Model predictive control of a thermally activated building system to improve energy management of an experimental building: Part II - Potential of predictive strategy

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Model predictive control of a thermally activated

building system to improve energy management of an

experimental building: Part II - Potential of predictive

strategy

Hugo Viot, Alain Sempey, Laurent Mora, Jean-Christophe Batsale, J.

Malvestio

To cite this version:

Hugo Viot, Alain Sempey, Laurent Mora, Jean-Christophe Batsale, J. Malvestio. Model predictive

control of a thermally activated building system to improve energy management of an experimental

building: Part II - Potential of predictive strategy. Energy and Buildings, Elsevier, 2018, 172,

pp.385-396. �hal-02356354�

Model

predictive

control

of

a

thermally

activated

building

system

to

improve

energy

management

of

an

experimental

building:

Part

II

-Potential

of

predictive

strategy

H.

Viot

∗

,

A.

Sempey,

L.

Mora,

J.C.

Batsale,

J.

Malvestio

University of Bordeaux, CNRS, Arts et Métiers ParisTech, I2M, UMR 5295, Esplanade des Arts et Métiers, Talence 33400, France

Keywords:

Model predictive control TABS

Floor heating system Energy management Optimal control

a

b

s

t

r

a

c

t

ThermallyActivatedBuildingSystems(TABS)aredifficulttocontrolduetothetimelagbetweenthe con-trolsendingandtheresponseoftheindoortemperature.Energymanagementofsystemshavingsucha highinertiacanbeimprovedbyoptimizingtherestarttimethankstobothoccupancyandweather antic-ipation.Predictivecontrolissuitableforsystemswithnumerousconstrainedinputsandoutputswhose objectivefunctionvaries overtimesuchas buildingswithintermittentoccupancy.Thisworkproposes touseaModel PredictiveControl(MPC)foroneTABSinparticular:afloorheatingsystem(FHS)ofan experimentalbuilding.Conventionalcontroltechniquesandastateoftheartonthepredictivecontrolof FHSarepresented.Acompletecontrolloop(sensor,actuator,controller)wasimplementedonan experi-mentalroom.ThepredictivecontrollerthatintegratethemodelselectedinPartIiscomparedwithtwo conventionalcontrolstrategies.Theenergysavingpotential ofthepredictivecontrollerisconfirmedby bothlocalexperimentationandsimulationonthreeclimates.Theenergysavingiscloseto40%overthe wholeheatingseasonwithanimprovedorequivalentcomfortsituationcomparedtotheothertwo ref-erencestrategies.Theabsolutegainisconstantovertheheatingperiodbutthemostsignificantrelative gainsareobtainedinthemid-season.

1. Introduction

The importanceofcontrol inthe buildingenergyperformance is oftenunderestimated.The on/off,PI orPIDregulatorsare suit-abletofollowaconstantsetpointbuttheuseofintermittent sce-narios is more appropriate to decrease energyexpenditure. Con-ventionalregulatorsmaynotbealwayssuitablefortransientstate controlofsystemshavingsomeinertiasuchasbuildings.The prin-ciple ofclosed-loop control isbased on thefeedback ofthe con-trolledvalue.Whenthecontrolofahighinertiasystem(time de-lay)isdesired,conventionalcontroltechniquesbasedonafast sys-tem response are nolonger sufficient. TABSare used in a « pas-sive » way forbasic heatingin buildings withintermittent heat-ing. Intermittenceisoftenmanagedby anadditionalheating sys-temwhoseusecouldbelimitedbyafinercontroloftheTABS.In thiswork,attentionisfocusedonthepredictive controlofaFHS, whichisthemostwidespreadTABS.Overthelastdecade,FHShave become popular thanks to low-temperature boilers suited to the operatingtemperaturesofthissystem.AFHScanbeused:

∗ _{Corresponding author.}

E-mail address: hugo.viot@u-bordeaux.fr (H. Viot).

 alone to ensure a comfort temperature during the day with an idleat night, this scenario mainly concerns the individual dwellings,

 withanauxiliarysystemtopermanentlyensureabasic temper-ature while the auxiliary heating system ensures the comfort temperatureduringtheday.

AFHS isan efficientsystembutdelicate tocontrol. The heat-ingpowerofaFHS isgenerallymodulateddependingonoutdoor conditionsby usinga« heatingcurve » givingthecorrespondence betweenthe watersupplytemperatureTws andthe outside

tem-peratureTe(Fig.1).Theprincipleistocompensatetheheatlosses

through envelopewhich depends on the inside/outside tempera-ture difference. Thus, the water supply temperature of the floor variesconstantly. Losses evolve almost linearly withthe temper-aturedifferenceandtheheatingcurveisastraightline.Theslope dependsonthecharacteristicsoftheenvelope,thedesiredcomfort temperatureandthe sizeofthe floor.Thisregulationistherefore basedonacontinuousmeasurementoftheoutsidetemperature.A typicalFHSinstallationincludesthefollowingelements:

 an outdoor temperature sensor located north and protected fromdirectsunlight,

Fig. 1. Classical FHS regulation.

Nomenclature

Variables,parameters,abbreviations

AHU AirHandlingUnit

BEMS BuildingEnergyManagementSystem

C thermalcapacitance(J.K−1)

Cp specificheatcapacity(J.kg−1.K−1) Dh Degree-hour(°C.h)

UDD UnifiedDegree-day(°C.day)

E energyconsumption(kWh) FCU FanCoilUnit

FHS FloorHeatingSystem

I interval

IG freeinternalgains(kWh)

J costfunction

L heatlosses

m controlhorizon ˙

m massflow(kg.s−1) MPC ModelPredictiveControl

p predictionhorizon PID Proportional-Integral-Derivative P power(W) r setpoint R thermalresistance(m².K.W−1) T temperature(°C)

TABS ThermallyActivatedBuildingSystems

w weight Subscripts c controllable comf comfort e exterior eco economic i interior nc uncontrollable tot total wr waterreturn ws watersupply

Vectorsandmatrices A statematrix

B inputmatrix

C outputmatrix

D feedthroughmatrix

X statevector

U vectorofinputs

Y outputvector

 a three-way valve adjusting the watersupply temperature by mixingthewatercomingfromtheboilerandthewaterreturn temperature,

 apumpforwatercirculationinthepipes,

 anindoortemperaturesensor,alsoknownas« remotesensor», which is often required to prevent overheating due to occu-pantsorsolargains.

 aregulatoractingonthepositionofthethree-wayvalveto ad-justthe water supply temperatureaccording to the measure-mentoftheoutsidetemperature. Theregulatorcanshutdown thepumpormodifytheheatingcurveifthesetpointisreached thankstoaremotesensor.

The major part of FHS are used in the residential sector. A studybytheNationalUnionofManufacturers ofComponentsand Integrated Heating Systems(COCHEBAT) revealsthat 40% ofnew homesin Franceare equippedwithaFHS [1].Thesesystems are effectivewhenthesettingsareappropriate.Nevertheless,the con-trolisbasedonreal-timemeasurements andisnot ableto antic-ipatethefuture disturbances.The potential ofsuch a systemcan thereforebefurtherimprovedbyaddingintelligenceusingaModel PredictiveControl(MPC)technique.

First,a stateofthe artintroducesthe variousresearch studies carriedoutonthepredictivecontrolofTABS.Thefollowingsection presentsthemethodtoshowthepotentialofapredictivestrategy ontheexperimental room.Theused equipment,measuredvalues and control logic are presented. Finally, the experiment and the simulationresultsofthecomparisonbetweentworeference strate-giesandthepredictivecontrolarepresentedinordertoconclude ontherelevanceofsuchcontrol.

Fig. 2. MPC and receding horizon principle with m = p.

2. Principleandstateoftheartonpredictivecontroltechnics forFHS

MPCisacontroltechniquebasedontheoptimizationofa con-strainedproblem.Controllableinputsandoutputsarepredictedby a model in order to fulfill an objective described by a function. ThemodelisatthecoreoftheMPClogic.Itpredictsthebehavior ofthe systemtobe controlledandchooses an optimaltrajectory. Feedbackisprovidedbyrepeatingthisprocedureateachtimestep. Thiscontrollercomprises:

 a prediction model: describes the thermal behavior of the buildingsubjectedtocontrollableanduncontrollableinputs,  asetpoint:thedesiredinteriortemperature,

 constraints: the available maximum power, rate of de-scent/climb,

 disturbances:forecastsofuncontrollableinputs(weather, occu-pation),

 acostfunction:constraintontheindoor temperature(comfort criterion)andonenergyconsumption(economiccriterion). First, we must choose a model and define a cost function. These choices are not independent since the model depends on theobjective.AsspecifiedbyKouvaritakisandCannon[2],anMPC control isbasedonprediction,optimizationandrecedinghorizon principle.TheoutputsequenceofthemodelYkispredictedbythe

simulation at each time step k witha state model(Eq.(1)).The vector U_k containsthem controllableinputstobe optimizedU_c|k

andthenuncontrollablepredictedinputsUnc|k(Eq.(2))fora

pre-dictionhorizoncorrespondingtoptimesthesamplingperiod(Eq. (3)).Thefeedbackisensuredbyoptimizingthecontrollableinputs that minimize the cost function at time step k over the predic-tion horizon(Eqs.(4) and(5)).The termJy|k allows the ny

num-berofmodeloutputsytofollowtheirrespectivesetpointr,which areassumedtobeknown.ThetermJ_u|kensuresthat thenc

num-ber ofcontrol variables u remain within their rangeconstrained by the user. Similarly, the term J_u|k constrains the variation of

thecontrolvariablesbetweentwotimesteps(Eq.(6)).Weightswy_, wu_,wu_{areassignedrespectivelytooutputs,commandsand}

com-mandvariations.Thescalarssy_,su_,su _{allowtorespectthe}

homo-geneity.ThecostfunctiondependsonU_c|kandtheoptimalcontrol sequence denoted U∗c|k isdetermined by minimizing Jk (Eq.(7)).

Thecommanduc senttotheactuatorscorrespondstothefirst

el-ement u∗c|k of the optimalcontrol U∗c|k (Eq. (8)). The

minimiza-tionofthecostfunctionisrepeatedatthenexttimestepwiththe sameprediction horizonthat movesaccordingto theprincipleof recedinghorizon(Fig.2).



Xk+1=AXk+BUk Yk=CXk+DUk (1) BUk=BcUc|k+BncUnc|k (2) Uk=

⎡

⎢

⎢

⎣

u1,c | k um,c | k u1,nc | k un,nc | k u1,c | k+1 um,c | k+1 u1,nc | k+1 un,nc | k+1 . . . · · · ... ... · · · ... u1,c | k+p−1 um,c | k+p−1 u1,nc | k+p−1 un,nc | k+p−1

⎤

⎥

⎥

⎦

(3) Jk=Jy|k+Ju|k+Ju|k (4)

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎩

Jy|k = ny j=1 p i=1 wy i, j sy_{i, j} ·

(

rj|k+i− yj|k+i

)

2 Ju_|k = nu j=1 p −1 i=0 wu i, j su i, j ·

(

uj|k+i− uj,target|k+i

)

2 J_u|k= nu j=1 p −1 i=0 wu i, j su i, j ·

(

uj|k+i− uj|k+i−1

)

2 (5)

⎧

⎨

⎩

U≤ Uk≤ U



U≤



Uk≤



U Y≤ Yk≤ Y (6) U_c∗_|k=argminJk (7) uc=u∗c|k (8)

The choice of the sampling time step Tsample dependson the

desiredapplication. A low samplingperiodallows a better rejec-tionofunknowndisturbances.However,itsvaluealsodependson thedynamicsofthemodelsincethesmallerthesamplingperiod is,thegreateristhecomputationaleffort.Itisthereforenecessary tomakeacompromise betweenthedesiredperformance andthe computingpower.Withasmallsamplingperioditismoredifficult toextendthemcontrolhorizonastheprocessorneedstooptimize

m∗Tsampleoperations.Thecontrolhorizoncorrespondstothe

num-berofsamplingperiodsonwhichthecontrolisoptimizedateach time step.When m is small,the calculation time is reducedand thecontrol becomesmore stable. The choiceof thecontrol hori-zonisofgreatimportanceanddependsonthesupposeddynamic responseofthesystem.Forpredictionhorizon,asmallpvaluecan makethecontrolunstableandlosethepredictiveaspect.

Only a few papers deal with the particular case of a predic-tive controlofa FHS (Table 1).Chen [3]hasshowntheutility of theMPCforanelectricFHSandspecifiesthatconventionalcontrol technicscannotcompensatethephaseshifteffectforintermittent heating. The works of Cho and Zaheer-Uddin [4] study the con-trolof theFHS (simulation andexperimental) intwo test cham-berswith28sensorsperroom.Aforecastingmodelisusedto esti-matethefutureoutdoortemperature.Thebuildingbehavioris de-scribedby apolynomial functionofthe outsidetemperature.The

Ta b le 1 P apers dealing with MPC in v ol ving FHS contr ol. Au to rs Ye a r Model Cos t function Simulation/Experiment Compar e d st ra te g ie s MPC ga in Re f Chen 20 02 T ransf er functions comfort economic S/E on/of f PI mor e sta b le contr o l [3] Cho and Zaheer -Uddin 20 03 Po ly n o m ia l comfort economic S/E sc he dule + PID 1 0–20% [4] Pri v ar a et al. 20 1 0 St at e-space comfort economic S on/of f+ PID + heating curv e 17–29% [5] Ver h els t et al. 20 11 ODE comfort economic S heating curv e + PID 5% [6] Kar lsson and Hag ent of t 20 11 2R2C comfort S mo ving a v er ag e re le v ance fo r int e rmitt e ntl y occupie d building [7] Candane d o and A thienitis 20 1 2 T ransf er functions comfort economic S PID re le v ance of connecting thermal solar panels to FHS [8] Sourbr on et al. 20 1 3 4R2C comfort economic S sc he dule + PID 7% [9] Berthou 20 1 3 6R2C comfort economic po w er S sc he dule 5% [1 0] Li et al. 20 1 5 8R4C comfort economic S PID 17 % [1 1] Wa n g et al. 20 17 St at e-space comfort economic S PI 8% smoo ther t em per atur e tr ansition [1 2]

MPCstrategy iscomparedtoasetpoint scenariooverathree-day wintersequenceandshowsenergysavingsof20%andlower tem-peraturevariations.IntheworksofPrivaraetal.[5],aradiant ceil-ingisusedbuttheprincipleisthesameasaFHS.TheMPC with a24hhorizoniscomparedwiththreemanagementstrategies:an on/off regulator,aweather-compensatedcontrolandaPIDwhere thewatersupplytemperaturedependsondeviationfromthe set-point.Energysavingsof29%andbettercomfortareachievedwith theMPC.InthecaseofVerhelstetal.[6]theFHSisconnectedto aheatpump.Aheatingcurve iswell adaptedandeffectiveto en-surecomfort, butitdoesnotallow exploitingthethermal capac-ityofthe slabtoreduce costs. ForthisreasontheMPC is neces-sary.Theauthorspointoutthatreactivesystemsareoftenelectric heaters which explains why many publications deal with reduc-ingthepeakloaddemandonthenetwork(hourlypricingsystem). Thepredictionhorizonisalso24hwithatimestepof30min(48 sequencestooptimize).TheMPC’suseresultsinasavingof5%of theenergyexpendedbythecompressor.InKarlssonandHagentoft publication[7],theoptimalplanisbasedonthepowerinjectedto the floor, this optimum power is then transformed into a corre-spondingwatersupplytemperature. Themeasurementofthe wa-ter returntemperatureallows compensatingforecastingerrors.In the worksof CandanedoandAthienitis [8]and Lietal.[11],the FHS is connected to a solar thermal panel. A simplified building modelisobtainedfromadetailedmodel.Thestudiedroomhasa large glazedarea and iswell insulated.The comparisonbetween the MPC and a PID control is performed using Matlab/Simulink. The results are conclusive for the tested building. The paper of Sourbronetal.[9]dealswiththeinfluenceofuncertaintiesonthe qualityofpredictivecontrolinthecaseofaFHScoupledwith ad-ditional fan coil units. The quality of the control decreases with theuncertainties:measurementerror,predictionerrorandmodel error.Theimpactoftheseerrorsisevaluatedonthreecriteria: en-ergyconsumedbytheFHS,byfancoilunitsandcomfort.The au-thorshighlightthepotentialofcouplingslowandfastsystemsbut warnaboutimportantparameters.Thustheinitialtemperatureof thefloor isparamount.Berthou [10]comparesthree strategiesof optimization:

 restarttimeoptimization:theenergypriceisconstant andthe optimizationisdone onthevalue oftheidletemperature set-point,thisstrategyallowsupto20%ofenergysaving,

 priceoptimization:thepriceofenergyvariesandheating con-trolisanticipatedtostoreheatwhentheenergyischeap.The economicgainisabout8%,

 poweroptimization:thepowerpeakislimitedbyoptimization andreducedby50%.

IntheworksofWangetal.[12],aMPCstrategyisusedtokeep theroom within arangeoftemperaturethrough thecontrol ofa FHS connectedto an air/water heatpump. The energy consump-tionis reducedby 8%compared toa PI control.The bibliography confirmsthat predictivecontrol isthe mostinterestingtechnique comparedto conventionalonesfortemperateclimates and build-ings/systemswithimportantinertia.

3. Potentialofapredictivecontrolstrategyappliedtoan experimentalbuilding

To confirm the conclusion of the state of the art section, the MPC strategy is compared with two conventional management strategieson theexperimental room involvingthreesystems (see PartI): aFHS, threefancoilunits(FCU)andadualflow air han-dlingunit(AHU).

Fig. 3. Complete control loop architecture.

3.1. Experimentalsetup

Acompletecontrolstructurewasdevelopedforthe implemen-tationofpredictivecontrol.Additionalinstrumentationwasadded andaboxwithanoptimizerwassetup witha partnercompany. Fig.3showsthegeneralarchitectureoftheinstallation:

 aset ofsensorsis installedinparallel withtheexisting ones, whichallows toknowthe stateof thebuilding(temperature), the external conditions (temperature, solar radiation) and oc-cupants’ behavior (presence, windows/doors openings). Some sensorsare useddirectlyforthecontrol whileothersareonly usedforinformationpurposestoexplainunexpected phenom-ena(openingsensors,temperaturesensorsinadjacentrooms). Threetemperaturesensorsallowtohaveanideaofthe hetero-geneitiesinthevolumeoftheroom.The outdoortemperature sensorisplacedontheroofabovetheworkshopandprotected fromsolarradiation.Thethreesolarfluxsensorsareplacedon a matandorientedin thesouth,west andeast directions re-spectively.Theycanmeasuretheglobalsolarhemisphericflux. ThesupplyandreturnwatertemperaturesoftheFHSare mea-suredbytwo contacttemperaturesensorsplacedbetweenthe copperpipeandtheinsulatingsheath.Twomovementsensors locatedintheoppositecornersareusedtodetecttheoccupants forFCUandAHUcontrol,

 actuatorsalreadyinstalledforthedefaultbuildingenergy man-agement system (BEMS) act on the systems. The water

sup-ply temperature of the FHS is regulated by the opening of a three-way valve.FCUarealsosuppliedwithhotwaterthrough the opening of a three-way valve but the temperatureis im-posed and the blowing temperature is approximately 35°C. The powercontrol isdone withtheblowingspeed which can vary between three positions thanks to electrical relays. For theAHU,theflow isimposedby thestandard[13].Itissetat 1080m3_h−1_(18m3_h−1_.occupant−1_{).Thisflowismechanically}

controlledbyashutter,

 a box centralizes the information of the sensors and sends the commands to the actuators. It ensures the reactive layer (FCU/AHU)butalsothepredictivelayer(FHS)byapplicationof the optimal control sequence received from the remote opti-mizer.Theboxisplacedintheadjacentofficeandreceivesthe dataofthesensorsthankstoradiowaves.Thisdataisthen re-trievablethroughawebservice,

 a remoteoptimizerorschedulerreceivessensorinformations through the box, processes this data and calculates the opti-mal control sequence (water supplytemperature ofFHS).The sequence issenttotheboxandthentothe actuator(PID set-pointofthethree-wayvalve),

 a USB donglereceives data from thesensors through propri-etaryX2DorX3Dprotocol,

 Modbus enclosures permit communication between the box andtheactuatorscontrolledin0–10Vorbinary,

 an Ethernetswitch allows data sending to actuators through an Ethernetgateway and the Modbus TCP/IP protocol. It also allows communication betweenthe box andthe remote opti-mizer,

 connectors allow the actuators to receive either commands from the defaultBEMS or from thepredictive controller. This makes itpossibleto comparethestrategiesandto quickly re-storethebuildingtonormaloperationbyasimpleconnection. Theoptimizerusesthe5R4CmodelidentifiedinPartI.As spec-ifiedbyBénardetal.[14,15],controltechniquesbasedon program-mingandsoftwareintelligencefacemanyobstacles(manufacturers andusers) due to the evolution of know-how compared to cur-rentmethods.The control structure onthe experimental room is thesimplestwaytointroduceoptimalcontrolwithout fundamen-tallychangingtheinstallation.Indeed,thecontroliscarriedoutby aconventionalPIDregulator whosesetpoint resultsfroman opti-mizationrealizedbyaremotecomputer.

3.2.Comparedstrategies

The reference strategies consist in two ways to ensure com-fort.Oneisdoneby theFCUwhiletheFHSguaranteesaconstant basetemperaturewithaheatingcurve.Fortheotherone,theFHS partlyensurescomfortduringoccupancyperiods.Thusthree man-agementstrategiesarestudiedfortheFHS:

 reference1(ref 1):the heatingcurve isadjusted toensurean indoor basetemperature of 16°C. The FHS is programmedto runcontinuously.ThepowerdeliveredbytheFHSdependsonly on the outsidetemperature without considering the occupied periods.Theanticipativeeffectisnull,

 reference2 strategy (ref 2):theFHS is activatedduring occu-pancy periods with a fixed restart time defined by the user (scenario).Duringtheweekitisswitchedonalldayfrom6:00 am to6:00pmwitharestarttime twohours beforeoccupied periods (8 am).On Monday, the FHS is launched three hours beforeoccupiedperiods(5am)toconsidertheweek-end ther-maldischarge. Whenitison,thewatersupplytemperatureis calculatedwiththeheatingcurvetoensureanindoor tempera-tureofabout20°C.Here,theanticipativeeffectisbasedonthe experience of the manager. However, it is fixed and doesnot dependonexternalconditions.

 predictivecontroller(MPC):FHScontroliscarriedoutbyaMPC basedonoccupancyandoutdoorconditionsanticipation.Thus, anticipativeeffectisvariableandoptimized.

These strategies differ only in the way the FHS is piloted (Table2).FCUandAHUarecontrolled similarlyinallthreecases. Theyoperateduringtheweekfrom8:00amto12:00pmandfrom 1:30pmto6:00pmwithasetpointtemperatureof20°C.The con-trolisperformedbyactingonthefanspeedofFCUdependingon setpointdeviation(Eq.(9)).Whenpresenceisdetected onatleast oneofthetwosensors,theyswitchon.TheAHUworkseveryday oftheweekfrom8:00amto6:00pmandisalsosubjectto pres-encedetection(Eq.(10)).A15mintime-outinpresencedetection avoidsshort cycles.For the predictive strategy, the time step for measureddataistenminutesandthepredictionhorizonis24h. Theroleofthescheduleristodeterminetheoptimumwater sup-plytemperatureTws oftheFHS.Twsis acontinuousvariable

con-strained between20°C and 35°C (Eq.(11)). The optimalcontrol sequenceisdeterminedwithaconstraintoncomfortandcost:

 comfort:theindoortemperatureTireferringtoacomfort

tem-perature (see Part I),is constrained within a comfort interval

Icomf,thesuperiorlimitissetat23°C.Theinferiorlimitvaries

with the occupancy (19°C for occupied periods and16°C for theremainingtime),

 cost: the FHS power is calculated by Eq. (12) and integrated overtimetoobtaintheFHSenergyconsumption.

This is equivalentto minimize the following cost function on the predictionhorizon(Eq.(13)),whereJcomf isan assessmentof

comfortandJecoisacostestimation(Eq.(14)).

Tws∈[20◦C; 25◦C] (11) Pf hs=m˙Cp

(

Tws− Twr

)

(12) J= thoriz  t0 Jcom f

(

t

)

· dt+ thoriz  t0 Jeco

(

t

)

· dt (13)

⎧

⎪

⎪

⎨

⎪

⎪

⎩

Jcom f=









Ti− Tcom f ort,max



2

i f Ti≥ Tcom f ort,max



Ti− Tcom f ort,min



2

i f Ti≤ Tcom f ort,min

0 i f Ti∈Icom f

Jeco=Pf hs

(14)

3.3. Potentialestimationmethod

The overall method is summarized in the diagram in Fig. 4. Firstly, the three strategies are compared experimentally for one month measurement series. The first reference strategy was applied from 19/12/2015 to 22/01/2016 and the second from 23/01/2016to 21/02/2016.The predictivestrategy isimplemented between11/04/2016and06/05/2016.

Thereafter, strategies are simulated in the Simulink environ-ment using theMPC toolbox [16]. The 5R4C model allows simu-latingthethermalresponseofthebuildingforthethreestrategies andalso serves as internal model forMPC. The resultsare com-pared to the experimental results to ensure that the simulation modelsarereliable.

Finally,the threecontrol strategies are simulatedover a com-pleteheating season from05/10 to 29/04. The room is occupied every work day(Monday-Friday) from8:00 am to12:00 pmand from 1:30 pm to 6:00 pm. The building is unoccupied for two weeks (Christmas holidays) from 19/12 to 02/01 and one week (winter holidays) from 20/02 to 27/02. The simulations are car-ried out fromnormalized meteofiles forthree differentcities of France:Clermont-Ferrand,AgenandStrasbourg.Twoquantitiescan be compared: the unified degree-day (UDD) which reflects the harshoftheclimateandthenumberofhoursofsunshineperyear (Fig.5).Thesedataareprovidedbythenationalserviceof meteo-rologyandareaveragedover30years(1951–1980)forUDDand20 yearsforsunlight(1991–2010).Agen’sclimateisthemildestwith weakannualUDDsandhighsunshine rate.Conversely,Strasbourg climateisthe roughest withhighUDDsandlower sunshine rate. Clermont-Ferrandisanintermediary.

Control strategies are compared on the basis of energy con-sumption and comfort. The energy consumption of the FHS and FCU are calculated by integrating their respective power signals. Forcomfortevaluationtheliteraturedistinguishestwoapproaches: rational approach independent of occupant actions and adaptive approachwheretheoccupantisanactorofhiscomfortandableto carryoutactions.Itisdifficulttouseadaptivemethodstoevaluate comfortfor optimalcontrol becauseit dependson unmeasurable data.Therationalmethodcommonlyusedforpapersdealingwith optimalcontrolis thediscomfortratecalculatedfroma tempera-tureinterval.ItisusedbyGhiaus[17],Sourbron[18]andGweder et al. [19] for the control of heating floors andceilings. Thus, a discomfortratebetween19°Cand23°Cischosen duringthe oc-cupiedperiods.

Table 2

Comparison of strategies.

Fig. 4. Procedure for potential estimation of MPC control.

Fig. 5. Temperate climate compared.

Theexperimental resultsarenotdirectlycomparablesincethe external and internal conditions are different. Thus, two correc-tionsmustbemadetotheexperimentalresults.Theref1strategy servesasthebasisofcalculation:

 gainscorrection:thesumofthepowersgeneratedbythesolar contribution,occupantsandAHU isintegratedtocalculatethe contributionoffreeinternalgainsonenergybalance(Eq.(15)). Theydecreasetheenergytobeprovidedbytheheatingsystem. Thusthegaindifferencewiththeref1strategyisaddedtothe initialconsumption.

Fig. 6. (a) Degree-hours and (b) internal gains of experimental measurement series.

 correctiononclimaticconditions:heatlossesareapproximately proportional to the indoor-outdoor temperature difference. A

Fig. 7. Experimental and simulated results with on-site measurement series.

methodforcomparing climaticconditionsconsistsin calculat-ingthedegree-hours.Thisindicatorcorresponds tothesumof the deviations between the interiorsetpoint temperature and thehourlymeanoutsidetemperature(Eq.(16)).Theratioofthe degree-hourswiththeref1strategydefinesacorrectivefactor toincreaseordecreasetheheatlossesoftheothertwo strate-gies.

IG=

t



0

(

Psolar

(

t

)

+Pahu

(

t

)

+Poccupant

(

t

)

)

· dt (15)

Dh= n  h=0 Tsetpoint,h−



Tmax,h− Tmin,h 2



(16) Etot,init=L− IG (17)

⎧

⎨

⎩

Etot=L∗− IG+



IG− IGre f 1



L∗=L∗Dhre f 1 Dh L=Etot,init+IG (18)

⎧

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎩

Etot=

(

Etot,init+IG

)

∗

Dhre f 1 Dh − IGre f 1 Ef hs= Ef hs,init E_tot,init ∗ Etot Ef cu= Ef cu,init

Etot,init ∗ Etot

(19)

Theenergyneedisequaltotheheat lossesLminusfreegains (Eq.(17)).Thecorrectionontheclimaticconditionsallows to cal-culate a corrected heat loss L∗. The gain correction is done by addingthegaindifferencewithref1(Eq.(18)).Thecorrected en-ergyconsumption,denotedEtot,isthereforedeterminedbythe

Fig. 8. Behavior of ref 1, ref 2 and MPC strategies for a typical cold week.

(E_fcu)are thesameafterthecorrection. Thedegree-hoursand in-ternalgainsvaluesarepresentedinFig.6.

4. Resultsandanalysis

The experimental results highlight the behavior of the three controllers.

 ref 1: the energy consumption over the studied period is 848kWh.Thisstrategyhastheworstcomfortindicator(13.5%). The discomfortmostlyoccursduringthe restartperiod inthe morning.Thetemperatureof20°Cisreachedonlyinthe mid-dle or at the end of the morning (arrow 1). The FCU are stronglyused(81%)comparedtotheFHS(19%)whichoperates asbasicheating(arrows2),

 ref 2:the corrected energyconsumption overthe studied pe-riod is 1300kWh. The fixed restart time penalize the energy consumption indicator butlogicallyallows a relative improve-mentincomfort(3.5%)belowthesymbolicvalueof10%mainly usedin eco-labels.Thisstrategyignores the weather forecasts butthefixedanticipation of2hmakes itpossibletoreachthe comfort quickly in the morning (arrow 3). The FHS is much moresolicited sinceitrepresents71%ofconsumptionandthe useofFCUisthereforeless(arrows4),

 MPC:the corrected energy consumption over the studied pe-riod is 1137kWh. The predictive controller makes maximum useoftheFHS(82%).Theoptimalstrategyistothermallyload

thefloorslabupstreamoftheoccupiedperiod(arrow5).Then theinertiaofthefloorslaballowsaslowdecreasein tempera-tureandtheFCUareswitchedononlyatthebeginningofthe occupation period(arrows 6).The predictive strategy allowsa high level of comfort (1.1%) fora moderate energy consump-tion. Itislower thanref 2butgreaterthan ref1(thanksto a degraded comfort).Thisresultisconsistentwiththepredictive control philosophy of making acompromise betweencomfort andenergyconsumption.

Theexperimentalsequences aresimulatedby insertingthe in-putdata(weather,occupancy,gains)intoMatlab/Simulink environ-ment.The results are also givenin Fig.7. The ref1 controller is wellsimulatedsincethedeviationsaresmallforallthecompared values.Aslightover-useofFCU(88%)isobservedcomparedtothe experiment(81%),whichjustifiesthedifferenceof14%onthetotal energyconsumption anda slightly lower discomfort rate. Never-theless, it is complicated to obtain better resultsthat are linked to the uncertainties of the 5R4C model of Part I.The calculated discomfort rates are also similar since the evolutions of interior temperature are close. The ref 2 controller has more differences betweentheexperimentalandsimulationresults.Thereisalsoan overconsumptionofthe FCUinsimulation(46%versus 29%).This maybe dueto the delaybetweenaction andmeasurement with thesensorinexperimentationwhileinsimulationtheeffectis in-stantaneous.Inaddition,theFCUmanualremotecontrolmayhave been modifiedby students (no locking possible) andcreates

un-Fig. 9. Behavior of ref 1, ref 2 and MPC strategies for a typical mid-season week.

certaintyontherealuselevelofFCU.Thisseemstobe confirmed by the observed deviations inthe FCU power signals. In the ex-periments, theFCUare lessusedincomparisonwiththe simula-tion.However, the resultsforthiscontrollerare correctsincethe temperaturevariationsremainsimilar.The predictivecontrolleris correctly simulated (1130kWh compared to 1137kWh) since the optimalexperimental control sequenceis verycloseto the simu-latedone.Itisthereforeconsistentthattemperatureevolutionsare close.Thesimulationmodelsareconsideredreliabledespite devia-tionsduetomodelingerrorsandrelativeuncertaintyintheuseof FCU.Indeed,thetrendsarethesameforthethreestrategies:

 ref1:poorcomfort,lowconsumptionbutstronguseofFCU,  ref2:goodcomfort, highconsumption,shareduseofboth

sys-tems,

 MPC:goodcomfort, intermediateconsumptionandhighuseof FHS (comfortfeeling improvedby low airvelocitiescompared toFCU).

These strategies are used to obtain results over a complete heatingseason with threeclimates. Fig. 8and Fig.9 presentthe behavior of each controller, respectively on a representative cold week (January) andmid-season week (November).For thesetwo weeks,fivegraphsareplotted:indoortemperatureevolution,FHS andFCUpowersignal,forecastofoutdoortemperatureandgains, and energy/comfortindicators.For thecold week, the ref 1 con-troller has ahighlevel ofdiscomfort (22%).Insufficient powerof theFHSandthedelayedeffectofFCUleadstodiscomforthoursat thebeginningoftheday(arrow1).FCUareheavilysolicitedwitha ratioof88%.Theref2controllertendstooverheatthebuilding (ar-row2)which logicallyincreasesthe energyneed butreducesthe rateofdiscomfort(2%).Inthiscase,theFHShasautilizationrate of87%. The predictivecontroller achievesthebest energy perfor-mance. Forthisweek,thegain ofthepredictivecontroller is43% and24% respectivelycomparedto theref1 andref 2controllers. The energy consumption is thus lower for an improved comfort (ref 1) orequivalent(ref 2).This energygain isexplained bythe anticipationofheatgains(solar,occupant).Thegraphofpower de-manddemonstratesthat theFHSstartsatthesametime between thepredictivecontrollerandref2(arrow3).However,the predic-tive controller has a higher peak demand on the FHS (arrow 4) andisturnedoff atmid-morning(arrow5)inanticipationofsolar contributionsinparticular.Theref2controlleranticipatesonlythe restart timebutnot theexternal conditions.Theoptimalstrategy ofpredictive controllercouldpermit torefine theref2controller withanimportantloadonlyinthemorning.

In the mid-season the temperatures are milder andthe ref 1 controller onlyuses FCUsince thewatersupply temperature cal-culatedfromthe outsidetemperatureis low.Like thecold week, ahigherlevelofdiscomfortthanwiththeotherstrategies(7%)is observed witha comfort temperaturereached during the morn-ing.Theref2controllerreducesthediscomfortrateto3%,butthe energyconsumptionremains higherthantheref1controller.The predictivecontrollersavesenergyandimprovessignificantcomfort byactivatingthreelevers:

 when the nights are still cold, the behavior is similar to the coldweek, that istherestart isdoneatthe sametime asthe ref2 strategy 2(2hbefore) butin a shorterandintense way (arrows6),

 whenthetemperaturesaremilder,therestartisdonelater (ar-rows7),

 whenthetemperaturesaremildandimportantgainsare fore-casted,theFHSisnotused(arrows8).

Forthismid-seasonweek, thegainofthepredictivecontroller is53% and65% respectivelycomparedtotheref1andref2 con-trollers.

TheMPCallowsasignificantimprovementonbothaspects: en-ergyandcomfort. Theaimofconductingsimulationsovera com-pleteheatingseasonistoseewhentheenergysavingsarerealized. For this purpose, a monthly average of the energy consumption (for the three climates) is established. The monthly relative en-ergygainsoftheMPCcomparedtothereferencestrategiesis cal-culated(Fig. 10(a)).It appears thatthe predictive strategyalways offers the best results in particular in October, March and April. Theefficiencyofthepredictivecontrol inthemid-seasonis high-lighted. On the October-November and March-April periods, the relativegainishigher(45%onaverage)thanthatduringthe cold-estmonthsinwinter(December-February)withanaveragegainof 25%.Theabsolutegainisrelatively constantthroughoutthe heat-ingseason (Fig.10(b)).In winter,the interestisall thegreateras thetemperatures are low (January).Over the whole heating sea-son(October-April),60%oftheeconomyisdoneinthemid-season and40% during winter.Differences in climatic conditions donot leadtosignificantchangesintheanalysisofthethreestrategiesin termsofconsumption,comfortorutilizationratio.Theoverall en-ergysaving(averageversusref1andref2)is41%forAgen,39%for Clermont-Ferrandand37%forStrasbourg.Theusefulnessof predic-tivecontrolintemperateclimateisthereforeproved.

5. Conclusionandoutlines

Thethreecontrollerspresentedwerefirstcomparedforthe ex-perimentalbuildingoverperiodsofonemonthandthensimulated overa heatingseason.After theclimatic correction,the compari-son wasmade fromthree indicators: energyconsumption of the twosystems,utilizationratioanddiscomfortrate:

 through complete heating season for three climates.The pre-dictivecontrollerdemonstratesthebestperformanceonthe in-dicatorswithanequivalentorimprovedcomfortsituation,the energyconsumptioncanbereducedby30%to40%,

 themonthlydistributionofenergysavingsshowsagreater rel-ativegaininthemid-season(45%)comparedtothetwo refer-encecontrollers,itis25%onaverageoverthewintermonths,  theabsolutegainisallthegreaterastheclimateistemperate.

The conclusions presented for MPC are only permitted under three essential conditions. The first one is to have a low-order model that reproduces the dynamic response of the building to controllableanduncontrollableinputs.Thesecondoneisto prop-erly set-up the optimization procedure with the cost function, theprediction andcontrolhorizon. The last one requiresto have knowledgeaboutfuture indoor andoutdoorconditionswith reli-ableforecasts.

Thisworkthereforeprovidesanewdemonstrationfora partic-ularcaseofthepotential forenergysavingsachievableby predic-tivecontrol.Nevertheless,itisnecessarytorelativizethevalueof thegains forthe predictive controllersince these resultsare ob-tainedfor a givenbuilding butcompared withclassical manage-mentstrategies.It wouldbe interesting todetermine ifitis pos-sible,thanks to thepredictive control, to dispense withauxiliary heating systems and evaluate the associated impact on comfort. Indeed,the resultsindicate that comfort is slightly degraded for agreatlyimprovedenergymanagement.Thisworkhighlightsthat MPC maximizes the use of the FHS and limits the on/off cycles ofthe FCU reducing thewear andtear. Itcould be accompanied byan economic studytoevaluate areturnon investmentperiod. Privara et al.[5] estimated this duration to be two years. It has beenshownthat severalcontrolstrategiescanpresentan accept-ablelevelofcomfortbutaverydifferentenergyconsumptionfrom singletodouble.Althoughimprovingthethermalpropertiesofthe enveloperemainsthemosteffectivewaytoreduce energybills,it

ispossible to achieve significant savings without envelope refur-bishmentsorchangingthesystem.Itisthusaninterestingmeans ofactioninadditionto thepanel ofexistingsolutions forenergy efficiency.

In ordertocompletethiswork, itwouldberelevant to repro-ducethisstudyforawholerangeofperformance,fromold build-ings(before the first thermalregulation) to contemporary build-ings.Thus,itwouldbepossibletoquantifyapotentialatthe dis-trictscale. Predictive control could also be deployedon a neigh-borhoodscaleforpowerpeakreduction.Thepresentedpredictive controltechniqueisflexibleandcantakeintoaccountother crite-riadependingon themodelandthewritingofthecost function. Indeed,it ispossible to integrate other physicalequations inthe internal model of MPC (economic, acoustic or physiological con-straintsforexample). Finally,thepotential of sucha controller is notlimitedtotheframework oftheseworkssinceits application ismulti-scale,multifunctionandmulticriteria.

Acknowledgments

This work was carried out in the context of the PRECCISION project“PREdiction and IntelligentControl Command by SImula-tionandNumericalOptimization” (2013–2016)andfundedbythe French National Agency of Research. The authors would like to thank Deltadore and Vesta-System companies for technical sup-port.

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