Network Reconfguraton n Dstrbuton Systems Usng a Modfed TS Algorthm ZHANG DONG,FU ZHENGCAI,ZHANG LIUCHUN,SONG ZHENGQIANG School of Electroncs, Informaton and Electrcal Engneerng Shangha Jaotong Unversty No. 1954, Huashan road, Shangha CHINA Abstract: -Ths paper presents a modfed TS algorthm for network reconfguraton n dstrbuton systems. TS algorthm s an effcent meta-heurstc searchng algorthm, and t has advantages of both hgh effcency of local search of hll-clmbng method and global search ablty of ntellgent algorthm. However, snce network reconfguraton s a complcated combnatoral optmzaton problem wth many constrants to be satsfed, TS algorthm s hard to reach the global optmum wth hgh searchng effcency when drectly used. In dstrbuton network, each te swtch s only assocated to one loop network. Based on ths structure property and settng attrbute values to each sectonalzng swtch to decompose each te swtch assocated loops, TS algorthm s modfed to make optmzaton process be carred out n the contnuous soluton spaces and the global optmum soluton can be ganed along wth the hgh searchng effcency. The proposed method s tested wth two typcal dstrbuton systems and the promsng results are ganed. Key-Words: -dstrbuton network, TS algorthm, network reconfguraton, greedy searchng, power loss 1 Introducton Dstrbuton network s desgned n the loop structure but operated radally. It conssts of a lot of sectonalzng swtches and te swtches. By changng the open/closed status of sectonalzng and te swtches, the topologcal structures of the dstrbuton network are altered to reduce actve power losses when operatng condton changes. Durng normal operatng condtons, networks are reconfgured manly for two purposes: (1) to reduce the system real power losses and (2) to releve overloads n the network. And meanwhle t s necessary to satsfy the equalty constrants and nequalty constrants. Algorthms proposed by prevous researchers for network reconfguraton problem usually are the followng two man classes: (1) Heurstc algorthms [1-4],.e. branch-exchange algorthm, optmal flow pattern algorthm, etc. (2) Intellgent algorthms [5-9],.e. genetc algorthm, smulated annealng algorthm, TS algorthm, etc. The former all are greedy searchng algorthms. Ths knd of algorthms are easy to be mplemented and wth hgh searchng effcency, but generally they can t obtan the global optmum soluton. The latter can lead the search converge to the global optmum soluton at the probablty 1 n theory, but t nvolves a huge amount of calculatons and really s a tme consumng method. TS algorthm s a good, effcent ntellgent searchng algorthm. The searchng speed s much faster than that of GA and SA algorthms. Snce t s a sngle way searchng algorthm compared wth GA, t s very easy to be trapped nto the local optma although the tabu dea s ntroduced to escape from the local optma. So how to modfy TS algorthm and make t done much better global search s meanngful. In ths paper, based on the new encodng manner of te swtches and sectonalzng swtches, whch can guarantee the search n the contnuous soluton spaces, TS algorthm s modfed and then appled to solve the network reconfguraton problem. 2 Problem formulaton In ths paper, the objectve functon s to mnmze actve power losses. The problem s formulated mathematcally as follows: n mn F = P + K G( x) (1) = 1 where: P s the actve power losses at branch ; K s the penalty coeffcent; G (x) s the penalty functon of system constrants volaton Equalty constrant s operatng constrant,.e. power flow equaton. Inequalty constrants nclude bus voltage, branch capacty constrants, as follows: 1
V Where mn S V V max S max V mn and V max bus voltage magntude, S and are low and up bounds of S max are branch power flow and ts up capacty bound. Besdes equalty and nequalty constrants mentoned above, there are stll constrants n topologcal structure. The structure of dstrbuton network must be a radal confguraton and there should be no nodes wthout power supply path. 3 Modfed TS algorthm and ts use n network reconfguraton 3.1 TS Algorthm TS algorthm s an extended local search algorthm. Through ntroducng tabu lst, recordng the latest solutons reached, TS algorthm can escape from current regon and search other regon by usng the nformaton n tabu lst to gude the followng searchng process. Therefore, TS algorthm has advantages of hgh searchng effcency of local searchng algorthm and global searchng ablty of ntellgent algorthm. The optmzaton procedure of TS algorthm generally can be descrbed as follows: Step 1: form an ntal soluton at a certan way, and establsh tabu lst. Step 2: If stop rule s satsfed, then stop searchng and output the fnal results. Otherwse, select canddate solutons that meet the tabu requrements to form the neghborhood N ( H, x ) of current soluton x. Fnd the best one x next among them to replace the current soluton( x = x next ),and f t better than the best-so-far soluton, replaced the best-so-far. Upgrade the tabu lst, repeat step 2. H denotes the neghborhood of current soluton. N ( H, x ) denotes the selected neghborhood of current soluton. 3.2 Modfed TS algorthm In dstrbuton network, te swtch assocated loop networks have some shared branches. If TS algorthm s used drectly, there wll be many nfeasble solutons, whch volate structure constrants, n the optmzng process, and ths wll brng consderable negatve nfluence to searchng effcency and optmzng qualty. In ths paper, the loop networks correspondng to te swtches are decomposed frst by usng attrbute values of sectonalzng swtches. Then TS algorthm s modfed correspondngly to make good use of network confguraton propertes and to elmnate nfeasble solutons n the searchng process. The algorthm s developed as follows: (1) Set attrbute values to each sectonalzng swtches and decompose the network. In ths paper, the number of the sendng node of a branch s used to number sectonalzng swtch. For example, n the topologcal structure of the network llustrated n Fg. 1, swtch 5 refers to the swtch n the branch that lnks node 4 and node 5. The swtch set of loop network correspondng to te swtch 24-28 s: {3, 4, 5, 25, 26, 27, 28, 22, 23, 24}, the swtch set of loop network correspondng to te swtch 7-20 s: {2, 3, 4, 5, 6, 7, 18, 19, 20}. Among them, swtch set {3, 4, 5} are the shared swtches of these two loop networks. Of course, these shared swtches should have same attrbute values. To guarantee no nfeasble solutons be created n the optmzng process, the swtches wth the same attrbute values should be only one n the status of open. Usng swtch attrbute values, network reconfguraton problems then are decomposed nto each ndependent loop network reconfguraton sub-problems. The dmenson of the network scale s reduced. (2) Te swtches are encoded nto one character strng and sectonalzng swtches are encoded nto strngs correspondng to each te swtch. Under the radal network topologcal structure condton, fnd out all sectonalzng swtches of a loop when closed a te swtch, encode them nto one character strng and ths strng s the searchng neghborhood of ths te swtch. At the begnnng, the states of sectonalzng swtches are set as " 1 ", and the state of the te swtches are set as " 0 ".As llustrated n Fg.1, te swtches are numbered as table.1. Table 1. Te swtch character strng Branches 7-20 8-14 11-21 17-32 24-28 Swtches 33 34 35 36 37 number strng status 0 0 0 0 0 Fg.1 Sngle lne dagram of the 33-bus system 2
Sectonalzng swtch sets{2 3 4 5 6 7 18 19 20} correspondng to te swtch 33 are encoded as table 2. Table 2. Sectonalzng swtch character strng Swtches 2 3 4 5 6 7 18 19 20 strng status 1 1 1 1 1 1 1 1 1 Whle dong neghborhood search tres, the open/close status are exchanged only between a te swtch and a sectonalzng swtch n the correspondng sectonalzng swtch character strng. In ths way, the structure constrants wll not be volated n the network reconfguraton process. When fnshed a set of neghborhood searchng tres, fnd an exchange, whch result n the maxmum power loss reducton, and exchange both open/close status and locatons n correspondng strngs between te swtch and sectonalzng swtch. (3) Modfed TS algorthm. In ths paper, accordng to the swtch encodng manner mentoned above, the TS algorthm s modfed as follows: 1) In neghborhood search tres of a te swtch, f soluton s mproved, the tabu s not ntroduced. It wll make good use of the gradent drop search characterstcs and enhance the searchng effcency of TS algorthm. 2) Set receptve probablty. When soluton stops mprovng n the neghborhood search of a te swtch, then at ths preset receptve probablty, randomly select a sectonalzng swtch n the correspondng strngs to exchange wth ths te swtch and record ths exchange n tabu lst to make search process jump out of the local optmum regon. Ths mprovement has two advantages:1) tabu lst s used as conventonal TS algorthm; 2) probablty s ntroduced to dsturb search course to jump out of local optmum regon easly. 3) Tabu search s carred out wthn each loop network. In each teraton, every te swtch does a set of neghborhood search. It tself has the tabu search characterstc and avods the greedy search wthn the each teraton. A te swtch and the correspondng sectonalzng swtch set form a tabu search space. The attrbute value of sectonalzng swtches s used to ensure the feasble swtch exchange n the loop network. 4) Determnaton of tabu table. In ths paper, tabu lst s set wthn each loop networks and the lengths all are 1. 3.3 The procedure of the algorthm To mnmze actve power losses, the procedure of the modfed TS algorthm n the network reconfguraton s shown n Fg.2 and descrbed as Fg.2 Flowchart of the Modfed TS algorthm follows: (1) Readng network data and formng dstrbuton network topologcal structure. (2) Formng code strng of te swtches, and scannng network to form the sectonalzng swtch code strngs correspondng to each te swtch. And settng attrbute values to each sectonalzng swtch. (3) Calculatng network power flow of the ntal network structure and recordng t as the best-so-far soluton and recordng the correspondng network topologcal structure. (4) Carryng out neghborhood search from the frst te swtch, and determnng the optmal neghborhood swtch exchange. If the actve power losses of ths optmal swtch exchange s smaller than the best-so-far, executng ths swtch exchange and updatng the record of the best-so-far and ts correspondng network structure wth ths exchange. (5) Carryng out neghborhood search of te swtches one by one n the each teraton then the number of teraton s added by 1. (6) If stop rule s satsfed, stop searchng, output the best-so-far soluton and correspondng structure topology. Else go to step (4). Where stop rule s the preset teratve tmes. 4 Test results The sample system has nomnal voltage of 12.66kV. It has 32 branches and 5te lnes. The system data can be found n [3]. Results of network reconfguraton are gven n table 3. 3
Table 3. Results before and after reconfguraton Orgnal network Modfed TS algorthm TS algorthm 17-32 31-32 31-32 11-21 8-9 8-9 Te swtch set 8-14 13-14 13-14 24-28 24-28 27-28 7-20 6-7 6-7 loss(kw) 202.681 139.553 139.98 The lowest bus voltage(p.u.) 0.9131 0.9378 0.9322 As shown n table 3, the actve power losses of the dstrbuton network are reduced greatly after network reconfguraton. And the optmzaton performance of the modfed TS algorthm s better than that of TS algorthm. Effcency comparson s gven n Table 4. The computer system s a P3/500HZ computer. It s noted that the modfed TS algorthm have 53 teratve tmes to reach global optmum soluton and TS algorthm s faled to reach the same global optmum soluton. The dfference at the computaton tme s neglectable. Table 4: Effcency comparson of two algorthm. Modfed TS TS algorthm algorthm Frst tme to reach the 53 7 optmum soluton Optmum soluton 139.553 139.98 Defned teraton number 100 100 CPU run tme(s) 0.161 0.16 power flow tmes 751 708 Searchng process s gven n Fg.3. It s clear that TS algorthm s gotten stuck n the local optmum and can t escape from t, whereas the modfed TS algorthm s jumped out of the local optmum and reach the global optmum soluton. The modfed TS algorthm has better global searchng ablty at the cost of mnor mparment of searchng effcency. Fg.3 Searchng process About the same test system, result comparsons wth other methods are gven n table 5. The method used n [2] s a branch exchange method. The method used n [7] s a genetc algorthm and the method used n [8] s an evolutonary programmng algorthm. From table 5, t s noted that the proposed modfed TS algorthm has better optmzng performance than that of other methods. Table 5 Result comparson of dfferent methods n [2] n [7] n [8] Proposed Te lne set (6-7) (9-10) (26-27) (29-30) (7-20) (8-9) (8-14) (27-28) (17-32) (5-6), (8-9), (24-28) (31-32) (6-7) (8-9) (24-28) (31-32) Power Loss(kW) 161.01 146.37 142.83 139.553 Lowest V. (p.u.) 0.9043 0.9367 0.9390 0.9378 Lowest V. Bus 30 32 32 31 5 Concluson In ths paper, a modfed TS algorthm s proposed for network reconfguraton n dstrbuton systems. Through set attrbute values to sectonalzng swtches, the dstrbuton network reconfguraton problem s decomposed nto each te swtch assocated loop network reconfguraton sub-problems ndependently. Based on ths mprovement, the TS algorthm s modfed, by settng tabu table n each loop and settng receptve probablty of soluton evolvng stagnaton, to enhance the capacty of global search. Test results proved the global search ablty and the valdty of the proposed modfed TS algorthm. References: [1] S.Cvanlar,J.J.Granger, and S.S.H.Le, Dstrbuton Feeder Reconfguraton for Loss Reducton, IEEE Trans. on Power Delvery, vol.3,1988, pp.1217-1223 [2] M.E. Baran, F.F. Wu, Network reconfguraton n dstrbuton systems for loss reducton and load balancng, IEEE Trans. Power Delvery. Vol.4, No.2, 1989, pp.1401-1407. [3] J.Y.Fan, L.Zhang and J.D.McDonald, Dstrbuton Network Reconfguraton: sngle loop optmzaton, IEEE Trans. Power Systems, Vol.11,No.3,1996, pp.1643-1647 [4] H.D.Chang and R.M.Jean-Jumeau, Optmal network reconfguraton dstrbuton system:part1:a new formulaton and a soluton methodology, IEEE Trans. Power Delvery, vol.5, 1990, pp.1902-1909 4
[5] D.Jang and R.Baldck, Optmal electrc dstrbuton system swtch reconfguraton and capactor control, IEEE Trans. Power System, vol.11, 1996, pp.890-897 [6] Y.J.Jean and J.C.Km, An Effcent Smulated Annealng Algorthm for Network Reconfguraton n Large-Scale Dstrbuton Systems, IEEE Trans. Power Delvery, vol. 17, 2002, pp.1070-1078 [7] Y.H. Yng, Y.H. Saw, Genetc Algorthm Based Network Reconfguraton for Loss Mnmzaton n Dstrbuton Systems, Power Engneerng Socety General Meetng, IEEE, Vol.1, 2003, pp.13-17 [8] B.Venkatesh, R.Ranjan, H. B. Goo. Optmal Reconfguraton of Radal Dstrbuton Systems to Maxmze Loadablty. IEEE Trans. on Power Systems, vol. 19, No.1, 2004,pp.260-266 [9] Hroyuk Mor and Yoshhro Ogta, A parallel tabu search based method for reconfguratons of dstrbuton systems, Power Engneerng Socety Summer Meetng, IEEE,Vol.1, 2000, pp.73-78 5