An EnergySaving Control Strategy on Central AirConditioning System.docx

An EnergySaving Control Strategy on Central AirConditioning System.docx

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AnEnergySavingControlStrategyonCentralAirConditioningSystem

AnEnergy-SavingControlStrategyonCentralAir-ConditioningSystem

●ByShengXing1,YinJuan2,ShangJingfu3,YuYang4,WuZhangxian5

1.StateGridInformation&TelecommunicationCo.,Ltd.

2.ChinaHuadianFinanceCorporationLimited

3.StateGridACEngineeringConstructionCompany

4.NortheastChinaElectricPowerDispatching&CommunicationCenter

5.NorthChinaElectricPowerUniversity

Abstract:

Anenergy-savingcontrolstrategybasedonpredictivecontrolforcentralair-conditioningsystemsisproposedinthispaper.Thecoldloadmodelisdevelopedtodescribethedynamiccharacteristicsoftemperaturecontrolsystems,andthenparametersinthecoldloadmodelandinthecentralair-conditioningsystemmodelareestimated.Generalizedpredictivecontrol（GPC）isusedtoestablishanoptimizationmodeltominimizetheconsumptionofenergyandthecontrolerroroftemperature.Thesimulatedannealing（SA）algorithm,combinedwithquadraticprogramming,isadoptedtosolvetheoptimalproblem.ContrastedwiththesimulationoftraditionalPIDcontrol,theresultsprovetheeffectivenessofthisproposedstrategy.

Keywords:

centralair-conditioning;predictivecontrol;energysaving;time-delaysystem;simulatedannealing

Introduction

ElectricenergyisthemostimportantformofpurchasedenergyinChina[1].Forthisreason,theefficiencyofelectricenergyshouldbeimproved,sinceenergyconservationisanecessaryconcernfordevelopingcountrieswhichhaveexperiencedrapiddevelopment.InChina,theboomintheconstruction,tourismandcommerceindustrieshascreatedanincreasingdemandforairconditioning[2].Currently,electricalcentralairconditioningsystemsaccountfor20%ofthetotalelectricityconsumptioninChina[3].Inevitably,forairconditioningsystems,moreefficientcontrolstrategiesbasedonenergy-savingtargetsneedtobedeveloped.

Accordingtorecentstudies,numerousresearchershavefocusedtheireffortsonfuzzycontroltheoriestobeimplementedoncentralair-conditioningsystems[4],[7].Meanwhile,someresearchersusepredictivecontrolstrategytocompensatethelongdelayintemperaturecontrol[5],[6].Besides,WangandBurnettproposedanonlineoptimalcontrolstrategy,inwhichanadaptiveandderivativemethodisusedtodeterminetheset-pointforpressure[8].

Asthemainfactorinfluencingtemperatureinabuilding,thecoldloadmustbeconsidered.Furthermore,thecoldloadcoulddynamicallyreflecttheneededcoldenergy.Inordertoenhancethesystemoperatingefficiencyandgetastablecontrolperformance,ageneralizedpredictivecontrolstrategybasedoncoldloadisproposedinthispaper.Anintroductionofcoldloadandmodelingthetemperaturecontrolfunctionareillustratedinsection2,whiletheoptimalformulationandalgorithmareproposedinsection3.Insection4,thesimulationispresentedandtheconclusionisgiveninsection5.

Modelingoftemperaturecontrolsystem

Thedescriptionofcoldenergyoutput

Incentralair-conditioningsystems,hotairfromthebuildingtransfersheattochilledwater,causingthetemperatureofchilledwatertoincrease.Chilledwaterpumpsareusedtorecirculatethechilledwaterandtransferheattocoolingwaterbyrefrigerationmachines,whichmakechilledwatercoldagain.Next,coolingwaterisrecirculatedbycoolingpumpsandfinallyheatisreleasedintoatmosphereinthecoolingtower.Inthispaper,itisassumedthatasetofcirculatingsystemsforair-conditioningcouldbedividedintoonecoolingwaterpump,onechilledwaterpumpandonerefrigerationmachine,andtherearetotallyNresetsofsuchsystemsinthecentralair-conditioningsystemofabuilding.

Accordingtothelawsofthermodynamics,thecoldenergyoutputintimekcanbewrittenasfollows:

cold_energy（k）=sk·CwΔt1F1,k

（1）

skCwΔt2F2,k=skCwΔt1F1,k-Qrm

（2）

where,

sk:

thenumberofcirculationsystemusedintimek;

Cw:

thespecificheatcapacityofwater;

F1,k,F2,k:

therespectiveflowsofchilledandcoolingwater;

Δt1,Δt2:

therespectivetemperaturevariationofthechilledwaterandcoolingwater;

Meanwhile,Qrmrepresentstheheatgeneratedbytherefrigerationmachine,whichisproportionaltothecubeofflowandcouldbedefinedasfollows:

（3）

whereηistheefficiencyoftherefrigerationmachineandαisaproportionfactor.

Themodelofcoldload

Thecoldloadinthebuildingcanbedeterminedbythefollowingfourfactors:

theheatbroughtbythebuildingsurface,whichisproportionaltothebuilding’ssurfacearea（Pt）,theheatbroughtbywindsfromcentralairconditioningsystem（Pw）,theheatemittedbypeopleinthebuilding（Pf）,theheatproducedbyelectricequipmentinthebuilding（Pe）.Sothecoldloadcanbedescribedasfollows:

cold_load=Pf+Pw+Pt+Pe（4）

Weassumecoldloadperpersontobeaconstant（theconstantequals30Winsummer）.Meanwhile,Ptcanbedescribedasafunctionofsurfacearea:

Pt=KF（tL,k-tn）（5）

inwhichKstandsforthermalconductivityandFstandsforthesurfacearea,whiletnandtL,kstandforthesettemperatureinthebuildingandthetemperatureoutsidethebuildingintimek,respectively.

Sincetheroofandthesideofabuildinghavedifferentthermalconductivities,

（2）wouldberewrittenasfollows:

Pt=（K1Froof+K2Fwall）（tL,k-tn）（6）

Forsimplicity,weassumePwisproportionaltoPtandthecoefficientisβ,so

（1）canberewrittenasfollows:

cold_load（k）=30Pfk+（1+β）（K1Froof+K1Fwall）（tL,k-tn）+Pc（7）

Pfkrepresentstheflowofpeopleinthebuildingintimek,andobeysaPoisson-process,whichhasbeenprovenasthemostapproximatedistributionofpeopleflowinlargebuildings,andcanbedefinedasfollows:

（8）

inwhichλistheexpectationofpeopleflow.

From

（1）to（8）,theunknownparametersareα,PEandλ,whichcanbefittedusingexperimentdataofleastsquaremethod.

Thepredictivemodeloftemperaturecontrol

Inacentralair-conditioningsystem,thecoldenergyproducedbyair-conditioningwouldsatisfythecoldloadfirstly,andthentheredundantcoldenergyleftwouldmaintainthetemperatureatasetvalue.Ifthecoldenergycannotsatisfythecoldload,thetemperatureinthebuildingwillrise.Meanwhile,thereal-timetemperaturetransmittedbythetransducerinthebuildingwouldfeedbacktomaketheoutputofthecoldenergymoreexactly,asshowninFig.1.

Sincethetemperatureinthebuildingisdifficulttochange,afirst-orderinertiaelementwithapuredelayisusedtosimulatethedynamicprocessofthebuildingwheninputvariableschange.Sothetransferfunctioncanbewrittenasfollows,

（9）

Thatis,

（10）

whereTistheinertiatimeconstantandgequaltoCairFairisthegain.

Theequationabovecanbediscretizedasfollows:

（11）

whereT0isthesampletimeandNisaninteger.Thedelayingtimeτ=NT0

（12）

whereDToutrepresentsthechangeofToutwhileU（k-N）standsforthedifferencebetweencoldenergyandcoldload,andcanbedefinedasfollows:

DTout（k）=Tout（k）-Tout（k-1）（13）

U（k-N）=cold_energy（k-N）-cold_load（k-N）（14）

Coldenergyandcoldloadcanbecalculateby

（1）and（7）,byusingdataintimek-N.

GPCbasedcontrolstrategy

SinceD.W.ClarkepresentedtheprincipleoftheGeneralizedPredictiveControl（GPC）inAutomationin1987,GPChasbecomethemostpopularModelPredictiveControlmethodinbothindustryandacademicapplications,inwhichithasbeenfoundveryeffectiveandrobust.InGPC,whichbelongstothegroupofrollingoptimization,asetoffuturecontrolsignals（Psignalsinthispaper）aregeneratedineachsamplinginterval,butonlythefirstelementofthecontrolsequenceisappliedtothesysteminput.

Optimizationformulation

Accordingto

（2）and（3）,sinceΔt1andΔt2mustbemaintainedinanacceptablerange（whichmakesthemimpossibletobecontrolvariables）,buttwooftheotherthreevariable（sk,ΔF1,kandΔF2,k）canbeusedascontrolvariables.Inthispaper,skandF1,kareselectedascontrolvariables.Intheobjectfunction,energycostandtemperaturecontrolerroraretakenintoconsideration.

Wedefine:

whereF1,maxandF2,maxstandforthemaximumflowofthechilledwaterpumpandcoolingwaterpump,respectively.

Inaddition,temperatureoutputinthefuturePstepscanbepredictedbytheequation:

Tout（k0+n）=Tout（k0）-DTout（k0+n）n=0,1...P（17）

DTout（k0+n）canbeobtainedby（12）,andTout（k0）isthecurrenttemperatureinthebuildingwhichcanbetransudedbysensors,sothetemperatureinthenextPstepscanbepredictedby（17）andtheerroroftemperatureoutputcanbedefined:

（18）

Accordingto（15）-（18）,theoptimizationmodelcanbeestablishedasfollows:

whereF1,minandF2,minrepresenttheminimumflowofthechilledwaterpumpandcoolingwaterpump,respectively,andPisusedtodesignatethenumberoffuturesignalsgeneratedinasample’stime.Inaddition,W1*andW2*representtheprocessweighingandfinalstateweighing,whileW*1andW*2standfortheenergy-savingweighingandtemperature-accuracy.

SolutionalgorithmbasedonSA

Foreverysamplinginterval,anoutputsignal,including{F1,k,sk},canbeobtainedbysolvingtheoptimizationmodeldescribedabove.However,thisoptimizationmodelisanonlinearprogrammingproblemwithintegerconstraints,whichcannotbesolvedbythetraditionalDiophantineequation.Inordertoensuretheaccuracyofthesolutionaswellastherealtimecapability,anoptimizationalgorithmbasedonsimulatedannealing（SA）ispresentedinthispaper.

Sincethesolutionefficiencylargelydependsontheinitialvalueofsk,aparticulartreatmentshouldbeadopted.Firstly,weassumethenum