Simulation Model for Coal Crushing System of a Typical Thermal Power Plant First A. Sorabh Gupta and Third C. P.C. Tewari

Transcription

1 Internatonal Journal of Engneerng and Technology Vol. No. June Smulaton Model for Coal Crushng System of a Typcal Thermal ower lant Frst A. Sorabh Gupta and Thrd C..C. Tewar Abstract The am of ths study s to develop an avalablty smulaton model that can be used for evaluatng the performance of coal crushng system of a thermal power plant usng probablty theory and Markov brth-death process. The present system under study conssts of fve subsystems wth three possble states.e. full capacty workng reduced capacty workng and faled. Falure and repar rates of all subsystems are assumed to be constant. After drawng transton dagram dfferental equatons have been generated and solved usng recursve approach. Then steady state avalablty s determned whch s the developed avalablty smulaton model. Besdes some avalablty matrces are also developed whch provde varous performance or avalablty levels for dfferent combnatons of falure and repar rates of all subsystems. Hence performance of coal crushng system s analyzed and evaluated. The developed model helps the plant management n gettng the nformaton about maxmum avalablty of each of the fve subsystems wth optmum values of falure/repar rates and n comparatve evaluaton of alternatve mantenance strateges. Index Terms Avalablty Mantenance decsons Steady state probabltes and Transton dagram. Symbols and Notatons The symbols and notatons used n the present paper are as follows: : Indcate the subsystems n full capacty workng state. : Indcate the subsystems n reduced workng state. : Indcate the subsystems n faled state. A B C D E : Denotes the full capacty workng states of subsystems A B C D and E respectvely. B B : Denotes that the subsystem B s workng wth standby unts. C : Denotes that the subsystem C s workng n reduced capacty. a b c d e : Denotes the faled states of subsystems A B C D and E respectvely. ( : Indcate the probablty that at tme 't' the subsystems are workng n full capacty wthout stand by unt. ( : Indcate the probabltes that at tme 't' the subsystems are workng n full capacty wth standby unts. ( and : Indcate the probabltes that at tme 't' the subsystems are workng n reduced capacty. ( and -8: Indcate the probabltes that at tme 't' the subsystems are n faled states. and -: Indcate the mean falure rates and repar rates of subsystems A B C D and E respectvely. d/dt : Indcate the dervatve w.r.t. tme (. Av. : Steady state avalablty of the system. I. INTRODUCTION Over the years as engneerng systems have become more complex and sophstcated the relablty predcton of engneerng systems s becomng ncreasngly mportant because of factors such as cost rsk of hazard competton publc demand and usage of new technology. Hgh relablty level s desrable to reduce overall cost of producton and rsk of hazards for larger more complex and sophstcated systems such as thermal power plant. It s necessary to mantan the steam thermal power plant to provde relable and unnterrupted electrcal supply for long tme. In order to obtan regular and economcal generaton of electrcal power plant should be mantaned at suffcently hgh avalablty level correspondng to mnmum overall cost []. erformance modellng s an actvty n whch the performance of a system s characterzed by a set of performance parameters whose quanttatve values are used for evaluatng the system s avalablty. erformance modellng has a very mportant role n the coal crushng system of a thermal power plant. Accordng to Barabady et al. [] the most mportant performance measures for reparable system desgners and operators are system relablty and avalablty. Avalablty and relablty are good evaluatons of a system s performance. Ther values depend on the system structure as well as the component avalablty and relablty. These values decreases as the component ages ncreases;.e. ther servng tmes are nfluenced by ther nteractons wth each other the appled mantenance polcy and ther envronment []. For the predcton of avalablty several mathematcal models [ to 8] have been dscussed n lterature whch handle wde degree of complextes. Most of these models are based on the Markovan approach wheren the falure and the repar rates are assumed to be constant. In other words the tmes to falure and the tmes to repar follow exponental dstrbuton. The consderable efforts have been made by the researchers [9 to ] provdng general methods for the predcton of system relablty desgnng equpments wth specfed relablty fgures demonstraton of relablty values [] ssues of mantenance nspecton repar and replacement and noton of mantanablty as desgn parameter []. Kuren [] developed a smulaton model for analyzng the avalablty.e. measure of performance of an arcraft tranng faclty. The model was useful for evaluatng varous mantenance alternatves. Consderaton of systems wth randomly falng reparable components s of nterest n many engneerng felds [ to 8]. The work under study presents a relablty and performance evaluaton model to predct the operatonal avalablty of coal crushng system of a steam thermal power plant stuated n north Inda. Further smulaton has also become an mportant tool for assessng the avalablty of complex process plants. The advantage wth the smulaton model s that the non-markovan falure and the repar processes can be modeled easly [9]. Some of the salent features of the developed avalablty model are as follows: ) The model provdes an ntegrated modellng and analyss framework for performance evaluaton of the coal crushng system of a thermal power plant

2 Internatonal Journal of Engneerng and Technology Vol. No. June ) The model combnes a strong mathematcal foundaton wth an ntutve graphcal representaton. ) The transton dagram (fgure ) represents the varous possble states of the system. A. Organzaton of paper The secton presents and dscusses the processng and descrpton of coal crushng system used for developng the transton dagram. The assumptons used for development of model are also lsted n ths secton. Secton descrbes the development of a avalablty smulaton model. Secton descrbes the performance evaluaton made n ths study. Secton and 6 descrbes the results and concluson respectvely. II. COAL CRUSHING SYSTEM The need for havng an effcent and relable coal crushng system s well recognzed n vew of the large capacty power statons beng nstalled n Inda. A thermal power plant s a complex engneerng system comprsng of varous systems: coal handlng steam generaton coolng water condensate ash handlng power generaton feed water and coal crushng system. For regular and economcal generaton of power t s necessary to mantan each subsystem of coal crushng system. Amongst the several utltes coal crushng system consttutes an essental part of the power generaton system of a thermal power plant. Coal crushng system wth whatever may be the operatonal ntentons.e. contnuous or ntermttent s expected to furnsh excellent performance. The hgh performance of such coal crushng system can be acheved wth hghly relable power plant and perfect mantenance. In ths system the coal from coal bunkers after passng through connectng rods then mll boxes and then through conveyors enters n to the bg sze shell where crushng of rough coal n to peces less than nches ( mm) n sze takes place. The crushng acton takes place wth the help of a large number of small sze metallc balls present n the shell. The crushed coal then transferred n to the boler for steam generaton operaton. A. Assumptons The followng assumptons are made n developng the probablstc smulaton model; ) Falure/repar rates are constant over tme and statstcally ndependent. ) A repared unt s as good as new performance wse for a specfed duraton []. ) Suffcent repar facltes are provded.there are no smultaneous falures []. ) Standby unts are of the same nature as that of actve unts. ) System tme between falure and repar tme follows an exponental dstrbuton. 6) Servce ncludes repar and/or replacement []. ) The system may work at reduced capacty. The transton dagram [] (as gven n fgure ) of the coal crushng system shows the varous possble states and helps n developng the dfferent dfferental equatons. Based on the transton dagram and developed dfferental equatons an avalablty smulaton model has been developed. The falures and repars for ths purpose have been modelled as a brth and death process. The falure and repar rates of all subsystems of coal crushng system can be obtaned wth the help of hstory cards and mantenance sheets of varous subsystems of the coal crushng system avalable wth mantenance personnel of the thermal plant. B. System Descrpton The performance of the any system depends on arrangement confguraton and performance of ts subsystems. A typcal system conssts of a number of subsystems connected to each other logcally n seres n parallel or n combnaton of seres and parallel n most of the cases. Before analyzng the falure data t s better to descrbe the confguraton of coal crushng system and classfy t nto varous subsystems so that the falures can be categorzed. The present system conssts of followng fve subsystems: ) The assembly of two conveyors (n seres) consttutng one subsystem denoted by A and falure of any conveyor results n to system falure. ) Four connectng rods two workng at a tme and another two are n standby mode consttutng another subsystem and s denoted by B falure of whch leads to system falure. ) Two coal bunkers (n parallel) consttutng one subsystem and s denoted by C. Falure of any coal bunker reduces the capacty of plant and loss n producton. Complete falure occurs when both bunkers fals. ) Sngle shell s another subsystem denoted by D arranged n seres wth other subsystems. Falure of ths subsystem causes the complete falure of the system. ) Two mll boxes consttutng one subsystem and s denoted by E. Falure of any mll box causes the complete falure of the system. - -

3 Internatonal Journal of Engneerng and Technology Vol. No. June Fgure : Transton dagram of coal crushng system III. DEVELOMENT OF SIMULATION MODEL Markov state transton dagram s helpful n analyzng relablty and avalablty of a reparable system. All possble flow of states for the present system under consderaton has been descrbed n a transton dagram whch s logcal representaton of all possble state s probabltes encountered durng the avalablty analyss of coal crushng system []. The falure and repar rates of the dfferent subsystems are used as standard nput nformaton to the model. Formulaton s carred out usng the jont probablty functons based on the transton dagram. A. Markov Approach Accordng to Markov f ( ) represent the probablty of t zero occurrences n tme t. The probablty of zero occurrences n tme (t s gven by Equaton (eq.) ;.e t (. ( ) () ( t Smlarly t (.. (.. ( ) () ( t Where s the falure rate and s the repar rate respectvely. The eq. shows the probablty of one occurrence n tme (t and s composed of two parts namely (a) probablty of zero occurrences n tme t multpled by the probablty of one occurrence n the nterval t and (b) the probablty of one occurrence n tme t multpled by the probablty of no occurrences n the nterval t as stated by Srnath []. Then smplfyng and puttng t one gets d ( ). () dt The performance modellng s an actvty n whch the performance of a system s characterzed by a set of performance parameters (repar and falure rates) whose quanttatve values are used to assess the system s avalablty []. The system starts from a partcular state at tme t and reaches another state (faled) or reman n the same state (operatve) durng the tme nterval t. The state of the system defnes the condton at any nstant of tme and the nformaton s useful n analyzng the current state and n the predcton of the falure state of the system. Modellng s done usng a smple probablstc consderaton and dfferental equatons are developed usng a Markov brth-death process [6]. Usng the concept used n eq. and varous probablty consderatons the followng dfferental equatons assocated wth the transton dagram of coal crushng system are formed [6]. d dt () d ( ( dt () d ( ( 6( dt (6) d dt 8. () - 8 -

4 Internatonal Journal of Engneerng and Technology Vol. No. June d ( dt (8).. d ( ( dt (9).. d dt m mj () Wth the ntal condton () ; zero otherwse. Snce any thermal plant s a process ndustry where raw materal s processed through varous subsystems contnuously tll the fnal product s obtaned. Thus puttng dervatve of all probabltes equal to zero yelds the long run avalablty of the thermal plant system. Therefore by puttng d / dt at t [8] nto dfferental equatons one gets; ( m m ) j () Where n eq. () when m then j ; 6 j ; j ; 6 j ; j ; j m then j ; 6 j m then 8 j ; j ; 8 j m then j ; 9 j ; j ; 9 j ; j ; j Now puttng the values of probabltes from equaton () n equatons to 9 and solvng these equatons recursvely yelds the values of all state probabltes n terms of full workng state probablty.e.. C C 6 9 C 8 C Where C to C are constants. C 6 B. Normalzng Condton The probablty of full workng capacty (wthout standby unts) namely s determned by usng normalzng condton: (.e. sum of the probabltes of all workng states reduced capacty and faled states s equal to ) []. 8.e therefore ( ) ( C C C C C ) ( ) ( ) C C C C C C. Steady State Avalablty (Av.) () The steady state avalablty of coal crushng system may be obtaned as summaton of all full workng and reduced capacty workng state probabltes. Hence Av. Or Av. ( C C C C C ) () Equaton represents the avalablty smulaton model of the coal crushng system. IV. ERFORMANCE EVALUATION The developed model s used to predct the avalablty hence to evaluate the performance of coal crushng system of thermal power plant for known nput values of falure and repar rates of ts subsystems. The performance of the system s manly affected by the falure and repar rates of ts subsystem. From mantenance hstory sheet of coal crushng system and through the dscussons wth the plant personnel 6-9 -

5 Internatonal Journal of Engneerng and Technology Vol. No. June approprate falure and repar rates of all subsystems are taken and avalablty matrces are prepared accordngly by puttng these falure and repar rates values n eq. the avalablty smulaton model (Av.). Ths model forms the foundaton for all other performance mprovement actvtes (e.g. soluton desgn and development mplementaton and analyss). These unt parameters ensure the hgh avalablty or performance of the coal crushng system. Ths model ncludes all possble states of nature that s falure events ( ) and the dentfcaton courses of acton.e. repar prortes ( ). Tables to represent the avalablty matrces for varous subsystems of the coal crushng system. These matrces smply reveal the varous avalablty levels for dfferent combnatons of falure and repar rates. On the bass of analyss made the best possble combnaton ( ) may be selected. These avalablty values n avalablty matrces further helps n () obtanng the optmum values of falure and repar rates of varous subsystems of the crushng system for maxmum avalablty () dentfyng the subsystem whch ensures the maxmum avalablty as shown n table 6. V. RESULTS AND DISCUSSION The performance of coal crushng system s analyzed wth the developed avalablty smulaton model. On the bass of avalablty values as gven n avalablty matrces ndcated n table to and plots n fgure to 6 the followng observatons are made whch reveals the effect of falure and repar rates of varous subsystems on the avalablty of coal crushng system. A. Subsystem A: Conveyors The effect of falure and repar rates of conveyor subsystem on the avalablty of coal crushng system s shown n table and fgure. It s observed that for some known values of falure / repar rates of other four subsystems (as gven n table ) as falure rate of conveyor ncreases from. (once n hrs) to. (once n hrs) the system avalablty decreases by about %. Smlarly as repar rate of conveyor ncreases from. (once n hrs) to. (once n hrs) the system avalablty ncreases by about 9 %. TABLE : AVAILABILITY MATRIX OF CONVEYOR SUBSYSTEM OF COAL CRUSHING SYSTEM Avalablty (Av)..... Constant values Effect of falure rate ( ) Effect of repar rate ( ) Fgure : Effect of falure and repar rates of conveyor subsystem on system avalablty B. Subsystem B: Connectng rods The effect of falure and repar rates of connectng rods subsystem on the avalablty of coal crushng system s depcted n table and fgure. It s observed that for some known values of falure / repar rates of other four subsystems (as gven n table ) as falure rate of connectng rods ncreases from. (fve falures n hrs) to. (once n hrs) the system avalablty decreases by about %. Smlarly as repar rate of connectng rod ncreases from. (once n hrs) to.6 (once n hrs) the system avalablty ncreases slghtly and shows ncreasng trend.

6 Internatonal Journal of Engneerng and Technology Vol. No. June TABLE : AVAILABILITY MATRIX OF CONNECTING ROD SUBSYSTEM OF COAL CRUSHING SYSTEM Avalblty (Av) Constant values Effect of falure rate ( ) Effect of repar rate ( ) Fgure : Effect of falure and repar rates of connectng rod subsystem on system avalablty C. Subsystem C: Coal bunkers The effect of falure and repar rates of coal bunkers subsystem on the avalablty of coal crushng system s depcted by table and fgure. It s observed that for some known values of falure / repar rates of other four subsystems (as gven n table ) as falure rate of coal bunker ncreases from. (thrteen falures n hrs) to. (once n hrs) the system avalablty decreases by about %. Smlarly as repar rate of coal bunker ncreases from. (once n hrs) to. (once n hrs) the system avalablty ncreases by about %. TABLE : AVAILABILITY MATRIX OF COAL BUNKER SUBSYSTEM OF COAL CRUSHING SYSTEM Avalablty (Av) Constant values Effect of falure rate ( ) Effect of repar rate ( ) Fgure : Effect of falure and repar rates of coal bunkers subsystem on system avalablty - 6 -

7 Internatonal Journal of Engneerng and Technology Vol. No. June D. Subsystem D: Shell The effect of falure and repar rates of shell subsystem on the avalablty of coal crushng system s shown by table and fgure. It s observed that for some known values of falure / repar rates of other four subsystems (as gven n table ) as falure rate of shell ncreases from. ( falures n hrs) to. (once n hrs) the system avalablty decreases by about 6 %. Smlarly as repar rate of shell ncreases from.6 (once n hrs) to. (once n hrs) the system avalablty ncreases slghtly and shows ncreasng trend. TABLE : AVAILABILITY MATRIX OF SHELL SUBSYSTEM OF COAL CRUSHING SYSTEM Avalablty (Av) Constant values Effect of falure rate ( ) Effect of repar rate ( ) Fgure : Effect of falure and repar rates of shell subsystem on system avalablty E. Subsystem E: Mll boxes The effect of falure and repar rates of mll box subsystem on the avalablty of coal crushng system s shown by table and fgure 6. It s observed that for some known values of falure / repar rates of other four subsystems (as gven n table ) as falure rate of mll box ncreases from. (fve falures n hrs) to. (twenty fve falures n hrs) the system avalablty decreases by about %. Smlarly as repar rate of mll box ncreases from.8 (once n hrs) to. (once n hrs) the system avalablty ncreases by about %. TABLE : AVAILABILITY MATRIX OF MILL BOX SUBSYSTEM OF COAL CRUSHING SYSTEM Avalablty (Av) Constant values

8 Internatonal Journal of Engneerng and Technology Vol. No. June Effect of falure rate ( ) Effect of repar rate ( ) Fgure 6: Effect of falure & repar rates of mll box subsystem on system avalablty. F. The maxmum avalablty level for each subsystem wth ther correspondng optmum values of falure and repar rates s gven n table 6 whch further helps n dentfyng the subsystem wth maxmum avalablty. It s observed that frst subsystem.e. conveyor s havng maxmum avalablty (8.86%). TABLE 6: OTIMUM VALUES OF FAILURE AND REAIR RATES OF VARIOUS SUBSYSTEMS OF THE COAL CRUSHING SYSTEM S. Falure rates ( ) Repar rates ( ) Maxmum avalablty level No %... 6.%....6 % %...6 % VI. CONCLUSION The system avalablty has been excellent manly because of the low falure rate supported by the state of the art repar facltes. It can thus be concluded that ths avalablty smulaton model provdes the varous avalablty levels for dfferent combnatons of falure and repar rates for each and every subsystem. One may select the best possble combnaton of falure events and repar prortes for each subsystem. It can be concluded from tables to and fgures to 6 that as falure rate ncreases the avalablty decreases and as repar rate ncreases the avalablty ncreases. The developed model helps n determnng the optmal mantenance strateges whch wll ensure the maxmum overall avalablty of coal crushng system. It s also concluded that frst subsystem (conveyors) s havng maxmum avalablty. The correspondng optmum values of falure and repar rates for maxmum avalablty level for each subsystem are avalable. Such results are found hghly benefcal to the plant management for the avalablty and performance analyss of coal crushng system of a thermal power plant. Further these results help n makng the decsons related to mantenance to be performed n thermal plant. REFERENCES [] S. Gupta.C. Tewar and A.K. Sharma Relablty and avalablty analyss of ash handlng unt of a steam thermal power plant (art-i) Internatonal journal of Engneerng Research and Industral Applcatons 8 vol. (V) pp. -6. [] J. Barabady and U. Kumar Avalablty allocaton through mportance measures Internatonal journal of qualty & relablty management vol. (6) pp [] S. Gupta.C. Tewar and A.K. Sharma Development of smulaton model for performance evaluaton of feed water system n a typcal thermal power plant Journal of Industral Engneerng Internatonal to be publshed. [] E. Balaguruswamy Relablty Engneerng. New Delh: Tata Mc Graw Hlls 98. [] B.S. Dhllon Relablty Engneerng n Systems Desgn and Operaton. New York: Van Nostrand-Renhold 98. [6].S. Rajpal K.S. Shshoda and G.S. Sekhon An artfcal neural network for modellng relablty avalablty and mantanablty of a reparable system Journal of Relablty Engneerng and System Safety 6 vol. 9 pp [] A.Y. Zerwck A focused approach to relablty avalablty and mantanablty for crtcal pressure vessels and ppng Internatonal Journal of ressure Vessels and png 996 vol. 66 pp. 6. [8] N. Arora and D. Kumar Avalablty analyss of steam and power generaton systems n thermal power plant Mcro Electron Relablty 99 vol. () pp [9] A.K. Govl Relablty Engneerng. New Delh: Tata McGraw-Hll publshng company Ltd

9 Internatonal Journal of Engneerng and Technology Vol. No. June [] L.S. Srnath A Text book on Relablty Engneerng. rd Ed. East-West ress Ltd. 99. [] A.K. Sharma Relablty analyss of varous complex systems n thermal power staton. M. Tech Thess. Haryana INDIA: Kurukshetra Unversty (REC Kurukshetra) 99. [] B.S Dhllon Desgn Relablty Fundamentals and Applcaton. CRC ress LLC 999. [] K.C. Kuren Relablty and avalablty analyss of reparable system usng dscrete event smulaton h.d. Thess IIT Delh 988. [] R. Barlow and F. roschan Statstcal Theory of Relablty and Lfe Testng robablty Models New York: Holt Rnehart and Wnston Inc 9. [] A. ages and M. Gondran System Relablty Evaluaton and redcton n Engneerng. Sprnger; New York 986. [6] J.K. Vauro and. Tamm Modellng the loss and recovery of electrc power Nuclear Eng Des. 99 pp [] E.E. Lews Introducton to Relablty Engneerng. New York: Wley 996. [8] J.K. Vauro Relablty characterstcs of components and systems wth tolerable repar tmes Journal of Relablty Engneerng System Safety 99 vol. 6 pp.. [9] S. Gupta.C. Tewar and A.K. Sharma Avalablty smulaton model and performance analyss of coal handlng unt of a typcal thermal plant South Afrcan Journal of Industral Engneerng 9 vol. () pp 9-. [] S. Gupta.C. Tewar and A.K. Sharma erformance modellng and decson support system of feed water unt of a thermal power plant South Afrcan Journal of Industral Engneerng 8 vol. 9 () pp. -. [] R. Khanduja.C. Tewar and D. Kumar Avalablty analyss of bleachng system of paper plant Journal of Industral Engneerng Udyog ragat N.I.T.I.E. Mumba (Inda) 8 vol. () pp. -9. [].C. Tewar D. Kumar and N.. Mehta Decson support system of refnng system of sugar plant Journal of Insttuton of Engneers (Inda) vol. 8 pp. -. [] L.S. Srnath Relablty Engneerng. rd edton East-West ress vt. Ltd. New Delh 99 [] S. Kumar D. Kumar and N.. Mehta Mantenance management for ammona synthess system n a urea fertlzer plant Internatonal Journal of Management and System 999 vol. () pp. -. [] S. Kumar.C. Tewar and R. Sharma Smulated avalablty of co coolng system n a fertlzer plant Industral Engneerng Journal (Indan Insttuton of Industral Engneerng Mumba Inda) vol. 6() pp. 9-. [6] S. Gupta.C. Tewar and A.K. Sharma erformance evaluaton model and decson support system for coal handlng system of a typcal thermal plant Internatonal Journal of Appled Engneerng Research 8 vol. () pp Bographcal Notes Sorabh Gupta born at Radaur (dstrct Yamuna Nagar Haryana Inda) on Feb. 96 workng as Head of Department and Assocate rofessor n the Department of Mechancal Engneerng at Haryana College of Technology & Management Kathal Haryana (Inda). He receved hs Bachelor of Engneerng (B.E.) degree from Dr. B.A.M.U. Aurangabad Maharashtra Inda and Master of Technology from Guru Nanak Dev Engneerng College Jalandhar unjab Inda. resently he s about to complete hs h.d. n Industral Engneerng from Natonal Insttute of Technology Kurukshetra Haryana (Inda). He has years of experence n teachng and research. He has publshed research papers n nternatonal journal; another 8 are communcated n nternatonal journals. He has publshed and presented twenty fve research papers n Internatonal/ Natonal Conferences. Hs felds of nterests are Modellng Stochastc Behavor of system n Industry and Mantenance Engneerng. Dr..C. Tewar s Assstant rofessor n the Department of Mechancal Engneerng at Natonal Insttute of Technology Kurukshetra Haryana (Inda). He receved hs Bachelor of Engneerng (B.E.) and M.E. from IIT Roorkee (Inda) and h.d. from Kurukshetra Unversty Kurukshetra Haryana (Inda). He has years of experence n teachng and research. He has publshed more than papers n Internatonal and Natonal journals and conferences. Hs felds of nterests are Mantenance Engneerng and Qualty and Relablty Analyss. 6