Reliability evaluation of distribution network based on improved non. sequential Monte Carlo method

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1 3rd Iteratoal Coferece o Mecatrocs, Robotcs ad Automato (ICMRA 205) Relablty evaluato of dstrbuto etwork based o mproved o sequetal Mote Carlo metod Je Zu, a, Cao L, b, Aog Tag, c Scool of Automato, Wua Uversty of tecology, Wua, Hube, , Ca a @qq.com, b 03609@qq.com, c @qq.com Keywords: Relablty evaluato; No sequetal Mote Carlo samplg; Stratfed samplg; Power system; Dstrbuto etwork. Abstract. I ts paper te dea of stratfcato s utlzed to form a omogeeous-stratfed samplg metod, wc ca crease te effcet of power system radom fault state evaluato. Applyg ts metod for relablty evaluato oly geerates a small umber of depedet radom umbers, t decrease te amout of calculato ad crease te effcet. Te mproved o sequetal Mote Carlo metod s te demostrated ad mplemeted te relablty evaluato of RBTS-BUS5 system case, llustratg ts algortm ca be used relablty evaluato of dstrbuto etwork. Itroductos I order to obta te relablty dex of ger precso, t ofte requres a log calculato tme. I order to reduce te smulato tme ad mprove te covergece speed of Mote Carlo metod, we ca use te metod of varace reducto. Te usual metods of varace reducto are stratfed samplg metod,mportace samplg metod, te varable cotrol metod ad dual varable metod[-4] ad so o. However, tere are some restrctve codtos of tese metods use. I ts paper,we use scattered samplg tecque to reduce te varace, dfferet from oter tradtoal samplg metod were s samplg terval uform segmetato, take eac samplg terval mea value of expermet fucto as te ew expermetal fucto of te system every samplg, so as to reduce te smulato varace, mprove smulato accuracy. Te metod ca greatly reduce te samplg umber does ot exst ay costrats, ad terefore ave a very good adaptablty. Te basc prcple of o sequetal Mote Carlo metod Te o sequetal Mote Carlo smulato metod [5] s ofte referred to as te state samplg metod. Ts metod s based o te system state s a combato of all elemets, ad eac state of te elemet s determed by samplg probablty of compoets te state. Eac elemet s avalable to be smulated by a uform dstrbuto te terval of [0, ]. Assume tat eac elemet as two states of falure ad work, ad falure of compoets are depedet eac oter. Let s deote te state elemet, radom umber R te terval of [0, ] for te elemet, make Q o bealf of te falure probablty, geeratg a uform 205. Te autors - Publsed by Atlats Press 535

2 { 0 ( work state) f R> Q s = ( falure state) f 0 R Q () Te system state wt N elemets s represeted by te vector s: s = (s,...,s,...s ) N We a system state s selected te sample, amely carres o aalyzg te system to determe weter t s a fault codto, f t s, te estmate rsk dex fuctos of te state. We te umber of samples s large eoug, te frequecy of samplg system of S may be regarded as te probablty of te ubased estmato,.e. m (s) P(s) = (2) M Were: M s te samplg umber, m( s) s te umber of tmes of S appeared te samplg system state. Samplg prcple of dstrbuted samplg metod ad ts mplemetato process [6] Te tradtoal samplg metod s drectly geerated uformly dstrbuted radom umbers te terval of [0, l], ad determe te system stocastc state by te radom umber. But scattered samplg algortm dvded terval [0, ] to sub tervals. Ad te legts of sub tervals meet max{f,f 2,...f m }, were, f,f 2,...f m are te forced falure probablty of system compoets. or a radom umber x, t ca produce state varables (X,X 2,...X,...X ) te tervals. I te sub terval X s determed accordg to te type 3 Ï x < + f Ô X = (3) Ì Ô - - x < or x + f ÔÓ By te above formula dcates, we a radom umber vector X was geerated, we ca obta state vectors X,X 2,...X,...X troug te use of scattered samplg tecque, t greatly mprove te effcecy te use of radom umber. Take te artmetc average value of expermetal fucto (X ), (X 2 ),... (X ),... (X ) eac sub terval as a radom fucto of vector X (X) = Â (X ) = (4) I order to realze te scattered samplg algortm, we ca use te calculated rsk dex te loss of load probablty ad te expected power ot suppled value to aceve, te pecewse terval[-/,/], Te expermetal fucto s defed as follows: We computg, expermetal fucto as follows: Ï load cuttg system (X ) = Ì (5) Ó 0 No load cuttg syste m We computg, expermetal fucto as follows: 536

3 Ï ÔÂ P load cuttg system (X ) = (6) Ì ÔÓ Amog tem, 0 No load cuttg system Ps te value of load mus te total power outputtg. Te ew expermetal fucto s: k (X ) ( X ) = Â (7) = Te expected value formula of (X) s: E ( ) = Â N (X) (8) N = I te formula above, (X) s te system t samplg expermet fucto. Te varace estmato formula of (X) s: V( ) [ (X)-E( )] N 2 =Â (9) = N Applcato of dstrbuted samplg metod te relablty evaluato of dstrbuto etwork Use te metod above to evaluate te relablty for RBTS-BUS5 le of IEEE relablty testg system. RBTS-BUS 5 s a typcal rural power dstrbuto etwork as sow g.. Table ad Table 2 separately lsted te approprate le data ad user data. Te rest data values were cosdered as: te value of le falure rateg L s 0.2 tme - (km a), te value of repar tme L s.5 [7]. g. RBTS-BUS 5 Te structure of rg etwork Table.Te le data of RBTS-BUS5 rg etwork Le umber Legt (km),6,9,3,4,8, ,7,8,2,5,6,9, ,3,5,0,,7,

4 Table 2.Te user data of RBTS-BUS5 rg etwork Load pot Category λ/tme α r/ tme - maxmum average umber load (kw) load (kw) of users,2,3,4 Resdet ,6,7 Agrculture ,9,0, Resdet ,3 Agrculture Te calculato flow cart of mproved o sequetal Mote Carlo metod as sow g. 2: g.2 Te calculato flow cart of mproved o sequetal Mote Carlo metod Te teory based o te o-sequetal Mote Carlo smulato algortm of probablty, scattered samplg metod ad aalytcal udgmet were as follows. Te rsk assessmet of power dstrbuto system as bee doe by usg mproved ad umproved Mote Carlo metod respectvely. Te calculated rsk dex were te loss of load probablty ad te expected power ot suppled value. Te covergece rate of s slower ta rate of, so te varato coeffcet of as bee take as covergece crtero order to balace computatoal accuracy of bot tese paper.te assessmet results of RBTS-BUS5 rg etwork structure by two metods as sow table 3 Table 3.Te rsk assessmet results of RBTS-BUS5 by Uform samplg metod ad scattered samplg metod Metod K V V

5 Were, metod ad 2 represet mproved ad umproved Mote Carlo metod respectvely, K s te samplg tmes, V ad V mea varaces of test fuctos wc correspod to te rsk dcators ad respectvely, varace coeffcet of te correspodg ad respectvely. ad are te Coclusos Te results of rsk assessmet te above examples dcated tat metod 2 reduces te samplg varace to a certa extet ad mprove te covergece speed of te Mote Carlo metod compared wt metod for te same samplg umber. or stace, te example aalyss of RBTS-BUS5 revealed tat te varaces of test fuctos ( V ad V ) calculated by metod are ad respectvely, te varaces calculated by metod 2 are about ad respectvely after tmes of samplg calculato. Te rato of te varace of Test fuctos calculated by metod ad te varace by metod 2 were about 5.04% ad 3.68% respectvely. I oter words, metod as better covergece property compared wt metods 2. Ts ca also be verfed by sze relatosp of varace coeffcet of two metods. or example, te varaces coeffcet ( ad ) calculated by metod are ad.9793 respectvely, te varaces coeffcet calculated by metod 2 are about ad respectvely after 0000 samplg calculato. Te rato of te former ad te latter were 23.55% ad 39.6% respectvely. Wat s more, te rato was 23.65% ad 39.87% after tmes of samplg calculato. g. 3 ad g. 4 descrbed te cage law ad cotrast about V ad V of te two metods. g.3 te value of dfferet samplg g.4 te value of EPN S dfferet tmes uder te metod of ad 2 samplg tmes uder te metod of ad 2 Lterature Refereces [] Zage ag. Computer smulato ad Mote-Carlo metod [M].Beg: Beg Isttute of Tecology Press, 988. [2] DMITRII L,ARKADII N,REUVEN Y R.A fast Mote-Carlo metod for evaluatg relablty dexes[j].ieee TRANS. o Relablty,999,48(3):

6 [3] Mg Dg, Segu L. Metod for speed up covergece of Mote-Carlo metod smulato relablty calculato[j].automato of Electrc Power Systems,2000,24(2):6-9. [4] Zog Xu. Mote-Carlo metod [M].Saga: Saga Scece ad Tecology Press, 985. [5] Bllto R, L Weyua. Relablty Assessmet of Electrc Power Systems Usg Mote Carlo Metods [M]. New York ad Lodo: Pleum Press, 994. [6] Lzao Lv,Applcato of mproved o sequetal Mote Carlo metod power grd operato mode rsk assessmet[d], College of electrcal ad Iformato Egeerg, Hua uversty,20. [7] Huawe Zag. Ivestmet beefts aalyss of feeder automato mode. Joural of QLu Normal Uversty,202,27(2),

Idea is to sample from a different distribution that picks points in important regions of the sample space. Want ( ) ( ) ( ) E f X = f x g x dx

Idea is to sample from a different distribution that picks points in important regions of the sample space. Want ( ) ( ) ( ) E f X = f x g x dx Importace Samplg Used for a umber of purposes: Varace reducto Allows for dffcult dstrbutos to be sampled from. Sestvty aalyss Reusg samples to reduce computatoal burde. Idea s to sample from a dfferet