ControlofsuperheaterforelectricalsteamboileratEsbjergpowerplantPeriod:November1st2009January7th2010Duedate:January7th2010Student:RasmusHolmgaardRasmussenSupervisor:ZhenyuYang
1
Titlepage
Title:ControlofsuperheaterforelectricalsteamboileratEsbjergpowerplantDuedate:7.January2010
Abstract:Thisprojectfocusesonmodelingofanelectricalsuperheater,placedatDONGEnergyspowerplantinEsbjerg.Basedonthemodelacontrollerforthesuperheaterismade.Theentiresystemisthentestedandcomparedtodatafromthephysicalpowerplant.
ThetestmadetotheobtainedsystemisdonebyusingSimulink.
Duetothetimeconsiderationssomeofthemodelhasnotbeenlinearised.Howeverithasbeenshownhowtolinearizeamodel.
Supervisors:ZhenyuYang
Student:RasmusHolmgaardRasmussen
2
Preface
ThisreportiswrittenasdocumentationformyfinalprojectatAalborgUniversityEsbjerg.Thepurposeofthereportistogivethereaderinsightintowhichconsiderationsandprocessesthatwasusedduringtheproject.
Thereportisdividedintofourparts.Firstananalysisofalltheregulationsloopsontheelectricalsteamboiler.Thepurposeofthisanalysisistofindasingleareawhichneedstobemodeled.Thesecondpartpresentstheworkwithmodeling,systemidentification,controldesignandtesting.Thethirdpartisconclusion.Thefourthandlastpartisappendix.
InthebackofthereportaCDisenclosedcontainingadigitalcopyofthereportalongwiththeSimulinkprogram.
DONGEnergyshouldhavethanksforthehelpandhospitalityenjoyedduringthisproject.
AalborgUniversityEsbjerg,fall2009
____________________________RasmusHolmgaardRasmussen
3
Contents
1 Analyses.............................................................................................................................4
1.1 Physicalinfluences....................................................................................................5
1.2 Regulationspecifications...........................................................................................6
1.3 Analyticconclusion....................................................................................................7
2 Systemdescription............................................................................................................8
3 Modeling...........................................................................................................................9
3.1 Massflowentering....................................................................................................9
3.2 Thetemperaturechange.........................................................................................13
3.3 Massflowleaving....................................................................................................17
4 Identification...................................................................................................................17
4.1 Verifyingofvalvemodel..........................................................................................17
4.2 Thetemperaturechange.........................................................................................20
4.3 Massflowleaving....................................................................................................22
5 Simulink...........................................................................................................................22
6 Controller........................................................................................................................26
7 Testandverification........................................................................................................27
8 Conclusion.......................................................................................................................30
9 Appendix.........................................................................................................................31
10 References...................................................................................................................32
4
1 Analyses
AtthepowerplantinEsbjerg,DONGEnergyhasanelectricalsteamboiler.Thesteamboilerisusedwhenthepowerplantisstarteduporisrunningatlowload.
Thesteamboilerismadeofanoutertank,innertankandanelectricalsuperheater.Intheinnertanktherearetwotimesthreeelectrodeswhichheatsupthewater.Theoutertankgetswaterfromamaintank.Thiswatercanbefilledintotheinnertankandbackagain.Sincethewaterintheinnertankcangobackintotheoutertank,therehastoberoomforitelsetheboilerwillbeoverflowed.Tomakesurethattheboilerwouldntbeoverflowedtherearetwomaximumlevels,whichthelevelhastostaybelow.Themorewaterintheinnertankthemoreeffectwillbeuseandthereforetheamountofsteamproducedwillincreaseiftheamountofwaterintheinnertankisincreased.Whensteamisproducedapressureinsidetheboilerwillbebuild.Thehigherthepressureisthehigherthesteamtemperatureis.Thepressureintheboilerishigherthanthepressureinthesteampipethatisconnectedtotheboiler,acontrollablevalvemakessurethatthepressuredoesntgettohighortoolowintheboilerandthesteampipe.Whenthepressuredropsthetemperaturewilldropandtheamountofdewinthesteamwillincrease.Thesteamneedstobedrysothesteampipeswonnotgetcloggedbyscaleandmore.Toensuredrysteamandahightemperaturethereisasuperheater.
Foralloftheabovementionedtohappeninaregularmannersomecontrollershastobedeveloped.
Thetotalamountofwater:Mustcontrolthetotalamountofwaterinthetwotanksandmakesurethatthereisroomintheoutertankforthewaterintheinnertank.
Thelevelofwaterintheinnertank.Controlsthelevelintheinnertankbasedontheeffect.Howeverifthepressureistoohighorproperthereisnoneedformoresteamandthereforethelevelintheinnertankhastobeloweredorholdsteady.Sothepressurehastobetakenasafactorinthecontrolforthelevelintheinnertank.
Temperatureoutofthesuperheater.Athirdcontrollermustcontrolthetemperatureofthesteamcomingoutofthesuperheater.
Pressureintheboilerandinthesteampipe.Finalacontrollerhastocontrolthevalvethatensuresthatthepressureintheboilerorinthesteampipedoesntgettohighorlow.
5
OnFigure1alltheregulationthatisneededfortheElectricalsteamboiler,forauxiliarysteamonEsbjergpowerplant,canbeseen.
Figure1Allregulationfortheelectricalsteamboiler
TheProjectsgoalsaretherefore:
Establishadynamicmodelforoneoftheareasthatneedtobecontrolled.
Testandverifythedynamicmodelinsimilaritytotherealsystem,withdatafromtherealsystem.
Developacontrollerbasedonthedynamicmodel.
1.1 PhysicalinfluencesThissectionwillgiveanoverviewofthethingsthatwillhaveaninfluenceonthemodelsandthecontrollers.
Thetotalamountofwater:Thelevelsinthetwotanksarethemaininfluence.Thepressuredoesnthaveanydirectinfluenceonethelevelsbecausewaterisalmostincompressible.Howeverwhensteamisproducedthelevelwillvirtualraisebecausetherewillbesomeabsorptionofthesteaminthewater.Thehigherpressurethemorethesteamwillbeforced
6
into/closertothewater.Therearetwodifferentvalveswhichdeliverthewatertotheoutertank,thecharacteristicsofthesetwovalvesmustbeincludedaswell.
Thelevelofwaterintheinnertank.Againthesteamhasaninfluenceandthepressuredirectonthewatercanbeignored.Themorewaterthereisintheinnertankthemoreeffectwillbeused,whichmeansmoresteamwillbeproduced.Whenthewaterisvaporizedfeedwaterhastoenterthetank,andwhensteamismadethepressurewillraise,whichaspreviousmentionedwillhaveaninfluenceonthelevel.Thepressurehavealsoaninfluenceonthelevelbecauseifthepressureistolowtherehastobeproducedmoresteam,ifthepressureiscorrectthereonlyhavetobeproducedtheamountofsteamthatisused,ifthepressuregetstohighthenthereshouldntbeproducedmoresteam.Onevalvecontrolshowmuchwaterthereiscomingintothetank,anotheriscontrollinghowmuchwaterthereiscomingoutagain.Thetwovalvesareconnectedsowhenoneisopentheotherisclosedandreversed.Ifthetwovalvesare50%openthesameamountiscominginasthereisbeingpouredoutandtherebythelevelwillremainthesame.Thecharacteristicsofthetwovalvesarealsohavinganinfluenceonthismodelandthiscontroller.
Temperatureoutofthesuperheater.Thesuperheateriselectronic,thereforeitistheeffectthatiscontrol.Whenthetemperaturegetslowerthanthesetpointtheeffecthastoincrease.Whenthetemperaturegettohightheeffectdecreases.Theamountofsteamgoingthroughthesuperheaterhasaninfluenceonhowmucheffecttherewillbeused.Iftheamountofsteamincreaseandtheeffectiskeptsteady,thenthetemperatureonthesteamgoingoutofthesuperheaterwilldecrease.
Pressureintheboilerandinthesteampipe.Thevalves,whichcreatesthepressuredrop,characteristic,isthemaininfluence.Anotherinfluenceisthepressuredifferenceonthetwosidesofthevalve.
1.2 Regulationspecifications Thetotalamountofwater:
Forthisregulationloopthereisonlyonedemand,whichistherehastoberoomforthewaterfromtheinnertankintheoutertank.
Thelevelofwaterintheinnertank.Somehowthisregulationhastofindalevelbasedontheeffectandpressure.Theeffectismorealimitation;theboilercanatmaxuse30MWanythingbelowisaccepted.Thepressurehastobeunderamaximumandatanidealrunningpressure,whichisat20bar.
7
Temperatureoutofthesuperheater.Thisloopmustholdthetemperatureonthesteamoutofthesuperheaterat230C.
Pressureintheboilerandinthesteampipe.Aspreviousmentionedthepressureinsidetheboilermustbeat20bar,besidesholdingthatpressuretheregulationmustalsoholdapressureat11.5barinthesteampipe.
1.3 AnalyticconclusionBasedontheanalysisofthecontrolloopsIhavedecidedtocontinuewiththesuperheater,becausethesuperheateristheonlyregulationthatdoesnotdirectlydependononeoftheotherregulations.
8
2 Systemdescription
Aspreviousmentionedthesuperheatersassignmentistoensuredrysteamandatemperatureat230C.Todothistherearesomeelectrodeswhichwillheatthesteamgoingthroughthesuperheater.Tocontrolthetemperaturetheeffectthroughtheelectrodesisregulated.Themassflowenteringandthemassflowleavinghasabiginfluenceonhowmucheffectisneeded.AsitcanbeseenonFigure2thereisavalvebeforethesuperheater,thisvalveiscontrollingthepressureinthesteamboilerandthepressureafterthevalve.Sothecontrolofthevalvehasnothingtodowiththesuperheater,howevertheopeningofthevalvedetermineshowmuchsteamthatwillenterthesuperheaterandthereforealsohowmuchthatwillleave.FurthermoreitcanbeseeninFigure2thatthemeasurementofthetemperatureisplacedoutsidethesuperheaterthereforeitwilltakesometimetoregisterwhatkindofinfluenceanincreaseoradecreaseintheeffecthasonthetemperature.
Figure2Systemoverview
Itisassumedthatthecontrollerforthevalveiscontrollingthepressuresonbothsidesofthevalveperfectly.Itisalsoassumedthatthesteambeforethevalve/comingoutofthesteamboilerissaturatedsteam.
Heatlosttothesurroundingsisignoredsinceitishardtofindbecausethesystemisisolatedanditisnotpossibletogetthetemperaturebetweenthepipesandtheisolation.
Thesuperheaterisonlystartedwhenthereisaflowabove1.0kg/s.
9
3 ModelingInTable1(itisinAppendix)themainsymbolsforthefollowingsectionisexplained.
Figure3showswhatneedstobemodeledandwhattheinputsandoutputsare.Itisnotnecessarytomodeltheeffectandthestarttemperature,sinceitistheeffectwhichhastobecontrolledandthestarttemperatureisseenasaconstant.
3.1 MassflowenteringTofindthemassflowenteringthevalvebeforethesuperheaterhastobemodel.Themassflowenteringcanberewrittenas:
(3.1)Where isthedensityonthesteamentering.
Tofind ,whichistheenergyinthemass,theBernoulliprincipleisused.
TheBernoulliprincipleisasimplificationofBernoullisequation,whichstates,thatthesumofallformsofenergyinafluidflowingalonganenclosedpath(astreamline)isthesameatanytwopointsofthatpath.Influidflowwithnoviscosity,andtherefore,oneinwhichapressuredifferenceistheonlyacceleratingforce;theprincipleisequivalenttoNewtonslawsofmotion.TheBernoulliequationcanbewrittenas:
(3.2)
isthevelocity, isthegravitationalforceandwhere
(3.3)
isthepressureand isthedensity.
Theninsertingthis
(3.4)
Since isthefluidthermodynamicenergyperunitmassandisthereforeaconstant,itcanbemovetotherightsideoftheequation,whichthereforebecomes:
TemperatureTemperature
change
Massflowentering
Massflowleaving
Effect Starttemperature
Figure3Overviewofmodels
10
(3.5)
Becausethemassconsistsofsteam,whichismostgas,thegravitationalforce( )isverysmallandcanbeneglected.Theequationnowis:
(3.6)
Figure4Flowthroughthevalve
Ifthisequationisusedintwopoints(1and2)asshowninFigure4,itwilldescribetheflowthroughthevalveandwillleadtothefollowing:
(3.7)
12
2 (3.8)
Therebytherelationshipbetweenthevelocitiesandthepressuresdifferences,betweenthesteampipebeforethevalveandthesteampipeafterthevalve/beforethesuperheater.Howeverthevelocitiesarenotknownandtheequationisonlyconsideringtheenergybalanceregardingthevalve.
Tofindthevelocitiesthecrosssectionalareaofthevalvehastobetakenintoaccount.
11
Figure5illustrationoftheopeningofthevalve
InFigure5itcanbeseenthattheopeningcreatesseveralcrosssectionalareasA0,A1andA2.
ThedifferencebetweenA0andA2iscalledvenacontractaandwillbereferredtoasthecontractioncoefficient.Thecontractioncoefficienthastobefound,whichcanbedonebythefollowing:
, (3.9)
Tofindingthevelocitiesthroughthevalve,themassbalancewillbeused.
(3.10)where
(3.11)
thereforeequation(3.10)becomes:
(3.12)Sincethemassgoingintothevalveisequaltothemassgoingoutofthevalvetheycanbesetupasfollowing:
(3.13)
(3.14)Thenisolating
AndinsertingA2fromequation(3.9)
(3.15)
12
Nowthat isfounditcanbeinsertedintotheequationattainedfromusingtheBernoulliprinciple,equation(3.8),whichthengives:
2
Isolating
2 1
2
1
(3.16)
Thevelocityoutofthevalveandintothesteampipeisobtained,givingarelationshipbetweentheorifice/openingofthevalveandthevelocity .
Nowusingequation(3.16)onequation(3.11)asitisassumedthatequation(3.13)isvalid.
2
1
OnceagaintheexpressionforA2isinserted.
(3.17)
Equation(3.17)istheninsertedinto(3.1)
(3.18)
13
Where isthedensityofthesteambeforethevalve, isthedensityofthesteamafterthevalve/beforethesuperheater, isthepressurebeforethevalve, isthepressureafterthevalve.
Therebythemassflowintothesuperheaterisfound.
3.2 ThetemperaturechangeMassbalance:
(3.19)
isthemassflowofthesteamthatleavesthesuperheater, isthevolumeofthesteaminsidethesuperheaterandwherethedensitycanbewrittenas:
. (3.20)
Energybalance:
Itisassumedthatthepressureafterthevalveisconstantthereforethechanceintheinnerenergycanbewritteninasthefollowing:
(3.21)
(3.22)
Furthermoretheenergybalanceisgivenby:
(3.23)
where
14
(3.24)Insertingthisintoequation(3.23)
Sincetheelectricaleffectismeasuredinwatts,whichis theenergyisequaltotheeffect.
isthatenergythatisusedtoheatupthesteamenteringthesuperheatertothetemperatureinsidethesuperheater.
(3.25)where isthemass,butthemassflowforthesteamenteringisusedinstead, isthe
specificheatcapacityand isthetemperaturedifferencefromstarttotheend.
canbefoundbylookingatthesteaminsidethesuperheaterandthesteamentering
isfoundbyrearrangingtheidealgasformula
Thereforeequation(3.25)becomes:
15
Insertingthisintoequation(3.23)
Theninserting fromthemassbalance,equation(3.19)
(3.26)
Combiningthetwoformulasfromtheenergybalance,equations(3.22)and(3.26).
Thespecificenthalpyonthesteamleaving( )canbefoundbythefollowingformula:
16
Inserting gives:
Sincetheflowismeasuredinkg/sitisamassflowwhichmeans and.
where
so
17
whichmeans
(3.27)
3.3 MassflowleavingTherehasalreadybeenmadanequationforthemassflowleavingthesuperheaterinequation(3.19),whichis:
4 Identification
4.1 VerifyingofvalvemodelThemaximumdiameteroftheorificeis111.125mm
Iftheorificeissharpatypicalvalueofcoefficientofcontractionis0.64.
111.1252 9698.6978 0.00009699
18
Thenthemaximumareaofthevalveorificeis0.00009699 .0.00009699 valve opening %
Thediameterofthesteampipeis15cm,thereforetheareaofthesteampipeis:
1502 17671.4587 0.0001767
0.6420bar 2000kPa
11.5bar 1150kPa
273.15
2000kPa 0.018214C 273.15 8.314472
360004050,40
8,888 3
273.15
1150kPa 0.018188C 273.15 8.314472
207003834,22
5,3988 3
0 2 1
122
1 1 01 1
2
1150kPa 0.64 0.00009699 valve opening %
2 2000kPa
8.8881150kPa
5.3988
1 8.888 0.64 0.00009699 valve opening %8.888 0.0001767
2
19
71.38464 valve opening % 2 225022.5023 213010.2986
1 0.00055170.001571 valve opening %2
71.38464 valve opening % 154.99811 0.3512 valve opening % 2
Ifthevalveis100%open
71.38464 100% 154.99811 0.35098 100% 2
71.38464 154,99810.8766585671.38464 176.8056
12621.2006 11.8162
Inthedatasheetthemaximumflowoutofthevalvecanbe43200 whichis12 .Thereforethemodelisassumedtobecorrect.
Howevertheequation(3.18)isnonlinearandthereforeitislinearisedusingTaylor,whichgives:
273915832783988861321301338457012475880078570760549798248448000 valve opening %
11.0634 valve opening % (4.1)Figure6showsaplotofequation(3.18),theblue,andaplotofthelinearisedequation(4.1),thered.Itcanbeseenthataround0.5or50%adeviationisstarting,aftersomecalculation
thelinearisedequationissatisfyingfrom0to52%wherethedeviationis0.0984 .
20
4.2 ThetemperaturechangeItisassumedthattheinternalenergybeforethevalveisthesameafterthevalve.Thereforethe canbefound,asitisassumedthatthesteambeforethevalveissaturatedsteamataconstantpressureon20bar.
2599.5
8.314472
18 0.018
2590 thisisfoundinasteamtable.
Thevolumeofthesteam(Vs)isassumedtobethesameasthevolumeofthesuperheater,becausetherehasbeenrunningsteamthroughthesuperheatersometimebeforethesuperheaterisstarted.Thevolumeofthesuperheateris404literswhichis0.404m3.
Figure6Relationshipbetweenvalveopeningandmass flow
21
iscalculatedbytheformulafromthemassbalancewhereitisassumedthatTslhis230Csincethisisthetemperaturethatisthesetpoint.
11.5 whichisthepressureinthesuperheater.
11.5 0.018230 273.15 8.314472
0.2074183.427 4,95 10
273.15where
issettobeaconstantat188C.Thevalueof isobtainedfromthetemperaturemeasurementafterthesuperheaterjustbeforethesuperheateristurnedon.
188C 273.15 461.15 Whenthesevaluesareinsertedintoequation(3.27)thefollowingisobtained:
2599.5 0.018 8.314472 461.15 0.404m 4,95 10 2590
2599.5 0.018 8.314472 461.15 0.404m 4,95 10 2590
0.404m 4,95 10 2590
2590
11.5 0.4040.018 8.314472 230
230
11.5 0.4040.018 8.314472 230
188
0.404m 4,95 10 2590
Itcannowbeseenthatthetemperaturechange isafunctionofthemassflowentering,
themassflowleavingandoftheeffect.
22
4.3 Massflowleaving
canbewrittenas:
273.15
where
. (4.2)
Adifferentialfunctioncanberewrittenasthefollowing:
Thereforeequation(4.2)becomes
273.15
8.314472 11.5 0.018
188 273.15 8.314472
1.7211188 2.2711 10
5 SimulinkTheequationsobtainedhavebeenwrittenintotheprogramSimulink,whichisaprograminMatlab.
InFigure7themodelofthesuperheaterinSimulinkcanbeseen.
23
Figure7Simulink
RunningtheSimulinkprogramwiththeValveopeningon100%thefollowinggraphsisobtained:
Figure8Temperaturewiththevalve100%open
24
Figure9Effectusedwhenthevalveis100%open
Figure10MassFlowwhenthevalveis100%open
Itcanbeseenthattheeffectisalmost1500kWandthemassflowforbothentering(theyellow)andleaving(thepurple)isabitabove11kg/s.Ittakesalmost4000secondstogetthetemperatureat230C.
Thenrunningtheprogramwhitthevalveopeningat10%givesthefollowinggraphs:
25
Figure11Temperaturewiththevalve10%open Figure12Effectwiththevalve10%open
Figure13Massflowwiththevalve10%open
Nowthemassflowsandtheeffecthasnowgonedowntoaround1.1kg/sand150kW.Thetimeforthetemperaturetogetto230Cisnowaround1000seconds.
Fromthesetworunsoftheprogramiscanbeseenthatthemoresteamthatneedstobeheatedthemoreeffectwillbeused,whichwasexpected.
26
6 ControllerThecontrollerwasmanualtunedbysettingallvaluestozeroandthenincreasingthegainKpuntiltheoutputwasstartingtooscillate,thesettingittothehalfofthatvalue.NexttheKivaluewasincreaseduntilanyoffsetiscorrectinsufficienttimefortheprocess.ItwasnotnecessarytouseaKdvalue.ThereforethecontrollerisaPIcontroller,withthefollowingvalues:
Kp=1000
Ki=15
27
7 TestandverificationTherehasmadetwotypesoftests.Onewheretheeffectwaschangedandtheflowwaskeptstabiletoseewhattheeffectchangewoulddotothetemperature.
Theeffectwaschanged5%,from48%to43%whichis720kWto645kW,theflowwasat1.5kg/sthetemperaturewentfrom230Cto220Conthemeasurementatthepowerplant.Themeasurementsfromthepowerplanthavethenbeenputintoequation(3.26)whichgaveatemperaturechange:
720kW
91.7138
645kW
82.1603
Thismeansthatthetemperaturewith720kWwillbe9.5535Chigherthanthetemperaturewith645kW.Themeasurementatthepowerplantcannotmeasurewithdecimalsandthereforethetestisseenasasuccessandthemodelforthetemperaturechangeiscorrect.
Thesametestwasdonewithonly1%changeintheeffectthisgaveattemperaturechangeon2Candifthedataisputintotheequationitgivesatemperaturechangeon1.9107againthisisasuccess.
Theothertestwastokeeptheeffect,thetemperatureandthevalveopeningconstantbecausewhenthetemperatureisnotchangingthemassflowleavingisthesameasthemassflowentering.Thiscanbeseeninequation(3.19):
0
0
Theflowmeasuredwas1.5kg/swithavalveopeningat14%
Thentheopeningofthevalvewasputintothelinearisedequationforthevalveequation(4.1)whichgave:
28
1.5489Themeasurementatthepowerplantcannotshowmorethanonedecimal.Thetestshowedthatthemodelofthevalveiscorrect.
Atthepowerplanttheeffectwasstabilearound180kWwhenthevalvewas13%open.When13%valveopeningisputintotheSimulinkprogramthegraphsshowninFigure14andFigure15isobtained.
Figure14Temperaturewithvalveopeningat13%
29
Figure15Effectwithvalveopeningat13%
ItcanbeseenthattheeffectusedintheSimulinkprogramisalittlehigherthanitwasatthepowerplant,butitisacceptably.
30
8 ConclusionIngeneralitcanbeconcludedthatacontrollerfortheelectricalsuperheateratEsbjergpowerplanthasbeenmade.Thegoalsoftheprojecthasbeenachieved,adynamicmodelhasbeenmade,acontrollerforthatmodelhasbeenfoundbymanualtuninganddatafromthepowerplanthasbeeninsertedintothemodelwithsuccess.
Notallmodelshasbeenlinearisedthisisduetothetimeconsideration,butthemodelforthevalvehasbeenusedtoshownhowamodelcouldbelinearised.Sincetheentiresystemisnotlinearthecontrollercannotbefound/madeinatheoreticalway,likerootlocusandmore.
ThereweresomedeviationbetweenthemeasurementatthepowerplantandtheeffectusedinSimulink.Thiscouldbeduetosomevariationsinmycalculations,forinstancethedensityofthesteamcouldbecalculatedtobealittlebitofwhatitreallyis,whichwillhaveabiginfluenceonthetemperaturechange.Anotherthingthatcouldgivedeviations,isthatsomeofthevariableshasbeenseenasconstantsforinstancethetemperaturethatthereisinsidethesuperheater.Athirdthingisthatatthepowerplantthemeasurementisnotcorrect,whenthesuperheaterisnotstartedoritdoesnotusedanyeffectthemeasurementshowsthat6kWisused.Ithasnotbeenpossibletotestifthis6kWisconstantorlinear.
Thecontrollermadeinthisprojectandthecontrolleratthepowerplantcannotbecomparedtoeachotherbecausethecontrolleratthepowerplanthasanintegrationtimewhereasthecontrollerinthisprojecthasanintegrationgain.
ThemodelsmadearenotfarfromtherealsuperheatersincetheeffectusedinboththeSimulinkprogramandatthepowerplantisalmostthesame.Whenlookingatthemassflowsthemodelsisalmostthesameasatthepowerplant.
31
9 AppendixThetablebelowshowsthemainsymbolsofthemodelingpartofthereport.
Table1NomenclatureforMassbalanceandenergybalance.
Symbol Unit Meaning venacontracta
Specificheatcapacityofsteamatconstantpressure Theeffectthatisputintothesuperheater1 1 Massflowintothesuperheater
Massflowoutofthesuperheater
Specificenthalpyofthesteamentering
Specificenthalpyofthesteamleaving
Molarmassofgasinsteam
Massofsteam
Massflowofsteamenteringthesuperheater
Massflowofsteamleavingthesuperheater
Pressureinthesuperheater
Densityofsteamenteringthesuperheater
Densityofsteamleavingthesuperheater
Idealgasconstant Internalenergyofsteam
Thetemperaturedifferencefromstarttotheend Temperatureofsteamleaving Thisisaconstantwhereitisassumedthatthetemperatureis
230C.Itisusedtocalculated % Percentthevalvebeforethesuperheaterisopen Volumeofthesteaminsidethesuperheater
32
10 References
Books
1. FeedbackControlofDynamicSystems,5thedition;GeneF.Franklin,J.D.Powell,A.EmamiNaeini
2. Reguleringsteknik,4thedition;OleJannerup,PaulHaaseSrensen;ISBN:8750209825
3. OptimizationofChemicalProcesses;ThomasF.Edgar,David.M.Himmelblau
4. IntroductiontoChemicalEngineeringThermodynamiics,SixthEdition,J.M.Smith/H.C.VanNess/M.M.Abbott,ISBN:0071189572
Webpages
1. http://www.spiraxsarco.com/resources/steamtables/saturatedsteam.asp
2. http://www.lru.dk/nvg/pdf/Opslag19b.pdf
3. http://en.wikipedia.org/wiki/Specific_heat_capacity#Heat_capacity
4. http://en.wikipedia.org/wiki/Vena_contracta
Allwebpageshavebeenaccessedthe06thJanuary2010.
Top Related