A = 1737 Rsh = 18664501A = 1737 Rsh = 82735534

Voltage in volts

(b)






















1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

10

8

6

4

2

00 10 20 30 40

Voltage in volts

Curr

ent i

n am

pere

s

(a)

Pow

er in

wat

ts

200

150

100

50

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

00 10 20 30 40

(b)




9 Conclusion


Data Availability




Acknowledgments


References









1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)













































































Io1113858 1113859Isc Voc



(13)


Ioopt1113876 1113877

Isc Voc

Isc

exp VocANsVt( 11138571113858 1113859 (14)


Io1113858 1113859Isc Pmpp




Ioopt1113876 1113877

Isc Pmpp

Isc minus Impp

exp VmppANsVt1113872 1113873 (16)


Io1113858 1113859Voc Pmpp




Ioopt1113876 1113877

VocPmpp

Impp


(18)


4

3

2

10 02 04 06 08 1


BP3235TKC200GT

BP SX150MSX60

Idea

lity

fact

or (A

)



ParametersPV module

SolarexMSX60

BP-SX150






Jo DT3 exp

minusqEg

kT1113888 1113889 (19)




Io IoSTC

T

TSTC1113890 1113891

3

expqEg

ANsk

1TSTC

minus1T

1113890 1113891 (20)





Io Ioopt STC

T

TSTC1113890 1113891

3

expqEg

ANsk

1TSTC

minus1T

1113890 1113891 (21)



Rsh Vmpp + ImppRs


(22)


Rsh Voc minus IscRs


(23)











zI

zV minus

Io

ANsVt

1 +zI

zVRs1113888 1113889exp

V + IRs

ANsVt

1113888 1113889 minus1

Rsh1 +

zI

zV1113888 1113889Rs1113896 1113897

(26)


zI

zV1113890 1113891

IIsc

minus1

Rsh (27)


zI

zV1113890 1113891

VVoc

minus1Rs

(28)


zP

zV

zI

zV1113888 1113889V + I O (29)


minusImpp

Vmpp minus

Io

ANsVt

1 minusImpp

VmppRs1113888 1113889exp

Vmpp + ImppRs

ANsVt

1113888 11138891113896 1113897

minus1

Rsh1 minus

Impp

VmppRs1113888 1113889

(30)















ANsVt

1113888 11138891113888

minusVmpp + ImppRs

Rsh1113889

(33)






























ANsVt

1113888 1113889 minusV

Rshminus

IRs

Rsh1113888 1113889

(36)



1

0

022 023 024 025 026Rs (Ω)

R sh (

Ω)

A = 1792 (BP3235T)

middot105

(a)

6

4

2

R sh (

Ω)

Rs (Ω)

0

minus2

minus402 022 023

A = 1809 (KC200GT)

middot104

02

(b)

R sh (

Ω)

Rs (Ω)

2

0

minus2

minus4

minus6

03 031 032 033 034 035

A = 196 (BPSX150)

middot105

(c)

R sh (

Ω)

Rs (Ω)

4

2

0


middot105

A = 1702 (MSX60)

(d)





Start

DatasheetIsc Impp

Vmpp Voc

Ao equation (12)

Ioopt equation (14)


No

Yes


Pmpp equation (33)

Select A lt A0


Io equation (14)

Iph equation (9)

Stop





















Ao =1801956

A = 1792 Rsh = 10663747A = 1792 Rsh = 11460561

A = 1792 Rsh = 9970158A = 1792 Rsh = 9360957

2351

235

2349

2348299 301 303 305 307

00008000060000400002

037194 37196 37198 372

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

(a)

Ao = 1801956

A = 18626 Rsh = 10663A = 18626 Rsh = 99272

A = 18626 Rsh = 115168A = 18626 Rsh = 125195

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

2355235

2345234

2335233

2325232

296

00008000060000400002

037198

30 304 308

372

(b)


Ao = 181928

A = 1809 Rsh = 11161044 A = 1809 Rsh = 12196776

A = 1809 Rsh = 10286957A = 1809 Rsh = 9539412

200252002

200152001

20005200

264 266 268 27

00008000060000400002

032897 32899 32901

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

(a)

Ao = 181928

A = 1882 Rsh = 64429A = 1882 Rsh = 61269

A = 1882 Rsh = 67935A = 1882 Rsh = 71845

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

2001995

1991985

1981975

197256 264 272

00008000060000400002

032891 32895 32899

(b)






15015

1501

15005

00008000060000400002

043498 43502 43506 4351

Pow

er in

wat

ts

150

100

50

00 10 20 30 40

3462 3482 3502

Ao = 196721

A = 196 Rsh = 45557158 A = 196 Rsh = 50010224

A = 196 Rsh = 41830674A = 196 Rsh = 38666358

Voltage in volts

(a)

150

100

50

Pow

er in

wat

ts

00 10 20 30 40

1501498149614941492

342 35 358

00008000060000400002

043498 43503 43508 43513

Ao = 196721

A = 2007 Rsh = 1001381 A = 2007 Rsh = 786056

A = 2007 Rsh = 1379317A = 2007 Rsh = 2215812

Voltage in volts

(b)


60599598597596595594

00008000060000400002

021099 21103 21107

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

168 17 172 174 176

Ao = 170418

A = 17 Rsh = 3127832 A = 17 Rsh = 2603693

A = 17 Rsh= 168173 A = 17 Rsh = 114849

Voltage in volts

(a)

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

60

598

596

594

592

00008000060000400002

0

168 17 172 174 176

21094 21098 21102 21106

Ao = 170418

A = 1737 Rsh = 10529594 A = 1737 Rsh = 73386

A = 1737 Rsh = 18664501A = 1737 Rsh = 82735534

Voltage in volts

(b)






















1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

10

8

6

4

2

00 10 20 30 40

Voltage in volts

Curr

ent i

n am

pere

s

(a)

Pow

er in

wat

ts

200

150

100

50

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

00 10 20 30 40

(b)




9 Conclusion


Data Availability




Acknowledgments


References









1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)












































































Jo DT3 exp

minusqEg

kT1113888 1113889 (19)




Io IoSTC

T

TSTC1113890 1113891

3

expqEg

ANsk

1TSTC

minus1T

1113890 1113891 (20)





Io Ioopt STC

T

TSTC1113890 1113891

3

expqEg

ANsk

1TSTC

minus1T

1113890 1113891 (21)



Rsh Vmpp + ImppRs


(22)


Rsh Voc minus IscRs


(23)











zI

zV minus

Io

ANsVt

1 +zI

zVRs1113888 1113889exp

V + IRs

ANsVt

1113888 1113889 minus1

Rsh1 +

zI

zV1113888 1113889Rs1113896 1113897

(26)


zI

zV1113890 1113891

IIsc

minus1

Rsh (27)


zI

zV1113890 1113891

VVoc

minus1Rs

(28)


zP

zV

zI

zV1113888 1113889V + I O (29)


minusImpp

Vmpp minus

Io

ANsVt

1 minusImpp

VmppRs1113888 1113889exp

Vmpp + ImppRs

ANsVt

1113888 11138891113896 1113897

minus1

Rsh1 minus

Impp

VmppRs1113888 1113889

(30)















ANsVt

1113888 11138891113888

minusVmpp + ImppRs

Rsh1113889

(33)






























ANsVt

1113888 1113889 minusV

Rshminus

IRs

Rsh1113888 1113889

(36)



1

0

022 023 024 025 026Rs (Ω)

R sh (

Ω)

A = 1792 (BP3235T)

middot105

(a)

6

4

2

R sh (

Ω)

Rs (Ω)

0

minus2

minus402 022 023

A = 1809 (KC200GT)

middot104

02

(b)

R sh (

Ω)

Rs (Ω)

2

0

minus2

minus4

minus6

03 031 032 033 034 035

A = 196 (BPSX150)

middot105

(c)

R sh (

Ω)

Rs (Ω)

4

2

0


middot105

A = 1702 (MSX60)

(d)





Start

DatasheetIsc Impp

Vmpp Voc

Ao equation (12)

Ioopt equation (14)


No

Yes


Pmpp equation (33)

Select A lt A0


Io equation (14)

Iph equation (9)

Stop





















Ao =1801956

A = 1792 Rsh = 10663747A = 1792 Rsh = 11460561

A = 1792 Rsh = 9970158A = 1792 Rsh = 9360957

2351

235

2349

2348299 301 303 305 307

00008000060000400002

037194 37196 37198 372

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

(a)

Ao = 1801956

A = 18626 Rsh = 10663A = 18626 Rsh = 99272

A = 18626 Rsh = 115168A = 18626 Rsh = 125195

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

2355235

2345234

2335233

2325232

296

00008000060000400002

037198

30 304 308

372

(b)


Ao = 181928

A = 1809 Rsh = 11161044 A = 1809 Rsh = 12196776

A = 1809 Rsh = 10286957A = 1809 Rsh = 9539412

200252002

200152001

20005200

264 266 268 27

00008000060000400002

032897 32899 32901

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

(a)

Ao = 181928

A = 1882 Rsh = 64429A = 1882 Rsh = 61269

A = 1882 Rsh = 67935A = 1882 Rsh = 71845

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

2001995

1991985

1981975

197256 264 272

00008000060000400002

032891 32895 32899

(b)






15015

1501

15005

00008000060000400002

043498 43502 43506 4351

Pow

er in

wat

ts

150

100

50

00 10 20 30 40

3462 3482 3502

Ao = 196721

A = 196 Rsh = 45557158 A = 196 Rsh = 50010224

A = 196 Rsh = 41830674A = 196 Rsh = 38666358

Voltage in volts

(a)

150

100

50

Pow

er in

wat

ts

00 10 20 30 40

1501498149614941492

342 35 358

00008000060000400002

043498 43503 43508 43513

Ao = 196721

A = 2007 Rsh = 1001381 A = 2007 Rsh = 786056

A = 2007 Rsh = 1379317A = 2007 Rsh = 2215812

Voltage in volts

(b)


60599598597596595594

00008000060000400002

021099 21103 21107

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

168 17 172 174 176

Ao = 170418

A = 17 Rsh = 3127832 A = 17 Rsh = 2603693

A = 17 Rsh= 168173 A = 17 Rsh = 114849

Voltage in volts

(a)

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

60

598

596

594

592

00008000060000400002

0

168 17 172 174 176

21094 21098 21102 21106

Ao = 170418

A = 1737 Rsh = 10529594 A = 1737 Rsh = 73386

A = 1737 Rsh = 18664501A = 1737 Rsh = 82735534

Voltage in volts

(b)






















1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

10

8

6

4

2

00 10 20 30 40

Voltage in volts

Curr

ent i

n am

pere

s

(a)

Pow

er in

wat

ts

200

150

100

50

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

00 10 20 30 40

(b)




9 Conclusion


Data Availability




Acknowledgments


References









1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)











































































zI

zV minus

Io

ANsVt

1 +zI

zVRs1113888 1113889exp

V + IRs

ANsVt

1113888 1113889 minus1

Rsh1 +

zI

zV1113888 1113889Rs1113896 1113897

(26)


zI

zV1113890 1113891

IIsc

minus1

Rsh (27)


zI

zV1113890 1113891

VVoc

minus1Rs

(28)


zP

zV

zI

zV1113888 1113889V + I O (29)


minusImpp

Vmpp minus

Io

ANsVt

1 minusImpp

VmppRs1113888 1113889exp

Vmpp + ImppRs

ANsVt

1113888 11138891113896 1113897

minus1

Rsh1 minus

Impp

VmppRs1113888 1113889

(30)















ANsVt

1113888 11138891113888

minusVmpp + ImppRs

Rsh1113889

(33)






























ANsVt

1113888 1113889 minusV

Rshminus

IRs

Rsh1113888 1113889

(36)



1

0

022 023 024 025 026Rs (Ω)

R sh (

Ω)

A = 1792 (BP3235T)

middot105

(a)

6

4

2

R sh (

Ω)

Rs (Ω)

0

minus2

minus402 022 023

A = 1809 (KC200GT)

middot104

02

(b)

R sh (

Ω)

Rs (Ω)

2

0

minus2

minus4

minus6

03 031 032 033 034 035

A = 196 (BPSX150)

middot105

(c)

R sh (

Ω)

Rs (Ω)

4

2

0


middot105

A = 1702 (MSX60)

(d)





Start

DatasheetIsc Impp

Vmpp Voc

Ao equation (12)

Ioopt equation (14)


No

Yes


Pmpp equation (33)

Select A lt A0


Io equation (14)

Iph equation (9)

Stop





















Ao =1801956

A = 1792 Rsh = 10663747A = 1792 Rsh = 11460561

A = 1792 Rsh = 9970158A = 1792 Rsh = 9360957

2351

235

2349

2348299 301 303 305 307

00008000060000400002

037194 37196 37198 372

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

(a)

Ao = 1801956

A = 18626 Rsh = 10663A = 18626 Rsh = 99272

A = 18626 Rsh = 115168A = 18626 Rsh = 125195

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

2355235

2345234

2335233

2325232

296

00008000060000400002

037198

30 304 308

372

(b)


Ao = 181928

A = 1809 Rsh = 11161044 A = 1809 Rsh = 12196776

A = 1809 Rsh = 10286957A = 1809 Rsh = 9539412

200252002

200152001

20005200

264 266 268 27

00008000060000400002

032897 32899 32901

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

(a)

Ao = 181928

A = 1882 Rsh = 64429A = 1882 Rsh = 61269

A = 1882 Rsh = 67935A = 1882 Rsh = 71845

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

2001995

1991985

1981975

197256 264 272

00008000060000400002

032891 32895 32899

(b)






15015

1501

15005

00008000060000400002

043498 43502 43506 4351

Pow

er in

wat

ts

150

100

50

00 10 20 30 40

3462 3482 3502

Ao = 196721

A = 196 Rsh = 45557158 A = 196 Rsh = 50010224

A = 196 Rsh = 41830674A = 196 Rsh = 38666358

Voltage in volts

(a)

150

100

50

Pow

er in

wat

ts

00 10 20 30 40

1501498149614941492

342 35 358

00008000060000400002

043498 43503 43508 43513

Ao = 196721

A = 2007 Rsh = 1001381 A = 2007 Rsh = 786056

A = 2007 Rsh = 1379317A = 2007 Rsh = 2215812

Voltage in volts

(b)


60599598597596595594

00008000060000400002

021099 21103 21107

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

168 17 172 174 176

Ao = 170418

A = 17 Rsh = 3127832 A = 17 Rsh = 2603693

A = 17 Rsh= 168173 A = 17 Rsh = 114849

Voltage in volts

(a)

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

60

598

596

594

592

00008000060000400002

0

168 17 172 174 176

21094 21098 21102 21106

Ao = 170418

A = 1737 Rsh = 10529594 A = 1737 Rsh = 73386

A = 1737 Rsh = 18664501A = 1737 Rsh = 82735534

Voltage in volts

(b)






















1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

10

8

6

4

2

00 10 20 30 40

Voltage in volts

Curr

ent i

n am

pere

s

(a)

Pow

er in

wat

ts

200

150

100

50

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

00 10 20 30 40

(b)




9 Conclusion


Data Availability




Acknowledgments


References









1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)











































































ANsVt

1113888 11138891113888

minusVmpp + ImppRs

Rsh1113889

(33)






























ANsVt

1113888 1113889 minusV

Rshminus

IRs

Rsh1113888 1113889

(36)



1

0

022 023 024 025 026Rs (Ω)

R sh (

Ω)

A = 1792 (BP3235T)

middot105

(a)

6

4

2

R sh (

Ω)

Rs (Ω)

0

minus2

minus402 022 023

A = 1809 (KC200GT)

middot104

02

(b)

R sh (

Ω)

Rs (Ω)

2

0

minus2

minus4

minus6

03 031 032 033 034 035

A = 196 (BPSX150)

middot105

(c)

R sh (

Ω)

Rs (Ω)

4

2

0


middot105

A = 1702 (MSX60)

(d)





Start

DatasheetIsc Impp

Vmpp Voc

Ao equation (12)

Ioopt equation (14)


No

Yes


Pmpp equation (33)

Select A lt A0


Io equation (14)

Iph equation (9)

Stop





















Ao =1801956

A = 1792 Rsh = 10663747A = 1792 Rsh = 11460561

A = 1792 Rsh = 9970158A = 1792 Rsh = 9360957

2351

235

2349

2348299 301 303 305 307

00008000060000400002

037194 37196 37198 372

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

(a)

Ao = 1801956

A = 18626 Rsh = 10663A = 18626 Rsh = 99272

A = 18626 Rsh = 115168A = 18626 Rsh = 125195

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

2355235

2345234

2335233

2325232

296

00008000060000400002

037198

30 304 308

372

(b)


Ao = 181928

A = 1809 Rsh = 11161044 A = 1809 Rsh = 12196776

A = 1809 Rsh = 10286957A = 1809 Rsh = 9539412

200252002

200152001

20005200

264 266 268 27

00008000060000400002

032897 32899 32901

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

(a)

Ao = 181928

A = 1882 Rsh = 64429A = 1882 Rsh = 61269

A = 1882 Rsh = 67935A = 1882 Rsh = 71845

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

2001995

1991985

1981975

197256 264 272

00008000060000400002

032891 32895 32899

(b)






15015

1501

15005

00008000060000400002

043498 43502 43506 4351

Pow

er in

wat

ts

150

100

50

00 10 20 30 40

3462 3482 3502

Ao = 196721

A = 196 Rsh = 45557158 A = 196 Rsh = 50010224

A = 196 Rsh = 41830674A = 196 Rsh = 38666358

Voltage in volts

(a)

150

100

50

Pow

er in

wat

ts

00 10 20 30 40

1501498149614941492

342 35 358

00008000060000400002

043498 43503 43508 43513

Ao = 196721

A = 2007 Rsh = 1001381 A = 2007 Rsh = 786056

A = 2007 Rsh = 1379317A = 2007 Rsh = 2215812

Voltage in volts

(b)


60599598597596595594

00008000060000400002

021099 21103 21107

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

168 17 172 174 176

Ao = 170418

A = 17 Rsh = 3127832 A = 17 Rsh = 2603693

A = 17 Rsh= 168173 A = 17 Rsh = 114849

Voltage in volts

(a)

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

60

598

596

594

592

00008000060000400002

0

168 17 172 174 176

21094 21098 21102 21106

Ao = 170418

A = 1737 Rsh = 10529594 A = 1737 Rsh = 73386

A = 1737 Rsh = 18664501A = 1737 Rsh = 82735534

Voltage in volts

(b)






















1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

10

8

6

4

2

00 10 20 30 40

Voltage in volts

Curr

ent i

n am

pere

s

(a)

Pow

er in

wat

ts

200

150

100

50

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

00 10 20 30 40

(b)




9 Conclusion


Data Availability




Acknowledgments


References









1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)

















































































ANsVt

1113888 1113889 minusV

Rshminus

IRs

Rsh1113888 1113889

(36)



1

0

022 023 024 025 026Rs (Ω)

R sh (

Ω)

A = 1792 (BP3235T)

middot105

(a)

6

4

2

R sh (

Ω)

Rs (Ω)

0

minus2

minus402 022 023

A = 1809 (KC200GT)

middot104

02

(b)

R sh (

Ω)

Rs (Ω)

2

0

minus2

minus4

minus6

03 031 032 033 034 035

A = 196 (BPSX150)

middot105

(c)

R sh (

Ω)

Rs (Ω)

4

2

0


middot105

A = 1702 (MSX60)

(d)





Start

DatasheetIsc Impp

Vmpp Voc

Ao equation (12)

Ioopt equation (14)


No

Yes


Pmpp equation (33)

Select A lt A0


Io equation (14)

Iph equation (9)

Stop





















Ao =1801956

A = 1792 Rsh = 10663747A = 1792 Rsh = 11460561

A = 1792 Rsh = 9970158A = 1792 Rsh = 9360957

2351

235

2349

2348299 301 303 305 307

00008000060000400002

037194 37196 37198 372

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

(a)

Ao = 1801956

A = 18626 Rsh = 10663A = 18626 Rsh = 99272

A = 18626 Rsh = 115168A = 18626 Rsh = 125195

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

2355235

2345234

2335233

2325232

296

00008000060000400002

037198

30 304 308

372

(b)


Ao = 181928

A = 1809 Rsh = 11161044 A = 1809 Rsh = 12196776

A = 1809 Rsh = 10286957A = 1809 Rsh = 9539412

200252002

200152001

20005200

264 266 268 27

00008000060000400002

032897 32899 32901

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

(a)

Ao = 181928

A = 1882 Rsh = 64429A = 1882 Rsh = 61269

A = 1882 Rsh = 67935A = 1882 Rsh = 71845

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

2001995

1991985

1981975

197256 264 272

00008000060000400002

032891 32895 32899

(b)






15015

1501

15005

00008000060000400002

043498 43502 43506 4351

Pow

er in

wat

ts

150

100

50

00 10 20 30 40

3462 3482 3502

Ao = 196721

A = 196 Rsh = 45557158 A = 196 Rsh = 50010224

A = 196 Rsh = 41830674A = 196 Rsh = 38666358

Voltage in volts

(a)

150

100

50

Pow

er in

wat

ts

00 10 20 30 40

1501498149614941492

342 35 358

00008000060000400002

043498 43503 43508 43513

Ao = 196721

A = 2007 Rsh = 1001381 A = 2007 Rsh = 786056

A = 2007 Rsh = 1379317A = 2007 Rsh = 2215812

Voltage in volts

(b)


60599598597596595594

00008000060000400002

021099 21103 21107

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

168 17 172 174 176

Ao = 170418

A = 17 Rsh = 3127832 A = 17 Rsh = 2603693

A = 17 Rsh= 168173 A = 17 Rsh = 114849

Voltage in volts

(a)

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

60

598

596

594

592

00008000060000400002

0

168 17 172 174 176

21094 21098 21102 21106

Ao = 170418

A = 1737 Rsh = 10529594 A = 1737 Rsh = 73386

A = 1737 Rsh = 18664501A = 1737 Rsh = 82735534

Voltage in volts

(b)






















1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

10

8

6

4

2

00 10 20 30 40

Voltage in volts

Curr

ent i

n am

pere

s

(a)

Pow

er in

wat

ts

200

150

100

50

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

00 10 20 30 40

(b)




9 Conclusion


Data Availability




Acknowledgments


References









1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)












































































Start

DatasheetIsc Impp

Vmpp Voc

Ao equation (12)

Ioopt equation (14)


No

Yes


Pmpp equation (33)

Select A lt A0


Io equation (14)

Iph equation (9)

Stop





















Ao =1801956

A = 1792 Rsh = 10663747A = 1792 Rsh = 11460561

A = 1792 Rsh = 9970158A = 1792 Rsh = 9360957

2351

235

2349

2348299 301 303 305 307

00008000060000400002

037194 37196 37198 372

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

(a)

Ao = 1801956

A = 18626 Rsh = 10663A = 18626 Rsh = 99272

A = 18626 Rsh = 115168A = 18626 Rsh = 125195

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

2355235

2345234

2335233

2325232

296

00008000060000400002

037198

30 304 308

372

(b)


Ao = 181928

A = 1809 Rsh = 11161044 A = 1809 Rsh = 12196776

A = 1809 Rsh = 10286957A = 1809 Rsh = 9539412

200252002

200152001

20005200

264 266 268 27

00008000060000400002

032897 32899 32901

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

(a)

Ao = 181928

A = 1882 Rsh = 64429A = 1882 Rsh = 61269

A = 1882 Rsh = 67935A = 1882 Rsh = 71845

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

2001995

1991985

1981975

197256 264 272

00008000060000400002

032891 32895 32899

(b)






15015

1501

15005

00008000060000400002

043498 43502 43506 4351

Pow

er in

wat

ts

150

100

50

00 10 20 30 40

3462 3482 3502

Ao = 196721

A = 196 Rsh = 45557158 A = 196 Rsh = 50010224

A = 196 Rsh = 41830674A = 196 Rsh = 38666358

Voltage in volts

(a)

150

100

50

Pow

er in

wat

ts

00 10 20 30 40

1501498149614941492

342 35 358

00008000060000400002

043498 43503 43508 43513

Ao = 196721

A = 2007 Rsh = 1001381 A = 2007 Rsh = 786056

A = 2007 Rsh = 1379317A = 2007 Rsh = 2215812

Voltage in volts

(b)


60599598597596595594

00008000060000400002

021099 21103 21107

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

168 17 172 174 176

Ao = 170418

A = 17 Rsh = 3127832 A = 17 Rsh = 2603693

A = 17 Rsh= 168173 A = 17 Rsh = 114849

Voltage in volts

(a)

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

60

598

596

594

592

00008000060000400002

0

168 17 172 174 176

21094 21098 21102 21106

Ao = 170418

A = 1737 Rsh = 10529594 A = 1737 Rsh = 73386

A = 1737 Rsh = 18664501A = 1737 Rsh = 82735534

Voltage in volts

(b)






















1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

10

8

6

4

2

00 10 20 30 40

Voltage in volts

Curr

ent i

n am

pere

s

(a)

Pow

er in

wat

ts

200

150

100

50

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

00 10 20 30 40

(b)




9 Conclusion


Data Availability




Acknowledgments


References









1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)

























































































Ao =1801956

A = 1792 Rsh = 10663747A = 1792 Rsh = 11460561

A = 1792 Rsh = 9970158A = 1792 Rsh = 9360957

2351

235

2349

2348299 301 303 305 307

00008000060000400002

037194 37196 37198 372

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

(a)

Ao = 1801956

A = 18626 Rsh = 10663A = 18626 Rsh = 99272

A = 18626 Rsh = 115168A = 18626 Rsh = 125195

Pow

er in

wat

ts

250

200

150

100

50

00 10 20 30

Voltage in volts

2355235

2345234

2335233

2325232

296

00008000060000400002

037198

30 304 308

372

(b)


Ao = 181928

A = 1809 Rsh = 11161044 A = 1809 Rsh = 12196776

A = 1809 Rsh = 10286957A = 1809 Rsh = 9539412

200252002

200152001

20005200

264 266 268 27

00008000060000400002

032897 32899 32901

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

(a)

Ao = 181928

A = 1882 Rsh = 64429A = 1882 Rsh = 61269

A = 1882 Rsh = 67935A = 1882 Rsh = 71845

Pow

er in

wat

ts

200

150

100

50

00 5 10 15 20 25 30

Voltage in volts

2001995

1991985

1981975

197256 264 272

00008000060000400002

032891 32895 32899

(b)






15015

1501

15005

00008000060000400002

043498 43502 43506 4351

Pow

er in

wat

ts

150

100

50

00 10 20 30 40

3462 3482 3502

Ao = 196721

A = 196 Rsh = 45557158 A = 196 Rsh = 50010224

A = 196 Rsh = 41830674A = 196 Rsh = 38666358

Voltage in volts

(a)

150

100

50

Pow

er in

wat

ts

00 10 20 30 40

1501498149614941492

342 35 358

00008000060000400002

043498 43503 43508 43513

Ao = 196721

A = 2007 Rsh = 1001381 A = 2007 Rsh = 786056

A = 2007 Rsh = 1379317A = 2007 Rsh = 2215812

Voltage in volts

(b)


60599598597596595594

00008000060000400002

021099 21103 21107

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

168 17 172 174 176

Ao = 170418

A = 17 Rsh = 3127832 A = 17 Rsh = 2603693

A = 17 Rsh= 168173 A = 17 Rsh = 114849

Voltage in volts

(a)

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

60

598

596

594

592

00008000060000400002

0

168 17 172 174 176

21094 21098 21102 21106

Ao = 170418

A = 1737 Rsh = 10529594 A = 1737 Rsh = 73386

A = 1737 Rsh = 18664501A = 1737 Rsh = 82735534

Voltage in volts

(b)






















1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

10

8

6

4

2

00 10 20 30 40

Voltage in volts

Curr

ent i

n am

pere

s

(a)

Pow

er in

wat

ts

200

150

100

50

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

00 10 20 30 40

(b)




9 Conclusion


Data Availability




Acknowledgments


References









1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)













































































15015

1501

15005

00008000060000400002

043498 43502 43506 4351

Pow

er in

wat

ts

150

100

50

00 10 20 30 40

3462 3482 3502

Ao = 196721

A = 196 Rsh = 45557158 A = 196 Rsh = 50010224

A = 196 Rsh = 41830674A = 196 Rsh = 38666358

Voltage in volts

(a)

150

100

50

Pow

er in

wat

ts

00 10 20 30 40

1501498149614941492

342 35 358

00008000060000400002

043498 43503 43508 43513

Ao = 196721

A = 2007 Rsh = 1001381 A = 2007 Rsh = 786056

A = 2007 Rsh = 1379317A = 2007 Rsh = 2215812

Voltage in volts

(b)


60599598597596595594

00008000060000400002

021099 21103 21107

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

168 17 172 174 176

Ao = 170418

A = 17 Rsh = 3127832 A = 17 Rsh = 2603693

A = 17 Rsh= 168173 A = 17 Rsh = 114849

Voltage in volts

(a)

Pow

er in

wat

ts

60

40

20

00 5 10 15 20

60

598

596

594

592

00008000060000400002

0

168 17 172 174 176

21094 21098 21102 21106

Ao = 170418

A = 1737 Rsh = 10529594 A = 1737 Rsh = 73386

A = 1737 Rsh = 18664501A = 1737 Rsh = 82735534

Voltage in volts

(b)






















1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

10

8

6

4

2

00 10 20 30 40

Voltage in volts

Curr

ent i

n am

pere

s

(a)

Pow

er in

wat

ts

200

150

100

50

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

00 10 20 30 40

(b)




9 Conclusion


Data Availability




Acknowledgments


References









1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)





























































































1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

10

8

6

4

2

00 10 20 30 40

Voltage in volts

Curr

ent i

n am

pere

s

(a)

Pow

er in

wat

ts

200

150

100

50

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

00 10 20 30 40

(b)




9 Conclusion


Data Availability




Acknowledgments


References









1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)











































































9 Conclusion


Data Availability




Acknowledgments


References









1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

10

8

6

4

2

00 10 20 30 40

Curr

ent i

n am

pere

s

(a)Po

wer

in w

atts

1000 Wm2

800 Wm2

600 Wm2

400 Wm2

200 Wm2

Voltage in volts

200

150

100

50

00 10 20 30 40

(b)










































































afastandaccurateanalyticalmethodforparameter … · 2020. 5. 15. · comparative study of the two...

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