Optimal Capacitor Placement in a Radial Distribution System using Plant Growth Simulation Algorithm

Transcription

1 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal, omputer, Energetc, Electronc and ommuncaton Engneerng ol:, No:9, 8 Optmal apactor Placement n a Radal Dstrbuton System usng Plant Growth Smulaton Algorthm R. Srnvasa Rao and S.. L. Narasmham Internatonal Scence Index, Electrcal and omputer Engneerng ol:, No:9, 8 waset.org/publcaton/83 Abstract Ths paper presents a new and effcent approach for capactor placement n radal dstrbuton systems that determne the optmal locatons and sze of capactor wth an objectve of mprovng the voltage profle and reducton of power loss. The soluton methodology has two parts: n part one the loss senstvty factors are used to select the canddate locatons for the capactor placement and n part two a new algorthm that employs Plant growth Smulaton Algorthm (PGSA s used to estmate the optmal sze of capactors at the optmal buses determned n part one. The man advantage of the proposed method s that t does not requre any external control parameters. The other advantage s that t handles the objectve functon and the constrants separately, avodng the trouble to determne the barrer factors. The proposed method s appled to 9, 34, and 85-bus radal dstrbuton systems. The solutons obtaned by the proposed method are compared wth other methods. The proposed method has outperformed the other methods n terms of the qualty of soluton. Keywords Dstrbuton systems, apactor placement, loss reducton, Loss senstvty factors, PGSA. I. INTRODUTION HE loss mnmzaton n dstrbuton systems has assumed Tgreater sgnfcance recently snce the trend towards dstrbuton automaton wll requre the most effcent operatng scenaro for economc vablty varatons. Studes have ndcated that as much as 3% of total power generated s wasted n the form of losses at the dstrbuton level []. To reduce these losses, shunt capactor banks are nstalled on dstrbuton prmary feeders. The advantages wth the addton of shunt capactors banks are to mprove the power factor, feeder voltage profle, Power loss reducton and ncreases avalable capacty of feeders. Therefore t s mportant to fnd optmal locaton and szes of capactors n the system to acheve the above mentoned objectves. Snce, the optmal capactor placement s a complcated combnatoral optmzaton problem, many dfferent optmzaton technques and algorthms have been proposed n the past. Schmll [] developed a basc theory of optmal capactor placement. He presented hs well known /3 rule for the placement of one capactor assumng a unform load and a unform dstrbuton feeder. Duran et al [3] consdered the capactor szes as dscrete varables and employed dynamc programmng to solve the problem. Granger and Lee [4] developed a nonlnear programmng based method n whch capactor locaton and capacty were expressed as contnuous varables. Granger et al [5] formulated the capactor placement and voltage regulators problem and proposed decoupled soluton methodology for general dstrbuton system. aran and Wu [6, 7] presented a method wth mxed nteger programmng. Sundharajan and Pahwa [8] proposed the genetc algorthm approach to determne the optmal placement of capactors based on the mechansm of natural selecton. In most of the methods mentoned above, the capactors are often assumed as contnuous varables. However, the commercally avalable capactors are dscrete. Selectng nteger capactor szes closest to the optmal values found by the contnuous varable approach may not guarantee an optmal soluton [6]. Therefore the optmal capactor placement should be vewed as an nteger-programmng problem, and dscrete capactors are consdered n ths paper. As a result, the possble solutons wll become a very large number even for a medum-szed dstrbuton system and makes the soluton searchng process become a heavy burden. In ths paper, apactor Placement and Szng s done by Loss Senstvty Factors and Plant Growth Smulaton Algorthm (PGSA respectvely. The loss senstvty factor s able to predct whch bus wll have the bggest loss reducton when a capactor s placed. Therefore, these senstve buses can serve as canddate locatons for the capactor placement. PGSA s used for estmaton of requred level of shunt capactve compensaton to mprove the voltage profle of the system. The proposed method s tested on 9, 34 and 85 bus radal dstrbuton systems and results are very promsng. The advantages wth the Plant Growth Smulaton algorthm (PGSA s that t treats the objectve functon and constrants separately, whch averts the trouble to determne the barrer factors and makes the ncrease/decrease of constrants convenent, and that t does not need any external parameters such as crossover rate, mutaton rate, etc. It adopts a gudng search drecton that changes dynamcally as the change of the objectve functon. The remanng part of the paper s organzed as follows: Secton II gves the problem formulaton; Secton III senstvty analyss and loss factors; Sectons I gves bref descrpton of the plant growth smulaton algorthm; Secton Internatonal Scholarly and Scentfc Research & Innovaton (9 8 97

2 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal, omputer, Energetc, Electronc and ommuncaton Engneerng ol:, No:9, 8 Internatonal Scence Index, Electrcal and omputer Engneerng ol:, No:9, 8 waset.org/publcaton/83 develops the test results and Secton I gves conclusons. II. PROLEM FORMULATION The objectve of capactor placement n the dstrbuton system s to mnmze the annual cost of the system, subjected to certan operatng constrants and load pattern. For smplcty, the operaton and mantenance cost of the capactor placed n the dstrbuton system s not taken nto consderaton. The three-phase system s consdered as balanced and loads are assumed as tme nvarant. Mathematcally, the objectve functon of the problem s descrbed as: mn f mn(ost ( where OST s the objectve functon whch ncludes the cost of power loss and the capactor placement. The voltage magntude at each bus must be mantaned wthn ts lmts and s expressed as: where mn ( max s the voltage magntude of bus, mn and max are bus mnmum and maxmum voltage lmts, respectvely. The power flows are computed by the followng set of smplfed recursve equatons derved from the sngle-lne dagram depcted n Fg n P, Q P, Q P -, Q - P, Q P +, Q + P n, Q n P L, Q L ( P Q. P PL R, (3 P Q P L+, Q L+ Q Q ( R L, P L, Q L X ( R,, X. P, P L+, Q L+ Fg. Sngle-lne dagram of a man feeder ( P Q. X,. Q ( P Q. P Ln, Q Ln where P and Q are the real and reactve powers flowng out of bus, and P L and Q L are the real and reactve load powers at bus. The resstance and reactance of the lne secton between buses and + are denoted by R,+ and X,+, (4 (5 respectvely. The power loss of the lne secton connectng buses and + may be computed as P Loss ( P Q (, R,. (6 The total power loss of the feeder, P T,Loss, may then be determned by summng up the losses of all lne sectons of the feeder, whch s gven as n T,Loss PLoss(, P (7 onsderng the practcal capactors, there exsts a fnte number of standard szes whch are nteger multples of the smallest szeq. esdes, the cost per kar vares from one sze to another. In general, capactors of larger sze have lower unt prces. The avalable capactor sze s usually lmted to Q LQ (8 max where L s an nteger. Therefore, for each nstallaton locaton, there are L capactor szes Q, Q, 3Q,..., LQ avalable. Gven the annual nstallaton cost for each compensated bus, the total cost due to capactor placement and power loss change s wrtten as n c c P PT,Loss ( K cf K Q OST K (9 where n s number of canddate locatons for capactor placement, K p s the equvalent annual cost per unt of power loss n $/(kw-year; K cf s the fxed cost for the capactor placement. The constant K s the annual capactor nstallaton cost, and, =,,...,n are the ndces of the buses selected for compensaton. The bus reactve compensaton power s lmted to n c Q Q ( where Q and Q L are the reactve power compensated at bus and the reactve load power at bus, respectvely. III. SENSITIITY ANALYSIS AND LOSS SENSITIITY FATORS The canddate nodes for the placement of capactors are L Internatonal Scholarly and Scentfc Research & Innovaton (9 8 97

3 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal, omputer, Energetc, Electronc and ommuncaton Engneerng ol:, No:9, 8 Internatonal Scence Index, Electrcal and omputer Engneerng ol:, No:9, 8 waset.org/publcaton/83 determned usng the loss senstvty factors. The estmaton of these canddate nodes bascally helps n reducton of the search space for the optmzaton procedure. onsder a dstrbuton lne wth an mpedance R+jX and a load of P eff + jq eff connected between p and q buses as gven below. Actve power loss n the k th lne s gven by, * R k whch can be expressed as, I k p ( Peff [ q ] Qeff [ q ]R[ k ] Plneloss [ q ] ( ( [ q ] Smlarly the reactve power loss n the k th lne s gven by ( Peff [ q] Qeff [ q] X[ k] Qlneloss[ q] ( ( [ q] Where, P eff [q] = Total effectve actve power suppled beyond the node q. Qeff[q] = Total effectve reactve power suppled beyond the node q. Now, both the Loss Senstvty Factors can be obtaned as shown below: P ( * Q [ q]* R[ k] lneloss eff (3 Q ( [ q] eff Q Q lneloss eff R+jX k th -Lne ( * Qeff [ q]* X[ k] ( [ q] anddate Node Selecton usng Loss Senstvty Factors: (4 The Loss Senstvty Factors ( Plneloss Qeff are calculated from the base case load flows and the values are arranged n descendng order for all the lnes of the gven system. A vector bus poston bpos[] s used to store the respectve end buses of the lnes arranged n descendng order of the values ( Plneloss Qeff.The descendng order of ( Plneloss Qeff elements of bpos[] vector wll decde the sequence n whch the buses are to be consdered for compensaton. Ths sequence s purely governed by the ( Plneloss Qeff and hence the proposed Loss Senstve oeffcent factors become very powerful and useful n capactor allocaton or Placement. At these buses of bpos[] vector, normalzed voltage magntudes are calculated by q P eff + jq eff consderng the base case voltage magntudes gven by (norm[]=[]/.95. Now for the buses whose norm[] value s less than. are consdered as the canddate buses requrng the apactor Placement. These canddate buses are stored n rank bus vector. It s worth note that the Loss Senstvty factors decde the sequence n whch buses are to be consdered for compensaton placement and the norm[] decdes whether the buses needs Q-ompensaton or not. If the voltage at a bus n the sequence lst s healthy (.e., norm[]>. such bus needs no compensaton and that bus wll not be lsted n the rank bus vector. The rank bus vector offers the nformaton about the possble potental or canddate buses for capactor placement. The szng of apactors at buses lsted n the rank bus vector s done by usng Plant Growth Smulaton Algorthm. I. PLANT GROWTH SIMULATION ALGORITHM The plant growth smulaton algorthm [5] s based on the plant growth process, where a plant grows a trunk from ts root; some branches wll grow from the nodes on the trunk; and then some new branches wll grow from the nodes on the branches. Such process s repeated, untl a plant s formed. ased on an analogy wth the plant growth process, an algorthm can be specfed where the system to be optmzed frst grows begnnng at the root of a plant and then grows branches contnually untl the optmal soluton s found. y smulatng the growth process of plant phototropsm, a probablty model s establshed. In the model, a functon g(y s ntroduced for descrbng the envronment of the node Y on a plant. The smaller the value of g(y, the better the envronment of the node for growng a new branch. The outlne of the model s as follows: A plant grows a trunk M, from ts root o. Assumng there are k nodes M, M, M3,.., Mk that have better envronment than the root on the trunk M, whch means the functon g(y of the nodes and satsfy g( M < g( o then morphactn concentratons M, M,., Mk of nodes M, M, M3,, MK are calculated usng g( g( M M (,,... k (5 k ( g( g( M. Random number M M Mk Fg. Morphactn concentraton state space The sgnfcance of equaton (5 s that the morphactn concentraton of a node s not only dependent on ts envronmental nformaton but also depends on the Internatonal Scholarly and Scentfc Research & Innovaton (

4 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal, omputer, Energetc, Electronc and ommuncaton Engneerng ol:, No:9, 8 Internatonal Scence Index, Electrcal and omputer Engneerng ol:, No:9, 8 waset.org/publcaton/83 envronmental nformaton of the other nodes n the plant, whch really descrbes the relatonshp between the morphactn concentraton and the envronment. From (5, we can dervate k M, whch means that the morphactn concentratons M, M,., Mk of nodes M, M, M3,, MK form a state space shown n Fg.. Selectng a random number n the nterval [, ], s lke ball thrown to the nterval [, ] and wll drop nto one of M, M,, Mk n Fg., then the correspondng node that s called the preferental growth node wll take prorty of growng a new branch n the next step. In other words, MT wll take prorty of growng a new branch f the selected satsfes T ( or M T T T M M ( T,3,..., k. For example, f random number drops nto M, whch means M M, then the node M wll grow a new branch m. Assumng there are q nodes m, m, m3,.., mq, whch have a better envronment than the root, on the branch m, and ther correspondng morphactn concentratons are m, m,., mq. Now, not only the morphactn concentratons of the nodes on branch m need to be calculated, but also the morphactn concentratons of the nodes except M (the morphactn concentraton of the node M becomes zero after growng the branch m on trunk M need to be recalculated after growng the branch m. The calculaton can be done usng (6, whch s ganed from (5 by addng the related terms of the nodes on branch m and abandonng the related terms of the node M M mj where g( g( j g( g(, q k ( g( ( g( M mj g( g( (,3,... k ( j,,... q M mj. (6 k q We can also dervate M, j mj from (6. Now, the morphactn concentratons of the nodes (except M on trunk M and branch m wll form a new state space (The shape s the same as Fg., only the nodes are more than that n Fg.. A new preferental growth node, on whch a new branch wll grow n the next step, can be ganed n a smlar way as M. Such process s repeated untl there s no new branch to grow, and then a plant s formed. From the vewpont of optmal mathematcs, the nodes on a plant can express the possble solutons; g(y can express the objectve functon; the length of the trunk and the branch can express the search doman of possble solutons; the root of a plant can express the ntal soluton; the preferental growth node corresponds to the basc pont of the next searchng process. In ths way, the growth process of plant phototropsm can be appled to solve the problem of nteger programmng. A complete algorthm for the proposed method of capactor placement s gven below:. nput the system data such as lne and load detals of the dstrbuton system, constrants lmts etc.;. form the search doman by gvng the range of capactor ratngs (kar ratngs avalable whch corresponds to the length ofthe trunk and the branch of a plant; 3. gve the ntal soluton X (X s vector whch corresponds to the root of a plant, and calculate the ntal value objectve functon (power loss; 4. let the ntal value of the basc pont X b, whch corresponds to the ntal preferental growth node of a plant, and the ntal value of optmzaton X best equal to X o, and let F best that s used to save the objectve functon value of the best soluton X best be equal to f(x o, namely, X b = X best = X o and F best = f(x o ; 5. dentfy the canddate buses for capactor placement usng Loss Senstvty Factors; 6. ntalze teraton count, =; 7. for j=n to m(wth step sze, where m s the mnmum avalable sze and n s maxmum avalable sze; 8. search for new feasble solutons: place kar at senstve nodes n a sequence startng from basc pont X b =[X b,x b,.x b,..x n b ], where X b corresponds to the ntal kar; 9. for each soluton X b n step 8, calculate the nodes voltages of the buses;. f the node voltage constrants s satsfed go to step ; otherwse abandon the possble soluton X b and goto step ;. calculate powerloss f(x b for each soluton of X b n step 8 and compare wth f(x o. Save the feasble solutons f f(x b less than f(x o ; Otherwse goto step ;. f >=N max go to step 6; otherwse goto step 4; 3. calculate the probabltes,,. k of feasble solutons X,X,.X k, by usng equaton (5, whch corresponds to determnng the morphatn concentraton of the nodes of a plant; 4. calculate the accumulatng probabltes,,. k of the solutons X,X,.X k. Select a random number Internatonal Scholarly and Scentfc Research & Innovaton (

5 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal, omputer, Energetc, Electronc and ommuncaton Engneerng ol:, No:9, 8 Internatonal Scence Index, Electrcal and omputer Engneerng ol:, No:9, 8 waset.org/publcaton/83 from the nterval [ ], must belong to one of the ntervals [ ], (, ],.,( k-, k ], the accumulatng probablty of whch s equal to the upper lmt of the correspondng nterval, and t wll be the new basc pont X b for the next teraton, whch corresponds to the new preferental growth node of a plant for next step; 5. ncrement by + and return to step 6; 6. output the results and stop. The flow chart for the proposed method based on the algorthm s gven n the fg. 3. Start =+ Input data (lne and load data and constrant lmts Intalze X o and compute f(x o Assgn X b = X o Senstvty analyss for dentfyng potental locatons and ntalze = For j=m to n (capactor mn. and max. Sze Place capactors at senstvty nodes and search for new feasble solutons Node voltage computaton oltages volatng the constrants? No Yes ompute f(x b for all possble solutons of [X b ] f (X p <f(x o No Yes Save possble feasble soluton set No N max Yes Probabltes of all feasble solutons New basc pont X b for next teraton Fg. 3 Flow chart for proposed method Abandon possble soluton [X b ] Output Stop. TEST RESULTS The proposed method has been programmed usng MATLA and run on a Pentum I, 3-GHz personal computer wth.99 G RAM. The effectveness of the proposed method for loss reducton by capactor placement s tested on 9 bus, 34 bus and 85 bus radal dstrbuton systems. The results obtaned n these methods are explaned n the followng sectons. A. 9 - us system The frst test case for the proposed method s a -bus, sngle feeder, radal dstrbuton system [6] shown n fg.4. Ths system has zero laterals. The rated lne voltage of the system s 3 k. The detals of the feeder and the load characterstcs are gven n Table S Lne No. Fg. 4 A 9-Secton feeder TALE ILOAD AND LINE DATA OF 9-US SYSTEM From To R,+ X,+ P L Q L us, us,+ ( ( (kw (kar For ths test feeder, K P s selected s selected to be 68 $/(kw-year [6]. ommercally avalable capactors szes wth $/kar are used n the analyss. Table shows the example of such data. TALE II AAILALE THREE PHASE APAITOR SIZES AND OSTS Sze (kar ost ($ Only fxed capactors are used n the analyss and the margnal cost of capactors (K c [8] gven n Table 3 are used to compute the total annual cost. The fxed cost of the capactor, K cf s selected as $ [] wth a lfe expectancy of ten years (the mantenance and runnng costs are neglected. The substaton voltage (bus s consdered as. p.u. The lmt of voltage magntude s taken between.9 ~. p.u. The method of senstve analyss s used to select the canddate nstallaton locatons of the capactors to reduce the search space. The buses are ordered accordng to ther senstvty value ( Plneloss Qeff (.e., bus 6, 5, 9,, 8 and 7. Top four buses are selected as optmal canddate locatons and then amount of kar to be njected n the selected buses s optmzed by PGSA. Internatonal Scholarly and Scentfc Research & Innovaton (

6 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal, omputer, Energetc, Electronc and ommuncaton Engneerng ol:, No:9, 8 Internatonal Scence Index, Electrcal and omputer Engneerng ol:, No:9, 8 waset.org/publcaton/83 TALE III POSSILE SIZES OF APAITORS AND SIZES IN $/KAR j c Q j $/kar j c Q j $/kar j c Q j $/kar j c Q j $/kar Usng ths method, the capactors of ratng,,, 47 kar are placed at the optmal canddate locatons 6, 5, 9, and respectvely. The ntal power loss s kw and t s reduced to kw after capactor placement usng the proposed method. The results of the proposed method are shown n Table 4. Table 4 also shows the comparson of results wth Fuzzy reasonng [9] and Partcle Swarm Optmzaton (PSO []. The mnmum and maxmum voltages before capactor placement are.8375 p.u (bus and.999 p.u (bus and these are mproved to.9 p.u (bus and.999 p.u (bus after capactors placement. TALE I SIMULATION RESULTS OF 9-US SYSTEM Items Uncompensated ompensated Fuzzy PSO [] Proposed reasonng [9] Total losses (kw Loss reducton (% Optmal locatons and Sze n kar Total kar Annual ost 3,674 9,4 8,58 8,34 ($/year Net Savngs ---,55 3,9 3,334 ($/year %Savng From Table 4, t s observed that the power loss obtaned wth the proposed method s less than the Fuzzy reasonng [9] and PSO []. The optmal canddate locatons are the same wth all methods but the total kar njected by the proposed method s less than the other two. The selecton of the allowable consecutve teratve number N max depends hghly on the solved problem. The N max value s tred from to 5. All of the results converge to the same optmal soluton wth N max greater than 4. The convergence characterstcs of power loss of the PGSA n ths test system are shown n fg. 5. It can be observed that the number of teratons taken s only four on ths computer. The PU tme needed s only.6 seconds us system The second test case for the proposed method s a 34-bus radal dstrbuton system []. Ths system has a man feeder and four laterals (sub-feeders. The sngle lne dagram s shown n fg. 6. The lne and load data of the feeders are taken from the reference []. The rated lne voltage of the system s k. S Fg. 5 onvergence curve of PGSA Fg bus dstrbuton network confguraton Smlar to test case, the senstve analyss method s used to select the canddate nstallaton locatons of the capactor to reduce the search space. The buses are ordered accordng to ther senstvty value as {9,,,, 3, 4, 5, 6, and 7}. Top three buses are selected as optmal canddate locatons and the amount of kar njected are, 639, and kar respectvely. The constants K P, K, and K cf are same as n test case. The power loss before and after capactor placement are.67 and 6.7 kw. The mnmum and maxmum voltages before capactor placement are.947 p.u (bus 7 and.994 p.u (bus and are mproved to 973 p. and. p.u after capactor placement respectvely at the buses 7 and. The N max value s tred from to 8. All of the results converge to the same optmal soluton wth N max greater than 8. The results of the proposed method are compared wth the results of PSO method [] and Heurstc based method [] and s shown n Table 5. The mplementaton shows that the sub-feeder connected to node 6 of man feeder only need the compensaton. From the results shown n Table 5, t s observed that the optmal canddate nstallaton locatons are three for the proposed and PSO methods [], but t s four for the Heurstc method []. The c Internatonal Scholarly and Scentfc Research & Innovaton (

7 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal, omputer, Energetc, Electronc and ommuncaton Engneerng ol:, No:9, 8 Internatonal Scence Index, Electrcal and omputer Engneerng ol:, No:9, 8 waset.org/publcaton/83 power loss and net annual savngs obtaned wth proposed method are less than PSO methods and Heurstc based. The PU tme needed by the proposed method s sec. TALE SIMULATION RESULTS OF 34-US SYSTEM Items Uncompensated ompensated Heurstc PSO [] Proposed based [9] Total losses (kw Loss reducton (% Optmal locatons and Sze n kar Total kar Annual ost 37,4 33,8 9,936 8,484 ($/year Net Savng ($/year -- 4,89 7,36 8, us system The thrd test case s 85-bus radal dstrbuton system whch s same as n Das et al [3]. The lne data and feeder characterstcs are taken from reference [3]. ased on senstvty analyss buses 8, 58, and 7 are selected as optmal canddate locatons for the capactor placement. Usng proposed PGSA, the amount of kar njected are, 98, and kar at the above buses. The constants n the objectve functon are same as test case. The N max value tred from to 8 and all of the results converge to the same optmal soluton wth N max greater than 8. The mnmum and maxmum voltages before compensaton are.8877 and.995 p.u and are mproved to.9657 and.999 p.u respectvely. The power loss power loss before and after compensaton and net savngs are shown n Table 6. TALE I SIMULATION RESULTS OF 85-US SYSTEM Items Un-compensated ompensated PSO [] Proposed Total losses (kw Loss reducton (% Optmal locatons and Sze n kar Total kar Annual ost ($/year 53,4 9,5 8,585 Net Savng ($/year --- 3,99 4,455 The Table 6 also shows the comparson of results wth the PSO method []. From the results t s observed that the power loss after compensaton and net annual savngs are almost the same, but optmal canddate locatons wth the proposed method s less than the PSO method. The PU tme needed by the proposed method s.4 sec. I. ONLUSION A new and effcent approach that employs loss senstvty factors and PGSA for capactor placement n the dstrbuton system has been proposed. The loss senstvty factors are used to determne the canddate locatons of the buses requred for compensaton. The PGSA s used to estmate the requred level of shunt capactve compensaton at the optmal canddate locatons to enhance the voltage profle the system and reduce the actve power loss. The smulaton results based on 9, 34, 85-bus systems have produced the best solutons that have been found usng a number of approaches avalable n the lterature. The advantages of the proposed method are: t handles the objectve functon and the constrants separately, avodng the trouble to determne the barrer factors; the proposed approach does not requre any external parameters; 3 the proposed approach has a gudng search drecton that contnuously changes as the change of the objectve functon. Ths method places the capactors at less number of locatons wth optmum sze and offers much net annual savng n ntal nvestment. REFERENES [] Y. H. Song, G. S. Wang, A. T. Johns and P.Y. Wang, Dstrbuton network reconfguraton for loss reducton usng Fuzzy controlled evolutonary programmng, IEEE Trans. Gener., trans., Dstr., ol. 44, No.4, July 997. [] J.. Schmll, "Optmum Sze and Locaton of Shunt apactors on Dstrbuton Feeders," IEEE Transactons on Power Apparatus and Systems, vol. 84, pp , September 965. [3] H. Dura "Optmum Number Sze of Shunt apactors n Radal Dstrbuton Feeders: A Dynamc Programmng Approach", IEEE Trans. Power Apparatus and Systems, ol. 87, pp , Sep 968. [4] J. J. Granger and S. H. Lee, Optmum Sze and Locaton of Shunt apactors for Reducton of Losses on Dstrbuton Feeders, IEEE Trans. on Power Apparatus and Systems, ol., No. 3, pp. 5-8, March 98. [5] J.J. Granger and S. vanlar, olt/var control on Dstrbuton systems wth lateral branches usng shunt capactors as oltage regulators-part I, II and III, IEEE Trans. Power Apparatus and systems, vol. 4, No., pp , Nov [6] M. E aran and F. F. Wu, Optmal Szng of apactors Placed on a Radal Dstrbuton System, IEEE Trans. Power Delvery, vol. No., pp. 5-7, Jan [7] M. E. aran and F. F. Wu, Optmal apactor Placement on radal dstrbuton system, IEEE Trans. Power Delvery, vol. 4, No., pp , Jan [8] Sundharajan and A. Pahwa, Optmal selecton of capactors for radal dstrbuton systems usng genetc algorthm, IEEE Trans. Power Systems, vol. 9, No.3, pp , Aug [9] H. N. Ng, M. M. A. Salama and A. Y. hkhan, apactor Allocaton by Approxmate Reasonng: Fuzzy apactor Placement, IEEE Trans. Power Delvery, vol. 5, no., pp , Jan.. [] H..hn, Optmal Shunt apactor Allocaton by Fuzzy Dynamc Programmng, Electrc Power Systems Research, pp.33-39, Nov [] N. I. Santoso, O. T. Tan, Neural- Net ased Real- Tme ontrol of apactors Installed on Dstrbuton Systems, IEEE Trans. Power Delvery, vol. PAS-5, No., pp. 66-7, Jan. 99. [] M. Kaplan, "Optmzaton of Number, Locaton, Sze, ontrol Type and ontrol Settng Shunt apactors on Radal Dstrbuton Feeder", IEEE Trans. on Power Apparatus and System, ol.3, No.9, pp , Sep 84. [3] hun Wang and Hao Zhong heng, Reactve power optmzaton by plant growth smulaton algorthm, IEEE Trans. on Power Systems, ol.3, No., pp. 9-6, Feb. 8. [4] J-Pyng hou, hung-fu hang and hng-tzong Su, apactor placement n large scale dstrbuton system usng varable scalng hybrd dfferental evoluton, Electrc Power and Energy Systems, vol. 8, pp , 6. [5] hun Wang, H. Z. hengand L. Z Yao, Optmzaton of network reconfguraton n large dstrbuton systems usng plant growth smulaton algorthm, DRPT 8 onference, Nanjng, hna, pp , 6-9, Aprl 8. Internatonal Scholarly and Scentfc Research & Innovaton (

8 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal, omputer, Energetc, Electronc and ommuncaton Engneerng ol:, No:9, 8 Internatonal Scence Index, Electrcal and omputer Engneerng ol:, No:9, 8 waset.org/publcaton/83 [6] aghzouz. Y and Ertem S, Shunt capactor szng for radal dstrbuton feeders wth dstorted substaton voltages, IEEE Trans Power Delvery, ol. 5, pp.65 57, 99. [7] J.. unch, R. D. Mller, and J. E. Wheeler, Dstrbuton system ntegrated voltage and reactve power control, IEEE Trans. Power Apparatus and Systems, vol., no., pp , Feb. 98. [8] S. F. Mekhamer et al, New heurstc strateges for reactve power compensaton of radal dstrbuton feeders, IEEE Trans Power Delvery, ol. 7, No. 4, pp.8 35, October. [9] Su. T and Tsa., A new fuzzy reasonng approach to optmum capactor allocaton for prmary dstrbuton systems, Proc IEEE on Industral Technology onf, 996; pp [] D. Das, Reactve power compensaton for radal dstrbuton networks usng genetc algorthms, Electrc Power and Energy Systems, vol. 4, pp ,. [] Prakash K. and Sydulu M, Partcle swarm optmzaton based capactor placement on radal dstrbuton systems, IEEE Power Engneerng Socety general meetng 7. pp. -5. [] M.hs, M. M. A. Salama and S. Jayaram, apactor Placement n dstrbuton system usng heurstc search strateges, IEE Proc-Gener, Transm, Dstrb, vol, 44, No.3, pp. 5-3, May 997. [3] Das et al, Smple and effcent method for load flow soluton of radal dstrbuton network, Electrc Power and Energy Systems, vol. 7, No.5, pp , 995. [4] H. D. hang, J..Wang, O. ockngs, and H. D. Shn, Optmal capactor placements n dstrbuton systems: Part & Part II, IEEE Trans. Power Delvery, vol. 5, pp , Apr. 99. [5] M. Jaeger and P. H. De Reffye, asc concepts of computer smulaton of plant growth, Journal of oscence (Inda, ol. 7, No. 3, pp. 75-9, September 99. R. Srnvasa Rao s a research scholar n Jawaharlal Nehru Technologcal Unversty, Hyderabad, INDIA. Hs areas of nterest nclude electrc power dstrbuton systems and power systems operaton and control. S..L Narasmham s Professor of omputer Scence and Engneerng Department, Jawaharlal Nehru Technologcal Unversty, Hyderabad, INDIA. Hs areas of nterests nclude real tme power system operaton and control, ANN, Fuzzy logc and Genetc Algorthm applcatons to Power Systems. Internatonal Scholarly and Scentfc Research & Innovaton (