EVOLUTIONARY OPTIMIZATION APPROACH FOR FINDING GPPP OF A PV ARRAY SYSTEM UNDER HETEROGENEOUS OPERATING CONDITION

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1 Journal of Electrcal Engneerng EVOLUTIONARY OPTIMIZATION APPROACH FOR FINDING GPPP OF A PV ARRAY YTEM UNDER HETEROGENEOU OPERATING CONDITION R.PON VENGATEH 1,.EDWARD RAJAN 1 Assstant Professor (enor Grade), Professor, Department of Electrcal and Electroncs Engneerng, Mepco chlen Engneerng College, vaas-66005, TamlNadu, Inda. Emal: vengateshme@ mepcoeng.ac.n; sedward@mepcoeng.ac.n Abstract: Ths research wor nvestgates an evolutonary optmzaton approach for fndng Global Pea Power Pont (GPPP) of a Photovoltac (PV) array system under Heterogeneous operatng condtons. The presence of a by-pass dode ntroduces multple peas n the Power-Voltage (P-V) and multple steps n Current-Voltage (I-V) characterstcs of a PV array under Heterogeneous operatng condtons. The Partcle warm Optmzaton (PO) and Bacteral Foragng Optmzaton (BFO) technques have been ncorporated to determne the effectve GPPP under shadow condtons. The effects of cogntve coeffcent of ndvdual partcles (C 1 ) and the socal coeffcent of all partcles (C ) play a major role n fndng the optmum soluton n the search space of PO are also studed. The BFO algorthm has a large number of control parameters when compared to PO and t shows sgnfcant mprovements n terms of convergence speed and fnal accuracy towards reachng the GPPP. The mathematcal model of proposed PV system have been developed and smulated n Matlab-smuln envronment to trac the GPPP. The smulated results of Incremental Conductance (INC) method, PO and BFO are evaluated and compared for dfferent shadng patterns of the PV array system. From the obtaned results, t s found that the BFO algorthm gves consderable mprovements than INC and PO algorthms. Key words: Photovoltac, Global Pea Power Pont, Incremental Conductance, Partcle warm Optmzaton algorthm and Bacteral Foragng Optmzaton algorthm. 1. Introducton. Ths research paper focuses the explotaton of green energy for promotng the PV system. The sun radates more photons whch are suffcent to generate electrcal power for meetng the energy demands [1]. olar energy has certan ntermttent ssues, not shnng at nght and also durng daytme there may be cloudy or rany weather and partal shadow effects whch reduce the ntensty of sunlght fallng on the PV modules. The change n solar rradaton (G) and the effects of shadow over the PV panel are referred as Heterogeneous condtons. A major challenge n usng a PV generaton s to tacle ts nonlnear I-V characterstcs, whch results n the necessty of detecton of a unque Pea Power Pont (PPP) on ts P-V curve. A PV array system (3x3 PV modules) ncludng bypass dodes and blocng dodes developed for ths study s shown n Fg.1. It s mportant to consder the effects of bypass dodes and blocng dodes n a PV array under Heterogeneous operatng condton. The resultng P-V characterstc curve becomes more complex and exhbts multple peas. The presence of multple peas reduces the effectveness of the PV system and t s also mportant to dentfy the optmum PPP under dfferent shadng patterns []. Fg.1 Bloc dagram of the proposed PV system. Ths research paper ams to employ an evolutonary optmzaton algorthm for fndng GPPP and to enhance performance of the PV array system under Heterogeneous operatng condtons. The research paper s organzed as follows: The secton- dscusses the non-lnear characterstcs of a PV array under shadng patterns, secton-3 llustrates the concept of PO algorthm and parameter selecton to optmze the locaton of GPPP n the P-V characterstc curve and the secton-4 explans a global optmzaton BFO algorthm for achevng the optmum locaton of global maxma through multples of local maxma under dfferent shadng condtons of a PV array by mmcng the foragng behavoral characterstcs of Eschercha col (E. co bactera. The secton-5 deals wth comparson of results obtaned from INC, PO and BFO algorthms and dscusson. The secton-6 ends wth the concluson part of the research wor fndngs. 1

2 a Journal of Electrcal Engneerng. P-V and I-V Characterstcs of a PV Array under dfferent hadng Patterns The modelng of PV system has been comprehensvely llustrated n earler studes [3, 4] wth the effects of bypass dodes and blocng dodes. The parameters of the PV module have been obtaned from the manufacturer datasheet (M450) for ths analyss purpose. The Matlab-smuln for shadng pattern-1 s llustrated n Fg.. The calculated maxmum power (P max ) s accounted as 51.8W, 151W, W and W under Homogenous & Heterogeneous condtons whch are tabulated n Table- 1. The varaton n the value of P max s due to the loss of radatons caused by the effects of partal shadngs and low solar rradatons over the PV panels. methods struc by the Local Pea Pont (LPP) and t fal to trac the GPPP under Heterogeneous shadng patterns. The next secton llustrates the effectve tracng of GPPP under shadngs by employng evolutonary optmzaton technques. Fg.3 I-V characterstcs of PV array under Homogenous and Heterogeneous condton Fg. Matlab-smuln of PV array under shadng pattern-1 Table 1 P max of PV array under dfferent shadng patterns hadng olar rradaton (W/m ) P max. (W) Pattern Homogenous condton (TC) 51.8 The consequence of by-pass dode and the nonlnearty behavor of the PV array under Heterogeneous condtons are notced as multple steps n I-V & multple peas n a P-V characterstc curve whch are plotted n Fg.3 and Fg.4 respectvely. Moreover, the conventonal Fg.4 P-V characterstcs of PV array under Homogenous and Heterogeneous condtons 3. Partcle warm Optmzaton Algorthm PO s an effectve meta-heurstc technque that can be mplemented to optmzaton problems [5-9] havng many local optmal ponts and t s adopted here to realze the GPPP under shadowed condtons of the PV array. The ntellgence of warms wth ther movement towards the global soluton starts from a random selecton & t contnues n a search space from prevous teratons and also the accuracy of the soluton s acheved by evaluatng ts ftness functon. The partcles eep trac of ts coordnates n the soluton of search space are assocated wth the personal best (p best ) soluton that has been acheved by that ndvdual partcles and the trac of the best soluton as compared wth any other partcles n the neghborhood of the search space s representng the global best (g best ) of that partcle obtaned whch s llustrated n Fg.5.

3 Journal of Electrcal Engneerng A detaled procedure for mplementng the PO algorthm for fndng GPPP s llustrated n Fg. 6. The problem has been formulated wth the objectve of two dmensons (D) as a functon of PV array voltage (V PV ) and PV array current (I PV ) whch helps to trac the pea power. Fg.5 Partcle movements n the search space of PO. At each tme step, the partcles move wth velocty (v ) from ts poston ( ) towards ther p best locatons and each partcle ultmately progress to reach an optmal or close to an optmal global soluton n the search space. The partcle s poston and ther velocty n the search space are expressed n equaton (1) and equaton () respectvely. 1 1 (1) v v 1 w. v C r ( g C r ( p 1 1 best best, () where, - teraton number, w - nerta weght, C 1 - cogntve coeffcent of ndvdual partcles, C - socal coeffcent of all partcles. The random varables (r 1 & r ) are unformly dstrbuted (0-1) and t contnues the stochastc movement wthn teratons. The range of velocty [0, v max ], helps the search space n closer to area of the global soluton. The p best, stores the best poston of the th partcle as expressed n equaton (3) and g best stores the best poston of all the partcles showng the GPPP locaton n the multple peas of the P-V curve. The occurrence of varatons n the solar rradatons and amount of partal shadng mae power fluctuatons n the PV system. In ths study, the PV panel voltage has been fxed from 0 to V oc and current from 0 to I sc and t depends on the confguraton of the PV array system. (3) P when F( ) F( ) (4) (5) The evaluaton of the partcles s carred out based on the PV panel output power and whch s represented as a ftness evaluator (F) for the partcles. The poston of th partcle locaton ( ) at th teraton s expressed n equaton (4), whch shows the poston of the number of partcles (N) n the search space of the problem under the consderaton. ) best, [ 1, N 1, F( 1) F( F( ) ) P N ) ] Fg.6 Flow chart for fndng GPPP usng PO algorthm. In ths study, the number of partcles s approxmated as 100 and durng the ntalzaton phase, these partcles can be placed n a fxed poston or be placed n the space randomly. The peas of the P-V curve occur nearly at multples of 80% of the PV module open crcut voltage (V oc ) and the mnmum dsplacement between successve peas s also nearly 80% of V oc. Therefore, the partcles are ntalzed on fxed postons whch cover the entre search space of the soluton. 3

4 Journal of Electrcal Engneerng The cogntve coeffcent of ndvdual partcles and the socal coeffcent of all partcles play a major role n fndng the optmum soluton n the search space. The greater value of C 1 fnds the better ndvduals and hgher value of C fnds the best ndvduals among the all partcles n the soluton space whch s referred as a global soluton. The sum of C 1 and C s accounted as the value of 4 [10-11]. In ths research wor the effectve value of fndng GPPP s analysed for the dfferent combnaton of C 1 and C values and t s llustrated that the napproprate desgn values of C 1 and C leads the local maxmum rather than the global one and t affects the convergence speed and accuracy also. The four dfferent combnatons of C 1 and C values have been taen to study ther effects n fndng the GPPP n the search space under shadng patterns of the PV array. The Matlab M-Fles has been developed for fndng the optmum GPPP locaton under dfferent shadng patterns of solar rradaton. The smulated performance curve for shadng pattern-1 and shadng pattern- for dfferent values of C 1 and C has been plotted n Fg.7 and Fg.8 respectvely. The smulaton responses llustrated that the best convergence reaches closer to the global soluton for the values of C 1 =0.1 and C =3.9 and for other values, the solutons are dverged from the global solutons where the GPPP s located. Inerta weght (w) s the other mportant parameter whch nfluences the convergence of ths algorthm [1] and also t helps to control the velocty of the partcles movng towards the GPPP. The hgher value of the nerta weght (w 0.8) speeds up the convergence to the optmum soluton whereas lower value narrows down the range of the search space. In ths wor the nerta weght s assumed as 0.9. Fg.7 Performance curve for dfferent values of C 1 and C under shadng pattern-1 Fg.8 Performance curve for dfferent values of C 1 and C under shadng pattern- Fg. 9 Performance curves obtaned by PO at the end of 5 th teraton Fg. 10 Performance curves obtaned by PO at the end of convergence 4

5 Journal of Electrcal Engneerng The performance curve for shadng pattern-1 and pattern- has been llustrated n Fg.9 and Fg.10 at the end of 5 th teraton and durng convergence respectvely. The stochastc behavor of the warm ntellgence s ncorporated n fndng the GPPP of the PV array system under three dfferent shadng condtons and the smulated results are tabulated n Table- whch shows the pea power (P mp ) detected values. Moreover, the PO algorthm s adaptve and t s ntalzed by sensng the changes n the operatng levels of the PV array system and also t prevents the convergence of the problem at the local maxma locaton. Table Pea power detecton usng PO algorthm hadng pattern V mp I mp P mp (Watts) (Volts) (Amps) Bacteral Foragng Optmzaton Algorthm In ths research wor a new evolutonary computaton technque, BFO approach has been realzed to acheve the GPPP from multples of LPP under dfferent shadng condtons of a PV array system by mmcng the behavor of E. col bactera. An E. col present n our ntestnes undergoes mportant stages such as Chemotaxs, warmng, Reproducton, Elmnaton & Dspersal for ts survval. A socal and non-socal foragng strateges are two categores, the former one uses ts own energy and get help from other members n the populaton, but the later one follows ts own energy and do not see help from others n the same soluton space. Here, the socal foragng strategy s adopted to fnd the global soluton among the local maxma. Durng the foragng process of Chemotaxs stage, when the bactera are not fndng a better soluton, t wll turn to a new drecton (tumble acton) and evaluate the new ftness value. If t s really mproved, then t wll contnue to steps n the same drecton (run process) untl no sgnfcant mprovement n ftness value has been found or reaches a predetermned threshold number of movng steps. Hence, an E. col bacterum performs the tumble and /or run operaton (movement of the bactera) durng ts entre lfetme s expressed n equaton (6) as below; represent the poston of each member n the populaton of the -bactera at the j th chemotactc step. ( j 1, ( c( ) ( ) (6) T ( ). ( ) where θ ( represents the poston of each member n the populaton of the th bacterum at j th chemotactc step, th reproducton step and l th elmnaton & dspersal step, c() s related to the step sze n the arbtrary path specfc by the tumble (run length unt) and a unt length vector n the random drecton [-1, 1] s represented by Δ [13,14]. Ths movement of an E. col s contnued untl a bacterum reaches the drecton of the global soluton regon to explore ts local and global search propertes separately. Computaton of the ftness value for the th bacterum, J (, usng equaton (7) s llustrated below: J (, J (, Jcc ( (, p( ) (7) set J Last = J (, and to save ths value because there s a possble to get a better results durng the tumble. J (, (8) Last J In warmng stage, the group behavor has been observed that, each E. col bacterum wll sgnal other va attractants to warm together. A group of E. col cells organze themselves n a travelng pathway helps them to comprehend nto groups and, thus, move as concentrc patterns of swarms wth hgh bacterum densty [15]. The sgnalng functon between cells can be represented usng the equaton (9). The left sde of the equaton s the objectve functon whch has been added wth the actual objectve functon of the problem under study. p represents the dmenson of the search space (number of varables) whch s to be optmzed. In ths research wor the dfferent values of the panel voltage (V PV ) and panel current (I PV ) formulate the search space of the soluton. J cc (, P( ) J (, ( ) 1 d att exp ( watt ( m m ) )) ( hrep exp( wrep 1 m1 1 m1 (9) (10) w attractant (w att ), h attractant (h att ), w repellant (w rep ) and h repellant (h rep ) are the dfferent coeffcents used n the evaluaton process of BFO. After a certan number of complete swms, the better half of the populaton undergoes the reproducton and elmnatng the rest of the populaton. In order to escape local optma, an elmnaton dsperson event s carred out where some bactera are lqudated at random wth a very small probablty and the new replacements are ntalzed at arbtrary locatons of the search space solutons. The health of bacterum can be computed by usng the equaton (11). J health p N c 1 j1 (11) Furthermore, n reproducton the least healthy bactera de and the other healthest bactera each splt nto two bactera, whch are placed n the same locaton. Ths maes the populaton of bactera constant n the evoluton process. Besdes, n elmnaton and dspersal, any one bacterum s elmnated from the total set by cc ( ( ) )) J ( p m m 5

6 Journal of Electrcal Engneerng dspersng t to an arbtrary poston on the optmzaton feld. Elmnaton and Dspersal help n reducng the behavor of stagnaton.e. beng trapped n a premature soluton pont or local optma. After many generatons, poor foragng strateges are ether elmnated or shaped nto good ones. A comprehensve procedure for fndng GPPP under shadowed condton usng BFO s llustratng n Fg.11. A functon to be optmzed s developed wth followng expresson usng Matlab M-Fle program. J (, j 1, Lve_ fn( P( V pv, I pv) (1) The parameter settngs of BFO algorthm has been tabulated n Table-3. Table 3 Parameter settngs of BFO algorthm Parameters Values No. of bacterum() 100 Maxmum number of steps(n s ) 3 Number of chemotactc steps(n c ) 1 Number of reproducton steps(n re ) 4 Number of elmnaton and dspersal steps (N ed ) 4 Length of swm ( 1 Probablty of elmnaton/dsperson (P ed ) 0.1 The sze of the step taen n the random drecton specfed by the tumble C() 0.1 Fg.11 Flowchart representaton of BFO algorthm for fndng GPPP of PV array Fg.1 Performance curve of BFO under dfferent shadng patterns before convergence 6

7 Journal of Electrcal Engneerng Fg.13 Performance curve of BFO under dfferent shadng patterns after convergence Before and after convergence of the performance curves under the three shadng patterns are llustrated n Fg.1 and Fg.13 respectvely. The results obtaned usng BFO algorthm proves that the locaton of P mp s very closer to the GPPP under all shadng condtons wth faster convergence speed and good accuracy wthout beng struc wth local maxma ponts. 5. Comparatve Analyss of Results Ths research wor also compares the smulaton results wth conventonal INC algorthm, whch t fals to fnd the GPPP under the shadowed condtons. BFO has converged to the optmal soluton to many problems where the most analytcal methods fal to converge and also has ts advantages such as less computatonal burden, global convergence, less computatonal tme requrement. PO and BFO methods are able to dscrmnate the global PPP from local PPP under shadowed condtons. The comparatve results analyss has been taen for INC, PO and BFO algorthms n fndng the GPPP of PV array under dfferent partal shadng condtons and s tabulated n Table 4. Table 4 Comparatve analyss of results obtaned from INC, PO and BFO algorthms hadng pattern 1 3 MPPT Tech. V mp (Volts) I mp (Amps) P mp (Watts) INC PO BFO INC PO BFO INC PO BFO P max calculated The P mp values obtaned from these algorthms are also compared wth the calculated P max value and t s found that, BFO algorthm locates a global soluton very close to the P max. Moreover, the BFO algorthm has a large number of control parameters as compared to PO algorthm, t shows sgnfcant mprovements n terms of convergence speed and fnal accuracy towards reachng the GPPP durng shadng condtons. Table-5 llustrates the elapsed tme taen for PO and BFO for reachng the GPPP under dfferent shadng patterns. BFO shows sgnfcant mprovement n searchng the GPPP. Table 5 Comparson of pea power and elapsed tme for PO and BFO algorthms PO BFO hadng Pattern P mp Elapsed P mp Elapsed (Watts) tme (sec) (Watts) tme (sec) Concluson Ths proposed wor has been nvestgated an evolutonary optmzaton method for fndng the GPPP of a PV array system under Heterogeneous operatng condtons. The P-V and I-V characterstcs of a PV array system under these condtons have been studed where t exhbts multple peas n the P-V curve. The computatonal ntellgence of a PO and BFO algorthms are descrbed to dentfy the global operatng pont of a PV array system under shadow condtons. Moreover, the effects of cogntve coeffcent of ndvdual partcles and the socal coeffcent of all partcles values n PO for fndng an optmum soluton n the search space are also evaluated. The PO and BFO methods are showng ther ablty n dstngushng the global soluton from local maxma under shadowed condtons. Also, the BFO algorthm locates a global soluton very near to the maxmum power than INC and PO algorthms wth better convergence speed & accuracy towards the fndng of GPPP under shadng condtons of a PV system. 7

8 Journal of Electrcal Engneerng References 1. Parh J. and Parh K.: Growng pans-meetng Inda s energy needs n the face of lmted fossl fuels, IEEE Power Energy Mag., vol. 10, no. 3, pp , 01.. Evagela V., Parasevada and tavros A.: Papathanassou, enor Member, Evaluaton of MPP Voltage and Power of mc- PV Modules n Partal hadng Condtons, IEEE Transactons on Energy Converson, vol. 6, no. 3, pp , Patel H. and Agarwal V.: MATLAB-based modelng to study the effects of partal shadng on PV array characterstcs, IEEE Transactons on Energy Converson, vol. 3, no. 1, pp , Pon Vengatesh R. and Edward Rajan.: Investgaton of the effects of homogeneous and heterogeneous solar rradatons on mult-crystal PV module under varous confguratons, IET Renewable Power Generaton, vol.9, no.3, pp , Lang-Ru Chen, Chh-Hu Tsa, Yuan-L Ln, and Yen- hn La: A Bologcal warm Chasng Algorthm for Tracng the PV Maxmum Power Pont: IEEE Transactons on Energy Converson, vol. 5, no., pp , Myatae M., Veerachary M., Torum F., Fuj N. and Ko H.: Maxmum power pont tracng of multple photovoltac arrays: A PO approach, IEEE Trans. Aerospace Electronc ystem, vol. 47, no. 1, pp , Ishaque K., alam Z., Amjad M. and Mehlef.: An mproved partcle swarm optmzaton (PO)-based MPPT for PV wth reduced steady-state oscllaton, IEEE Trans. Power Electroncs, vol. 7, no. 8, pp , Aug Masafum Myatae, Mummad Veerachary, Fuhta Torum, Nobuho Fu Hdeyosh Ko.: Maxmum Power Pont Tracng of Multple Photovoltac Arrays: A PO Approach, IEEE Transactons on Aerospace and Electronc ystems, vol. 47, no.1, pp , Jan Wang L. F. and ngh C.: Multcrtera desgn of hybrd power generaton systems based on a modfed partcle swarm optmzaton algorthm, IEEE Transacton on Energy Conversaton, vol. 4, no. 1, pp , Q L,Werong Chen, Youy Wang, huu Lu, and Junbo Ja: Parameter Identfcaton for PEM Fuel-Cell Mechansm Model Based on Effectve Informed Adaptve Partcle warm Optmzaton, IEEE Transactons on Industral Electroncs, vol. 58, no. 6, pp , Ratnaweera A., Halgamuge. and Watson H.: elforganzng herarchcal partcle swarm optmzer wth tmevaryng acceleraton coeffcents, IEEE Transacton on Evoutnary. Compuaton, vol. 8, no.3, pp , Zh-Hu Zhan, Jun Zhang, Yun L, Henry hu-hung Chung: Adaptve Partcle warm Optmzaton, IEEE Transactons on ystem and Cybernetcs part B: Cybernetcs, vol. 39, no. 6,pp , Veysel Gaz, Kevn Passno M.: Bactera Foragng Optmzaton, warm tablty and Optmzaton, prnger pp.33-49, Pages wagatam Das, Arjt Bswas, ambarta Dasgupta, and Ajth Abraham: Bacteral Foragng Optmzaton Algorthm: Theoretcal Foundatons, Analyss, and Applcatons, Foundatons of Computatonal Intellgence, vol.3, pp 3-55, Kevn Passno G.: Bommcry of Bacteral Foragng for Dstrbuted Optmzaton and Control, IEEE Control ystems Magazne, 00. 8