Interconnections between Reliability, Maintenance and Availability

Transcription

1 Intrconnctons btwn Rlablty, Mantnanc and Avalablty Cataln Mha, Sorn Abagu, Larsa Zotanu and Elna Hlra Translvana Unvrsty of Brasov, 29, Erolor Str., Brasov, Romana Abstract. Th assuranc of powr qualty dpnds on factors whch nflunc th prformancs of th avalablty: th rlablty and ts support th mantnanc. Ths papr dals wth th ntractons btwn th ndcators of rlablty, mantnanc, avalablty and wth th mthods for th calculaton of th rlablty ndcators. For an ovrhad ln of 0 kv th charactrstcs of th rlablty of th systm ar dtrmnd by modlng and analyzng ts functonalty by th Markov procss of contnuous tm. Th valu of th avalablty ndx and th mantnanc functon functon contrbuts to ascrtan for th studd cas that th valu of th avalablty coffcnt has th sam valu wth th probablty of succss and th probablty of rparng an qupmnt s closly connctd to th mantnanc functon Kywords: Rlablty, mantnanc, avalablty, Markov procss, lctrc lns, Introducton Th qupmnt usd on th powr systms s rlatvly old and ncrass th fnancal ffort for thr mantnanc. Thrfor appar faturs of th lctrcal systms that ar closly ntrrlatd, such as: rlablty, avalablty and mantnanc, thr ntractons dtrmnng th qualtatv and quanttatv aspcts of th analyzd systm, ts saf opraton. Th rlablty, as a fatur of th systm n fulfllng th spcfc functons n a crtan prod of tm, contnus to b th subjct of many rsarchs [],[5],[7] and [0]. Thr ar many paprs [2],[8],[2] and [3] that hav as a rsarch subjct th mantnanc, thr goal bng to dtrmn th optmum tchncal organsatonal actons to mantan or to rpar th systm functonalty. Concrnng th systm avalablty, thr s analysd from ths pont of vw: th systm capacty of fulfllng ts functon n a crtan momnt wthn a prod of tm. Takng n account th ncssts for an ncrasng qualty of th dlvrd lctrcal nrgy, thr mrgs th mportanc of a nw approach n dalng wth th aspcts of rlablty, avalablty and mantnanc, n ordr to dvlop ffcnt mthods for calculatng th paramtrs/charactrstcs n rlaton wth th opraton tm.

2 442 C. Mha, S. Abagu, L. Zotanu and E. Hlra Ths papr analyss th connctons btwn rlablty, avalablty, mantnanc and th Markov chans s th proposd mthod for dtrmnng th ndcators of th corrlaton btwn rlablty, avalablty mantnanc and th probablty of falur for an ovrhad ln of 0 kv. 2 Contrbuton to Tchnologcal Innovaton Th valuaton of rparng probablty for qupmnt, that can b ntgratd rapdly n th mantnanc program of studd systms, rprsnts an nnovaton n tchncal doman basd on th analyss of rlablty ndcators, contrbutng to mplmntaton of th ntgratd concpt rlablty, mantnanc and avalablty. 3 Charactrstcs Masurs for Rlablty, Mantnanc and Avalablty Th saf opraton of a tchncal systm s dfnd by th totalty of charactrstcs, Rlablty, Mantnanc and Avalablty. Th functon of Rlablty s dfnd by th rlaton: ( ) R t 0 = t ( ) z t dt whr z(t) - rat of falur s dfnd lk th probablty of unntrruptd opraton untl th momnt of tm t. Th rlaton () appls to any law of dstrbuton of opraton tm. For th xponntal rpartton of opraton tm, th rat of falur s: z(t) = λ It rsults: ( t ) = λ = const. ( ) R t, () ( t) t = λ (2) Mantanablty (M) rprsnts a safty functon and conssts n th probablty for an nstallaton (or an qupmnt) to r-ntr nto opraton aftr a crtan tm whn th mantnanc actons wr mad []. Th mantnanc functon s dfnd by th rlaton: M t = (3) whr: s th ntnsty of rpar, rprsntng th probablty that for a dvc whch was faulty at th momnt t, to b rpard n th nxt vry short prod of tm. For an xponntal rpartton of th rparng prods: ( ) const. t =

3 Intrconnctons btwn Rlablty, Mantnanc and Avalablty Rlablty Masurs Rlablty masurs of rparabl systms can b catgorzd nto thr groups [3]: o Masurs basd on th systm s frst falur, o Stady-stat masurs, o Tm-spcfc masurs. As tm advancs progrsss, th rparabl systm rachs a stady-stat condton. Ths mans that crtan stmats of systm masurs do not chang wth tm. Ths masurs nclud avalablty, man tm btwn falurs MTBF, man tm to falur MTTF, man tm to rpar MTTR, and th xpctd numbr of falurs pr unt tm (falur frquncy). Th followng rlatons ar wll known: MTBF = ( ) A( ) MTTF = ( ) A( ) MTRF = ( ). (4) Hr A( )and ν( ) ar rspctvly th stady-stat avalablty and falur frquncy of th systm. Thrfor, MTTF, MTTR, and MTBF can asly b found from th stady-stat avalablty and falur frquncy. In Fg. thr ar shown th lnks btwn Rlablty, Mantnanc, Avalablty. Fg.. Connctons btwn rlablty, mantnanc and avalablty. Analyzng Fg., t can undrln that th rlablty of a systm s charactrzd by th st of masurs that gv nformaton on th prformanc of th systm functonalty n a prod of tm.

4 444 C. Mha, S. Abagu, L. Zotanu and E. Hlra 4 Calculaton of Systm Rlablty Indcators. Cas Study It consdr th cas of a 0 kv ovrhad powr ln shown n (Fg.2), wth rpar and falur ntnsts usd n th dsgn and provdd by th Normatv [9]. It ams at dtrmnng th charactrstcs of systm analyss and adoptng a modl of ts opraton usng contnuous tm Markov procsss that can b usd for opraton and mantnanc srvcs of ovrhad powr ln ownr. Bara Vs: 0, kv GRID SB I-0 SL LEA 3, kmtrs I2-0 Trafo 600, kva Consumator Vs: 20, kv Fg. 2. Th schm of supply of a consumr to 20 kv through 0 kv ovrhad ln. In Tabl Thr ar lstd th avrag valus ctd n tchncal ltratur [6] for th followng paramtrs: th ntnsty of falur, th ntnsty of rpar for a 0 kv nstallaton. Tabl. Intnsts of rpar and falur n nstallatons of 0 kv. Elmnts of ovrhad powr ln Intnsty of falur λ [yar - ] Intnsty of rpar [yar - ] Collctor bar,3x0-2 75,2 Brakr ln cll 3x0-2 75,2 Transformr 0 kv/mv 2x0-2 2,0 0 kv ovrhad ln,3x ,5 Bar and ln sparator 0,4x Bng a sral systm componnts, to study som lmnts of th schm s consdrd a systm of 7 lmnts charactrzd by ndcators of rlablty λ and. In such a schm, falur of any of th tms that gos nto thm has th ffct of rmovng all succssful schms n th stat. Fg. 3. Equvalnt schm for calculatng th rlablty ndcators of 7 lmnts connctd n srs. Th schma lmnts can b consdrd dpndnt or ndpndnt, th stats whch may tak dffrnt lmnts of th schm. If th tms ar functonally dpndnt, th numbr of stats s qual to (n +). - n stat 0 - all lmnts ar n opraton, - n stat - lmnt s dfctv, - n stat n - lmnt 2 s dfctv.

5 Intrconnctons btwn Rlablty, Mantnanc and Avalablty 445 Thr s no possblty of transton from stats wth a dfctv componnt n stats wth two dfctv lmnts or stats wth two dfctv lmnts n stats wth thr dfctv lmnts, snc at th falur of on lmnt, th schm s dcommssond, thrfor thr s assumd that th othr lmnts can not b damagd. Stats dnomnaton: -succssful stat (all lmnts n srvc): 0 -falur stat:, 2, 3,...,7. Transton graph for a systm wth lmnts n srs s shown n Fgur 4. Fg. 4. Graphcal rprsntaton of transtons for th srs schdul. 4. Calculaton and Analyss of Rlablty Masurs Basd on th analyss of stat transtons [] has mad th transton ntnsts matrx. Transton ntnsts matrx, column matrx of absolut probablty and matrx quaton of stat of absolut possblty tndng to constant valus ndpndnt of tm. If th systm wth n lmnts srs, matrcs ar gvn blow: n λ K n P0 λ P K 0 = 0 K K K K K λ Pn n 0 K n (5) Calculaton of succss and falur probablts s carrd out by solvng th rlaton (5), whr P0 s th probablty for th systm to b n workng ordr, P-P7 corrspondng to 7 stats of transton. In ths cas:

6 446 C. Mha, S. Abagu, L. Zotanu and E. Hlra P 0 = = 0,998 λ + ; P 0,007 0 ; 0, ; 2 0,06 0 ; λ = P0 = 0, ; 0, ; 0,06 0 ; 0, (6) For an opraton tm plannd for th Tp = 8200 h/yar th followng masurs ar calculatd: Probablty of succss: Probablty of rjcton: PS = P 0 = 0,998 (7) 7 P = P = 0,002 (8) R Man total succss tm: M[ α( Tp ) = PsT p = Tp = 0, = 883,6 h / yar λ + 7 (9) Man total falur tm: 7 λ M[ β( Tp ) = PRT p = T = 0, = 6,4 / 7 p h yar (0) λ + Man numbr of damags: Tp M[ ν ( Tp )] = P q0 jtp = P0 q0 jtp = P0 ( λ λn ) Tp = + = = 0, ,936 0,3 Man duraton of a succssful stat: M[ α( Tp )] M[( Tf )] = = = M[ β( T )] λ 4 0 Man duraton of contnuous opraton (a stat of falur): p yar λ λ () (2)

7 Intrconnctons btwn Rlablty, Mantnanc and Avalablty 447 λ M[ β ( T p )] M[( Td )] = MTBF = = = 0,0087 yar M[ v( T )] λ p (3) Snc th systm s studd wth a srs structur s nfrrd that th falur of any componnt of th systm gnrats damag of th ntr ln. Thrfor, t s of tantamount mportanc to hav a systm wth ntnsty of rpar and an ntnsty of falur, such as: λ = = λ = 0,4 yar M[ T ] p λ = = = 4,75 M[ T ] λ d yar Dtrmnaton of avalablty and mantnanc functons To wrt th coffcnt of avalablty and mantnanc functon wll b usd for rpar and falur, th ntnsts quvalnt to th systm analyzd. M[ Td ] = = 8760 = 60,58 days 4,75 (5) 4,75 A = = = 0,998 λ + 4,75 + 0,4 Mantanablty functon s: (4) M = t (6) Aftr analyss, w hav th followng cass prsntd n Tabl 2. Tabl 2. Probablty of rpar of ovrhad ln. Tm rqurd for rpar [h] Probablty to b rpard [%] t =.6% t = % t = % t = % It s notd that for th tm to rpar th ovrhad ln of 0 kv, for t = h, th probablty for that ln to b rpard s.6%, and th accptabl probablty (96.32%) rpar for ovrhad ln studd, lads to a mnmum for 8 days. 5 Conclusons Th mthod usd for dtrmnng th charactrstcs of rlablty s asy to apply and almost draw up and provdd mantnanc plans and procdurs and lkws and mantnanc programs rlatd qupmnt or systms studd.

8 448 C. Mha, S. Abagu, L. Zotanu and E. Hlra Th cas study was prformd wth th paramtrs of profssonal norms, whch s usful for dsgn calculatons. For opratng systms s usful to ntroduc th valu of opratng paramtrs that may substantat mor rgorous mantnanc plans. Calculatd data wr compard wth data mnng from SC Elctrca SA (Elctrcty Dstrbuton Company from Romana) and thy ar th valus around whch confrms th valdty of th calculaton. Rfrncs. Ntu, V.I., Ionscu, C.: Fabltata n nrgtca. Edtura Ddactca s Pdagogca, Bucurst, (980) 2. McMahon B.: Rlablty and mantnanc practcs for australan and nw zaland transmsson lns, 'Th Rlablty of Transmsson and Dstrbuton Equpmnt', 2S37, Confrnc Publcaton No. 406 (995) 3. Jacob D., Amar S. V., Analyss of Complx Rparabl Systms, RAMS, IEEE (2005) 4. Mttas, A.: Rlablty Prdctons basd on Customr Usag Strss Profls, IEEE, RAMS (2005) 5. Martnscu, I., Popscu, I.: Analza fabltat s scurtat sstmlor. Edtura Unvrstat Translvana Brasov, Brasov (2002) 6. Ntu, V.I.: Fabltat, dsponbltat, mntnanta n nrgtca. Edtura Thnca Bucurst, (987) 7. Mhoc, Gh., Muja, A., Datcu, E.: Bazl matmatc al tor fabltăţ. Edtura. Daca, Cluj Napoca (976) 8. Boşanu, L.: Fabltat ş mntnanţă îndrumar d lucrăr practc. Insttutul Polthnc Bucurst (992) 9. NTE 005/06/00: Normatv prvnd mtodl ş lmntl d calcul al sguranţ în funcţonar a nstalaţlor lctrc. 0. Stllman, R.: Powr Ln Mantnanc wth Mnmal Rpar and Rplacmnt. In: IEEE Procdngs Annual Rlablty and Mantanablty Symposum (2003). Kccoglu, D.: Rlablty Engnrng Handbook, vol. 2, DEStch Publcaton Inc., Pnnsylvana USA (2002) 2. Rglr, D. M., Hodgkns, W. R, Allan, R. N.: Quanttatv rlablty analyssof dstrbuton systms: rpar tms. In: Powr Engnrng Journal (997) 3. Fulvo E. O.: An Optmal Sparng Modl for th Opratonal Avdablty toapproach th Inhrnt Avalablty. In: Procdngs Annual Rlablty and Mantanablty Symposum (200)