SOFT COMPUTING OPTIMIZATION TECHNIQUES FOR SOLAR PHOTOVOLTAIC ARRAYS

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1 ARPN Jounal of Engneeng and Appled Scences Asan Reseach Publshng Netwok (ARPN). All ghts eseved. SOFT COMPUTING OPTIMIZATION TECHNIQUES FOR SOLAR PHOTOVOLTAIC ARRAYS Ramapabha R. and Mathu B. L. Depatment of Electcal and Electoncs Engneeng, SSN College of Engneeng, Chenna, Tamlnadu, Inda E-Mal: ABSTRACT Ths pape pesents the soft computng optmzaton technques to addess the Maxmum Powe Pont Tackng (MPPT) of Sola Photovoltac (SPV) aay unde patal shaded condtons. Patal shaded SPV modules poduce seveal local maxmum powe ponts, whch makes the tackng of the Global Maxmum Powe Pont (GMPP) a dffcult task. Most of conventonal tackng methods fal to wok popely unde patal shaded condtons. Methods poposed by some authos tack the GMPP wth some lmtatons. In ths pape, thee dffeent soft computng technques lke Genetc algothm (GA), Dffeental evoluton (DE) and Patcle Swam optmzaton (PSO) technques have been appled fo GMPP tackng. The pefomances of these technques ae compaed n espect of the tackng tme and accuacy. Keywods: sola photovoltac aay, soft computng methods, optmzaton, global maxmum powe pont tackng, DE, PSO. INTRODUCTION In ecent yeas ntellgence technques have been used wdely n the Maxmum Powe Pont Tackng (MPPT) pocess of SPV systems. Especally unde non unfom and patally shadng condtons, whee thee s a dffculty to tack tue GMPP n the pesence of local MPPs. (Chen et al., 200). Theefoe, fo satsfactoy esults, all envonmental condtons (especally nstantaneous clmate changes and patal shadng) must be taken nto account n the desgn pocess of MPPT. Atfcal ntellgence can poduce appopate solutons fo these condtons. Atfcal ntellgence-based MPPT algothms ae the most advantageous systems n tems of electcal effcency. In ths pape thee dffeent optmzaton technque vz; Genetc Algothm (GA), Dffeental Evoluton (DE) and Patcle Swam Optmzaton (PSO) technques have been used fo GMPP tackng. These technques ae compaed n espect of the tackng tme and accuacy. the electcal chaactestcs of SPV aay wth bypass dodes unde patal shaded condtons. Fgue-. Fve paamete model of SPV cell wth bypass dode. PROBLEM FORMULATION Necessty of optmzaton algothm The standad one dode o 5 paamete model used to epesent the SPV module s shown n Fgue-. The modelng and smulaton of SPV aay unde patal shaded condtons dscussed by Ramapabha and Mathu, 2009; Patel and Agawal, 2008a; Patel and Agawal, 2008 s used n ths pape. The patal shade has moe mpact on sees connected modules. To avod the stess on low llumnated cells, bypass dodes ae connected n ant paallel wth a module/goup of cells. The ntoducton of bypass dodes ntoduces multple peaks n P-V chaactestcs. The smulaton of sees connected SPV aay chaactestcs unde patal shaded condton wth bypass dode s shown n Fgue-2. The model s developed usng MATLAB M-fle. The detaled explanaton of the effect of bypass dodes n the chaactestcs has been dscussed by Ramapabha and Mathu, 2009 and Slveste et al., Fgue-2 shows Fgue-2. Chaactestcs of sees connected SPV modules unde patal shaded condton. Fom Fgue-2, t s obseved that P-V chaactestc has multple peaks due to patal shadng (Patel and Agawal, 2008a). Among the multple peaks one s GMPP and othes ae local peak powe ponts. In ths stuaton the conventonal MPPT algothm could fal to detemne the actual GMPP o even taps nto one of the local peaks. Theefoe, consdeable amount of possble 70

2 ARPN Jounal of Engneeng and Appled Scences Asan Reseach Publshng Netwok (ARPN). All ghts eseved. SPV powe s not utlzed. Hence the powe should be optmzed to havest the maxmum powe poduced by SPV aay. Defnton of objectve functon A Nonlnea optmzaton poblem can be stated n mathematcal tems as gven n equaton (). Fnd ( y, y,... ) Y = () 2 yn such that F(Y) s mnmum o maxmum subject to the constant and bounds ae gven by equaton (2). g j (Y) 0, j =,2,..m and y j L y y j U, j =,2...n (2) whee F s the objectve functon to be mnmzed o maxmzed, y j s ae vaables, g j s constant functon, y L j and y U j ae the lowe and uppe bounds on the vaables. In ths wok the objectve functon consdeed s F(Y) = Maxmzaton of SPVA powe, P PV The vaable y = SPVA cuent, I PV. The constant s I PVmax I PV I PVmn. Hee, y U j = I PVmax. Genetc algothm GA based optmzaton (Goldbeg, 989) s an adaptve heustc seach technque that nvolves geneaton, systematc evaluaton and enhancement of potental desgn soluton untl a stoppng cteon s met. Thee ae thee fundamental opeatos nvolved n the seach pocess of a genetc algothm: selecton, cossove and mutaton. Selecton s a pocess whch chooses a chomosome fom the cuent geneaton s populaton fo ncluson n the next geneaton s populaton accodng to the ftness. Cossove opeato combnes two chomosomes to poduce a new chomosome (offspng). Mutaton opeato mantans genetc dvesty fom one geneaton of populaton to the next and ams to acheve some stochastc vaablty of GA n ode to get a qucke convegence. Dffeental evoluton algothm DE algothm s a populaton based algothm lke genetc algothms usng cossove, mutaton and selecton opeatos. DE uses the dffeences of andomly sampled pas of object vectos to gude the mutaton opeaton nstead of usng the pobablty dstbuton functon as othe evolutonay algothms (Pce at al., 2005). DE based optmzaton pocess s descbed below: A. Intalzaton DE stats wth a populaton of M P M-dmensonal seach vaable vectos. The th vecto of the populaton at the cuent geneaton s gven by [ y (t), y (t), y (t)...y (t)] Y (t) =,,2,3, M (3) Thee s a feasble numecal ange fo each seach-vaable, wthn whch value of the paamete should le fo bette seach esults. Intally the poblem paametes o ndependent vaables ae ntalzed n the feasble numecal ange. If the j th paamete of the gven poblem has ts lowe and uppe bound as L U yj and y j espectvely, then the j th component of the th populaton membes s ntalzed as gven by equaton (4). y,j L j U j (0) = y + and(0,) (y y ) (4) B. Mutaton In each teaton, to change the populaton membe Y (t), a Dono vecto V (t) s ceated. To ceate V (t) fo each th membe, thee othe paamete vectos (,2, 3 vectos) ae selected n andom fashon fom the cuent populaton. A scala numbe F scales the dffeence of any two of the thee vectos and the scaled dffeence s added to the thd one to obtan the dono vecto V (t). The mutaton pocess fo j th component of each vecto s expessed by equaton (5). v,j (t + ) = y (t) + F (y (t) y (t)) (5),j 2,j L j 3, j The method of ceatng dono vecto demacates between vaous DE schemes. Pce and ston (2005) have suggested ten dffeent mutaton stateges. The above mutaton stategy s efeed as DE/and/. Ths scheme uses a andomly selected vecto Y and only one weghted dffeence vecto F (Y2 Y3) s used to petub t. In ths wok mutaton stategy DE/best/ s used. In ths scheme the vecto to be petubed s the best vecto of the cuent populaton and the petubaton s caused by sngle dffeence vecto as gven by equaton (6). v,j (t + ) = y (t) + F (y (t) y (t)) (6) best,j 2, j C. Cossove To ncease the potental dvesty of the populaton a cossove opeato s used. DE uses two knds of coss ove schemes namely Exponental and Bnomal. In ths wok bnomal cossove s used. In ths cossove scheme, the cossove s pefomed on each of the Q vaables wheneve a andomly pcked numbe between 0 and s wthn the cossove (CR) value. The scheme may be outlned as gven by equaton (7). u,j(t) = v, j(t) f (and(0,)) < CR (7) = (t) else y, j In ths way fo each tal vecto Y (t) an offspng vecto (t) s ceated. U D. Selecton Selecton opeato s used to detemne whch one of the taget vecto and the tal vecto wll suvve n the next geneaton. DE nvolves the Dawnan pncple of Suvval of the fttest n ts selecton pocess. The 7

3 ARPN Jounal of Engneeng and Appled Scences Asan Reseach Publshng Netwok (ARPN). All ghts eseved. selecton pocess may be outlned as gven by equaton (8). Y (t + ) = U (t) f f (U (t)) f (Y (t) (8) = Y (t) f f (Y (t) < f (U (t)) whee f s the functon to be mnmzed. If the new tal vecto yelds a bette value of the ftness functon, t eplaces ts taget n the next geneaton; othewse the taget vecto s etaned n the populaton. Patcle swam optmzaton (PSO) PSO s developed by Kennedy and Ebehat (995). It was found to be elable n solvng non-lnea poblems wth multple optma. In PSO, a numbe of patcles fom a swam that evolve o fly thoughout the feasble hypespace to seach fo futful egons n whch optmal soluton may exst. Each patcle has two vectos assocated wth t, the poston (Z ) and velocty (V ) vectos. In N-dmensonal seach space, Z = [z, z 2... z N ] and V = [v, v 2,...v N ] ae the two vectos assocated wth each patcle. Dung the seach, membes of the swam nteact wth each othes n a cetan way to optmze the seach expeence. Thee ae dffeent vaants of patcle swam paadgms but the most commonly used one s the gbest model whee the whole populaton s consdeed as a sngle neghbohood thoughout the flyng expeence (Kennedy and Ebehat 995). In each teaton, patcle wth the best soluton shaes ts poston coodnates (gbest) nfomaton wth the est of the swam. Each patcle updates ts coodnates based on ts own best seach expeence (pbest) and gbest accodng to the equatons (9) and (0). k k k k k k ( pbest z ) + c and ( gbest z ) v + = wv + c and (9) z k+ k k+ = z + v (0) whee c and c 2 ae two postve acceleaton constants, they keep balance between the patcle s ndvdual and socal behavo when they ae set equal; and and and 2 ae two andomly geneated numbes wth a ange of [0, ] added n the model to ntoduce stochastc natue n patcle s movement; and w s the neta weght (Equaton ) and t keeps a balance between exploaton and explotaton. In ou case, t s a lnealy deceasng functon of the teaton ndex. w max w mn w(k) = w max te te () max whee te max s the maxmum numbe of teaton, te s the cuent teaton numbe, w max s the ntal weght and w mn s the fnal weght. In concluson, an ntal value of w aound, wth a gadual declne towad 0 s consdeed as a pope choce. The most mpotant facto that govens the PSO pefomance n ts seach fo optmal soluton s to mantan a balance between exploaton and explotaton. Exploaton s the PSO ablty to cove and 2 2 exploe dffeent aeas n the feasble seach space whle explotaton s the ablty to concentate only on pomsng aeas n the seach space and to enhance the qualty of potental soluton n the futful egon. Exploaton eques bgge step szes at the begnnng of the optmzaton pocess to detemne the most pomsng aeas then the step sze s educed to focus only on that aea. Ths balanced s usually acheved though pope tunng of PSO key paametes (Chatuved et al., 2009). Just lke n the case of othe evolutonay algothms, PSO has many key featues that attacted many eseaches to employ t n dffeent applcatons n whch conventonal optmzaton algothms mght fal such as: It only eques a ftness functon to measue the qualty of a soluton nstead of complex mathematcal opeatons lke gadent, Hessan, o matx nveson. Ths educes the computatonal complexty and eleves some of the estctons that ae usually mposed on the objectve functon. It s less senstve to a good ntal soluton snce t s a populaton based method. It can be easly ncopoated wth othe optmzaton tools to fom hybd ones. It has the ablty to escape local mnma snce t follows pobablstc tanston ules. Moe nteestng PSO advantages can be emphaszed when compaed to othe membes of evolutonay algothms lke: It can be easly pogammed and modfed wth basc mathematcal and logc opeatons. It s nexpensve n tems of computaton tme and memoy. It eques less paamete tunng. It woks wth dect eal valued numbes that elmnates the need to do bnay conveson of classcal canoncal genetc algothm. SIMULATION AND COMPARISON OF ALGORITHMS TO ADDRESS GMPPT The genetc algothm mplementaton steps ae gven below: Step : Read numbe of modules connected, nsolaton patten and tempeatue fo each module. Step 2: Defne objectve functon (Equaton ) and dentfy the paametes. Step 3: Geneate ntal populaton. Step 4: Evaluate the populaton by objectve functon. Step 5: Test convegence. If satsfed then stop else contnue. Step 6: Stat epoducton pocess by applyng genetc opeatos: Selecton, Cossove and Mutaton. Step 7: Evolve new geneaton. Go to step 3. The DE algothm mplementaton pocess s gven below: Step : Read numbe of modules connected, nsolaton patten and tempeatue fo each module. 72

4 ARPN Jounal of Engneeng and Appled Scences Asan Reseach Publshng Netwok (ARPN). All ghts eseved. Step 2: Intalze DE paametes lke M, CR, M P, F and Gen max. Step 3: Randomly geneate ntal populaton. Step 4: Evaluate the populaton by objectve functon (equaton-) and detemne best ft vecto. Step 5: Fo evey vecto n the populaton fnd the vecto dffeence of two andomly selected vectos and mutate wth the best vecto of the cuent populaton to obtan dono vecto usng equaton (6). Step 6: Obtan the tal vecto based on peset cossove constant usng equaton (7). Step 7: Fo the ente populaton, evaluate the objectve functon value of tal vecto and ceate a new populaton by selectng the taget o tal vecto based on the value of objectve functon. Step 8: Test convegence. If satsfed then stop else go to step3. The PSO algothm mplementaton (Myatake et al., 2007; Azab, 2009) pocess s gven below: Step : Read numbe of modules connected, nsolaton patten and tempeatue fo each module. Step 2: Intalze PSO paametes such as w max, w mn, c, c 2 and Ite max. Step 3: Geneate ntal populaton of N patcles (desgn vaables) wth andom postons and veloctes. Step 4: Compute objectve value, cuent and powe. Step 5: Measue the ftness of each patcle. Step 6: Update pesonal best: Compae the ftness value of each patcle wth ts pbests. If the cuent value s bette than pbest, then set pbest value to the cuent value. Step 7: Update global best: Compae the ftness value of each patcle wth gbest. If the cuent value s bette than gbest, set gbest to the cuent patcle s value. Step 8: Update veloctes: Calculate veloctes V k+ usng equaton (9). Step 9: Update postons: Calculate postons Z k+ usng equaton (0). Step0: Retun to step 4 untl the cuent teaton eaches the maxmum teaton numbe. Step: Output the optmal value of SPVA cuent and coespondng SPVA powe n the last teaton. All the algothms have been wtten n M-fle codng. The paamete settngs fo dffeent algothms ae shown fom Tables to 3. Table-2. DE Paametes. Numbe of desgn vaables Populaton sze M P 20 Cossove constant, CR 0.8 Scalng facto fo mutaton, F 0.0 Maxmum Geneatons, Gen max 50 Table-3. PSO Paametes. Numbe of desgn vaables Numbe of patcles 20 Acceleaton constants c =.5 c 2 =.5 Ineta weght w max = 0.9 w mn = 0.4 Maxmum teatons, Ite max 50 The pefomance of the optmzaton technque n tems of convegence wth GA, PSO and DE s shown n Fgue-3. Fom Fgue-3, t s clea that PSO method conveges eale than the GA and DE. In ode to vefy the obustness of the algothms, smulatons wee caed out fo 30 ndependent uns (Yn et al., 200). Fom the esults n Table-4 t s evdent that the PSO method s moe obust than the GA and DE as the standad devaton of the ftness values fo 20 uns s vey low n the PSO method. Table-. GA Paametes. Numbe of desgn vaables Populaton sze, M P 20 Cossove ate, CR 0.8 Mutaton ate, F 0.0 Maxmum geneatons, Gen max 50 Selecton scheme Roulette wheel Cossove Two pont Mutaton Unfom Fgue-3. Convegence chaactestcs of GA, DE and PSO based methods. 73

5 ARPN Jounal of Engneeng and Appled Scences Asan Reseach Publshng Netwok (ARPN). All ghts eseved. Table-4. Compason of dffeent algothms fo a patcula adance patten (30 ndependent uns fo a patcula adance patten G = 000W/m 2 ; G 2 = 600W/m 2 ; G 3 = 300W/m 2 ). Algothm GA DE PSO Best soluton Wost soluton Aveage value Standad devaton A compason among dffeent algothms lke Fbonacc seach method, bnay seach method, GA, DE and PSO fo dffeent set of adance levels s pesented n Table-5. Table-5. Compason of dffeent algothms fo dffeent set of adaton levels. Fgue-4.Valdaton of PSO fo GMPP tackng of patal shaded SPVA. CONCLUSIONS Ths pape descbes the optmzaton pocedue to fnd GMPP of patal shaded SPVA usng thee dffeent optmzaton technques wth the objectve of maxmzng the powe. Fom the esults t s seen that n tems of global exploaton DE and PSO outpefom GA. The esults show that the convegence chaactestcs of PSO algothm ae bette as compaed to DE and GA. The PSO method has been found to be moe obust as t gves mnmum standad devaton than the othe methods. The esults show PSO algothm s supeo n tems of soluton qualty, global exploaton and statstcal soundness. REFERENCES Chatuved K.T., Pandt M. and Svastava L Patcle Swam Optmzaton wth Tme Vayng Acceleaton Coeffcents fo Non- Convex Economc Powe Dspatch. Intenatonal Jounal of Electcal Powe and Enegy Systems. 3(6): Chen L.R, Tsa C.H., Ln Y.L. and La Y.S A bologcal swam chasng algothm fo tackng the PV maxmum powe pont. IEEE Tansactons on Enegy Conveson. 25(2): It ensues the effectvess of PSO as compaed wth othe algothms. The pefomance of the PSO s valdated gaphcally (Fgue-4) by compang ts output (maked n geen colo) wth that of the bnay seach method (maked n ed colo). In all the cases, PSO gves the optmum powe (global peak) whch s matched wth the esult of bnay seach. In PSO ntally, the patcles ae andomly ntalzed. Theefoe, the ntal powe s always hgh. Ths ntal powe coesponds to the 0 th teaton. As the algothm pogesses, the convegence s dastc and t fnds a global maxma vey quckly. The numbe of teatons needed fo the convegence s seen to be 5-0, fo ths applcaton envonment. Goldbeg D. E Genetc Algothms n Seach, Optmzaton and Machne Leanng. Addson-Wesley, Readng, Massachusetts, Halow, England. Kennedy J. and Ebehat R Patcle swam optmzaton. Poceedngs of IEEE Intenatonal Confeence on Neual Netwoks (ICNN 95). 4: Myatake M., Inada T., Hatsuka I., Zhao H., Otsuka H. and Nakano M Contol chaactestcs of a Fbonacc-seach-based maxmum powe pont tacke when a photovoltac aay s patally shaded. Poceedngs of the 4 th Intenatonal Confeence on Powe Electoncs and Moton Contol. 2: Patel H. and Agawal V. 2008a. MATLAB-Based Modelng to Study the Effects of Patal Shadng on PV 74

6 ARPN Jounal of Engneeng and Appled Scences Asan Reseach Publshng Netwok (ARPN). All ghts eseved. Aay. IEEE Tansactons on Enegy Conveson. 23(): Patel H. and Agawal V. 2008b. Maxmum Powe Pont Tackng Scheme fo PV Systems Opeatng Unde Patally Shaded Condtons. IEEE Tansactons on Industal Electoncs. 55(4): Pce K., Ston R. and Lampnen J Dffeental Evoluton - A Pactcal Appoach to Global Optmzaton. Spnge, Beln Hedelbeg, New Yok, USA. Ramapabha R. and Mathu B.L MATLAB based Modellng to Study the Influence of Shadng on Sees Connected SPVA. 2 nd Intenatonal Confeence on Emegng Tends n Engneeng and Technology, ICETET-09. pp , Decembe. Ramapabha R. and Mathu B.L Modellng and Smulaton of Sola PV Aay unde Patal Shaded Condtons. ICSET Reteved on May 6, 2009 fom IEEE exploe. Slveste S., Boonat A. and Choude. A Study of bypass dodes confguaton on PV modules. Appled Enegy 86. pp Yn J. J., Tang W. and Man K. F A Compason of Optmzaton Algothms fo Bologcal Neual Netwok Identfcaton. IEEE Tansactons on Industal Electoncs. 57(3):