Dragan Kalaba 1, Milan Đorđević 1, Vladan Ivanović 2

Transcription

1 Draga Kalaba, Mila Đorđević, Vlada Ivaović DETERMINING THE RELIABILITY FUNCTIONS OF THE BOILER TUBING SYSTEM IN POWER PLANT NIKOLA TESLA, BLOCK A4 ODREĐIVANJE FUNKCIJA POUZDANOSTI CEVNOG SISTEMA KOTLA U TERMOELEKTRANI NIKOLA TESLA, BLOK A4 Origiali auči rad / Origial scieific paper UDK /UDC: Rad primlje / Paper received: 0..0 Keywords boiler ubig sysem reliabiliy Weibull disribuio Absrac The objecive of his paper is a represeaio of he probabilisic reliabiliy assessme of boiler ubig sysem i he fossil fuel power pla. Exploiaio research of he reliabiliy idicaors of a boiler ubig sysem i he fossil fuel power pla Nikola Tesla, Block A4 durig useful life period is based o a eleve-year failure daabase. By applyig he reliabiliy heory, based o saisics ad heory of possibiliy, ad usig simple ad complex woparameer Weibull disribuio, he heoreical reliabiliy fucios of he specified sysem are deermied. Obaied probabilisic laws of failure occurrece by differe Weibull disribuio models are compared i order o evaluae how close lised mahemaical disribuios describe behaviour of such a sysem i erms of reliabiliy. Show resuls make possible o acquire a beer kowledge of curre sae of he sysem, as well as a more accurae esimaio of is behaviour durig fuure exploiaio. INTRODUCTION Reliabiliy has become oe of he highes prioriies of power sysems, ad i raks alog wih cos ad efficiecy as a measure of successful operaio. The geeral objecive of maieace is o make use of he releva iformaio regardig failures ad repairs. Therefore i is imperaive o ivesigae he reliabiliy characerisics of he sysem, for akig ecessary measures regardig maximizaio of he power supply. The boiler ubig sysem is oe of he mos impora sysems of he hermal power pla from he sadpoi of reliabiliy, sice i is he mos suscepible o failures. Boiler ubes have limied life ad could fail due o various failure mechaisms, //. Ouages i he process of he boiler ubig sysem direcly cause ouages of power pla ad disrupio i he power sysem. Reliabiliy evaluaio of a boiler ubig sysem demads sarig cosideraios: defiiio of sysem boudaries o limi he exe of he aalysis; Adresa auora / Auhor's address: ) Uiversiy of Prišia i Kosovska Mirovica, Faculy of Techical Scieces, Kosovska Mirovica, Serbia dragakalaba@gmail.com ) Uiversiy of Moeegro, Faculy of Mechaical Egieerig, Podgorica, Moeegro Ključe reči cevi sisem kola pouzdaos Vejbulova raspodela Izvod Cilj ovog rada je predsavljaje verovaose ehike za proceu pouzdaosi cevog sisema kola u ermoelekrai. Eksploaacioo israživaje pokazaelja pouzdaosi u ermoelekrai 'Nikola Tesla, Blok A4' okom ormalog radog veka zasovao je a jedaaesogodišjoj pogoskoj dokumeaciji o zasojima. Primeom eorije pouzdaosi, zasovaoj a saisici i eoriji verovaoće, korišćejem prose i složee dvo-paramearske Vejbulove raspodele, određee su eoreske fukcije pouzdaosi avedeog sisema. Verovaosi zakoi pojave zasoja dobijei različiim modelima Vejbulove raspodele su upoređei kako bi se proceila precizos kojom avedee maemaičke raspodele opisuju pouzdaos avedeog sisema. Prikazai rezulai pružaju mogućos boljeg uvida u reuo saje sisema, kao i preciziju proceu jegovog poašaja okom buduće eksploaacije. selecio of he aalysis mehod, i order o be able o sudy he pheomea correcly. Corol limis are adoped i order o deermie he rasmissio limis of he hermal power subsysems wihi he hermal scheme, //. Based o he releva exploiaio daa of uplaed ouages of he cosidered sysem, he followig hree asks relaed o deermiig he characerisics of radom variables are solved, //: creaig a hypohesis of he class of disribuio fucio o which he radom value belogs, o he basis of aalysig he saisical maerial, validaio of he hypohesis, deermiig he ukow parameers of he disribuio ad evaluaio of heir accuracy. Havig i mid he probabilisic aure of he problem aalysed, he Weibull model has bee used, as he mos commo soluio o egieerig problems of his kid /4-8/. The paper discusses he developme of Weibull model for reliabiliy evaluaio of boiler ubig sysem of a hermal power pla usig he probabilisic approach ad 67

2 Deermiig he reliabiliy fucios of he boiler ubig sysem Određivaje fukcija pouzdaosi cevog sisema kola u scruiizes he possibiliies ad limiaios of he suggesed model, /9-/. I a broader scope, his approach ca be reaed as a par of he risk-based aalysis i srucural iegriy assessme. DETERMINING RELIABILITY FUNCTIONS USING SIMPLE WEIBULL DISTRIBUTION This paper preses a exploiaio research o he reliabiliy of he boiler ubig sysem i he power pla Nikola Tesla, Block A4 (TENT-A4) (isalled capaciy of 08. MW) which was coduced i he period from 996 o 006. Failure evidece ecessary for deermiig reliabiliy idicaors for he cosidered sysem are preseed i Table. Operaig ime iervals ha iclude all releva daa required for sysem aalysis are defied for oe year periods, or 8760 workig hours. Ierpreaio of daa is oe of he key elemes of he heory of reliabiliy. Usig probabiliy ad saisical aalyses, he reliabiliy of a power sysem ca be sudied i deph, //. The primary quesio ha requires a aswer is which heoreical disribuio model bes fis exisig daa. The physical properies of he sochasic process ha is aalysed i some cases may sugges possible form of probabiliy disribuio. Whe a law of probabilisic disribuio is based o empirical daa, he mahemaical form of he disribuio is usually o easy o deermie, /4/. Table. The exploiaio reliabiliy compoes of he boiler ubig sysem i he power pla TENT-A4. Observaio period Reliabiliy i Tk i T i T i N i Ni i N i f i F i R i i MR (-) (year) (h) (-) (-) (-) (h-) (-) (-) (h-) (%) The behaviour of hermal power sysems i erms of reliabiliy could be bes approximaed by he Weibull disribuio, while usig ormal, logormal ad expoeial disribuios could lead o cosiderable disagreemes, //. The Weibull disribuio is oe of he mos widely used i reliabiliy aalysis, due o fac ha wih a appropriae choice of is parameers, all hree regios of he bahub curve ca be represeed. The Weibull disribuio is very flexible ad capable of modellig life of mechaical sysems wih ime depede failure rae, /, 6/. Failures of such sysems are domiaed by agig ad mechaical wear. I his sudy, he graphical mehod ad probabiliy papers are applied for aalysis of he saisical se of daa obaied by he exploiaio survey of he boiler ubig sysem i TENT-A4. The graphical mehod is chose due o is relaive simpliciy ad capabiliy of providig a beer udersadig abou he behaviour of ay repairable sysem, /7/. The wo-parameer Weibull disribuio is seleced i order o simplify graphical aalysis. Priciples of cosrucig probabiliy ploig graph paper ad empirical daa ery are described by may auhors, /, 8/. Afer calculaig failure probabiliies, he correspodig cumulaive perceage of failures ( i, F( i )0%) are ploed i a Weibull probabilisic paper (Fig. ). Media rak posiios are used isead of oher rakig mehods because media raks are a a specific cofidece level (0%). By drawig he bes fied sraigh lie hrough he ploed pois oe ca obai parameer values from he Weibull paper as: =.74; =.67. Aalyical expressios for heoreical reliabiliy fucios which represe disribuio laws of he observed radom variable, obaied by simple wo-parameer Weibull disribuio are, /9/: reliabiliy (Eqs.() ad ()): Rs() exp () 8.67 R () exp40 () s failure desiy (Eqs.() ad (4)): fs() exp () f ( ) exp s (4) failure rae (Eq.()): f () s( ) () R () 68

3 Deermiig he reliabiliy fucios of he boiler ubig sysem Određivaje fukcija pouzdaosi cevog sisema kola u DETERMINING RELIABILITY FUNCTIONS USING COMPLEX WEIBULL DISTRIBUTION Afer calculaig of failure probabiliies (Table ) ad ploig imes ad heir correspodig rak values i a Weibull probabilisic paper, i could be oed ha wo sraigh lies beer fi hose pois ha oe lie (Fig. ). F() , I is assumed ha he daa are ihomogeeous, i.e. hey do o have he same characer, ad ca be approximaed wih complex disribuio. The sample of failure probabiliies is divided io wo pars, /0/, afer which he media rak is calculaed (Tables ad ) ad ploed for each (as show i Fig. ) , 0, 0,.67 0, P (h) Figure. Weibull probabiliy paper for simple disribuio. F() , , 0, 0,.9 0, P (h) Figure. Weibull probabiliy paper complex disribuio. 69

4 Deermiig he reliabiliy fucios of he boiler ubig sysem Određivaje fukcija pouzdaosi cevog sisema kola u Table. Values of exploiaio idicaors lie I. Tk i N i N MR i Table. Values of exploiaio idicaors lie II. Tk i N i i i N MR By drawig he bes possible sraigh lies hrough he ploed pois (Fig. ) we obai he Weibull disribuio parameers for boh lies: I =., I =.9 II = 7.9, II =.4 The parameers for he bes fied saisical daa are esimaed by he leas-square mehod. Theoreical reliabiliy fucios for each ierval are (Eqs.(6)-(9)): I RI () exp (6) I f c() R c c i R II () exp II R I () exp.8 0 R II II (7) 7.9 (8) 6.4 exp 4.80 (9) Aalyical expressios for heoreical reliabiliy fucios which represe he disribuio laws of he observed radom variable, obaied by simple wo-parameer Weibull disribuio are, /0/: reliabiliy (Eqs.(0) ad ()): I II Rc () RI () RII () (0) 7.9 R ( c ) 0.44exp exp 4.80 failure desiy (Eqs.() ad ()): I I df I I fc() exp d I I I II II II II exp II II II f ( ).7780 exp.80 c exp 4.80 failure rae (Eq.(4)): ().7780 exp exp 4.80 () 0.44exp exp Graphical comparisos bewee exploiaio ad obaied values for heoreical fucios of reliabiliy, failure desiy ad failure rae of boiler ubig sysem i TENT-A4 durig he cosidered observaio period are show i Figs., 4 ad, respecively. () () () (4) The daa required for drawig exploiaio reliabiliy idicaors were give i ab.. Figure. Exploiaio ad heoreical forms of he reliabiliy fucios. Figure 4. Exploiaio ad heoreical forms of he failure desiy fucios. 70

5 Deermiig he reliabiliy fucios of he boiler ubig sysem Određivaje fukcija pouzdaosi cevog sisema kola u Figure. Exploiaio ad heoreical forms of he failure rae fucios. CONCLUSION Applicaio of he reliabiliy heory eabled deermiaio of he heoreical disribuio laws of radom variable accordig o he exploiaio research of he boiler ubig sysems i TENT-A4. The iiial hypohesis ha he disribuio of he observed radom variable approaches he Weibull disribuio has bee cofirmed. Resuls of his sudy have show ha reliabiliy of boiler ubig sysem could be more precisely represeed wih simple, ha wih complex Weibull disribuio, bu he differeces are o sigifica. Empirical forms of he failure desiy ad failure rae show zigzag-ype behaviour, wha is almos impossible o be exacly represeed by ay disribuio fucio. The compariso of empirical ad he heoreical failure desiy fucios displays ha fucios obaied by boh simple ad complex Weibull disribuio pracically failed o reproduce empirical daa. Fially, beer machig bewee empirical ad heoreical failure rae fucio obaied by complex Weibull disribuio is demosraed. I has led us o he coclusio ha for describig he heoreical disribuio law of he failure rae durig he useful life period of he boiler ubig sysem, i is more precise o use raher complex ha he simple disribuio. REFERENCES. Dooley, B., W. McNaugho, Boiler Tubes Failures, Elecric Power Research Isiue, Califoria, (99).. Kalaba, D., Thermal Power Sysem Reliabiliy (i Serbia), Uiversiy of Prišia, Faculy of Techical Scieces, Kosovska Mirovica, (0).. Barlow, R., C. Claroi, F. Spizzichio, Reliabiliy ad Decisio Makig, Chapma ad Hall, New York, (99). 4. Waye, N., Weibull predicio of a fuure umber of failures, Qualiy ad Reliab. Egg. Ier., 6 (000): -6.. Nordma, D.J., W.Q. Meeker, Weibull predicio iervals for a fuure umber of failures, Techomerics, 44 (00): Maavž, A., J. Krope, D. Goričaec, N. Gubeljak, The impac of ageig o mechaical characerisics of resi boded wheels, Srojarsvo, 49 (007): Maríek, Z., V. Královcová, The reliabiliy characerisic of power pla ui, Aca Elecroechica e Iformaica, 0 (00): Che, Y., X. Che, B. Zhao, Applicaio of Weibull disribuio i uclear power pla reliabiliy daabase, Aomic Eergy Sci. ad Tech. 7 (00), ISSN: CN: - 044/TL. 9. Barlow, R., Egieerig Reliabiliy, SIAM, Philadelphia, PA, USA, (998). 0. Milčić, D., M. Mijajlović, Mehods for cosrucig of hermal power sysem based o reliabiliy (i Serbia), Proc. h Symp. o Thermal Sci. ad Egg. of SCG, Sokobaja, Serbia, (007).. Milčić, D. e al., Exploiaio researches of he hermo-eergeic sysem's availabiliy, Proc. h Symp. o Thermal Sci. ad Egg. of Serbia, Sokobaja, Serbia, pp.90-97, (0).. Kalaba, D., e al., Deermiig he reliabiliy of hermal power sysem i Gacko hermal power pla (i Serbia), Elekroprivreda, (00): -.. Zio, E., A iroducio o he basics of reliabiliy ad risk aalysis, World Scieific Publishig Co. Ld., Sigapore, (007). 4. Rausad, M., H. Arjlo, Sysem Reliabiliy Theory; Models, Saisical Mehods ad Applicaios (secod ediio), Joh Wiley & Sos Ic., New York, (004).. Kalaba, D., Z. Radaković, M. Đorđević, S. Kiri, Deermiig he heoreical reliabiliy fucio of hermal power sysem usig simple ad complex Weibull disribuio, Thermal Sciece, 8 (04): S9-S8. 6. Nelso, W., Weibull predicio of a fuure umber of failures, Qual. ad Reliab. Egg Ier., 6 (000): Kalaba, D., e al., Deermiig he availabiliy fucio of he hermal power sysem i power pla "Nikola Tesla, Block A4", Proc. h Ier. Cof. o Power Plas, Zlaibor, Serbia, pp , (0). 8. Milčić, D., Reliabiliy of Mechaical Sysems (i Serbia), Uiversiy of Niš, Faculy of Mech. Egg., Niš, Serbia, (00). 9. Murhy, P., X. Mi, J. Reya, Weibull Models, Wiley, New York, (004). 0. Milčić, D., M. Mijajlović, Reliabiliy of Mechaical Sysems - Collecio of Solved Tasks (i Serbia), Uiversiy of Niš, Faculy of Mech. Egg., Niš, Serbia, (008). 7