Testing and demonstration of model predictive control applied to a radiant slab cooling system in a building test facility

Lawrence Berkeley National Laboratory

Recent Work

Title

Testing and demonstration of model predictive control applied to a radiant slab cooling

system in a building test facility

Permalink

https://escholarship.org/uc/item/0sq1h8hw

Authors

Pang, X

Duarte, C

Haves, P

et al.

Publication Date

2018-08-01

DOI

10.1016/j.enbuild.2018.05.013

Peer reviewed

eScholarship.org

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Testing

and

demonstration

of

model

predictive

control

applied

to

a

radiant

slab

cooling

system

in

a

building

test

facility

Xiufeng Pang

a,∗

_{, Carlos Duarte}

b

_{, Philip Haves}

a

_{, Frank Chuang}

c

a Lawrence Berkeley National Laboratory, One Cyclotron Road, MS 90R3147, Berkeley, CA 94720, USA b University of California-Berkeley, Berkeley, CA 94720, USA

c Tesla, Inc., Palo Alto, CA 94304, USA

a

b

s

t

r

a

c

t

Radiantslabsystemshavethe potentialtosignificantlyreduceenergyconsumptioninbuildings. How-ever,control ofradiantslabsystemsischallenging.Classicalfeedbackcontrolisinadequateduetothe large thermalinertiaofthesystemsandheuristicfeed-forwardcontrol oftenleadstounacceptable in-doorcomfortand maynotachievethefull energysavingspotential.Modelpredictivecontrol(MPC)is nowattractingincreasinginterestinthebuildingindustryandholdspromiseforradiantsystems. How-ever,anoften-citedbarriertoitsimplementationinthebuildingindustryisthehighcomputationalcost and complexity relative tothe feedback controlsused inconventional systems. Theobjectives ofthis study wereto(i) verifythe correctoperationofan opensourceMPCtoolchain developedfor radiant slabsystems,and(ii)demonstrateitsefficacyinatestfacility.AmatchedpairofcellsintheFLEXLAB buildingtestfacilityattheLawrenceBerkeleyNationalLaboratorywasusedinthestudy.Theproposed MPCtoolchainwas implementedinone celland theperformance comparedtothatofthe othercell, whichused aconventionalheuristic control strategy.Theresults showed thatthe simplifiedMPC ap-proachappliedinthetoolchainworkedasexpectedandrealized energysavings overtheconventional control strategy.The MPCyielded42% chilled water pump power reductionand 16% cooling thermal energysavings,whilemaintainingequalorbetterindoorcomfort.

1. Introduction

Heating, ventilation, andair conditioning (HVAC) systems ac-countfor about44%ofthe totalenergyuse inU.S. buildings[1]. Theenergyconsumption ofHVACsystemshasbeen showntobe sensitivetothequalityofthecontrol;enhancedcontrol strategies canyieldsavingsof2%−16%[2]whileincorrectcontrolandother control-relatedfaultscanincreaseconsumptionby_∼10%.1

Most HVAC systems found in buildings constructed after the 1980s use forcedair systems, typically variable-air-volume (VAV) distributionsystems [5]in NorthAmerica. Forcedairsystems, or all-airsystems,aredesignedtoprovideanindoorairheatbalance to maintainoccupant thermal comfort. Theseall-air systems can respondrelativelyquicklytochangesinzoneairtemperaturesdue tothelow thermalinertiaoftheairinthe occupiedspace.Thus,

∗ _{Corresponding author.}

E-mail address: [email protected] (X. Pang).

conventional feedback controllers are generally adequate for this typeofapplication.

Radiant heating and cooling systems meet 50% or more of the thermal loadin the occupied space through long-wave radi-ant exchange.Radiant systems offer severaladvantagesover typ-ical all-air HVACsystems, enablingthem to reduce HVACenergy consumption whilemaintainingequal orbetteroccupant thermal comfort[6].Asaresult,radiantsystemsarefindingincreasing ap-plication inhighperformance buildings[7],withoverhalf ofthe zeronetenergybuildingsinNorthAmericausingradiantsystems

[8].Thiscurrentstudyisfocusedonhydronicradiantslabcooling systems,alsocalledthermallyactivatedbuildingsystems[9].These systemsusetubesembeddedintheslabtocirculatechilledwater throughtheslabanduserelativelylargeareas,typicallythewhole floor, ceiling, or both surfaces,for heat exchange, thereby reduc-ingthetemperaturedifferencebetweenthechilledwaterandthe occupiedspace[9].Theadvantagesare:

• improvedheattransportefficiencyfromtheuseofwaterrather thanair,

1 A meta-study of commissioning identified 16% median actual savings from retro-commissioning [3], and a study of 481 operational issues identified in exist- ing commercial buildings found that control problems accounted for > 75% of the causes of energy waste [4].

• higherchilledwatersupplytemperaturesthan areusedin all-airsystems,enablinggreateruseofwater-sidefreecooling[10], and

• the ability to control the building’s thermal mass for energy storage[11,12].

However,radiantslabsystemsarechallengingtocontroldueto their large thermalinertia. The time taken to respondto control signals is typically several hours or more [13], making feedback controlofzonetemperatureinfeasible.Anyattempttoswitchover quicklyfromheatingtocoolingorviceversawillresultinwasted energy [14] andit is recommended that switchovertime should be greater than24 h[15,16].The problem, incooling mode,now becomesmanagingtheheatextractionratewhileconsideringthe building’sthermal masswithin asingledayto avoidboth under-and over-cooling of the space during occupied hours. Although there is no clear consensus on a common control strategy, cur-rentcontrolmethodsforradiantslabsystemstypicallyuse heuris-tic feed-forward control, in which the supply watertemperature orflowrateisbasedonambientwet-bulbtemperature,occupancy schedulesorutilitytariffs[17–19],orsomecombinationthereof,to maintainarelativelyconstantslabtemperatureforallhoursofthe day.Theadvantageofthiscontrolstrategyisthatthepeakcooling capacityoftheplantsystemcanbereducedsincetheheat extrac-tionrateisspreadover24hbutitmaynotallowforactivecontrol ofthe thermalstorageintheslab.Controlofthethermalstorage inthe slabenablesload shifting,inwhichthe loadprofileofthe HVACsystemis manipulatedforthe buildingstakeholders’ bene-fit.TheoperationoftheHVACsystemcanbeshiftedtonighttime hourswherefavorableweatherconditionsandelectricityprices ex-ist [20].TheabilityoftheHVACsystemtoshiftloadalsoenables a large fraction ofthe loadof thebuilding to participatein util-itydemandresponseprograms,whichaimtostabilizepowergrids

[21].

The radiantslab research communityhasbeen actively devel-opingcontrolstrategies,withtheaimofexploitingtheadvantages ofradiantslabcoolingsystemsdiscussedabove.Amajorefforthas beenundertakeninmodelpredictivecontrol(MPC)[19,22].Model predictive control (MPC) is an advanced control method that is now attracting increasing interest in the buildings industry [23– 25].MPCcanuseforecastsofweather[26],occupancy,andenergy price signals[27,12,28]to manage thermal energystorage,e.g. in radiantslabs,toimproveoccupantthermalcomfortandreduce en-ergyconsumptionandcosts[12,23].InMPC,anoptimization prob-lem is solved on-line to obtain the current control action [29]. MPC returns a sequence of optimalcontrol actions basedon the currentstateanddynamicmodeloftheplant,systemconstraints, andminimization ofa cost function; onlythe firstcontrol action of thesequence isapplied andthe procedureis repeatedat pre-determinedintervals. Anoftencitedbarriertoitsimplementation in the buildingindustry is its highcomputational cost and com-plexity. In this study, it was shown that with the proper model structure, the modelcan be identified andis accurate enough to implementrealtime controlandrealizeenergysavingsover con-ventionalcontrollersandtheprocesscanbesimplifiedthroughthe useofanopensourceMPCtoolchain.

The main contributions of this experimental study are the demonstration of aMPC model structure forradiantslab cooling systemsthatcan beeasilyidentified,robust,andaccurateenough tobeusedforreal-timecontrolandthedirectcomparisonofMPC toheuristic controlbasedona fixedoperationalscheduleusinga matchedpairoftestcells.

The rest of the paperis organized asfollows. Section 2.1 de-scribes the MPC controller used in this study with more detail.

Sections 2.2–2.4 describes the test facility, measurement instru-mentation, and experimental setup used to carry out thisstudy.

Sections3and4givesthe experimentresultsandconcluding re-marks,respectively.

2. Methodology

2.1. MPCcontroller

TheMPC controllerhas thegoal ofdetermininga binary con-troloutput(ON/OFF)oftheradiantslabsystemthatminimizesthe weightedcombinationofcomfortviolationsandenergy consump-tionoverapredictionhorizonofNtimesteps.Thecontrolproblem isdefinedinEq.(1)[31]. min c_k,h_k t+N  k=t



ρ

max

{

x_{z,k− x}max,k,0,xmin,k− xz,k

}

+ck+hk



sub jecttoxk+1 =



_A coolxk+Wcooldk i fck=1,hk=0 Aheatxk+Wheatdk i fck=0,hk=1 Acoastxk+Wcoastdk i fck=0,hk=0

∀

k∈

{

t,...,t+N− 1

}

(1)

wherex_k=[x_slab,k x_z,k] andd_k=[d_sol,k d_oat,k d_hg,k] are the state anddisturbance vectors, respectively, xslab,k is slab temper-ature [°C], xz,k is zone operativetemperature [°C], dsol,k is solar irradiance[W/m2_],d

oat,kisoutdoordry-bulbairtemperature[°C],

dhg,kis the sumofthe heatgains fromthe lights, miscellaneous loadsandoccupants[W],xmax,kandxmin,karethemaximumand minimumboundsforthezone operativetemperature[°C],c_kand

hkareindicatorvariablesforthecoldandhotwatervalves, respec-tively,and

ρ

istheweighttoadjustbetweencomfortsatisfaction andenergyconsumption.Thesubscripttindicatestheactualtime whentheoptimizationtakesplacewhilekindicatesthefuture pre-dictionsbeyondtimet.

Theoptimizationproblemin(1)canbeequivalentlyformulated asamixed-integer linearprogram;thestepsare describedbriefly below.Thereaderisreferred toBorrellietal.[32] foramore in-depth discussion of MPC and hybrid system modeling. The tem-peratureviolationcostin(1)isformulatedasamaximumofthree linearpieces.Thiscost termis transformedintoa linearprogram bymeans ofslackvariables.At eachtime step,aslack variableis introducedandsetgreaterthanorequaltothethreelinearpieces atthattimestep.Thetemperatureviolationcostthenbecomesthe sumoftheslackvariables.Next,theswitchedsystemdynamicscan beformulatedinsimplifiedformasfollowsforeachtimestepk.

xk+1=z1+z2+Acoastxk+Wcoastdk (2a)

z1=



Acoolxk+Wcooldk− Acoastxk− Wcoastdk i f ck=1

0 i f ck=0 (2b)

z2=



Aheatxk+Wheatdk− Acoastxk− Wcoastdk i f hk=1

0 i f hk=0

(2c)

ck+hk≤ 1 (2d)

The remaining switched dynamics are then reformulated as mixed-integerlinearconstraintsasfollows.

−M1ck+z1≤ Acoolxk+Wcooldk− Acoastxk− Wcoastdk (3a)

m1ck− z1≤ −Acoolxk− Wcooldk+Acoastxk+Wcoastdk (3b)

m1

(

1− ck

)

+z1≤ 0 (3c)

Model Idenficaon HDF5 Finite-Horizon Opmizaon HDF5 Radiant systems Time series data

System model Control inputs

System states & disturbances

Fig. 1. System diagram of the MPC toolchain.

−M2hk+z2≤ Aheatxk+Wheatdk− Acoastxk− Wcoastdk (3e)

m2hk− z2≤ −Aheatxk− Wheatdk+Acoastxk+Wcoastdk (3f)

m2

(

1− hk

)

+z2≤ 0 (3g)

−M2

(

1− hk

)

− z2≤ 0 (3h)

where

M1=max

(

Acoolxk− Wcooldk− Acoastxk+Wcoastdk

)

m1=min

(

Acoolxk− Wcooldk− Acoastxk+Wcoastdk

)

M2=max

(

Aheatxk− Wheatdk− Acoastxk+Wcoastdk

)

m2=min

(

Aheatxk− Wheatdk− Acoastxk+Wcoastdk

)

.

This issometimes referred toasthe big-Mformulationofthe switchedaffinesystem.

InFengetal[30],asimilarMPCformulationwasimplemented inMATLAB. The modeling language YALMIP wasused to formu-latethe mixed-integer linearprogram andthe commercialsolver Gurobi was used to solve the problem. Unfortunately, the soft-waretoolchainwasaccessibleonlytouserswithacademicorpaid commercial licenses. In order to make the software more freely available andtransparent to users, it wasdecided to rewrite the toolchainusingonlyopen-sourcedsoftware.

In the current implementation,Julia has replaced MATLAB as theprogramminglanguage whileCOIN–ORBranch andCut(CBC) hasreplacedGurobiasthemixed-integersolver.Juliaoffersan op-timizationmodelinglanguage,namedJuMP,aspartofits optimiza-tionpackageJuliaOpt.JuliaOptalsoincludesthenecessarymodules tointerfacewiththird-partysolverssuchasCBC.Theoptimization problemwasmodeledusingJuMPbutreformulatedusingthe big-Mmethodtoexpresstheswitched-systemdynamics(thiswas un-necessary inYALMIP since YALMIP allowed for logical constraint switching).The JuMPformulationisthenpassedtoCBCusingthe JuliaOptinterface. CBC, whileslowerthanGurobiforlarger prob-lems,solvestheprobleminreasonabletimegiventhecontrol sam-plinginterval(1hour).Allsystemdynamicsandoptimization solu-tiondataaresavedusingtheHDF5dataformat.HDF5isafastand space-efficientwaytostoreandtransferdataandhasinterfacesfor mostpopularlanguage,suchasPython,MATLAB,JuliaandC/C++. Thisensures that there is a reliable way forcross-platform soft-waretoaccesstheinformationgeneratedbytheJuliacode.

TheMPCtoolchainconsistsoftwomainmodules,model identi-ficationandcontroloptimization.Thesystemdiagramisshownin

Fig.1.Themodelidentificationmodulereceivestime-seriessystem responsedatafromtheradiantslab systemconcerned to identify asimplified,switched-systemmodel.The modulesolves a nonlin-earleastsquaresoptimizationproblemtofitthemodelparameters

Acool,Aheat,Acoast, Wcool, Wheat andWcoast to the data. The model

parametersare savedinHDF5fileformat tobeaccessedby other modules.

Thefinite-horizonoptimizationmodulereadsthesystemmodel parameters from the HDF5 file as well as the current system statevariablesanddisturbancespassedinfromtheradiantsystem concerned as function arguments. The optimization module then solvestheenergycostminimizationproblemdefinedinEq.(1)to arriveatthecontrolinputstotheradiantsystemconcernedto ap-plyatthecurrenttime.ThecontrolinputsarealsostoredinHDF5 formatforlateraccess.

2.2. Testfacility

The experiments were carried out inthe Facility forLow En-ergy eXperiments (FLEXLAB [33]) at the Lawrence Berkeley Na-tionalLaboratory(LBNL).FLEXLABhasfourtestbeds,asshownin

Fig.2,andeachtestbedconsistsoftwoside-by-sidecellswiththe samedimensionsandconstruction.Thethermalisolationresulting fromthenearadiabatic wallsbetweenadjacentcellsallowstheir performance to be analyzed independently. The test bedused in thisstudyconsistsofapairofmatchedcells(1Aand1B,shownin

Fig.2),eachis9.14m× 6.09m× 4.88mwithafloorareaof56m2

and hasPEX tubing embedded in a dense concrete topping slab 100mm thick. The two cellssharea chiller andboiler plantand eachcell hasdedicated secondaryloopsforchilledwaterandhot waterasshowninFig.3.Thesecondarychilledwaterandhot wa-tersupplytemperaturecanbemaintainedatdesiredsetpointsby mixingthesupplyandreturnwaterusingathree-waymodulating valve.Thewatertemperaturesandflowratesofboth theprimary andsecondaryloopsweremeasured.Theconventionalcontrol sce-nariowasimplementedinCell1AandtheMPCwasimplemented inCell1BInthisstudy,thefocuswasonthecoolingperformance. Theradiantslab systeminside thecell isshowninFig.4.Hot waterorchilled waterisselectedusing automatedcontrol valves withmanualoverrides.Theradiantslabsystemisdividedintofour sub-systems,eachcontainingmultiplecircuitsofPEXtubing, serv-ingfloorareasof19.5m2_,9.6m2_,5.8m2_and21.1m2_{,respectively.}

The nominaldiameterof thetubing is15.9mm, andthe internal diameteris12.7mm,withatubespacingof0.23moncenter.

Single-paneclearwindowsareusedonthesouthfaçadesofthe two cells and the window area is 10.76 m2 _{(5.88m (L)× 1.83m}

(H)).

In orderto simulate a typical office,workspaces consistingof thermalmanikins,desksandpartitionsweresetup,togetherwith artificiallights,asshowninFig.5.Themanikinswerewoundwith heating tape and the supply voltage adjusted to produce sensi-ble heat dissipation rates of _∼80 W each, corresponding to the metabolic rateofsedentaryofficeworkers inalow humidity en-vironment. The advantage of the thermal manikins is that their radiative/convectivesplits,andthecharacteristicsoftheirthermal plumes, are more realistic than the heatedcylinders specified in theEuropeanStandardE14240.Thetotaloverheadlightingpower is∼180Wineachcell.Pingpongballsensorswereusedto mea-suretheoperativetemperatureinbothcells.

2.3. Instrumentation

FLEXLABiswellinstrumentedwithresearch-gradesensorsand meters. The most relevant measurements in the experiments re-portedherearelistedinTable1.

Theroom operativetemperaturewasapproximatedby the av-erage ofthe readings of three grey-painted ping-pong ball globe thermometers, as shown in Fig. 5. Humphreys reported that for lowairvelocity(<0.15m/s),a40mmdiameterglobehasradiative andconvective lossesinthe sameratio asthehuman body [34]. The three ping-pong ball sensors were placed on desks nearthe

Fig. 2. General view of the test facility.

Fig. 3. Schematic diagram of the chilled and hot water plant.

Table 1

Measurements in the experiment along with the accuracy ratings.

Measurement Accuracy

Room operative temperature ±0.2 K

Radiant slab water flow rate ±1%

Radiant slab chilled water supply and return temperature ±0.1 K

Slab temperature ±0.1 K

Global horizontal irradiance ±5% or ±10 W/m 2

Circulation pump power ±2% of reading

Total lighting power ±1% of reading

Total manikin power ±1% of reading

window, inthe middleofthecell andattheback ofthe cell re-spectively.

Theslabtemperaturesweremeasuredbythreeimmersion-type sensors installedin thermowellsthat are about13mmbelowthe

surface, along the cell’s North-South center line.The sensors are at1.8m, 4.6m and 7.6m from the southwall (the window) and arepositionedhalfwaybetweenadjacenttubes.Theaverageofthe readingsfromthesethreesensorswasusedtorepresentthe tem-peratureoftheslab.

2.4.Experiment 2.4.1. Preparation

Thesevencircuits ofthe radiantslabsystemineachcellwere balancedtoensureanevendistributionofwaterflowrateineach circuit. The secondary chilled waterpump speeds were adjusted tosupply26.5lpmofwatertoeachradiantslabsystemandeach circuithada flowrateof 3.8lpm.Thechilled watersupply tem-peraturewasfixedat11°C.

Fig. 4. Radiant slab manifold system diagram.

Fig. 5. Test cell setup.

The manikinsandlightsofboth cellswerecontrolled by digi-talplug-intimersandprogrammedto beonfrom8amto 6pm. The average internal load in Cell 1A was 571.7W (391.5W from manikinsand180.2Wfromlights)and600.7WinCell1B(424.8W frommanikinsand175.9Wfromlights).Theinternalheatgain in 1B(runningtheMPC)was∼5%greaterthantheinternalheatgain in1A.

FLEXLAB uses a customized control systemthat hasa Python interfacetoexecutecontrolcommandsandaccessitsdatabase.The SimpleMeasuringandActuationProfile(sMAP)[35] developedat the University of California, Berkeley, is used for data archiving. Allautomated control deviceshad beentestedandcalibrated for properoperation.

2.4.2. ValidationofMPCtoolchain

Validation oftheMPC toolchain involvedtestingofthe model identificationmoduleandthefinite-horizon optimizationmodule, shownin Fig. 1. The computer that ran the MPC toolchain used 64-bitUbuntu 16.04 asthe operating system andhad an i7-860 2.80GHzquadcoreprocessor.

The process used to validate the model identification module is shown in Fig. 6. A Python script was developed to execute step-tests of the radiant system in Cell 1B to produce time se-ries data formodel identification.The data were storedin sMAP andthenexported manuallyto acsvfile,whichwasthenpassed to the model identificationmodule where the model parameters wereidentifiedandsavedinHDF5fileformat.Lastly,theidentified modeltookinputsfromthetimeseriesdataandcomputed predic-tions. The modelidentification module is considered validatedif themodelparametersaresuccessfullyidentifiedandtheresulting modelcanpredicttheradiantsystemperformancereasonablywell andmeet the following criteria: a Coefficient ofVariation of the Root-Mean-SquareError(CV[RMSE])<10%andaNormalizedMean BiasError(NMBE)_<5%[36].

CV

(

RMSE

)

=



_ n i=1

(

yi− ˆyi

)

2 n−1 ¯y (4) NMBE= n i=1

yi− ˆyi

(

n− 1

)

× ¯y (5)

Start experiment Step tests Cell 1B sMAP Model idenficaon Model parameters idenfied? Validaon fails No Yes Model predicon Predicon vs. measurement Meet criteria? Validaon fails No Yes Validate successfully

Fig. 6. Procedure for testing and validating the model identification module.

where,

yi=measuredhourlydata, ˆ

yi=modelpredictedhourlydata, ¯y₌averagemeasureddata,

n=numberofdatapoints.

Oncethemodelidentificationmodulehadbeenvalidated, val-idation of the finite-horizon optimization module followed, as showninFig.7.Radiantslabradiantsystemshavelargetime con-stants, with the response time of the surface temperature to a control input being several hours [14]. In this study, the control horizon, N, hadbeen empirically set to 12 h, andthe optimiza-tion problemrun every hour, using a time-step of one hour. At each time step,onlythe controlatthe currenttimewasapplied. New valuesofthestate variablesanddisturbances weresampled ateachtime-stepandthecyclerepeated.

The outsideair temperatureandsky coverforecast data were obtainedfromtheU.S.NationalWeatherServicewebsite[37].The

Fig. 7. Procedure for testing and validating the optimization module.

forecastglobalhorizontalirradiancevalueson each daywere de-termined using historical data measured at FLEXLAB on a daya yearpreviouslyforwhichtheforecastskycoverprofilewasclosely similar.Forexample,theforecastofglobalhorizontalirradianceon Oct11th,2017consistedofhourlydatameasuredonOct6th,2016, theskycoverprofileonOct6th,2016 beingcloselysimilartothe forecastskycoveronOct11th,2017.

APythonscriptwasdevelopedtoobtainthestatevariables,i.e. theslabtemperatureandthezoneoperativetemperature,andthe disturbances,i.e.thesolarirradiance,theoutdoorairtemperature andtheinternalheatgains,fromtheFLEXLABdataacquisition sys-temand pass them tothe finite-horizon optimizationmodule at eachtime step.Usingtheidentifiedmodelparameters, the finite-horizonoptimizationmodulesolvestheoptimizationproblem de-finedinEq.(1).The finite-horizonoptimizationmoduleis consid-eredvalidatedifasolutionispresentedandthecomputingtimeis lessthanthetimestep.

2.4.3. MPCvs.heuristiccontrolcomparison

After the MPC toolchain was validated, its effectiveness was evaluatedbycomparingitsperformancetothatofaheuristic con-trol strategy that turns the radiant slab system on three hours prior to occupancy and turns it off one hour before occupancy ends.Atypicalofficebuildingoccupancyscheduleof8:00to18:00 wasusedandtheinternalloads(themanikinsandthelights)were enabled/disabled on the same schedule. Soft constraints and no hardconstraintswereimposedontheoperativetemperature.xmax

andxmin were set to 26°C and19°C, respectively, forhours

be-tween7:00 and17:00and47°Cand10°Cforallother hours.No constraints were imposed on the slab temperature but some

is-Fig. 8. Internal conditions in the “free response” mode.

Fig. 9. Internal conditions in the “radiant slab activated” mode.

suesto considerin practiceare condensationon theslab surface andthermaldiscomfort that mayarise fromthe closecontact of occupant’sfeetwithacoldsurface. Variousvaluesofthevariable

ρ

were tested anda value of100 was found to yield a reason-abletrade-off between energyuseandthermal discomfort,based onengineering judgment. Pythonscripts were developedto read thecontrol signalsfromtheHDF5file, sendthemtotheFLEXLAB andreturnthesystemoutputstotheoptimizationblock.

Before theMPCvs. heuristiccontrol experiment, itwas neces-sarytocompareCell1AandCell1Binthe“freeresponse” andthe “radiantslabactivated” modesside by side toassesshow closely thetwocellsmatchedeachotherandensurethetwocellsstartoff atthe similar initial conditions for the MPC vs. heuristic control experiment. In the“free response” mode, there is no mechanical coolingorheatingand thechanges inthe interiorconditionsare theresultsoftheweatherandinternalgaindisturbances,whereas inthe “radiantslab activated” mode, the radiantslab systems in both cells are activated with the chilled water flow rate at 26.5 lpmandthechilledwatertemperatureat∼11°C.

The“free response” experimenttookplaceduringSep23– 25, 2017,andthe“radiantslabactivated” experimenttookplaceduring Sep27– 29,2017.TheresultswereshowninFigs.8and9 respec-tively.In the“free response” experiment,Cell1A startedoff with theoperativetemperatureat31.86°Candtheslabtemperatureat 29.35°C,andCell1Bstartedoff withtheoperativetemperatureat 29.94°Candtheslabtemperatureat26.82°C,atnoon.The differ-encesbetweentheinitialoperativetemperaturesandbetweenthe slabtemperatureswere1.92Kand2.53Krespectively.Inthe “radi-antslabactivated” experiment,Cell1Astartedoff withthe

opera-Fig. 10. “Radiant slab activated” model identification and validation.

tive temperatureat37.19°C andtheslabtemperatureat32.80°C, andCell1Bstartedoff with theoperativetemperatureat34.42°C andtheslabtemperatureat28.62°C.Thedifferencesbetweenthe initial operative temperatures andbetween the slab temperature were2.77Kand4.18K,respectively.Ittookabout42hforthe“free response” and36hforthe“radiantslabactivated” toreachstatic states.As can beseen fromFigs. 8and9, thetwo cellsmatched each other well in both the“free response” modeand the “radi-antslab activated” mode.The average differenceof theoperative temperatures was0.11K andof the slabtemperatures was0.19K inthe“freeresponse” modeand0.16Kand0.03K,respectively,in the“radiantslabactivated” mode.

3. Resultsanddiscussions

3.1. ValidationofMPCtoolchain

Asthestudyfocused onthecoolingperformance,theswitched discrete model,describedin Eq.(1), could only selectthemodes cooling orcoasting;thus,only themodelparameters forthe two modesneededtobeidentified.Step-testswereperformedto iden-tifymodelparametersA_cool,Acoast,Wcool,andWcoast.Thestep-tests wererun tocollecttwo datasetsof12hours inthe coolingmode in whicha step changeof the chilledwater flow from0 to 26.5 lpm was executed with the manikins and the lights operating on the schedule from 8:00 to 18:00. State anddisturbance vari-ables, i.e. the room operative temperature, the slab temperature, themanikinsandlightingpower,theoutsideairtemperature,and the globalhorizontal irradiance, were monitored at one-hour in-tervals.One12hdatasetwasusedtoidentifythemodel parame-tersandtheothertovalidatethem.Thesameprocedurewasused forthecoastingmodelparameter,withtwodatasets of24h.The modelparametersweresuccessfullyidentifiedandthecomparison betweenthe predictions and the measurements is presented be-low.

Fig. 10 presents the results of the cooling mode model iden-tification andvalidation. Two datasets were used to validate the robustnessoftheidentifiedmodelwithdifferentdisturbances.The topchartshowsthemodelpredictionvs. theactualmeasurement using the same dataset for the model identification. The middle andbottomchartsshowthemodelpredictionvs. actual measure-ment usingdifferentdatasets. Thedata usedinthe bottom chart (Validation 2) were generated using similar disturbances as the trainingdata,whilethedatainthemiddlechart(Validation1)was generatedwithdisturbancesthatwereconsiderablydifferentfrom thetrainingdata,asshowninFig.11.Theslabtemperatureshowed

Fig. 11. Disturbances of the identification and validation datasets.

Fig. 12. “Free response” model identification and validation.

lessdeviationthantheroomoperativetemperature.Themaximum roomoperativetemperatureerrorwas±1.8°C.

Fig.12 showstheresultsofthecoastingmodemodel identifi-cationandvalidation.Themodelidentifiedforthecoastingmode hasbetterperformance thanthecoolingmode,andthemaximum operativetemperatureerroriswithin±1.0°C.

Fig. 13. Distribution of computation time for solving the MPC problem. Table 2

CV(RMSE) and NMBE of the validation dataset.

Operation Dataset Variable CV(RMSE) NMBE

Cooling Validation 1 Operative temperature 5.2% −3.4% Cooling Validation 1 Slab temperature 3.4% −3.2% Cooling Validation 2 Operative temperature 2.1% −0.2% Cooling Validation 2 Slab temperature 1.5% 1.4% Coasting Validation Operative temperature 2.4% 1.7% Coasting Validation Slab temperature 1.5% 1.2%

Table 2 shows the CV(RMSE) and NMBE of the validation datasets. The two coefficients are both well below the 10% for CV(RMSE)and5%forNMBErequirements.

TheFinite-HorizonOptimizationmodulewasalsovalidated suc-cessfully.Optimalsolutionswerepresentedateachtime step dur-ingthevalidationperiodof24h.Fig.13showsthedistributionof thecomputation time to solvethe MPC problem. The computing timeforeachtimestepvariedfrom6.68to9.87swithameanof 7.33s.Fig.14showsasnapshotofitsrunningstatus.

3.2.MPCvs.heuristiccontrol

Side-by-side measurements were made for a period of eight days,startingonOct11th, 2017.The internal loadswere reduced by∼75%toemulatelowloadconditionsfromOct16thtoOct18th. TheresultswereshowninFigs.15–17.Thecomparisonfocuseson the room operativetemperature andthe energyperformance. As thetwo cellssharethe same chiller, thereis no direct measure-mentofthechillerelectricityconsumptionofeachcase.The

Fig. 15. Comparison of the average room operative temperature.

Fig. 16. Comparison of the rate of thermal energy consumption.

Fig. 17. Comparison of the pump power consumption and the corresponding energy consumption.

ing thermal energy, calculated asthe product of the chilled wa-tercapacityrateandthedifferencebetweenthechilledwater sup-plyandreturntemperaturesoftheradiantslabsystem, wasused asaproxyforthechillerelectricityconsumption.Theenergy per-formanceconsistsoftwocomponents,thecoolingthermalenergy andthechilledwaterpumpingenergy.

Fig. 15 compares the room operative temperature. As can be seenfromthefigure,mostofthetime,theroomoperative temper-aturesin both cases were maintained within the set-point range from19°Cto 26°C (indicatedby the shade area) duringthe oc-cupied hours of 8:00–18:00. The exceptions mainly occurred in theearlymorningwheretheroomoperativetemperaturesinboth caseswere lowerthan 19°Candtheperformanceoftheheuristic controlisworsethanthatoftheMPC.Thisbehaviorisaninherent characteristicofradiantslabsystems astheyrely onthe thermal

mass of the slab to store sufficient cooling capacity in the early morning.However,withcarefullyselectedvalueofthevariable

ρ

, atrade-off betweenenergyuseandthethermaldiscomfortcanbe achievedtoreduceovercoolingintheearly morning.OnOct14th and15th,the highoutsideairtemperatureandclearskyresulted inanincreasedcoolingloadwhichapproachedthecooling capac-ityoftheradiantslabsysteminbothcells,andthustheroom op-erativetemperatureinbothcellswereslightlyhigherthan26°C.

Fig. 16 compares the rate of consumption of thermal energy whileFig.17compares thepumppowerconsumption. Theupper chart showsthecumulative value andthelower chart showsthe instant measurement. The cumulative thermal energy consump-tionusing theMPC was503.0MJandwas598.9MJusing heuris-tic control, yielding a thermal energysaving of 16.0% duringthe eight days of the experimental period, which indicates a 16.0% chillerelectricitysavingsfromtheMPC.Thecumulativechilled wa-terpumpelectricityconsumptionwiththeMPCwas11.6kWhand withtheheuristiccontrolwas20.2kWh,yieldinganelectricity sav-ing of 42.6%. The savings are more substantial when the system operatesatpartialloadconditions,i.e.whentheroomcoolingload issmallerthanthecoolingcapacityoftheradiantslab.Whenthe room coolingload approachesthecooling capacityoftheradiant slab,thebenefitofMPCdiminishes.Ascanbeseenfromthedata onOct15th,theMPConlyshiftedtheoperatinghoursofthepump andthetotalpumprunningtimewasjustonehourlessthanthat withtheconventionalcontrol.

4. Conclusions

TheopensourceMPCtoolchainwastestedandvalidatedinthe FLEXLEBtestfacility.The identifiedmodelreasonablyrepresented theperformance oftheradiantslabsystemwitha CV(RMSE)less than10% andaNMBElessthan 5%.TheFinite-Horizon Optimiza-tionmodulesuccessfullysolvedtheoptimizationproblemandthe averagecomputingtimewas7.33sperzoneforaonehour time-step. In order for the computation time to be small compared to thetime-step ina largebuilding,which couldhave 100–1,000 zones,some formofparallel processingwouldberequired, possi-blyusingagraphicscard;furtherinvestigationisrequired.

During the eight day experimental period, the MPC yielded 42.6% chilled waterpumpingenergy reduction and16.0% cooling thermalenergysavings when comparedto the conventional con-troloftheradiantslabsystem, whilemaintainingequal orbetter indoorcomfort.

The MPC toolchain needs to performstep testsof theradiant slab systemtocollect dataformodel identification.Thedata can be obtainedactively orpassively dependingon theactual condi-tions.Thepassiveapproachispreferredasthenormaloperationof theradiantsystemwouldnot beinterrupted. Thisisessentialfor theMPCtoolchaintobewidelyacceptedandappliedintheHVAC industry. Therefore,future research is neededto investigate how thedatacollectedpassivelywouldimpactthemodelaccuracyand how model accuracy would impact the performance of the MPC toolchain.

Acknowledgments

The U.S. Department of Energy (DOE) andthe Department of Science and Technology (DST) of the Government of India (GOI) jointly funded this work under the U.S.-India Partnership to Ad-vanceClean EnergyResearch (PACE-R)program’s “U.S.-India Joint Center for Building Energy Research and Development” (CBERD) project.The AssistantSecretary forEnergy Efficiency and Renew-able Energy, Office of BuildingTechnology, State and Community Programs,oftheU.S.DOEunderContract.No.DE-AC02-05CH11231

supported the U.S.CBERD activity. The DST of the GOI, adminis-tered by the Indo-U.S. Science and Technology Forum, supported theIndianCBERDactivity.

TheauthorswishtothankFrancescoBorrelli,TravisWalterand SarahKoehlerfortheir assistancewiththisproject.

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