ControlofsuperheaterforelectricalsteamboileratEsbjergpowerplantPeriod:November1st2009January7th2010Duedate:January7th2010Student:RasmusHolmgaardRasmussenSupervisor:ZhenyuYang

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Titlepage

Title:ControlofsuperheaterforelectricalsteamboileratEsbjergpowerplantDuedate:7.January2010

Abstract:Thisprojectfocusesonmodelingofanelectricalsuperheater,placedatDONGEnergyspowerplantinEsbjerg.Basedonthemodelacontrollerforthesuperheaterismade.Theentiresystemisthentestedandcomparedtodatafromthephysicalpowerplant.

ThetestmadetotheobtainedsystemisdonebyusingSimulink.

Duetothetimeconsiderationssomeofthemodelhasnotbeenlinearised.Howeverithasbeenshownhowtolinearizeamodel.

Supervisors:ZhenyuYang

Student:RasmusHolmgaardRasmussen

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Preface

ThisreportiswrittenasdocumentationformyfinalprojectatAalborgUniversityEsbjerg.Thepurposeofthereportistogivethereaderinsightintowhichconsiderationsandprocessesthatwasusedduringtheproject.

Thereportisdividedintofourparts.Firstananalysisofalltheregulationsloopsontheelectricalsteamboiler.Thepurposeofthisanalysisistofindasingleareawhichneedstobemodeled.Thesecondpartpresentstheworkwithmodeling,systemidentification,controldesignandtesting.Thethirdpartisconclusion.Thefourthandlastpartisappendix.

InthebackofthereportaCDisenclosedcontainingadigitalcopyofthereportalongwiththeSimulinkprogram.

DONGEnergyshouldhavethanksforthehelpandhospitalityenjoyedduringthisproject.

AalborgUniversityEsbjerg,fall2009

____________________________RasmusHolmgaardRasmussen

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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

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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.

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OnFigure1alltheregulationthatisneededfortheElectricalsteamboiler,forauxiliarysteamonEsbjergpowerplant,canbeseen.

Figure1Allregulationfortheelectricalsteamboiler

TheProjectsgoalsaretherefore:

Establishadynamicmodelforoneoftheareasthatneedtobecontrolled.

Testandverifythedynamicmodelinsimilaritytotherealsystem,withdatafromtherealsystem.

Developacontrollerbasedonthedynamicmodel.

1.1 PhysicalinfluencesThissectionwillgiveanoverviewofthethingsthatwillhaveaninfluenceonthemodelsandthecontrollers.

Thetotalamountofwater:Thelevelsinthetwotanksarethemaininfluence.Thepressuredoesnthaveanydirectinfluenceonethelevelsbecausewaterisalmostincompressible.Howeverwhensteamisproducedthelevelwillvirtualraisebecausetherewillbesomeabsorptionofthesteaminthewater.Thehigherpressurethemorethesteamwillbeforced

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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.

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Temperatureoutofthesuperheater.Thisloopmustholdthetemperatureonthesteamoutofthesuperheaterat230C.

Pressureintheboilerandinthesteampipe.Aspreviousmentionedthepressureinsidetheboilermustbeat20bar,besidesholdingthatpressuretheregulationmustalsoholdapressureat11.5barinthesteampipe.

1.3 AnalyticconclusionBasedontheanalysisofthecontrolloopsIhavedecidedtocontinuewiththesuperheater,becausethesuperheateristheonlyregulationthatdoesnotdirectlydependononeoftheotherregulations.

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2 Systemdescription

Aspreviousmentionedthesuperheatersassignmentistoensuredrysteamandatemperatureat230C.Todothistherearesomeelectrodeswhichwillheatthesteamgoingthroughthesuperheater.Tocontrolthetemperaturetheeffectthroughtheelectrodesisregulated.Themassflowenteringandthemassflowleavinghasabiginfluenceonhowmucheffectisneeded.AsitcanbeseenonFigure2thereisavalvebeforethesuperheater,thisvalveiscontrollingthepressureinthesteamboilerandthepressureafterthevalve.Sothecontrolofthevalvehasnothingtodowiththesuperheater,howevertheopeningofthevalvedetermineshowmuchsteamthatwillenterthesuperheaterandthereforealsohowmuchthatwillleave.FurthermoreitcanbeseeninFigure2thatthemeasurementofthetemperatureisplacedoutsidethesuperheaterthereforeitwilltakesometimetoregisterwhatkindofinfluenceanincreaseoradecreaseintheeffecthasonthetemperature.

Figure2Systemoverview

Itisassumedthatthecontrollerforthevalveiscontrollingthepressuresonbothsidesofthevalveperfectly.Itisalsoassumedthatthesteambeforethevalve/comingoutofthesteamboilerissaturatedsteam.

Heatlosttothesurroundingsisignoredsinceitishardtofindbecausethesystemisisolatedanditisnotpossibletogetthetemperaturebetweenthepipesandtheisolation.

Thesuperheaterisonlystartedwhenthereisaflowabove1.0kg/s.

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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

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(3.5)

Becausethemassconsistsofsteam,whichismostgas,thegravitationalforce( )isverysmallandcanbeneglected.Theequationnowis:

(3.6)

Figure4Flowthroughthevalve

Ifthisequationisusedintwopoints(1and2)asshowninFigure4,itwilldescribetheflowthroughthevalveandwillleadtothefollowing:

(3.7)

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2 (3.8)

Therebytherelationshipbetweenthevelocitiesandthepressuresdifferences,betweenthesteampipebeforethevalveandthesteampipeafterthevalve/beforethesuperheater.Howeverthevelocitiesarenotknownandtheequationisonlyconsideringtheenergybalanceregardingthevalve.

Tofindthevelocitiesthecrosssectionalareaofthevalvehastobetakenintoaccount.

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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)

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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)

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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

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(3.24)Insertingthisintoequation(3.23)

Sincetheelectricaleffectismeasuredinwatts,whichis theenergyisequaltotheeffect.

isthatenergythatisusedtoheatupthesteamenteringthesuperheatertothetemperatureinsidethesuperheater.

(3.25)where isthemass,butthemassflowforthesteamenteringisusedinstead, isthe

specificheatcapacityand isthetemperaturedifferencefromstarttotheend.

canbefoundbylookingatthesteaminsidethesuperheaterandthesteamentering

isfoundbyrearrangingtheidealgasformula

Thereforeequation(3.25)becomes:

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Insertingthisintoequation(3.23)

Theninserting fromthemassbalance,equation(3.19)

(3.26)

Combiningthetwoformulasfromtheenergybalance,equations(3.22)and(3.26).

Thespecificenthalpyonthesteamleaving( )canbefoundbythefollowingformula:

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Inserting gives:

Sincetheflowismeasuredinkg/sitisamassflowwhichmeans and.

where

so

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whichmeans

(3.27)

3.3 MassflowleavingTherehasalreadybeenmadanequationforthemassflowleavingthesuperheaterinequation(3.19),whichis:

4 Identification

4.1 VerifyingofvalvemodelThemaximumdiameteroftheorificeis111.125mm

Iftheorificeissharpatypicalvalueofcoefficientofcontractionis0.64.

111.1252 9698.6978 0.00009699

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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

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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 .

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4.2 ThetemperaturechangeItisassumedthattheinternalenergybeforethevalveisthesameafterthevalve.Thereforethe canbefound,asitisassumedthatthesteambeforethevalveissaturatedsteamataconstantpressureon20bar.

2599.5

8.314472

18 0.018

2590 thisisfoundinasteamtable.

Thevolumeofthesteam(Vs)isassumedtobethesameasthevolumeofthesuperheater,becausetherehasbeenrunningsteamthroughthesuperheatersometimebeforethesuperheaterisstarted.Thevolumeofthesuperheateris404literswhichis0.404m3.

Figure6Relationshipbetweenvalveopeningandmass flow

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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.

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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.

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Figure7Simulink

RunningtheSimulinkprogramwiththeValveopeningon100%thefollowinggraphsisobtained:

Figure8Temperaturewiththevalve100%open

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Figure9Effectusedwhenthevalveis100%open

Figure10MassFlowwhenthevalveis100%open

Itcanbeseenthattheeffectisalmost1500kWandthemassflowforbothentering(theyellow)andleaving(thepurple)isabitabove11kg/s.Ittakesalmost4000secondstogetthetemperatureat230C.

Thenrunningtheprogramwhitthevalveopeningat10%givesthefollowinggraphs:

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Figure11Temperaturewiththevalve10%open Figure12Effectwiththevalve10%open

Figure13Massflowwiththevalve10%open

Nowthemassflowsandtheeffecthasnowgonedowntoaround1.1kg/sand150kW.Thetimeforthetemperaturetogetto230Cisnowaround1000seconds.

Fromthesetworunsoftheprogramiscanbeseenthatthemoresteamthatneedstobeheatedthemoreeffectwillbeused,whichwasexpected.

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6 ControllerThecontrollerwasmanualtunedbysettingallvaluestozeroandthenincreasingthegainKpuntiltheoutputwasstartingtooscillate,thesettingittothehalfofthatvalue.NexttheKivaluewasincreaseduntilanyoffsetiscorrectinsufficienttimefortheprocess.ItwasnotnecessarytouseaKdvalue.ThereforethecontrollerisaPIcontroller,withthefollowingvalues:

Kp=1000

Ki=15

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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:

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1.5489Themeasurementatthepowerplantcannotshowmorethanonedecimal.Thetestshowedthatthemodelofthevalveiscorrect.

Atthepowerplanttheeffectwasstabilearound180kWwhenthevalvewas13%open.When13%valveopeningisputintotheSimulinkprogramthegraphsshowninFigure14andFigure15isobtained.

Figure14Temperaturewithvalveopeningat13%

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Figure15Effectwithvalveopeningat13%

ItcanbeseenthattheeffectusedintheSimulinkprogramisalittlehigherthanitwasatthepowerplant,butitisacceptably.

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8 ConclusionIngeneralitcanbeconcludedthatacontrollerfortheelectricalsuperheateratEsbjergpowerplanthasbeenmade.Thegoalsoftheprojecthasbeenachieved,adynamicmodelhasbeenmade,acontrollerforthatmodelhasbeenfoundbymanualtuninganddatafromthepowerplanthasbeeninsertedintothemodelwithsuccess.

Notallmodelshasbeenlinearisedthisisduetothetimeconsideration,butthemodelforthevalvehasbeenusedtoshownhowamodelcouldbelinearised.Sincetheentiresystemisnotlinearthecontrollercannotbefound/madeinatheoreticalway,likerootlocusandmore.

ThereweresomedeviationbetweenthemeasurementatthepowerplantandtheeffectusedinSimulink.Thiscouldbeduetosomevariationsinmycalculations,forinstancethedensityofthesteamcouldbecalculatedtobealittlebitofwhatitreallyis,whichwillhaveabiginfluenceonthetemperaturechange.Anotherthingthatcouldgivedeviations,isthatsomeofthevariableshasbeenseenasconstantsforinstancethetemperaturethatthereisinsidethesuperheater.Athirdthingisthatatthepowerplantthemeasurementisnotcorrect,whenthesuperheaterisnotstartedoritdoesnotusedanyeffectthemeasurementshowsthat6kWisused.Ithasnotbeenpossibletotestifthis6kWisconstantorlinear.

Thecontrollermadeinthisprojectandthecontrolleratthepowerplantcannotbecomparedtoeachotherbecausethecontrolleratthepowerplanthasanintegrationtimewhereasthecontrollerinthisprojecthasanintegrationgain.

ThemodelsmadearenotfarfromtherealsuperheatersincetheeffectusedinboththeSimulinkprogramandatthepowerplantisalmostthesame.Whenlookingatthemassflowsthemodelsisalmostthesameasatthepowerplant.

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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.