Journal of Applied Science and Agriculture, 9(4) April 2014, Pages: Journal of Applied Science and Agriculture

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1 Journa of Apped cence and Agrcuture 9(4) Apr 204 ages: AENI Journas Journa of Apped cence and Agrcuture IN Journa home page: Optma Expanson annng of Dstrbuton ystem and acement Usng BO Hossen Faahzadeh-Abarghoue eyyed Hossen Hossenan Behrooz Vahd and 2 aeed Hasanvand Eectrca Engneerng Department Amrkabr Unversty of Technoogy Tehran Iran. 2 Young Researchers and Ete ub Khorramabad Branch Isamc Azad Unversty Khorramabad Iran. A R T I E I N F O Artce hstory: Receved 20 January 204 Receved n revsed form 6 Apr 204 Accepted 25 Apr 204 Avaabe onne 5 May 204 Key words: annng Dstrbuted Generaton Bnary artce warm Optmzaton Weghted Aggregaton Method. A B T R A T A new method to sove the snge and mut-objectve dstrbuton expanson pannng probems ncudng s nvestgated n ths paper. The szng and pacement of as we as the requred power of the man grd woud be optmzed usng proposed method to meet the demand. Bnary artce warm Optmzaton (BO) agorthm s used to sove the optmzaton probem for three objectve functons: tota expanson cost tota votage devaton and tota system oss. The goa of presented mode s to satsfy operatona and economc requrements by usng as an aternatve canddate for dstrbuton system pannng to avod or at east reduce the expandng exstng substatons and upgradng exstng feeders. The 30-bus dstrbuton system s used n ths work to evauate the proposed agorthm. The conventona Weghted Aggregaton Method s used to sove the mut-objectve optmzaton probem so that further objectve functons and constrants can be easy added to the proposed agorthm. Optmzaton resuts show that the has economca and eectrca advantages n comparson wth the tradtona method. 204 AENI ubsher A rghts reserved. To te Ths Artce: Hossen Faahzadeh-Abarghoue eyyed Hossen Hossenan Behrooz Vahd and aeed Hasanvand. Optma Expanson annng of Dstrbuton ystem and acement Usng BO. J. App. c. & Agrc. 9(4): NOMENATURE J Mut-objectve functon J MO TE TVD Objectve functon of the tota expanson cost J Objectve functon of the tota votage devaton J Objectve functon of the tota system osses T EM Eectrcty market prce ($/ MWh) F j Fxed cost of the transformer j n the substaton ($/unt) F j Fxed cost of the unt j n the oad bus ($/unt) O j Operaton cost of the unt j n the oad bus ($/MW) σ Bnary decson varabe of the unt j n the oad bus j σ Bnary decson varabe of the transformer j n the substaton j σ j Bnary decson varabe of the feeder ower generated from the unt j n the oad bus (MVA) Tota power generated from dstrbuted generaton n the oad bus (MVA) Dstrbuted generaton capacty mt n the oad bus (MVA) Tota power transferred from eectrcty market n the substaton (MVA) Maxmum substaton capacty mt n the substaton (MVA) Tota actve power transferred from eectrcty market n the substaton (MW) orrespondng Author: aeed Hasanvand Young Researchers and Ete ub Khorramabad Branch Isamc Azad Unversty Khorramabad Iran. Te: E-ma: saeedhasanvand@gma.com

2 405 aeed Hasanvand et a 204 Journa of Apped cence and Agrcuture 9(4) Apr 204 ages: Q Tota reactve power transferred from eectrcty market n the substaton (MVAR) D D Q j Tota actve power consumpton n the bus (MW) Tota reactve power consumpton n the bus (MVAR) pf ower factor of the unt j n the oad bus Feeders set upgrade cost of the feeder ($) R X I Resstance of the feeder Reactance of the feeder urrent of the feeder ower transferred from the feeder (MVA) Therma capacty mt of the feeder (MVA) V β d TN N N tr M Votage of the bus (per unt) resent worth factor Dscount factor Tota number of system buses et of buses capabe for substaton expanson Maxmum number of transformers at each bus et of buses capabe for nstang unts (oad buses) M Maxmum number of consdered at each bus dg BK w t T Back-up protecton unt n the oad bus Weghtng factor Incrementa tme ntervas (n years) Horzon pannng year (n years) INTRODUTION Eectrc uttes have hstorcay satsfed customer demands by generatng eectrcty centray and dstrbutng t through an extensve transmsson and dstrbuton system. As demand ncreases the utty generates more eectrcty. Once demand exceeds a certan eve the capacty of the generaton transmsson and dstrbuton systems may become dmnshed. Ths stuaton has ed to power shortages and power quaty ssues. Dstrbuton panners must ensure that there are enough substaton and feeder capactes to meet the oad forecasts wthn the pannng horzon. In genera the prmary goa n any expanson pannng s to satsfy the growth of demand as economca reabe and safe as possbe. adtona dstrbuton pannng strateges are based on an estabshed rue-based experence. The oad growth vaue s forecasted unt t reaches a predetermned threshod; then a new capacty must be added to the eectrc system. Ths new capacty s obtaned by addng new substatons or expandng exstng substaton s capactes and ther new feeders or both of them (Khator.K and.. eung 997). The optons for ths ruebased strategy are mted and vad ony f the economc aspects do not vary rapdy. If the economc varatons are sgnfcant ths rue-based strategy must be readjusted to ncude nontradtona aternatve capacty s nvestment optons to address the varyng economc envronments (Quntana V.H. et a. 993). Dstrbuted generaton () s one of the new aternatve optons for dstrbuton system panners. Despte the great varety of methods for tradtona dstrbuton system pannng there are few studes avaabe n the terature for the probem consderng sources. The possbty of consderng as a feasbe aternatve to tradtona dstrbuton system pannng s dscussed n (Dugan R.. et a. 999). In (Brown R.E. and.a.a. Freeman 200) the authors present a network capacty snge stage expanson agorthm based on successve emnaton capabe of deferrng network expanson by optmay usng sources n new or exstng substatons. In (Ouyang W. et a. 200) a dstrbuton system pannng method consderng for cuttng peak tme s proposed to mnmze the costs of feeder nvestments nvestments energy oss and the addtona cost of sources. Effects of on substatons expanson s not consdered n ths work. In (E-Khattam W. et a. 2005) the authors deveoped a mode for statc dstrbuton system pannng consderng sources. The

3 406 aeed Hasanvand et a 204 Journa of Apped cence and Agrcuture 9(4) Apr 204 ages: proposed mode ntegrates a comprehensve optmzaton mode and panner s experence to acheve optmum szng and pacement of dstrbuted generaton. In ths mode mnmzaton of s nvestment operatng costs tota payments toward compensatng for system osses aong the pannng perod and dfferent costs accordng to the avaabe aternatve scenaros s nvestgated. In (Haffner. et a. 2008) a mutstage mode for dstrbuton system pannng consderng opton s presented. The objectve functon whch s mnmzed n ths mode s the present vaue of tota nstaaton costs (feeders and substatons) of operatng and mantanng the network and cost of dstrbuted generaton. In (Aut G.W. and J.R. Mcdonad 2000) mportance of consderaton n dstrbuton system pannng has been dscussed. The am of the mode whch s proposed n ths paper s to satsfy the operatona and economc requrements by usng as an aternatve canddate for dstrbuton system pannng and avodng or at east reducng expandng exstng substatons and upgradng the exstng feeders. The proposed method w determne new szng and pacement of as we as the requred power to be mported from the man grd to meet the demand n an optmum way. Ths optmzaton probem s soved by Bnary artce warm Optmzaton (BO) agorthm for three objectve functons: tota expanson cost tota votage devaton and tota system osses. In comparson wth the od methods the proposed approach not ony consders the system pannng economc cost but aso consders other aspects n the optmzaton process by assgnng and evauatng the dfferent weghts for dfferent objectve functons depend on ther mportance for panner n the system pannng. The saent feature of the proposed optmzaton mode whch makes ths method dfferent from prevous methods s usng bnary decson varabes. Ths provdes the optmum decsons wthout any need for roundng the souton. The probem formuatons constrants objectve functons brefy descrpton about bnary partce swarm optmzaton agorthm snge and mut-objectve and proposed method for expanson pannng probem are presented n foowng sectons. Then the resuts of proposed methods on IEEE 30-Bus system for snge and mut-objectve expanson pannng w be presented. Fnay concusons are gven n the ast secton. MATERIA AND METHOD Objectve Functons: Tota Expanson ost (TE): The expanson cost functon conssts of four terms: the cost of the new transformers n the substaton cost of the dstrbuted generaton cost of the new feeders upgrade and the cost of the actve power osses. New transformers and s have fxed and varabe parts. The cost of new feeders upgrade and actve power osses are respectvey fxed and varabe. The fxed cost s spent durng the nstaaton phase and ncudes the cost of the constructon equpment etc. The varabe cost s the cost of the operaton and depends many on the oadng of the equpment durng the operaton perod. An exstng substaton s represented as a power source whch can suppy power at a gven unt varabe cost up to a prescrbed upper bound (E-Khattam W. et a. 2005). J TE = U + + F + () Whereas : Fxed and varabe cost for substaton expanson U = U N = T t ( ) t N Ntr F EM + j= j j 8760 β = σ (2) : Fxed and varabe cost for F Mdg F T t Mdg O ( j ( + j ) + ( j j j j ) j BK 8760 β pf. σ σ (3) M j= t= M j= : Fxed cost of upgradng the feeders = = F σ (4) : Varabe cost for tota system osses T t 2 ( R I ) EM = 8760 β (5) t = = Whereas β s the present worth factor whch equas = ( + d) Tota Votage Devaton (TVD): The expresson of tota votage devaton n the system s: TN = = J TVD V β (Ws H ). (6) Where V s the votage n per unt at the system bus.

4 407 aeed Hasanvand et a 204 Journa of Apped cence and Agrcuture 9(4) Apr 204 ages: Tota ystem osses (T): Tota system osses can be expressed as: J T = = 2 R I (7) robem onstrants: Network power baance: Tota power consumpton shoud be equa to the tota generaton. Ths constrant s met n oad fow cacuaton (Dond. et a. 2002) consderng the cost of avaabe power sources and dspatchng them. In ths approach unts are assumed as negatve oads. N N Q + + Mdg 2 D = N j= pf j j R j = I σ (8) M Mdg 2 N j= pf ( j j ) = D σ X I = Q (9) j Dstrbuton feeder s therma mt: When the oad grows the feeder s therma capacty may exceed ther nomna vaues. If ths probem occurs addtona nvestment w be requred for renforcement of these feeders: M = (0) ansformer and unt maxmum capacty: ower devered by each transformer and unt must be wthn the upper mt of ther capactes. N () M (2) Votage devaton: Votage vaue of each bus shoud reman wthn acceptabe mts as foowng: V MIN V V = TN (3) Maxmum penetraton: ummaton of tota capacty n the grd shoud be ess than some percentage (say 30%) of the tota oad. Bnary artce warm Optmzaton (BO): The artce warm Optmzaton (O) agorthm was ntroduced by James Kennedy and Russe Eberhart n 995 (Kennedy J. and R.. Eberhart 995). O s a popuaton based heurstc search technque n whch each partce represents a potenta souton wthn the search space and s characterzed by a poston a veocty and a record of ts past performance. At each fght cyce the objectve functon for each partce wth respect to ts current poston s evauated. The obtaned vaue measures the quaty of the partce (Eberhart R. and Y. h 200). The (orgna) process for mpementng the goba verson of O s as foowng (Kennedy J. and R.. Eberhart 995; Eberhart R. and Y. h 200):... Intazng a popuaton (array) of partces wth random postons and veoctes on d-dmensons n the probem space...2. For each partce the desred optmzaton ftness functon n d varabes s evauated...3. omparng partces ftness evauaton wth partces best. If current vaue s better than best then best vaue w be equa to the current vaue...4. omparng ftness evauaton wth the popuaton's overa prevous best. If current vaue s better than G best then G best w be updated...5. hangng the veocty and poston of the partce accordng to equatons (4) and (5) respectvey: V d d ( ) ( X X ) + rand ( ) ( X X ) = w V + rand best d 2 Gbest d (4)

5 408 aeed Hasanvand et a 204 Journa of Apped cence and Agrcuture 9(4) Apr 204 ages: X d = X d + Vd (5)..6. Gong to step 2 unt a crteron that s usuay a maxmum number of teratons s met. The Bnary O agorthm (BO) was ntroduced by Kennedy and Eberhart (997) to aow the O agorthm to operate n bnary probem spaces. The BO has a structure smar to the standard O but the veocty vector s st contnuous whch s used to defne the probabty of a bt to be 0 or. The ony dfference between standard O and Bnary O agorthm s the poston vector of the partce. In BO ths vector s a vector of bnary dgts rather than a vector of contnuous vaues and the poston update equaton changes to (Kennedy and Eberhart (997): rand() < ( Vd ) X d = (6) 0 otherwse Where (x) s the sgmod functon: ( x) = (7) x + e The BO s senstve to sgmod functon saturaton whch occurs when veocty vaues are ether too arge or too sma. In such cases the probabty of a change n bt vaue approaches to zero so mts exporaton. For 0 veocty the sgmod functon returns a probabty of 0.5 mpyng that there s a 50% chance for the bt to change (erc M. 2004; Ngatchou. et a. 2005). Fg. shows the fowchart of BO. The roposed Agorthm for nge-objectve Optmzaton: The bnary strng of partce poston s shown n Fg. 2. Ths strng conssts of two man parts. One of them s reated to the set of buses that are capabe of substaton expanson. Ths part ncudes n(n) bytes whch has N tr bts. Each byte ndcates a bus whch s capabe of substaton expanson. The summaton of bts n ths byte shows the number of transformers nstaed n ths bus. The other part shows the set of oad buses and unts can be nstaed on t. Ths part ncudes n(m) bytes whch has M dg bts. Each byte ndcates a bus and unts can be nstaed on t. The summaton of bts n ths byte shows the number of unts. o the bnary strng of partce poston has m bts whch equas to the tota possbe ocatons of the s. The tota number of transformers whch can be nstaed on substaton expanson buses s mentoned as beow: m = n( N) N + n( M ) (8) tr M dg Fg. : Fow chart of bnary partce swarm

6 409 aeed Hasanvand et a 204 Journa of Apped cence and Agrcuture 9(4) Apr 204 ages: A transformers and unts are n bnary representaton whch s ustrated n Fg. 2. In the bnary strng of partce postonσ andσ are bnary decson varabes. These varabes are generated by seectng a j j random bnary vaue wth unform probabty over the optmzed parameter search space (0 or ). Fg. 2: Bnary trng of artce oston After generatng bnary strng of partce poston ths strng s decoded and summaton of unts or transformers n each byte s nstaed on the correspondng bus. Then the power fow s run. After runnng power fow the feeders' therma capacty s evauated and the exceeded feeders are upgraded and the power fow s run agan unt a exceeded feeders are repaced. Then the objectve functon s evauated. In the next stage the saturaton vaues evauated n the prevous stage are cacuated and added to the objectve functon f summaton of tota substatons capacty and tota power generated from dstrbuted generaton s ess than tota oad demand or the votage of each bus s not n the predetermned votage range. Once these stages are accompshed for a partces the goba best ftness wth ts correspondng bnary strng s determned accordng to the BO agorthm. Then veoctes and postons are updated accordng to the BO agorthm unt teraton reaches ts maxmum vaue. The proposed agorthm for nge-objectve optmzaton s shown n the Fg 3. Fg. 3: Fow chart of proposed method for snge-objectve optmzaton

7 40 aeed Hasanvand et a 204 Journa of Apped cence and Agrcuture 9(4) Apr 204 ages: Mut-Objectve Optmzaton wth Weghtng um Method: Many rea-word probems nvove smutaneous optmzaton of severa objectve functons. Mutobjectve optmzaton wth such objectve functons gves rse to a set of optma soutons nstead of one optma souton. The reason for the optmaty of many soutons s that no one s consdered to be better than any others wth respect to a objectve functons. These optmum soutons are known as areto-optma soutons (Ngatchou. et a. 2005). Ths s partcuary mportant n optma pacement and szng of where the dstnctveness of the pannng objectves whch may confct each other (e.g. nvestments cost.vs. the tota votage devaton or system osses) has a sgnfcant mpact on the search for a feasbe confguraton. The mut-objectve optmzaton gves a better smuaton of the rea word. Often characterzed by contrastng goas t gves the panner the capabty of makng the fna decson by seectng some ndvdua pont of vew and a trade-off between a wde range of sutabe soutons. There are varous technques to optmze mut objectve functons smutaneousy. The most mportant technque s the Weghts um Method (WM) (arpne G. et a. 2005). The Weghted um Method s used to combne the objectve functons as a snge objectve optmzaton probem. Ths snge objectve functon s constructed as a sum of objectve functons mutped by weghtng factors.by changng the vaue of the weghts the areto optma souton set can be easy obtaned (Ngatchou. et a. 2005; Dng Y. et a. 2006): N = mn f ( x) = mn w f ( x) (9) w 0 =... k & = w = k (20) By changng the weghts a areto optma souton can be generated. In a varant of ths method caed onventona Weghted Aggregaton (WA) the weghts are ncrementay changed. For each combnaton of weghts the probem s soved so a new areto optma souton s generated (Km I.Y. and O.. de Weck 2006; arsopouos K.E. and M.N. Vrahats 2002). In some cases dfferent objectve functons have dfferent magntudes. o t s requred to fnd normazaton of objectve functons (Dng Y. et a. 2006; arsopouos K.E. and M.N. Vrahats 2002). Each objectve functon s normazed as foowng: J( x) Jmn J ( x) = (2) J J max mn In ths paper for sovng dstrbuton system pannng three objectve functons are combned as beow and then the program w run based on the agorthm ustrated n Fg. 4. J MO = w JTE + w JTVD + w J (22) 2 3 O Fg. 4: Fow chart of proposed method for mut-objectve optmzaton

8 4 aeed Hasanvand et a 204 Journa of Apped cence and Agrcuture 9(4) Apr 204 ages: ase tudy And Numerca Resuts: The studed system n ths paper ncudes kv dstrbuton system wth 30 buses s shown n Fg 4. (Emnogu U. and M.H. Hocaogu 2005; aama M.M.A. and A.Y. hkhan 993). The system has man feeder and three ateras. The capacty of the transformers at the source bus s assumed to be 2 MVA at bus number and the oads are at buses The capacty of the system s MVA. The therma capacty of the feeders assumed to be 2 MVA. However a 30% oad growth s forecasted after 4 years from the base year and the power demand w be approxmatey 3.29 MVA. A backup unt shoud be nstaed n case of any faure or schedued mantenance ntervas. The system power factor s set to be 0.85 for the and the sze of the 's s mutpe of 0. MVA. The maxmum number of the capacty at each bus s 0.3 MVA (3 unts) pus the backup. The new three phase 0 MVA transformer unt s used n the case of substaton expanson. Feeders upgrade to hgher capacty mt (20 MVA) wth an mpedance of Z 20MVA = j0.279 Ω/Km. The votage range s supposed to be n the [0.9.] nterva. For the cost data the eectrcty market prce s consdered to be 70 $/MWh for purchasng power from the man grd. The prce of the unt s 0.5 M$/MVA and the runnng cost of the s assumed to be 70 $/MWh. The fxed cost of the new 0 MVA transformer s 0.2 M$. The cost of upgradng the feeders to hgher capacty (20 MVA feeders) s 0.5 M$/Km and the dscount rate s consdered to be 2.5% (E-Khattam W. et a. 2005). Fg. 5: 30-bus dstrbuton system nge-objectve Resuts: The comparson of the optma snge-objectve numerca s presented n Fg 5. The frst coumn shows the substaton expanson opton wthout nstang any dstrbuted generator. One transformer s nstaed to meet the demand and four feeders are upgraded because ther power fow s hgher than therma capacty. In the next coumns the opton and the substaton expanson wth dfferent objectve functons s consdered. In the opton the feeders aren t needed to be upgraded because the presence n the oad sde reduces feeders power fow under ther therma mts. The system votages are mproved for the opton n the system n comparson wth the system whch s expanded wth tradtona substaton expanson. When the unts are added n the oad sde the oad on the system s reduced and the feeders are ess oaded causng n ncreasng of the votages at a nodes. The votage devatons on the system and power osses are reduced consderaby n the presence of the n the system. Tabe : nge-objectve numerca resuts

9 42 aeed Hasanvand et a 204 Journa of Apped cence and Agrcuture 9(4) Apr 204 ages: Fg. 6 and Fg 7. show the bus votage profe and feeders power fow n a soutons. It s cear that the votage profe n opton soutons s better than the votage profe n the substaton expanson case and aso feeders power fow and consequenty tota system osses are decreased and feeder upgradng s not necessary. These mprovements are advantages of usng the n the dstrbuton system. Mut-Objectve Resuts: Intay 66 combnatons of weghng factors are generated by an ncrement of 0.. Then for each combnaton probem s soved. After emnatng dentca soutons 5 non-domnated soutons are obtaned. Each souton s shown wth ts correspondng tota expanson cost tota votage devaton tota system osses the ocatons and the sze of the s shown n Fg. 8. The decson maker can choose the optma souton based on the mportance of the dfferent objectves and the budget constrants. Aso areto front of soutons s represented n Fg. 9. Fg. 6: omparson of system bus votage for TE TVD and T objectve functon Fg. 7: omparson of system feeder power fow for TE TVD and T objectve functon Tabe 2: Mut-Objectve numerca resuts

10 43 aeed Hasanvand et a 204 Journa of Apped cence and Agrcuture 9(4) Apr 204 ages: Fg. 8: areto soutons front oncusons: Ths work was based on optmzaton of dstrbuton system pannng ncudng usng BO. The optmzaton mode provded two optons to meet the eectrca oad growth: Instang new transformer wth upgradng the feeders and addng unts n the oad buses. Ths mode evauates more dfferent stuatons and soutons. Athough the pannng probem becomes much more compex when pacement and feeder upgrades are consdered together t provdes more dverse expanson soutons for uttes. The Weghtng um Method (WM) has been successfuy used to generate the non-domnated soutons set for the mut-objectve dstrbuton pannng probem. Ths method offers fexbty to assgn and evauate dfferent weghts for dfferent objectve functons dependng on ther mportance n the system pannng. Optmzaton resuts anayss of 30-bus rada dstrbuton system show that the s ntroduce eectrca benefts to the system n compare wth the tradtona opton ncudng new transformers addton at the exstng substaton and upgradng the overoaded feeders whe the nvestment of both optons s amost equa. Impcty the mode dscussed n ths paper assumes that new s may be nstaed by dstrbuton company (DIO). Athough t may be practca n some cases t s not true for some stuatons. REFERENE Khator.K and.. eung 997. ower Dstrbuton annng: A Revew Of Modes And Issues. IEEE ans. On ower yst 2(3): Quntana V.H. H.K. Temraz and K.W. Hpe 993. Two-tage ower ystem-dstrbuton annng Agorthm. IEE roceedngs Generaton ansmsson and Dstrbuton 40(3): Dugan R.. T.E. Mcdermott and G.I. Ba 999. Dstrbuton annng For Dstrbuted Generaton. n IEEE ower Engneerng ocety Wnter Meetng New York UA pp: Brown R.E. and.a.a. Freeman 200. Anayzng The Reabty Impact Of Dstrbuted Generaton. n IEEE ower Engneerng ocety ummer Meetng Vancouver B anada pp: Ouyang W. H. heng X. Zhang and. Yao 200. Dstrbuton network pannng method consderng dstrbuted generaton for peak cuttng. Energy onverson and Management 5(2): E-Khattam W. Y.G. Hegazy and M.M.A. aama An Integrated Dstrbuted Generaton Optmzaton Mode For Dstrbuton ystem annng. IEEE ansactons On ower ystems 20(2): Haffner..F. Aves erera. Aberto erera and.. Barreto Mutstage Mode for Dstrbuton Expanson annng Wth Dstrbuted Generaton art I: robem Formuaton. IEEE ansactons on ower Devery 23(2): Aut G.W. and J.R. Mcdonad annng For Dstrbuted Generaton Wthn Dstrbuton Networks In Restructured Eectrcty Markets. IEEE ower Engneerng Revew 20(2): Ws H ower Dstrbuton annng Reference Book North arona; Marce Dekker. Dond. D. Bayoum. Haeder D. Juan and M. uter Network Integraton of Dstrbuted ower Generaton. Journa of ower ources06(-2): -9.

11 44 aeed Hasanvand et a 204 Journa of Apped cence and Agrcuture 9(4) Apr 204 ages: Kennedy J. and R.. Eberhart 995. artce swarm optmzaton. n IEEE Internatona onference on Neura Networks erth WA pp: Eberhart R. and Y. h 200. artce warm Optmzaton: Deveopments Appcatons and Resources. n roceedngs IEEE Internatona onference on Evoutonary omputaton eou: pp: Kennedy J. and R.. Eberhart 997. A Dscrete Bnary Verson of the artce warm Agorthm. n IEEE Internatona onference on ystems Man And ybernetcs Orando F pp: erc M Dscrete artce warm Optmzaton Iustrated By The aveng aesman robem. n New Optmzaton Technques In Engneerng pp: Ngatchou. A. Zare and M.A. E-harkaw areto Mut Objectve Optmzaton. n roceedngs of the 3th Internatona onference on Integent ystems Appcaton to ower ystems Arngton VA pp: arpne G. G. e. Mocc F. o and A. Russo Optmsaton of Embedded Generaton zng And tng By Usng A Doube ade-off Method. IEE roceedngs Generaton ansmsson and Dstrbuton 52(4): Dng Y.. Gregov O. Grodzevch and et a Dscussons on Normazaton and Other Topcs n Mut-Objectve Optmzaton. n roceedngs to the Feds-MITA Industra robem ovng Workshop Toronto pp: Km I.Y. and O.. de Weck adaptve Weghted um Method for Mutobjectve Optmzaton: A New Method for areto Front Generaton. tructura and Mutdscpnary Optmzaton 3(2): arsopouos K.E. and M.N. Vrahats artce swarm optmzaton method n mutobjectve probems. n roceedngs of the AM ymposum on Apped omputng (A) Madrd pan pp: Emnogu U. and M.H. Hocaogu A new power fow method for rada dstrbuton systems ncudng votage dependent oad modes. Eectrc ower ystems Research 76(): aama M.M.A. and A.Y. hkhan 993. A smpfed network approach to the VAR contro probem for rada dstrbuton systems. IEEE ansactons on ower Devery 8(3):