International Journal on Power Engineering and Energy (IJPEE) Vol. (4) No. (4) ISSN Print ( ) and Online ( X) October 2013

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1 Internatonal Journal on Power Engneerng and Energy (IJPEE) Vol. (4) No. (4) ISSN Prnt (34 738) and Onlne (34 730X) October 03 Soluton of The Capactor Allocaton Problem Usng A New Accelerated Partcle Swarm Optmzaton Algorthm R.H.Shehata Electrcal Power and Machnes Dept., An Shams Unversty, Abbassa, Caro, Egypt S. F. Mehamer Electrcal Power and Machnes Dept., An Shams Unversty, Abbassa, Caro, Egypt M. A. L. Badr Electrcal Power and Machnes Dept., An Shams Unversty, Abbassa, Caro, Egypt Abstract- Many nature nspred meta-heurstc algorthms have been attempted for reactve power compensaton of radal dstrbuton feeders. In ths paper, we ntroduce and mplement a novel accelerated partcle swarm optmzaton technque. Results of the proposed approach are compared wth prevous s to show the superorty of the proposed usng three actual dstrbuton feeders (of 9 bus, 5 bus, and 69 bus feeders). Ths new smple technque has the ablty to gve the best results for maxmum reducton n system losses and costs among all prevous studed technques. Index Terms- Capactor placement, accelerated partcle swarm optmzaton technque, loss Reducton, Cost functon. I. INTRODUCTION The nstallaton of shunt capactors on radal dstrbuton systems s essental for power flow control, mprovng system stablty, power factor correcton, voltage profle management, and loss mnmzaton. It s mportant to fnd the optmal sze and locaton of capactors requred to mnmze feeder losses (power and energy), and the sutable tme to swtch the capactors on and off. The soluton technques for the capactor allocaton problem can be classfed nto four categores []: analytcal, numercal programmng, heurstc, and artfcal ntellgence-based (AI- Based). AI-based s nclude genetc algorthms, smulated annealng, expert systems, artfcal neural networs, and fuzzy logc. A survey of all capactor allocaton categores s presented n [] and []. Heurstc search technques have been ntroduced for dstrbuton system loss reducton frst by reconfguraton [3], [4]. Ref. [3] presents a formula for estmatng the change n losses caused by the transfer of a group of loads from one feeder to another by the closng and openng of some connectng swtches. Ref. [4] develops a feeder reconfguraton strategy usng heurstcs for the removal of transformer overloads and feeder constrant problems. Recently, the deas presented n [3] and [4] were adapted to the feld of capactor placement for reactve power compensaton n dstrbuton feeders. Ref. [5] presents a heurstc strategy to reduce system losses by dentfyng senstve nodes at whch capactors should be placed. These nodes are determned by frst dentfyng the branch n the system wth largest losses due to reactve currents. Then the node, whch contrbutes the largest load affectng the losses n that branch, s selected as the canddate node. The capactor sze s the value that gves mnmum system real losses. A load flow s performed next to ensure that no voltage volaton taes place. The process s repeated for the next canddate node untl no further loss reducton s acheved. Ths does not guarantee a mnmzaton n the cost functon or maxmzaton n the net savng functon. Ref. [6] modfes the of [5] to overcome ths dsadvantage so ther technque attaned good results n both loss and cost reductons but ths technque does not acheve the best reductons. Ref. [7] proposes a of mnmsng the loss assocated wth the reactve component of branch currents by placng capactors at optmal locatons. The frst fnds the locaton of the capactors n a sequental manner (loss mnmzaton by a sngly located capactor). Once each of the capactor locaton s dentfed, the optmal capactor sze at each selected locaton for all capactors are determned smultaneously, to avod over-compensaton at any locaton, through optmzng the loss savng equatons. Ths nvolves the soluton of a set of lnear algebrac equatons. The dsadvantage of ths s that t neglects the cost-beneft analyss whch n turn depends on the cost of the capactor ban and energy savng. Fuzzy systems-based s have the advantage of accountng for uncertanty n data and the compromse between voltage profle mprovements and cost and loss reductons. Ref. [8] presents a fuzzy based approach for capactor placement for a 9-bus feeder. Two membershp functons for real power losses and voltage senstvty have been defned to reduce the effort of fndng the optmal locatons. The whole problem has been presented as a fuzzyset optmzaton problem to mnmze the real losses and capactor cost wth voltage lmt constrants. They used the ntersecton prncple n fuzzy logc as the fuzzy decson to fnd the capactor locaton then a varatonal has been used to fnd capactor szes to attan mnmum cost wthout volatng the voltage constrants. In Ref. [9], exactly the same procedures usng the same feeder have been mplemented but wth two dfferent membershp functons. In fact, ther membershp functons for real power losses and voltage are the fundamental part of the membershp functons that have been used n [8]. Reference Number: JO-P

2 Internatonal Journal on Power Engneerng and Energy (IJPEE) Vol. (4) No. (4) ISSN Prnt (34 738) and Onlne (34 730X) October 03 However, they have acheved relatvely better results by ntroducng a certan constant n the real loss membershp functon dependng on ther experences. In Ref. [0], the authors used the membershp functons forms of [8] but replacng the real losses by reactve losses and the ntersecton decson (usng mn. operator) by product decson. They used the product fuzzy decson to determne the locaton of the capactors and fnd the capactor szes. They used an analytcal based on dfferentatng a well-defned net savng functon of power and energy losses wth respect to capactor sze, thus obtanng the optmum capactor sze. Ref. [] ntroduces a study of prevous wor usng fuzzy and heurstc strateges. The effect of varyng some parameters n the membershp functons to get better results s dscussed. Also the effect of selecton of parameters that should be used n fuzzy modellng s nvestgated. The advantages of fuzzy and heurstc s presented are combned n a new fuzzy-heurstc dea. Ths combned technque s verfed, by the applcaton to test feeders, to gve better results. Dfferent fuzzy decson-mang forms are appled to the fuzzy modellng problem. Fnally a recommendaton s made for the most effcent way to get a soluton equal or very close to the optmal. Ref. [] ams to study dstrbuton system operatons by the ant colony search algorthm (ACSA).The objectve of ths study s to present new algorthms for solvng the optmal feeder reconfguraton problem, the optmal capactor placement problem, and the problem of a combnaton of the two. In Ref. [3], Dfferental Evoluton (DE) Algorthm along wth Dmenson Reducng Dstrbuton Load Flow (DRDLF) has been used. Ths load flow dentfes the locaton of the capactors and the Dfferental Algorthm determnes the sze of the capactors such that the cost of the energy loss and the capactor to be mnmum. Ref. [4] presents a refned genetc algorthm whch uses prm's algorthm n order to obtan spannng trees (radal confguraton), wth random costs for every branch. At every generaton, the power flow calculatons are made only f the canddate soluton s unque. In Ref. [5], Self Adaptve Hybrd Dfferental Evoluton (SAHDE) along wth senstvty factors algorthm has been proposed to solve the capactor placement problem. The purpose of the loss senstvty factors s to dentfy the senstve buses of the dstrbuton system. Wth the ntegraton of (SAHDE), the amount of capactors to be ncluded at the dentfed locatons has been found A two-stage ology s used n [6] for the optmal capactor placement problem. In the frst stage, fuzzy approach s used to fnd the optmal capactor locatons and n the second stage, an artfcal bee colony algorthm s used to fnd the szes of the capactors. The szes of the capactors correspondng to maxmum loss reducton have been determned. The wor presented n [7] ntroduces a new algorthm based on a combnaton of fuzzy, Dynamc Programmng (DP), and Genetc Algorthm (GA) approach es for capactor allocaton n dstrbuton feeders. The proposed of ths artcle uses fuzzy reasonng for sttng of capactors n radal dstrbuton feeders, (DP) for szng and fnally (GA) for fndng the optmum shape of membershp functons whch are used n fuzzy reasonng stage In Ref. [8], capactor placement and szng are done by loss senstvty factors and partcle swarm optmzaton respectvely, but the dsadvantage of ths s that t narrows the search space for the possble capactor locatons. Ref. [9] presents a fuzzy and Partcle Swarm Optmzaton (PSO) for the placement of capactors on the prmary feeders of radal dstrbuton systems to reduce the power losses and to mprove the voltage profle. A two-stage ology s used for the optmal capactor placement problem. In the frst stage, fuzzy approach s used to fnd the optmal capactor locatons and n the second stage, Partcle Swarm Optmzaton s used to fnd the szes of the capactors. The szes of the capactors correspondng to maxmum annual savngs are determned by consderng the cost of the capactors. Also ths technque narrows search space for possble capactor locatons whch results n not reachng maxmum system losses reducton. Ref. [0] presents an approach for capactor placement n radal dstrbuton feeders to reduce the real power losses and to mprove voltage profle. The locaton of the nodes where the capactors should be placed s decded by set of rules gven by the fuzzy expert systems [FES].Then szng of capactors s modeled as an optmzaton problem and objectve functon s solved usng a Hybrd Partcle Swarm Optmzaton (HPSO) technque. In Ref. [ ], reactve power s mnmzed usng partcle swarm optmzaton (PSO) algorthm.it s appled to standard reactve power wth voltage devaton problem by combnng of two objectve functons; real power loss and voltage profle mprovement. In ths paper, we revew and mplement accelerated partcle swarm optmzaton (PSO) algorthm appled to three actual dstrbuton feeders. Ths technque s not a tral and error optmzaton technque. It s set of defnte arranged procedures guaranteed to lead to the global optmal soluton. Ths new has the ablty to gve the best results concernng maxmum reducton n system losses and costs wth voltage profle mprovement wthout voltage volatons. II. PROBLEM FORMULATION A. Basc Concept of Partcle Swarm Optmzaton Partcle swarm optmzaton (PSO) s a populaton-based optmzaton technque that s orgnally nspred by the socologcal behavor assocated wth brd flocng and fsh schoolng []. One of the man advantages of PSO s that t needs no gradent nformaton derved from the objectve functon. The aforementoned feature s a common property of all evolutonary algorthms (EA), ncludng PSO, allowng them to be used on functons where the gradent s ether Reference Number: JO-P

3 Internatonal Journal on Power Engneerng and Energy (IJPEE) Vol. (4) No. (4) ISSN Prnt (34 738) and Onlne (34 730X) October 03 unavalable (due to the dscontnuty of most of real functons), or computatonally expensve to obtan. The man dea of the PSO algorthm s to mantan a populaton of partcles (agents), referred to as swarm, where each partcle represents a potental soluton to the objectve functon under consderaton. Each partcle n the swarm can memorze ts current poston that s determned by evaluaton of the objectve functon, velocty, and the best poston vsted durng ts flyng tour n the problem search space referred to as personal best poston ( pbest). The personal best poston s the one that yelds the hghest ftness value for that partcle. For a mnmzaton tas, the poston havng a smaller functon value s regarded to as havng a hgher ftness. Also the best poston vsted by all the partcles are memorzed,.e. the best poston among all pbest postons referred to as global best poston ( gbest). The partcles of the swarm are assumed to travel the problem search space n a dscrete rather than contnuous tme steps. At each tme step (teraton), the velocty of each partcle s modfed usng ts current velocty and ts dstance from pbest and gbest accordng to: pbest s v = v + c rand ) + ( * () * v + c ( gbest s ) * rand() * () s the th velocty component at teraton rand() s random number between 0 and s s the current poston n the th dmenson c, c pbest gbest are the acceleraton coeffcents s the personal best poston n the th dmenson s the global best poston n the th dmenson s the tme step Usually the value of the velocty s clamped to the range v max, v ] to reduce the possblty that the partcle mght [ max fly out of the search space. If the space s defned by the bounds [ x max, xmax ], then the value of v max s typcally set so that v = x, where 0. [4]. After that, max max each partcle s allowed to update ts poston usng ts current velocty to explore the problem search space for a better soluton as follows: s + = s + v + * t It s a common practce n PSO lteratures to choose a unty tme step ( ), accordngly ( ) s set to one throughout ths wor. The personal best poston s updated after the th teraton accordng to: () + pbest ff f ( s ) f ( pbest ) + pbest = + + (3) s ff f ( s ) < f ( pbest ) Referrng to (), the velocty update equaton has three terms; the frst term represents the partcle s memory of ts current velocty (change n poston) n the dfferent dmensons of the search space, the second term s assocated wth cognton snce t only taes nto account the partcle s own experence, whle the thrd one represents the socal nteracton between the partcles. These three components are shown n Fg. [3]. Each agent updates each locaton accordng to the nteracton of the above three components, as llustrated n Fg.. A better way to understand the mechansm of the stochastc search done by PSO s to thn of each teraton not as a process of replacng the prevous populaton wth a new one (death and brth), but rather as a process of adaptaton []. Attemptng to ncrease the rate of convergence of the standard PSO algorthm to a global optmum, the nerta weght has been ntroduced n the velocty update equaton [4]. The nerta weght s a scalng factor assocated wth the velocty durng the prevous tme step. Accordng to ths modfcaton proposed, equaton () s modfed to: v ( pbest s + c * rand ()* ( gbest s ) + c * rand () * = wv ) + where w s the nerta weght (4) The nerta weght governs how much of the prevous velocty should be retaned from the prevous tme step. The nerta weght s set to decrease lnearly from 0.9 to 0.4 durng the course of a smulaton. Ths settng allows the PSO to explore a large area at the start of the smulaton (when the nerta weght s large), and to refne the search later by usng a small nerta weght. In addton, dampng the oscllatons of the partcles around gbest s another advantage ganed by usng a decreasng nerta weght. These oscllatons are recorded when a large constant nertal weght s used. Accordngly, dampng such oscllatons asssts the partcles of the swarm to converge to the global optmal soluton. In bref, the nerta weght can be lened to the temperature parameter encountered n smulated annealng []. In bref, the PSO algorthm can be summarzed as follows [5]:. Create an ntal swarm, wth a random dstrbuton and random ntal veloctes. Reference Number: JO-P

4 Internatonal Journal on Power Engneerng and Energy (IJPEE) Vol. (4) No. (4) ISSN Prnt (34 738) and Onlne (34 730X) October 03. Calculate a velocty vector for each partcle, usng the partcle's memory and the nowledge ganed by the swarm. 3. Update the poston of each partcle, usng ts velocty vector and prevous poston. 4. Update the personal best poston of each partcle, and the global best poston of all partcles. 5. Go to step and repeat untl convergence, or the termnaton crtera s met. ( socal nteracton) v gbest ( cognton) v pbest v + s + It s mportant to realze that the velocty term models the rate of change n the poston of the partcle. Therefore, the changes nduced by the velocty update equaton represent acceleraton, whch explans the name of acceleraton coeffcents for the constants c and c. The acceleraton coeffcents can be thought of as a balance between exploraton (searchng for a good soluton) and explotaton (tang advantage of someone else's success). Too lttle exploraton and the partcles wll all converge on the frst good soluton encountered, whle too lttle explotaton and the partcles wll never converge,.e. they wll just eep searchng. There s another way of loong at ths rather than behavors (exploraton and explotaton). What mu st be properly balanced s ndvdualty and socalty,.e. trats that nfluence behavor. Ideally, ndvduals prefer beng ndvdualstc yet they stll le to now what others have acheved so that they can learn from. pbest gbest pbest O rgnal ve locty Ve locty towards pbest Ve locty towards gbest Re sultant ve locty Fg. The three components of the velocty update equaton. s v Fg. The poston updates operaton of agents. B. Accelerated Partcle Swarm Optmzaton From Ref.[6] t s shown that the standard partcle swarm optmzaton (PSO) uses both the current global best g* and ndvdual best S *.The reason of usng the ndvdual best s prmarly to ncrease the dversty n qualty solutons, however, ths dversty can be smulated usng some randomness.subsequently, there s no compellng reason for usng the ndvdual best. A smplfed verson whch could accelerate the convergence of the algorthm s to use global best only. Thus n the accelerated partcle swarm optmzaton.the velocty vector s generated by a smpler formula v = v + * ( 0.5) + ( g * s ) (5) + where ɛ s a random varable wth values from 0 to. Here the shft 0.5 s purely out of convenence. we can also use a standard normal dstrbuton αɛ n where ɛ n s drawn from N(0,) to replace the second term Now the update of poston s smply s = s + v (6) + + In order to ncrease the convergence even further, we can also wrte the update of the locaton n sngle step s + = ( ) s + g * + Ths smpler verson wll gve the same order of convergence. The typcal values for ths accelerated PSO acceleraton constants are α 0. ~ 0.4 and β 0.~ 0.7 t s worth pontng out that the parameters α and β should be n general related to the scales of the ndependent varables S and search doman A further mprovement to accelerated PSO s to reduce the randomness as teratons proceed.ths means that we can use a monotoncally decreasng functon such as n (7) Reference Number: JO-P

5 Internatonal Journal on Power Engneerng and Energy (IJPEE) Vol. (4) No. (4) ISSN Prnt (34 738) and Onlne (34 730X) October 03 t = 0 (8) where α ~ s the ntal value of randomness parameter. Here t s the number of teratons or tme steps. 0 < γ < s a control parameter. C. The Algorthm Steps The algorthm steps can be summarzed as: a. Perform a load flow calculaton for the uncompensated feeder and determne actve power losses. Defne the cost functon. We wll defne the cost functon as the form used n [4], whch depends on system losses P loss, capactor sze Q c, and capactor cost K c, as follows: Cost = K p c * P loss + K j Q j= Where K p s the cost per power loss ($/W/year), j=, represent the selected buses. b. Intalze the swarm by generatng randomly (n) number of partcles & set teraton counter =0 c. Evaluate ftness value (objectve functon) of each partcle d. If ftness (x) > ftness (pbest), then pbest = x e. If ftness (x) > ftness (gbest), then gbest = x f. Run the load flow for reactve power compensaton and store objectve functon value g. Update teraton counter h. Update the partcles veloctes usng equaton (5). Calculate partcles new postons usng equaton (7) j. Chec that there s no volaton to the specfed constrants.. Re-evaluate ftness value of each partcle at the new locatons & correspondng the current global best l. Now, run the load flow for reactve power compensaton wth updated partcles. m. If the teraton number exceeds the maxmum number of teratons, then Output the optmal soluton. otherwse go to step (c) From ths algorthm, we note that attenton s placed on power loss reducton, cost mnmzaton and voltage profle mprovement wthout voltage volatons. III. IMPLEMENTATTION AND RESULTS A. The Frst Feeder The 9-bus radal dstrbuton feeder of [8] s the frst feeder to be studed. The rated voltage s 3 V. The system s shown n Fg. 3. The feeder data s gven n [8]. S c j (9) Fg.3 The 9-bus Test Feeder The objectves of capactor placement are to reduce the power loss and eep voltages wthn prescrbed lmts wth mnmum cost. Consderng nvestment cost, there are a fnte number of standard capactor szes that are nteger multples of the smallest sze Q c. The cost per VAr vares from one sze to another. Generally, larger szes are cheaper than smaller ones. Let the maxmum permssble capactor sze be Qc max = L * Qc 0 (0) Where L s an nteger. Then at each selected locaton, there are L szes to choose from. For the test feeder, K p s selected to be $ 68/W [7]. Commercally avalable capactor szes wth $/VAr are used n the analyss. Table I shows an example of such data. For reactve power compensaton, the maxmum capactor sze Q c max should not exceed the reactve load,.e. 486 VAr. Ths results n 7 possble capactor szes shown n Table II wth ther correspondng cost/var. The values of the 7 choces are derved from Table II by assumng a capactor lfe expectancy of 0 years (the operatng costs are neglected) [7]. TABLE I AVAILABLE 3-PHASE CAPACITOR SIZES AND COST Sze (VAr) Cost ($) TABLE II POSSIBLE CHOICES OF CAPACITOR SIZES AND COST/VAr J Q c (VAr) $/VAr J Q c (VAr) $/VAr J Q c (VAr) $/VAr J Q c (VAr) $/VAr From load flow soluton for ths feeder, before compensaton, the total actve and reactve loads are W and VAr. The cost functon and the total power losses are $ 3,675 and W respectvely. The Reference Number: JO-P

6 Internatonal Journal on Power Engneerng and Energy (IJPEE) Vol. (4) No. (4) ISSN Prnt (34 738) and Onlne (34 730X) October 03 maxmum and mnmum bus voltage magntudes are and pu respectvely, where the voltage of the substaton (bus no. 0) s assumed to be pu, thus we have generally V.0 pu. We mplemented our proposed accelerated PSO and the results were promsng.the real power loss has been reduced from ts ntal confguraton loss of KW to KW. Also the annual cost per year has been reduced from 3, 675 K$ to 5, 69 K$. Also the mnmum voltage n pu s 0.9 and the maxmum voltage n pu s.005. The optmal sze of the capactors at the buses, 4, 6, 9 s 4050, 350, 650 and 50 VAr, respectvely. Our optmzed result has been compared wth the prevous publshed wors for the capactor placement problem and results are shown n Table III Total annual cost for PSO n [8] s calculated accordng to Table II. TABLE III COMPARISON OF OPTIMIZATION RESULTS OBTAINED THROUGH DIFFERENT METHODS FOR 9- BUS RADIAL DISTRIBUTION FEEDER Parameters Fnal power loss(w) Fuzzy & Heurstc [8] Hybrd [7] Self Adaptve Dfferental Evoluton [5] PSO [8] Proposed The power factor s 0.7.The total apparent power 75 VA. Total actve and reactve power losses of ths system are 6.79 W and 57.3 VAr respectvely.the voltage range s V.0 p.u. Here voltage profle mprovement s not a target..fgure 5 shows that our proposed leads to better results compared wth the PSO used n [8] regardng the actve power losses ( W) of the system. The optmal szes of the capactors at buses 3, 6, are 900, 300 and 50 VAr, respectvely. The actve power losses after compensaton s 3.3 W wth total capactor sze nstalled of 350 VAr. The total annual cost ($/year ) s calculated and found to be 5,77 $. C. The Thrd Feeder The thrd test feeder s a.66 V, 69-bus dstrbuton feeder. The feeder conssts of man feeder and seven laterals. The scheme of ths feeder s shown n fgure 6. The data of ths feeder s gven n [8]. Before compensaton, the cost s $37,653; ths s based on the prevously defned cost functon, and the total actve and reactve loads are 380. W and VAr. The actve and reactve losses are 4. W and 0.7 VAr respectvely. The voltage range s V.0 p.u. Total Annual cost ($/year) 6,380 6,30 8,340 7, 608 5,69 B. The Second Feeder The second feeder, shown n Fg. 4, s V and conssts of 5 buses. The data of ths feeder s gven n [9]. Fg. 5 Comparson of the actve power losses of the second feeder after compensaton usng proposed technque and PSO of [8] 7e 8e S e Fg. 4 The 5-bus Test Feeder Reference Number: JO-P

7 Internatonal Journal on Power Engneerng and Energy (IJPEE) Vol. (4) No. (4) ISSN Prnt (34 738) and Onlne (34 730X) October and DE n [3]. As shown, our proposed technque gves the least annual costs. Fg. 6 Scheme of the 69-bus radal dstrbuton system Table IV shows a comparson between dfferent s used for actve power loss mnmzaton, cost reducton and voltage profle mprovement of ths feeder. From ths comparson, t s obvous that our proposed algorthm gves the optmum actve power loss reducton after capactor nstallaton. The actve power loss after compensaton s 45. W. The optmal szes of the capactors placed at the buses 6, 37, 49, and 55 are 300, 600, 350, and 50 VAr, respectvely. TABLE IV SYSTEM CONDITIONS WITHOUT AND WITH CAPACITORS PLACEMENT USING DIFFERENT OPTIMIZATION METHODS FOR THE 69 BUS SYSTEM Parameters Fnal power loss(w) Total Capactor Sze (VAr) Total Annual cost ($/year) Mn. Bus voltage Max. Bus voltage Before Capactor After Capactor placement usng DE [3] After Capactor placement usng GA [30 ] After Capactor placement usng proposed _ _ 30,93 8,607 4, In Fg. ( 7 ), the total annual cost of the capactors usng our proposed accelerated partcle swarm optmzaton s compared wth PSO n [8], Genetc Algorthms, GA n [30] Fg.7 Comparson of annual cost ($/year) for dfferent optmzaton s wth proposed technque IV. CONCLUSIONS Ths paper ensures that the accelerated partcle swarm technque can be consdered powerful for solvng the capactor allocaton problem for radal dstrbuton feeders. Regardless of the feeder nature, our proposed gves the maxmum power loss and cost reducton accompaned by better voltage profle mprovement wthout buses voltage volaton. The technque converges to the optmal soluton wth hgh qualty. Also the codng of accelerated PSO s smple and gves more accurate results. V. REFERENCES [] H. N. Ng, M. M. A. Salama, A. Y. Chhan, Classfcaton of Capactor Allocaton Technques, IEEE Trans. on Power Delvery, Vol. 5, No., Jan. 000, pp [] G. A. Bortgnon, M. E. El-Hawary, A Revew of Capactor Placement Technques for Loss Reducton n Prmary Feeders on Dstrbuton Systems, Canadan Conference on Electrcal and Computer Engneerng, Vol., 995, pp [3] S. Cvanlar, J. J. Granger, H. Yn, S. S. H. Lee Dstrbuton Feeder Reconfguraton for Loss Reducton, IEEE Trans. on Power Delvery, Vol.3, No.3, July.988, pp [4] T. Taylor, D. Lubeman, Implementaton of Heurstc Search Strateges for Dstrbuton Feeder Reconfguraton, IEEE Trans. on Power Delvery, Vol. 5, No., 990, pp [5] T. S. Abdel Salam, A.Y. Chhan, R. Hacam, A New Technque for Loss Reducton Usng Compensatng Capactors Appled to Dstrbuton Systems wth Varyng Load Condton, IEEE Trans. on Power Delvery, Vol. 9, No., 994, pp [6] M. Chs, M. M. A. Salama, S. Jayaram, "Capactor Placement n Dstrbuton Systems Usng Heurstc Search Strateges ", IEE Proceedngs, Generaton, Transmsson and Dstrbuton, Vol. 44, No. 3, 997, pp [7] M. H. Haque, Capactor Placement n Radal Dstrbuton Systems for Loss Reducton, IEE Proceedngs, Generaton, Reference Number: JO-P

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