Application of Artificial Bee Colony in Model Parameter Identification of Solar Cells

Transcription

1 Energies 015, 8, ; doi: /en Aricle OPEN ACCESS energies ISSN Applicaion of Arificial Bee Colony in Model Parameer Idenificaion of Solar Cells Rongjie Wang 1,, *, Yiju Zhan 3 and Haifeng Zhou 1 1 Marine Engineering Insiue, Jimei Univerisy, 176 Shigu road, Jimei Disric, Xiamen 36101, China; jmuwrj@163.com Fujian Provincial Key Laboraory of Naval Archiecure and Ocean Engineering, 176 Shigu road, Jimei Disric, Xiamen 36101, China 3 School of Engineering, Sun Ya-sen Universiy, Panyu Disric, Guangzhou , China; yjzhan@zd100com.cn * Auhor o whom correspondence should be addressed; roger81107@163.com; Tel.: ; Fax: Academic Ediors: Tapas Mallick and Senhilarasu Sundaram Received: 8 April 015 / Acceped: 0 July 015 / Published: 4 July 015 Absrac: The idenificaion of values of solar cell parameers is of grea ineres for evaluaing solar cell performances. The algorihm of an arificial bee colony was used o exrac model parameers of solar cells from curren-volage characerisics. Firsly, he bes-so-for mechanism was inroduced o he original arificial bee colony. Then, a mehod was proposed o idenify parameers for a single diode model and double diode model using his improved arificial bee colony. Experimenal resuls clearly demonsrae he effeciveness of he proposed mehod and is superior performance compared o oher compeing mehods. Keywords: arificial bee colony; solar cell; parameers idenificaion; single diode model; double diode model 1. Inroducion Solar energy is one of he mos promising renewable sources ha are currenly being used worldwide o conribue o meeing rising demands of elecric power. Phoovolaic (PV) is capable of

2 Energies 015, direcly convering solar energy o elecriciy in a quie environmen wihou polluing he amosphere. I has been repored ha PV is he fases growing power-generaion echnology in he world, wih an annual average increase of 55% beween 008 and 014 [1]. PV sysems comprise of differen pars cenered around a solar panel ha ypically has arrays of inerconneced solar cells. The solar cell convers he energy of phoons coming from he sunligh direcly ino elecrical energy on he basis of phoovolaic effec. Formulaing an equaion ha describes he performance of phoovolaic cells under illuminaion or in dark condiions, one from which he cells physical parameers can be resored, is of grea value in he field of phoovolaic engineering. The model of a solar cell is used o predic he behavior of a real solar cells under various environmenal condiions and hereafer o generae curren-volage (I-V) and power-volage (P-V) characerisic curves. The modeling of PV cells consiss of wo seps: he mahemaical model formulaion and he idenificaion of heir parameer values. There are wo widely used nonlinear equivalen circui models for solar cells: single diode model and double diode model [,3]. The single diode model conains five unknown parameers while he double diode model has seven unknown parameers. Accurae idenificaion of he parameers plays an imporan role in solar cell simulaion, performance evaluaion, design, opimizaion and conrol. Therefore, parameer deerminaion wih he help of a capable opimizaion echnique is necessary. During he las decade, several idenificaion mehods have been repored o approximae differen parameers of solar cells. Generally, he idenificaion mehods can be caegorized ino analyical mehods, linear sysem idenificaion mehods and meaheurisic search mehods. Dependency on he accuracy of hese key poins is a major deficiency of he analyical approach [4]; he measured daa usually conains noise due o device inaccuracy and oher elecrical disurbances. By uilizing he mapping of ransfer funcion in [5], he diode model is convered as an equivalen oupu of a dynamic sysem. Correspondingly, he dimension of he parameer space is reduced from five o one. The one parameer is hen idenified by a simple inegral-based linear square. By performing a separaion of he independen variables from he dependen ones among he five parameers of one diode model, a reduced form of he five parameer model has been obained in [6]. Compared wih oher mehods, he mehods in [5,6] have simpler operaion requiremens and higher accuracy. Unforunaely, [6] only discussed abou he parameers idenificaion of one diode model. The disadvanage of mehod in [5] ha i requires he knowledge of he full I-V curve daa. In addiion, many meaheurisic mehods were inroduced in relaed lieraures, such as he paricle swarm opimizaion (PSO) [7], he geneic algorihm (GA) [8], he differenial evoluion (DE) algorihm [9] and ec. Alhough heurisic mehods presen a higher probabiliy of obaining a global soluion in comparison wih analyical ones, hey have imporan limis. In case of GA and PSO, hey mainain a rend ha concenraes oward local opima, since heir eliis mechanism forces premaure convergence [10,11]. Such a behavior becomes worse when he opimizaion algorihm faces muli-modal funcions. The resuls depend on he conrol parameers of he DE algorihm and an inappropriae choice of hese parameers may resul in he DE failing o converge or in a very slow convergence o he global opimal poin [1]. Parameer idenificaion of PV solar cells and modules is sill a challenging problem which requires ha he he obained physical parameers mach well wih realiy. The non-lineariy and muli-modal naure of he solar cells require a high performance opimizaion mehod.

3 Energies 015, Arificial bee colony (ABC) is a new opimizaion algorihm developed by Karaboga in 005 [13]. I has been used o find an opimal soluion in numerical opimizaion problems. This algorihm is inspired by he behavior of honey bees when seeking a qualiy food source. The performance of ABC algorihm has been compared wih oher opimizaion mehods. The comparison resuls showed ha ABC can produce a more opimal soluion and, hus, i is more effecive han he oher mehods in several opimizaion problems [14 16]. However, hese ABC algorihms converge slowly, especially a he middle and las sages of he search process. The main reason is ha ABC is good a exploraion bu poor a exploiaion. An ideal opimizaion algorihm should properly balance exploraion and exploiaion during he search process. In order o balance he exploraion and exploiaion of ABC during he search process, we propose o make major changes by inroducing he bes-so-far mechanism o generae a new soluion wih beer qualiy and conrol he diversiy of generaions. In his paper, he improved ABC is applied o idenify he opimal parameers of solar cells. The paper is organized as follows. Secion describes he mahemaical formulaions of he problem. Secion 3.1 provides he descripion of he employed arificial bee colony algorihm. Secion 3. presens he ABC algorihm in solving he parameers idenificaion process of solar cell models. Finally, he performance of he proposed mehod is numerically evaluaed in Secion 4 while Secion 5 is devoed o he concluding remarks.. Problem Formulaion.1. Single Diode Model Figure 1 shows he equivalen circui for single diode model, he cell oupu curren I is compued by qv [ RI s ] VRI s I Iph IL{exp 1} akt R where k, T and q are he Bolzmann consan, emperaure, and magniude of charge on an elecron, respecively. V and IL are he oupu volage of cell and reverse sauraion curren of he diode, respecively. The resisance Rsh in parallel wih he diode represens he shun resisance ha can occur in real solar cells across he surfaces, a pin holes in he p-n juncions, or a grain boundaries. Ish is he Rsh curren. The series resisance Rs accouns for all volage drops across he ranspor resisances of he solar cell and is connecions o a load. The curren source Iph is he phoocurren from he illuminaion for he sun. a is he non-physical diode idealiy facor. We denoe θ1 by θ1 = [Rsh, Rs, IL, Iph, a] in his aricle. I is clear ha for such a model here is θ1 o be esimaed. sh (1) Figure 1. Single diode model of solar cells.

4 Energies 015, Double Diode Model Figure shows he equivalen circui for double diode model, he cell oupu curren I is compued by qv ( RI s ) qv ( RI s ) VRI s I Iph IL1{exp 1} IL{exp 1} akt 1 akt Rsh () where IL1 and IL are he diffusion and sauraion curren, respecively. a1 and a are he diffusion and recombinaion diode idealiy facors, respecively. In single diode model, he diffusion and recombinaion currens are linearly independen, boh currens are ofen combined ogeher under he inroducion of a non-physical diode idealiy facor a. Equaion () has seven unknown parameers (Rsh, Rs, IL1, IL, Iph, a1, a), and denoe θ as θ = [Rsh, Rs, IL1, IL, Iph, a1, a]. Figure. Double diode model of solar cells. Consequenly, he objecive of parameer idenificaion of PV solar cells is o idenify he θ1 in a single diode model or θ in a double diode model from he I-V daa measuremens. 3. Parameer Idenificaion of Solar Cells Using ABC 3.1. Arificial Bee Colony Algorihm The ABC algorihm is inspired by he behavior of honey bees when seeking a qualiy food source. The bees are caegorized ino hree groups: employed bees, onlooker bees, and scou bees. Employed bees are responsible from exploiing he necar sources already explored, and hey give informaion o he oher waiing bees in he hive abou he qualiy of he food source which hey are exploiing. Onlooker bees wai in he hive and esablish a food source o exploi depending on he informaion shared by he employed bees. Scous search he environmen in order o find a new food source depending on an inernal moivaion, exernal clues, or randomly. In ABC algorihm, he posiion of a food source represens a possible soluion o he opimizaion problem. To enhance he exploiaion and exploraion processes, we propose o make major changes by inroducing he bes-so-far mehod. The deails of he proposed algorihm are described as follows. In he firs sep, randomly disribued iniial food source posiions are generaed. Similarly wih oher opimizaion algorihms, random values beween he lower and he upper boundaries of

5 Energies 015, he parameers are assigned for he parameers of soluions. The process can be represened by Equaion (3). θ(, ld) θmin ( d) rand(0,1)[ θmax ( d) θ min ( d)] (3) where l = 1,,, NF, d = 1,,, D, NF is he number of candidae soluion, D is he dimension of soluion. θmax(d) and θmin(d) are upper and lower bound of candidae soluion d-h dimension, respecively. Afer iniializaion, he populaion is evaluaed and is subjeced o repeaed cycles of he search processes of he employed bees, he onlooker bees and scou bees. In employed bee phase, he posiion of he new food source is calculaed by Equaion (4). θ (, ) (, ) [ (, ) (, )] EB ld θ ld ld θ ld θ rd (4) where θeb is a new soluion in employed bee phase. φld is a random number beween [ 1 1]. r is uniformly disribued random ineger number in he range [1 NF], r l. Afer producing a new soluion by Equaion (4), he algorihm applies he greedy selecion rule o memorize he new candidae soluion by forgeing he old one or keeps he old soluion. The old soluion in he employed bee s memory will be replaced by he new candidae soluion if he new posiion has a beer finess value. In he nex sep, employed bees will reurn o heir hive and share he finess value of heir new food sources wih he onlooker bees, and hen onlooker bees use he informaion from all employed bees o make a decision on a new soluion. This process is simulaed by he procedure given in Equaion (5). θ OB θbes ( d) ld[ θ( l, d) θ( r, d)] pl p (, ld) θ( r1, d) ld[ θ( l, d) θ( r, d)] pl p (5) where θob is a new soluion in onlooker phase, θbes is he bes-so-far soluion. r1 and r are ineger number randomly chosen in [1 NF], r1 r l. l1 p NF l1 N Fl () p l l 1,,, N NF Fl () p F l, pl is calculaed by Equaion (6). where F(l)is he finess funcion of l-h candidae soluion. In he hird sep, any food source posiion ha does no improve he finess value will be abandoned and replaced by a new posiion ha is deermined by a scou bee. This helps avoid subopimal soluions. The new soluion by he scou bee will be calculaed by Equaion (7). F θsb(, ld) θbes ( d) ld[ θ(, ld) θ ( rd, )] (7) where θsb is a new soluion in scou bee phase. If he non-improvemen number kcoun(l) of he l-h soluion exceeding he predeermined number klimi, he abandoned soluion θ is replaced wih θsb. For clariy, he opimizaion mechanism of he improved ABC algorihm in his aricle and original ABC algorihm in [13] are shown as Figure 3, respecively. The line wih arrow and doed line wih arrow represen single- and muli-ieraion. I is obvious ha our algorihm has a beer convergence speed han he original ABC algorihm. The pseudo-code of he improved ABC algorihm is illusraed in Table 1. (6)

6 Energies 015, Figure 3. Opimizaion mechanism of differen ABC algorihms: (a) original ABC algorihm; (b) improved ABC algorihm. Table 1. Pseudocode of he improved ABC algorihm. Iniialize Phase: se maximum number of ieraion k max, k limi, N F, D; Generae iniial θ(l, d) by (3), l = 1,,, N F, d = 1,,, D. while (erminaion crierion is me.) Employed Bee Phase for l=1 o NF Calculae θeb( ld, ) by (4). Calculae finess funcion JEB( l) of θeb( l). if JEB( l) beer han J( l), θ( l)= θeb( l), kcoun ( l)= 0; else kcoun ( l)= kcoun ( l)+1. end Selecing he bes-so-far soluion θbes from θ, and calculae p l by (6); Onlooker Bee Phase for l=1 o NF Calculae new θob( l) by (5). Calculae finess funcion JOB( l) of θob( l). if JOB() l beer han J(), l θ()= l θob(), l kcoun ()= l 0; else kcoun ()= l kcoun ()+1. l end Scou Bee Phase for l=1 o NF if kcoun ( l) klimi Calculae new θsb( l) by (7). Calculae finess funcion JSB( l) of θsb( l). if JSB( l) beer han J( l), θ( l)= θsb( l), kcoun ( l)= 0. end ieraion = ieraion + 1 end

7 Energies 015, Parameer Idenificaion of Solar Cells Using Arificial Bee Colony Algorihm We considered he problem of parameer idenificaion as an opimizaion problem where he parameer se is sough ha produces he bes approximaion o he I-V measuremens obained by he rue solar cell. An objecive funcion in Equaion (8) was defined o evaluae he maching qualiy beween a candidae parameer se and he experimenal daa. where, for single diode modal, θ = θ1 and J(θ) is described as θ arg min J ( θ ) (8) 1 qv ( RI s ) V RI s θ ph L N akt (9) Rsh J( ) I I I {exp 1} here, he subscrip of V and I is he discree ime index, N is he numbers of sampling poin in ime-domain. Whereas for he double diode model such funcion is described as 1 qv ( RI s ) qv ( RI s ) V RI s J( θ ) I Iph IL1{exp 1} IL{exp 1} N akt 1 akt R (10) sh Here θ = θ. Figure 4. Flowchar of he proposed mehod.

8 Energies 015, In Equaions (9) and (10), he values of V and I are experimenally colleced from he solar cell. The parameer idenificaion is a process ha minimizes he difference beween he measured daa and he calculaed curren by adjusing he model parameers θ. I is clear ha he smaller he J(θ), he more accurae he model is. The proposed approach of parameer idenificaion of PV solar cells encodes he parameers of he solar cell as a candidae soluion. Therefore, each food source uses θ1 or θ as decision variables wihin he opimizaion algorihm. For clariy, he flowchar in Figure 4 illusraes he proposed mehod which is used o idenify he opimal parameers of he solar cell models. 4. Experimenal Secion In his secion, firsly six commonly used benchmark funcions are used o es he performance of he proposed improved ABC algorihm. Then, he I-V characerisic of a diameer commercial silicon solar cell is used o evaluae he efficiency of he proposed parameer idenificaion mehod. All he experimens in his paper were run on he same hardware (Inel Core i3-310 Quad wih.1 GHz CPU and GB memory) Numerical Experimens and Resuls Unimodal and mulimodal benchmark funcions as shown in Equaions (11) (16) were used in his experimen. The aim is o minimize fi(β), I = 1,,, 6. We validae he performance of improved ABC algorihm (IABC) by comparing i wih he origin ABC algorihm in [14], DE in [1], and PSO in [16]. The conrol parameers in hese algorihms are given in Table. Figure 5 shows he comparison of he convergence speed of four differen opimizaion algorihms. Table 3 presens he mean and sandard deviaion of he 0 runs of he four opimizaion algorihms on he six funcions. The Mean column is he average oupu values of benchmark funcions. The Sd column shows he sandard deviaion of he resuls. Moreover, Bes, Median and Wors of soluions obained in he 0 runs by each algorihm. Sphere funcion: D f ( β 1 ) d 1 d (11) where he range of β is [ ] D, D = 30. The global minimum of he Sphere funcion is 0, and is characerisic is unimodal and separable. Griewank funcion: D 1 ( ) cos( ) D d f β d d 1 d 1 d (1) where he range of β is [ ] D, D = 30. The global minimum of he Griewank funcion is 0, and is characerisic is mulimodal and non-separable. Ragsrigin funcion: D d 10cos( d ) f3( β ) 10 d 1 (13)

9 Energies 015, where he range of β is [ ] D, D = 4. The global minimum of he Ragsrigin funcion is 0, and is characerisic is mulimodal and separable. Figure 5. Convergence curve of difference opimizaion algorihms: (a) Sphere funcion; (b) Griewank funcion; (c) Ragsrigin funcion; (d) Rosenbrock funcion; (e) Ackley funcion; (f) Schaffer funcion. Table. Conrol parameers of opimizaion algorihm. Algorihm IABC ABC DE PSO Parameers Populaion size = 30 k limi = 5 Populaion size = 30 Muaion facor = Crossover consan = 0.5 Populaion size = 30 Learning facors c 1 = c = Ineria weigh aken from 0.9 o 0.4

10 Energies 015, Table 3. Comparison of esing resul of differen opimizaion algorihms. Benchmark Funcion IABC Algorihm ABC Algorihm DE Algorihm PSO Algorihm Sphere funcion Griewank funcion Ragsrigin funcion Rosenbrock funcion Ackley funcion Schaffer funcion Rosenbrock funcion: Bes Median Wors Mean Sd Bes Median Wors Mean Sd Bes Median Wors Mean Sd Bes Median Wors Bes Median Bes Median Wors Bes Median Bes Median Wors Mean Sd D β ) [100( ) ( d d d 1 (14) d 1 f4 ( )] 1 where he range of β is [ 30 30] D, D = 30. The global minimum of he Rosenbrock funcion is 0, and is characerisic is unimodal and non-separable. Ackley funcion: D D 5( ) 0 exp(1) 0exp[ 0. (1/ ) d ] exp[(1/ ) cos( d)] d1 d1 f β D D (15) where he range of β is [ 3 3] D, D =. The global minimum of he Ackley funcion is 0, and is characerisic is mulimodal and non-separable.

11 Energies 015, Schaffer funcion: f D sin ( d ) 0.5 d 1 6( β ) 0.5 D (16) [ ( d )] d 1 where he range of β is [ ] D, D =. The global minimum of he Schaffer funcion is 0, and is characerisic is mulimodal and non-separable. In Table 3, we compare he resuls using he same number of ieraions. The Mean is relaively low, which implies faser convergence speed among experimenal runs. The Sd is relaively low, which implies higher consisency among experimenal runs. The Bes, Median and Wors are relaively low, which implies a beer qualiy soluion han oher algorihms among experimenal runs. The resuls in Figure 1 and Table 3 ha indicaes ha he IABC can converge o he opimal soluion more quickly on almos all benchmark funcions when i is compared wih he oher algorihms. The resuls show he proposed algorihm gives beer soluions han oher algorihms in all cases of benchmark funcions. 4.. Parameer Idenificaions and Resuls In order o prove he performance of he proposed mehod, i has been esed using he I-V characerisic of a 57 mm diameer commercial silicon solar cell [17,18]. The experimenal daa has been colleced from he sysem under one sun (1000 W/m ) in sandard es condiions. Table 4 repors experimenal values of volage and curren. The experimen presens he resuls of five differen algorihms when hey are employed o idenify he cell parameers considering he single and double diode models. For parameer idenificaion, he conrol parameers for IABC, ABC, DE and PSO are he same as hose in Table. In addiion, he conrol parameers arificial bee swarm opimizaion (ABSO) in [19] is he same wih hose in [19] as given by Equaion (17). During he opimizaion process, he objecive funcion is minimized wih respec o he parameers range. The upper and lower bounds of he parameers are shown in Table 5. The idenified parameers are employed o reconsruc he I-V characerisic. The relaive error e() in Equaion (17) is used o furher confirm he accuracy of he idenified model. Figures 6 and 7 illusrae he resuls comparison of four mehods for boh he single and he double diode models. c1max cmax.5 c1min cmin 1.5 αmax 0.03 (17) αmin 0.0 ne 5 e () I I() c (18) where Ic() is a curren calculaed by he respecive model. The smaller e() is, he higher accuracy he idenified model demonsraes.

12 Energies 015, Table 4. Terminal I-V measuremens. Measuremen Measured V Measured I Table 5. Upper and lower range of he solar cell parameers. Parameers Lower Upper R s /Ω R sh /Ω I ph /A 0 1 I L, I L1, I L /A 0 1 a, a 1, a 1 Figures 6 and 7 are he average of 0 independen experimens. Figures 6a and 7a indicae ha he I-V characerisic found by IABC is in good agreemen wih he experimenal daa. The smaller e() value in Figures 6 and 7 mean ha our proposed mehod provides beer accuracy. Comparing he proposed mehod oucomes wih oher mehods resuls in he above experimens, he proposed mehod clearly ouperformed oher compeing mehods.

13 Energies 015, Figure 6. The comparison of he resuls of four mehods for he single diode model: (a) comparison beween he I-V characerisics generaed using our proposed mehod and he measured daa; (b) relaive error for each measured value based on he idenified parameers using IABC algorihm; (c) relaive error for each measured value based on he idenified parameers using ABC algorihm; (d) relaive error for each measured value based on he idenified parameers using DE algorihm; (e) relaive error for each measured value based on he idenified parameers using PSO algorihm; (f) relaive error for each measured value based on he idenified parameers using ABSO algorihm.

14 Energies 015, Figure 7. The comparison of he resuls of four mehods for he double diode model: (a) comparison beween he I-V characerisics generaed using our proposed mehod and he measured daa; (b) relaive error for each measured value based on he idenified parameers using IABC algorihm; (c) relaive error for each measured value based on he idenified parameers using ABC algorihm; (d) relaive error for each measured value based on he idenified parameers using DE algorihm; (e) relaive error for each measured value based on he idenified parameers using PSO algorihm; (f) relaive error for each measured value based on he idenified parameers using ABSO algorihm.

15 Energies 015, To furher invesigae he qualiy of he idenified parameers, we pu hem ino he power vs. volage (P-V) characerisic which is reconsruced. The P-V characerisic resuled from he idenified model along experimenal daa is shown in Figures 8 and 9, respecively. The similariy beween he model resuls and he performance of he real sysem proves he superioriy of he proposed mehod. Figure 8. Comparison beween he P-V characerisics resuling from he experimenal daa and he single diode model. Figure 9. Comparison beween he P-V characerisics resuling from he experimenal daa and he double diode model. Recenly, a deerminisic approach was used o solve he problem of parameer idenificaion for solar cells, such as [5,6,0], ec. Firsly, he comparison beween he proposed mehod, he mehod in [0] (see.d) and he mehod in [5] is made in erms of compuaional cos. The compuaional cos of he proposed mehod is as follows: n sep [5 ( N F N s )(15NN F 8)] imes addiional and/or subracion operaion for single diode model, n sep [7 ( N F N s )(0NN F 1)] imes addiional and/or subracion operaion for double diode model, and n sep [( N F N s )(0N 7)] imes muliplicaion and/or division operaion for single diode model, n sep [( N F N s )(0N 9)] imes muliplicaion and/or division operaion for double diode model, noe ha nsep is he number of funcion evaluaions. The compuaional cos of he mehod in [0] (see.d) is as follows: 831( nguess nsep ) imes addiional and/or subracion

16 Energies 015, operaion, and 0 44( nguess nsep ) imes muliplicaion and/or division operaion. Here n Guess is he evaluaion number which deermines he iniial value of Rs and a. The compuaional cos of he mehod in [5] is as follows: 0 n (8N 18) imes addiional and/or subracion operaion, and sep nsep N imes muliplicaion and/or division operaion, and 10 9nsep 40 ( 9) imes inegraion operaion. In he sandard condiion, he opimal parameer value of hree differen mehods is summarized in Table 6. The nsep of he proposed mehod are 603 and 93 for he single and double diode models, respecively. The nsep of he proposed in [5] is 3 while he nguess and nsep of he mehod in [0] are 147 and 178. Noe ha he value of nguess and nsep are differen from [0] because we and [0] chose differen iniial values for he independen parameers Rs and a. Table 6. Idenified parameers afer applying differen mehods. Parameers The Proposed Mehod Single Diode Model Double Diode Model The Mehod in [0] The Mehod in [5] R s /Ω R sh /Ω I ph /A I L (or I L1 )/A I L /A a (or a 1 ) a J(θ) In he subsequence, we made a comparison beween he proposed mehod, he mehod in [0] (see.d) and he mehod in [5] by conducing an experimen under nonsandard es condiions. The Rmse index defined by Equaion (19) is used o measure accuracy of differen mehods. The experimen resuls of one diode model was summarized in Table 7, while he experimen resuls of wo diode models was summarized in Table 8. 1 Rmse I I N [ c( )] (19) Table 7. Resuls obained by differen mehods for he single diode model in nonsandard es condiions. Tesing Temperaure Mehods The Mehod in [0] The Proposed Mehod 5 C C C C

17 Energies 015, Table 8. Resuls obained by differen mehods for he double diode model in nonsandard es condiions. Tesing Temperaure Mehods The Mehod in [5] The Proposed Mehod 5 C C C C The resul comparison for single diode model is shown in Table 7. The Rmse is relaively low, which also implies higher accuracy among experimens. The Rmse of he proposed mehod is slighly bigger han he resul of he mehod in [0] a T = 5 C, T = 50 C and T = 75 C, and only smaller han he resul of he mehod in [0] a T = 100 C. From he resuls comparison shown in Table 7, he mehod in [0] yields he beer resul in erms of Rmse han he proposed mehod in some cases. In general, [0] has benefi in ha hey uilize reduced forms o decrease he dimension of he parameer space. The mehod in [5] furher reduces he dimension of he parameer space o one. However, he mehod in [5] usually reurns precise resuls only when a high number of poins on he I-V curve are available. I may be why he Rmse of he proposed mehod is smaller han he resul of he mehod in [5] shown in Table 8. The mehod in [0] has deficiencies: (1) a differen soluion can be achieved if differen reduced forms are used; () no direcly applicable o muli-diode model parameer idenificaion due o he limiaion of Lamber W funcion formalism. The ABC algorihm is very suiable for he search for a global opimal soluion, such as model parameer idenificaion of solar cells in his paper. Unique soluions are achieved if he algorihm converges o he same value, so he firs drawback of [0] can be avoided. I can also be used for he muliple-diode model. To examine he noise impacs for he disinc performance of he proposed mehod, in he las experimen, he measured daa V is added wih varied whie Gaussian noise of varying SNR (signal o noise raio, SNR) from 10 o 35 db. Moreover, we compared he single diode model wih he double diode model. The esimae performance is evaluaed by Equaion (19). Figure 10 shows he comparison of resuls of wo models. Figure 10. Robusness of he wo differen models agains noise.

18 Energies 015, According o he resul in Figure 10, he single diode model demonsraes a beer performance for noise robusness han he double diode model when SNR is below 15 db. However, he double diode model displays beer performance for noise robusness han he single diode model when SNR exceeds 15 db. 5. Conclusions In his paper, an improved arificial bee colony algorihm had been proposed o idenify he parameers in he complex nonlinear solar cell models. We propose o make major changes by inroducing he bes-so-far mechanism o generae a new soluion wih beer qualiy and conrol he diversiy of generaions. In he numerical benchmark experimens, i is shown ha improved ABC can effecively find beer soluions han he original ABC and he oher wo commonly used algorihms. Afer he validaion of he algorihm, improved ABC had been employed o idenify he unknown values of solar cell parameers from he experimenally measured I-V characerisics. For solar cell models, he experimen resuls of double and single models show ha he proposed mehod gives comparable performance o oher convenional mehods. As a resul, he proposed mehod can be a good candidae o solve he idenified problems wih parameers of complex nonlinear solar cell models. Acknowledgmens This work is suppored by he Naional Naural Science Foundaion of China ( ), he Foundaion of Fujian Educaion Commiee for Disinguished Young Scholars (JA14169), he Scienific Research Foundaion of Jimei Universiy (ZQ013001, ZC01301) and Open Projec of Arificial Inelligence Key Laboraory of Sichuan Province (014RYJ03). Auhor Conribuions Rongjie Wang and Haifeng Zhou conceived and developed he ideas behind he research. Rongjie Wang carried ou he performance analysis and simulaions, and wroe he paper under supervision of Yiju Zhan. Conflics of Ineres The auhors declare no conflic of ineres. References 1. WHO. 014 Global Saus Repor. Available online: hp:// Resources/GSR/014/GSR014CN.pdf (accessed on 1 January 015).. Han, L.; Koide, N.; Chiba, Y. Modeling of an equivalen circui for dye-sensiized solar cells. Appl. Phys. Le. 004, 84, Askarzadeh, A.; Rezazadeh, A. An Innovaive global harmony search algorihm for parameer idenificaion of a PEM fuel cell model. IEEE Trans. Ind. Elecron. 01, 59, Saleem, H.; Karmalkar, S. An analyical mehod o exrac he physical parameers of a solar cell from four poins on he illuminaed J-V curve. IEEE Elecron Dev. Le. 009, 30,

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