Research Article A Population Classification Evolution...

Research ArticleA Population Classification Evolution Algorithm forthe Parameter Extraction of Solar Cell Models

Yiqun Zhang12 Peijie Lin12 Zhicong Chen12 and Shuying Cheng12

1College of Physics and Information Engineering and Institute of Micro-Nano Devices and Solar Cells Fuzhou UniversityFuzhou 350116 China2Jiangsu Collaborative Innovation Center of Photovoltaic Science and Engineering Changzhou 213164 China

Correspondence should be addressed to Shuying Cheng sychengfzueducn

Received 11 May 2016 Revised 21 June 2016 Accepted 22 June 2016

Academic Editor Tamer Khatib

Copyright copy 2016 Yiqun Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

To quickly and precisely extract the parameters for solar cell models inspired by simplified bird mating optimizer (SBMO) a newoptimization technology referred to as population classification evolution (PCE) is proposed PCE divides the population into twogroups elite and ordinary to reach a better compromise between exploitation and exploration For the evolution of elite individualswe adopt the idea of parthenogenesis in nature to afford a fast exploitation For the evolution of ordinary individuals we adopt aneffective differential evolution strategy and a randommovement of small probability is added to strengthen the ability to jump outof a local optimum which affords a fast exploration The proposed PCE is first estimated on 13 classic benchmark functions Theexperimental results demonstrate that PCE yields the best results on 11 functions by comparing it with six evolutional algorithmsThen PCE is applied to extract the parameters for solar cell models that is the single diode and the double diodeThe experimentalanalyses demonstrate that the proposed PCE is superior when comparing it with other optimization algorithms for parameteridentification Moreover PCE is tested using three different sources of data with good accuracy

1 Introduction

The rising cost of fossil fuels atmospheric pollution andglobal energy shortage have prompted the development anduse of renewable energy [1 2] PV (photovoltaic) systemssuch as solar cells have recently received significant attentionwith characteristics of renewability clean-type convenienceand low noise technique [1 3 4] PV systems usually operatein outdoor environment and their PV arrays are prone todeteriorate andmay even undergo various faults due to harshweather condition and aging which greatly affect the solarenergy utilization efficiency and even cause safety issuesTherefore in order to optimize PV systems it is crucialto evaluate the actual behavior of PV arrays in operationthrough accurate modeling based on experimental dataNumerous mathematical models have been proposed toclarify the characteristic of a PV system under different oper-ating conditions However in practical terms two solar cellmodels are the most frequently used the single and doublediode models [3 5] Although the double diode model canachieve more precise results than the single diode model the

ability to achieve an adequate concession between simplifiedand precise results in the single diode model is a morepreferable option [6] Accurate parameters of a mathematicalmodel is crucial to simulate estimate and optimize solarcell systemsTherefore it is necessary to consider parametersidentification with a feasible optimization approach [7]

The techniques utilized to identify the parameters ofPV models in the literature can be divided in two groupsdeterministic techniques and heuristic techniques [2] Deter-ministic techniques that is least squares [8] Lambert 119882functions [9] and iterative curve fitting [10] force somemodel constraints like convexity and differentiability whichmust be exactly used Thus these deterministic methodsdrastically depend on initialization and can also be easyto fall into a local optimum [2] Recently based on thetheory of reproduction and evolution of different biologicalpopulations many heuristic technologies have been pro-posed to deal with the parameter estimation issues of solarcells such as particle swarm optimization (PSO) [11 12]genetic algorithms (GA) [13ndash15] differential evolution (DE)[4 16ndash18] pattern search (PS) [19] simulated annealing

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2016 Article ID 2174573 16 pageshttpdxdoiorg10115520162174573

2 International Journal of Photoenergy

(SA) [20] harmony search (HS) [21] and artificial beeswarmoptimization (ABSO) [3] Althoughheuristicmethodspresent a higher probability of obtaining a global solutionin comparison with deterministic ones they have impor-tant limits [13] In case of GA and PSO they maintaina trend that concentrates toward local optima since theirelitist mechanism forces premature convergence [2] Suchbehavior becomes worse when the optimization algorithmfaces multimodal functions On the other hand due to thefact that SA and HS are single-searcher algorithms theirperformance is sensitive to the starting point of the searchhaving a lower probability to localize the global minimum inmultimodal problems than population algorithms such asGAand PSO [2] Therefore GA PSO SA and HS present badperformance when they are applied to multimodal and noisyobjective functionsTherefore there is the possibility to yieldbetter performance with more capable algorithms

In biological populations birds have around 10000 livingspecies which are the most species of tetrapod vertebrates[22] In birds the courtship behavior is innate During themating season a bird tries to find spouse(s) with goodgenes for raising a brood that can survive for a longertime which is similar to that of a search for the optimalsolution To develop a more capable heuristic optimizationalgorithm Askarzadeh and Rezazadeh [22] propose a birdmating optimizer (BMO) In BMO algorithm there are fourbreeding strategies monogamy polygamy polyandry andpromiscuity Experimental results indicate the superior per-formance of BMOHowever there are twomain drawbacks inBMO (1) numerous types of birds and (2) numerous numbersof tunable parameters To overcome these disadvantagesAskarzadeh and dos Santos Coelho [6] propose a simplifiedBMOalgorithm (SBMO) In SBMOalgorithm all birds in thepopulation are ranked according to their objective functionvalues such that the bird with the best objective functionvalue is ranked first Then these birds are divided into threetypes for breeding based on their rank These three breedingstrategies are parthenogenesis monogamy and polygamyrespectivelyThe SBMOalgorithm reduces the computationalcomplexity and yields good performance on PV modules

However SBMO has a disadvantage of slow convergenceFirstly the disturbance coefficient in Type 1 (parthenogene-sis) is very small which means the exploitation space is verylimitedThus it is not easy to find a better solution Secondlyin Type 2 (monogamy) a female mating bird is randomlyselected from Type 1 Therefore the selected female matingbird may be not the optimal The convergence speed of Type2 is limitedThirdly Type 3 (polygamy) plays a similar role toType 2 which means SBMO has no effective strategy to avoidtrapping in a local optimum

The parameter estimation method should be reliableaccurate and fast for a range of different types of cellsestimation To further improve the efficiency and reliabilityof parameters identification of photovoltaic models herewe propose a new optimization technique referred to aspopulation classification evolution (PCE) to overcome theslow convergence of SBMO In PCE we divide the populationinto two categories that is elite and ordinaryThe elite are theparthenogenesis corresponding to the neighborhood-based

search known as the local search strategy to afford exploita-tion In the elite evolution strategy we magnify the exploita-tion space to accelerate convergence In the ordinary weemploy DE mutation ldquoDEbest1rdquo operator to guide an indi-vidual to be close to the global optimum Then a crossoveroperator following mutation is employed to increase thediversity of the population In addition we add a randommovement of small probability for the evolution of ordinaryindividuals to further increase the diversity of the populationand overcome the premature convergence Obviously theordinary evolution is corresponding to the global search toafford exploration To estimate the performance of PCE it isfirst compared with five well-known evolutional algorithms(EAs) SBMO cuckoo search (CS) artificial bee colony(ABC) improved adaptive differential evolution (IADE) andself-adapting control parameters in differential evolution(called jDE) on 13 classic benchmark functions And a start-of-the-art evolutional algorithm called generalized oppo-sitional teaching learning based optimization (GOTLBO)is also adopted to compare with PCE PCE has a fasterconvergence speed and higher accuracy than these six EAs onmost benchmark functions through emulation In additionPCE is applied to extract the parameters of both the singleand double diode model The emulation data indicate thatthe proposed PCE is superior when comparing it with otherparameter extractionmethodsMoreover PCE is tested usingthree different sources of data with good accuracy

Organization of the remainder of the paper is as followsFor Section 2 solar cell identification is depicted In Section 3the SBMO algorithm is depicted Section 4 specifies theimplementation of our proposed PCE In Section 5 PCEis estimated on 13 classic benchmark functions Then inSection 6 PCE is applied to extract the parameters of PVmodels The conclusions are depicted in Section 7

2 Problem Statement

21 Solar Cell Models An accurate mathematical modeldescribing the electrical characteristics of solar cells is neededin advance Some equivalent circuit models are used tosimulate the current-voltage (119868-119881) behavior for solar cells butonly two models are employed in practice the double diodemodel and the single diode model In this subsection thesemodels are tersely discussed

211 Double Diode Model Under the illumination the idealsolar cell model is a photogenerated current source that isshunted by a rectifier diode [3 13 21] Figure 1 shows theequivalent circuit of the double diode model According toKirchhoff rsquos law of electric current and the Shockley equationthe 119868-119881 relationship is formulated as

119868119905= 119868ph minus 119868d1 minus 119868d2 minus 119868sh

= 119868ph minus 119868sd1 [exp(119902 (119881119905+ 119877119904119868119905)

1198991119896119879

) minus 1]

minus 119868sd2 [exp(119902 (119881119905+ 119877119904119868119905)

1198992119896119879

) minus 1] minus119881119905+ 119877119904119868119905

119877sh

(1)

International Journal of Photoenergy 3

where 119868119905is the terminal current 119868ph denotes the photogen-

erated current 119868d1 and 119868d2 are the first and second diodecurrents and 119868sh is the shunt resistor current 119868sd1 and 119868sd2denote the diffusion and saturation currents respectively 119881

119905

denotes the terminal voltage119877119904and119877sh denote the series and

shunt resistances respectively q is the electronic charge 119879(K) denotes the cell temperature 119896 is the Boltzmann constant1198991and 119899

2denote the diffusion and recombination diode

ideality factors respectivelyThis double diode model includes seven unknown

parameters (119868ph 119868sd1 119868sd2 119877119904 119877sh 1198991 and 1198992) to be estimatedfrom (1) To reflect the solar cell performance as well as that ofthe real system it is crucial to acquire an accurate parametersrsquoidentification

212 Single Diode Model Figure 2 shows the single diodemodel that is widely employed for modeling solar cells dueto its simplicity It is calculated as follows

119868119905= 119868ph minus 119868sd [exp(

119902 (119881119905+ 119877119904119868119905)

119899119896119879) minus 1] minus

119881119905+ 119877119904119868119905

119877sh (2)

where 119868sd is reverse saturation current of diode and 119899 is thediode ideality factor

For this model five parameters (119868ph 119868sd 119877119904 119877sh and 119899)would be estimated in (2)

22 Objective Function The unknown parameters areobtained from the I-V data with an optimization algorithmIn this optimization method each solution is denoted by avector 119909 where 119909 = [119868ph 119868sd1 119868sd2 119877119904 119877sh 1198991 1198992] for thedouble diode model and 119909 = [119868ph 119868sd 119877119904 119877sh 119899] for thesingle diode model For expressing the objective function tobe optimized (1) and (2) are altered as follows

119891 (119881119905 119868119905 119909) = 119868

119905minus 119868ph

+ 119868sd1 [exp(119902 (119881119905+ 119877119904119868119905)

1198991119896119879

) minus 1]

+ 119868sd2 [exp(119902 (119881119905+ 119877119904119868119905)

1198992119896119879

) minus 1]

+119881119905+ 119877119904119868119905

119877sh

119891 (119881119905 119868119905 119909) = 119868

119905minus 119868ph + 119868sd [exp(

119902 (119881119905+ 119877119904119868119905)

119899119896119879) minus 1]

+119881119905+ 119877119904119868119905

119877sh

(3)

During the optimization process we adopt the RMSE asthe objective function [1 3] to reflect the difference betweenthe real data and simulated data which is defined by

119865 (119909) = radic1

119873

119873

sum

119894=1

(119891119894(119881119905 119868119905 119909))2

(4)

where N is the number of the simulated dataFor this optimization case the objective function 119865(119909) in

(4) would be minimized

+Vt

It

Rs

Id1 Id2

RshIph

Ish

Figure 1 Single diode model

+Vt

It

Rs

Id

RshIph

Ish

Figure 2 Double diode model

3 The Simplified Bird Mating Optimizer

In SBMO [6] the birds are ranked according to their objectivefunction values such that the bird with the best objectivefunction value is ranked first Then these birds are dividedinto three types for breeding based on their rank

Type 1 The birds of this type are called females that havebetter objective function values than others The number ofthese birds (119873

1) is determined by

1198731= round(119873119875

10) (5)

For breeding female birds employ the following expres-sion based on the idea of parthenogenesis [6 23ndash25]

if rand gt rand

V119894= 119909119894+rand sdot (rand minus rand)

10sdot 119909119894

else

V119894= 119909119894

end

(6)

where119909119894is the target vector related to the bird V

119894is themutant

vector related to the birdrsquos brood and rand is a randomnumber within [0 1] and it is worthwhilementioning that therandom numbers are different


Type 2 The birds of this type are referred to as male birdsThe number of these birds (119873

2) is determined by

1198732= round(7 sdot 119873119875

10) (7)

For breedingmale birds are interested inmatingwith onefemale bird

V119894= 119909119894+ rand sdot (119909

119904minus 119909119894) (8)

where119909119904is a target vector that is randomly selected fromType

1 for the interesting mate of the male bird


3) is determined by

1198733= 119873119875 minus 119873

1minus 1198732 (9)

For breedingmale birds are interested inmatingwith twofemale birds

V119894= 119909119894+ rand sdot (119909

1199041minus 119909119894) + rand sdot (119909

1199042minus 119909119894) (10)

where 1199091199041

and 1199091199042

are two target vectors which are randomlyselected fromType 1 for the interestingmates of themale bird

4 The Proposed Population ClassificationEvolution Algorithm

In PCE all individuals in the population are ranked accordingto their objective function valuesThe population are dividedinto two types of evolution based on their rank as follows

Type 1 The individuals of this type in the population arereferred to as elite individuals that have better objectivefunction values than others The number of these elites (119873

1)

is determined by (5)

We employ the following expression for the evolution ofelite individuals

V119894= 119909119894+ (rand minus rand) sdot 119909

119894 (11)

It is worthwhile mentioning that we modify (6) and thedisturbance coefficient from (11) is larger than that of (6)which can expand the exploitation space At the early stageof the optimization process the larger search step wouldbe faster to search a better solution which can accelerateconvergence

Type 2 The individuals of this type are referred to asordinary individuals The number of these individuals (119873

2)

is determined by

1198732= 119873119875 minus 119873

1 (12)

The DE algorithm [26] which is primarily employed fornumerical optimization problems is a parallel direct searchtechnology that uses NP D-dimensional vectors In ordinaryindividuals we employ the differential evolution ldquoDEbest1rdquomutation operator [27] that uses the information of the bestindividual in the population to guide an individual to beclose to the global optimum which helps to accelerate theconvergence speed The ldquoDEbest1rdquo operator is as follows

V119894= 119909best + rand sdot (119909119903

1

minus 1199091199032

) (13)

where indexes 1199031and 1199032denote mutually different integers

randomly generated from the range [1 NP] 119909best is the best-so-far solution with the best fitness (ie lowest objectivefunction value for a minimization problem) in the currentpopulation

Although the ldquoDEbest1rdquo operator can accelerate theconvergence speed another aspect should be consideredPlaying a guiding role only through 119909best makes it easierto trap in a local optimum Thus a crossover operatorfollowing mutation is employed to increase the diversityof the population The crossover operator is employed togenerate the trial vector 119906

119894between 119909

119894and V119894

119906119894119895=

V119894119895 if rand le Cr or 119895 == 119903119899 (119894)

119909119894119895 otherwise

(14)

where Cr isin [0 1] denotes the crossover rate which is set fromthe user rand isin [0 1] denotes a uniform random numberand 119903119899(119894) isin (1 2 119863) denotes a randomly generated indexthat insures that 119906

119894obtains at least one ingredient from V

119894

In addition because Type 3 plays a similar role to Type2 in SBMO we remove Type 3 then a random movementof small probability is added to further increase populationdiversity and strengthen the ability of jumping out of a localoptimum for the ordinary evolution [28] The expression ofthe random movement is defined as follows

for 119895 = 1 119863

V119894119895= 119886119895+ rand sdot (119887

119895minus 119886119895)

end

(15)

where 119886119895and 119887119895are the initial lower bound and upper bound

of the 119895th dimension of the 119894th vector respectively


Step 1 (Initialization)(11) Randomly initialize the entire individuals of population 119875 = 119909

1 1199092 119909

119873119875 within the upper

bound and lower bound(12) Evaluate fitness of the population 119875 according to the objective function

Step 2 (The population classification evolution)Rank the119873119875 individuals according to their fitness then determine the number of each individualtype and classify them and obtain the best individualfor 119894 = 1 119873119875 (all119873119875 individuals in the population)if individual 119894th belongs to Type 1

(elite individuals evolution)Produce the elite individual evolution with (11)

else(ordinary individuals evolution)Produce the ordinary individual evolution with (16)

end ifEvaluate whether the evolutionary individual can replace the previous individual using greedyselection scheme based on the survival of the fittest idea in the nature

end forStep 3 If the termination criteria is satisfied stop otherwise go to Step 2

Algorithm 1 Pseudocode of the proposed algorithm

Therefore using (13) (14) and (15) the method ofordinary individuals evolution can be defined as follows

if rand lt Dep

V119894= 119909best + rand sdot (119909119903

1

minus 1199091199032

)

for 119895 = 1 119863

if rand le Cr or 119895 == 119903119899 (119894)

V119894119895= V119894119895

else

V119894119895= 119909119894119895

end if

end for

else

for 119895 = 1 119863

V119894119895= 119886119895+ rand sdot (119887

119895minus 119886119895)

end for

end if

(16)

where Dep isin [0 1] denotes the probability of differentialevolution in ordinary individuals Here Dep is set to 09which means the probability of the randommovement is 01

An optimization algorithm should be able to satisfactorilycompromise between exploitation and exploration to effec-tively probe the search space [6] In the proposed populationclassification evolution approach the individuals in Type 1are the neighborhood-based search known as the local search

strategy to afford exploitation Conversely the other individ-uals (Type 2) of the populationmove through the search spacewith respect tomemory and randomness known as the globalsearch to afford exploration The random movement in Type2 is utilized to generate a new individual which may explorea better solution to overcome the premature convergence

The pseudocode of the proposed PCE algorithm is sum-marized in Algorithm 1

5 Simulation Experiments on BenchmarkFunctions

51 Experimental Setup To evaluate the optimal perfor-mance of PCE 13 widely used standard benchmark functionsare applied from [1 29] The search space space dimensionand optimal value of the 13 functions are listed in Table 11198911ndash1198917belong to unimodal functions and 119891

8ndash11989113

belong tomultimodal functions

The proposed PCE algorithm is compared with six EAsnamely SBMO [6] CS [30] ABC [31] IADE [17] jDE [29]andGOTLBO [1] It is worthwhilementioning that GOTLBO[1] recently proposed by Brest et al is efficiently utilizedto identify the parameters for PV models Table 2 lists theconfiguration values of tunable parameters of the mentionedalgorithms with reference to the relevant literature

To simulate the optimization performance among thedifferent algorithms the performance criteria are employedas follows [1]

(i) ANFES ANFES represents the average number ofobjective function evaluations It is employed to storethe number of objective function evaluations when asolution x satisfying119865(119909)minus119865(119909lowast) le 120576 is found for eachrun where 119865(119909lowast) is the best value and 120576 is a rathersmall positive constant as the required accuracy for


Table 1 Benchmark functions

Benchmark function Dimension Domain Optimum

1198911=

119863

sum

119894=1

1199092

11989430 [minus100 100]

119863 0

1198912=

119863

sum

119894=1

10038161003816100381610038161199091198941003816100381610038161003816 +

119863

prod

119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [minus10 10]

119863 0

1198913=

119863

sum

119894=1

(

119894

sum

119895=1

119909119895)

2

30 [minus100 100]119863 0

1198914= max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119863 30 [minus100 100]

119863 0

1198915=

119863minus1

sum

119894=1

[100 (119909119894+1minus 1199092

119894)2

+ (1 minus 119909119894)2

] 30 [minus30 30]119863 0

1198916=

119863

sum

119894=1

[1003816100381610038161003816119909119894 + 05

1003816100381610038161003816]2 30 [minus100 100]

119863 0

1198917=

119863

sum

119894=1

1198941199094

119894+ rand(0 1) 30 [minus128 128]

119863 0

1198918= minus

119863

sum

119894=1

(119909119894sin(radic1003816100381610038161003816119909119894

1003816100381610038161003816)) 30 [minus500 500]119863

minus12569487

1198919=

119863

sum

119894=1

(1199092

119894minus 10 cos (2120587119909

119894) + 10) 30 [minus512 512]

119863 0

11989110= minus20 exp(minus02 times radic 1

119863

119863

sum

119894=1

1199092

119894) minus exp( 1

119863

119863

sum

119894=1

cos (2120587119909119894)) + 20 + 119890 30 [minus32 32]

119863 0

11989111=

1

4000

119863

sum

119894=1

1199092

119894minus

119863

prod

119894=1

cos(119909119894

radic119894) + 1 30 [minus600 600]

119863 0

11989112=120587

11986310 sin2 (120587119910

1) +

119863minus1

sum

119894=1

(119910119894minus 1)2

[1 + 10 sin2 (120587119910119894+1)] + (119910

119863minus 1)2

+

119863

sum

119894=1

119906 (119909119894 10 100 4)

119910119894= 1 +

119909119894+ 1

4

119906 (119909119894 119886 119896 119898) =

119896 (119909119894minus 119886)119898

119909119894gt 119886

0 minus119886 lt 119909119894lt 119886

119896 (minus119909119894minus 119886)119898

119909119894lt minus119886

30 [minus50 50]119863 0

11989113= 01sin2 (3120587119909

1) +

119863minus1

sum

119894=1

(119909119894minus 1)2

[1 + sin2 (3120587119909119894+1)] + (119909

119863minus 1)2

+

119863

sum

119894=1

119906 (119909119894 5 100 4) 30 [minus50 50]

119863 0

Table 2 Parameter configuration of seven EAs

Algorithm ParametersSBMO 119873119875 = 30

CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 100 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 50 119869119903 = 1PCE 119873119875 = 100 Dep = 09 Cr = 015

different issues ANFES can evaluate the convergencespeed for an optimization technology

(ii) SR (Successful Rate) SR represents the number ofsuccessful runs among all runs The successful runsignifies that the algorithm can achieve119865(119909)minus119865(119909lowast) le

120576 before the max number of objective function eval-uations (MaxNFES) condition terminates the opti-mization process

Here the results are obtained in 50 independent runsto ensure a fair comparison for all involved algorithms Forfunctions 119891

1(119909)ndash119891

13(119909) MaxNFES = 10000D and 120576 = 10minus8

[1 32]

52 Experimental Results Table 3 demonstrates the exper-imental results of seven EAs on 13 standard benchmarkfunctions BestMeanWorst and Std signify the best objec-tive function value mean objective function value worstobjective function value and standard deviation respectivelyTable 4 shows that six EAs achieve the number of the bestperformances on 13 benchmark functions

For the unimodal functions1198911ndash1198917 PCE yields the optimal

results on all unimodal functions GOTLBO yields the


Table 3 Simulation results for 13 standard benchmark functions

Benchmark functions Methods ResultsBest Mean Worst Std

1198911

SBMO 227119864 minus 290 577119864 minus 244 233119864 minus 242 0CS 124119864 minus 57 314119864 minus 53 614119864 minus 52 995119864 minus 53

ABC 367119864 minus 16 613119864 minus 16 771119864 minus 16 938119864 minus 17

IADE 255119864 minus 149 113119864 minus 145 463119864 minus 144 653119864 minus 145

jDE 313119864 minus 63 246119864 minus 61 554119864 minus 60 796119864 minus 61

GOTLBO 0 0 0 0PCE 0 0 0 0

1198912

SBMO 390119864 minus 144 165119864 minus 126 825119864 minus 125 117119864 minus 125

CS 121119864 minus 35 595119864 minus 33 174119864 minus 31 248119864 minus 32




GOTLBO 158119864 minus 288 354119864 minus 282 689119864 minus 281 0PCE 0 0 0 0

1198913


ABC 809119864 + 02 228119864 + 03 476119864 + 03 854119864 + 02

IADE 244119864 minus 18 582119864 + 02 355119864 + 03 938119864 + 02


GOTLBO 0 980119864 minus 306 490119864 minus 304 0PCE 0 0 0 0

1198914


CS 832119864 + 00 172119864 + 01 281119864 + 01 442119864 + 00

ABC 904119864 + 00 171119864 + 01 267119864 + 01 349119864 + 00

IADE 502119864 minus 01 651119864 + 00 310119864 + 01 722119864 + 00

jDE 320119864 minus 04 467119864 minus 01 354119864 + 00 665119864 minus 01


1198915

SBMO 289119864 + 01 290119864 + 01 290119864 + 01 197119864 minus 02

CS 133119864 minus 10 467119864 + 00 679119864 + 01 993119864 + 00

ABC 308119864 minus 03 257119864 minus 01 317119864 + 00 532119864 minus 01

IADE 110119864 minus 06 196119864 + 00 125119864 + 01 263119864 + 00

jDE 792119864 minus 01 110119864 + 01 672119864 + 01 108119864 + 01

GOTLBO 604119864 + 00 925119864 + 00 145119864 + 01 176119864 + 00

PCE 939119864 minus 29 228119864 minus 26 652119864 minus 25 934119864 minus 26

1198916

SBMO 0 111119864 + 01 112119864 + 02 215119864 + 01

CS 0 814119864 minus 33 770119864 minus 32 129119864 minus 32


IADE 0 800119864 minus 01 500119864 + 00 107119864 + 00

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

1198917






GOTLBO 326119864 minus 05 916119864 minus 05 209119864 minus 04 424119864 minus 05



Table 3 Continued


1198918

SBMO minus1253938532 minus808803669 minus6499235445 930119864 + 03

CS minus1256948661 minus1204697452 minus1130610604 252119864 + 02

ABC minus1256948662 minus1256948662 minus1256948661 128119864 minus 06

IADE minus1207583083 minus1111832618 minus9598627861 553119864 + 02

jDE minus1256948662 minus1256948662 minus1256948662 735119864 minus 12

GOTLBO minus1146253150 minus934352209 minus787130159 702119864 + 02

PCE minus1256948662 minus1256948662 minus1256948662 280119864 minus 12

1198919

SBMO 106119864 + 02 158119864 + 02 200119864 + 01 208119864 + 01

CS 995119864 minus 01 792119864 + 01 199119864 + 01 416119864 + 01


IADE 190119864 + 01 371119864 + 01 744119864 + 01 104119864 + 01

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989110

SBMO 0 511119864 minus 01 800119864 + 00 204119864 + 00

CS 931119864 minus 01 189119864 + 00 393119864 + 00 660119864 minus 01


IADE 711119864 minus 15 122119864 minus 01 150119864 + 00 374119864 minus 01


GOTLBO 0 270119864 minus 15 355119864 minus 15 153119864 minus 15

PCE 0 0 0 0

11989111

SBMO 0 118119864 minus 01 103119864 + 00 324119864 minus 01



IADE 0 845119864 minus 03 586119864 minus 02 124119864 minus 03

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989112

SBMO 941119864 minus 01 939119864 + 00 192119864 + 01 522119864 + 00

CS 157119864 minus 32 228119864 minus 01 276119864 + 00 566119864 minus 01



jDE 157119864 minus 32 157119864 minus 32 157119864 minus 32 155119864 minus 29GOTLBO 209119864 minus 32 369119864 minus 31 165119864 minus 30 580119864 minus 31


11989113

SBMO 300119864 minus 02 125119864 + 01 416119864 + 01 117119864 + 01

CS 135119864 minus 32 368119864 minus 01 806119864 + 00 129119864 + 00





Italics highlight the best performance

optimal results on 2 functions jDE yields the optimal resulton 1 function The other four EAs do not obtain the optimalperformance

For the multimodal functions1198918ndash11989113 PCE obtains the

optimal result on 4 functions 1198918ndash11989111 jDE also obtains the

optimal results on 4 functions 1198919and 119891

11ndash11989113 GOTLBO

obtains the optimal results on 2 functions 1198919and 119891

11

whereas the other four EAs do not obtain the optimalperformance

In general on 13 benchmark functions PCE is superiorto the other six EAs obtaining the best performance on 11functions 119891

1ndash11989111


Table 4 The number of the optimal performances on 13 standardbenchmark functions

SBMO CS ABC IADE jDE GOTLBO PCE1198911ndash1198917

0 0 0 0 1 2 71198918ndash11989113

0 0 0 0 4 2 4Total 0 0 0 0 5 4 11

Table 5 The SR and ANFES results

SBMO CS ABC IADE jDE GOTLBO PCE

1198911

SR 100 100 100 100 100 100 100ANFES 14976 56917 15767 23718 53966 5866 2030

1198912

SR 100 100 100 100 100 100 100ANFES 20926 78857 23665 33140 72332 9418 3184

1198913

SR 100 58 0 24 60 100 100ANFES 15154 NA NA NA NA 11188 2424

1198914


1198915

SR 0 4 0 0 0 0 100ANFES NA NA NA NA NA NA 19102

1198916

SR 42 100 100 48 100 100 100ANFES NA 57883 15894 NA 20656 2446 604

1198917

SR 0 0 0 0 0 0 0ANFES NA NA NA NA NA NA NA

1198918


1198919

SR 0 0 100 0 100 100 100ANFES NA NA 40633 NA 108546 7183 2252

11989110

SR 94 0 100 90 100 100 100ANFES NA NA 27697 NA 78486 8869 3138

11989111

SR 88 68 100 48 100 100 100ANFES NA NA 43508 NA 56358 6172 2116

11989112

SR 0 64 100 72 100 100 100ANFES NA 68284 14300 NA 47606 36547 4752

11989113

SR 0 86 100 74 100 22 100ANFES NA 183838 16521 NA 52686 NA 6574

Note NA implies that 119865(119909) minus 119865(119909lowast) le 120576 is not achieved until MaxNFESItalics highlight the best performance

The SR andANFES are listed in Table 5 For the unimodalfunctions119891

1ndash1198917 PCEobtains optimal results compared to the

other six EAs for the optimal SR on 6 functions 1198911ndash1198916 For

function 1198915 only the SR of PCE can reach 100 GOTLBO

obtains the optimal SRon 5 functions1198911ndash1198914and1198916 CSABC

and jDE obtain the optimal SR on 3 functions 1198911-1198912and f6

SBMO obtains the optimal SR on 4 functions 1198911ndash1198914 IADE

obtains the optimal SR on 2 functions1198911-1198912 For the ANFES

PCE exhibits a faster convergence speed than the other sixEAs on 6 functions 119891

1ndash1198916

For themultimodal functions1198918ndash11989113 PCE ABC and jDE

yield the optimal SR on 5 functions GOTLBO obtains theoptimal SR on 4 functions For the ANFES values PCE

obtains the best results among seven EAs on 5 functionswhereas the other six EAs do not obtain the optimal ANFES

53 Discussion The common benchmark functions havebeen applied to estimate the optimization performance ofPCE compared with six representative EAs According to theexperimental results we can summarize the following

(i) PCE has a faster convergence speed than SBMO CSABC IADE jDE and GOTLBO on all unimodalfunctions Additionally PCE obtains the optimal per-formance on all unimodal functions when comparingit with these six EAs

(ii) On most multimodal functions PCE has a fasterconvergence speed and higher accuracy than SBMOCS ABC IADE jDE and GOTLBO

(iii) PCE is especially suitable to be used on unimodalfunctions

On the whole the proposed PCE algorithm has the bestperformance among all compared algorithms

6 Parameter Extraction for SolarCell Models Using PCE

The 119868-119881 characteristics of a commercial silicon solar cell(RTC France) with 57mm diameter are employed to test theperformance of PCE for parameter extraction technologyThe real data have been employed under 1 sun (1000Wm2) at33∘C [1 8] The (119868-119881) characteristics of the extracted param-eters by PCE are compared with the (119868-119881) characteristicswhich are obtained from [8]The 119868-119881data are listed inTable 6For the single and double diode models the search spaces ofeach parameter are listed in Table 7 [1 4]

61 Comparison with Other EAs In this subsection PCEis compared with six EAs for solar cell models to show itsoptimization performance

For a single diode model MaxNFES is 10000 whereasfor a double diode model MaxNFES is 20000 The constant120576 is set to be 0002 for both the single diode model and thedouble diode model [1] The configuration values of tunableparameters of the mentioned algorithms with reference tothe relevant literature are presented in Table 8 and everyalgorithm is independently run 50 times

Table 9 shows the comparative results for the single diodemodel PCE obtains best results among the best mean worstand Std RMSE values jDE obtains the best RMSE value thesame as PCE with a value of 986022119864 minus 04 For the SR valueCS jDE GOTLBO and PCE achieve a value of 100 PCEobtains best value of 1380 in terms of ANFES ObviouslyPCE has a more stable performance compared with other sixalgorithms for the single diode model based on RMSE SRand ANFES

For a single diode model the convergence graph ofdifferent EAs is plotted in Figure 3 Figure 3 shows that inthe whole stage PCE converges the fastest followed by jDEPCE is capable of successively converging toward the optimalsolutions during the whole evolutionary process


Table 6 The 119868-119881 data of the solar cell RTC France

119881119905(V) 119868

119905(A)

1 minus02057 0764

2 minus01291 0762

3 minus00588 07605

4 00057 07605

5 00646 076

6 01185 0759

7 01678 0757

8 02132 0757

9 02545 07555

10 02924 0754

11 03269 07505

12 03585 07465

13 03873 07385

14 04137 0728

15 04373 07065

16 0459 06755

17 04784 0632

18 0496 0573

19 05119 0499

20 05265 0413

21 05398 03165

22 05521 0212

23 05633 01035

24 05736 minus001

25 05833 minus0123

26 059 minus021

Table 7 The search spaces for a single diode model and doublediode model

Parameter Lower bound Upper bound119868ph (A) 0 1119868sd 119868sd1 119868sd2 (120583A) 0 1119877119904(Ω) 0 05

119877sh (Ω) 0 100119899 1198991 1198992

1 2

Table 8 Parameter settings of seven EAs


CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 20 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 20 119869119903 = 04PCE 119873119875 = 100 Dep = 09 Cr = 015

For the double diode model the comparative data areshown in Table 10 PCE obtains best results among thebest mean worst and Std RMSE values SR and ANFES

SBMOCSABCIADE

jDEGOTLBOPCE

2000 4000 6000 8000 10000 120000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)Figure 3 The convergence graph of different EAs for the singlediode model

0 05 1 15 2 2510minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

SBMOCSABCIADE

jDEGOTLBOPCE

NFES

Figure 4 The convergence graph of different EAs for the doublediode model

compared with the other six EAs which means PCE issuperior to other six algorithms

For a single diode model the convergence graph ofdifferent EAs is plotted in Figure 4 Figure 4 shows that inthe whole stage PCE converges the fastest Therefore PCEis capable of successively converging toward the optimalsolutions during the whole evolutionary process

62 Compared with the Results of the Literature In thissubsection PCE are comparedwith119877cr-IJADE [4] ABSO [3]


Table 9 Simulation results for the single diode model

Algorithm RMSE SR ANFESBest Mean Worst Std Mean Std

SBMO 103062119864 minus 03 388890119864 minus 03 474555119864 minus 02 714069119864 minus 03 44 NA NACS 102642119864 minus 03 146928119864 minus 03 194019119864 minus 03 242769119864 minus 04 100 5859 1407ABC 148749119864 minus 03 331301119864 minus 03 775872119864 minus 03 110844119864 minus 03 8 NA NAIADE 986068119864 minus 04 137137119864 minus 03 375573119864 minus 03 542916119864 minus 04 92 NA NAjDE 986022119864 minus 04 110575119864 minus 03 154390119864 minus 03 137055119864 minus 04 100 1734 822GOTLBO 986179119864 minus 04 130270119864 minus 03 198800119864 minus 03 275957119864 minus 04 100 3438 2325PCE 986022119864 minus 04 986022119864 minus 04 986022119864 minus 04 305726119864 minus 12 100 1380 661Note NA implies that 119865(119909) minus 119865(119909lowast) le 120576 is not achieved until MaxNFESItalics highlight the best performance

PCE

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

Rcr-IJADE

(a)

Rcr-IJADEPCE

02 04 06 08 1 12 14 16 18 20NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

(b)

Figure 5 The convergence graphs of different EAs for (a) the single diode model and (b) the double diode model

IGHS [21] and GOTLBO [1] in terms of the five parametersfor the single diode model or the seven parameters forthe double diode model Additionally the optimal RMSEvalue is also compared from the related literature Thesealgorithms are adopted for comparison because of their goodperformance

Table 11 records the comparative results for a single diodemodel PCE and 119877cr-IJADE achieve the optimal RMSE valuethat is 986022119864 minus 04 which is better than other comparedalgorithmsTheRMSE values fromgood to bad forGOTLBOABSO and IGHS are 987442119864 minus 04 99124119864 minus 04 and99306119864 minus 04 respectively The computational cost of anoptimization algorithm adopts the NFES to characterizationNFES in the last row of Table 11 is the number of objectivefunction evaluations for one run [1] The NFES for PCE 119877cr-IJADE and GOTLBO are set to be 10000 whereas the NFESfor ABSO and IGHS are set to be 150000

For the double diode model the comparative results arerecorded in Table 12 PCE and 119877cr-IJADE achieve the optimalRMSE value that is 98248119864 minus 04 which is better than

other compared algorithms GOTLBO obtains the secondbest RMSE value (983117119864 minus 04) which is rather close tothe RMSE value of PCE and 119877cr-IJADE The RMSE valuesfrom good to bad for ABSO and IGHS are 98344119864 minus 04 and98635119864minus04 respectivelyTheNFES for PCE119877cr-IJADE andGOTLBO are set to be 20000 whereas the NFES for ABSOand IGHS are set to be 150000

According to Tables 11 and 12 it is clear that the results ofPCE are similar to those of 119877cr-IJADETherefore the conver-gence graphs of both PCE and 119877cr-IJADE that are employedto further demonstrate the optimization performance areplotted in Figure 5 The convergence graph for the singlediode model shows that PCE has a faster convergence speedthan 119877cr-IJADE Since about 6700 NFEs the convergence ofPCE and 119877cr-IJADE is almost consistent The convergencegraph for the double diodemodel shows that in the early stagePCE has faster convergence Later the convergence speeds ofboth PCE and 119877cr-IJADE are very close and tend to be of asimilar value Therefore PCE has a faster convergence speedthan 119877cr-IJADE for both the single and double diode model


Real dataSimulated data

minus02 minus01 0 01 02 03 04 05 06minus03Voltage (V)

minus04

minus02

0

02

04

06

08

1Cu

rren

t (A

)

(a)


minus04

minus02

0

02

04

06

08

1

Curr

ent (

A)


(b)

Figure 6 Comparison results from the real data and simulated data obtained by PCE for (a) the single diode model and (b) the double diodemodel

Table 10 Simulation results for the double diode model


SBMO 111833119864 minus 03 390818119864 minus 03 160974119864 minus 02 299964119864 minus 03 22 NA NACS 105191119864 minus 03 172124119864 minus 03 267872119864 minus 03 443650119864 minus 04 74 NA NAABC 100024119864 minus 03 161831119864 minus 03 255927119864 minus 03 334299119864 minus 04 88 NA NAIADE 983214119864 minus 04 152217119864 minus 03 373289119864 minus 03 568918119864 minus 04 86 NA NAjDE 983021119864 minus 04 103218119864 minus 03 103218119864 minus 03 147210119864 minus 04 100 4390 2873GOTLBO 985986119864 minus 04 124102119864 minus 03 195115119864 minus 03 239333119864 minus 04 100 5416 3914PCE 982483119864 minus 04 986100119864 minus 04 102516119864 minus 03 599505119864 minus 06 100 1860 1105Note NA implies that 119865(119909) minus 119865(119909lowast) le 120576 is not achieved until MaxNFESItalics highlight the best performance

Figure 6 shows the 119868-119881 behaviors obtained by PCE alongwith the real data for the single diode model and doublediode model The results explicitly manifest the simulateddata obtained by PCE as being highly consistent with the realdata which indicates that the identified parameters with PCEare rather precise

63 Results for PCE Tested with an Experimental Datafrom the Manufacturerrsquos Data Sheet Here the proposedPCE technique is employed to extract the optimal param-eters of the single diode model for three solar modulesof different types (monocrystalline (SM55) [33] thin-film(ST40) [34] and multicrystalline (KC200GT) [35]) The(119868-119881) characteristics of the extracted parameters by PCEare compared with the (119868-119881) characteristics which areobtained from the manufacturerrsquos data sheets for the samemodules and at the same environmental conditions Thereal data was collected at five different irradiance levels ofmainly 1000Wm2 800Wm2 600Wm2 400Wm2 and

200Wm2 with constant temperature and at three differentlevels of temperatures with constant irradiance

The optimal parameters are extracted and illustrated inTables 13ndash15 of the single diode model for the three typesof the solar modules at different temperatures MoreoverTable 16 is provided for the optimal extracted parametersat different levels of irradiance The (119868-119881) characteristics areplotted for the three solar modules at different temperaturesas shown in Figures 7ndash9 and at different irradiance levels asshown in Figures 10ndash12

It can be observed that the estimated optimal parametersby PCE technique indicate a more accurate (119868-119881) curvesover the entire ranges of the real data set with very lowRMSE at all irradiance levels and temperature values undertest This also shows the good performance of the proposedPCE technique Moreover the new PCE technique achievesaccurate extraction of the solar modules parameters at lowirradiance which is very crucial when themodule is subjectedto certain mismatch conditions such as partial shading


Table 11 Data comparison of the single diode model from the related literature

Algorithm IGHS ABSO 119877cr-IJADE GOTLBO PCE119868ph (A) 07608 07608 0760776 0760789 0760776119868sd (120583A) 03435 0360623 0323921 0324506 0323021119877119904(Ω) 003659 003659 0036377 0036358 0036377

119877sh (Ω) 532845 522903 53718526 53631998 53718525n 14874 147878 1481184 1481538 1481074RMSE 99306119864 minus 04 99124119864 minus 04 986022119864 minus 04 987442119864 minus 04 986022119864 minus 04NFES 150000 150000 10000 10000 10000Italics highlight the best performance

Table 12 Data comparison of the double diode model from the related literature

Algorithm IGHS ABSO 119877cr-IJADE GOTLBO PCE119868ph (A) 07608 076077 0760781 0760810 0760781119868sd1 (120583A) 09731 026713 0225974 0166249 0226015119877119904(Ω) 00369 003657 003674 0036952 003674

119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992

14281 198152 2 1865679 2RMSE 98635119864 minus 04 98344119864 minus 04 98248119864 minus 04 983117119864 minus 04 98248119864 minus 04NFES 150000 150000 20000 20000 20000Italics highlight the best performance

minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C

Figure 7 Comparison between real data and the simulated data byPCE for monocrystalline SM55 at different temperatures

7 Conclusions

In this paper inspired by the mating strategies we develop anovel optimization method referred to as PCE to overcomethe slow convergence of SBMO In PCE there are threeadjustable parameters119873119875 (all individuals in the population)Dep (the differential evolution probability) and Cr (the

minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C


Figure 8 Comparison between real data and the simulated data byPCE for thin-film ST40 at different temperatures

crossover rate) In this study the parameters are tuned to119873119875 = 100 Dep = 09 and Cr = 015

To verify the optimization performance of PCE wecompare it with six EAs that is SBMO CS ABC IADEjDE and GOTLBO PCE is initially estimated on 13 classicbenchmark functions The simulated data indicate that PCE


5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C


Figure 9 Comparison between real data and the simulated data byPCE for multicrystalline KC200GT at different temperatures

5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C


Figure 10 Comparison between real data and the simulated data byPCE for monocrystalline SM55 at different irradiances

has a faster convergence speed and higher accuracy and it hasthe best results on 11 functions among these six algorithms

Then PCE is applied to accurately estimate the parameterof solar cell models like the single and double diode modelPCE performs the best performance among the six algo-rithms For the single diodemodel PCE yields the best RMSEvalue of 986022119864 minus 04 For the double diode model PCEyields the best RMSE value of 98248119864 minus 04 Compared withother optimization algorithms in the literature such as IGHSABSO 119877cr-IJADE and GOTLBO the final convergence ofPCE and 119877cr-IJADE is almost consistent for both the singleand double diode model However the convergence graphsfor both the single and double diode models show that in

5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C

Figure 11 Comparison between real data and the simulated data byPCE for thin-film ST40 at different irradiances

5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)


Figure 12 Comparison between real data and the simulated data byPCE for multicrystalline KC200GT at different irradiances

the early stage PCE has a faster convergence speed comparedwith 119877cr-IJADE In addition PCE is tested using threedifferent sources of data at different irradiance levels withconstant temperature and at three different temperatureswith constant irradiance From the experiment results RMSEfor various weather conditions reached the value of 10minus5Therefore the parameter extraction performance of theproposed PCE technique is verified with good accuracy

Therefore the proposed PCE technique provides a goodbalance between exploration and exploitation The newtechnique provides another optional method to extractparameters of solar cell models In the future researchby mathematical analysis using a dynamic system such as


Table 13 The extracted parameters for monocrystalline SM55 PVmodule by PCE at different temperatures and values of irradiance of1000Wm2

Parameters Temperature(25∘C) (40∘C) (60∘C)

Monocrystalline SM55119868ph (A) 3455710 3490212 3536219119868sd (120583A) 000288916 002139623 023703510119877119904(Ω) 0495620 0495663 0495628

119877sh (Ω) 2999873 2998248 2998124119899 1123473 1123268 1123354RMSE 482119864 minus 05 651119864 minus 05 473119864 minus 05

Table 14 The extracted parameters for thin-film ST40 PV moduleby PCE at different temperatures and values of irradiance of1000Wm2

Parameters Temperature(25∘C) (40∘C) (55∘C) (70∘C)

Thin-film ST40119868ph (A) 2596880 2614915 2632917 2650986119868sd (120583A) 2789916 11564938 42589211 140543289119877119904(Ω) 0798689 0799007 0799080 0799203

119877sh (Ω) 3003258 2996235 2993048 2974168119899 1499926 1499275 1499222 1498911RMSE 388119864 minus 05 340119864 minus 05 379119864 minus 05 817119864 minus 05

Table 15 The extracted parameters for multicrystalline KC200GTPV module by PCE at different temperatures and values of irradi-ance of 1000Wm2


Multicrystalline KC200GT119868ph (A) 8221126 8301147 8381114119868sd (120583A) 000400505 0107120 1825925119877119904(Ω) 0298004 0298043 0297969


the Markov chains we are going to prove and explain theconvergence of the proposed approach

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (no 61574038) the Science Founda-tion of Fujian Education Department (no JK2014003 andno JA14038) the Science Foundation of Fujian Science ampTechnology Department (no 2015H0021 nos 2015J05124and 2016H6012) and the Scientific Research Foundation for

Table 16 The extracted parameters for three different types of PVmodules by PCE at different values of irradiance and temperaturesof 25∘C

Parameters Monocrystalline Thin-film MulticrystallineSM55 ST40 KC200GT

119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241


the Returned Overseas Chinese Scholars State EducationMinistry (no LXKQ201504)

References

[1] X Chen K Yu W Du W Zhao and G Liu ldquoParameters iden-tification of solar cell models using generalized oppositionalteaching learning based optimizationrdquo Energy vol 99 pp 170ndash180 2016

[2] D Oliva E Cuevas and G Pajares ldquoParameter identification ofsolar cells using artificial bee colony optimizationrdquo Energy vol72 pp 93ndash102 2014


[3] A Askarzadeh and A Rezazadeh ldquoArtificial bee swarm opti-mization algorithm for parameters identification of solar cellmodelsrdquo Applied Energy vol 102 pp 943ndash949 2013

[4] W Gong and Z Cai ldquoParameter extraction of solar cell modelsusing repaired adaptive differential evolutionrdquo Solar Energy vol94 pp 209ndash220 2013

[5] K Ishaque Z Salam H Taheri and A Shamsudin ldquoA criticalevaluation of EA computational methods for photovoltaic cellparameter extraction based on two diode modelrdquo Solar Energyvol 85 no 9 pp 1768ndash1779 2011

[6] A Askarzadeh and L dos Santos Coelho ldquoDetermination ofphotovoltaic modules parameters at different operating condi-tions using a novel bird mating optimizer approachrdquo EnergyConversion and Management vol 89 pp 608ndash614 2015

[7] W Han H-H Wang and L Chen ldquoParameters identificationfor photovoltaic module based on an improved artificial fishswarm algorithmrdquo ScientificWorld Journal vol 2014 Article ID859239 12 pages 2014

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

[9] A Ortiz-Conde F J G Sanchez and J Muci ldquoNew methodto extract the model parameters of solar cells from the explicitanalytic solutions of their illuminated IndashV characteristicsrdquo SolarEnergy Materials and Solar Cells vol 90 no 3 pp 352ndash3612006

[10] Q Niu L Zhang and K Li ldquoA biogeography-based optimiza-tion algorithm with mutation strategies for model parameterestimation of solar and fuel cellsrdquo Energy Conversion andManagement vol 86 pp 1173ndash1185 2014

[11] M Ye X Wang and Y Xu ldquoParameter extraction of solar cellsusing particle swarm optimizationrdquo Journal of Applied Physicsvol 105 no 9 Article ID 094502 2009

[12] H Wei J Cong X Lingyun and S Deyun ldquoExtractingsolar cell model parameters based on chaos particle swarmalgorithmrdquo in Proceedings of the International Conference onElectric Information and Control Engineering (ICEICE rsquo11) pp398ndash402 IEEE Wuhan China April 2011

[13] J A Jervase H Bourdoucen and A Al-Lawati ldquoSolar cellparameter extraction using genetic algorithmsrdquo MeasurementScience and Technology vol 12 no 11 pp 1922ndash1925 2001

[14] M Zagrouba A Sellami M Bouaıcha and M Ksouri ldquoIden-tification of PV solar cells and modules parameters using thegenetic algorithms application to maximum power extractionrdquoSolar Energy vol 84 no 5 pp 860ndash866 2010

[15] M R AlRashidi M F AlHajri K M El-Naggar and A K Al-Othman ldquoA new estimation approach for determining the I-V characteristics of solar cellsrdquo Solar Energy vol 85 no 7 pp1543ndash1550 2011

[16] K Ishaque and Z Salam ldquoAn improved modeling method todetermine the model parameters of photovoltaic (PV) modulesusing differential evolution (DE)rdquo Solar Energy vol 85 no 9pp 2349ndash2359 2011

[17] L L Jiang D L Maskell and J C Patra ldquoParameter estimationof solar cells and modules using an improved adaptive differen-tial evolution algorithmrdquo Applied Energy vol 112 pp 185ndash1932013

[18] K Ishaque Z Salam S Mekhilef and A Shamsudin ldquoParam-eter extraction of solar photovoltaic modules using penalty-based differential evolutionrdquo Applied Energy vol 99 pp 297ndash308 2012

[19] M F AlHajri K M El-Naggar M R AlRashidi and A KAl-Othman ldquoOptimal extraction of solar cell parameters usingpattern searchrdquo Renewable Energy vol 44 pp 238ndash245 2012

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

[21] A Askarzadeh and A Rezazadeh ldquoParameter identificationfor solar cell models using harmony search-based algorithmsrdquoSolar Energy vol 86 no 11 pp 3241ndash3249 2012

[22] AAskarzadeh andA Rezazadeh ldquoAnewheuristic optimizationalgorithm formodeling of proton exchangemembrane fuel cellbirdmating optimizerrdquo International Journal of EnergyResearchvol 37 no 10 pp 1196ndash1204 2013

[23] K Katayama and H Narihisa ldquoOn fundamental design ofparthenogenetic algorithm for the binary quadratic program-ming problemrdquo in Proceedings of the IEEE Congress on Evolu-tionary Computation pp 356ndash363 May 2001

[24] M Barukcic S Nikolovski and F Jovıc ldquoHybrid evolutionary-heuristic algorithm for capacitor banks allocationrdquo Journal ofElectrical Engineering vol 61 no 6 pp 332ndash340 2010

[25] J Wu and H Wang ldquoA parthenogenetic algorithm for thefounder sequence reconstruction problemrdquo Journal of Comput-ers vol 8 no 11 pp 2934ndash2941 2013

[26] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997

[27] S Das A Abraham U K Chakraborty and A KonarldquoDifferential evolution using a neighborhood-based mutationoperatorrdquo IEEE Transactions on Evolutionary Computation vol13 no 3 pp 526ndash553 2009

[28] W-C Yeh ldquoOrthogonal simplified swarm optimization for theseriesndashparallel redundancy allocation problem with a mix ofcomponentsrdquo Knowledge-Based Systems vol 64 pp 1ndash12 2014

[29] J Brest S Greiner B Boskovic M Mernik and V ZumerldquoSelf-adapting control parameters in differential evolution acomparative study on numerical benchmark problemsrdquo IEEETransactions on Evolutionary Computation vol 10 no 6 pp646ndash657 2006

[30] X-S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 CoimbatoreIndia December 2009

[31] D Karaboga and B Basturk ldquoA powerful and efficient algo-rithm for numerical function optimization artificial bee colony(ABC) algorithmrdquo Journal of Global Optimization vol 39 no 3pp 459ndash471 2007

[32] P N Suganthan N Hansen J J Liang et al ldquoProblem defini-tions and evaluation criteria for theCEC 2005 special session onreal-parameter optimizationrdquo KanGAL Report 2005005 2005

[33] SHELL Shell SM55 photovoltaic solar module httpwwwsolarquestcommicrosolarsupplierssiemenssm55pdf

[34] Characteristics of a PV module PV module shell solar ST 40httpohodasopxplshell-st40-solar-panelphp

[35] Kyocera KC200GT high efficiency multicrystal photovoltaicmodule 2012 httpwwwkyocerasolarcomassets0015195pdf

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


(SA) [20] harmony search (HS) [21] and artificial beeswarmoptimization (ABSO) [3] Althoughheuristicmethodspresent a higher probability of obtaining a global solutionin comparison with deterministic ones they have impor-tant limits [13] In case of GA and PSO they maintaina trend that concentrates toward local optima since theirelitist mechanism forces premature convergence [2] Suchbehavior becomes worse when the optimization algorithmfaces multimodal functions On the other hand due to thefact that SA and HS are single-searcher algorithms theirperformance is sensitive to the starting point of the searchhaving a lower probability to localize the global minimum inmultimodal problems than population algorithms such asGAand PSO [2] Therefore GA PSO SA and HS present badperformance when they are applied to multimodal and noisyobjective functionsTherefore there is the possibility to yieldbetter performance with more capable algorithms

In biological populations birds have around 10000 livingspecies which are the most species of tetrapod vertebrates[22] In birds the courtship behavior is innate During themating season a bird tries to find spouse(s) with goodgenes for raising a brood that can survive for a longertime which is similar to that of a search for the optimalsolution To develop a more capable heuristic optimizationalgorithm Askarzadeh and Rezazadeh [22] propose a birdmating optimizer (BMO) In BMO algorithm there are fourbreeding strategies monogamy polygamy polyandry andpromiscuity Experimental results indicate the superior per-formance of BMOHowever there are twomain drawbacks inBMO (1) numerous types of birds and (2) numerous numbersof tunable parameters To overcome these disadvantagesAskarzadeh and dos Santos Coelho [6] propose a simplifiedBMOalgorithm (SBMO) In SBMOalgorithm all birds in thepopulation are ranked according to their objective functionvalues such that the bird with the best objective functionvalue is ranked first Then these birds are divided into threetypes for breeding based on their rank These three breedingstrategies are parthenogenesis monogamy and polygamyrespectivelyThe SBMOalgorithm reduces the computationalcomplexity and yields good performance on PV modules

However SBMO has a disadvantage of slow convergenceFirstly the disturbance coefficient in Type 1 (parthenogene-sis) is very small which means the exploitation space is verylimitedThus it is not easy to find a better solution Secondlyin Type 2 (monogamy) a female mating bird is randomlyselected from Type 1 Therefore the selected female matingbird may be not the optimal The convergence speed of Type2 is limitedThirdly Type 3 (polygamy) plays a similar role toType 2 which means SBMO has no effective strategy to avoidtrapping in a local optimum

The parameter estimation method should be reliableaccurate and fast for a range of different types of cellsestimation To further improve the efficiency and reliabilityof parameters identification of photovoltaic models herewe propose a new optimization technique referred to aspopulation classification evolution (PCE) to overcome theslow convergence of SBMO In PCE we divide the populationinto two categories that is elite and ordinaryThe elite are theparthenogenesis corresponding to the neighborhood-based

search known as the local search strategy to afford exploita-tion In the elite evolution strategy we magnify the exploita-tion space to accelerate convergence In the ordinary weemploy DE mutation ldquoDEbest1rdquo operator to guide an indi-vidual to be close to the global optimum Then a crossoveroperator following mutation is employed to increase thediversity of the population In addition we add a randommovement of small probability for the evolution of ordinaryindividuals to further increase the diversity of the populationand overcome the premature convergence Obviously theordinary evolution is corresponding to the global search toafford exploration To estimate the performance of PCE it isfirst compared with five well-known evolutional algorithms(EAs) SBMO cuckoo search (CS) artificial bee colony(ABC) improved adaptive differential evolution (IADE) andself-adapting control parameters in differential evolution(called jDE) on 13 classic benchmark functions And a start-of-the-art evolutional algorithm called generalized oppo-sitional teaching learning based optimization (GOTLBO)is also adopted to compare with PCE PCE has a fasterconvergence speed and higher accuracy than these six EAs onmost benchmark functions through emulation In additionPCE is applied to extract the parameters of both the singleand double diode model The emulation data indicate thatthe proposed PCE is superior when comparing it with otherparameter extractionmethodsMoreover PCE is tested usingthree different sources of data with good accuracy

Organization of the remainder of the paper is as followsFor Section 2 solar cell identification is depicted In Section 3the SBMO algorithm is depicted Section 4 specifies theimplementation of our proposed PCE In Section 5 PCEis estimated on 13 classic benchmark functions Then inSection 6 PCE is applied to extract the parameters of PVmodels The conclusions are depicted in Section 7

2 Problem Statement

21 Solar Cell Models An accurate mathematical modeldescribing the electrical characteristics of solar cells is neededin advance Some equivalent circuit models are used tosimulate the current-voltage (119868-119881) behavior for solar cells butonly two models are employed in practice the double diodemodel and the single diode model In this subsection thesemodels are tersely discussed

211 Double Diode Model Under the illumination the idealsolar cell model is a photogenerated current source that isshunted by a rectifier diode [3 13 21] Figure 1 shows theequivalent circuit of the double diode model According toKirchhoff rsquos law of electric current and the Shockley equationthe 119868-119881 relationship is formulated as

119868119905= 119868ph minus 119868d1 minus 119868d2 minus 119868sh

= 119868ph minus 119868sd1 [exp(119902 (119881119905+ 119877119904119868119905)

1198991119896119879

) minus 1]

minus 119868sd2 [exp(119902 (119881119905+ 119877119904119868119905)

1198992119896119879

) minus 1] minus119881119905+ 119877119904119868119905

119877sh

(1)




119905







119868119905= 119868ph minus 119868sd [exp(

119902 (119881119905+ 119877119904119868119905)

119899119896119879) minus 1] minus

119881119905+ 119877119904119868119905

119877sh (2)




119891 (119881119905 119868119905 119909) = 119868

119905minus 119868ph

+ 119868sd1 [exp(119902 (119881119905+ 119877119904119868119905)

1198991119896119879

) minus 1]

+ 119868sd2 [exp(119902 (119881119905+ 119877119904119868119905)

1198992119896119879

) minus 1]

+119881119905+ 119877119904119868119905

119877sh

119891 (119881119905 119868119905 119909) = 119868

119905minus 119868ph + 119868sd [exp(

119902 (119881119905+ 119877119904119868119905)

119899119896119879) minus 1]

+119881119905+ 119877119904119868119905

119877sh

(3)


119865 (119909) = radic1

119873

119873

sum

119894=1

(119891119894(119881119905 119868119905 119909))2

(4)



+Vt

It

Rs

Id1 Id2

RshIph

Ish


+Vt

It

Rs

Id

RshIph

Ish





1) is determined by

1198731= round(119873119875

10) (5)


if rand gt rand


10sdot 119909119894

else

V119894= 119909119894

end

(6)


119894is themutant




2) is determined by

1198732= round(7 sdot 119873119875

10) (7)


V119894= 119909119894+ rand sdot (119909

119904minus 119909119894) (8)




3) is determined by

1198733= 119873119875 minus 119873

1minus 1198732 (9)


V119894= 119909119894+ rand sdot (119909

1199041minus 119909119894) + rand sdot (119909

1199042minus 119909119894) (10)

where 1199091199041

and 1199091199042





1)




119894 (11)



2)

is determined by

1198732= 119873119875 minus 119873

1 (12)


V119894= 119909best + rand sdot (119909119903

1

minus 1199091199032

) (13)




119894between 119909

119894and V119894

119906119894119895=

V119894119895 if rand le Cr or 119895 == 119903119899 (119894)

119909119894119895 otherwise

(14)



119894


for 119895 = 1 119863

V119894119895= 119886119895+ rand sdot (119887

119895minus 119886119895)

end

(15)





1 1199092 119909










if rand lt Dep

V119894= 119909best + rand sdot (119909119903

1

minus 1199091199032

)

for 119895 = 1 119863

if rand le Cr or 119895 == 119903119899 (119894)

V119894119895= V119894119895

else

V119894119895= 119909119894119895

end if

end for

else

for 119895 = 1 119863

V119894119895= 119886119895+ rand sdot (119887

119895minus 119886119895)

end for

end if

(16)







8ndash11989113








1198911=

119863

sum

119894=1

1199092

11989430 [minus100 100]

119863 0

1198912=

119863

sum

119894=1

10038161003816100381610038161199091198941003816100381610038161003816 +

119863

prod

119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [minus10 10]

119863 0

1198913=

119863

sum

119894=1

(

119894

sum

119895=1

119909119895)

2

30 [minus100 100]119863 0

1198914= max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119863 30 [minus100 100]

119863 0

1198915=

119863minus1

sum

119894=1

[100 (119909119894+1minus 1199092

119894)2

+ (1 minus 119909119894)2

] 30 [minus30 30]119863 0

1198916=

119863

sum

119894=1

[1003816100381610038161003816119909119894 + 05

1003816100381610038161003816]2 30 [minus100 100]

119863 0

1198917=

119863

sum

119894=1

1198941199094

119894+ rand(0 1) 30 [minus128 128]

119863 0

1198918= minus

119863

sum

119894=1

(119909119894sin(radic1003816100381610038161003816119909119894

1003816100381610038161003816)) 30 [minus500 500]119863

minus12569487

1198919=

119863

sum

119894=1

(1199092

119894minus 10 cos (2120587119909

119894) + 10) 30 [minus512 512]

119863 0


119863

119863

sum

119894=1

1199092


119863

119863

sum

119894=1

cos (2120587119909119894)) + 20 + 119890 30 [minus32 32]

119863 0

11989111=

1

4000

119863

sum

119894=1

1199092

119894minus

119863

prod

119894=1

cos(119909119894

radic119894) + 1 30 [minus600 600]

119863 0

11989112=120587

11986310 sin2 (120587119910

1) +

119863minus1

sum

119894=1

(119910119894minus 1)2

[1 + 10 sin2 (120587119910119894+1)] + (119910

119863minus 1)2

+

119863

sum

119894=1

119906 (119909119894 10 100 4)

119910119894= 1 +

119909119894+ 1

4

119906 (119909119894 119886 119896 119898) =

119896 (119909119894minus 119886)119898

119909119894gt 119886

0 minus119886 lt 119909119894lt 119886

119896 (minus119909119894minus 119886)119898

119909119894lt minus119886

30 [minus50 50]119863 0

11989113= 01sin2 (3120587119909

1) +

119863minus1

sum

119894=1

(119909119894minus 1)2

[1 + sin2 (3120587119909119894+1)] + (119909

119863minus 1)2

+

119863

sum

119894=1

119906 (119909119894 5 100 4) 30 [minus50 50]

119863 0



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 100 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 50 119869119903 = 1PCE 119873119875 = 100 Dep = 09 Cr = 015





1(119909)ndash119891


[1 32]







1198911





GOTLBO 0 0 0 0PCE 0 0 0 0

1198912







1198913


ABC 809119864 + 02 228119864 + 03 476119864 + 03 854119864 + 02

IADE 244119864 minus 18 582119864 + 02 355119864 + 03 938119864 + 02



1198914


CS 832119864 + 00 172119864 + 01 281119864 + 01 442119864 + 00

ABC 904119864 + 00 171119864 + 01 267119864 + 01 349119864 + 00

IADE 502119864 minus 01 651119864 + 00 310119864 + 01 722119864 + 00



1198915

SBMO 289119864 + 01 290119864 + 01 290119864 + 01 197119864 minus 02

CS 133119864 minus 10 467119864 + 00 679119864 + 01 993119864 + 00


IADE 110119864 minus 06 196119864 + 00 125119864 + 01 263119864 + 00

jDE 792119864 minus 01 110119864 + 01 672119864 + 01 108119864 + 01

GOTLBO 604119864 + 00 925119864 + 00 145119864 + 01 176119864 + 00


1198916

SBMO 0 111119864 + 01 112119864 + 02 215119864 + 01



IADE 0 800119864 minus 01 500119864 + 00 107119864 + 00

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

1198917









Table 3 Continued


1198918








1198919

SBMO 106119864 + 02 158119864 + 02 200119864 + 01 208119864 + 01

CS 995119864 minus 01 792119864 + 01 199119864 + 01 416119864 + 01


IADE 190119864 + 01 371119864 + 01 744119864 + 01 104119864 + 01

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989110

SBMO 0 511119864 minus 01 800119864 + 00 204119864 + 00

CS 931119864 minus 01 189119864 + 00 393119864 + 00 660119864 minus 01





PCE 0 0 0 0

11989111

SBMO 0 118119864 minus 01 103119864 + 00 324119864 minus 01




jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989112

SBMO 941119864 minus 01 939119864 + 00 192119864 + 01 522119864 + 00






11989113

SBMO 300119864 minus 02 125119864 + 01 416119864 + 01 117119864 + 01

CS 135119864 minus 32 368119864 minus 01 806119864 + 00 129119864 + 00












11



1ndash11989111




0 0 0 0 1 2 71198918ndash11989113

0 0 0 0 4 2 4Total 0 0 0 0 5 4 11



1198911

SR 100 100 100 100 100 100 100ANFES 14976 56917 15767 23718 53966 5866 2030

1198912

SR 100 100 100 100 100 100 100ANFES 20926 78857 23665 33140 72332 9418 3184

1198913


1198914


1198915


1198916

SR 42 100 100 48 100 100 100ANFES NA 57883 15894 NA 20656 2446 604

1198917


1198918


1198919

SR 0 0 100 0 100 100 100ANFES NA NA 40633 NA 108546 7183 2252

11989110

SR 94 0 100 90 100 100 100ANFES NA NA 27697 NA 78486 8869 3138

11989111

SR 88 68 100 48 100 100 100ANFES NA NA 43508 NA 56358 6172 2116

11989112

SR 0 64 100 72 100 100 100ANFES NA 68284 14300 NA 47606 36547 4752

11989113

SR 0 86 100 74 100 22 100ANFES NA 183838 16521 NA 52686 NA 6574











1ndash1198916

















119881119905(V) 119868

119905(A)

1 minus02057 0764

2 minus01291 0762

3 minus00588 07605

4 00057 07605

5 00646 076

6 01185 0759

7 01678 0757

8 02132 0757

9 02545 07555

10 02924 0754

11 03269 07505

12 03585 07465

13 03873 07385

14 04137 0728

15 04373 07065

16 0459 06755

17 04784 0632

18 0496 0573

19 05119 0499

20 05265 0413

21 05398 03165

22 05521 0212

23 05633 01035

24 05736 minus001

25 05833 minus0123

26 059 minus021



119877sh (Ω) 0 100119899 1198991 1198992

1 2



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 20 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 20 119869119903 = 04PCE 119873119875 = 100 Dep = 09 Cr = 015


SBMOCSABCIADE

jDEGOTLBOPCE

2000 4000 6000 8000 10000 120000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log


0 05 1 15 2 2510minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

SBMOCSABCIADE

jDEGOTLBOPCE

NFES









PCE

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

Rcr-IJADE

(a)

Rcr-IJADEPCE

02 04 06 08 1 12 14 16 18 20NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

(b)










minus04

minus02

0

02

04

06

08

1Cu

rren

t (A

)

(a)


minus04

minus02

0

02

04

06

08

1

Curr

ent (

A)


(b)
















119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992


minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C


7 Conclusions


minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C






5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




119905







119868119905= 119868ph minus 119868sd [exp(

119902 (119881119905+ 119877119904119868119905)

119899119896119879) minus 1] minus

119881119905+ 119877119904119868119905

119877sh (2)




119891 (119881119905 119868119905 119909) = 119868

119905minus 119868ph

+ 119868sd1 [exp(119902 (119881119905+ 119877119904119868119905)

1198991119896119879

) minus 1]

+ 119868sd2 [exp(119902 (119881119905+ 119877119904119868119905)

1198992119896119879

) minus 1]

+119881119905+ 119877119904119868119905

119877sh

119891 (119881119905 119868119905 119909) = 119868

119905minus 119868ph + 119868sd [exp(

119902 (119881119905+ 119877119904119868119905)

119899119896119879) minus 1]

+119881119905+ 119877119904119868119905

119877sh

(3)


119865 (119909) = radic1

119873

119873

sum

119894=1

(119891119894(119881119905 119868119905 119909))2

(4)



+Vt

It

Rs

Id1 Id2

RshIph

Ish


+Vt

It

Rs

Id

RshIph

Ish





1) is determined by

1198731= round(119873119875

10) (5)


if rand gt rand


10sdot 119909119894

else

V119894= 119909119894

end

(6)


119894is themutant




2) is determined by

1198732= round(7 sdot 119873119875

10) (7)


V119894= 119909119894+ rand sdot (119909

119904minus 119909119894) (8)




3) is determined by

1198733= 119873119875 minus 119873

1minus 1198732 (9)


V119894= 119909119894+ rand sdot (119909

1199041minus 119909119894) + rand sdot (119909

1199042minus 119909119894) (10)

where 1199091199041

and 1199091199042





1)




119894 (11)



2)

is determined by

1198732= 119873119875 minus 119873

1 (12)


V119894= 119909best + rand sdot (119909119903

1

minus 1199091199032

) (13)




119894between 119909

119894and V119894

119906119894119895=

V119894119895 if rand le Cr or 119895 == 119903119899 (119894)

119909119894119895 otherwise

(14)



119894


for 119895 = 1 119863

V119894119895= 119886119895+ rand sdot (119887

119895minus 119886119895)

end

(15)





1 1199092 119909










if rand lt Dep

V119894= 119909best + rand sdot (119909119903

1

minus 1199091199032

)

for 119895 = 1 119863

if rand le Cr or 119895 == 119903119899 (119894)

V119894119895= V119894119895

else

V119894119895= 119909119894119895

end if

end for

else

for 119895 = 1 119863

V119894119895= 119886119895+ rand sdot (119887

119895minus 119886119895)

end for

end if

(16)







8ndash11989113








1198911=

119863

sum

119894=1

1199092

11989430 [minus100 100]

119863 0

1198912=

119863

sum

119894=1

10038161003816100381610038161199091198941003816100381610038161003816 +

119863

prod

119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [minus10 10]

119863 0

1198913=

119863

sum

119894=1

(

119894

sum

119895=1

119909119895)

2

30 [minus100 100]119863 0

1198914= max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119863 30 [minus100 100]

119863 0

1198915=

119863minus1

sum

119894=1

[100 (119909119894+1minus 1199092

119894)2

+ (1 minus 119909119894)2

] 30 [minus30 30]119863 0

1198916=

119863

sum

119894=1

[1003816100381610038161003816119909119894 + 05

1003816100381610038161003816]2 30 [minus100 100]

119863 0

1198917=

119863

sum

119894=1

1198941199094

119894+ rand(0 1) 30 [minus128 128]

119863 0

1198918= minus

119863

sum

119894=1

(119909119894sin(radic1003816100381610038161003816119909119894

1003816100381610038161003816)) 30 [minus500 500]119863

minus12569487

1198919=

119863

sum

119894=1

(1199092

119894minus 10 cos (2120587119909

119894) + 10) 30 [minus512 512]

119863 0


119863

119863

sum

119894=1

1199092


119863

119863

sum

119894=1

cos (2120587119909119894)) + 20 + 119890 30 [minus32 32]

119863 0

11989111=

1

4000

119863

sum

119894=1

1199092

119894minus

119863

prod

119894=1

cos(119909119894

radic119894) + 1 30 [minus600 600]

119863 0

11989112=120587

11986310 sin2 (120587119910

1) +

119863minus1

sum

119894=1

(119910119894minus 1)2

[1 + 10 sin2 (120587119910119894+1)] + (119910

119863minus 1)2

+

119863

sum

119894=1

119906 (119909119894 10 100 4)

119910119894= 1 +

119909119894+ 1

4

119906 (119909119894 119886 119896 119898) =

119896 (119909119894minus 119886)119898

119909119894gt 119886

0 minus119886 lt 119909119894lt 119886

119896 (minus119909119894minus 119886)119898

119909119894lt minus119886

30 [minus50 50]119863 0

11989113= 01sin2 (3120587119909

1) +

119863minus1

sum

119894=1

(119909119894minus 1)2

[1 + sin2 (3120587119909119894+1)] + (119909

119863minus 1)2

+

119863

sum

119894=1

119906 (119909119894 5 100 4) 30 [minus50 50]

119863 0



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 100 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 50 119869119903 = 1PCE 119873119875 = 100 Dep = 09 Cr = 015





1(119909)ndash119891


[1 32]







1198911





GOTLBO 0 0 0 0PCE 0 0 0 0

1198912







1198913


ABC 809119864 + 02 228119864 + 03 476119864 + 03 854119864 + 02

IADE 244119864 minus 18 582119864 + 02 355119864 + 03 938119864 + 02



1198914


CS 832119864 + 00 172119864 + 01 281119864 + 01 442119864 + 00

ABC 904119864 + 00 171119864 + 01 267119864 + 01 349119864 + 00

IADE 502119864 minus 01 651119864 + 00 310119864 + 01 722119864 + 00



1198915

SBMO 289119864 + 01 290119864 + 01 290119864 + 01 197119864 minus 02

CS 133119864 minus 10 467119864 + 00 679119864 + 01 993119864 + 00


IADE 110119864 minus 06 196119864 + 00 125119864 + 01 263119864 + 00

jDE 792119864 minus 01 110119864 + 01 672119864 + 01 108119864 + 01

GOTLBO 604119864 + 00 925119864 + 00 145119864 + 01 176119864 + 00


1198916

SBMO 0 111119864 + 01 112119864 + 02 215119864 + 01



IADE 0 800119864 minus 01 500119864 + 00 107119864 + 00

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

1198917









Table 3 Continued


1198918








1198919

SBMO 106119864 + 02 158119864 + 02 200119864 + 01 208119864 + 01

CS 995119864 minus 01 792119864 + 01 199119864 + 01 416119864 + 01


IADE 190119864 + 01 371119864 + 01 744119864 + 01 104119864 + 01

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989110

SBMO 0 511119864 minus 01 800119864 + 00 204119864 + 00

CS 931119864 minus 01 189119864 + 00 393119864 + 00 660119864 minus 01





PCE 0 0 0 0

11989111

SBMO 0 118119864 minus 01 103119864 + 00 324119864 minus 01




jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989112

SBMO 941119864 minus 01 939119864 + 00 192119864 + 01 522119864 + 00






11989113

SBMO 300119864 minus 02 125119864 + 01 416119864 + 01 117119864 + 01

CS 135119864 minus 32 368119864 minus 01 806119864 + 00 129119864 + 00












11



1ndash11989111




0 0 0 0 1 2 71198918ndash11989113

0 0 0 0 4 2 4Total 0 0 0 0 5 4 11



1198911

SR 100 100 100 100 100 100 100ANFES 14976 56917 15767 23718 53966 5866 2030

1198912

SR 100 100 100 100 100 100 100ANFES 20926 78857 23665 33140 72332 9418 3184

1198913


1198914


1198915


1198916

SR 42 100 100 48 100 100 100ANFES NA 57883 15894 NA 20656 2446 604

1198917


1198918


1198919

SR 0 0 100 0 100 100 100ANFES NA NA 40633 NA 108546 7183 2252

11989110

SR 94 0 100 90 100 100 100ANFES NA NA 27697 NA 78486 8869 3138

11989111

SR 88 68 100 48 100 100 100ANFES NA NA 43508 NA 56358 6172 2116

11989112

SR 0 64 100 72 100 100 100ANFES NA 68284 14300 NA 47606 36547 4752

11989113

SR 0 86 100 74 100 22 100ANFES NA 183838 16521 NA 52686 NA 6574











1ndash1198916

















119881119905(V) 119868

119905(A)

1 minus02057 0764

2 minus01291 0762

3 minus00588 07605

4 00057 07605

5 00646 076

6 01185 0759

7 01678 0757

8 02132 0757

9 02545 07555

10 02924 0754

11 03269 07505

12 03585 07465

13 03873 07385

14 04137 0728

15 04373 07065

16 0459 06755

17 04784 0632

18 0496 0573

19 05119 0499

20 05265 0413

21 05398 03165

22 05521 0212

23 05633 01035

24 05736 minus001

25 05833 minus0123

26 059 minus021



119877sh (Ω) 0 100119899 1198991 1198992

1 2



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 20 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 20 119869119903 = 04PCE 119873119875 = 100 Dep = 09 Cr = 015


SBMOCSABCIADE

jDEGOTLBOPCE

2000 4000 6000 8000 10000 120000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log


0 05 1 15 2 2510minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

SBMOCSABCIADE

jDEGOTLBOPCE

NFES









PCE

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

Rcr-IJADE

(a)

Rcr-IJADEPCE

02 04 06 08 1 12 14 16 18 20NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

(b)










minus04

minus02

0

02

04

06

08

1Cu

rren

t (A

)

(a)


minus04

minus02

0

02

04

06

08

1

Curr

ent (

A)


(b)
















119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992


minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C


7 Conclusions


minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C






5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



2) is determined by

1198732= round(7 sdot 119873119875

10) (7)


V119894= 119909119894+ rand sdot (119909

119904minus 119909119894) (8)




3) is determined by

1198733= 119873119875 minus 119873

1minus 1198732 (9)


V119894= 119909119894+ rand sdot (119909

1199041minus 119909119894) + rand sdot (119909

1199042minus 119909119894) (10)

where 1199091199041

and 1199091199042





1)




119894 (11)



2)

is determined by

1198732= 119873119875 minus 119873

1 (12)


V119894= 119909best + rand sdot (119909119903

1

minus 1199091199032

) (13)




119894between 119909

119894and V119894

119906119894119895=

V119894119895 if rand le Cr or 119895 == 119903119899 (119894)

119909119894119895 otherwise

(14)



119894


for 119895 = 1 119863

V119894119895= 119886119895+ rand sdot (119887

119895minus 119886119895)

end

(15)





1 1199092 119909










if rand lt Dep

V119894= 119909best + rand sdot (119909119903

1

minus 1199091199032

)

for 119895 = 1 119863

if rand le Cr or 119895 == 119903119899 (119894)

V119894119895= V119894119895

else

V119894119895= 119909119894119895

end if

end for

else

for 119895 = 1 119863

V119894119895= 119886119895+ rand sdot (119887

119895minus 119886119895)

end for

end if

(16)







8ndash11989113








1198911=

119863

sum

119894=1

1199092

11989430 [minus100 100]

119863 0

1198912=

119863

sum

119894=1

10038161003816100381610038161199091198941003816100381610038161003816 +

119863

prod

119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [minus10 10]

119863 0

1198913=

119863

sum

119894=1

(

119894

sum

119895=1

119909119895)

2

30 [minus100 100]119863 0

1198914= max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119863 30 [minus100 100]

119863 0

1198915=

119863minus1

sum

119894=1

[100 (119909119894+1minus 1199092

119894)2

+ (1 minus 119909119894)2

] 30 [minus30 30]119863 0

1198916=

119863

sum

119894=1

[1003816100381610038161003816119909119894 + 05

1003816100381610038161003816]2 30 [minus100 100]

119863 0

1198917=

119863

sum

119894=1

1198941199094

119894+ rand(0 1) 30 [minus128 128]

119863 0

1198918= minus

119863

sum

119894=1

(119909119894sin(radic1003816100381610038161003816119909119894

1003816100381610038161003816)) 30 [minus500 500]119863

minus12569487

1198919=

119863

sum

119894=1

(1199092

119894minus 10 cos (2120587119909

119894) + 10) 30 [minus512 512]

119863 0


119863

119863

sum

119894=1

1199092


119863

119863

sum

119894=1

cos (2120587119909119894)) + 20 + 119890 30 [minus32 32]

119863 0

11989111=

1

4000

119863

sum

119894=1

1199092

119894minus

119863

prod

119894=1

cos(119909119894

radic119894) + 1 30 [minus600 600]

119863 0

11989112=120587

11986310 sin2 (120587119910

1) +

119863minus1

sum

119894=1

(119910119894minus 1)2

[1 + 10 sin2 (120587119910119894+1)] + (119910

119863minus 1)2

+

119863

sum

119894=1

119906 (119909119894 10 100 4)

119910119894= 1 +

119909119894+ 1

4

119906 (119909119894 119886 119896 119898) =

119896 (119909119894minus 119886)119898

119909119894gt 119886

0 minus119886 lt 119909119894lt 119886

119896 (minus119909119894minus 119886)119898

119909119894lt minus119886

30 [minus50 50]119863 0

11989113= 01sin2 (3120587119909

1) +

119863minus1

sum

119894=1

(119909119894minus 1)2

[1 + sin2 (3120587119909119894+1)] + (119909

119863minus 1)2

+

119863

sum

119894=1

119906 (119909119894 5 100 4) 30 [minus50 50]

119863 0



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 100 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 50 119869119903 = 1PCE 119873119875 = 100 Dep = 09 Cr = 015





1(119909)ndash119891


[1 32]







1198911





GOTLBO 0 0 0 0PCE 0 0 0 0

1198912







1198913


ABC 809119864 + 02 228119864 + 03 476119864 + 03 854119864 + 02

IADE 244119864 minus 18 582119864 + 02 355119864 + 03 938119864 + 02



1198914


CS 832119864 + 00 172119864 + 01 281119864 + 01 442119864 + 00

ABC 904119864 + 00 171119864 + 01 267119864 + 01 349119864 + 00

IADE 502119864 minus 01 651119864 + 00 310119864 + 01 722119864 + 00



1198915

SBMO 289119864 + 01 290119864 + 01 290119864 + 01 197119864 minus 02

CS 133119864 minus 10 467119864 + 00 679119864 + 01 993119864 + 00


IADE 110119864 minus 06 196119864 + 00 125119864 + 01 263119864 + 00

jDE 792119864 minus 01 110119864 + 01 672119864 + 01 108119864 + 01

GOTLBO 604119864 + 00 925119864 + 00 145119864 + 01 176119864 + 00


1198916

SBMO 0 111119864 + 01 112119864 + 02 215119864 + 01



IADE 0 800119864 minus 01 500119864 + 00 107119864 + 00

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

1198917









Table 3 Continued


1198918








1198919

SBMO 106119864 + 02 158119864 + 02 200119864 + 01 208119864 + 01

CS 995119864 minus 01 792119864 + 01 199119864 + 01 416119864 + 01


IADE 190119864 + 01 371119864 + 01 744119864 + 01 104119864 + 01

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989110

SBMO 0 511119864 minus 01 800119864 + 00 204119864 + 00

CS 931119864 minus 01 189119864 + 00 393119864 + 00 660119864 minus 01





PCE 0 0 0 0

11989111

SBMO 0 118119864 minus 01 103119864 + 00 324119864 minus 01




jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989112

SBMO 941119864 minus 01 939119864 + 00 192119864 + 01 522119864 + 00






11989113

SBMO 300119864 minus 02 125119864 + 01 416119864 + 01 117119864 + 01

CS 135119864 minus 32 368119864 minus 01 806119864 + 00 129119864 + 00












11



1ndash11989111




0 0 0 0 1 2 71198918ndash11989113

0 0 0 0 4 2 4Total 0 0 0 0 5 4 11



1198911

SR 100 100 100 100 100 100 100ANFES 14976 56917 15767 23718 53966 5866 2030

1198912

SR 100 100 100 100 100 100 100ANFES 20926 78857 23665 33140 72332 9418 3184

1198913


1198914


1198915


1198916

SR 42 100 100 48 100 100 100ANFES NA 57883 15894 NA 20656 2446 604

1198917


1198918


1198919

SR 0 0 100 0 100 100 100ANFES NA NA 40633 NA 108546 7183 2252

11989110

SR 94 0 100 90 100 100 100ANFES NA NA 27697 NA 78486 8869 3138

11989111

SR 88 68 100 48 100 100 100ANFES NA NA 43508 NA 56358 6172 2116

11989112

SR 0 64 100 72 100 100 100ANFES NA 68284 14300 NA 47606 36547 4752

11989113

SR 0 86 100 74 100 22 100ANFES NA 183838 16521 NA 52686 NA 6574











1ndash1198916

















119881119905(V) 119868

119905(A)

1 minus02057 0764

2 minus01291 0762

3 minus00588 07605

4 00057 07605

5 00646 076

6 01185 0759

7 01678 0757

8 02132 0757

9 02545 07555

10 02924 0754

11 03269 07505

12 03585 07465

13 03873 07385

14 04137 0728

15 04373 07065

16 0459 06755

17 04784 0632

18 0496 0573

19 05119 0499

20 05265 0413

21 05398 03165

22 05521 0212

23 05633 01035

24 05736 minus001

25 05833 minus0123

26 059 minus021



119877sh (Ω) 0 100119899 1198991 1198992

1 2



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 20 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 20 119869119903 = 04PCE 119873119875 = 100 Dep = 09 Cr = 015


SBMOCSABCIADE

jDEGOTLBOPCE

2000 4000 6000 8000 10000 120000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log


0 05 1 15 2 2510minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

SBMOCSABCIADE

jDEGOTLBOPCE

NFES









PCE

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

Rcr-IJADE

(a)

Rcr-IJADEPCE

02 04 06 08 1 12 14 16 18 20NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

(b)










minus04

minus02

0

02

04

06

08

1Cu

rren

t (A

)

(a)


minus04

minus02

0

02

04

06

08

1

Curr

ent (

A)


(b)
















119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992


minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C


7 Conclusions


minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C






5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



1 1199092 119909










if rand lt Dep

V119894= 119909best + rand sdot (119909119903

1

minus 1199091199032

)

for 119895 = 1 119863

if rand le Cr or 119895 == 119903119899 (119894)

V119894119895= V119894119895

else

V119894119895= 119909119894119895

end if

end for

else

for 119895 = 1 119863

V119894119895= 119886119895+ rand sdot (119887

119895minus 119886119895)

end for

end if

(16)







8ndash11989113








1198911=

119863

sum

119894=1

1199092

11989430 [minus100 100]

119863 0

1198912=

119863

sum

119894=1

10038161003816100381610038161199091198941003816100381610038161003816 +

119863

prod

119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [minus10 10]

119863 0

1198913=

119863

sum

119894=1

(

119894

sum

119895=1

119909119895)

2

30 [minus100 100]119863 0

1198914= max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119863 30 [minus100 100]

119863 0

1198915=

119863minus1

sum

119894=1

[100 (119909119894+1minus 1199092

119894)2

+ (1 minus 119909119894)2

] 30 [minus30 30]119863 0

1198916=

119863

sum

119894=1

[1003816100381610038161003816119909119894 + 05

1003816100381610038161003816]2 30 [minus100 100]

119863 0

1198917=

119863

sum

119894=1

1198941199094

119894+ rand(0 1) 30 [minus128 128]

119863 0

1198918= minus

119863

sum

119894=1

(119909119894sin(radic1003816100381610038161003816119909119894

1003816100381610038161003816)) 30 [minus500 500]119863

minus12569487

1198919=

119863

sum

119894=1

(1199092

119894minus 10 cos (2120587119909

119894) + 10) 30 [minus512 512]

119863 0


119863

119863

sum

119894=1

1199092


119863

119863

sum

119894=1

cos (2120587119909119894)) + 20 + 119890 30 [minus32 32]

119863 0

11989111=

1

4000

119863

sum

119894=1

1199092

119894minus

119863

prod

119894=1

cos(119909119894

radic119894) + 1 30 [minus600 600]

119863 0

11989112=120587

11986310 sin2 (120587119910

1) +

119863minus1

sum

119894=1

(119910119894minus 1)2

[1 + 10 sin2 (120587119910119894+1)] + (119910

119863minus 1)2

+

119863

sum

119894=1

119906 (119909119894 10 100 4)

119910119894= 1 +

119909119894+ 1

4

119906 (119909119894 119886 119896 119898) =

119896 (119909119894minus 119886)119898

119909119894gt 119886

0 minus119886 lt 119909119894lt 119886

119896 (minus119909119894minus 119886)119898

119909119894lt minus119886

30 [minus50 50]119863 0

11989113= 01sin2 (3120587119909

1) +

119863minus1

sum

119894=1

(119909119894minus 1)2

[1 + sin2 (3120587119909119894+1)] + (119909

119863minus 1)2

+

119863

sum

119894=1

119906 (119909119894 5 100 4) 30 [minus50 50]

119863 0



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 100 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 50 119869119903 = 1PCE 119873119875 = 100 Dep = 09 Cr = 015





1(119909)ndash119891


[1 32]







1198911





GOTLBO 0 0 0 0PCE 0 0 0 0

1198912







1198913


ABC 809119864 + 02 228119864 + 03 476119864 + 03 854119864 + 02

IADE 244119864 minus 18 582119864 + 02 355119864 + 03 938119864 + 02



1198914


CS 832119864 + 00 172119864 + 01 281119864 + 01 442119864 + 00

ABC 904119864 + 00 171119864 + 01 267119864 + 01 349119864 + 00

IADE 502119864 minus 01 651119864 + 00 310119864 + 01 722119864 + 00



1198915

SBMO 289119864 + 01 290119864 + 01 290119864 + 01 197119864 minus 02

CS 133119864 minus 10 467119864 + 00 679119864 + 01 993119864 + 00


IADE 110119864 minus 06 196119864 + 00 125119864 + 01 263119864 + 00

jDE 792119864 minus 01 110119864 + 01 672119864 + 01 108119864 + 01

GOTLBO 604119864 + 00 925119864 + 00 145119864 + 01 176119864 + 00


1198916

SBMO 0 111119864 + 01 112119864 + 02 215119864 + 01



IADE 0 800119864 minus 01 500119864 + 00 107119864 + 00

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

1198917









Table 3 Continued


1198918








1198919

SBMO 106119864 + 02 158119864 + 02 200119864 + 01 208119864 + 01

CS 995119864 minus 01 792119864 + 01 199119864 + 01 416119864 + 01


IADE 190119864 + 01 371119864 + 01 744119864 + 01 104119864 + 01

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989110

SBMO 0 511119864 minus 01 800119864 + 00 204119864 + 00

CS 931119864 minus 01 189119864 + 00 393119864 + 00 660119864 minus 01





PCE 0 0 0 0

11989111

SBMO 0 118119864 minus 01 103119864 + 00 324119864 minus 01




jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989112

SBMO 941119864 minus 01 939119864 + 00 192119864 + 01 522119864 + 00






11989113

SBMO 300119864 minus 02 125119864 + 01 416119864 + 01 117119864 + 01

CS 135119864 minus 32 368119864 minus 01 806119864 + 00 129119864 + 00












11



1ndash11989111




0 0 0 0 1 2 71198918ndash11989113

0 0 0 0 4 2 4Total 0 0 0 0 5 4 11



1198911

SR 100 100 100 100 100 100 100ANFES 14976 56917 15767 23718 53966 5866 2030

1198912

SR 100 100 100 100 100 100 100ANFES 20926 78857 23665 33140 72332 9418 3184

1198913


1198914


1198915


1198916

SR 42 100 100 48 100 100 100ANFES NA 57883 15894 NA 20656 2446 604

1198917


1198918


1198919

SR 0 0 100 0 100 100 100ANFES NA NA 40633 NA 108546 7183 2252

11989110

SR 94 0 100 90 100 100 100ANFES NA NA 27697 NA 78486 8869 3138

11989111

SR 88 68 100 48 100 100 100ANFES NA NA 43508 NA 56358 6172 2116

11989112

SR 0 64 100 72 100 100 100ANFES NA 68284 14300 NA 47606 36547 4752

11989113

SR 0 86 100 74 100 22 100ANFES NA 183838 16521 NA 52686 NA 6574











1ndash1198916

















119881119905(V) 119868

119905(A)

1 minus02057 0764

2 minus01291 0762

3 minus00588 07605

4 00057 07605

5 00646 076

6 01185 0759

7 01678 0757

8 02132 0757

9 02545 07555

10 02924 0754

11 03269 07505

12 03585 07465

13 03873 07385

14 04137 0728

15 04373 07065

16 0459 06755

17 04784 0632

18 0496 0573

19 05119 0499

20 05265 0413

21 05398 03165

22 05521 0212

23 05633 01035

24 05736 minus001

25 05833 minus0123

26 059 minus021



119877sh (Ω) 0 100119899 1198991 1198992

1 2



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 20 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 20 119869119903 = 04PCE 119873119875 = 100 Dep = 09 Cr = 015


SBMOCSABCIADE

jDEGOTLBOPCE

2000 4000 6000 8000 10000 120000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log


0 05 1 15 2 2510minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

SBMOCSABCIADE

jDEGOTLBOPCE

NFES









PCE

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

Rcr-IJADE

(a)

Rcr-IJADEPCE

02 04 06 08 1 12 14 16 18 20NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

(b)










minus04

minus02

0

02

04

06

08

1Cu

rren

t (A

)

(a)


minus04

minus02

0

02

04

06

08

1

Curr

ent (

A)


(b)
















119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992


minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C


7 Conclusions


minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C






5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




1198911=

119863

sum

119894=1

1199092

11989430 [minus100 100]

119863 0

1198912=

119863

sum

119894=1

10038161003816100381610038161199091198941003816100381610038161003816 +

119863

prod

119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [minus10 10]

119863 0

1198913=

119863

sum

119894=1

(

119894

sum

119895=1

119909119895)

2

30 [minus100 100]119863 0

1198914= max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119863 30 [minus100 100]

119863 0

1198915=

119863minus1

sum

119894=1

[100 (119909119894+1minus 1199092

119894)2

+ (1 minus 119909119894)2

] 30 [minus30 30]119863 0

1198916=

119863

sum

119894=1

[1003816100381610038161003816119909119894 + 05

1003816100381610038161003816]2 30 [minus100 100]

119863 0

1198917=

119863

sum

119894=1

1198941199094

119894+ rand(0 1) 30 [minus128 128]

119863 0

1198918= minus

119863

sum

119894=1

(119909119894sin(radic1003816100381610038161003816119909119894

1003816100381610038161003816)) 30 [minus500 500]119863

minus12569487

1198919=

119863

sum

119894=1

(1199092

119894minus 10 cos (2120587119909

119894) + 10) 30 [minus512 512]

119863 0


119863

119863

sum

119894=1

1199092


119863

119863

sum

119894=1

cos (2120587119909119894)) + 20 + 119890 30 [minus32 32]

119863 0

11989111=

1

4000

119863

sum

119894=1

1199092

119894minus

119863

prod

119894=1

cos(119909119894

radic119894) + 1 30 [minus600 600]

119863 0

11989112=120587

11986310 sin2 (120587119910

1) +

119863minus1

sum

119894=1

(119910119894minus 1)2

[1 + 10 sin2 (120587119910119894+1)] + (119910

119863minus 1)2

+

119863

sum

119894=1

119906 (119909119894 10 100 4)

119910119894= 1 +

119909119894+ 1

4

119906 (119909119894 119886 119896 119898) =

119896 (119909119894minus 119886)119898

119909119894gt 119886

0 minus119886 lt 119909119894lt 119886

119896 (minus119909119894minus 119886)119898

119909119894lt minus119886

30 [minus50 50]119863 0

11989113= 01sin2 (3120587119909

1) +

119863minus1

sum

119894=1

(119909119894minus 1)2

[1 + sin2 (3120587119909119894+1)] + (119909

119863minus 1)2

+

119863

sum

119894=1

119906 (119909119894 5 100 4) 30 [minus50 50]

119863 0



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 100 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 50 119869119903 = 1PCE 119873119875 = 100 Dep = 09 Cr = 015





1(119909)ndash119891


[1 32]







1198911





GOTLBO 0 0 0 0PCE 0 0 0 0

1198912







1198913


ABC 809119864 + 02 228119864 + 03 476119864 + 03 854119864 + 02

IADE 244119864 minus 18 582119864 + 02 355119864 + 03 938119864 + 02



1198914


CS 832119864 + 00 172119864 + 01 281119864 + 01 442119864 + 00

ABC 904119864 + 00 171119864 + 01 267119864 + 01 349119864 + 00

IADE 502119864 minus 01 651119864 + 00 310119864 + 01 722119864 + 00



1198915

SBMO 289119864 + 01 290119864 + 01 290119864 + 01 197119864 minus 02

CS 133119864 minus 10 467119864 + 00 679119864 + 01 993119864 + 00


IADE 110119864 minus 06 196119864 + 00 125119864 + 01 263119864 + 00

jDE 792119864 minus 01 110119864 + 01 672119864 + 01 108119864 + 01

GOTLBO 604119864 + 00 925119864 + 00 145119864 + 01 176119864 + 00


1198916

SBMO 0 111119864 + 01 112119864 + 02 215119864 + 01



IADE 0 800119864 minus 01 500119864 + 00 107119864 + 00

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

1198917









Table 3 Continued


1198918








1198919

SBMO 106119864 + 02 158119864 + 02 200119864 + 01 208119864 + 01

CS 995119864 minus 01 792119864 + 01 199119864 + 01 416119864 + 01


IADE 190119864 + 01 371119864 + 01 744119864 + 01 104119864 + 01

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989110

SBMO 0 511119864 minus 01 800119864 + 00 204119864 + 00

CS 931119864 minus 01 189119864 + 00 393119864 + 00 660119864 minus 01





PCE 0 0 0 0

11989111

SBMO 0 118119864 minus 01 103119864 + 00 324119864 minus 01




jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989112

SBMO 941119864 minus 01 939119864 + 00 192119864 + 01 522119864 + 00






11989113

SBMO 300119864 minus 02 125119864 + 01 416119864 + 01 117119864 + 01

CS 135119864 minus 32 368119864 minus 01 806119864 + 00 129119864 + 00












11



1ndash11989111




0 0 0 0 1 2 71198918ndash11989113

0 0 0 0 4 2 4Total 0 0 0 0 5 4 11



1198911

SR 100 100 100 100 100 100 100ANFES 14976 56917 15767 23718 53966 5866 2030

1198912

SR 100 100 100 100 100 100 100ANFES 20926 78857 23665 33140 72332 9418 3184

1198913


1198914


1198915


1198916

SR 42 100 100 48 100 100 100ANFES NA 57883 15894 NA 20656 2446 604

1198917


1198918


1198919

SR 0 0 100 0 100 100 100ANFES NA NA 40633 NA 108546 7183 2252

11989110

SR 94 0 100 90 100 100 100ANFES NA NA 27697 NA 78486 8869 3138

11989111

SR 88 68 100 48 100 100 100ANFES NA NA 43508 NA 56358 6172 2116

11989112

SR 0 64 100 72 100 100 100ANFES NA 68284 14300 NA 47606 36547 4752

11989113

SR 0 86 100 74 100 22 100ANFES NA 183838 16521 NA 52686 NA 6574











1ndash1198916

















119881119905(V) 119868

119905(A)

1 minus02057 0764

2 minus01291 0762

3 minus00588 07605

4 00057 07605

5 00646 076

6 01185 0759

7 01678 0757

8 02132 0757

9 02545 07555

10 02924 0754

11 03269 07505

12 03585 07465

13 03873 07385

14 04137 0728

15 04373 07065

16 0459 06755

17 04784 0632

18 0496 0573

19 05119 0499

20 05265 0413

21 05398 03165

22 05521 0212

23 05633 01035

24 05736 minus001

25 05833 minus0123

26 059 minus021



119877sh (Ω) 0 100119899 1198991 1198992

1 2



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 20 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 20 119869119903 = 04PCE 119873119875 = 100 Dep = 09 Cr = 015


SBMOCSABCIADE

jDEGOTLBOPCE

2000 4000 6000 8000 10000 120000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log


0 05 1 15 2 2510minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

SBMOCSABCIADE

jDEGOTLBOPCE

NFES









PCE

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

Rcr-IJADE

(a)

Rcr-IJADEPCE

02 04 06 08 1 12 14 16 18 20NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

(b)










minus04

minus02

0

02

04

06

08

1Cu

rren

t (A

)

(a)


minus04

minus02

0

02

04

06

08

1

Curr

ent (

A)


(b)
















119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992


minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C


7 Conclusions


minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C






5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




1198911





GOTLBO 0 0 0 0PCE 0 0 0 0

1198912







1198913


ABC 809119864 + 02 228119864 + 03 476119864 + 03 854119864 + 02

IADE 244119864 minus 18 582119864 + 02 355119864 + 03 938119864 + 02



1198914


CS 832119864 + 00 172119864 + 01 281119864 + 01 442119864 + 00

ABC 904119864 + 00 171119864 + 01 267119864 + 01 349119864 + 00

IADE 502119864 minus 01 651119864 + 00 310119864 + 01 722119864 + 00



1198915

SBMO 289119864 + 01 290119864 + 01 290119864 + 01 197119864 minus 02

CS 133119864 minus 10 467119864 + 00 679119864 + 01 993119864 + 00


IADE 110119864 minus 06 196119864 + 00 125119864 + 01 263119864 + 00

jDE 792119864 minus 01 110119864 + 01 672119864 + 01 108119864 + 01

GOTLBO 604119864 + 00 925119864 + 00 145119864 + 01 176119864 + 00


1198916

SBMO 0 111119864 + 01 112119864 + 02 215119864 + 01



IADE 0 800119864 minus 01 500119864 + 00 107119864 + 00

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

1198917









Table 3 Continued


1198918








1198919

SBMO 106119864 + 02 158119864 + 02 200119864 + 01 208119864 + 01

CS 995119864 minus 01 792119864 + 01 199119864 + 01 416119864 + 01


IADE 190119864 + 01 371119864 + 01 744119864 + 01 104119864 + 01

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989110

SBMO 0 511119864 minus 01 800119864 + 00 204119864 + 00

CS 931119864 minus 01 189119864 + 00 393119864 + 00 660119864 minus 01





PCE 0 0 0 0

11989111

SBMO 0 118119864 minus 01 103119864 + 00 324119864 minus 01




jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989112

SBMO 941119864 minus 01 939119864 + 00 192119864 + 01 522119864 + 00






11989113

SBMO 300119864 minus 02 125119864 + 01 416119864 + 01 117119864 + 01

CS 135119864 minus 32 368119864 minus 01 806119864 + 00 129119864 + 00












11



1ndash11989111




0 0 0 0 1 2 71198918ndash11989113

0 0 0 0 4 2 4Total 0 0 0 0 5 4 11



1198911

SR 100 100 100 100 100 100 100ANFES 14976 56917 15767 23718 53966 5866 2030

1198912

SR 100 100 100 100 100 100 100ANFES 20926 78857 23665 33140 72332 9418 3184

1198913


1198914


1198915


1198916

SR 42 100 100 48 100 100 100ANFES NA 57883 15894 NA 20656 2446 604

1198917


1198918


1198919

SR 0 0 100 0 100 100 100ANFES NA NA 40633 NA 108546 7183 2252

11989110

SR 94 0 100 90 100 100 100ANFES NA NA 27697 NA 78486 8869 3138

11989111

SR 88 68 100 48 100 100 100ANFES NA NA 43508 NA 56358 6172 2116

11989112

SR 0 64 100 72 100 100 100ANFES NA 68284 14300 NA 47606 36547 4752

11989113

SR 0 86 100 74 100 22 100ANFES NA 183838 16521 NA 52686 NA 6574











1ndash1198916

















119881119905(V) 119868

119905(A)

1 minus02057 0764

2 minus01291 0762

3 minus00588 07605

4 00057 07605

5 00646 076

6 01185 0759

7 01678 0757

8 02132 0757

9 02545 07555

10 02924 0754

11 03269 07505

12 03585 07465

13 03873 07385

14 04137 0728

15 04373 07065

16 0459 06755

17 04784 0632

18 0496 0573

19 05119 0499

20 05265 0413

21 05398 03165

22 05521 0212

23 05633 01035

24 05736 minus001

25 05833 minus0123

26 059 minus021



119877sh (Ω) 0 100119899 1198991 1198992

1 2



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 20 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 20 119869119903 = 04PCE 119873119875 = 100 Dep = 09 Cr = 015


SBMOCSABCIADE

jDEGOTLBOPCE

2000 4000 6000 8000 10000 120000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log


0 05 1 15 2 2510minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

SBMOCSABCIADE

jDEGOTLBOPCE

NFES









PCE

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

Rcr-IJADE

(a)

Rcr-IJADEPCE

02 04 06 08 1 12 14 16 18 20NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

(b)










minus04

minus02

0

02

04

06

08

1Cu

rren

t (A

)

(a)


minus04

minus02

0

02

04

06

08

1

Curr

ent (

A)


(b)
















119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992


minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C


7 Conclusions


minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C






5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Table 3 Continued


1198918








1198919

SBMO 106119864 + 02 158119864 + 02 200119864 + 01 208119864 + 01

CS 995119864 minus 01 792119864 + 01 199119864 + 01 416119864 + 01


IADE 190119864 + 01 371119864 + 01 744119864 + 01 104119864 + 01

jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989110

SBMO 0 511119864 minus 01 800119864 + 00 204119864 + 00

CS 931119864 minus 01 189119864 + 00 393119864 + 00 660119864 minus 01





PCE 0 0 0 0

11989111

SBMO 0 118119864 minus 01 103119864 + 00 324119864 minus 01




jDE 0 0 0 0GOTLBO 0 0 0 0

PCE 0 0 0 0

11989112

SBMO 941119864 minus 01 939119864 + 00 192119864 + 01 522119864 + 00






11989113

SBMO 300119864 minus 02 125119864 + 01 416119864 + 01 117119864 + 01

CS 135119864 minus 32 368119864 minus 01 806119864 + 00 129119864 + 00












11



1ndash11989111




0 0 0 0 1 2 71198918ndash11989113

0 0 0 0 4 2 4Total 0 0 0 0 5 4 11



1198911

SR 100 100 100 100 100 100 100ANFES 14976 56917 15767 23718 53966 5866 2030

1198912

SR 100 100 100 100 100 100 100ANFES 20926 78857 23665 33140 72332 9418 3184

1198913


1198914


1198915


1198916

SR 42 100 100 48 100 100 100ANFES NA 57883 15894 NA 20656 2446 604

1198917


1198918


1198919

SR 0 0 100 0 100 100 100ANFES NA NA 40633 NA 108546 7183 2252

11989110

SR 94 0 100 90 100 100 100ANFES NA NA 27697 NA 78486 8869 3138

11989111

SR 88 68 100 48 100 100 100ANFES NA NA 43508 NA 56358 6172 2116

11989112

SR 0 64 100 72 100 100 100ANFES NA 68284 14300 NA 47606 36547 4752

11989113

SR 0 86 100 74 100 22 100ANFES NA 183838 16521 NA 52686 NA 6574











1ndash1198916

















119881119905(V) 119868

119905(A)

1 minus02057 0764

2 minus01291 0762

3 minus00588 07605

4 00057 07605

5 00646 076

6 01185 0759

7 01678 0757

8 02132 0757

9 02545 07555

10 02924 0754

11 03269 07505

12 03585 07465

13 03873 07385

14 04137 0728

15 04373 07065

16 0459 06755

17 04784 0632

18 0496 0573

19 05119 0499

20 05265 0413

21 05398 03165

22 05521 0212

23 05633 01035

24 05736 minus001

25 05833 minus0123

26 059 minus021



119877sh (Ω) 0 100119899 1198991 1198992

1 2



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 20 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 20 119869119903 = 04PCE 119873119875 = 100 Dep = 09 Cr = 015


SBMOCSABCIADE

jDEGOTLBOPCE

2000 4000 6000 8000 10000 120000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log


0 05 1 15 2 2510minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

SBMOCSABCIADE

jDEGOTLBOPCE

NFES









PCE

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

Rcr-IJADE

(a)

Rcr-IJADEPCE

02 04 06 08 1 12 14 16 18 20NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

(b)










minus04

minus02

0

02

04

06

08

1Cu

rren

t (A

)

(a)


minus04

minus02

0

02

04

06

08

1

Curr

ent (

A)


(b)
















119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992


minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C


7 Conclusions


minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C






5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




0 0 0 0 1 2 71198918ndash11989113

0 0 0 0 4 2 4Total 0 0 0 0 5 4 11



1198911

SR 100 100 100 100 100 100 100ANFES 14976 56917 15767 23718 53966 5866 2030

1198912

SR 100 100 100 100 100 100 100ANFES 20926 78857 23665 33140 72332 9418 3184

1198913


1198914


1198915


1198916

SR 42 100 100 48 100 100 100ANFES NA 57883 15894 NA 20656 2446 604

1198917


1198918


1198919

SR 0 0 100 0 100 100 100ANFES NA NA 40633 NA 108546 7183 2252

11989110

SR 94 0 100 90 100 100 100ANFES NA NA 27697 NA 78486 8869 3138

11989111

SR 88 68 100 48 100 100 100ANFES NA NA 43508 NA 56358 6172 2116

11989112

SR 0 64 100 72 100 100 100ANFES NA 68284 14300 NA 47606 36547 4752

11989113

SR 0 86 100 74 100 22 100ANFES NA 183838 16521 NA 52686 NA 6574











1ndash1198916

















119881119905(V) 119868

119905(A)

1 minus02057 0764

2 minus01291 0762

3 minus00588 07605

4 00057 07605

5 00646 076

6 01185 0759

7 01678 0757

8 02132 0757

9 02545 07555

10 02924 0754

11 03269 07505

12 03585 07465

13 03873 07385

14 04137 0728

15 04373 07065

16 0459 06755

17 04784 0632

18 0496 0573

19 05119 0499

20 05265 0413

21 05398 03165

22 05521 0212

23 05633 01035

24 05736 minus001

25 05833 minus0123

26 059 minus021



119877sh (Ω) 0 100119899 1198991 1198992

1 2



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 20 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 20 119869119903 = 04PCE 119873119875 = 100 Dep = 09 Cr = 015


SBMOCSABCIADE

jDEGOTLBOPCE

2000 4000 6000 8000 10000 120000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log


0 05 1 15 2 2510minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

SBMOCSABCIADE

jDEGOTLBOPCE

NFES









PCE

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

Rcr-IJADE

(a)

Rcr-IJADEPCE

02 04 06 08 1 12 14 16 18 20NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

(b)










minus04

minus02

0

02

04

06

08

1Cu

rren

t (A

)

(a)


minus04

minus02

0

02

04

06

08

1

Curr

ent (

A)


(b)
















119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992


minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C


7 Conclusions


minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C






5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



119881119905(V) 119868

119905(A)

1 minus02057 0764

2 minus01291 0762

3 minus00588 07605

4 00057 07605

5 00646 076

6 01185 0759

7 01678 0757

8 02132 0757

9 02545 07555

10 02924 0754

11 03269 07505

12 03585 07465

13 03873 07385

14 04137 0728

15 04373 07065

16 0459 06755

17 04784 0632

18 0496 0573

19 05119 0499

20 05265 0413

21 05398 03165

22 05521 0212

23 05633 01035

24 05736 minus001

25 05833 minus0123

26 059 minus021



119877sh (Ω) 0 100119899 1198991 1198992

1 2



CS 119873119875 = 15 119875119886 = 025ABC 119873119875 = 150

IADE 119873119875 = 100

jDE 119873119875 = 20 1205911= 1205912= 01 119865

119897= 01 119865

119906= 09

GOTLBO 119873119875 = 20 119869119903 = 04PCE 119873119875 = 100 Dep = 09 Cr = 015


SBMOCSABCIADE

jDEGOTLBOPCE

2000 4000 6000 8000 10000 120000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log


0 05 1 15 2 2510minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

SBMOCSABCIADE

jDEGOTLBOPCE

NFES









PCE

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

Rcr-IJADE

(a)

Rcr-IJADEPCE

02 04 06 08 1 12 14 16 18 20NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

(b)










minus04

minus02

0

02

04

06

08

1Cu

rren

t (A

)

(a)


minus04

minus02

0

02

04

06

08

1

Curr

ent (

A)


(b)
















119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992


minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C


7 Conclusions


minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C






5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of





PCE

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

Rcr-IJADE

(a)

Rcr-IJADEPCE

02 04 06 08 1 12 14 16 18 20NFES

10minus4

10minus3

10minus2

10minus1

100

RMSE

(log

)

times104

(b)










minus04

minus02

0

02

04

06

08

1Cu

rren

t (A

)

(a)


minus04

minus02

0

02

04

06

08

1

Curr

ent (

A)


(b)
















119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992


minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C


7 Conclusions


minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C






5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




minus04

minus02

0

02

04

06

08

1Cu

rren

t (A

)

(a)


minus04

minus02

0

02

04

06

08

1

Curr

ent (

A)


(b)
















119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992


minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C


7 Conclusions


minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C






5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of







119877sh (Ω) 538368 546219 55485443 55158863 554831601198991

19213 146512 1451017 1427801 1450923119868sd2 (120583A) 01679 038191 0749347 0738203 07493401198992


minus05

0

05

1

15

2

25

3

35

4

Curr

ent (

A)


5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 60∘C

T = 40∘C

T = 25∘C


7 Conclusions


minus05

0

05

1

15

2

25

3

Curr

ent (

A)

5 10 15 20 250Voltage (V)

G = 1000Wm2

T = 55∘C

T = 70∘C

T = 40∘C

T = 25∘C






5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


5 10 15 20 25 30 350Voltage (V)

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)

G = 1000Wm2

T = 50∘C

T = 75∘C

T = 25∘C



5 10 15 20 250Voltage (V)

minus05

0

05

1

15

2

25

3

35

Curr

ent (

A)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C





5 10 15 20 250Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2


minus05

0

05

1

15

2

25

3

Curr

ent (

A) T = 25

∘C


5 10 15 20 25 30 350Voltage (V)

G = 1000Wm2

G = 800Wm2

G = 600Wm2

G = 400Wm2

G = 200Wm2

T = 25∘C

minus1

0

1

2

3

4

5

6

7

8

9

Curr

ent (

A)



















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of















Competing Interests


Acknowledgments




119866 = 1000Wm2

119868ph (A) 3455710 2596880 8221126119868sd (120583A) 000288916 2789916 000400505119877119904(Ω) 0495620 0798689 0298004


119866 = 800Wm2

119868ph (A) 2764556 2077492 6576922119868sd (120583A) 000287531 2776931 000399302119877119904(Ω) 0495699 0799113 0298074


119866 = 600Wm2

119868ph (A) 2073429 1558121 4932673119868sd (120583A) 000287555 27814890 000400713119877119904(Ω) 0495743 0798844 0297980


119866 = 400Wm2

119868ph (A) 1382294 1038787 3288464119868sd (120583A) 000287087 2768818 000398943119877119904(Ω) 0495802 0799834 0298126


119866 = 200Wm2

119868ph (A) 0691135 0519409 1644224119868sd (120583A) 000289179 2758105 000399516119877119904(Ω) 0495188 0801411 0298241



References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of












































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

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