Internatonal Journal on Electrcal Engneerng and Informatcs - Volume 7, Number 4, Desember 2015 Optmal Placement and Szng of s n the Dstrbuton System for Loss Mnmzaton and Voltage Stablty Improvement usng CABC Mohandas Natarajan, R. Balamurugan and L. Lakshmnarasmman Department of Electrcal Engneerng, Annamala Unversty, Annamala Nagar, Tamlnadu, Inda Abstract: Ths paper presents a chaotc artfcal bee colony (CABC) algorthm for optmal placement and szng of s on dstrbuton systems wth an am of reducng the power losses and mprovng voltage stablty. The explotaton ablty of solutons to the food searchng process s mproved n the CABC algorthm to avod the premature convergence of an artfcal bee colony algorthm. The proposed approach determnes the control varable settngs such as placement and sze of for mnmzaton of real power loss wth mpact of voltage stablty n the dstrbuton system. Further, the mpacts of on the dstrbuton system are studed wth an mportance on power losses and capacty savngs. The proposed approach s examned and tested on 33 bus and 69 bus radal test systems. The smulaton results of the proposed approach are compared to earler reported approaches. The smulaton results show the effectveness of the proposed approach. Keywords: dstrbuted generaton, chaotc artfcal bee colony, power loss, voltage stablty, radal dstrbuton systems. 1. Introducton The functon of a dstrbuton system s to delver electrcal power from the transmsson network to end users. The dstrbuted generaton () s a power source that can be playng an mportant role n the dstrbuton system n case of power demand. The dstrbuton systems are usually unbalanced and have a hgh R/X rato compared to transmsson systems, whch results wth the effect of hgh voltage drops and power losses n the dstrbuton feeders. The vtal tasks n the dstrbuton system are reducton of power losses and mprovement of the system voltage profle. Many research works have been carred out n ths drecton snce the supportng of analytcal and software approach. The plannng of handles wth the optmal placement and sze of n the dstrbuted system n order to reduce the real power loss and mprove the voltage profle and stablty. The mpact of real power njecton nto the dstrbuton system for mnmzng the power losses and voltage stablty has been reported n [1]. The plannng methodology used to evaluate any credts the utlty mght offer f the s n an approprate locaton to have real benefts for capacty relef [2]. The support an analytcal expresson used to compute the optmal sze and an effcent method to dentfy the related optmum locaton for placement for reducng the total power losses n prmary dstrbuton systems [3]. In [4], the author presented analytcal expressons have used to determne the optmum sze and power factor of dfferent types of s for mnmzng power losses n prmary dstrbuton systems. The genetc algorthm (GA) based approach to mnmze the power loss of the system for evaluated the optmal placement and sze of a wth dfferent loadng condtons s reported n [5]. A two-stage methodology of determne the optmal placement and capacty of s for loss reducton of dstrbuton systems. The frst stage of methodology s used to fndng placement and another one s the capacty of [6, 7]. The power stablty ndex and lne losses based for placement and szng of n the dstrbuton system s reported n [8]. The ntroducton of combned GA and partcle swarm optmzaton (PSO) methods and whch s used to calculate the placement and szng of n the dstrbuton system [9]. The loss senstvty factor (LSF) and smulated annealng (SA) technque are combned and whch s used to determne the locaton and sze of s n the radal networks [10]. Receved: December 3 rd, 2014. Accepted: October 22 nd, 2015 DOI: 10.15676/jee.2015.7.4.11 679
Mohandas Natarajan, et al. The bacteral foragng optmzaton (BFO) algorthm based optmal placement and sze of n the dstrbuton system for consderng the real power losses, operatonal costs and voltage stablty [11]. In [12], presents an analyss nto the effect of load models on the predcted energy losses of the dstrbuton system n plannng. A new voltage stablty ndex (VSI) s used to dentfy the most senstve node n the radal dstrbuton system wth dfferent types of load [13, 14]. The effcent forward and backward propagaton based load flow soluton technque has been mplemented n the radal networks s reported [15]. The artfcal bee colony (ABC) algorthm s a populaton based meta-heurstc approach and whch s nspred by ntellgent foragng behavour of honeybee swarm. It s mtates the behavours of real bees n searchng food sources and sharng the nformaton wth other bees [16, 17]. The performance of the ABC s compared wth other populaton based algorthms wth the beneft of employng fewer control parameters [18]. The modfed versons of ABC algorthm have been ntroduced n [19, 20] and t s used to solvng the real-parameter optmzaton problems. Most of the earler reported [9-11], the searchng ablty of algorthms at startng stage as a global run and end stage as a local run. Therefore, when solvng an optmzaton problem s mportance to explore the local optma at an end stage of algorthm run. Moreover, the local searchng ablty of earler reported algorthms s less. In ths paper, to encouragng the results n ths drecton for ntroducng a chaotc artfcal bee colony algorthm s mplemented to fnd the optmal placement and szng of s n the dstrbuton system so as to reduce the real power loss and mprove the voltage stablty. To mprove local optma and avod premature convergence of the soluton, the ABC algorthm s combned wth chaos. The local search capablty of the optmzaton problem s mproved usng a chaos theory. 2. Problem formulaton The objectve of the optmal placement and szng of s s to mnmze the real power loss n the radal dstrbuton system whch can be descrbed as follows, P loss, jnl P 2 j Q V 2 2 j r j (1) where, P loss = total system real power loss (MW) P j, Q j = real and reactve power flow n lne -j V = voltage at th bus r j = lne resstance of -j NL = number of lnes. Whle reducng the value of above functon s subject to a number of constrants as follows. A. Power Balance Constrants The algebrac sum of the entre recevng power s equal to the sum of entre sendng power plus lne loss over the complete dstrbuton network and power generated from unt. P (2) SS NB 2 P ( ) D NL j 1 P loss ( j) N k 1 P ( k) Q SS NB Q ( ) Q ( j) Q ( k) (3) 2 D NL j 1 loss N k 1 680
Optmal Placement and Szng of s n the Dstrbuton System for Loss Mnmzaton where, P D total system real power demand (MW) P total real power generated by (MW) Q D total system reactve power demand (MVAr) Q loss total system reactve power loss (MVAr) Q total reactve power generated by (MVAr) N number of. B. Real and Reactve Power Generaton Lmts The real and reactve power generaton of s controlled by ts lower and hgher lmts as follows, mn max P P P (4) Q mn Q Q (5) max C. Voltage Profle Lmts The voltage at each node of the radal dstrbuton network s defned as, mn max V V V (6) D. Lne Thermal Lmts The power carryng capacty of feeders should not exceed the thermal lmt of the lnes (S). S S (7) max, j (, j) 3. Types of Dstrbuted Generaton The unts are classfed nto four types n order to delver the real and reactve power capabltes of the dstrbuton system [4]. In ths approach, follow the report [10] for consderng that the type 1 (unty p.f) and type 2 (0.866 p.f) s only. A. Type 1 (P nject) Ths type of (e.g., Photovoltac, fuel cells and mcro turbnes) s havng the capacty of delverng the real power only and operates at unty power factor. P P P (8) D where, P s the net real power of node P s the real power njected at node P D s the real power demand of node. B. Type 2 (PQ nject) In ths type of (e.g., synchronous generator) s havng the capacty of delverng both real and reactve power. The power factor of s fxed at 0.866 leadng. By consderng a = (sgn) tan (cos -1 (PF)) as n [4], the reactve power output of s expressed as, Q (9) ap Q In ths type, a = (+1) tan (cos -1 (PF )) Q Q (10) D where, Q s the net reactve power of node 681
Mohandas Natarajan, et al. Q s the reactve power based of node Q D s the reactve power demand of node. In whch, sgn = +1; supplyng reactve power. sgn = -1; absorbng reactve power. PF = Power Factor of. 4. Effect of on Voltage Stablty The mpact of n the dstrbuton system s to ncreasng the real power loadng capacty of the system whch related to the voltage stablty. The voltage stablty ndex (VSI) gves the nformaton for voltage stablty of the radal dstrbuton systems. The varaton of ths factor whch ndcatng system voltage stablty n presence and absence of s. The VSI s defned as [13], VSI m2 V m1 4 4.0 P m2 x jjqm2 r jj 2 4.0 P m2 r jj Qm2 x jj V m 1 2 where, NB = total number of nodes jj = branch number VSI(m2) = voltage stablty ndex of node m2 (m2 = 2,3,.,NB) r(jj) = resstance of branch jj x(jj) = reactance of branch jj V(m1) = voltage of node m1 V(m2) = voltage of node m2 P(m2) = real power load fed through node m2 Q(m2) = reactve power load fed through node m2. (11) The evaluated value of VSI s greater than zero, whch ndcatng system operates n stable condton, otherwse system goes to nstablty. 5. An overvew of artfcal bee colony algorthm The ABC algorthm s an optmzaton algorthm that smulates the behavour of honey bees. In the ABC algorthm, the colony of artfcal bees can be classfed n to three sets, such as employed, onlookers and scouts. The bees are searchng wth specfc food sources are named as employed bees. The onlooker bees are watng on the dance area for makng the decson to choose a food source. The bees are search for food sources randomly called scouts. The man steps of the ABC algorthm are explaned as follows, Step 1 : Intalze the random populaton of food source, lmt and maxmum cycle number. Step 2 : Implement the employed bee procedure to adjust the food source of functon and calculate the correspondng ftness functon. Step 3 : Adjust the food source based on onlooker bee procedure and calculate the correspondng ftness functon. Step 4 : The specfc food source soluton s abandoned, whch s replaced by sendng the scout bee procedure. Step 5 : Update the cycle. The number of cycle reaches at maxmum cycle number (MCN) of the algorthm, prnt the fnest results of the optmzaton problem. 682
Optmal Placement and Szng of s n the Dstrbuton System for Loss Mnmzaton A. Chaotc local search The chaos theory s used to develop the searchng behavour and to avod the premature convergence of solutons n the optmzaton problem. The chaotc local search consders as a two well known maps such as logstc map and tent map. The chaotc local search can be descrbed as the followng logstc equaton as, cx k1 4cx k 1 cx k = 1, 2,.,n (12) where, cx s the th chaotc varable, and k s the maxmum number of teratons or 300. The chaotc local search has the followng procedure. k k The decson varables x s converted nto chaotc varables cx usng the equaton cx x lb k k =1, 2,..,n (13) ub lb where, lb and ub are the lower and upper bound of the x. Calculate the chaotc varables The chaotc varables equaton x lb cx k1 k1 cx k1 usng the equaton (12) for the next teraton. k1 cx s converted nto decson varables ub lb = 1, 2,..,n k1 x usng the followng (14) k1 Calculate the new soluton wth decson varables x. Revse the recent soluton of the problem f t has mproved ftness when compared to prevous one. B. Chaotc Artfcal Bee Colony algorthm The ABC algorthm s used to update the food source of the bees and whch s combned wth chaos theory s called CABC. In order to combnatons of ths algorthm has mproved the explotaton process of the searchng food source n the optmzaton problem. The CABC algorthm s used as the less number of control parameters. The CABC algorthm has the followng steps: Step 1: Intalze the random populaton, lmt, k and MCN. Step 2: Generate the ntal populaton x m lb rand * Step 3: Set the cycle = 1. x m, 1 ub lb usng the equaton as, 0 (15) Step 4: Send the employed bee procedure to adjust the food source m v m (16) x rand * m 1, 1 x x m k v usng the equaton as, where, x s a randomly selected food source, s a randomly chosen parameter ndex. k Calculate the ftness value of food source. If the new food source vector has better ftness value than older one, t replaces the old. 683
Mohandas Natarajan, et al. Step 5: Send the onlooker bee procedure to adjust the food source equaton (17) and (16). p m SN m 1 ft ( xm ) ft ( x ) m v m usng the probablty of where, SN denotes the sze of onlooker bees. Calculate the ftness value of correspondng food source. If the new food source vector has better ftness value than older one, t replaces the old. Step 6: Send the chaos theory procedure to adjust the food source (17) x usng the equaton (12), (13) and (14). Evaluate the ftness value of related food source. Apply the greedy selecton wth the purpose of fnd the best food source vector of the problem. Step 7: If there s any specfc food source solutons are abandoned, and t wll be replaced by a new randomly produced soluton v m for the scout bee usng the equaton (15). Step 8: Memorze the fnest food source poston acheved so far. Step 9: Cycle = Cycle + 1. Step 10: If the number of cycle attans at MCN, Prnt the fnest result of the problem. C. Implementaton of CABC algorthm to optmze the objectve functon The proposed CABC algorthm s developed and executed usng the MATLAB software. The frst mportant aspect of ths algorthm s to assgn the colony sze (CS) = 50, lmt (L) = (CS*D)/2, k = 300 and MCN = 200 of the problem. The CABC algorthm starts by creatng the ntal random populaton of the possble food source solutons. In ths approach, the placement and szng of s n the dstrbuton system are consdered as varable parameters n order to optmze the problem. The placement of s represented as the nteger varable of the problem. In ths connecton wth CABC algorthm can be reformulated by roundng off the food source poston to the nearest nteger. Set the number of cycles and then send the employed bee procedure n order to produce the new soluton. Further, to apply the greedy selecton between current soluton and t s dsturbng. Calculate the probablty of the soluton and send the onlooker bee procedure to adjust the soluton. Send the chaos theory procedure s to mprove the explotaton process of searchng the new food source soluton. To apply the greedy selecton process for both ends of onlookers and chaos theory procedures of the problem. The specfc food source solutons are abandoned by applyng the scout bee procedure to produce the new food source solutons. The generatng random populatons are wthn lmts and satsfed the above mentoned constrants. If the number of cycles reaches at maxmum, the algorthm whch t wll be stop and gves the optmal (or near optmal) value of placement and szng of s n the test systems. 6. Smulaton results To valdate the effectveness and robustness of the proposed CABC algorthm based optmal placement and szng of approach has been tested on usng 33-bus and 69-bus radal dstrbuton systems. The base values used are 100 MVA and 12.66 KV for both the test systems. The load and lne data of the 33-bus system s taken from the reference [22] and 69- bus system s gven n appendx. The man objectve of ths approach s to reducng the real power loss and mprovng voltage stablty of the test systems wth satsfed constrants. Three unts are optmally placed and szed of the test systems. To express the superorty of ths proposed CABC approach has a smulaton results have been compared wth varous algorthm results n the report, such as genetc algorthm (GA), partcle swarm optmzaton (PSO), GA/PSO n [9], smulated annealng (SA) n [10] and bacteral foragng optmzaton (BFO) n [11]. 684
Optmal Placement and Szng of s n the Dstrbuton System for Loss Mnmzaton A. 33-bus radal system The table 1 shows the results of real power loss, voltage stablty ndex, optmal placement and szng of the s of the system are obtaned by dfferent methods. These results confrm that the CABC approach to obtan the mnmum real power loss s 0.07279 MW (type 1) and 0.01535 MW (type 2) when compared to other methods. Resultant that the real power loss s reduced to 65.50 % (type 1) and 92.72 % (type 2) compared to base case condton. For the reducton of real power loss has greatly mproved the voltage profle and performance of the system. The graphcal representaton of the VSI of each node (except substaton) of the system s shown n fgure 1. The mnmum value of VSI s 0.8805 (type 1) and 0.9688 (type 2) of ths approach greatly mproved when compared to the absence of n the system. Fgure 1. Voltage stablty ndex of 33-bus radal system Fgure 1. Voltage stablty ndex of 69-bus radal system B. 69-bus radal system The table 2 shows the results of real power loss, voltage stablty ndex, optmal placement and szng of the s of the system are evaluated by dfferent methods. In ths system, the real power loss has come down to 0.07159 MW (type 1) and 0.00874 MW (type 2) or 68.18 % (type 1) and 96.12 % (type 2) when compared to other methods. The mnmum VSI of ths system s 0.9234 (type 1) and 0.9772 (type 2) and t s value of each node as shown n fgure 2. 685
Mohandas Natarajan, et al. Table 1. The performance analyss of 33-bus radal system wth s at dfferent power factors Method P loss (MW) VSI mn Bus no. P (MW) sze Q (MVAr) Base case 0.21099 0.6672 - - - GA [9] 0.10630 0.9258 PSO [9] 0.10535 0.9247 GA/PSO [9] 0.10340 0.9254 LSFSA [10] 0.08203 0.8768 BFOA [11] 0.08990 0.8868 CABC LSFSA [10] BFOA [11] 0.07279 0.8805 0.02672 0.9323 0.03785 0.9199 CABC 0.01535 0.9688 11 1.5000 0.0 29 0.4228 0.0 30 1.0714 0.0 8 1.1768 0.0 13 0.9816 0.0 32 0.8297 0.0 11 0.9250 0.0 16 0.8630 0.0 32 1.2000 0.0 6 1.1124 0.0 18 0.4874 0.0 30 0.8679 0.0 14 0.6521 0.0 18 0.1984 0.0 32 1.0672 0.0 13 0.8017 0.0 24 1.0913 0.0 30 1.0537 0.0 6 1.1976 0.6915 18 0.4778 0.2759 30 0.9205 0.5315 14 0.6798 0.3925 18 0.1302 0.0752 32 1.1085 0.6400 13 0.7616 0.4398 24 1.0304 0.5950 30 1.2000 0.6929 Power factor - Unty Unty Unty Unty Unty Unty 0.866 0.866 0.866 Table 2. The performance analyss of 69-bus radal system wth s at dfferent power factors Method P loss (MW) VSI mn Bus no. P (MW) sze Q (MVAr) Base case 0.22497 0.6833 - - - GA [9] PSO [9] GA/PSO [9] LSFSA [10] BFOA [11] CABC LSFSA [10] 0.01626 BFOA [11] CABC 0.08900 0.9736 0.08320 0.9609 0.08110 0.9703 0.07710 0.9655 0.07523 0.9254 0.07159 0.9234 0.9678 0.01825 0.9366 0.00874 0.9772 21 0.9297 0.0 62 1.0752 0.0 64 0.9925 0.0 17 0.9925 0.0 61 1.1998 0.0 63 0.7956 0.0 21 0.9105 0.0 61 1.1926 0.0 63 0.8849 0.0 18 0.4204 0.0 60 1.3311 0.0 65 0.4298 0.0 27 0.2954 0.0 61 1.3451 0.0 65 0.4476 0.0 17 0.5381 0.0 61 1.2000 0.0 64 0.5350 0.0 18 0.5498 0.3175 60 1.1954 0.8635 65 0.3122 0.1803 27 0.3781 0.2183 61 1.3361 0.7715 65 0.3285 0.1897 17 0.5458 0.3152 61 1.2000 0.6929 62 0.6332 0.3656 Power factor - Unty Unty Unty Unty Unty Unty 0.866 0.866 0.866 686
Optmal Placement and Szng of s n the Dstrbuton System for Loss Mnmzaton The tables 1 & 2 show the mnmum real power loss of the test systems determned by the dfferent methods. It s clear that the proposed CABC approach has better performance when compared to exstng technques. As a result of ths confrms that the CABC s well capable of explotaton process of the soluton. Fgure 3a. Convergence characterstcs of 33-bus radal system Fgure 3a. Convergence characterstcs of 33-bus radal system Fgure 3b. Convergence characterstcs of 69-bus radal system The fgures 1 & 2 show the voltage stablty ndex of each node of the test systems whch represent the real power type s better performance when compared to the base case and real (P) and reactve (Q) power nject type much better performance when compared to the above type. The fgure 3 (a & b) gves the convergence characterstcs of the CABC algorthm n terms of real power loss and n whch to get the best optmal soluton for mnmum number of cycles. The convergence curves are presented that the real power type. Moreover, the combnaton of real and reactve power nject type s also approxmately smlar to the convergence characterstcs of real power wth reasonable computatonal tme. 687
Mohandas Natarajan, et al. 7. Concluson The CABC algorthm has been developed for the determnaton of optmal placement and szng of s n the test systems. It has been successfully mplemented to the 33-bus and 69- bus systems for the mnmzaton of real power loss and to mproved system voltage stablty. Two dfferent types of unts are separately placed and szed n the test systems for mnmzaton of real power loss. The graphcal representaton of VSI results shows that the system voltage stablty s potentally mproved when the presence of. The comparson of smulaton results wth earler reported methods n the lterature demonstrates the superorty of the proposed algorthm to solve the real power loss mnmzaton of the test systems. The proposed algorthm can be mplemented for the soluton of the large scale system. 8. References [1]. H. Hedayat, S. A. Nabavnak, and A. Akbarmajd, A Method for Placement of Unts n Dstrbuton Networks, IEEE Trans., Power Del., vol. 23, no. 3, pp. 1620-1628, July 2008. [2]. R. C. Dugan, T. E. McDermott, and G. J. Ball, Plannng for dstrbuted generaton, IEEE Ind. Appl. Mag., vol. 7, no. 2, pp. 80-88, Mar-Apr.2001. [3]. N. Acharya, P. Mahat, and N. Mthulananthan, An analytcal approach for allocaton n prmary dstrbuton network, Electrcal Power and Energy Systems 28, pp. 669-678, 2006. [4]. D. Q. Hung, N. Mthulananthan, and R. C. Bansal, Analytcal Expressons for Allocaton n Prmary Dstrbuton Networks, IEEE Trans. On energy Con., vol. 25, no. 3, pp. 814-820, Sep. 2010. [5]. D. Sngh, D. Sngh, and K. S. Verma, GA based Optmal Szng & Placement of Dstrbuted Generaton for Loss Mnmzaton, World Acad., Sc, Engg., and Tech., vol. 1, pp. 93-99, 2007. [6]. M. P. Laltha, V. C. V. Reddy, V. Usha, and N. S. Reddy, Applcaton of fuzzy and PSO for placement for mnmum loss n radal dstrbuton system, ARPN Jour., of Engg., and Appled Sces., vol. 5, no. 4, pp. 30-37, Apr 2010. [7]. M. P. Laltha, V. C. V. Reddy, and N. S. Reddy, Applcaton of fuzzy and ABC for placement for mnmum loss n radal dstrbuton system, Iranan Journal of Elect., & Electronc Engg., vol. 6, no. 4, pp. 248-256, Dec. 2010. [8]. M. M. Aman, G. B. Jasmon, H. Mokhls, and A. H. A. Bakar, Optmal placement and szng of a based on a new power stablty ndex and lne losses, Electrcal Power and Energy Systems 43, pp. 1296-1304, 2012. [9]. M. H. Morad, and M. Abedn, A combnaton of genetc algorthm and partcle swarm optmzaton for optmal locaton and szng n dstrbuton systems, Electrcal Power and Energy Systems 34, pp. 66-74, 2012. [10]. S. K. Injet, and N. P. Kumar, A novel approach to dentfy access pont and capacty of multple s n a small, medum and large scale radal dstrbuton systems, Electrcal Power and Energy Systems 45, pp. 142-151, 2013. [11]. A. M. Imran, and M. Kowsalya, Optmal sze and stng of multple dstrbuted generators n dstrbuton system usng bacteral foragng optmzaton, Swarm and Evolut., Compt., 15 pp. 58 65, 2014. [12]. K. Qan, C. Zhou, M. Allan, and Y. Yuan, Effect of load models on assessment of energy losses n dstrbuted generaton plannng, Elect., Power and Energy Systems 33, pp.1243 1250, 2011. [13]. M. Chakravorty, D. Das, Voltage stablty analyss of radal dstrbuton networks, Electrcal Power and Energy Systems 23, pp.129-135, 2001. [14]. R. Ranjan, B. Venkatesh and D. Das, Voltage Stablty Analyss of Radal Dstrbuton Networks, Elect. Power Comp. and Syst., 31, pp. 501-511, 2003. 688
Optmal Placement and Szng of s n the Dstrbuton System for Loss Mnmzaton [15]. D. Thukaram, H.M.W. Banda, and J. Jerome, A robust three-phase power flow algorthm for radal dstrbuton systems, Electrc Power Systems Research 50, pp. 227 236, 1999. [16]. D. Karaboga, and B. Basturk, On the performance of artfcal bee colony (ABC) algorthm, Appled Soft Computng 8, pp. 687 697, 2008. [17]. D. Karaboga, and B. Basturk, A powerful and effcent algorthm for numercal functon optmzaton: artfcal bee colony (ABC) algorthm, Journal of Global Optmzaton 39, pp. 459-471, 2007. [18]. D. Karaboga, and B. Akay, A comparatve study of Artfcal Bee Colony algorthm, Appled Maths., and Comput., 214, pp. 108 132, 2009. [19]. D. Karaboga, and B. Akay, A modfed Artfcal Bee Colony (ABC) algorthm for constraned optmzaton problems, Appled Soft Computng 11, pp. 3021-3031, 2011. [20]. B. Akay, and D. Karaboga, A modfed Artfcal Bee Colony for real-parameter optmzaton, Informaton Scences 192, pp. 120 142, 2012. [21]. B. Lu, L. Wang, Y. Jn, F. Tang and D. Huang, Improved partcle swarm optmzaton combned wth chaos, chaos solutons and fractals 25, pp. 1261 1271, 2005. [22]. N. C. Sahoo and K. Prasad, A fuzzy genetc approach for network reconfguraton to enhance voltage stablty n radal dstrbuton systems, Energy Conv. and Managt., 47, pp. 3288-3306, 2006. Appendx Lne and load data for 69-radal dstrbuton system F T R (p.u.) X (p.u.) P (MW) Q (MVAr) 1 2 0.0003 0.0007 0 0 2 3 0.0003 0.0007 0 0 3 4 0.0009 0.0022 0 0 4 5 0.0157 0.0183 0 0 5 6 0.2284 0.1163 0.0026 0.0022 6 7 0.2378 0.1211 0.0404 0.0300 7 8 0.0575 0.0293 0.0750 0.0540 8 9 0.0308 0.0157 0.0300 0.0220 9 10 0.5110 0.1689 0.0280 0.0190 10 11 0.1168 0.0386 0.1450 0.1040 11 12 0.4438 0.1467 0.1450 0.1040 12 13 0.6426 0.2121 0.0080 0.0055 13 14 0.6514 0.2152 0.0080 0.0055 14 15 0.6601 0.2181 0 0 15 16 0.1227 0.0406 0.0455 0.0300 16 17 0.2336 0.0772 0.0600 0.0350 17 18 0.0029 0.0010 0.0600 0.0350 18 19 0.2044 0.0676 0 0 19 20 0.1314 0.0434 0.0010 0.0006 20 21 0.2131 0.0704 0.1140 0.0810 21 22 0.0087 0.0029 0.0053 0.0035 22 23 0.0993 0.0328 0 0 23 24 0.2161 0.0714 0.0280 0.0200 24 25 0.4672 0.1544 0 0 25 26 0.1927 0.0637 0.0140 0.0100 26 27 0.1081 0.0357 0.0140 0.0100 3 28 0.0027 0.0067 0.0260 0.0185 28 29 0.0399 0.0976 0.0260 0.0185 29 30 0.2482 0.0820 0 0 30 31 0.0438 0.0145 0 0 31 32 0.2190 0.0724 0 0 32 33 0.5235 0.1757 0.0140 0.0100 33 34 1.0656 0.3523 0.0195 0.0140 34 35 0.9196 0.3040 0.0060 0.0040 3 36 0.0027 0.0067 0.0260 0.0186 36 37 0.0399 0.0976 0.0260 0.0186 37 38 0.0657 0.0767 0 0 689
Mohandas Natarajan, et al. 38 39 0.0190 0.0221 0.0240 0.0170 39 40 0.0011 0.0013 0.0240 0.0170 40 41 0.4544 0.5309 0.0012 0.0010 41 42 0.1934 0.2260 0 0 42 43 0.0256 0.0298 0.0060 0.0043 43 44 0.0057 0.0072 0 0 44 45 0.0679 0.0857 0.0392 0.0263 45 46 0.0006 0.0007 0.0392 0.0263 4 47 0.0021 0.0052 0 0 47 48 0.0531 0.1300 0.0790 0.0564 48 49 0.1808 0.4424 0.3847 0.2745 49 50 0.0513 0.1255 0.3847 0.2745 8 51 0.0579 0.0295 0.0405 0.0283 51 52 0.2071 0.0695 0.0036 0.0027 9 53 0.1086 0.0553 0.0043 0.0035 53 54 0.1267 0.0645 0.0264 0.0190 54 55 0.1773 0.0903 0.0240 0.0172 55 56 0.1755 0.0894 0 0 56 57 0.9920 0.3330 0 0 57 58 0.4890 0.1641 0 0 58 59 0.1898 0.0628 0.1 0.0720 59 60 0.2409 0.0731 0 0 60 61 0.3166 0.1613 1.2440 0.8880 61 62 0.0608 0.0309 0.0320 0.0230 62 63 0.0905 0.0460 0 0 63 64 0.4433 0.2258 0.2270 0.1620 64 65 0.6495 0.3308 0.0590 0.0420 11 66 0.1255 0.0381 0.0180 0.0130 66 67 0.0029 0.0009 0.0180 0.0130 12 68 0.4613 0.1525 0.0280 0.0200 68 69 0.0029 0.0010 0.0280 0.0200 Mohandas Natarajan, He receved the B.E degree n Electrcal and Electroncs from Madras Unversty and M.E degree n Power Systems from Annamala Unversty, Inda n 2002 and 2008, respectvely. He s workng towards hs Ph.D. n the area of Voltage stablty analyss. Hs areas of nterest nclude network loss mnmzaton, dstrbuted generaton and applcaton of soft computng technques n power system engneerng. He s presently an Assstant Professor n Electrcal engneerng, Annamala Unversty, Annamala Nagar, Tamlnadu, Inda. R. Balamurugan, He receved hs B.E. n Electrcal and Electroncs Engneerng, M.E. n power System and Ph.D n Electrcal Engneerng, from Annamala Unversty, Inda n 1994, 1997 and 2008 respectvely. Hs areas of nterest nclude Dgtal Smulatons of Power Systems, Control Systems, Applcatons of Computatonal Intellgence Technques n Power System Engneerng, and Electrcal Machnes. He s presently an Assstant Professor n Electrcal Engneerng, Annamala Unversty, Annamala Nagar, Tamlnadu, Inda. L. Lakshmnarasmman, He receved hs B.E. n Electrcal and Electroncs Engneerng, M.E. n Power System and PhD n Electrcal Engneerng, from Annamala Unversty, Inda n 1993, 1999 and 2008 respectvely. He s presently an Assocate Professor n Electrcal Engneerng, Annamala Unversty, Annamala Nagar, Tamlnadu, Inda. Hs research nterests nclude power system analyss, power system economcs and applcaton of computatonal ntellgence technques to power system optmzaton problems. He s a member of IEEE and a lfe member of Indan Socety for Techncal Educaton. 690