FAULT LOCATION AND SERVICE RESTORATION METHOD FOR LARGE-SCALE DISTRIBUTION NETWORKS

Transcription

1 FAULT LOCATION AND SERVICE RESTORATION METHOD FOR LARGE-SCALE DISTRIBUTION NETWORKS A. Gonzáez, F. M. Echavarren, L. Rouco, T. Gómez Intituto de Invetigación Tecnoógica Univeridad Pontiicia Comia Madrid, Spain J. Cabeta Iberdroa Ditribución SAU Madrid, Spain Abtract Security o uppy reguation obige companie to deign optima operation procedure during emergency tate o the network. Beide, reiabiity contraint mut be conidered in order to obtain panning deciion abe to meet reguation. Reguation audit companie perormance by mean o power uppy reiabiity indexe. Thu, etimation o reiabiity indexe o medium votage (MV) ditribution network i a key iue. Thi paper preent a nove method to carry out the aut ocation and ervice retoration procee. For a peciic aut, the method etabihe the optima operation procedure to ocate it and to retore the ervice minimizing the non uppied energy (NSE). In addition, weak region o the tudied network can be ocated ince reiabiity indexe can be etimated or every inge network bu. The propoed approach comprie a heuritic agorithm or network reconiguration. Beide, it take into account rea operation criteria conidered during emergency tate o ditribution network. The method i abe to addre arge-cae and compex rea MV ditribution network. The perormance o the propoed method i iutrated conidering actua cenario o Iberdroa MV network in Madrid. Keyword: Faut Location, Service Retoration, Large-Scae Ditribution Network, Reconiguration, Heuritic Agorithm 1 INTRODUCTION Satiying the power quaity tandard, a we a reiabiity, are prioritie or ditribution companie. It ha recenty become an even more critica iue ince reiabiity reguation tend to be increaingy demanding. Reguation require companie to have a deep knowedge o their network in order to deign optima operation procedure during emergency tate o the network. Beide, ditribution companie ind themeve compeed to tudy the reiabiity perormance o the network in order to identiy weak region and deign uitabe panning action. Reguation audit power quaity and reiabiity o uppy by mean o the deinition and the etabihment o minimum vaue or power uppy reiabiity indexe [1]. Thereore, etimation o reiabiity indexe in medium votage (MV) ditribution network i a key iue or ditribution companie to deign operation and panning procedure. Athough the new mart grid paradigm i eading toward higher eve o network automation and contro [2], nowaday, mot o MV ditribution network keep a ow automation eve. A a reut, or mot ditribution network, both aut ocation and ervice retoration procee invove non-automated operation rue which entai direct deciion and action taken by operation ta. Moreover, mot manua witching operation mut be carried out by mobie maintenance crew. Thee procedure invove high vaue o non uppied energy (NSE). In the technica iterature, dierent approache or ervice retoration can be ound: caic optimization technique, genetic agorithm, imuated anneaing, taboo earch and knowedge-baed heuritic. The reconiguration probem, uing caica optimization technique [3-6], invove high computationa time. Moreover, the oution i commony untraceabe ince it i obtained oowing procee dierent than a rea ervice retoration proce. Genetic agorithm [7], imuated anneaing [8] and taboo earch [9, 10] are meta-heuritic agorithm widey ued to ove combinatory probem. Their main drawback i, a in the cae o caic optimization technique, that the oution i untraceabe ince the rue carried out in order to ove the probem are not reated to reconiguration or ervice retoration rue. Knowedge-baed heuritic agorithm appied to ervice retoration are widey known technique [11-16]. Propery et out knowedge-baed agorithm enure quai-optima, traceabe and interpretabe oution due to they are uuay obtained by oowing rue imiar to rea operation one. Furthermore, cacuation time are ower than thoe achieved with caica optimization technique and modern meta-heuritic. Thi paper preent a nove method to ove the aut ocation and ervice retoration probem or permanent aut. It etabihe the optima operation procedure to ocate the aut and to retore the ervice minimizing the NSE. The propoed approach comprie a heuritic agorithm or network reconiguration which conider ecurity (ine capacity and bu votage imit) and opera- 17 th Power Sytem Computation Conerence Stockhom Sweden - Augut 22-26, 2011

2 tiona contraint, uch a keeping the network radia and a ecure ytem reaying cheme. Beide, the method take into account actua operation criteria conidered during emergency tate o ditribution network. In addition to the optima operation procedure to ove the aut ocation and ervice retoration probem, the propoed approach i ueu to etimate reiabiity indexe or the network. Interruption time are cacuated or oad bue ater every witching. The imuation o the aut ocation and ervice retoration procee or every poibe aut in the network provide the expected reiabiity indexe or the compete network. Since ow computationa time are obtained, the enumeration method ha been eected. Thi anayi how up the weak region o the network. Thu, ueu reut are ao obtained or panning deciion. Faut ocation and ervice retoration procee are widey known, but no reerence dea with them a a combined probem. Many conuted reerence dea with aut ocation and ervice retoration procee eparatey. Faut ocation i preented a an independent probem whie ervice retoration approache away aume that the aut ha been previouy ocated [17, 18]. Thi aumption may ignore coniderabe uppy interruption time, even more when preent network, which are actuay ow automated network, are tudied. Moreover, rea ditribution ytem operator perorm imutaneouy both aut ocation and ervice retoration procee. In order to conider a the component o the tota uppy interruption time, the paper preent a knowedge-baed agorithm which optimize both aut ocation and ervice retoration procee imutaneouy. Simutaneity o both procee i required ince a partia retoration i eaibe when the aut i partiay ianded meanwhie it i ocated. Since actua network with a ow automation eve are tudied, imutaneou aut ocation and ervice retoration procee are conidered. Quai-optima reut and interpretabe and traceabe oution are expected. The paper i organized a oow. Section 2 preent the propoed method. Section 3 how a cae exampe in order to prove the perormance o the propoa. Section 4 concude, and ection 5 incude the bibiography. 2 FAULT LOCATION AND SERVICE RESTORATION PROCESSES For the imuation o the aiure o each ine or tranormer o the network, three tep are deined: aut ocation and ervice retoration, aut ioation and iand retoration and reiabiity indexe computation. In aut ocation and ervice retoration tage, optima witching equence i obtained. Remote igna, remote controed and manua operation procedure are conidered. Optima upport are computed when partia ervice retoration i poibe and uitabe. Support are computed uing an agorithm or network reconiguration [19]. Ater aut ocation and partia retoration, in aut ioation and iand retoration tage, the aut i ioated in the minimum indiviibe network area. A a reut, the minimum area i aected by repair time. When ianded area are generated in the aut ioation tep and partia retoration ha been not optima, ervice i inay retored in the unerved iand. Ater every inge deciion on the previou tep, uppy interruption time are computed or every cotumer. Partia vaue o reiabiity indexe o every inge cotumer are computed and accumuated vaue are updated or every imuated aut. 2.1 Faut ocation and ervice retoration Faut ocation and ervice retoration procee are conidered imutaneouy. Thi invove conidering ome operation rue which are oowed by ditribution ytem operator in rea aut ocation proce. Rea rue are ormuated by mean o an inteigent ogic and optimization criteria. Faut ocation proce i carried out irt uing automated device which may indicate the way o the aut current or may be remotey controed. Finay, the aut i conined to a upected area o the network where manua operation i carried out in order to deinitey ocate and ioate the aut. At eat one mobie maintenance crew i required. Manua proce entai a tria and error equence. Each tep trie to ioate the aut by pitting the upected area into two ubarea. Aterward, retoration i tried uptream the opened ectionaizing device. I the uptream breaker trip, the aut i ocated uptream rom the ectionaizing device. Otherwie, the aut i ocated downtream rom that device. Load to retore Search main upport Feaibe main upport? NO Secondary upport earched? NO Search econdary upport Figure 1 Main upport earch YES YES Bet upport No upport I the aut i ocated uptream rom the ectionaizing device, the downtream ubarea remain ioated rom the aut. In that cae, upport rom other eeder are earched and the retoration by mean o them i tudied. Support earch i carried out oowing tep hown in Figure 1. Firt, the oad o the ioated ubarea i determined. Secondy, open ine connecting the ioated ubarea 17 th Power Sytem Computation Conerence Stockhom Sweden - Augut 22-26, 2011

3 with uppied area o the network are earched. Thee open ine are caed main upport. Their margin i cacuated. The margin o a upport i deined a the maximum oad which can be uppied through a main upport whit maintaining branch power ow within capacity imit. The margin o a upport i i cacuated a the minimum among the pare capacity o every eement j whoe power ow i aected aong the path rom the interconnection point up to the ubtation: + margin = min( ) (1) i j j j where + maximum power ow o eement j; j j power ow o eement j. A upport i conidered eaibe i the correponding margin i equa or higher than the oad to retore and i the correponding witching oberve the votage contraint. I there are eaibe upport, the one with the highet margin i eected. Otherwie, or a ineaibe upport ound, econdary upport are earched in order to unoad the network which own the ineaibe main upport and make it eaibe. I any main upport become eaibe, the one with the highet expected margin, computed conidering the econdary upport, i eected. Secondary upport are earched oowing the proce hown in Figure 2. Secondary upport are earched or every ineaibe main upport. For each o them, the margin to recover i computed a the oad to recover minu the exiting margin. The virtua contraint i ocated. The virtua congetion i deined a the vioation o the imit which woud occur i the main upport i ued to retore the conidered oad. It i ocated in the branch whoe imit woud be vioated. Main upport YES No eaibe main upport Figure 2 Secondary upport earch Margin to recover Virtua contraint Search upport or virtua contraint Feaibe econdary upport? NO Feaibe main upport Open ine connecting the area downtream rom the virtua contraint with other uppied area o the network are earched. Thee open ine are caed econdary upport. They are conidered in order to traner ome oad rom the area ocated downtream rom the virtua contraint to other uppied area o the network. A econdary upport i eaibe when it margin i enough to recover the deired margin o the main upport and i the correponding witching oberve the votage contraint. I a eaibe econdary upport i ound, the correponding main upport i conidered eaibe. Once the upport are tudied, the bet witching to ectionaize the network in two ubarea i eected. For every poibe witch, the expected uptream and downtream retored oad are computed taking into account aiure rate o every uptream and downtream branch. Expected interruption time are ao computed in order to deine the eiciency o a witching operation a hown in (2). The eiciency o a witching operation meaure the expected avoided NSE in the next tep o the aut ocation and ervice retoration proce. µ d Pu µ d Pu + µ u Pd (2) e = max, NS S t t Where, or a witching : µ d probabiity o ocation downtream rom ; Pu power oad uptream rom ; µ u probabiity o ocation uptream rom ; Pd power oad downtream rom ; NS t interruption time i the upport i not conidered; t S interruption time i the upport i conidered. Interruption time incude time to reach the witch and time to open it. Interruption time depend on the peed o the mobie crew, the ditance covered by the crew (minimized uing [20]) and the characteritic o the witche. The eected witch to ectionaize the network i the one with the highet eiciency. Support i conidered i eiciency i a maximum when it i taken into account. Ater pitting the network into two ubarea, ix dierent ituation may occur (Figure 3), depending on where the aut i ocated (uptream or downtream o the witch) and whether a upport exit or not. In Figure 3, S repreent the utation o the aied network, S i the ubtation o the upporting network, CB i a circuit breaker, CB tand or the circuit braker o the upporting network, S mean the eected witch, S repreent the upporting witch and S -1 i the eected witch in the previou tep, which i conidered when it remain open in the current tep. Every cae invove a tria and error equence which entai opening S and coing CB. I the aut i ocated uptream rom S, CB wi trip. Otherwie, it wi remain coed. The oowing equence depend on the exitance or not o S -1 and S. Switche are uppoed to be manua operated and they are unabe to operate in charge, thereore an uptream CB i opened beore the witch i operated. Tabe 1 reume the equence or each cae. In Tabe 1, o mean open, c repreent coe and t tand or trip. The initia and the ina tate o every witching device i deined ( 0 or open, 1 or coed and i it i not conidered). 17 th Power Sytem Computation Conerence Stockhom Sweden - Augut 22-26, 2011

4 Uptream/ Initia tate Fina tate Cae S -1 downtream Support CB S -1 S S CB CB S -1 S S CB Sequence a NO downtream NO os ccb b NO uptream NO os ccb tcb cs c NO uptream YES os ccb tcb ocb cs ccb d YES downtream NO os ocb cs -1 ccb e YES uptream NO os ocb cs -1 ccb tcb os -1 ccb cs YES uptream YES os ocb cs -1 ccb tcb os -1 ccb ocb cs ccb Tabe 1: Summary o poibe cae and operation equence Interruption time i conidered or every witching. The combined aut ocation and ervice retoration probem inihe when no more witche exit in the upected area. Then, the aut i deinety ocated, but it i not neceariy ioated and the ervice retoration i not inihed. Thereore, two more tep are imuated in order to conider a the interruption time. Figure 3 Cae o aut ocation and ervice retoration 2.2 Faut ioation and iand retoration Once the aut i ocated, it mut be ioated in the minimum indiviibe iand in order to retore a much ervice a poibe, opening the nearet uptream and downtream witche (Figure 4). Figure 4 Faut ioation and iand retoration tage At the end o aut ioation tep, ome unerved iand may remain. In order to minimize NSE, iand retoration and aut ioation are conidered at the ame time. Main and econdary upport are computed or a the iand. I ervice retoration i eaibe, the operation equence i optimized conidering interruption time and expected retored oad o each upport. In thi tep, eiciency o an ioation witch i deined a hown in equation (3): e = Pd / t (3) Where, or an ioation witching : Pd power oad downtream rom ( Pd = 0 i t there i no eaibe upport); interruption time i the upport i conidered. Interruption time correponding to thi tep conider time to reach the witche, the upport witche and time to operate them. 2.3 Reiabiity indexe computation Each imuated aut contribute to annua expected NSE o a oad bu ( NSE ) a equation (4) how. Where: λ NSE = P T λ (4) aiure rate o a aut (meaured in number o aut per year) ; P power oad in bu ; T interruption time in bu caued by aut. Since utained aut have been conidered, a we a NSE, the mot common IEEE recommended utained interruption indexe have been conidered or reiabiity evauation o ditribution network [1]. The contribution o the aut to annua expected SAIFI o a oad bu ( (5). Where χ SAIFI ) i hown in equation SAIFI = χ λ (5) i a binary variabe whoe vaue i 1 i the aut aect to the oad bu and 0 otherwie. The contribution o the aut to annua expected SAIDI o a oad bu ( (6). SAIDI ) i hown in equation SAIDI = T λ (6) Annua expected NSE o a oad bu ( NSE ) i computed a hown in (7). (7) NSE = NSE = P T λ F F Where F i the et o aut which aect to oad bu. Annua expected SAIFI o a oad bu ( SAIFI ) i 17 th Power Sytem Computation Conerence Stockhom Sweden - Augut 22-26, 2011

5 computed a hown in (8). (8) SAIFI = SAIFI = λ F F Finay, annua expected SAIDI o a oad bu SAIDI ) i computed a hown in (9). ( (9) SAIDI = SAIDI = T λ F F 3 CASE STUDY 3.1 Faut ocation and ervice retoration In order to how the perormance o the method, it ha been teted with a ma educationa network mode (Figure 5). Network data are detaied in Appendix A. Parameter data are detaied in Appendix B Figure 5 Educationa network mode Tabe 2 how the detaied operation equence or the imuation o a peciic aut in ine ection 2-3. In addition, it how interruption time caued by every witching and the aggregated interruption time ater every witching. Finay, Tabe 2 ao how the poition o the crew or every operation. Ater our tep, the aut ocation i achieved. Firt tep correpond with cae b o ection 0. Second tep correpond with cae a. Ater tep 2, the ervice i partiay retored in oad bue 1, 2 and 18. However, interruption time increae or thee bue in ater tep becaue the tria and error equence entai trying to retore the ervice through ubtation 16. Third tep correpond with cae with a eaibe main upport in which i abe to operate in charge. Ater thi tep, ervice i partiay retored in bu 19 and no oad bu i aected in the upporting network. Fourth tep correpond to cae e. Ater thi tep, the aut i ocated in ine 2-3. However, aut i not optimay ioated. Step 5 and 6 correpond to aut ioation and iand retoration tage. Step 5 ioate the aut rom uptream bue and deinitey retore the ervice in oad bue 1, 2 and 18. Step 5 achieve aut ioation rom downtream bue. Thereore, tep 6 inihe the proce by retoring the ervice deinitey in oad bue 3, 4, 5, 6, 7, 8, 9, 19 and 20. An ineaibe main upport i ound in ince virtua congetion appear in In order to ove it, a eaibe econdary upport i ound in 15-21, and oad bue 10, 11, 13, 14, 15 and 19 are tranerred to the network uppied by the ubtation 501. Thi econdary upport make eaibe the main upport in Finay, the ervice i retored through the main upport Step Aggregate Time (min) Time (min) Operation Device Crew poition Open S Coe CB Trip CB Coe S Open S 2-3 S Coe CB 1-16 S Open S 3-19 S Open CB 1-16 S Coe S 2-3 S Coe CB 1-16 S Trip CB 1-16 S Open S 2-3 S Coe CB 1-16 S Coe RB S Open S 3-20 S Open CB 1-16 S Coe S 2-3 S Coe CB 1-16 S Trip CB 1-16 S Open S 2-3 S Coe CB 1-16 S Coe S 3-20 S Open S 2-3 S Coe CB 1-16 S Open CB S Open S S Coe CB S Open CB S Coe S S Coe CB S Open RB S Coe S 3-19 S Coe CB S 3-19 Tabe 2: Operation equence and interruption time 3.2 Reiabiity indexe anayi Appication o the method i iutrated or a part o the 20 kv ditribution network in Madrid. Thi network ha been choen becaue it ize may probe that the too i eicient when it i run in a arge network and imuation o actua incident have hown good agreement with the imuation output. Load and reiabiity data have been ditorted and no detaied data are provided in order to keep the privacy o the owner o the network. Deivered inormation i enough to how how reut o the propoed method may be ueu or panning tudie. Network conit o 1245 bue, 1321 ine ection, 38 tranormer and 578 oad bue. Bue are caiied in ix zone. Some zone cover urban area, but other zone have a more dipered demand and network i weaky mehed. The anayi o the annua expected NSE or every oad bu o a network ha been done. Figure 6 how the ditribution o expected NSE or every oad bu o the 17 th Power Sytem Computation Conerence Stockhom Sweden - Augut 22-26, 2011

6 tudied network. Figure 6 how that about 20% o the oad bue have an NSE o e than 10 kwh whie about 30% o the oad bue preent a NSE o more than 100 kwh. Thee are huge dierence among dierent oad bue and mean dierent need or dierent uer o the network. Figure 6 Ditribution unction o expected NSE or every oad bu A more detaied tudy i done rom reut hown in Figure 7. NSE i tudied or dierent zone o the network. Since network zone are reated to geograica zone and dierent demand concentration and dierent upport trength, reut eem to be coherent. ZONE 4 maintain a imiar and reduced NSE or every oad. Figure 7 Ditribution unction o expected NSE o network zone Mot zone preent the mot o it oad bue in reduced vaue o NSE, whit the 50% o them preent a ight increae and about the 20% preent vaue which may entai more peciic anayi in order to determine the convenience o taking action to reduce them. Finay, ZONE 2 preent an outtanding ditribution. In thi zone, 60% o the oad bue preent igniicant vaue and 20% o the oad bue deinitey require more peciic anayi in order to tudy uture action to reduce them. 4 CONCLUSIONS A new method or aut ocation and ervice retoration ha been preented. The propoed approach conider knowedge baed rue and a heuritic agorithm which optimize the upport o erved network area or ervice retoration. The method dea with the aut ocation and the ervice retoration probem the ame time a a combined probem in order to reduce interruption time in area where the partia retoration i poibe athough the aut i not deinitey ocated. The objective o the agorithm i to minimize the NSE o the compete proce. The output o the imuation o the proce i a detaied operation equence and the interruption time o every inge oad bu caued by a aut. In addition, the imuation o the equence o the aiure o every device o the network provide a computation o annua expected reiabiity indexe o every inge oad bu o the network. The paper detai the impemented rue and the propoed agorithm. In order to how the perormance o the method, it ha been teted with a ma educationa mode. Reut how the detaied operation equence or the imuation o a peciic aut. In addition, reiabiity indexe have been computed or a rea arge-cae network. The anayi o the annua expected NSE or every oad bu o a network turn on a ueu too in order to identiy weak area o the network. REFERENCES [1] "IEEE guide or eectric power ditribution reiabiity indice", IEEE Std 1366, 2001 Edition. [2] S. Kazemi, M. Fotuhi-Firuzabad, M. Sanaye- Paand, and M. Lehtonen, "Impact o Automatic Contro Sytem o Loop Retoration Scheme on the Ditribution Sytem Reiabiity", IET Generation, Tranmiion & Ditribution, [3] Q. Zhou, D. Shirmohammadi, and W.-H. E. Liu, "Ditribution Feeder Reconiguration or Service Retoration and Load Baancing", IEEE Tranaction on Power Sytem, vo. 12, nº 2, pp , May [4] G. J. Peponi, M. P. Papadopouo, and N. D. Hatziargyriou, "Ditribution Network Reconiguration to Minimize Reitive Line Loe", IEEE Tranaction on Power Deivery, vo. 10, nº 3, pp , Juy [5] V. Gamocanin, "Optima Lo Reduction o ditribution Network", IEEE Tranaction on Power Deivery, vo. 5, nº 3, pp , Augut [6] K. Aoki, T. Satoh, M. Itoh, H. Kuwabara, and M. Kanezahi, "Votage Drop Contrained Retoration o Suppy By Switch Operation In Ditribution Sytem", IEEE Tranaction on Power Deivery, vo. 3, nº 3, pp , Juy [7] Y. Fukuyama and C. Haio-Dong, "A parae genetic agorithm or ervice retoration in eectric power ditribution ytem", preented at IEEE Internationa Conerence on Fuzzy Sytem, Mar th Power Sytem Computation Conerence Stockhom Sweden - Augut 22-26, 2011

7 Powered by TCPDF ( [8] H. Mori and K. Takeda, "Parae imuated anneaing or power ytem decompoition", IEEE Tranaction on Power Sytem, vo. 9, nº 2, pp , May [9] H. Mori and Y. Ogita, "A Parae Tabu Search Baed Approach to Optima Network Reconiguration or Service Retoration in Ditribution Sytem", preented at 2002 IEEE Internationa Conerence on Contro Appication, Gagow, Scotand, UK, September 18-20, [10] S. Toune, H. Fudo, T. Genji, Y. Fukuyama, and Y. Nakanihi, "A Reactive Tabu Search or Service Retoration in Eectric Power Ditribution Sytem", preented at IEEE Word Congre on Computationa Inteigence, May [11] K. N. Miu, H.-D. Chiang, B. Yuan, and G. Daring, "Fat Service Retoration or Large-Scae Ditribution Sytem with Priority Cutomer and Contraint", IEEE Tranaction on Power Sytem, vo. 13, nº 3, pp , Aug [12] D. S. Popovic and R. M. Ciric, "A Muti-Objetive Agorithm For Ditribution Network Retoration", IEEE Tranaction on Power Deivery, vo. 14, nº 3, pp , Juy [13] H.-C. Kuo and Y.-Y. Hu, "Ditribution ytem oad etimation and ervice retoration uing a uzzy et approach", IEEE Tranaction on Power Deivery, vo. 8, nº 4, pp , Oct [14] Y. Y. Hu, H. M. Huang, H. C. Kuo, S. K. Peng, C. W. Chang, K. J. Chang, H. S. A. Yu, C. E. Chow, and R. T. Kuo, "Ditribution ytem ervice retoration uing a heuritic earch approach", Power Deivery, IEEE Tranaction on, vo. 7, nº 2, pp. 734, [15] W.-M. Lin and H.-C. Chin, "A New Approach or Ditribution Feeder Reconiguration or Lo Reduction and Service Retoration", IEEE Tranaction on Power Deivery, vo. 13, nº 3, pp , Juy [16] C.-S. Chen, C.-H. Lin, and H.-Y. Tai, "A Rue- Baed Expert Sytem With Coored Petri Net Mode or Ditribution Sytem Service Retoration", IEEE Tranaction on Power Sytem, vo. 17, nº 4, pp , November [17] L. Seung-Jae, C. Myeon-Song, K. Sang-Hee, J. Bo-Gun, L. Duck-Su, A. Bok-Shin, Y. Nam-Seon, K. Ho-Yong, and W. Sang-Bong, "An inteigent and eicient aut ocation and diagnoi cheme or radia ditribution ytem", Power Deivery, IEEE Tranaction on, vo. 19, nº 2, pp. 524, [18] M. Lehtonen, A. Matinen, E. Antia, and J. Kuru, "An advanced mode or automatic aut management in ditribution network", preented at Power Engineering Society Winter Meeting, IEEE, Jan [19] A. Gonzáez, F. M. Echavarren, L. Rouco, T. Gómez, and J. Cabeta, "A Too or Reconiguration o Large-Scae Ditribution Network", preented at 16th Power Sytem Computation Conerence (PSCC08), Gagow, Scotand,2008. [20] E. W. Dijktra, "A Note on Two Probem in Connexion with Graph", Numeriche Mathematk, vo. 1, pp , I. APPENDIX A In order to make the ma cae exampe reproducibe, network mode i decribed beow. The eected cae i a 20 kv ditribution network. Source are ited in node 16, 17 and 501. Sytem rating i 100 MVA. Aiming at maintain interpretabiity o the reut and impicity o the oution, aiure rate i the ame 6 ai/100km year or every ine. Eectric parameter, ength and type o ectionaizing device reated to a ine are preented in Tabe 3, where M tand or manua and RC tand or remote contro. Load i the ame 400 kw in every bu. Power rate are a conidered unimited except or ine 12-13, whoe vaue i 800 kva. Bu Number Operation From To R (pu) X (pu) Length (m) Operation Device time (min) M Switch RC Circuit breaker M Switch M Manua Switch None M Switch M Switch RC Switch M Switch M Switch RC Switch M Switch M Switch RC Contact breaker M Switch M Switch RC Circuit breaker RC Switch RC Switch RC Switch M Switch M Switch RC Switch M Switch M Switch RC Circuit breaker 0.5 Tabe 3. Educationa network mode parameter II. APPENDIX B The propoed method require the entry o ome execution data which may aect the reut. In order to make the cae exampe reproducibe, thoe parameter are detaied beow: Crew peed: 40 km/h Aowed overoad in ine: 10% Minimum aowed bu votage: 0.93 pu 17 th Power Sytem Computation Conerence Stockhom Sweden - Augut 22-26, 2011