Modeling and Control Algorithms to Improve Energy Efficiency in Buildings

MISSING IMAGE

Material Information

Title:
Modeling and Control Algorithms to Improve Energy Efficiency in Buildings
Physical Description:
1 online resource (131 p.)
Language:
english
Creator:
Goyal, Siddharth
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering, Mechanical and Aerospace Engineering
Committee Chair:
Barooah, Prabir
Committee Members:
Rao, Anil
Dixon, Warren E
Ingley, Herbert A, Iii
Khargonekar, Pramod P

Subjects

Subjects / Keywords:
control -- hvac -- model-reduction -- modeling -- mpc -- optimization -- predictive-control
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre:
Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
In this dissertation, we address the problem of how to improve energy efficiency of buildings while maintaining a comfortable and healthy indoor climate with minimum cost; Our primary focus is on commercial buildings with VAV (variable-air-volume)-based HVAC (heating, ventilation, and air-conditioning) systems. We believe that a cost effective solution to this problem is to update the existing control logics that operate the HVAC system with an improved control algorithm. Going forward with the approach of updating the control algorithm leads to a list of questions: 1. What type of improved control algorithm should be chosen?  - How the choice of a controller effects energy consumption and indoor climate?  - What are the computation and practical requirements to implement the controller? 2. What are the key control inputs that should be varied by the controller?  3. What type of information is required by the control algorithm? - Does the controller require a model of building dynamics? - What are the sensors required by the controller, and how they effect savings?  One option is to design a controller that requires the maximum amount of information, varies all the control inputs, and uses advanced computationally-expensive optimization methods. It is possible that such a controller may result in high savings, but the effort and cost required to design and implement such a controller may also be drastically high. Our goal is to design an appropriate controller that not only results in high savings while maintaining comfortable climate but also requires minimal additional investment. To address all the above questions and find out the appropriate controller, we propose and compare the performance of several control algorithms, which are of varying complexity and require varying amount of information. We divide the work presented in this dissertation into two parts. Examination of model-based control requires a model. In the first part, we develop a lumped parameter and physics-based model of hygro-thermal dynamics for a multi-zone building, which is called “full-scale” model. Though the full-scale model is a simplified lumped parameter model, it has a large number of states, which makes it unsuitable for real-time control, especially for the model-based control methods. Therefore, we develop a method for reducing the order of the hygro-thermal dynamic model for multi-zone buildings. The reduction method exploits the linear portion and sparsity pattern of the non-linear portion of the model to obtain the reduced order model. Simulation results for a four-zone building model show that the predictions of the zone temperatures and humidity ratios obtained from the reduced model are quite close to that of the full-scale model, and the computation time reduces by a factor of six or more. In the second part, we present several control algorithms and compare their performance and complexity. The goal of the control algorithms is to reduce the energy use over a conventional control algorithm, which we call a baseline (BL) controller, while maintaining thermal comfort and indoor air quality. Some of the proposed algorithms are applicable at zone-level, while other are applicable at AHU (air handling unit)-level. At the zone-level, the control inputs commanded by the controllers are supply air temperature and supply air flow rate. The control inputs commanded by the AHU-level controllers are supply air temperature, supply air flow rate, return air ratio, and the temperature of air leaving the cooling coils inside AHU. Three zone-level control algorithms: 1) MOBS, 2) MOBO, and 3) POBO are proposed, which vary in complexity and require varying amount of information. The MOBS controller is the simplest one among the proposed controllers since it is based on feedback logics and only requires occupancy measurements. Both the MOBO and POBO controllers are model predictive control (MPC)-based controllers, which are computationally expensive and require a hygro-thermal dynamics model. The MOBO controller requires occupancy measurements while the POBO controller requires occupancy predictions that are quite hard to obtain. Simulation results show that all the proposed controllers result in significant amount of energy savings over the baseline controller without sacrificing occupant health and comfort. Simulations also show that the feedback (MOBS) controller performs almost as well as the more complex MPC-based controllers (MOBO and POBO). Experimental results obtained from implementing the MOBS and MOBO controllers in Pugh Hall building at the University of Florida also correspond well with the simulations results. At the AHU-level, we propose two types of controllers, which again require varying amount of information and are of varying complexity. Simulation results show that occupancy measurement is the key information in reducing energy usage (56 - 69%). The energy savings can be increased by 15 - 20%, if the measurements of zone humidity and outside weather are also used in addition to occupancy measurements. Another important finding is that a feedback-based controller performs as well as MPC-based controller, if the same measurements are provided to both the controllers. It is observed through simulations that the effect of control inputs on the energy savings decreases in the following order: 1) supply air flow rate and temperature 2) return air ratio 3) conditioned air temperature, and the conditioned air temperature has almost negligible impact on energy savings when the return air ratio is varied. Therefore, a feedback controller, with supply air temperature, return air ratio, and supply air flow rate as the control variables, is the most appropriate control algorithm to be used for single-zone VAV HVAC systems due to its simplicity, low computation, and similar performance to that of more complex control algorithms.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Siddharth Goyal.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Barooah, Prabir.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2014-08-31

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045729:00001


This item is only available as the following downloads:


Full Text

PAGE 1

MODELINGANDCONTROLALGORITHMSTOIMPROVEENERGYEFFICIEN CYIN BUILDINGS By SIDDHARTHGOYAL ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2013

PAGE 2

c r 2013SiddharthGoyal 2

PAGE 3

ACKNOWLEDGMENTS IwouldliketoexpressmysinceregratitudetomyadvisorDr. PrabirBarooahfor hisinvaluableguidance,encouragement,andsupportthrou ghoutmyPh.D.program. Withouthisknowledgeandassistancethisdissertationwou ldnothavebeencompleted. Dr.Barooahtaughtmenotonlyhowtoconductresearchwithpa ssionandenthusiasm, butalsohowtoovercomethehurdlesfacedduringresearch.H ealsotaughtmethe waysofhowtopresentresultsinaconciseandclearmanner.I wouldliketothankhim forprovidingmetheopportunitytoworkwithhimandallthek nowledgehehasimparted tome. ItismypleasuretoextendmysinceregratitudetoDr.Herber tIngleyforhelping meunderstandthebasicconceptsofheating,ventilation,a ndair-conditioningsystems, whichistheprimaryapplicationareaofmyresearch.Iwould alsoliketothankDr. TimothyMiddelkoopforhelpingmeunderstandthefundament alsofdatabaseand sensorsimplementation,andtheinsightsoftheproblemsas sociatedwhiletransitioning fromtheorytopractice.IwouldalsoliketothankDr.Prasha ntG.Mehtaforseveral helpfuldiscussions. IwouldliketoacknowledgethehelpofPhysicalPlantDivisi onattheUniversityof Florida,especiallySkipRockwell,forhelpinguscollectt hedataandprovidingustimely updatesaboutthechangesinthebuildingthatweareusingas atest-bed. IwouldliketothankProfessorsPramodKhargonekar,Warren DixonandAnilRao forbeinginmycommittee,usingtheirprecioustimetoreadt hisdissertation,andgiving constructivecommentstoimprovethequalityandpresentat ionofthiswork. Ialsooffermyregardsandsincerethankstoallofthosewhos upportedmeinany respectduringthecompletionofthework. ThismaterialisbaseduponworksupportedbytheNationalSc ienceFoundation underGrantNo.0931885(CPS)and0955023(CAREER).Anyopin ions,ndings,and 3

PAGE 4

conclusionsorrecommendationsexpressedinthismaterial arethoseoftheauthor(s) anddonotnecessarilyreecttheviewsoftheNationalScien ceFoundation. 4

PAGE 5

TABLEOFCONTENTS page ACKNOWLEDGMENTS ..................................3 LISTOFTABLES ......................................7 LISTOFFIGURES .....................................8 LISTOFSYMBOLS ....................................10 ABSTRACT .........................................14 CHAPTER 1INTRODUCTION ...................................17 1.1MotivationandProblemStatement ......................17 1.2RelatedLiteratureandContributions .....................22 1.2.1Multi-zoneBuildingDynamicsModel .................22 1.2.2Non-linearBuildingDynamicsModelReduction ...........23 1.2.3Zone-levelControlAlgorithms .....................24 1.2.4AHU-levelControlAlgorithms .....................27 2HYGRO-THERMALMODELOFBUILDINGSANDORDERREDUCTION ...30 2.1ProblemStatement ...............................30 2.2Full-scaleModelofBuildingHygro-ThermalDynamics ...........31 2.3ModelReductionMethod ...........................36 2.3.1ReviewofBalancedTruncationMethodforLTISystem .......36 2.3.2ABalancedTruncation-likeReductionofNon-linearT hermalModel 37 2.3.3Non-Dimensionalization ........................40 2.4SimulationResults ...............................41 2.5ConclusionandOpenProblems .......................47 2.6DerivationofHumidityRatioDynamics ....................48 3ZONE-LEVELCONTROLALGORITHMS .....................50 3.1MotivationandProblemStatement ......................50 3.2ControlAlgorithms ...............................51 3.2.1 BL (Baseline)Controller ........................53 3.2.2 MOBS (MeasuredOccupancyBasedSetback)Controller .....54 3.2.3MPC-basedControllers ........................56 3.2.3.1 MOBO (MeasuredOccupancyBasedOptimal)Controller 59 3.2.3.2 POBO (PredictedOccupancyBasedOptimal)Controller 61 3.3PerformanceMetrics ..............................62 3.4SimulationResults ...............................64 3.4.1ModelCalibrationandValidation ...................64 5

PAGE 6

3.4.2ChoiceofParameters .........................65 3.4.3PerformanceComparison .......................68 3.5DiscussionandFutureWork .........................73 3.6ErrorAnalysisofDiscretizedModelofHygro-thermalDy namics ......75 4EXPERIMENTALRESULTS .............................77 4.1ModelValidation ................................77 4.2ExperimentalSetup ..............................78 4.3Results .....................................80 4.4ConclusionandDiscussion ..........................87 5AHU-LEVELCONTROLALGORITHMS ......................88 5.1MotivationandProblemStatement ......................88 5.2ControlAlgorithms ...............................89 5.2.1 A-FC ( AHU-LevelFeedbackControl ) .................91 5.2.2 A-MPC ( AHU-LevelModelPredictiveControl ) ............92 5.3SimulationParameters .............................97 5.3.1BuildingModelParameters ......................97 5.3.2Controllerparameters .........................97 5.4ComparisonResults ..............................98 5.5DiscussionandFutureWork .........................102 6QUALITYOFTHEMPCSOLUTION ........................104 6.1MotivationandProblemStatement ......................104 6.2ApproximatedLinearModelofPowerandHygro-themalDyn amics ....105 6.3ConvexOptimizationProblems ........................108 6.4SimulationResults ...............................111 6.5ConclusionandOpenProblems .......................113 6.6ErrorAnalysisinEnergyApproximation ...................114 6.6.1LinearConvexApproximation .....................114 6.6.2QuadraticConvexApproximation ...................115 7CONCLUSIONANDFUTUREWORK .......................117 7.1ConclusionoftheChapters ..........................117 7.2OverallConclusion ...............................120 7.3FutureWork ...................................121 7.3.1ImprovedModeling ...........................121 7.3.2DetailedAnalysisandImprovingControl ...............122 REFERENCES .......................................124 BIOGRAPHICALSKETCH ................................130 6

PAGE 7

LISTOFTABLES Table page 2-1Thetotalthermalresistanceandcapacitancevaluesint he4-zonebuilding. ..42 2-2Computationtimeversusmodelorder. c r Elsevier2012 .............46 3-1Complexityandinformationrequiredbyvariouscontrol lers. c r Elsevier2013 .53 3-2Totalthermalresistanceandcapacitanceofwindowandw alls. c r Elsevier2013 66 3-3Designparametersusedinthevariouszone-levelcontro llers. c r Elsevier2013 67 3-4Dailyenergyconsumption, % Savings,andviolations. c r Elsevier2013 ....69 4-1Dailyenergyconsumptionand % Savingswithvariouscontrollers. .......86 5-1Complexityandinformationrequirementsofvariouscon trolalgorithms. ....90 5-2DesignparametersusedinthevariousAHU-levelcontrol lers. ..........99 5-3Dailyenergyconsumption, % Savings,avg.temperatureandhumidityviolations 100 6-1Designparametersusedinthevariouscontrollers. ................111 6-2Equilibriumpointsusedforlinearization. ......................112 6-3Dailyenergyconsumption,averagecomfortviolation,a nd % Savings. .....113 7

PAGE 8

LISTOFFIGURES Figure page 2-1Afour-zonebuildinganditsVAV-basedHVACsystem. c r Elsevier2012 ....32 2-2AlumpedRCmodelforheatinteractionbetweenthezones. c r Elsevier2012 .34 2-3Inputs:massowrates m SAi andtotalinternalheatgain Q i c r Elsevier2012 .43 2-4Temperaturepredictions( 14 th ordervs. 40 th ordermodel). c r Elsevier2012 ..43 2-5Humiditypredictions( 14 th ordervs. 40 th ordermodel). c r Elsevier2012 ....44 2-6Temperaturepredictions( 8 th ordervs. 40 th ordermodel). c r Elsevier2012 ...45 2-7Humiditypredictions( 8 th ordervs. 40 th ordermodel). c r Elsevier2012 .....45 3-1Genericschemeforzone-levelcontroller'simplementa tion. c r Elsevier2013 .52 3-2Aschematicofthebaselinecontroller(“dualmaximum”) c r Elsevier2013 ..55 3-3Implementationofthe MOBO and POBO controllers. c r Elsevier2013 .....57 3-4Layoutofzone 247 onthe 2 nd oorinPughHallattheUniversityofFlorida. ..64 3-5Predictedandmeasuredtemperaturesinzone 247 c r Elsevier2013 ......65 3-6OAtemperatureandrelativehumidityinGainesville,FL ,USA. c r Elsevier2013 66 3-7Comfortenvelopeduringoccupiedandunoccupiedtimes. c r Elsevier2013 ..68 4-1Layoutofzone 241 onthe 2 nd oorinPughHall. .................78 4-2Predictedandmeasuredtemperaturesinzone 241 ................79 4-3Implementationschematicofthecontrolalgorithmsdur ingexperiments. ....80 4-4Interfaceofsecuritysoftwareduringexperiments. .................81 4-5Trueandmeasuredoccupancyinzone 241 forthe MOBS and MOBO controllers. 82 4-6Zone 241 temperatureduringtheexperimentsandsimulations. .........83 4-7Flowrateofairsuppliedtozone 241 duringtheexperimentsandsimulations. .84 4-8TemperatureofSAenteringzone 241 duringtheexperimentsandsimulations. 84 4-9Averagehumidityratioinzone 241 duringtheexperimentsandsimulations. ..85 4-10AverageCO 2 concentrationinzone 241 duringtheexperiments. .........86 5-1Flow-chartofthe Z-FC controllertodeterminethecontrolinputs. ........93 8

PAGE 9

5-2Layoutofazone(auditorium)ontherstoorofPughHall ...........97 9

PAGE 10

LISTOFSYMBOLS,NOMENCLATURE,ORABBREVIATIONS C pa Specicheatcapacityofairatconstantpressure= 1 : 006( kJ=kg= C ) C pw Specicheatcapacityofwatervaporatconstantpressure= 1 : 84( kJ=kg= C ) C i;j Thermalcapacitanceofaninternalnodeconnectingzone i and j ( kJ=K ) C ii Thermalcapacitanceof i th zone( kJ=K ) CLG Coolingset-point D H Humidityviolation D H Averagehumidityviolation D T Temperatureviolation D T Averagetemperatureviolation E C Energyconsumedbycontroller C E BC Energyconsumedbythebaselinecontroller H Relativehumidity HTG Heatingset-point K Numberofstepschosenforpredictionhorizon M Mass P Totalpower P F Fanpower P R Re-heatingpower,i.e.,powerconsumedinreheatingattheV AVbox P U Conditioningpower,i.e.,powerconsumedbychiller P da Pressureofdryair Q Heatload R g Specicgasconstantofdryair= 287 : 04( J=kg=K ) R i;j ;R mid i;j Thermalresistancesofpartofawallthatconnectszone i and j ( K=W ) RTG Re-heatingset-point R RA Returnairratio(ratioofreturnairtomixedairowrate) T Temperature 10

PAGE 11

T set Desiredset-point T RTG Re-heatingset-point T high Maximumtemperatureallowedinthezone T low Minimumtemperatureallowedinthezone V Volume W Humidityratio W high Maximumhumidityallowedinthezone W low Minimumhumidityratioallowedinthezone t Discretizationtime H Enthalpydifferenceofsupplyairandextractair IAQfactorofsafety e ( Temp ) Predictionerroroftemperaturebetweenfull-scaleandred ucedmodels e ( W ) Predictionerrorofhumidityratiobetweenfull-scaleandr educedmodels h Enthalpyofair h we Evaporationheatofwaterat 0 C = 2501( kJ=kg ) m Flowrate m OAp Amountoffreshoutsideairrequiredperperson m SAp Amountofsupplyairrequiredperperson m SAhigh Maximumamountofsupplyairduringoccupiedorunoccupiedt ime m SAlow Minimumamountofsupplyairduringunoccupiedtime m Az Amountoffreshoutsideairrequiredperunitarea n p Numberofpeople n pd Designednumberofpeople u Controllableinputvector v Exogenousinputvector A z Zoneoorarea Fanpowerconstant 11

PAGE 12

! H 2 0 Rateofwatervaporreleasedbyapersonduetorespiration( kg=sec ) Density superscriptsSA Supplyair:airleavingthevariable-air-volumebox CA Conditionedair:airbeingsuppliedbyairhandlingunit OA Outsideair EA Extractair:airbeingexhaustedfromthezone MA Mixedair:airbeingsendtoairhandlingunit occ Duringoccupiedtime unocc Duringunoccupiedtime s Solargain p People lin Linearizedaroundequilibriumpoint subscriptsd Discrete da Dryair ii th zone,where i =1 ;:::;N w Watervapor eq Equilibriumpoint rate Rateatwhichavariablecanincreaseordecrease max Maximumallowedvalue min Minimumallowedvalue AbbreviationsMPCModelPredictiveControl 12

PAGE 13

BL Baseline MOBS MeasuredOccupancyBasedSetback MOBO MeasuredOccupancyBasedOptimal POBO PredictedOccupancyBasedOptimal Z-FCZone-LevelFeedbackControlA-FCAHU-LevelFeedbackControlA-MPCAHU-LevelModelPredictiveControlAHUAirHandlingUnitVAVVariableAirVolumeHVACHeating,Ventilation,andAir-conditioningASHRAEAmericanSocietyofHeating,RefrigeratingandAirConditioningEngineers IAQIndoorAirQuality 13

PAGE 14

AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy MODELINGANDCONTROLALGORITHMSTOIMPROVEENERGYEFFICIEN CYIN BUILDINGS By SiddharthGoyal August2013 Chair:PrabirBarooahMajor:MechanicalEngineering Inthisdissertation,weaddresstheproblemof“howtoimpro veenergyefciency ofbuildingswhilemaintainingacomfortableandhealthyin doorclimate”withminimum cost;OurprimaryfocusisoncommercialbuildingswithVAV( variable-air-volume)-based HVAC(heating,ventilation,andair-conditioning)system s.Webelievethatacost effectivesolutiontothisproblemistoupdatetheexisting controllogicsthatoperatethe HVACsystemwithanimprovedcontrolalgorithm.Goingforwa rdwiththeapproachof updatingthecontrolalgorithmleadstoalistofquestions: 1.Whattypeofimprovedcontrolalgorithmshouldbechosen? -Howthechoiceofacontrollereffectsenergyconsumptiona ndindoorclimate? -Whatarethecomputationandpracticalrequirementstoimp lementthecontroller? 2.Whatarethekeycontrolinputsthatshouldbevariedbythe controller? 3.Whattypeofinformationisrequiredbythecontrolalgori thm? -Doesthecontrollerrequireamodelofbuildingdynamics?-Whatarethesensorsrequiredbythecontroller,andhowthe yeffectsavings? Oneoptionistodesignacontrollerthatrequiresthemaximu mamountof information,variesallthecontrolinputs,andusesadvanc edcomputationally-expensive optimizationmethods.Itispossiblethatsuchacontroller mayresultinhighsavings, buttheeffortandcostrequiredtodesignandimplementsuch acontrollermayalsobe drasticallyhigh.Ourgoalistodesignanappropriatecontr ollerthatnotonlyresultsin 14

PAGE 15

highsavingswhilemaintainingcomfortableclimatebutals orequiresminimaladditional investment.Toaddressalltheabovequestionsandndoutth eappropriatecontroller, weproposeandcomparetheperformanceofseveralcontrolal gorithms,whichare ofvaryingcomplexityandrequirevaryingamountofinforma tion.Wedividethework presentedinthisdissertationintotwoparts. Examinationofmodel-basedcontrolrequiresamodel.Inthe rstpart,wedevelopa lumpedparameterandphysics-basedmodelofhygro-thermal dynamicsforamulti-zone building,whichiscalled“full-scale”model.Thoughthefu ll-scalemodelisasimplied lumpedparametermodel,ithasalargenumberofstates,whic hmakesitunsuitablefor real-timecontrol,especiallyforthemodel-basedcontrol methods.Therefore,wedevelop amethodforreducingtheorderofthehygro-thermaldynamic modelformulti-zone buildings.Thereductionmethodexploitsthelinearportio nandsparsitypatternofthe non-linearportionofthemodeltoobtainthereducedorderm odel.Simulationresults forafour-zonebuildingmodelshowthatthepredictionsoft hezonetemperaturesand humidityratiosobtainedfromthereducedmodelarequitecl osetothatofthefull-scale model,andthecomputationtimereducesbyafactorofsixorm ore. Inthesecondpart,wepresentseveralcontrolalgorithmsan dcomparetheir performanceandcomplexity.Thegoalofthecontrolalgorit hmsistoreducetheenergy useoveraconventionalcontrolalgorithm,whichwecallaba seline( BL )controller,while maintainingthermalcomfortandindoorairquality.Someof theproposedalgorithms areapplicableatzone-level,whileotherareapplicableat AHU(airhandlingunit)-level. Atthezone-level,thecontrolinputscommandedbythecontr ollersaresupplyair temperatureandsupplyairowrate.Thecontrolinputscomm andedbytheAHU-level controllersaresupplyairtemperature,supplyairowrate ,returnairratio,andthe temperatureofairleavingthecoolingcoilsinsideAHU. Threezone-levelcontrolalgorithms:1) MOBS ,2) MOBO ,and3) POBO are proposed,whichvaryincomplexityandrequirevaryingamou ntofinformation.The 15

PAGE 16

MOBS controlleristhesimplestoneamongtheproposedcontrolle rssinceitis basedonfeedbacklogicsandonlyrequiresoccupancymeasur ements.Boththe MOBO and POBO controllersaremodelpredictivecontrol(MPC)-basedcont rollers, whicharecomputationallyexpensiveandrequireahygro-th ermaldynamicsmodel. The MOBO controllerrequiresoccupancymeasurementswhilethe POBO controller requiresoccupancypredictionsthatarequitehardtoobtai n.Simulationresultsshow thatalltheproposedcontrollersresultinsignicantamou ntofenergysavingsoverthe baselinecontrollerwithoutsacricingoccupanthealthan dcomfort.Simulationsalso showthatthefeedback( MOBS )controllerperformsalmostaswellasthemorecomplex MPC-basedcontrollers( MOBO and POBO ).Experimentalresultsobtainedfrom implementingthe MOBS and MOBO controllersinPughHallbuildingattheUniversityof Floridaalsocorrespondwellwiththesimulationsresults. AttheAHU-level,weproposetwotypesofcontrollers,which againrequirevarying amountofinformationandareofvaryingcomplexity.Simula tionresultsshowthat occupancymeasurementisthekeyinformationinreducingen ergyusage( 56 69% ). Theenergysavingscanbeincreasedby 15 20% ,ifthemeasurementsofzonehumidity andoutsideweatherarealsousedinadditiontooccupancyme asurements.Another importantndingisthatafeedback-basedcontrollerperfo rmsaswellasMPC-based controller,ifthesamemeasurementsareprovidedtobothth econtrollers.Itisobserved throughsimulationsthattheeffectofcontrolinputsonthe energysavingsdecreases inthefollowingorder:1)supplyairowrateandtemperatur e2)returnairratio3) conditionedairtemperature,andtheconditionedairtempe raturehasalmostnegligible impactonenergysavingswhenthereturnairratioisvaried. Therefore,afeedback controller,withsupplyairtemperature,returnairratio, andsupplyairowrateasthe controlvariables,isthemostappropriatecontrolalgorit hmtobeusedforsingle-zone VAVHVACsystemsduetoitssimplicity,lowcomputation,and similarperformanceto thatofmorecomplexcontrolalgorithms. 16

PAGE 17

CHAPTER1 INTRODUCTION 1.1MotivationandProblemStatement Buildingsareoneofthemainconsumersofenergyworldwide. IntheUnitedStates, theyaccountforabout 40% ofthetotalenergyconsumption[ 1 ].Heating,ventilation,and air-conditioning(HVAC)systemscontributetomorethan 50% oftheenergyconsumed inbuildings[ 1 ].PoordesignandinefcientoperationofHVACsystemcause alarge fractionofenergyusedtobewasted[ 2 3 ].Thoughtheenergyconsumptioninthe buildingscanbeimprovedthroughbetterHVACsystemdesign ,itrequiressubstantial investmenttoretrotanexistingbuildingwithimprovedHV ACequipment[ 4 ].Incontrast, improvingcontrolalgorithms(thatoperatetheHVACsystem )toachievehigherefciency isfarmorecosteffective.Indeed,thereisagrowingintere stindevelopingtechniques toimproveenergyefciencyinbuildings[ 5 – 15 ].Ourgoalisalsotoreduceenergy consumptioninbuildingsthroughtheuseofanimprovedcont rolalgorithmbutwith minimalinvestment(intermsofdesignandimplementation) Welimitourselvestocommercialbuildingswithvariable-a ir-volume(VAV)system becauseapproximately 30% ofthecommercialbuildingoorspaceintheUnitedStates isservedbyVAVsystems[ 16 ].InaVAVsystem,abuildingisdividedinto“zones”, whereazonecanbeasingleroomoracollectionofrooms.Thea irleavingthezones ismixedwithoutsideairbasedonthevalueofreturnairrati o,andthemixedairissent tooneormoreAHUs.TheairleavingthecoolingcoilsinanAHU iscalledconditioned air,whichiscooleddowntoconditionedairtemperaturetor educethehumidityratio. TheconditionedairgoestotheVAVboxofeachzone,wherethe conditionedairmaybe heatedupbyusingtheheatingcoilsbeforebeingsuppliedto thezone.Theairsupplied tothezoneiscalledsupplyair.Theowrateofthesupplyair iscontrolledthrough dampersinsidetheVAVbox.Therearefourcontrolinputstha tneedtobedecided forthesemulti-zoneVAVsystems.Twoofthecontrolinputs( thereturnairratioand 17

PAGE 18

conditionedairtemperature)aredecidedatAHUwhiletheot hertwocontrol(thesupply airtemperatureandsupplyairowrate)inputsaredecideda ttheVAVbox. Wedividethecontrolstrategieswefocuson,intotwoparts: 1)zone-leveland2) AHU-level.Thezone-levelstrategiescanbeappliedatanin dividualVAVboxinwhich thecontrolinputsthatneedtobedeterminedaretheowrate andtemperatureofthe supplyair.InAHU-levelstrategies,thecontrolinputstha tneedtobedeterminedbythe controllerarethereturnairratio,conditionedairtemper ature,supplyairtemperatureand owrate. Conventionalcontrolstrategiesinthemostexistingbuild ingsuseonlyzone temperaturemeasurementsbutdonotuseanymeasurementsof occupancy,zone humidity,andoutsideweather.Occupancyheremeansnumber ofpeopleinazone.The controlinputsattheVAVbox,whicharethesupplyairtemper atureandowrate,are determinedbytheconventionalcontrollersinsuchawaytha tthezonetemperature ismaintainedinspecicrangesbasedonpredeterminedoccu pancyschedules. Tomaintainindoorairquality(IAQ),theminimumairowrat esuppliedtoazoneis determinedbasedontheoccupancyschedulesandbuildingst andards,suchas ASHRAE(AmericanSocietyofHeating,RefrigeratingandAir -ConditioningEngineers) ventilationstandard62.1-2010[ 17 ].Zonesaretypicallyover-ventilatedastheminimum owrateisusually30–40 % ofthedesignedmaximum,especiallywhenthezoneisnot occupiedbutitisexpectedtobe,e.g.,in“daytime”mode.Th econtrolinputsattheAHU, whicharethereturnairratioandconditionedairtemperatu re,areusuallykeptconstant atpredeterminedvaluesirrespectiveofwhetherthebuildi ngisoccupiedornot.Thisis inefcientintermsofenergyusagesincetheindoorclimate ismaintainedevenduring unoccupiedtimes. Over-ventilationcanbepreventedbyapplyingdemandcontr olventilation(DCV)in whichthesupplyairowrateischangedbasedonreal-timeoc cupancymeasurements or CO 2 measurementsinsteadofapre-denedschedule.Real-timeo ccupancy 18

PAGE 19

measurementscanbeobtainedfrommotiondetectorssuchasP IRandultrasound sensors,whichareinexpensiveandworkwellinsmallofces paceswherethenominal occupancyvalueisone[ 6 18 ].Inverylargespaces, CO 2 measurementscanbe effectivelyusedforDCVinsteadofanoccupancysensor.DCV istypicallyusedinlarge spaceswiththehelpof CO 2 sensors;itislesscommonlyusedinsmallzonessuchas anofceroom.Effortsindevelopingoccupancymeasurement technologyarecarried outbyseveralresearchers;see[ 19 ]andreferencestherein. Assensorsand/oralgorithmsforinexpensiveyetreliabler eal-timeoccupancy measurement/estimationbecomeavailable,itshouldbepos sibletoreduceenergyuse furtherthanwhatcanbeachievedbycontrollingventilatio n.Forexample,wecansave energybyreducingtheairowrateaswellaslettingthetemp eraturevaryinawider rangeduringunoccupiedtimesthanthatofoccupiedtimes.I tispossibletoimprovethe energyefciencyfurtherbyvaryingtheinputsatAHU,i.e., RAratioandconditionedair temperature,inadditiontotheinputsattheVAVbox. Ourconjectureisthat“asubstantialamountofenergycanbe saved—while maintainingthermalcomfortandIAQ(indoorairquality)—b ycontrollingtheinputsat theVAVboxandAHU,andusingthemeasurementsofoccupancy, zonetemperature, zonehumidity,andoutsideweather”.However,howtodesign acontrollertoachievethis isnotobvious. Cautionisrequiredtodevelopacontrolalgorithm.Forinst ance,ifthezone temperatureduringunoccupiedtimeislettodeviatefarawa yfromwhatisconsidered comfortable,itmighttakeawhileforthezonetemperaturet ocomebacktoacomfortable conditionwhenthezonebecomesoccupiedagain.Thesamegoe sforhumidityand IAQ.Onehastobecarefulwhiledecidingthecontrolinputsa ttheAHU.Forexample, onemightthinkthatusinghighreturnairratioreducesthee nergyusedbycoolingcoils, buthighreturnairratiomightincreasethesupplyairowra teduetotheminimum ventilationrequirementsbyASHRAEstandard62.1-2010[ 17 ],whichmightendup 19

PAGE 20

increasingthetotalenergyconsumptioninsteadofreducin git.Similarly,onemight thinkthatincreasingtheconditionedairtemperatureredu cesthetotalenergyasless amountofenergyisconsumedbythecoolingcoils.However,i ncreasingtheconditioned airtemperaturemaycausethezonehumiditytodeviatefaraw ayfromacomfortable range,whichcanincreasethetotalenergyconsumptionashi ghsupplyairowrateis requiredtobringthezonehumiditybacktothecomfortabler ange.Itmaybepossible toavoidsuchtypeofscenarios,ifamodelofthermal,humidi tydynamics,andenergy consumptionisincorporatedintoacontroller.Furthermor e,thecontrollershouldalso havesomerobustnesstoerrorinthemeasurements. Assuggestedearlier,wecoulddesignsimplecontrolstrate gies,whichuse occupancymeasurements,toreduceenergyconsumptioninbu ildings.However, wearenotrestrictedtoonlysimplecontrolstrategies.Rec allthatourgoalisto reduceenergyconsumptionwhilemaintainingcomfortlevel andindoorairqualityin buildings.Anadvancedcontrolalgorithmbasedonoptimalc ontrolmethodssuchas MPC[ 5 20 21 ]—thatwillminimizetheenergyconsumptionasanobjective function subjecttotheconstraintsontemperature,humidity,comfo rtlevel,andIAQinthe building—mayalsohavemeritedifitleadstosufcientlyla rgeenergysavings.Optimal controltechniquesrequireadynamicmodelthatrelatesthe controlinputstotherelevant outputs(zonetemperatureandhumidityratioofeachzone). Amodelofthermaldynamicsofamulti-zonebuildingcanbeco nstructedfrom energyandmassbalanceequations.Modelingalltherelevan tphysicalphenomena willleadtoasetofcoupledpartialdifferentialequations ,whicharehighlycomplexin nature.Therefore,obtainingthepredictionsusingsucham odeliscomputationally expensive.However,animportantrequirementofadynamicm odelforuseinreal-time controlmethodssuchasMPCissimplicity,sinceoverlycomp lexmodelswithlarge statespacedimensionwillrenderthemtooslowforpredicti oninreal-time.Therefore, simpliedreducedordermodelsarerequiredforthereal-ti mecontrol.Resistor-capacitor 20

PAGE 21

(RC)networksarecommonlyusedforconstructingareducedo rdermodelofthe transientheatowthroughasolidsurface,suchasawall[ 22 – 25 ].Theresistancesand capacitancesarecarefullychosentomodelthecombinedeff ectofconductionbetween theairmassesseparatedbythesurface,aswellaslongwaver adiationandconvection betweenthesurfaceandtheairmassincontactwithit[ 24 26 ],[ 27 ,Chapters3,29, &31].ARCnetworkmodelofasolidsurfaceisasetoflineardi fferentialequations. Theheatandmoistureexchangedbetweenazoneandsupplyair canbemodeled withordinarydifferentialequations(ODEs),whicharenon -linearODEs.Assumingthat thereisnointer-zonethermalconvection,athermaldynami csmodelofabuildingcan beconstructedbylinkingthelinearODEscorrespondingtot heRCnetworksandthe non-linearODEscorrespondingtothemoistairenthalpydyn amics.Amodelofthe humiditydynamicscanbeconstructedusingmassbalanceequ ations.Thedynamics oftemperatureandhumidityarecoupled.Hence,thecombine dmodeliscalleda hygro-thermalmodel.Wecallsuchamodela“full-scale”mod el,whichisexplainedin Section 2.2 Eventhoughthefull-scalemodelitselfisasimpliedlumpe d-parametermodel,it hasalargestatespacedimensionevenforamoderatenumbero fzones.Forinstance, a 4 -zonebuildingmodelmayhaveastate-spacedimensionof 40 ormore,andamedium buildingwith 66 zonesmayhaveastate-spacedimensionof 500 ormore.Thus,sucha modelisnotrecommendedforareal-timemodel-basedcontro ltechniques,especially theonesthatrequireon-lineoptimizationbasedonmodelpr edictionsuchasMPC. Intheworkpresentedhere,werstproposeanovelmethodfor reducingtheorder ofafull-scalemodelofthethermaldynamicsofamulti-zone building.Theproposed modelreductionmethodexploitsaspecicstructureofthem odelthatisuniqueto multi-zonebuildingthermaldynamicsandexistingmodelre ductiontechniquesforLTI systemstoreducethemodelorder.Oncethereducedandsimpl iedmodelisbeing developed,wenextinvestigatehowmuchenergycanbesavedb ythecontrolalgorithms 21

PAGE 22

thatuseinformationofvariousmeasurements(zone-humidi ty/zone-temperature/occupancy/outside weather)andreducedmodeldynamics,andhowthesavingsdep endonthedelityof theinformation.Asmorene-grainedinformationisavaila ble,thecontrolalgorithmmay resultinmoreenergysavings,butthecontrolalgorithmmay becomemorecomplex. Forinstance,acontrollerequippedwithoccupancypredict ionscansavemoreenergy thantheonewithoccupancymeasurements,byturningtheair owlowandtemperature outsideacomfortablerange.Butdevelopingmodelstopredi ctoccupancyisnotan easytask.Wefocusonthecontrolalgorithmsthatcanbeused inexisting(andnew) commercialbuildings;thefourcontrolinputsthatneedtob edeterminedbythecontrol algorithmsarereturnairratio,conditionedairtemperatu re,supplyairtemperatureand owrate. 1.2RelatedLiteratureandContributions 1.2.1Multi-zoneBuildingDynamicsModel Althoughanumberofpapersonthermalmodelingofbuildings exist,quiteafew ofthemarelimitedtosinglezones[ 28 – 30 ]oraverysmallnumberofzones[ 31 ].The papers[ 14 15 32 ]modelconductionbetweenmultiplezones,butdonotmodelt he non-lineareffectsofhumidityonthetemperatureresponse .ThepaperbyWang[ 33 ] presentsafull-scalenon-linearmodelofmulti-zonebuild ingswithanarbitrarynumber ofzoneswithamodelofinter-zoneconvectionbasedontempe raturedifference. However,Wang[ 33 ]alsodoesnottakeintoaccountthenon-lineareffectofmoi stair ontemperature,andmoreoverusesa1R1Cmodelforconductio namongzones.Ithas beenshownthat1R1C—oreven2R1C—modelsarelessaccuratet han3R2Cmodelsin predictingtemperatureresponse,andthat3R2Cmodelsrepr esentthebestcompromise betweenpredictionaccuracyandmodelcomplexity[ 24 ].However,recentworkin[ 34 ] showsthattheparameterofareducedorderlumpedparameter modelcanbettedfrom themeasureddata,butthedatahastobesufcientlyrichand asignicantnumberof forced-responseexperimentsneedtobeconductedtogenera tethattypeofdata. 22

PAGE 23

Contribution:Wedevelopaphysicsbasedmodelofhygro-the rmaldynamicsfor amulti-zonebuilding,whichisobtainedbycombiningthedy namicsoftemperature (thermal)andhumidity(hygro)inazone.Thethermalmodelh asalinearpartanda non-linearpart.ThelinearpartcomesfromtheRCnetworkdu etotheheattransfer betweenzones,andthenon-linearpartcomesfromtheenergy exchangebetweenthe airsuppliedtoazoneandtheairextractedfromthatzone.Th edynamicsofhumidity arederivedusingmassbalancelaws,whichareasetofnon-li nearODEs. 1.2.2Non-linearBuildingDynamicsModelReduction Thefull-scalemodelisasetofnon-linearcoupledODEsthat areobtainedby massandenergybalance.Thereareanumberofwell-develope dtechniquesfor modelreductionoflinearsystems;see[ 35 ]forareview.However,modelreduction ofnon-linearsystemsisalessdevelopedarea.Someworkhas beendoneonmodel reductionofbilinearsystems[ 36 – 39 ].Sincethefull-scalemodelweconstructedisnot bilinear,thesemethodsarenotapplicable.Othernotablew orkonnon-linearmodel reductionincludestheenergy-functionbasedmethodof[ 40 ],theempiricalGramian basedmethodof[ 41 ].Theproposedmethodavoidsthecomputationaldifcultie s inobtainingtheenergyfunctionthatisrequiredbythemeth odof[ 40 ].Thoughthe methodproposedin[ 41 ]isquitegeneralsinceitdoesnotrequireanyspecicstruc ture ofthefull-scalemodel,itrequirescollectingextensivea ndsufcientlyrichsimulation datatoconstructtheso-calledempiricalGramians.Inaddi tion,thismethodisunable totakeadvantageofanyspecicstructuresincethemethodi sdevelopedforafully generalnon-linearmodel.Theinterestedreaderisreferre dto[ 42 ]forareview—aswell asacomparisonofmeritsandweaknesses—ofexistingnon-li nearmodelreduction techniques. Contribution:Wedevelopanovelmodelreductiontechnique thatisapplicable aslongasthefull-scalemodelhasaspecicsparsitystruct ure.Sincethefull-scale modelisbasedonbasicmassandheatbalance,weexpectthemo delreduction 23

PAGE 24

methodtobeapplicabletoawiderangeofbuildingsystems.I tisshownthatthezone temperatureandhumiditypredictionsbythereducedmodela requiteclosetothe predictionsbythefull-scalemodel;thecomputationtimet akenbythereducedorder modeldecreasedapproximatelybyafactorof 6 asthatofthefull-scalemodel.This modelreductionmethodnotonlyreducesthemodelorderbuta lsomakesthelinearpart ofthereducedmodelobservable.Sinceweonlyhavethemeasu rementsoftheoutputs (zonetemperatureandhumidity),observabilityofthenonl inearmodelisrequiredas weuseEKF(ExtendedKalmanFilter)toestimatethestates;t hestatesarerequiredto implementtheMPC-basedcontrollers.1.2.3Zone-levelControlAlgorithms Thereareanumberofrecentpapersthathaveinvestigatedth euseofoccupancy information(eithermeasurementsorpredictions)toreduc eenergyconsumptionin buildings.Thepapers[ 7 – 9 ]compareMPC-basedcontrollerswiththeconventional controllers.TheMPCcontrollersmentionedin[ 7 – 9 ]useoccupancypredictionswhile theconventionalcontrollersuseonlyday/nightschedules .Thepapers[ 7 – 9 ]report substantialenergysavingswithMPCcomparedtoconvention alcontrollers.However, theydonotinvestigatehowmuchenergysavingsarepossible withacontrollerthatis lesscomplexthanMPCandusesoccupancymeasurements,whic hareeasiertoobtain thanoccupancypredictions. Thepaper[ 21 ]comparesfourMPCstrategies:1)occupancyschedulebased controller,2)turnofflightingbasedonoccupancymeasure ments,3)turnofflightingand ventilationbasedonoccupancymeasurements,and4)occupa ncypredictionsbased controller.Thepaper[ 21 ]onlycomparestheMPCcontrollers,anddoesnotcomparea feedbackcontrollerwiththeMPCcontrollersthatusethesa meamountofinformation. Thispaperdoesnotconsiderhumidityintheproblemformula tion,whichisanimportant partofthermalcomfort.Also,theHVACsystemusedin[ 21 ]isdifferentthanthetypeof HVACsystemwestudy,i.e.,VAV-basedsystem. 24

PAGE 25

Anumberofpapershaveproposedsimplerule-basedcontroll ersthatuse occupancymeasurements,andconcludethatsignicantener gysavingsarepossible withtherule-basedcontrollerscomparedtotheconvention alcontrollersthatdonotuse occupancymeasurements[ 43 – 46 ].Wereferconventionalcontrollerstothecontrollers thatarecommonlyusedinthepracticeanddonotuseoccupanc yinformation(either measurementsorpredictions).Werefertorule-basedcontr ollersaseitheronly“if-else” logicsbasedcontrollersoracombinationofconventionalc ontrollersand“if-else”logics, wherethe“if-else”logicsarebasedoneitherreal-timeocc upancymeasurementsor predictions.Thecontrollerin[ 43 ]usesoccupancymeasurementstoturnofftheHVAC system,whilethecontrollersinpapers[ 44 – 46 ]modulateonlytheventilationratebased onmeasuredoccupancy.However,noneofthesepaperscompar erule-basedcontrol withcomplexcontrolschemessuchasMPC.WhileMPCmayrequi remoreinformation suchasdynamicmodelandoccupancypredictionsascompared torule-basedcontrol, MPCmayalsoleadtomoreenergysavings.Thepaper[ 6 ]comparesseveralrule-based controllersthatusevarioustypesofoccupancyinformatio n:twouseoccupancy predictionswhileoneusesbinaryoccupancymeasurements( presence/absence).It isconcludedthatsignicantenergysavingsarepossiblewi ththerule-basedfeedback controlthatusesbinaryoccupancymeasurementscomparedt othebaselinecontroller thatdoesnotuseoccupancymeasurements.Itisalsoconclud edthatasmallamount ofadditionalenergysavingsarepossibleifthepredictive rule-basedcontrolleris usedinsteadofthefeedbackcontroller.However,itdoesno tcomparethepredictive rule-basedcontrollerwithcomplexpredictivecontrolalg orithmssuchasMPC,which mayresultinmoreenergysavingsthantherule-basedcontro l. ThoughsomeofthepreviousworkhascomparedeitherMPCorru le-based controllerswithconventionalcontrollers,theydidnotco mpareallthree.Sincethe conventionalcontrollersusedinthepreviousworkforcomp arisonweredistinct,itis hardtocompareallthreefromthepreviouswork.Itisuseful toknowhowperformance 25

PAGE 26

(asmeasuredbyenergysavingsand/orcomfort)ofthecontro lalgorithmvarieswith itscomplexity.Inparticular,thevalueofoccupancymeasu rementsvs.occupancy predictionsisnotclearfromthepreviouswork.Sinceobtai ningthepredictionsaremuch moredifcultthanobtainingthemeasurements,itispartic ularlyusefultoknowtheir relativevalue.Though[ 6 ]comparesperformanceoftherule-basedcontrollersthatu se occupancypredictionswiththatofthefeedbackcontroller ,thefeedbackcontrolleruses onlypresence/absencemeasurementsbutnotoccupancymeas urements. Contribution:Werstproposethreecontrolalgorithms(on efeedback-basedand twoMPC-based)ofvaryingcomplexityandrequiringvarying amountofinformation. Thefeedback-basedcontrolleristhesimplestoneamongthe proposedcontrollers sinceitisbasedonsimplefeedbacklogicsandrequiresonly occupancyandzone temperaturemeasurements.BoththeMPC-basedcontrollers arecomputationally expensiveandrequireahygro-thermaldynamicsmodelinadd itiontothezone temperaturemeasurements.OneoftheMPC-basedcontroller requiresoccupancy measurementswhiletheotherMPC-basedcontrollerrequire soccupancypredictions. Wenextexaminetrade-offsbetweenenergysavingsachieved andtheinformation requirements/complexityofthecontrolalgorithmsinauni edmannerthrough simulationsandexperiments.Throughthesimulations,weh aveexaminedseveral typesofzoneswithvaryinglevelsofoccupancythatisexpos edtomultipleoutside weatherandclimateconditions.Simulationsshowthat1)oc cupancymeasurementis akeyfactorinsavingenergyconsumption,2)feedbackcontr olthatusesoccupancy measurementsperformsaswellasMPC-basedcontrol,3)addi tionalsavingswith MPCcontrollerthatusesoccupancypredictionsaresmall,a ndthus,theuseof MPCcontrollersatindividualzone-levelisnotjustied.W ehavealsoimplemented thefeedbackandMPCcontrollersthatuseoccupancymeasure mentsinazoneof PughHallintheUniversityofFloridacampus.Experimental resultsalsoconrmthe conclusionsthatwehaveobtainedduringthesimulations. 26

PAGE 27

Wehavealsoconvertedthenon-linearconvexproblemintoac onvexproblem, whichisusedbytheMPC-basedcontroller.Thisisdonetocom paretheperformance ofMPCvs.feedbackcontrollerwhenthesolutionobtainedby theMPC-basedcontroller correspondstotheglobalminima.Similarresultsatthezon e-levelasmentionedabove areobtainedevenwhenMPCprovidestheglobalsolution:1)M PCresultsin 45% savingsoverbaselinecontroland2)feedbackperformsasgo odasMPCwhenbothare allowedtohaveoccupancymeasurements.1.2.4AHU-levelControlAlgorithms Therehavebeenmanyrecentpapersthathavedevelopedcontr olalgorithms toreduceenergyconsumptioninbuildings.Someofthepaper s[ 14 47 48 ]use optimalcontrolbasedmethodsthatarecomplexandcomputat ionallyexpensive,while othersusefeedbackcontrollers[ 43 49 50 ]thataresimpleandeasytoimplement. Allofthepapersshowsignicantenergysavingsoverthecon ventionalbaseline controllers.Thestrategyin[ 14 ]controlsthereturnairratio,supplyairowrateand temperaturetominimizePredictedMeanVoteandenergycons umption.Thecontrol strategiesin[ 47 48 ]resetthesupplyairtemperature,ventilationrate,andch illed watertemperature.Thecontrollerin[ 49 ]resetsthestaticpressureresetandsupplyair temperaturewhileonlytheminimumsupplyairowrateisres etin[ 50 ]. Alloftheabovementionedpaperseithercomparecomplexopt imalcontrolmethods withconventionalcontrollers,orcomparethesimplefeedb ack-basedmethodswiththe conventionalcontrollers.However,theydidnotcompareal lthree,i.e.,theconventional, simplefeedback,andcomplexMPCcontrollers.Thesepapers donotinvestigatehow muchenergysavingsarepossiblewithacontrollerthatisle sscomplexandeasier toimplementascomparedtoanMPC,andusesthesameamountof informationas usedbyMPC.ItisimportanttoknowhowacomplexMPCcontroll erbenetsovera simplefeedbackcontroller.Noneofthepapersmentionedab oveshowtheeffectofthe typesofmeasurementsonthecontrollersperformance.Itis usefultoknowthisfroma 27

PAGE 28

practicalimplementationpointofviewsinceadditionalse nsorsimplyextrainvestment andeffort.However,itdoesnotnecessarilymeanthatusing additionalmeasurements willalwaysresultinhighenergysavings.Thecontrollersi nabovementionedpapers controlamaximumofthreevariables,thoughtherearefourp ossiblevariables(supply airtemperatureandowrate,conditionedairtemperature, andreturnairratio)thatcan becontrolled.Controllingallthefourvariablesmayresul tinhighsavings/comfort.Also, thesepapersdonotstudytheeffectofanindividualcontrol inputonthecontrollers performance. Contribution:Weproposetwotypesofcontrollers:asimple feedbackanda complexoptimization-basedMPC,andcomparetheirperform anceagainstthe performanceofconventionalcontroller.Weexaminetheeff ectofeachcontrolvariable andallthecontrolvariablesonenergyconsumption,therma lcomfort,andIAQ.Wealso studythevalueofmeasurementsandcontrolinputsintheper formanceoffeedback andMPCcontrollers.Theoutcomeofourstudyisthatthefeed backcontrollerperforms aswellasMPCprovidedthesamemeasurementstoboththecont rollers.Ourstudy showsthatoccupancymeasurementisthekeyinformationinm inimizingenergyusage. Weshowthattheeffectofthecontrolinputsontheenergycon sumptiondecreasesin thefollowingorder:1)SAowrateandtemperature2)RArati o3)CAtemperature. Furthermore,alloftheabovementionedpaperseitherdonot includetheconditionedair humidityratioorassumeconstanthumidityratio.However, theconditionedairhumidity ratiodependsontheconditionedairtemperature,whichwec onsiderinourworksince thedependencyofconditionedairtemperatureandhumidity canhaveasignicant impactonenergyconsumptionandthermalcomfort. DissertationOrganization:Thefull-scalehygro-thermal modelandthemodel reductionmethodtoreducethestatedimensionalityofthef ull-scalemodelispresented inChapter 2 .Chapter 3 describestheconventionalcontrolandtheproposedzone-l evel controlalgorithmsalongwiththeirsimulationresults.Ch apter 4 presentstheexperimental 28

PAGE 29

setupandtheperformanceoftheproposedcontrolalgorithm swhenthecontrollersare implementedinazoneinthePughHall.TheAHU-levelcontrol lersandtheirsimulation resultsarepresentedinChapter 5 .Aconvexapproximationoftheoptimizationproblem usedbytheMPC-basedcontrolleratthezone-level,andthep erformanceofthe MPC-basedcontrollerthatusestheapproximatedconvexpro blemispresentedin Chapter 6 .Chapter 7 summarizesthisdissertationanddiscussesthefuturework 29

PAGE 30

CHAPTER2 HYGRO-THERMALMODELOFBUILDINGSANDORDERREDUCTION 2.1ProblemStatement Inthischapter,wedevelopamodelofbuildinghygro-therma ldynamicsusing resistance-capacitance(RC)networkandmassbalancelaws fromphysics,which hasbeendescribedintheintroductionofChapter 1 .Thecombinedmodelofbuilding hygro-thermaldynamicsisasystemofcoupledODEs,whichwe call“full-scale”model. Eventhoughthefull-scalemodelitselfisasimpliedlumpe d-parametermodel,ithasa largespacedimensionevenforamoderatenumberofzones.In suchacase,themodel isnotsuitableforoptimal-controlbasedmethodssuchasMP Cthatrequireson-line optimizationbasedonmodelprediction.Therefore,weprop oseanovelmodelreduction methodinthischaptertoreducethestatedimensionalityof thefull-scalemodewhile maintainingsufcientlyhighaccuracyofthepredictionso foutputs.Theoutputsofthe modelarezonetemperaturesandhumidities,whiletheinput sareoutsidetemperature, outsidehumidity,heatgainsfromoccupantsandsolarradia tion,andsupplyairow ratesandsupplyairtemperatures.Theproposedmodelreduc tionmethodexploitsa specicstructureofthemodelthatisuniquetomulti-zoneb uildingthermaldynamics andexistingmodelreductiontechniquesforLTIsystemstor educetheorderoffull-scale model. Therestofthechapterisorganizedasfollows.Section 2.2 describesbriey thenon-linearmodelofbuildingthermaldynamics.Theprop osedmethodfororder reductionofthismodelisdescribedinSection 2.3 .Resultsfromnumericalsimulations arepresentedinSection 2.4 .Section 2.5 concludesthischapteranddiscussesthe possiblefuturework.Thederivationofhumiditydynamicsi nazoneispresentedin Section 2.6 30

PAGE 31

2.2Full-scaleModelofBuildingHygro-ThermalDynamics Inthissection,thefull-scalemodelofbuildinghygro-the rmaldynamicsisconstructed usingresistance-capacitancelumpedparametermodels.Th efull-scalemodelpredicts thezonetemperatureandhumidityratioforagiveninputval ueandinitialstate.The humidityratioofavolumeofmoistairisdenedastheratioo fthemassofwater presentintheairtothemassofdryair.Aschematicofafourzonebuildingwitha VAV-basedHVACsystemisshowninFigure 2-1 .Inthissystem,theconditionedair(CA) suppliedbyAHU,whichiscoldanddry,isdistributedtotheV AVboxesassociatedwith eachzone.TheVAVboxesmayheatuporchangetheowrateofth eairsuppliedtothe zone.ThecontrollogicsusedbytheVAVboxareexplainedlat erintheSection 3.2.1 TheairsuppliedtothezonebytheVAVboxiscalledsupplyair (SA).Theairexhausted fromthezoneiscalledextractair(EA).PartofEAisrecircu lated,whichiscalledreturn air(RA),andismixedwiththeoutsideair(OA)beforeitissu ppliedtotheAHU. AsshowninFigure 2-1 ,thebuildingmodelisseparatedintotwoparts:upstream anddownstream.The“upstream”partincludestheAHUdynami cs,whilethe“downstream” partincludesthedynamicsassociatedwiththeVAVboxes,zo netemperatureand humidity.Weignorethedynamicsintheupstreampartduetot woreasons.First,the sizeofthedownstreammodelismuchlargerthanthesizeofup streammodel.Thisis becauseanAHUservesmultiplezonesandthenumberofAHUsin alargebuildingis typicallysmall.Forinstance,thereare 3 AHUsina 66 -zonebuildingattheUniversity ofFloridacampus.The3-AHUmodelhasalmost20states,whil ethe66-zonethermal modelhasmorethan500numberofstates.Thus,thedownstrea mmodelrequires modelreductiontechniquesmuchmorethantheupstreammode l.Second,theAHUhas thefastestdynamicsintheHVACsystem,withatimeconstant ofaboutaminute[ 51 ], whereasthethermaldynamicsofthezonesarefarslowerwith timeconstantsinthe ordertensofminutes[ 28 ]tohours[ 25 ].Asaresult,itmaybepossibletoreplacethe dynamicsoftheAHUsandductsbystaticgainswithoutlosing toomuchaccuracy. 31

PAGE 32

WealsoignorethedynamicsoftheVAVboxessincetheVAVboxe shavemuchfaster dynamicsascomparedtothedynamicsofzonetemperatureand humidity. AHUZone 1Zone 2Zone 3 Zone 4OA RA VAV VAV VAV VAV CA Upstream Downstream m SA1 m SA2 m SA3 m SA4 Figure2-1.Afour-zonebuildinganditsVAV-basedHVACsyst em. c r Elsevier2012 Theassumptionsinvolvedduringtheconstructionofbuildi nghygro-thermal dynamicsarethat1)theairineachzoneiswellmixedsothatt hereisonlyonevalue associatedwithzonetemperatureandonewithhumidityrati o,2)thereisnointer-zone convection,3)inltrationorexltrationdoesnotexist,4 )eachwindowhasnegligible thermalcapacitanceascomparedtothewalls,oorsandceil ings,and5)theairleaving azone(EA)hasthesametemperatureandhumidityratioasthe airpresentinthezone, i.e., T EA i = T i ;W EA i = W i Theinputstothemodel,whicheffectthetemperatureandhum idityineachzoneare 1)owrate,temperature,andhumidityofSAineachzone,2)t hermalheatgaindueto occupants,solarradiation,lighting,andequipmentsinev eryzone,3)temperatureofthe outsideair,and4)amountofmoisturegeneratedbyoccupant s.Theoutputofthemodel thatweareinterestedinpredictingare T 1 ;:::T N W 1 ;:::W N ,where N isthenumberof 32

PAGE 33

zones.Thevector v ,whichconsistsofalltheinputsignalstothebuildinghygr o-thermal dynamics(i.e.,owrate,temperature,andhumidityofsupp lyair,outsidetemperature, heatgainduetotheoccupants,lightning,equipments,ands olarradiation)isdened below v =[ m SA1 ;:::;m SAN ;W SA 1 ;:::;W SA N ;T SA 1 ;:::T SA N ;Q p1 ;:::Q pN ;Q s1 ;:::Q sN ;T OA ] T : Weusearesistor-capacitorcircuittomodeltheheattransf erthroughasolid surfacesuchasawall,oor,cellingorwindow.Specically ,a3R2Cnetworkisused, i.e.,eachsolidsurfaceexceptwindowsismodeledasanetwo rkofthreeresistors andtwocapacitors,whileeachwindowismodeledasasingler esistorsincewindows areassumedtohavenegligiblethermalcapacitance.Also,e veryzonehasathermal capacitanceassociatedwithitduetotheheatcapacityofai r,furniture,andequipments inthezone.Then,theelementalRCmodelsconstructedforea chsurfacearecombined tocreatethemodeloftheentiremulti-zonebuilding. AnexampleofcreatingtheequivalentRCnetworkmodelofazo ne i surrounded byfourzones j;k;l ,and o isshowninFigure 2-2 .Thezone o representstheoutside. Wedonotconsideroorandceilinginthisexampleforsimpli city.Recallthatthezone i has C ii thermalcapacitance,andthewallthatseparatesthezone i and o hasthermal resistancesandcapacitancesof R i;o ;R mid i;o ;R o;i and C i;o ;C o;i correspondingtoits3R2C model.Combiningthe3R2Cmodelofeachwall,thedynamicsof T i ,thetemperatureof zone i ,canbewrittenas C ii T i = 1 R i;o + 1 R i;j + 1 R i;k + 1 R i;l T i + T i;o R i;o + T i;j R i;j + T i;k R i;k + T i;l R i;l + Q pi + H i : (2–1) Theterm H i willbeexplainedlaterinthissection.Thedynamicsofthev ariables T i;o ;T o;i ,whicharethetemperaturesofthe“internal”nodesofthewa llseparating i and 33

PAGE 34

o ,canbewrittenas C i;o T o;i = 1 R o;i + 1 R mid i;o # T o;i + T i;o R mid i;o + T OA R o;i + Q si ; C o;i T i;o = 1 R mid i;o + 1 R i;o # T i;o + T i R i;o + T o;i R mid i;o : (2–2) Thetotalthermalresistanceandcapacitancevaluesforeac hsolidsurfacecanbe Wall1Wall2Wall3Wall4i j k l o AZoneStructure T iTi;oTo;iTi;jTi;kTi;lTOATjT kTlRi;oRmid i;oRo;iRi;jRi;kR i;lC iiCi;oCo;iVoltageCi;jCi;kC i;lQpiQ si HiWall1Wall2Wall3Wall4 BEquivalentRC-networkmodel Figure2-2.AlumpedRCmodelforheatinteractionbetweenth ezones. c r Elsevier 2012 eithercomputedfrommaterialpropertiesandtheASHRAEgui delines[ 27 ]orttedfrom modelcalibrationexperiments[ 52 ].Oncethetotalthermalresistanceandcapacitance valuesaredecided,theformulasspeciedbyGoudaetal.[ 24 ]areusedtosplitthetotal capacitanceintotwocapacitancesandthetotalresistance intothreeresistances. Theenthalpydifference H i in( 2–1 )iscomputedusingthefollowingequation H i = m SAi h SAi ( T SA i ;W SA i ) m EAi h EAi ( T i ;W i ) ;i =1 ; 2 ;:::N: (2–3) Thoughweignoreinltration,itcanbeincludedifdesiredi n( 2–3 ).Thespecic enthalpies h ( ) i in( 2–3 )arecomputedfrompsychometricequations[ 27 ]as h SAi = C pa T SA i + W SA i ( h we + C pw T SA i ) ; (2–4) h EAi = C pa T i + W i ( h we + C pw T i ) : (2–5) 34

PAGE 35

Notethattheowrateofextractairleavingthezone i is m EAi ( t )= m SAi ( t )+ n pi ( t ) H 2 0 Thehumidityratiodynamicsarederivedfrommassbalancean dgaslawsas dW i dt = R g T i V i P da i n pi H 2 O + m SAi W SA i W i 1+ W SA i ;i =1 ; 2 ;:::N: (2–6) Detailedderivationof( 2–6 )isexplainedinSection 2.6 Combining( 2–1 )-( 2–6 )forallthezones i =1 ;:::;N ,thefull-scalemodelofthe entirebuildinghygro-thermaldynamicsisconstructed.Th efull-scalemodelincludes thedynamicsofthetemperatureofeachzone,temperatureof theinternalnodesfor eachsolidsurface,andhumidityineveryzone.Weassociate zonetemperatureorthe temperatureofinternalnode(i.e.,insidethesolidsurfac e)withauniquenode.Thetotal numberofnodes( n )ina N zonebuildingmodelis n = N + N int ; where N int isthenumberofnodescorrespondingtothetemperaturesins idesolid surfaces 1 .Thefull-scalemodelisasetofcoupledODEs,whichcanbeex pressed compactlyas T = AT + BU + f ( T;W;v ) ; (2–7) W = g ( T;W;v ) ; (2–8) wherevector T :=[ T 1 ;:::;T N ;:::;T n ] T 2 R n containsthetemperaturesassociated withallthenodes, U :=[ T OA ;Q p1 ;:::;Q pN ;Q s1 ;:::;Q sN ] T isasub-vectoroftheinput vector v asdenedin( 2–1 ), W :=[ W 1 ;W 2 ;:::;W N ] T ,andthenon-linearfunction f ( T;W;v ):=[ H 1 ; H 2 ;:::; H N ; 0 ;:::; 0] T 2 R n .Theentriesofthematrices 1 Thevariationsofoutsideairtemperaturesonthevarioussi desofabuildingcan betakenintoaccounteasilybyconsideringmorethanoneout sidetemperaturesas inputs.However,wedon'tconsidervariationsintheoutsid eairtemperaturestomake thenotationsimple. 35

PAGE 36

A 2 R n n and B 2 R n (2 N +1) aredeterminedbytheresistanceandcapacitancevalues correspondingtoeachsolidsurface,aswellasthezonecapa citances. Indexingofthenodesisdoneinawaythattherst N statesofthevector T correspondtothezonetemperatureof N zones,andtheremaining n N states correspondtothetemperaturesoftheinternalnodes.Asare sult,thefunction f has formedaspecialstructurewithnon-zeroentriesattherst N placesandzeroentriesat theremaining n N places.Therst N non-zeroentriescorrespondtotheheatgain orenthalpydifferenceduetomoistairinthe N zones.Thisspecialstructureof f willbe usefulintheproposedmodelreductionmethod,whichispres entednext. 2.3ModelReductionMethod Beforegettingintothemodelreductionof( 2–7 )-( 2–8 ),werstbrieyreview thebalancedtruncationmethodofmodelreductionfortheli neartimeinvariant(LTI) systems;seereferences[ 53 – 56 ]formoredetails.Then,wedescribetheproposed modelreductiontechniqueforthenon-linearmodelofthebu ildinghygro-thermal dynamicsinwhichbalancedtruncationisused.2.3.1ReviewofBalancedTruncationMethodforLTISystem ConsiderastableLTIsystemwitha p m transferfunction G ( s ) ,whichhas m inputs and p outputs.Supposeithasastate-spacerealizationas x = Ax + Bu;y = Cx + Du; (2–9) where x 2 R n isthestatevector, u 2 R m istheinputvectorand y 2 R p istheoutput vector.Thus, A 2 R n n ;B 2 R n m ;C 2 R p n ,and D 2 R p m .ThecontrollabilityGramian G ( c ) andobservabilityGramian G ( o ) of( 2–10 )aredenedas G ( c ) ( A;B ):= Z 1 0 e At BB T e A T t dt;G ( o ) ( A;C )= Z 1 0 e A T t C T Ce At dt: Considerastatetransformation x b = Rx ,whichgivesusthetransformedrealization x b = A b x b + B b u;y b = y = C b x b + Du; (2–10) 36

PAGE 37

where A b = RAR 1 ;B b = RB;C b = CR 1 .Thisiscalledabalancedrealizationif R ischoseninawaythatthecontrollabilityandobservabilit yGramians G ( c ) b ;G ( o ) b of( 2–10 ) arebothequalanddiagonal: G ( c ) b = G ( o ) b = 0BBBB@ 1 00 0 0 00 n 1CCCCA ;G ( c ) b = G ( c ) ( A b ;B b ) ;G ( o ) b = G ( o ) ( A b ;C b ) ; where 1 > 2 >:::> n > 0 .Toreducethefull-scale n th orderLTIsystem( 2–9 )toa q th orderLTIsystemsuchthat q
PAGE 38

eachzone.Recallfrom( 2–7 )thatthetemperaturedynamicsofthebuildingmodelare T = AT + BU + f ( T;W;v ) ; (2–11) where T 2 R n containsthe n temperaturestates.Theindexingofthestatevector T is doneinawaythat T canberewrittenas T = T T z ;T T nz T ; (2–12) wherethevector T z :=[ T 1 T 2 :::T N ] T containsthezonetemperatures,andthevector T nz 2 R N int containsthetemperaturesofthenodesinternaltowalls.Du etothespecic structureof f withrst N non-zeroentries, f canbedecomposedas f ( T;W;v )=[ f T a ( T z ;W;v )0 T( n N ) 1 ] T ; where f a 2 R N : (2–13) Wehavealsousedthefactthattheentriesofthevector f dependsonlyonthezone temperatures T z andnotonthetemperaturesofinternalnodes.Wenowintrodu cea ctitiousoutput Y ofthefollowingform: Y = CT;Y 2 R p ;p N; (2–14) wherethematrix C 2 R p n ischoseninawaythatvector Y contains T z ,thevectorof zonetemperatures,asasub-vector.Again,weindextheoutp ut Y insuchawaythatthe rst N elementsarezonetemperatures.Thus, Y canbeexpressedas Y := 264 T z Y nz 375 ; where T z = I N N 0 N ( p N ) Y; (2–15) where Y nz 2 R ( p N ) ,and I isanidentitymatrix.Combining( 2–11 )-( 2–15 ),weget 264 T W 375 = 264 AT + BU +[ f T a ( T z ;W;v )0 T( n N ) 1 ] T g ( T z ;W;v ) 375 ; (2–16) Y = CT: 38

PAGE 39

Wehaveagainusedthefactthat g ( ) dependsonthezonetemperaturesandnotonthe temperaturesofthenodesinternalofthewalls;seeSection 2.6 fordetails. Suppose T b := RT isastatetransformationinsuchawaythatthematrix R 2 R n n leadstoabalancedrealizationofthesystem T = AT + BU ,where A;B arethe correspondingmatricesfrom( 2–7 ).ThestabilityoftheLTIpart,whichfollowsfromthe physicsofRCnetworks,assuresthatthe R matrixexists.Thetransformationmatrix R canbecomputedeasily;e.g.,thecommand balreal inMATLAB c r .Afterapplyingthe transformation,eq.( 2–7 )-( 2–8 )canbeexpressedas 264 T b W 375 = 264 A b T b + B b U + R [ f T a ( T z ;W;v )0 T( n N ) 1 ] T g ( T z ;W;v ) 375 ; (2–17) Y = C b T b ; where A b = RAR 1 ;B b = RB;C b = CR 1 .Notethatthecomputationof R issolely basedontheLTIpartof( 2–7 ).Supposewewanttoreducethenumberoftemperature statesfrom n to r ( p r
PAGE 40

Wenoweliminatethelast n r statesof T b ,whichleadstothefollowing ( r + N ) th order approximation 264 T r W 375 264 A 11 T r + B 1 U + R 11 f r ( T z ;W;v ) ; g ( T z ;W ) 375 ; (2–20) Y C 1 T r : From( 2–20 ),itcanbewrittenthat T z C r T r ,where C r := I 0 C 1 .Usingthis and( 2–15 ),wenowignoretheapproximationerrorsandrewrite( 2–20 )as 264 T r W 375 = 264 A 11 T r + B 1 U + R 11 f r ( C r T r ;W;v ) ; g ( C r T r ;W ) 375 ; (2–21) Y = C 1 T r : Eq.( 2–21 )is ( r + N ) th orderreducedmodelofthefull-scalesystemmodel( 2–7 )-( 2–8 ). Sincewetruncatethe n r temperaturestatesbasedonthelinearpart,it isassumedimplicitlythat n r truncatedstatesdonoteffectthenon-linearterm signicantly.Simulationresultsinthenextsectionshowt hatthereducedordermodel predictionsareclosetothefull-scalemodelpredictions, whichsuggestthattheimplicit assumptionholdswelluptoaparticularorder r ofreducedmodel.Giventheinitial temperature T (0) andhumidityratio W (0) ofthefull-scalemodel,theinitialstatevalue T r (0) ofthereducedordermodelcanbecalculatedas T r (0)= R 11 R 12 T (0) : (2–22) 2.3.3Non-Dimensionalization ConsideranLTImodel x = Ax + Bu withtwoinputshavinganequaleffectonthe states.Supposetherstinputhasahighermagnitudethanth esecondinput.Inthis situation,theentryof B correspondingtotherstinputissmallerthantheentryof B correspondingtothesecondinput.Suchascenariomayleadt hebalancedtruncation 40

PAGE 41

todetermineincorrectlyaboutwhichinputhasthemosteffe ctontheoutput.This issuecanberesolvedbynon-dimensionalizingtheequation sandvariablessothatthe effectofinputsontheoutputisindependentoftheunitsoft hemeasurements/inputs. Sincetheinputstothemodel( 2–7 )-( 2–8 ),outsidetemperature(measuredin C ), solarradiationheatgain(measuredin KW ),differinthemagnitudeandunits,we rstnon-dimentionalizethestatesandinputs.Then,weapp lythebalancedreduction techniqueasmentionedinabovesection.Thisisdonetoprov idenumericalrobustness totheproposedreductionmethod. Wescalethevariables T;T OA ;Q s ,and Q p as T i = T i T i (0) ; T OA = T OA T OA char ; Q si = Q si Q schar ; Q pi = Q pi Q pchar ; (2–23) where T OA char isthecharacteristicoutsidetemperature, Q schar isthecharacteristicheatgain ofazonefromsolarradiation,and Q pchar isthecharacteristicheatgainofazonedue tooccupants.Theseareconstantswhosevaluescanbesetbyt heuser.Wechoose T OA char astheaverageofmaximumandminimumoftheoutsidetemperat uresrange expected.InthesimulationsreportedlaterinSection 2.4 ,wechoose T OA char =27 : 5 C Q schar =0 : 928 kW and Q pchar =0 : 26 kW .Thebuildingthermaldynamics( 2–7 )intermsof thenon-dimensionalvariablesdenedin( 2–23 )canbeexpressedas T = A s T + B s U + f s ( T;W; v ) (2–24) where U :=[ T 0 ; Q p1 ;:::; Q pN ; Q s1 ;:::; Q sN ] T ,and v isthescaledcounterpartof v .The statetransformationmatrix R iscalculatedbasedontheLTIpartof( 2–24 )instead of( 2–7 ).Oncethematrix R iscalculated,thismatrixisusedinthemethoddescribedin Section 2.3.2 ,andrestoftheprocedureissame. 2.4SimulationResults Inthissection,wecomparethezonetemperatureandhumidit yratiopredictions obtainedbythereducedordermodelandfull-scalemodel.Si mulationsareperformed 41

PAGE 42

usingMATLAB c r forthefour-zonebuildingshowninFigure 2-1 .Eachzonehasa volumetricareaof75 m 3 andoorareaof 25 m 2 .Eachwallis 5 m wideand 3 m tall.The northfacingwallofthezone 1 hasasmallwindowof 5 m 2 area,whiletheeastfacing wallsofthezones 2 and 4 havealargerwindowof 7 m 2 areaeach.Alltheexteriorwalls thatseparatethezonesfromtheoutsidehavethesameconstr uctiontype,andallthe internalwallsthatseparatethezoneshavethesameconstru ctiontype.Also,theoor andceilinghavethesameconstructiontypeasoftheexterna lwalls.Thetotalthermal resistanceperunitareaandtotalthermalcapacitanceperu nitareaoftheoor,ceiling, externalwalls,internalwalls,andwindowsareshowninTab le 2-1 .Thevaluesshown inTable 2-1 .areusedwiththeformulasin[ 24 ]tocomputethreeresistanceandtwo capacitancevaluesusedin3R2Cmodels.Table2-1.Thetotalthermalresistanceandcapacitanceval uesinthe4-zonebuilding. SurfaceTypeFloorandCeilingExternalWallsInternalWall sWindows Totalresistanceperunitarea2.692.690.450.3 ( m 2 K=W ) Totalcapacitanceperunitarea49349352( KJ=m 2 =K ) ThemaximumowratethattheHVACsystemcansupplyineachzo neis 0 : 25 kg=s and T SA i =12 : 8 C foreachzone.Ineachzone,thenumberofpeopleisauniforml y distributedrandomintegerbetween 0 and 4 .Outsideweatherconditionsarechosenfor asummerday(05/24/1996)ofGainesville,FL[ 57 ]. Aproportional-integral(PI)controllerisusedinthefull -scalemodelofeachzone tomaintainthezonetemperatureat 19 C .TheowratevaluescalculatedbythePI controllerareusedasinputsduringthesimulationsofther educedordermodeland full-scalemodel.Notethatalltheresultsshownherearefr omopenloopsimulations. ThePIcontrollerisusedonlyoncetoobtainthesetofinputs ,whichareusedforthe simulationsofreducedandfull-scalemodel.Thisisdoneto ensureuniformitywhile comparingthetimeconsumedduringthesimulations. 42

PAGE 43

Theinputsinthevector U arekeptconstantforevery 10 minutetimeinterval.All thetemperaturesandhumidityratiosareinitializedat 24 C and 0 : 01 ,respectively.Inputs suchasoutsidetemperature,outsidehumidityratio,mass owrates,andtotalinternal heatgainforeachzoneareshowninFigure 2-3 0 6 12 18 24 0 0.05 0.1 0.15 0.2 1 2 3 4 0 6 12 18 24 0 1 2 3 4 5 1 2 3 4 m SAi Q i ( kW )Time(hr) Time(hr) Figure2-3.Inputs:massowrates m SAi andtotalinternalheatgain Q i c r Elsevier2012 0 6 12 18 24 18 20 22 24 Ti Ti r 0 6 12 18 24 -1 0 1 2 3 4 1 2 3 4 T 1 ( C ) e ( Temp ) i ( C )Time(hr) Time(hr) Figure2-4.Temperaturepredictions( 14 th ordervs. 40 th ordermodel). c r Elsevier2012 43

PAGE 44

0 6 12 18 24 7 8 9 10 11 x 10 -3 Wi Wi r 0 6 12 18 24 0 5 10 15 x 10 -4 1 2 3 4 W 1 e ( W ) iTime(hr) Time(hr) Figure2-5.Humiditypredictions( 14 th ordervs. 40 th ordermodel). c r Elsevier2012 Simulationspresentedhereareperformedusingthe ode45 ODEsolverin MATLAB c r .Inguresandtheircaptions,superscript r representstheresultsobtained fromreducedordermodelandlegends1,2,3,4representther esultsforthe 1 st ; 2 nd ; 3 rd ; 4 th zone,respectively.Inparticular, T r i ;W r i arethepredictionsoftemperatureandhumidity ratioof i th zoneobtainedbyareducedordermodel.Correspondingly, e ( Temp ) i := T i T r i isthedifferencebetweenthepredictionsof i th zonetemperatureobtainedfromthe full-scalemodelandthereducedordermodel,while e ( W ) i = W i W r i isthedifference betweenthepredictionsofhumidityratioobtainedfromthe full-scalemodelandthe reducedordermodel. Thereare40statesinthefull-scalemodelofthefour-zoneb uilding.Weperformed simulationfortworeducedordermodels:(i)onewith 14 statesand(ii)onewith 8 states.Theminimumpossibleorderusingtheproposedmetho dis 8 asthereare 4 numberofzones.Figures 2-4 and 2-5 showthezonetemperaturesandhumidity ratios,respectively,forthe 14 th orderreducedmodel.Thermserrorinthetemperature predictionis 0 : 5 C ,whichisofthesameorderasthespatialvariationintemper ature thatexistsinsideazone.Thermserrorspresentedhereisfo rthezonethathasthe 44

PAGE 45

0 6 12 18 24 20 25 30 Ti Ti r 0 6 12 18 24 -6 -3 0 3 6 9 12 1 2 3 4 T 1 ( C ) e ( Temp ) i ( C )Time(hr) Time(hr) Figure2-6.Temperaturepredictions( 8 th ordervs. 40 th ordermodel). c r Elsevier2012 0 6 12 18 24 7 8 9 10 11 x 10 -3 Wi Wi r 0 6 12 18 24 0 5 10 15 x 10 -4 1 2 3 4 W 1Time(hr) Time(hr)e ( W ) iFigure2-7.Humiditypredictions( 8 th ordervs. 40 th ordermodel). c r Elsevier2012 maximumrmserroramongthefourzones.Themaximumerrorint hetemperature predictionsis 2 : 9 C ,whichappearsduringtheinitialtransients.Thermsandma ximum errorinthehumidityratiopredictionsare 1 : 4 10 4 and 16 10 4 ,whichare 1 : 6% and 18% ofthepredictionsbythefull-scalemodel,respectively.T hemaximumerrorisagain duetotheinitialconditionmismatches,whichoccursinthe rst 20 minutes.Aftertherst 20 minutes,theerrorisaround 1% .Webelievethatthelargeinitialerrorisduetothe 45

PAGE 46

Table2-2.Computationtimeversusmodelorder. c r Elsevier2012 ModelorderComputationtime Full-scale40189-397sec Reduced1438-77sec Maximallyreduced832-64sec differencebetweentheinitialconditionsofthereducedor derandthefull-scalemodel, whichoccursduetothetransformation( 2–22 ). Predictionsbythe 8 th orderreducedmodelareshowninFigure 2-6 andFigure 2-7 Temperaturepredictionsbythe 8 th orderreducedmodelshowlargererrorinboth transientandsteadystatebehaviorcomparedtothe 14 th ordermodel;cf.Figure 2-4 .It isknownthatreducingthemodelorderincreasesthepredict ionerrorssincethestates correspondingtothelargevaluesaretruncated.Therefore ,thermsandmaximumerror inthetemperaturepredictionsincreasesto 2 C and 9 : 7 C ,respectively,whenthemodel orderisreducedto 8 .However,theerrorinthehumidityratiopredictionsaresi milarto the 14 th ordercase,i.e.,thermsandmaximumerrorsare 1 : 39 10 4 and 16 10 4 .It seemstosuggestthatthevariationofhumidityratioduetot hetemperaturemismatchis small,andthatmodelorderhaslesseffectonhumidityratio thanontemperature.The comparisonresultsalsoillustrateatrade-offbetweenpre dictionaccuracyandreduced modelorder. Table 2-2 presentsacomparisonbetweenthecomputationtimesandmod elorder. ThetimesreportedinthetablearethetimesconsumedbyMATL AB c r 7.9.0(R2009b) inrunningasimulationofthefour-zonebuildingfor24hour sinaDellwithaT3400 2.16GHzIntelPentiumDualDuoprocessor.Thetableshowsth atthecomputation timereducesbyafactorof6whenthemodelorderisreducedby afactorof 5 (from 40 to 8 ).Wealsoperformedsimulationsfora66-zonebuildingmode lwith 2316 states. Thecomputationtimereducesbyafactorof 12 whenthemodelorderisreducedfrom full-scalevalue(i.e., 2316 )totheminimumpossiblevalue(i.e., 132 ). 46

PAGE 47

2.5ConclusionandOpenProblems Weproposedanovelmethodformodelreductionofaclassofno n-linearsystems thatmodelsthehygro-thermaldynamicsinamulti-zonebuil ding.Thefull-scalemodel ofthebuildingthermaldynamicsisconstructedusingalump edresistance-capacitance network.Thefull-scalemodelisnon-linearandhasalarger numberofstatesevenfor amoderatenumberofzones.Weexploitthespecicsparsitys tructureofthebuilding dynamicsmodelandexistingtechniquesforthereductionof linearsystemstopropose thereductionmethodfornon-linearsystems.Theproposedm ethodworksverywell insimulations,i.e.,thepredictionsofthezonetemperatu resandhumiditiesarequite closetothepredictionsofthefull-scalemodelevenwhenth emodelorderisreduced totheminimumpossible.Themaximumerrorsoccuronlydurin gtheinitialtransient phase,whichareduetomismatchintheinitialconditions.T heerrorintemperature andhumiditypredictionsstaysmallafterthetransients.I tseemsthatthetemperature predictionsaremoresensitivetomodelorderthanthehumid ityratiopredictions.Itis observedthatscalingofthestatesandinputsofthefull-sc alemodelisrequiredtoretain thepredictionaccuracyofthereducedmodel. Theproposedmodelreductionmethodisapplicableaslongas thefull-scalemodel hasthespecicsparsitystructureasthatof( 2–7 )-( 2–8 ).Weexpectthefull-scalemodel tobeapplicabletoawiderangeofbuildingsystemsastheful l-scalemodelisbasedon basicmassandheatbalance.Ifthereissignicantconvecti onbetweenthezones,this modelingframeworkmaynotbeapplicable.Inthissituation ,theassumptionsmadein constructingthefull-scalemodelwillnothold.However,t hemodelreductionmethod maystillbeapplicableaslongasthefull-scalethermalmod elhasthesamestructureas thatof( 2–7 )-( 2–8 ). Wehaveignoredthermalinteractionamongthezoneswhileco nstructingthe full-scalemodel.Constructingareducedordermodelsofin ter-zoneconvectiveheat transferisanotherimportantdirectiontoproceed.Wehave donepreliminaryworkin 47

PAGE 48

identifyingreducedorderRCnetworkmodelsofinter-zonec onvection,whichisreported in[ 58 ].Sincetheinter-zoneconventionmodelisalsoalumpedres istance-capacitance networkmodel,itcanbedirectlycombinedwiththefull-sca lemodel.Insuchacase,the proposedmodelreductioncanbedirectlyappliedsincethes tructuralpropertiesdonot changewiththeaugmentationoftheinter-zoneconvectionm odel. 2.6DerivationofHumidityRatioDynamics Thehumidityratio W ofazoneisdenedas W := M w M da ; (2–25) where M w isthemassofwatervaporand M da isthemassofdryairinthezone. Differentiating( 2–25 )withrespecttotimegivesus W = d dt M w M da = M w M da M w M da M 2 da = 1 M da ( M w W M da )= 1 V da da ( M w W M da ) ; (2–26) where V da isthevolumeofdryair(whichissameasthezonevolume V ),and da isthe densityofdryair.Itisknownfromtheidealgaslawthat da = P da R g T ,where P da isthe partialpressureofdryair, T istheairtemperature,and R g isthespecicgasconstantof dryair.Equation( 2–26 )cannowberewrittenas W = R g T VP da ( M w W M da ) : (2–27) Ignoringinltrationandexltrationintoandoutofthezon e,themassowrateofair leavingazone( m EA )canbedecomposedintodryairmassowrateandwatervapor massowrateas m EA = m EAda + m EAw ; (2–28) 48

PAGE 49

where m EAda and m EAw areratesofdryairandwatervaporratesleavingthezone, respectively.Wecanrewrite( 2–28 )as m EA =(1+ W EA ) m EAda =(1+ W ) m EAda ; (2–29) where W EA isthehumidityratiooftheairleavingthezone,andwehavea ssumedthat thehumidityratioofairinthezoneisthesameasthehumidit yratioofairgoingoutof thezone.Similarly,owrateofairenteringthezone( m in )canbewrittenas m SA =(1+ W SA ) m SAda ; (2–30) where m SAda istheowrateofdryairenteringthezoneand W SA isthehumidityratioof theairenteringthezone.Thefollowingequationsfollowfr ommassbalance: M w = n p H 2 O + m SAw m EAw ; M da = m SAda m EAda ; (2–31) where m SAw istheowrateofwatervaporenteringthezone.Equations( 2–29 ) and( 2–30 )canberearrangedtoprovide m EAda = 1 1+ W m EA ;m EAw = W 1+ W m EA ; m SAda = 1 1+ W in m SA ;m SAw = W SA 1+ W SA m SA : (2–32) Combining( 2–32 )and( 2–31 )with( 2–27 )leadsto W = R g T VP da n p H 2 O + m SA W SA W 1+ W SA : (2–33) Eq.( 2–6 )issimply( 2–33 )appliedtoeachzone. 49

PAGE 50

CHAPTER3 ZONE-LEVELCONTROLALGORITHMS 3.1MotivationandProblemStatement Inthischapter,weexaminehowmuchenergycanbesavedbycon trolalgorithms thatuseinformationofoccupancyandsystemdynamics,andh owthesavingsdepend onthedelityoftheinformation.Asmorene-grainedinfor mationisavailable,wemay beabletosavemore,butthecontrolalgorithmmaybecomemor ecomplex.Ourfocusis onthezone-levelcontrolalgorithmsthatcanbeusedinVAVb oxesofindividualzones inexisting(andnew)commercialbuildings:thecontrolinp utsthatthecontrollerhasto decidearetheowrateandtemperatureoftheairsuppliedto thezone. Therstandthesimplestcontrollerweproposeisarule-bas edfeedbackcontrol lawthatdecidesthecontrolinputsbasedoninstantaneousm easuredoccupancy. Thiscontrolstrategyiscalled MOBS (MeasuredOccupancyBasedSetback)sinceit typically“setsback”thezonetemperatureset-pointsand owratetosmallervalues duringunoccupiedtimes.Theothertwocontrollers,whichw epropose,areMPC-based controllers: MOBO (MeasuredOccupancyBasedOptimal)and POBO (Predicted OccupancyBasedOptimal).BothoftheMPC-basedcontroller sarecomplexand computationallyexpensiveastheycomputethecontrolinpu tsbysolvinganoptimization problem.Themaindifferencebetweenthe MOBO and POBO controllersisthat MOBO requiresoccupancymeasurements,whilethe POBO algorithmrequires occupancyprediction.Thus,complexityofthecontrolalgo rithmsincreasesinthe order BL MOBS MOBO POBO Bydoingthecomparisonoftheabovementionedcontrollers, weaddressthe followingfourquestions: 1.Howmuchsavingscanbeobtainedifasystemmodelandmeasu rements/predictions ofoccupancyareavailabletoacontroller? 2.Whatisthevalueofoccupancypredictionvs.occupancyme asurements? 50

PAGE 51

3.Howdothesavingsdependonthedelityofinformationand complexityofthe controller? 4.Whatistheworthofusingoptimalcontroltechniquesover afeedbackmethod? Therestofthechapterisorganizedasfollows.Thebaseline control(whichisa conventionalcontrolusedinpractice)andtheproposedcon trol,alongwiththemodelof powerconsumption,aredescribedinSection 3.2 .Section 3.3 describesperformance metricsrelatedtothermalcomfortandenergysavings.Simu lationresultstocompare theperformanceofthecontrollersarepresentedinSection 3.4 .Section 3.5 concludes theresultsanddiscussesthewaystoextendthisworkinthef uture.Anerroranalysisof Euler'sforwardmethodforbuildingdynamicmodelispresen tedinSection 3.6 3.2ControlAlgorithms Aschematicofatypicalmulti-zonecommercialbuildingwit haVAV-basedHVAC systemandaconceptualrepresentationofacontrolalgorit hmthatcanbeimplemented inazoneisshowninFigure 3-1 .Thecontrolinputsaredeterminedbyazone-climate controlalgorithminsuchawaythatthermalcomfortandIAQa remaintainedinthat zone.Thecontrolinputsdeterminedbyazone-levelcontrol algorithmaretemperature ( T SA )andowrate( m SA )oftheairsuppliedtothatzonebyitsVAVbox.Depending onthecontrolalgorithm,certainmeasurementsand/orpred ictionsmayberequiredby thecontrolalgorithmtocomputethecontrolinputs.Forins tance,thecommoncontrol methodsusedinpracticesuchassinglemaximumanddualmaxi mumlogics[ 59 Chapter47]requireonlyzonetemperaturemeasurements.Ho wever,acontrollerbased onoptimalcontroltechniquessuchasMPCrequiresmeasurem entsandpredictionsof outsidetemperature,solarradiation,occupancy,zonetem peratureandhumidity. Wenowdescribethe BL (baseline)controller,andthreeproposedcontrol algorithms, MOBS (MeasuredOccupancyBasedSetback), MOBO (Measured OccupancyBasedOptimal)and POBO (PredictedOccupancyBasedOptimal).The informationrequiredbyeachcontrolleranditscorrespond ingcomplexityareshownin 51

PAGE 52

Exogenous Inputs Control Inputs (u) SupplyAir (SA) ConditionedAir(CA) VAVVAVZoneControl AlgorithmZone ZoneOutputs OutsideTemperature( T OA ), SolarRadiation( Q s ),Occupancy( n p ) OutsideAir(OA) AHUDampersSATemperature( T SA ) SAFlowRate( m SA ) ReturnAir(RA) Figure3-1.Genericschemeforzone-levelcontroller'simp lementation. c r Elsevier2013 Table 3-1 .Thecomplexityoroverallcomplexityofacontrollerisde nedasthetotal amountofinformation,effort,andcomputationtimerequir edtoimplementthecontroller. Theinformationrequirementsincludemeasurements,predi ctions,andbuilding hygro-thermaldynamicsmodel.Increasingtheinformation requirementsincreases bothcostandeffortrequiredtoimplementthecontroller.F oreg.,moremeasurements requireinstallingextrasensorsthatincreasethecost.Th eeffortrequiredtoobtainthe measurementsandpredictionsishighlydependentontheirt ypes.Forinstance,the predictionsofoutsideweatherarerelativelyeasiertoobt ainascomparedtothatof occupancypredictions.Similarly,anumberofexperiments needtobeconductedto calibratedthebuildinghygro-thermaldynamicsmodel.The computationtimeandeffort requiredtoimplementanoptimalcontrollerinpracticeare muchhigherascompared tothatofan“if-else”controller.Basedontheaforementio nedfactors,thecomplexityor overallcomplexityofthecontrolalgorithmsincreasesint heorder:1) BL ,2) MOBS ,3) MOBO ,and4) POBO 52

PAGE 53

Table3-1.Complexityandinformationrequiredbyvariousc ontrollers. c r Elsevier2013 ControlTypeofoccupancyModelComputationOverall algorithminformationrequiredrequiredrequiredcomplex ity 1 BL NoneNoLowLow 2 MOBS MeasurementsNoLowMedium 3 MOBO MeasurementsYesHighHigh 4 POBO PredictionsYesHighVeryHigh 3.2.1 BL (Baseline)Controller AmongthecommoncontrollogicsusedattheVAVboxestomaint ainIAQand temperatureinazone,wechoosethedualmaximum[ 59 ,Chapter47]asthe“baseline controller”.Eventhoughthesinglemaximumcontrol[ 59 ,Chapter47]ismorecommon inexistingcommercialbuilding,dualmaximumisthemoreef cientofthetwo.Inthis strategy,thecontrollogicisdividedintofourmodesbased onthezonetemperature:(i) Re-heating(ii)Heating(iii)Dead-Bandand(iv)Cooling,w hichareshownschematically inFigure 3-2 .There-heatingmodeisturnedonifthezonetemperaturesta ysbelow the“Re-heatingSet-Point(RTG)”formorethan10minutes.S imilarly,thecoolingmode isturnedonifthezonetemperatureremainsabovethe“Cooli ngSet-Point(CLG)”for morethan10minutes.Theheatingmodeisturnedonifthezone temperaturestays betweenRTGand“HeatingSet-Point(HTG)”formorethan10mi nutes.Thedead-band modeisturnedonifthezonetemperaturestaysbetweenHTGan dCLGformorethan 10minutes.Inthere-heatingmode,thetemperatureofsuppl yairissettomaximum possiblevalue( T SA high ),andtheowrateofsupplyairisvariedusingaPIDcontroll erto maintainthezonetemperaturetoadesiredset-point T set .Intheheatingmode,theow rateofsupplyairowrateissettotheminimumallowedvalue ,andthetemperatureof supplyairiscontrolledbyaPIDcontrollersothatthezonet emperatureismaintained closetotheset-point( T set ).Theminimumallowedvaluefortheowrateisdetermined asfollows MinimumAllowedFlowRate= m SAp n pd + m SAlow ; 53

PAGE 54

where m SAp = m OAp = (1 R RA ) ;m SAlow = m Az A z = (1 R RA ) : (3–1) When =1 ,thesecalculationsyieldtheminimumairowrequirements speciedby ASHRAEventilationstandard62.1-2010[ 17 ].Sincethebaselinecontrollerdoesnot useoccupancymeasurements,theminimumallowedowrateis calculatedusingthe designedoccupancy n pd thatisassumedconstant.Wehavechosen > 1 tomake IAQrobusttomismatchesbetweenactualanddesignedoccupa ncy.Inthedead-band mode,nore-heatingisperformed,i.e., T SA = T CA ,andsupplyairowrateissetto theminimumallowedvalue( 3–1 ).Inthecoolingmode,noheatingorre-heatingis performed,i.e., T SA = T CA ,buttheowrateofsupplyairisvariedtomaintainthe desiredset-point T set inthezone. Thedesiredset-point T set usedbythePIDcontrollersduringthere-heating, heatingandcoolingmodesisusuallythetemperatureprefer redbytheoccupants.If thetemperaturepreferredbytheoccupantsisnotknown,the reareseveralotherways tochoosethevalueof T set .Onewayistochoose T set equalsto RTG HTG and CLG duringthere-heating,heating,andcoolingmodes,respect ively.Anotherwayistochose T set asanaverageof HTG and CLG duringallthemodes.Wechoose T set asthe averageof HTG and CLG inthischapter,i.e., T set = HTG + CLG 2 .Notethatanighttime setbackisusedbythebaselinecontrollerinwhichtheset-p oints RTG and HTG are decreasedwhiletheset-point CLG isincreasedduringapre-speciedperioddeemed “nighttime”.Theset-pointsarechangedbasedontheassump tionthatthezoneisnot occupiedduringthenight.Thisisdonetoreduceenergycons umption. 3.2.2 MOBS (MeasuredOccupancyBasedSetback)Controller Theproposed MOBS controllerrequiresoccupancymeasurementsinadditionto thezonetemperaturemeasurements.Itisquitesimilartoth e BL controllerdescribed inSection 3.2.1 ,exceptfortwokeydifferences.First,theminimumallowed ow mentionedin( 3–1 )iscalculatedbasedonthemeasuredoccupancyinsteadofth e 54

PAGE 55

n nrnrn rnrn rrn nr r rn rn r n r n nrnrn nr Figure3-2.Aschematicofthebaselinecontroller(“dualma ximum”). c r Elsevier2013 designoccupancy,whichisexpressedas MinimumAllowedFlowRateattime t = m SAp n p ( t )+ m SAlow ; (3–2) where n p ( t ) istheoccupancymeasuredattime t ,and m SAp m SAlow arecomputed using( 3–1 ).Second,thetemperatureset-pointsduringallthemodesa redetermined basedonwhetherthezoneisoccupiedornot: RTG ( t )= T unocc RTG HTG ( t )= T unocc low CTG ( t )= T unocc high 9>>>>=>>>>; if n p ( t )=0 ; RTG ( t )= T occ RTG HTG ( t )= T occ low CTG ( t )= T occ high 9>>>>=>>>>; if n p ( t ) 6 =0 : (3–3) Thechoiceofdesignvariables T unocc RTG ;T occ RTG ;T unocc low ;T occ low ;T unocc high ;T occ high involvesa trade-offbetweenenergysavingsandthermalcomfort.Clea rly,therange [ T occ low ;T occ high ] shouldbechoseninsuchawaythatoccupantsfeelcomfortabl eifthezonetemperature iswithinthisrange.Awiderrangewillresultsinreduceden ergyconsumption,since thecontrollermaybeabletoreducereheatingduringlowthe rmalloadconditionsand reducetheairowduringhighthermalloadconditions.Toow idearangewill,however, maketheoccupantsfeeluncomfortable.Asageneralrule,th eparametersforthe 55

PAGE 56

unoccupiedperiodsshouldbechosensothat [ T occ low ;T occ high ] [ T unocc low ;T unocc high ] ; (3–4) i.e.,thetemperatureisallowedtovarywithinawiderrange ofvaluesduringunoccupied periodsthaninoccupiedones.Thisisexpectedtoresultine nergysavingsaswell. However,eveninunoccupiedtimesitisnotrecommendedtole tthetemperaturedeviate toofarfromwhatisallowedduringoccupiedtimes.Otherwis e,whenthezonebecomes occupiedagain,itwilltakealongtimetobringthetemperat urebacktotherange allowedduringtheoccupiedtime,whichwillmakeoccupants feeluncomfortable.In addition,allowingtoolowtemperaturemaycausecondensat iononsurfacesleading tomoldgrowth.Similarly,choosingthereheatingset-poin ts( T unocc RTG ;T occ RTG )farfromthe heatingset-points( T unocc low T occ low )islikelytoresultinhighenergysavingsbutalsomakes peoplefeelmoreuncomfortable. Thealgorithmdescribedaboveistermed MOBS (MeasuredOccupancyBased Setback)controlbecause,ingeneral,itsetsbackthetempe ratures( RTG HTG ,and CLG )andtheowrateofsupplyairwhenthezoneisnotoccupied. 3.2.3MPC-basedControllers Inthissection,weproposetwoMPC-basedcontrolalgorithm s: MOBO and POBO Theblockdiagramoftheimplementationofthe MOBO and POBO controllersisshown inFigure 3-3 .Timeismeasuredwithadiscreteindex k =0 ; 1 ;::: ,wherethetimeperiod between k and k +1 isdenotedby t .BoththeMPC-basedcontrollerscomputethe controlinputs( T SA ( k ) ;m SA ( k ) )over K timeindicesbysolvinganoptimizationproblem, whichminimizestotalenergyconsumptionoverthatperiodw hilemaintainingthermal comfortandIAQ.Thecontrolinputsareappliedatthecurren ttimeindex k ,andthe optimizationproblemissolvedagainattimeindex k +1 tocomputethecontrolinputsfor thenext K timesteps.Thewholeprocessisrepeatedatthe ( k +1) -thtimeindex. 56

PAGE 57

Outputs Exogenous Inputs Optimal Control Inputs AHUInputs Zone MPC Estimated InitialState (Model) (Model) KALMANFILTERT SA m SA T z W zX 0 T OA Q sn pT CAWCAn pRRAFigure3-3.Implementationofthe MOBO and POBO controllers. c r Elsevier2013 Tosolvetheunderlyingoptimizationproblem,boththeMPCbasedcontrollersneed (i)predictionsoftheexogenousinputssuchas T OA W OA Q s and n p ,overthetime horizonofoptimization,(ii)amodelofthezonehygro-ther maldynamics,and(iii)initial stateofthehygro-thermaldynamicsmodel.Thepredictions ofexogenousinputs T OA W OA ,and Q s areassumedavailablefromweatherforecasts.Theprocesso fobtaining occupancypredictions( n p )isexplainedlaterwhenboththecontrollersareexplained indetail.Themodelofbuildinghygro-thermaldynamicsand power,whichisusedby boththecontrollers,isexplainednext.AnEKF(ExtendedKa lmanFilter)-basedstate observerisusedtoestimatetheinitialstateofthemodelat thestartoftheoptimization. Thecontinuous-timereducedordermodelofthebuildinghyg ro-thermaldynamics isthesameas( 2–21 ).Thecontinuous-timereducedordercoupledODEmodelis discretizedusingEuler'sforwardmethodtoobtainadiscre te-timemodel,whichcanbe expressedas T r ( k +1)= AT r ( k )+ Bv ( k )+ F ( T z ( k ) ;W z ( k ) ;u ( k ) ;v ( k )) ; W z ( k +1)= L ( T z ( k ) ;W z ( k ) ;u ( k ) ;v ( k )) ;T z ( k )= C 1 T r ; (3–5) where A and B arethematricesobtainedafterthediscretizationof( 2–21 ), F and L arethenon-linearfunctionsafterthediscretizationof( 2–21 ),thevector v ( k ) consistsof 57

PAGE 58

exogenousinputs,andthevector u ( k ) consistsofthecontrolinputs( m SA ( k ) ;T SA ( k ) ), i.e., u ( k )=[ m SA ( k ) ;T SA ( k )] T .TheinterestedreadercanrefertoSection 3.6 fortheerror analysisofEuler'sforwardmethodappliedtothebuildingt hermalmodel. Thetotalpowerconsumption P ( k ) atthetimeindex k ,whichisasumoffanpower P F ( k ) ,reheatingpower P R ( k ) ,andconditioningpower P U ( k ) ,isgivenby P ( k ) P F ( k )+ P U ( k )+ P R ( k ) : (3–6) Ifwewanttoemphasizethedependencyoftotalpowerontheco ntrolinputs,wewrite itas P ( u ( k ) .SinceweignoretheAHUdynamics,thepowerconsumedincond itioning theairisafunctionoftheinstantaneoustemperatureandhu midity.Thefanpower,the reheatingpower,andtheconditioningpoweraregivenby P U = m SA ((1 R RA ) h OA + R RA h EA h CA ) ;P F = m SA ;P R = m SA ( h SA h CA ) ; (3–7) where = P s f d m asshownin[ 60 ,Chapter4],[ 61 ,Chapter10],[ 62 ,Chapter21].The parameter isaunit-conversionconstant,whichdependsontheunitsch osenforthe fanpower,totalstaticpressure P s ,andowrate m SA ,eg., =1 = 6356 whentheunits offanpower,owrate,andtotalstaticpressureare Hp cfm ,and in:w:c: ,respectively. Theparameters f d ,and m aretheefcienciesoffan,drive,andmotorthatdrivesthe fan,respectively.Wehaveassumedaconstantvalueoftheto talstaticpressure.Since theefcienciesarealreadyconstantforaparticularfansy stem,theparameter turns outtobeaconstantthatdependsonthefansystem.Thespeci centhalpytermscanbe calculatedusing( 2–5 ).Theenergy E ( k ) consumedduringthetime [( k 1) t;k t ] is estimatedas E ( k )= tP ( u ( k )) : (3–8) 58

PAGE 59

3.2.3.1 MOBO (MeasuredOccupancyBasedOptimal)Controller Theproposed MOBO controllerisanMPC-basedcontrolstrategy.Inthisscheme weassumethattheinstantaneousoccupancymeasurementsat the k -thtimeindex areavailabletothecontroller.However,MPCrequirespred ictionsofallexogenous inputstoperformtheoptimizationinvolvedincomputingth econtrolinputs.Therefore, someformofoccupancypredictionsmustbeprovidedtotheco ntroller.Moreover, occupancypredictionsdeterminetherangeinwhichthezone temperatureisallowedto staybasedonwhetherthezoneisoccupiedornot.Sinceonlyi nstantaneousoccupancy measurementsareavailable,weassumethatthepredictedoc cupancyforthenext K timeindicesissameasthemeasuredoccupancyatthe k -thtimeperiod: n p ( i )= n p ( k ) ;i k Thecontrollogicisdividedintotwomodes:(i)Occupiedand (ii)Unoccupied,which areexplainedbelowindetail. OccupiedMode:Thecontrolleroperatesintheoccupiedmode ifthezoneis occupiedatthe k -thtimeindex,i.e.,themeasuredoccupancyatthebeginnin gofthe timeinterval [ k t; ( k +1) t ] isatleast 1 .Theoptimalcontrolinputsforthenext K time indicesarecomputedbysolvingthefollowingoptimization problem: U ? := arg min U G ( U ) ; (3–9) where U =[ u ( k ) T ; ;u T ( k + K )] T 2 R 2( K +1) and G ( U )= P k + K i = k E ( i ) ,subjecttothe followingconstraints: T occ low T z ( i ) T occ high ; W occ low W z ( i ) W occ high ; T CA T SA ( i ) T SA high m SAp n p ( i )+ m SAlow m SA ( i ) m SAhigh 9>>>>>>>=>>>>>>>; 8 i = k;:::;k + K: (3–10) Thersttwoconstraintsmeanthatthezonetemperatureandh umidityratioareallowed tovaryintherangeof[ T occ low T occ high ]and[ W occ low W occ high ] ,respectively.Thethirdconstraint 59

PAGE 60

simplytakeactuatorcapabilitiesintoaccount,sincetheV AVboxcanonlyincreasethe temperatureofthesupplyairabovetheconditionedairtemp erature.Theupperbound inthethirdconstraintisduetotheamountbywhichtherehea tcoilcanincreasethe temperatureofthesupplyair.Thefourthconstraintmeanst hatthereisalowerand upperboundontheowrateofsupplyairenteringthezone( m SA ).Thelowerboundon theowrateissameas( 3–2 ),whiletheupperbound m SAhigh reectsthemaximumow ratepossiblewhenthedampersintheVAVboxarecompletelyo pen. Thechoiceofthedesignvariables T occ low T occ high W occ low W occ high involveatrade-off betweenenergysavingsandpotentialoccupantdiscomfort. Asexplainedinthe MeasuredOccupancyBasedSetbackcontroller,thegreatert herangethatthe temperatureandhumidityareallowedtovaryin,boththepot entialenergysavings andoccupantdiscomfortarelarger. Aftersolvingtheoptimizationproblem( 3–9 )–( 3–10 )attime k ,onlythepartof U correspondingtothecurrenttimeindex k isimplemented. UnoccupiedMode:Thecontrolleroperatesintheunoccupied modeifthemeasured occupancyatthetimeindex k ,i.e.,atthebeginningofthe k -thtimeperiod,isobserved tobe 0 Atthe k -thtimeindex,theoptimalcontrolinputsforthenext K timeindicesare obtainedbysolvingthefollowingoptimizationproblem: U ? := arg min U G ( U ) ; (3–11) subjecttothefollowingconstraints: T unocc low T z ( i ) T unocc high W unocc low W z ( i ) W unocc high m SAlow m SA ( i ) m SAhigh T CA T SA ( i ) T SA high 9>>>>>>>=>>>>>>>; 8 i = k;:::;k + K: (3–12) 60

PAGE 61

Thereasonfortheseconstraintsisthesameasthatexplaine dpreviouslyinthe Section 3.2.3.1 .Theconstraintsonthezonetemperatureandhumidityratio duringthe unoccupiedmode,however,arechoseninsuchawaythat[ T unocc low T unocc high ] [ T occ low T occ high ], and[ W unocc low W unocc high ] [ W occ low W occ high ].Thisallowsthecontrollertoletthetemperature andhumidityratiotovaryinawiderangewhenthezoneisunoc cupied,whichleads toreducedenergyusage.Thechoiceoftheparametersforthe unoccupiedtimesalso involvesatrade-offasmentionedintheSection 3.2.3.1 .Thefarthertheparameters arefromtheircounterpartsfortheoccupiedmode,thegreat eristheenergysavings potential,butalsogreateristheriskofoccupantdiscomfo rtwhenoccupancychanges. 3.2.3.2 POBO (PredictedOccupancyBasedOptimal)Controller Theproposed POBO controllerisalsoanMPC-basedcontrolstrategy,whichis similartothePOBOcontrollerbutwithanimportantdiffere nce.The POBO controller hasaccesstooccupancypredictionsfromthetimeindex k to k + K .Theoptimalcontrol inputsforthenext K timeindicesareobtainedbysolvingthefollowingoptimiza tion problem: U ? := arg min U G ( U ) ; (3–13) subjecttothefollowingconstraints: T occ low T z ( i ) T occ high ; if n p ( i ) 6 =0 W occ low W z ( i ) W occ high ; if n p ( i ) 6 =0 T CA T SA ( i ) T SA high m SAp n p ( i )+ m SAlow m SA ( i ) m SAhigh 9>>>>>>>=>>>>>>>; 8 i = k;:::;k + K: (3–14) Thersttwoconstraintsmeanthatthezonetemperatureandh umidityratioareallowed tovaryintheallowedrangeof[ T occ low T occ high ]and[ W occ low W occ high ] ,respectively,during theoccupiedtime.However,therearenoconstraintsonthez onetemperatureand humidityratiowhenthezoneisnotoccupied.Thelasttwocon straintsaresameasthe lasttwoconstraintsoftheoptimizationproblem( 3–9 )–( 3–14 ).Oncetheoptimization 61

PAGE 62

problem( 3–13 )–( 3–14 )issolvedattime k ,onlythepartof U correspondingtothe currenttimeindex k isimplemented. Remark1. Bychoosing > 1 ,weensurethatforallthecontrollerstheminimumow rateduringunoccupiedtimesisgreaterthanthatprescribe dbyASHRAEventilation standard62.1-2010[ 17 ].Theprimaryreasonfordoingsoistomaketheresulting IAQrobusttotheerrorsinoccupancymeasurementsorpredic tions.Italsomakes IAQrobusttotheuncertaintyinthemeasuredowrateanddam perposition.By ensuringgoodIAQevenduringthetimeswhenthezoneispredi ctedtobeunoccupied (whethercorrectlyornot),theproblemofpredictingtheef fectofcontrolinputsonIAQis eliminatedfortheproposedcontrollers. 3.3PerformanceMetrics Theenergyconsumedbyacontroller C overaperiod T is E C = P i = T t i =1 E C ( i ) where E C ( i ) istheenergyconsumedbythecontroller C duringthetime [( i 1) t;i t ] calculatedusing( 3–8 ).Anenergyrelatedperformancemetricisthe“ % savingsoverthe baselinecontroller”thatisdenedas %Savings= E BC E C E BC ; (3–15) where E C and E BC aretheenergyconsumedbythecontroller C andthebaseline controller,respectively,overthesametimeperiod.Thepa rameter T ischosenas 24 hrs inthisdissertation. Wechoosetwometricsforanalyzingthethermalcomfortrela tedperformanceof thecontrollers:(i)TemperatureViolation D T and(ii)HumidityViolation D H ,whichare denedas D T = 8>>>><>>>>: T z ( t )+ T occ low ; if T z ( t ) T occ high and n p ( t ) 6 =0 0 ; otherwise 9>>>>=>>>>; ; 62

PAGE 63

D H = 8>>>><>>>>: W z ( t )+ W occ low ; if W z ( t ) W occ high and n p ( t ) 6 =0 0 ; otherwise 9>>>>=>>>>; : Themetrics( D T / D H )measurethedeviationofthezonetemperature/humidityfr om theallowedrangeduringoccupiedtimes.Thetemperaturean dhumidityviolations areconsidered 0 duringtheunoccupiedtimessincethereisnooneinthezone. The averagetemperatureviolation( D T )andtheaveragehumidityviolation( D H )duringtime period T aredenedas D T = 1 T Z T 0 D T ( t ) dt 1 L L X k =1 D T ( k ) ; D H = 1 T Z T 0 D H ( t ) dt 1 L L X k =1 D H ( k ) ; (3–16) where L = T= t .AccordingtoASHRAE[ 27 ,Chapter8],aslongaspeopleare wearingclothingofthermalresistancebetween 0 : 0775 m 2 K=W and 0 : 155 m 2 K=W doingprimarilysedentaryactivity,andtheairspeedinthe zoneislessthan 0 : 2 m=s thenensuringthatthetemperatureandhumidityofthezones tayswithincertainrange ensuresthermalcomfortofoccupants(seeFigure 3-7 inSection 3.4.2 ).Therefore, withappropriatechoiceoftheparameters T occ ( ) and W occ ( ) ,thetemperatureandhumidity violationsdenedabovecanbeusedasmetricsforthermalco mfort.ThoughPredicted MeanVote(PMV)[ 27 ,Chapter8]isawidelyusedmetrictoevaluatethermalcomfo rt,it isafunctionofcomplexfactorssuchasmetabolismrate,clo theswornbytheoccupant, etc.,whichisquitedifculttocomputeinreal-time.There fore,weusetemperatureand humidityviolationstoevaluatethethermalcomfort,which aresimplertocomputeaswell asmorerobusttoassumptionsmadeabouttheoccupants. ThoughIAQisasimportantconcernasthermalcomfort,ifnot more,wedonot deneametrictomeasure“IAQperformance”oftheproposedc ontrollers.Though CO 2 andvolatileorganiccompoundscontributetopoorIAQ,ther eisnowelldened numericalmeasuretocalculateIAQ[ 63 ].Instead,weimposeconstraintsonthe 63

PAGE 64

minimumowratesuchthatIAQismaintainedbyallthepropos edcontrollers,even duringunoccupiedtimes(seealsoRemark 1 ). 3.4SimulationResults 3.4.1ModelCalibrationandValidation Datafromzone 247 inPughHallattheUniversityofFlorida,Gainesville,FL,U SAis usedtocalibratethemodel( 2–7 ),whichisshowninFigure 3-4 .Zone 247 isaninterior roomonthe 2 nd oorinthePughHall,whichonlyhasinteriorwalls.Eachint eriorwallin zone 247 hasaheightof 2 : 7 m andthewidthoftheinternalwallsisshowninFigure 3-4 nrr Figure3-4.Layoutofzone 247 onthe 2 nd oorinPughHallattheUniversityofFlorida. Measurementsofthezonetemperatures,supplyairtemperat uresandowrates areobtainedfromtheBuildingAutomationSystemat10-minu teintervals.Themodelis calibratedbytuningthetotalthermalresistanceperunita reaofthe“internalwalls”to minimizetheerrorbetweenthemeasuredtemperatureandthe predictedtemperature ofthezone.Datafora48hourtimeperiod(Jan29–Jan30,2011 )isusedtocalibrate themodel.Itisassumedthattherearenooccupantsduringth istimeasthistime correspondstoaweekend.Thecomparisonbetweenthemeasur edandpredicted temperatureswiththecalibratedmodelareshowninFigures 3-5A – 3-5B .Thevalidation dataset(midnightFeb5ththroughmidnightofFeb6th,2011) alsoischosenduringa 64

PAGE 65

weekend.ItisclearfromFigure 3-5B thatthetemperaturepredictionsbythemodelare closetothemeasuredvalues. 0 10 20 30 40 21.5 22 22.5 23 23.5 24 24.5 Time(hr) SimulatedMeasuredZoneTemp( C)ACalibration 0 10 20 30 40 16 18 20 22 24 26 Time(hr) SimulatedMeasuredZoneTemp( C)BValidation Figure3-5.Predictedandmeasuredtemperaturesinzone 247 c r Elsevier2013 3.4.2ChoiceofParameters Simulationsarecarriedoutforamodelofthreeseveraltype sofzones.Allthe zoneshaveoneexternalwall,onewindow,andthreeinternal walls.Thethreeinternal wallsareofthesametype.Itisassumedthattheoorandthec ellingareperfectly insulated,andthewindowshavenegligiblethermalcapacit ance.Eachzonehasthe samewindowandsameexternalwallconstruction,buttheint ernalwallsconstruction varyfromzonetozone.Atype1 zonehasinternalwallsofhighthermalresistanceand lowthermalcapacitance.Theinternalwallsofatype2 zonehavelowthermalresistance andhighthermalcapacitancewhiletheinternalwallsofaty pe3 zonehavelowthermal resistanceandlowthermalcapacitance.Wedonotconsidera zonewithinternalwalls ofhighthermalcapacitanceandhighthermalresistanceast hisisunusual.Thereason tochoosethesethreetypesofinternalwallsforthisstudyi sthatthePughHallhas thesetypesofinternalwalls.Therelativethermalresista nceandcapacitancevalues ofanytwotypesofinternalwallswithrespecttothevalueso fthethirdtypeofinternal wallareknownfromtheirmaterialproperties.Therefore,i fthethermalresistance andcapacitanceofanytypeofinternalwallareknown,theth ermalcapacitancesand 65

PAGE 66

resistancesoftheothertwotypesofinternalwallscanbees timatedbyusingtheir relativevalues.Theresistanceandcapacitancevaluesfor thezonetype3 areobtained bythecalibrationandvalidationforthedynamicmodelofzo ne 247 ,whichisofzone type3 ,asshownearlierinSection 3.4.1 .Thetotalthermalresistanceandcapacitance valuesoftheinternalwallsofzonetype3 areincreasedtoestimatetheresistanceand capacitanceoftheinternalwalloftype1 andtype2 zones.Theresultingresistanceand capacitancevaluesareshowninTable 3-2 Table3-2.Totalthermalresistanceandcapacitanceofwind owandwalls. c r Elsevier 2013 InternalWallExternalWallWindow ZoneTotalThermalTotalThermalTotalThermalTotalTherma lTotalThermal TypeResistance( m 2 K W )Capacitance( kJ m 2 K )Resistance( m 2 K W )Capacitance( kJ m 2 K )Resistance( m 2 K W ) 1 2.731 2 0.53682.73680.5 3 0.531 Theboundariesofeachzonethatareseparatedfromthezonet hroughthe internalwallsareassumedtohaveaconstanttemperatureof 22 : 2 C.Theexternal wallseparatesazonefromoutsideweather.Threetypesofou tsideweatherconditions areconsidered:cold,hot,andpleasant.Figure 3-6 showsthetemperatureandhumidity dataforthecold(Jan14,2011),hot(Jul31,2011),andpleas ant(Mar16,2011)days inGainesville,FL,USA.“Pleasantweather”isnon-standar dterminology;weuseitto denotetheweatherthatisneitherhotnorcold. 0 5 10 15 20 0 10 20 30 Cold Hot Pleasant Time(hr)T OA ( C) AOutsideTemperature 0 5 10 15 20 20 40 60 80 Cold Hot Pleasant Time(hr) H OA (%) BRelativeHumidity Figure3-6.OAtemperatureandrelativehumidityinGainesv ille,FL,USA. c r Elsevier 2013 66

PAGE 67

Themaximumowratesuppliedbyallthecontrollersischose nas 0 : 125 kg=s FromASHRAEventilationstandard62.1-2010[ 17 ]requirementsandreturnairratio showninTable 3-3 ,itturnsoutthat m SAp =0 : 005 kg=s and m SAlow =0 : 015 Kg=s and. Thesevaluesarecomputedusing( 3–1 ),with A z =25 m 2 .Forthe BL controller,the MinimumAllowedFlowRateischosenas 0 : 05 kg=s ,whichcorrespondstoadesigned occupancyofapproximately 5 personsforthatgivenzone.Thisisalsotheminimum owratethatiscurrentlybeingusedbytheexistingcontrol logicinzone 247 ofPugh Hall.TheIAQfactorofsafetyischosenas =1 : 7 sothattheminimumowratefor the MOBS MOBO ,and POBO controllersduringtheunoccupiedmodeturnsouttobe m SAlow =0 : 0255 Kg=s .Forthe BL controller,thetemperatures:RTG,HTG,andCLG aresetto 21 : 8 C, 21 : 9 C,and 23 : 6 C,respectively,from 6:30 a.m.to 10:30 p.m. Duringthetime 10:30 p.m.– 6:30 a.m.,thetemperatures:RTG,HTG,andCLGfor the BL controllerarechosenas 20 : 9 C, 21 : 1 C,and 24 : 4 C,respectively.Thisnighttime setbackiscurrentlyusedinthePughHall. OtherdesignparametersareshowninTable 3-3 .ItisshowninTable 3-3 thatthe set-points( RTG HTG ,and CTG )arechangedsymmetricallyaroundtheset-point T set basedonwhetherthezoneisoccupiedornot.Since T set = RTG + CLG 2 asmentionedin theSection 3.2.1 ,thedesiredset-point T set staysconstant. Itisalsoassumedthattheinitialvaluesofallthetemperat uresstates(i.e.,zone temperatureandtemperaturevaluescorrespondingtothein teriorofthewalls)andzone humidityratioare 22 : 2 C and 0 : 009 ,respectively. Table3-3.Designparametersusedinthevariouszone-level controllers. c r Elsevier 2013 TemperatureParameters T set T SA low T SA high T unocc RTG T occ RTG T occ low T occ high T unocc low T unocc high T CA ( C )( C )( C )( C )( C )( C )( C )( C )( C )( C ) 22.812.830.020.921.821.923.621.124.412.8 HumidityandOtherParameters W unocc low W occ low W unocc high W occ high W CA K t TR RA n pd ( g kg )( g kg )( g kg )( g kg )( g kg )(min)(hr)( % ) 7.47.410107.431024405 67

PAGE 68

InFigure 3-7 ,thecomfortenvelopespeciedin[ 27 ,Chapter8]isshowninthe stripedblackarea,andtheenvelopechosenhereduringtheo ccupiedandunoccupied timeisshownindashedredandblueboxes,respectively.The comfortenvelopeis denedbytheconstraintsonthezonetemperatureandhumidi tyratio.Aslongas certainassumptionsonoccupantsclothingetc.,aresatis ed(seeSection 3.3 ),thermal comfortisensurediftemperatureandhumidityratioaremai ntainedwithintheshaded regionsshowninthegure.Theconstraintsonthezonetempe ratureandhumidityratio arechosensothatwhentheyaremet,thezone-climatemeetst heASHRAEmandated conditions[ 27 ]. nrrr nrrr Figure3-7.Comfortenvelopeduringoccupiedandunoccupie dtimes. c r Elsevier2013 3.4.3PerformanceComparison Inthissection,wecomparetheperformanceof BL MOBS MOBO ,and POBO control algorithmsthataredescribedinSection 3.2 .Simulationsareperformedusing MATLAB c r ;whileIPOPT[ 64 ]isusedtosolvetheoptimizationproblemsforthe MOBO and POBO controlalgorithms. Eachzoneisoccupiedbyapersonfrom 8:00 a.m.to 12:00 p.m.,and 1:00 p.m. to 5:00 p.m.,everyday,whichistheoccupancyproleusedduringth esimulationsfor allthecontrollers.The MOBS and MOBO controllersuseinstantaneousoccupancy measurements,whilethe POBO controllerusesoccupancypredictions.Theoccupancy 68

PAGE 69

measurementscanbeobtainedusingCO 2 sensors[ 6 19 ],whiletheoccupancy predictionscanbeestimatedusingthedynamicoccupancymo dels[ 6 18 ].Inthis work,weassumethatoccupancypredictionsareavailableto the POBO controller. Thetotaldailyenergyconsumption,averagetemperaturevi olation,averagehumidity violation,and % savingsoverthebaselinecontrollerareshowninTable 3-4 .Itisclear fromthetablethatdependingonthezonetypeandoutsidewea ther,the MOBS and MOBO controllersresultin42–59 % and45–59 % energysavings,respectively, overthebaselinecontroller.Recallthatboththe MOBS and MOBO controllersuse occupancymeasurements;notpredictions.Wealsoseefromt hetablethatthe POBO controller—whichrequiresoccupancypredictions—canres ultinadditional energysavingsoverthe MOBS and MOBO controllersbyanamountvaryingfrom 1% to 13% ,againdependingonzonetypeandweather.Allthecontrolle rshavevery smallaveragetemperatureviolation,anduniformlyzeroav eragehumiditydiscomfort, irrespectiveofthezonetypeorweather.RecallthatIAQism aintainedatalltimesdueto theconstraintontheminimumairowrate.Theresultsindic atethattheenergysavings fromtheproposedcontrollersareachievedwithminimalimp actoneitherthermal comfortorIAQ.Table3-4.Dailyenergyconsumption, % Savings,andviolations. c r Elsevier2013 ColdHotPleasant ZoneControl E Savings D T D H E Savings D T D H E Savings D T D H TypeSchemeMJ % C g kg MJ % C g kg MJ % C g kg BL 93.4-0.0070179.4-0.003078.3-0.0040 1 MOBS 53.542.70.026097.545.60.014041.547.00.0180 MOBO 50.645.80.006093.747.70.004039.050.10.0060 POBO 41.555.60083.953.20033.657.100 BL 86.8-0.0050173.7-0.001072.2-0.0030 2 MOBS 42.151.40.016079.654.20.001029.958.60.0080 MOBO 40.253.70.004080.054.00030.258.20.0010 POBO 35.958.70078.954.60028.460.700 BL 91.9-0.0070178.4-0.002076.8-0.0040 3 MOBS 49.745.90.023092.248.30.013038.449.90.0210 MOBO 47.348.50.006090.049.50.002036.252.80.0050 POBO 40.556.00083.353.30032.957.200 69

PAGE 70

Theenergysavingsareduetothereductionofsupplyairowr ateandtheincrease intheallowabletemperaturerangewhenthezoneisnotoccup ied.Reductionofthe owratedecreasesfan-,conditioning-,andreheating-ene rgyconsumption.Increasing theallowabletemperaturerangeresultsinlessreheatinge nergyusageattheVAVbox, becausethezonetemperatureisallowedtobelowerduringun occupiedtimesthanwhat thebaselinecontrollerallows.Foreveryzone,thetotalen ergyconsumptionismaximum duringhotweatherbecausetheAHUconsumesmoreenergytoco nditionthehotand humidoutsideairthantoconditionthecolddryair.Amongth ethreeweathers,pleasant weatherleadstotheminimumenergyconsumptionduetothesm allconditioning andreheatingenergyrequirements.Foraxedzone,thefane nergyconsumptionis approximatelythesameduringalltheweatherconditions. Givenacontrollerandanoutsideweather,weobservethat E zonetype 2 < E zonetype 3
PAGE 71

Theaveragetemperatureviolation D T witheitherthe BL controllerorthe MOBS controller ismorethantheaveragetemperatureviolation D T withthe MOBO controllerforaxed zone.Thisoccursbecausethe BL and MOBS controllerswaitfor10minutestoturnon theheating/coolingmode.Amongallthecontrollers,theav eragetemperatureviolation D T ismaximumforthe MOBS controller.Sincethe MOBS controllerincreasesthe temperaturerangeduringthedaytimeifunoccupied,ittake slongtimeforthezone temperaturetocomebacktotheallowablerangewhenthezone becomesoccupied again.However,the BL controllerdoesnotincreasetheallowabletemperatureran ge duringthedaytimeevenifthezoneisnotoccupied.Therefor e,theaveragetemperature violationwiththe MOBS controllerismorethantheaveragetemperatureviolationw ith the BL controller. Thesimulationresultsshownaboveareforthecasewhenoccu pancyvaries between0and1,andforGainesville,FL,USAlocation.Wehav ealsoconducted simulationsforthreemorecases:i)occupancyvariesbetwe en0and3;location: Gainesville,FL,USA,ii)occupancyvariesbetween0and1;l ocation:Phoenix,AZ, USA,andiii)occupancyvariesbetween0and3;location:Pho enix,AZ,USA.The weatherdaysforPhoenixarechosenasJan14,Jul31,andMar1 6of2011,whichare thesamedayschosenforGainesville;seeSection 3.4.2 .Verysimilar % savingsover thebaselinecontroller,andaveragetemperature/humidit yviolations,areobtainedforall thecasesbyalltheproposedcontrollers. MPCvs.feedback,withoccupancymeasurements:Whilethe MOBS controller usessimplerule-basedfeedbackcontrolthatrequirestemp eratureandoccupancy measurements,the MOBO controllerisamuchmorecomplexMPC-basedcontrol schemethatrequirespredictionsofrelevantstatevariabl esandexogenoussignals.Yet, theresultsaboveshowthattheperformanceofthe MOBS and MOBO controllersare quitesimilarintermsofenergysavingsandthermalcomfort .Thisisduetothefactthat withoutoccupancypredictions,theMPC-basedcontrolleri snotabletotakeadvantage 71

PAGE 72

ofitspowerfuloptimizationalgorithm.Ifthepredictions areavailable,MPC-basedcontrol maybeabletoreducetheairowandletthetemperature“vary ”,thussavingenergy, andthenbringitbackuprightbeforethezoneisabouttobeoc cupied.Intheabsence ofsuchpredictions,theMPC-controllercanonlydowhatawe ll-designedfeedback controllerwillalsodo,i.e.,setbackthezonetemperature whenthezoneisunoccupied, butnottoomuchsothatitcanbechangedquicklywhenoccupan cychanges,and maintainsomeminimumairowtoensuregoodIAQ. Onemainconcernduringtheinitialstagesoftheresearchwa sthattheslow thermaldynamicsofatypicalzone,alongwiththelimitatio nsoftheactuators,willmake theresponseoftheclosed-loopcontrolsystemtooslowtoen sureoccupantcomfort duringthetransitionperiodwhenoccupancychanges.Howev er,thesimulationresults reportedhereshowthatthisconcerncanbemitigatedbyappr opriatechoiceofthe allowedtemperatureandhumiditybands. Utilityofoccupancypredictions:Onesurprisingobservat ionisthattheadditional savingsofthe POBO controlleroverthe MOBS and MOBO controllersaresmall, 1–13 % ,eventhoughthe POBO controllerusesoccupancypredictionswhilethe othertwoonlyusemeasurements.Onecouldexpectlargeener gysavingsbythe POBO controllerasoccupancypredictionsareavailableandthec ontrollercanturn theairowratequitelow.Thesmalladditionalsavingsared uetotheventilation requirements.ASHRAEventilationstandard62.1-2010[ 17 ]requiresacertainamount ofoutsideair,whichdependsontheoorareaevenwhenthezo neisunoccupied.For atypicalmediumsizedofcewithasmalldesignoccupancy(1 -5people),theresulting minimumowrateturnsouttobeasignicantfractionofthen ominalairowrateduring occupiedperiods.Savingswouldbemoreiftheventilationr atesduringtheunoccupied timesweretobesmallerthanwhatareprescribedbycurrents tandards.Forinstance, theolderASHRAEventilationstandard62.1-2001[ 65 ]didnotrequireoutsideairsupply duringunoccupiedtimes.Wehavealsoperformedsimulation swithaminimumairow 72

PAGE 73

rateof 0 duringunoccupiedtimes.Inthatcasethesavingswiththe POBO controller increasesuptoabout 80% overthebaselinecontroller.Thatis,theadditionalsavin gs possiblewithoccupancypredictions—comparedtooccupanc ymeasurements—now turnsouttobeabout 40% 3.5DiscussionandFutureWork Weexaminehowacontrollerperformanceisaffectedbyitsco mplexity,wherethe goalofthecontrolleristominimizeenergyconsumptionwhi lemaintainingcomfort levelinazoneinacommercialbuildingwithaVAV-basedHVAC system.Forthat purpose,weproposethreecontrolalgorithmsofvaryingcom plexityandrequiring varyingamountofinformation: MOBS MOBO and POBO .Theperformanceofthe proposedcontrollersarecomparedthroughsimulationswit hthatofaconventional controller( BL controller).The BL controllerusestemperaturefeedbackbutnotreal-time occupancyinformation.Incontrast,theproposed MOBS and MOBO controllersrequire occupancymeasurements,andtheproposed POBO controllerrequiresoccupancy predictions.Whilethe MOBS controllerisafeedback-basedcontrolalgorithm,the MOBO and POBO controllersareMPC-basedalgorithms.Simulationresults showthat alltheproposedcontrollersleadto 50% energysavingsonaverage(dependingonzone type,weather,climate,designoccupancy,etc.)withnegli gibleimpactonIAQorthermal comfort. Thestudyshowsthatevenasimplefeedback-basedalgorithm canperformas wellasanMPC-basedalgorithmaslongasonlyoccupancymeas urementsare available.Anotherconclusionofthisstudyisthattheaddi tionalenergysavingswith anMPC-basedcontrolthatusesoccupancypredictions—over onethatonlyuses measurements—aresmall.Thesmalladditionalsavingsared uetotherestrictionon theminimumairowduringtheunoccupiedtimesthatcomesfr omcurrentASHRAE ventilationstandard62.1-2010[ 17 ].Theminimumventilationraterequirementsduring theunoccupiedtimearetotakeoutthewatervaporreleasedb ytheequipment, 73

PAGE 74

furniture,etc.,whichcontributeasignicantamounttoth eminimumventilation requirementsduringtheoccupiedtimesforatypicalmedium sizedofce.Iflower ventilationratesareallowedduringunoccupiedtimes,ase arlierstandardsdid[ 65 ],itis possibletosavesignicantlymoreenergybyusingoccupanc ypredictions;assuming ofcoursethatsuchpredictionscanbeobtained.Inthatcase ,thesignicantenergy savingswillcomefromthereductionintheenergyconsumedt oconditiontheairat AHUespeciallyduringtheunoccupiedtimeastheminimumall owedowratesare lowduringthattime.However,withthecurrentstandards[ 17 ],MPC-basedcontrol providesonly 1 13% energysavingsovermuchsimplerfeedback-basedstrategie s, evenwhenoccupancypredictionsareavailable.Atthesamet ime,considerableeffort isrequiredindeveloping/calibrating/validatingthedyn amicmodelsrequiredbythe controller,andthenumericaloptimizationinvolvedmaket hecontrollercomputationally complex.Therefore,theuseofMPC-basedzone-climatecont rolofexistingVAVsystems maynotbeeconomicallyjustied.Afeedbackcontrollerist hemostappropriatecontrol algorithmtobeusedatthezone-levelasitissimple,comput ationallyfast,requires minimalinvestmentinhardwareandsoftware,andresultsin energysavingsquitesimilar tothatofmuchmorecomplexcontrolalgorithms. Thisstudyshowsthatoccupancymeasurementisanimportant componentof energy-efcientzone-climatecontrol.Ifthezoneisdesig nedforasinglepersonsuch asanofce,amotiondetectorcanbeusedtomeasureoccupanc y.However,ifthe zoneisdesignedformultipleoccupants,obtainingaccurat einstantaneousoccupancy isnottrivialthoughseveralalgorithmshavebeendevelope d[ 6 18 19 ].Development ofreliableyetinexpensivesensorsthatcanmeasureoccupa ncywillgreatlyfacilitate thedeploymentofoccupancy-basedenergy-efcientbuildi ngcontrol.Thecontrollers proposedherehavesomerobustnesstoerrorsinoccupancyme asurementsduetotheir higher-than-neededminimumairow. 74

PAGE 75

3.6ErrorAnalysisofDiscretizedModelofHygro-thermalDy namics Supposewehaveasetofcontinuous-timeordinarydifferent ialequationsas T = f ( t;T ) ; (3–17) where T =[ T 1 ;T 2 ;:::;T N ] T 2 R N isatemperaturevectorand f =[ f 1 ;f 2 ;:::;f N ] T Thediscretizationof( 3–17 )at n th timeindex,with t beingthetimeindex,usingEuler's forwardmethodleadstothefollowingexpression T n +1 = T n + tf ( t n ;T n ) : (3–18) UsingTaylorseriesexpansionaround t n onthedynamicsof T 1 ,whichistherstrow in( 3–18 ), T 1 canbewrittenas T 1 ( t n +1 )= T 1 ( t n )+ hf 1 ( t n ;T ( t n ))+0 : 5 t 2 T 1 ( 1 ) ; where 1 2 [ t n ;t n +1 ] : (3–19) Byapplyingmeanvaluetheoremonfunction f 1 ,weget f 1 ( t n ;T ( t n ))= f 1 ( t n ;T n ) f 1 T ( 1 )( T ( t n ) T n ) ; (3–20) where f 1 T = df dT ,and 1 2 [ T n ;T ( t n )] .Combining( 3–19 )and( 3–20 ), T 1 canbeexpressed as T 1 ( t n +1 )= T 1 ( t n )+ tf 1 ( t n ;T n ) tf 1 T ( 1 )( T ( t n ) T n )+0 : 5 t 2 T 1 ( 1 ) : (3–21) Subtracting( 3–18 )from( 3–21 )givesusthefollowingequation E 1 ( t n +1 )= E 1 ( t n )+ tf 1 T ( 1 ) E +0 : 5 t 2 T 1 ( 1 ) ; (3–22) where E =[ E 1 ;E 2 ;:::E N ] ,and E i = T i ( t n ) T i n ;i 2 1 ; 2 :::;N .Combining( 3–22 )ina vectorformforevery i from 1 to n ,wecancompactlyrewriteas E ( t n +1 )=( I + t [ f 1 T ( 1 ) T ;f 2 T ( 2 ) T ;:::;f N T ( n ) T ] T ) E +0 : 5 t 2 [ T 1 ( 1 ) ; T 2 ( 2 ) ;:::; T N ( n )] T : (3–23) 75

PAGE 76

Using2-normonboththesides,theaboveequationcanbewrit tenas j E ( t n +1 ) j (1+ tK ) j E n j +0 : 5 t 2 [ M;M;:::;M ] T ; (3–24) where K = max ( j f 1 T ( 1 ) j ; j f 2 T ( 2 ) j ;:::; j f N T ( n ) j ) ,and M = max ( j T 1 ( 1 ) j ; j T 2 ( 2 ) j ;:::; j T N ( n ) j ) whichfurtherimpliesthat j E i ( t n +1 ) j (1+ tK ) j E i n j +0 : 5 t 2 M; forany i 2 [1 ;N ] : (3–25) Aftersubstitutingallthevaluesusedbythemodel,asprovi dedinSection 3.4 ,inthe aboveexpression,itisfoundthat M =2 : 5 10 5 and K =2 10 4 .Usingthevalues of M and K in( 3–25 )givesustheglobaltruncationerrornorm j E n j as 1 : 62 C in 30 min whichiscalculatedusingtheformula j E n j < M t 2 K ( e Kt n 1) Notethattheglobaltruncationerrorshownaboveisobtaine dthroughavery conservativeanalysis.Ithasalsobeenshownin[ 66 ]thatthistypeofanalysisisvery conservative.Wehavesimulatedthecontinuousmodelanddi scretizedmodelfor thesameinputs,andthemaximumdifferencebetweenthetemp eraturepredictedby thecontinuousanddiscretizedmodelsislessthan 0 : 1 C .Moreover,allthecontrol algorithmshavesomedegreeoftemperaturefeedbackbuilti n,whichtakestheactual measurementsandupdatesthecontrolinputsbasedonthemea surements.Thetime atwhichallthecontrollersusefeedbackislessthantheopt imizationhorizonforwhich theaboveerroranalysisisdone.Foreg.,theoptimizationt imehorizonis 30 min forthe MOBO controller,anditusesfeedbackafterevery 10 min .Theglobaltruncationerror in 10 min is 0 : 48 C ,whichismuchlessthantheglobalerrorfor 30 min .Furthermore, themeasurementsfrompre-installedsensorsinthebuildin ghavearesolutionof 0 : 5 C. Therefore,webelievethattheglobaltruncationerrorobta inedthroughthisdiscretization issmallenoughforthepurposeofcontrollers'comparison. 76

PAGE 77

CHAPTER4 EXPERIMENTALRESULTS Inthelastchapter,theperformanceofthe BL MOBS MOBO ,and POBO controllers wascomparedthroughsimulations.Itwasshownthatthe MOBS and MOBO controllers resultin 40 60% energysavingsoverthe BL controllerwhenoccupancymeasurements areused.Also,the MOBS controllerperformsaswellasthe MOBO controller.Inthe lastchapter,onlysimulationswereperformed.Inthischap ter,wedescribeexperiments inwhichthe BL MOBS ,and MOBO controllersareimplementedinazoneinPughHall attheUniversityofFlorida.Itisshownthattheexperiment alresultscorrespondwell withthesimulationresults:1) 60 70% energysavingswhilemaintainingcomfortlevel areobtainedwiththecontrollersthatuseoccupancymeasur ements,2)feedback-based controllerperformsaswellasadvancedMPC-basedcontroll er.Theexperimentsalso revealedthatthedeviationbetweenpredictedandactualca nbelargeduetouncertainty inactuatorresponse. Therestofthischapterisorganizedasfollows.Section 4.1 describesthegeometry andmodelcalibration/validationofthezoneusedwhilecon ductingtheexperiments. Experimentalsetupandthechoiceofparametersusedbythec ontrollersaredescribed inSection 4.2 .Section 4.3 showstheresultsobtainedfromthecontrollersduring experimentsandsimulations.Section 4.4 concludesthechapterwithadiscussionofthe results. 4.1ModelValidation Experimentsareperformedinzone 241 onthesecondoorinPughHallatthe UniversityofFloridacampus,Gainesville,FL,whichissho wninFigure 4-1 .Zone 241 isatypicalsmallofce,whichhasaNorth-facingwindowofa rea 2 : 8 m 2 .Zone 241 has threeinternalwalls(Wall 1 ,Wall 2 ,andWall 3 )andoneexternalwall(Wall 4 ).TheWall 1 Wall 2 ,Wall 3 ,andWall 4 havedimensionsof 4 : 8 m 2 : 7 m 4 : 8 m 2 : 7 m 5 : 2 m 2 : 7 m and 5 : 2 m 2 : 7 m ,respectively.Theinternalwallsofzone 241 areofsametypeasthatof 77

PAGE 78

zone 247 .Therefore,weusethetunedresistanceandcapacitanceval uesoftheinternal wallsofzone 247 duringtheconstructionofzone 241 hygro-thermaldynamicsmodel. nnrrrrrrrr rr Figure4-1.Layoutofzone 241 onthe 2 nd oorinPughHall. Theresistanceandcapacitancevaluesofthewallsandwindo wofzone 241 arethesameaspreviouslyshowninTable 3-2 .Thevalidationofzone 241 model isshownintheFigure 4-2 .DatausedforthevalidationstartsfrommidnightofFeb 5thandendsatmidnightofFeb6th,2011.Inshort,wehaveuse dthedataofzone 247 tondtheresistanceandcapacitancevaluesoftheinternal walls,usedthese resistance-capacitancevaluestoconstructthemodelofzo ne 241 ,andusedthedata ofzone 241 tovalidateitsmodel.Thisisdoneprimarilytoshowtherobu stnessofthe modeltothelocationchangeofthezonethathasthesametype ofinternalwallsinthe building. 4.2ExperimentalSetup Theimplementationschematicofthecontrolalgorithmsand theinterfaceofsafety softwareduringtheexperimentsareshowninFigures 4-3 and 4-4 ,respectively.As showninFigure 4-3 ,adatabase 1 iscreatedinthePughHallsysteminwhichthe real-timedatafromalltheexistingsensorsandactuatorsa restored.Anotherdatabase 78

PAGE 79

0 10 20 30 40 16 18 20 22 24 26 Time(hr)ZoneTemperature(C)SimulatedMeasured Figure4-2.Predictedandmeasuredtemperaturesinzone 241 named 2 iscreatedthatreplicatesthedatabase 1 ,butseparatedfromthedatabase 1 througharewallduetosecurityreasons.Zone 241 doesnothaveaoccupancy sensor.However,the MOBS and MOBO controllersrequireoccupancymeasurements. Therefore,wehaveinstalledaPIR(PassiveInfra-Red)sens orthatdetectswhether thezoneisoccupiedornot.Sincezone 241 isatypicalsmall-ofce,itisreasonableto assumethatthepossibleoccupancyinthezoneiseither 0 or 1 Therearetwocomputersthatareusedtoconductthecontrole xperiments:control computerandsafetycomputer.Thecontrolcomputerperform sthreefunctions:1) obtainsdatafromthePIRsensorandtheexistingsensorsint hebuildingsuchas zonetemperature,VAVdamperposition,supplyairowrate, supplyairtemperature, reheatvalvepositionsensors,etc.,2)computesthecontro linputsusingthecontrol algorithmsdescribedinSection 3.2 ,and3)writesthecommandedcontrolinputsto database 2 .Database 1 receivesthecommandedcontrolinputsfromdatabase 2 ,and thecommandedcontrolinputsinthedatabase 1 areimplementedontheVAVbox.The databasedesignandmaintenanceareperformedbyDr.Timoth yMiddelkoop. 79

PAGE 80

Figure4-3.Implementationschematicofthecontrolalgori thmsduringexperiments. Thesafetycomputerrunsthesafetysoftwarethatobtainsth esensorsmeasurements fromtheexistingsensorsthroughthedatabase,andchecksi fthesensorsmeasurements areinapre-denedallowedrange.Thesafetysoftwareautom aticallyresetsthe controlinputsandswitchesthecontrollertothedefaultbu ildingcontrollerifthesensor measurementsarenotinapre-denedrange.Thesafetysoftw areisdevelopedusing theGUItoolsinMATLAB c r ;seegure 4-4 forthegraphicalinterfaceofthesafety software.Thesafetysoftwarealsohasanoptionofmanually resettingonecontrolinput orallthecontrolinputsforagivenperiodoftime. 4.3Results Theexperimentsareperformedforthreedaysstartingfromt hemidnightofMay4th, 2012andendingatthemidnightofMay6th,2012.The MOBS controllerisimplemented 80

PAGE 81

Figure4-4.Interfaceofsecuritysoftwareduringexperime nts. onMay4th,2012,whilethe MOBO controllerisimplementedonMay5th,2012.Welet thebuildingoperatedbythedefaultcontroller(i.e.,the BL controller)onMay6th,2012. Wedonotimplementthe POBO controllerasitrequiresoccupancypredictionsthatare quitehardtoobtaininpractice.Also,the POBO controllerdoesnotofferasignicant advantageoverthe MOBO controllerintermsofenergysavingsorcomfortlevelas concludedduringthesimulationsinSection 3.4 .Thedesignparametersusedbythe controllersduringtheexperimentsarethesameasmentione dinSection 3.4.2 .Inallthe gures,thelegends:Baseline, MOBS MOBO representtheresultsobtainedfromthe BL MOBS ,and MOBO controllers,respectively. Theoccupancyproleschosenduringtheexperimentsaresho wninFigures 4-5A and 4-5B ,respectively.Nearlyidenticaloccupancyproleswerema intainedduring eachofthethreetestdays.Theguresshowthetrueandmeasu redoccupancyfor the MOBS and MOBO controllers.The BL controllerdoesnotrequireanytypeof occupancyinformation. 81

PAGE 82

Alongwiththeexperiments,wehavealsodonesimulationsfo rthe BL MOBS ,and MOBO controllerswiththeoutsideweatherandoccupancyconditi onssameasduring theexperiments.Thisisdonetocomparetheexperimentswit hsimulations. 0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 Measured Time(hr) True Occupancy(no) A MOBS (May5th,2011) 0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 Measured Time(hr) True Occupancy(no) B MOBO (May6th,2011) Figure4-5.Trueandmeasuredoccupancyinzone 241 forthe MOBS and MOBO controllers. Figures 4-6A and 4-6B showthetemperatureofzone 241 obtainedfromthe experimentsandsimulations,respectively.Inboththegu res,the BL controller maintainsaconstanttemperaturethroughouttheday.Howev er,the MOBS and MOBO controllersletthezonetemperaturereduceduringtheunoc cupiedtimeand bringthetemperaturebackwhenthezoneisoccupiedagain.T hisisbecausethe allowedtemperaturerangeduringtheunoccupiedtimeishig herthantheallowed temperaturerangeduringtheoccupiedtime.Forthe MOBS controller,thezone temperatureduringthesimulationsandexperimentsbehave sinasimilarfashion exceptfortherstfewhours.Thismismatchduringtherstf ewhoursisduetothelow owratesuppliedbythe MOBS controllerintheexperiments.Thereasonforthelow owratesuppliedbythe MOBS controllerwillbeexplainedlater. Thecontrolinputs:SAowrateandSAtemperatureareshowni nFigures 4-7 and 4-8 ,respectively.ItisclearfromFigure 4-7 thatthe BL controllersuppliesahigh 82

PAGE 83

0 5 10 15 20 20.5 21 21.5 22 22.5 23 23.5 Time(hr) Baseline MOBSMOBO ZoneTemperature(C) AExperiments 0 5 10 15 20 21 21.5 22 22.5 23 Time(hr) Baseline MOBSMOBO ZoneTemperature(C) BSimulations Figure4-6.Zone 241 temperatureduringtheexperimentsandsimulations. andaconstantamountofowratethroughouttheday.However ,theamountofow ratessuppliedbythe MOBS and MOBO controllersarelowduringtheunoccupiedtime duetothelowrequirementontheminimumowratetheduringt hattime.Theamount ofowratessuppliedbythe MOBS and MOBO controllersincreaseduringtheoccupied timesduetotheincreaseinminimumowratesrequirementdu ringthattime.Thereare twosuddenincreasesintheowratessuppliedbythe MOBS and MOBO controllers. Thesuddenincreasesareduetothechangeofoccupancyfrom 0 to 1 andlowzone temperaturebeforetheoccupancy-change.Therefore,alar geamountofowrateis suppliedtobringthetemperaturebacktothecomfortablera nge.TheSAtemperature forthe BL and MOBS controllersisusuallyoscillatingduringboththesimulat ionsand experimentsduetothecontrollersoftenswitchingbetween heatingandcoolingmodes. Notethatthezone 241 originallydoesnothaveahumidityorCO 2 sensor. Therefore,wehaveinstalledtwohumidityandtwoCO 2 sensorsduringtheexperiments tomonitorIAQinsidezone 241 .Theaveragehumidityratioobtainedbythesensors duringtheexperimentsandsimulationsisshowninFigures 4-9A and 4-9B ,respectively. ItisclearfromFigure 4-9A thatthehumidityratiostaysinacomfortablerangeforthe 83

PAGE 84

0 5 10 15 20 0 50 100 150 200 250 300 350 Baseline MOBSMOBO Time(hr)SAFlowRate(kg/sec) AExperiments 0 5 10 15 20 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Baseline MOBSMOBO Time(hr) SAFlowRate(kg/sec) BSimulations Figure4-7.Flowrateofairsuppliedtozone 241 duringtheexperimentsandsimulations. 0 5 10 15 20 10 15 20 25 30 35 40 Baseline MOBSMOBO Time(hr)SATemperature(C) AExperiments 0 5 10 15 20 15 20 25 30 35 Baseline MOBSMOBO Time(hr) SATemperature(C) BSimulations Figure4-8.TemperatureofSAenteringzone 241 duringtheexperimentsand simulations. MOBS and MOBO controllersthroughouttheday.However,thehumidityrati oobtained fromthe MOBS controllerismorethanthatofthe MOBO controller.Thisisbecause theowratesuppliedbythe MOBS controllerislessthantheowratesuppliedbythe MOBO controller.Thereasonforthelowerowratesuppliedbythe MOBS controller isexplainedlaterinthissection.Thehumidityratiodurin gthesimulationsincreases duringtheoccupiedtimeanddecreasesduringtheunoccupie dtimeduetothewater vaporreleasedbytheoccupants.TheaverageCO 2 concentrationinzone 241 forthe 84

PAGE 85

MOBS and MOBO controllersisshowninFigure 4-10 .Itisshowninthegurethatthe CO 2 concentrationstayslessthan 600 ppm throughouttheday.Basedonthehumidity andCO 2 concentrationshownintheFigures 4-9A – 4-10 ,IAQisalwaysmaintainedbyall thecontrollers. Sincethebuildingisoperatedbythe BL controllerthatalwayssupplieshighow rateandmaintainsIAQ,itisreasonabletoassumethatthehu midityratioandCO 2 concentrationforthe BL controlleralwaysstayinthecomfortablerange.Therefore ,we didnotcollecthumidityandCO 2 dataforthe BL controller. 0 5 10 15 20 7 7.5 8 8.5 9 9.5 10 x 10 -3 MOBSMOBO Time(hr) HumidityRatio AExperiments 0 5 10 15 20 7.5 8 8.5 9 x 10 -3 Baseline MOBSMOBO Time(hr) HumidityRatio BSimulations Figure4-9.Averagehumidityratioinzone 241 duringtheexperimentsandsimulations. Thecomparisonofcontrollersperformanceintermsofdaily energyconsumption and % savingsisshowninTable 4-1 .Itisclearfromthetablethatthe MOBS and MOBO controllersresultin 60 70% energysavingsoverthebaselinecontrolleras concludedinSection 3.4 .Inthesimulations,the MOBS controllerperformsaswellas the MOBO controller,whichisalsosameastheresultsshowninSectio n 3.4 .However, the MOBS controllerresultsinslightlymoreenergysavingsascompa redtothe MOBO controllerduringtheexperiments,whichisnotpredictedf romthesimulations. Thisdiscrepancyisbecauseofthelowowratesuppliedbyth e MOBS controller.The 85

PAGE 86

0 5 10 15 20 400 420 440 460 480 500 520 540 560 CO 2 Concentration(ppm) MOBSMOBO Time(hr) Figure4-10.AverageCO 2 concentrationinzone 241 duringtheexperiments. lowowrateresultsinlessenergyconsumptionsincelessen ergyisrequiredbythefan topushlowerairowratethroughtheductsandlessenergyis consumedbyAHUto conditiontheloweramountofair.Table4-1.Dailyenergyconsumptionand % Savingswithvariouscontrollers. ExperimentalResultsSimulationResults ControllerDailyEnergySavings(%)DailyEnergySavings(% ) Consumption(MJ)Consumption(MJ) BL 127-129MOBS 37715954 MOBO 51605954 Thereasonforthelowowrateduringtheoperationofthe MOBS controllerisdue totheuncertaintyintheactuatordynamicsinsidetheVAVbo x.Duringtheexperiments, wehaveuseda2-dimensionallookuptable,whichprovidesth edamper-commandand valve-commandvaluesgiventhedesiredowrateandtempera tureofthesupplyair. ThedampersintheVAVboxescontroltheowrate,andtherehe atingvalvecontrols thetemperatureofsupplyair.Thelookuptableisconstruct edusingafewdaysofdata whileassumingaconstantpressuredifferenceacrossthedu cts,whichisnotalways true.Therefore,thereisanuncertaintyintheactuatordyn amics,whichcausesowrate valuestochangeevenforaxeddamperposition.Itsohappen edthattheresponse 86

PAGE 87

curvesusedduringthe MOBS experimentsledtolowerowrate.Thisisnotexpectedto happenallthetime.However,furtherexperimentsareneede dtoverifythis. 4.4ConclusionandDiscussion Wehaveimplementedthe BL MOBS and MOBO controlalgorithmsinzone 241 ofPughHallattheUniversityofFloridacampus.Theperform anceofthecontrollers hasbeencomparedthroughexperimentsandsimulations.The conclusionaboutthe controllers'performancefromtheexperimentsisalmostth esametotheconclusion obtainedthroughthesimulationsinSection 3.4 :(i)boththecontrollers(feedback-and MPC-based)thatuseoccupancymeasurementsresultin 60 70% energysavings,and (ii)feedback-basedcontrollerperformsalmostaswellasM PC-basedcontrolleraslong asboththecontrollersuseoccupancymeasurements.Howeve r,thekeydifferencein theperformancebetweenthesimulationsandexperimentsis thatthe MOBS controller wasobservedtoperformbetterthanthe MOBO controller.Thiswasbelievedtobea chanceoccurrence,duetotheuncertaintyinthedynamicsof theactuatorinsidethe VAVbox. 87

PAGE 88

CHAPTER5 AHU-LEVELCONTROLALGORITHMS 5.1MotivationandProblemStatement Ithasbeenshowninthepreviouschaptersthatasignicanta mountofenergycan besavedbyusingreal-timeoccupancymeasurements(instea dofusingpredened occupancyschedules)todecidezone-levelcontrolcommand sattheVAVboxes,while thecontrolinputsattheAHUarekeptconstant.Itislikelyt hatenergyefciencycan beimprovedfurtherbyvaryingtheAHUinputs,i.e.,returna irratioandconditionedair temperature,inadditiontotheinputsattheVAVbox. Inthischapter,therefore,wefocusontheAHU-levelcontro lalgorithms,whichnot onlyvarytheSAtemperatureandowratebutalsothereturna irratioandconditioned airtemperature.Inthischapter,weonlyfocusonasingle-z oneVAVsystem.Ina single-zoneVAVsystem,oneAHUservesonlyonezoneandheat ingcoilsareinsidethe AHU.Thefourcontrolinputsthatneedtobedeterminedarere turnairratio,conditioned airtemperature,supplyairtemperatureandowrate.Inthi schapter,weexaminethe performanceofcontrolalgorithmsthatusezone-humidity/ zone-temperature/occupancy/outside weathermeasurementstoreduceenergyusecomparedtoconve ntionalcontrol algorithmsthatdonotusesuchmeasurements.Someofthecon trolalgorithms areoptimalcontrolstrategiesthatarecomputationallyex pensive,requiresensor measurementsaswellaspredictionsfromahygro-thermaldy namicmodel,while othersarefeedbackstrategiesthataresimple,easytoimpl ement,andrequireonly sensormeasurements.Wecomparetheperformanceoftheseco ntrollers,whichvary severaltypesofcontrolinputs,requirevaryingamountofi nformation,andareofvarying complexity.Bydoingthecomparisoninsuchaway,weaddress thefollowingthree questions: 88

PAGE 89

1.Howmuchsavingscanbeobtainedifasystemmodelandmeasu rementsof zonetemperatureandhumidity,outsidetemperatureandhum idity,andoccupancyare availabletoacontroller? 2.Howdothesavingsdependonthedelityofinformationand complexityofthe controller? 3.Amongthecontrollablevariables,whichis(are)thekeyo ne(s)thathavethemost effectonenergyuseandthermalcomfort? Notethatthecontrolalgorithmsarepresentedforasinglezonehere,buttheyare alsoapplicabletomultiplezones. Therestofthechapterisorganizedasfollows.Theproposed controlalgorithmsare describedinSection 5.2 .Section 5.3 showstheparameterusedforsimulationstudy. SimulationresultsarepresentedinSection 5.4 .Theconclusionfromthesimulations andfutureworkarediscussedinSection 5.5 5.2ControlAlgorithms Thefourcontrolalgorithms BL ( Baseline ), Z-FC ( Zone-LevelFeedbackControl ), A-FC ( AHU-LevelFeedbackControl ),and A-MPC ( AHU-LevelModelPredictiveControl ),alongwiththeirspecialcasesaredescribedinthissecti on.The BL isabaselinecontrollerand Z-FC isthe MOBS controller,whichwerepresentedin Section 3.2 .However,the A-FC and A-MPC controllersarenovelcontrolalgorithms. Wehavenamedthe MOBS controllerasthe Z-FC controllerinthischaptersincethe newnameclearlydifferentiatesthezone-levelcontrolalg orithmfromtheAHU-level controlalgorithms,whichismucheasiertocomprehend.Inf ormationrequirements andcomplexityofthecontrollersaresummarizedinTable 5-1 .SinceasingleAHUis considered,subscriptCAcorrespondstotheairthatisdown streamofthecoolingcoils butupstreamofthereheatcoils,whilesubscriptSAcorresp ondstodownstreamofthe reheatcoil.Weassumethattherearenopre-heatcoils. 89

PAGE 90

Table5-1.Complexityandinformationrequirementsofvari ouscontrolalgorithms. ControlControllableFixedMeasurementsPredictionsMode lComputationOverall algorithmsInputsInputsrequiredrequiredrequiredrequi rementscomplexity 1 BL T SA m SA T CA R RA T -NoVeryLowVeryLow 3 Z-FC T SA m SA T CA R RA T n p -NoVeryLowLow 4 A-FC T SA T CA m SA R RA T W n p T OA W OA -NoMediumMedium 5 A-FC specialcase1 T SA m SA R RA T CA T W n p T OA W OA -NoMediumMedium 6 A-FC specialcase2 T SA T CA m SA R RA T W n p T OA W OA -NoMediumMedium 7 A-MPC T SA T CA m SA R RA T W n p T SA m SA T OA W OA Q s YesHighVeryHigh 8 A-MPC specialcase1 T SA m SA R RA T CA T W n p T SA m SA T OA W OA Q s YesHighVeryHigh 9 A-MPC specialcase2 T SA T CA m SA R RA T W n p T SA m SA T OA W OA Q s YesHighVeryHigh 90

PAGE 91

5.2.1 A-FC ( AHU-LevelFeedbackControl ) The A-FC controllerisafeedbackstrategytodetermineallfourinpu ts:theSA temperature,SAowrate,CAtemperature,andRAratio.Aow chartthatdescribes the A-FC controlalgorithmindetailisshowninFigure 5-1 .Thealgorithmcanbe summarizedinfoursteps:ateverytimeindexk,(1)obtainme asurements,(2)determine theRAratiobydoingexhaustivesearch,(3)determinetheCA tempbasedontheMA enthalpy,OAenthalpy,andzonehumidity,and(4)recalcula tetheRAratiotoensure zonehumidityconstraintsaresatised. Step 2 determinestheRAratio,SAtemperature,andSAowratebydo ing exhaustivesearchoverRAratioandusingthestrategydescr ibedinthe Z-FC controller. Atthecurrenttimeindex k ,the Z-FC controllerisusedtocalculatetheSAowrateand temperatureforthecurrentvalueoftheRAratio( R RA ( k ) ).Sincethe Z-FC controller cancalculatetheSAowrateandtemperatureforagivenRAra tio,andtheenergy consumption( 3–8 )dependsonthefourcontrolinputs,i.e.,SAtemperature,S Aow rate,RAratio,CAtemperature,theenergyconsumedby Z-FC canbeexpressedasa functionof R RA and T CA asfollows: E ( k )= F Z-FC ( R RA ( k ) ;T CA ( k ) ;G Z-FC ( R RA ( k ))) ; (5–1) wherefunction G Z-FC isusedby Z-FC tocalculatetheSAowrateandtemperature, andfunction F Z-FC calculatestheenergyconsumptionforgivenvaluesofthefo ur controlinputs.Wekeeptheconditionedairtemperaturexe dat T CA ( k ) andcalculate theenergyconsumptionforeachRAratiointherange[ max ( R RA ( k ) R RA rate t;R RA min ) min ( R RA ( k )+ R RA rate t;R RA max )] .TheRAratiocorrespondingtothelowestenergy consumptionischosen.TherangeoftheRAratioisdictatedb ythephysicalconstraints onthedamperposition,e.g.,thedamperpositioncannotcha ngequicklyinaveryshort timeperiod,andsodoestheRAratio.Weassumethatthemaxim umallowablerateat whichtheRAratiocanchange(increase/decrease)isknown, anddenoteitby R RA rate .It 91

PAGE 92

isalsoimportanttomakesurethatthesearchrangeoftheRAr atioshouldbeasubset oftherange [ R RA min ;R RA max ] .OncetheRAratioisdecided,the Z-FC controllerisusedto calculatetheothertwocontrolinputs,SAtemperatureandS Aowrate. Instep 3 ,theCAtemperatureisincreasedtoreducetheenergyconsum ption,and theCAtemperatureisdecreasedwhenthezonehumidityratio goesfartherfromthe allowablerangesincereducingtheCAtemperaturealsoredu cestheSAhumidityratio. Theallowablerangeofthezonehumidityratiois [ W unocc low ;W unocc high ] duringunoccupied times.Duringoccupiedtimes,themaximumandminimumhumid ityvaluesare W occ low and W occ high .BasedonthesamereasonsprovidedfortherateoftheRArati o,thereisa maximumallowablerate T CA rate atwhichtheCAtemperaturecanchange.Also,theCA temperatureshouldalwaysbeintheallowablerange [ T CA min ;T CA max ] Step 4 makessurethattheSAowratewithminimumCAhumidityishig henough tomaintainthezonehumiditywithintheallowablerange.Ot herwisetheRAratiois decreased,whichincreasestheminimumowrateduetotheve ntilationconstraintsas in( 3–2 ). Whileevaluatingtheperformanceofthe A-FC controller,weconsidertwospecial casestostudytheeffectofeachcontrolinputindividually ontheperformanceofenergy savingsandthermalcomfort.Thetwospecialcasesaredescr ibedbelow: SpecialCase1:TheCAtemperatureiskeptconstantatthemin imumvalue T CA min i.e., T CA max = T CA min ,and T CA rate =0 SpecialCase2:TheRAratioiskeptconstant,whichmeanstha t R RA max = R RA min ,and R RA rate =0 Notethatthe Z-FC controllerisaspecialcaseofthe A-FC controllerwhenboththe RAratioandCAtemperaturearekeptconstant.5.2.2 A-MPC ( AHU-LevelModelPredictiveControl ) The A-MPC controlleralsodeterminesallfourinputsasinthe A-FC controller, butbyusinganMPC-basedstrategythatsolvesanoptimizati onproblemtoobtain 92

PAGE 93

1 2 3 4 Yes Yes Yes No No No Getmeasurementsat k th timeindex: T ( k ) ;W ( k ) ;T OA ( k ) ;W OA ( k ) ;n p ( k ) Exhaustivesearchof R RA using Z-FC forthelowestenergy, R RA 2 [ max ( R RA ( k ) R RArate t;R RAmin ) ;min ( R RA ( k )+ R RArate t;R RAmax )] Calculate h MA ( k ) and h CA ( k ) h MA ( k ) >h CA ( k ) ? W ( k ) 2 AllowedRange? T CA ( k +1)= min ( T CA ( k )+ T CA rate t;T CA max ) T CA ( k +1)= max ( T CA ( k ) T CA rate t;T CA min ) T CA ( k +1)= T CA min and W ( k ) 2 AllowedRange? R RA ( k +1)= min ( R RA ( k ) + R RArate t R RAmax ) Controlinputsatk+1are: T SA ( k +1) m SA ( k +1) ;R RA ( k +1) ;T CA ( k +1) T CA ( k +1)= T CA ( k ) Figure5-1.Flow-chartofthe Z-FC controllertodeterminethecontrolinputs. thecontrolinputs.The A-MPC controllerrequiresadditionalinformationsuchas hygro-thermaldynamicsmodelandpredictionsofoutsidewe ather.Thecontrolinputs over K timeindicesareobtainedbysolvingaconstrainedoptimiza tionproblem: minimizetotalenergyconsumptionoverthatperiodwhilema intainingthermalcomfort andIAQ.Thecontrolinputsareappliedatthecurrenttimein dex k .Theoptimization problemissolvedagainattimeindex k +1 tocomputethecontrolinputsforthenext K timeinstants.Thewholeprocessisrepeatedadinnitum. 93

PAGE 94

Tosolvetheunderlyingoptimizationproblem,thecontroll erneeds(i)predictions oftheexogenousinput v ( k ) overthetimehorizonofoptimization,and(ii)amodelof thezonehygro-thermaldynamicsaswellasitsinitialstate .Predictionsof T OA W OA and Q s (partof v ( k ) )areassumedavailablefromweatherforecasts.Itisassume dthat theinstantaneousoccupancymeasurementsareavailableat thetimeindex k .The predictedoccupancyoverthepredictionhorizon K isassumedtobethesameasthe measuredoccupancyatthe k -thtimeperiod: n p ( i )= n p ( k ) ;i k .Themodelsforenergy consumptionandhygro-thermaldynamicsusedbythecontrol leraretheonespresented inSection 3.2.3 .AnEKF(ExtendedKalmanFilter)-basedstateobserverisem ployedto estimatethestateoftheplant. Thecontrollogicisdividedintotwomodes:(i)Occupiedand (ii)Unoccupied,which areexplainedbelowindetail. OccupiedMode:Thecontrolleroperatesintheoccupiedmode ifthemeasured occupancyatthe k -thtimeindex,i.e.,atthebeginningofthetimeinterval [ k t; ( k + 1) t ] ,isatleast 1 .Theoptimalcontrolinputsforthenext K timeindicesareobtainedby solvingthefollowingoptimizationproblem: U ? := arg min U G ( U ) ; (5–2) where U =[ z T ( k ) ; ;z T ( k + K )] T 2 R 4( K +1) z ( k )=[ m SA ( k ) ;T SA ( k ) ;T CA ( k ) ;R RA ( k )] T and G ( U )= P k + K i = k E ( i ) ,subjecttothefollowingconstraints: 94

PAGE 95

T occ low T ( i ) T occ high ; W occ low W ( i ) W occ high ; T CA ( i ) T SA ( i ) T SA high m SAp n p ( i )+ m SAlow m SA ( i ) m SAhigh R RA ( i ) min ( R RA ( i 1)+ R RA rate t;R RA max ) R RA ( i ) max ( R RA ( i 1) R RA rate t;R RA min ) T CA ( i ) min ( T CA ( i 1)+ T CA rate t;T CA max ) T CA ( i ) max ( T CA ( i 1) T CA rate t;T CA min ) 9>>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>>; 8 i = k;:::;k + K: Thersttwoconstraintsspecifytherangeinwhichthezonet emperatureand humidityratioareallowedtovary.Thethirdconstraintiss implytotakeintoaccount actuatorcapabilities.Thefourthconstraintmeansthatth ereisalowerandupperbound ontheowrateenteringthezone( m SA ).Thelowerboundontheowrateissame as( 3–1 ),whiletheupperbound m SAhigh reectsthemaximumowratepossiblewhenthe dampersintheVAVboxarecompletelyopen.Thelastfourcons traintscorrespondto theupperandlowerboundsontheRAratioandCAtemperatured uetothelimitation onthemaximumrateatwhichtheRAratioandCAtemperatureca nchangefromtheir currentvalues,whicharethesameconstraintsasinSection 5.2.1 Asinthe Z-FC controller,thechoiceofthedesignvariables T occ low T occ high W occ low W occ high involvesatrade-offbetweenenergysavingsandoccupantdi scomfort. UnoccupiedMode:Ifthemeasuredoccupancyatthetimeindex k ,i.e.,atthe beginningofthe k -thtimeperiod,isobservedtobe 0 ,thenthecontrolleroperatesinthe unoccupiedmode.Attime k ,theoptimalcontrolinputsforthenext K timeindicesare obtainedbysolvingthefollowingoptimizationproblem: U ? := arg min U G ( U ) ; (5–3) subjecttothefollowingconstraints: 95

PAGE 96

T unocc low T ( i ) T unocc high W unocc low W ( i ) W unocc high m SAlow m SA ( i ) m SAhigh T CA ( i ) T SA ( i ) T SA high R RA ( i ) min ( R RA ( i 1)+ R RA rate t;R RA max ) R RA ( i ) max ( R RA ( i 1) R RA rate t;R RA min ) T CA ( i ) min ( T CA ( i 1)+ T CA rate t;T CA max ) T CA ( i ) max ( T CA ( i 1) T CA rate t;T CA min ) 9>>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>>; 8 i = k;:::;k + K: Thereasonfortheseconstraintsisthesameasthatexplaine dpreviously. Theconstraintsonthezonetemperatureandhumidityratioi ntheunoccupied mode,however,arechosentobesuchthat[ T unocc low T unocc high ] [ T occ low T occ high ],and[ W unocc low W unocc high ] [ W occ low W occ high ].Thechoiceoftheparametersfortheunoccupiedtimesalso involvesatrade-off.Thefarthertheyarefromtheircounte rpartsduringtheoccupied mode,thegreateristheenergysavingspotential,butalsot hegreateristheriskof occupantdiscomfortwhenoccupancychanges. Asinthe A-FC controller,wealsoconsidertwospecialcasesforthe A-MPC controller tostudytheeffectofeachcontrolinputindividuallyonthe controllerperformance.The twospecialcasesareexplainedbelow: SpecialCase1:TheCAtemperatureiskeptconstantat T CA min SpecialCase2:TheRAratioiskeptconstant. Remark2. Theoverallcomplexityofthecontrolalgorithmsincreases intheorder1) BL 2) Z-FC ,3) A-FC ,and4) A-MPC .Notethattheallthecontrollerssupplytheminimum owrateprescribedbyASHRAEventilationstandard62.1-20 10[ 17 ]duringoccupied andunoccupiedtimes,whichensuresthatIAQismaintainedb yallthecontrollers.In thisway,weeliminatetheproblemofanalyzingtheeffectof controlinputsonIAQ. 96

PAGE 97

5.3SimulationParameters 5.3.1BuildingModelParameters Simulationsarecarriedoutforamodelofanauditoriumfrom therstoorina building(PughHall)attheUniversityofFloridacampus,Ga inesville,FL,whichisshown inFigure 5-2 .ThisauditoriumisservedbyadedicatedAHU.Parametersof thedynamic modelforthiszonearecalibratedusingthemeasureddatain amannerdonein[ 20 ]. N S E W Auditorium OutsideOutside Outside Hallway21.3m20.7m Figure5-2.Layoutofazone(auditorium)ontherstoorofP ughHall. 5.3.2Controllerparameters Themaximumowrateforallthecontrollersischosenas 4 : 6 kg=s .Forthe BL and Z-FC controllers,theRAratioandCAtemperatureareassumedtoh aveconstantvalues of 0 : 6 and 12 : 8 C ,respectively.Forthe BL controller,thetemperatures:RTG,HTG,and CLGaresetto 21 : 8 C, 21 : 9 C,and 23 : 6 C,respectively,from 6:30 a.m.to 10:30 p.m. Duringthetime 10:30 p.m.– 6:30 a.m.,thetemperatures:RTG,HTG,andCLGfor the BL controllerarechosenas 20 : 9 C, 21 : 1 C,and 24 : 4 C,respectively.Thisnighttime setbackiscurrentlyusedinthePughHall.Therelativehumi dityoftheconditionedairis 97

PAGE 98

assumedconstantat 90% .Otherdesignparametersusedbythecontrollersareshown inTable 5-2 5.4ComparisonResults Wenowcomparetheperformanceof BL Z-FC A-FC ,and A-MPC control algorithms,alongwiththespecialcasesofthe A-FC and A-MPC controllers,through simulations.SimulationsareperformedusingMATLAB c r ;whileIPOPT[ 64 ]isusedto solvetheoptimizationproblemsfortheMPC-basedcontroll ers. ThehallwayshowninFigure 5-2 isassumedtohaveaconstanttemperatureof 22 : 2 C.Threetypesofoutsideweatherconditions:1)cold(Jan14 ,2011),hot(Jul31, 2011),andpleasant(Mar16,2011),areconsideredinGaines ville,FL.Weatherdatafor thislocationisobtainedfrom[ 67 ].Thezoneisoccupiedby200peoplefrom 8:30 a.m. to 4:30 p.m.Thisisthecurrentoccupancyproleintheauditoriumo fthePughHall, whichisusedasalecturehall. Thetotaldailyenergyconsumption,averagetemperaturevi olation,average humidityviolation,and % savingsoverthebaselinecontrollerforthreedifferentwe ather conditionsareshowninTable 5-3 .Itisclearfromthetablethatallthecontrollersresult in 56 85% savingsovertheconventionalbaselinecontroller(depend ingonoutside weatherandthetypeofcontroller).Thetemperatureandhum idityviolationsarevery closetozeroforallthecontrollers,whichmeansthattheth ermalcomfortismaintained byallthecontrollers. Therearethreereasonsforhighenergysavingsbythe Z-FC A-FC and AMPC controllersoverthe BL controller.Therstreasonisthereductionoftheow rateandincreaseintheallowabletemperaturerangeduring unoccupiedtimes. Reductionintheowratedecreasesfan-,conditioning-,an dreheating-energy consumption.Increasingtheallowabletemperatureranger esultsinlessreheating energyconsumptionsincethezonetemperatureisallowedto belowerduring 98

PAGE 99

Table5-2.DesignparametersusedinthevariousAHU-levelc ontrollers. Temperatureandtimerelatedparameters T set T SA high T unocc RTG T occ RTG T occ low T occ high T unocc low T unocc high T CA min T CA max T CA rate K; t T ( C )( C )( C )( C )( C )( C )( C )( C )( C )( C )( C min )(no.,min,hr) 22.830.020.921.821.923.621.124.412.815.60.130,1,24 Humidityandotherparameters W unocc low W occ low W unocc high W occ high m OAp m Az m SAhigh R RA min R RA max R RA rate n pd A z ( g kg )( g kg )( g kg )( g kg ) ( kg sec )( kg m 2 )( kg sec ) ( % )( % )( % min ) ( m 2 ) 7.47.411110.0042 3 : 05 10 4 4.60805210238 99

PAGE 100

Table5-3.Dailyenergyconsumption, % Savings,averagetemperatureandhumidityviolations. ColdHotPleasant Control E Savings D T D H E Savings D T D H E Savings D T D H SchemeMJ % C g kg MJ % C g kg MJ % C g kg BL 3142-0.00807598-0.00603877-0.0070 Z-FC 98068.80.0150318758.10.0130168756.50.0140 A-FC specialcase182673.70.0150228070.00.0010.00165983.00 .0110.002 A-FC specialcase279774.60.0120259565.80.0050.003110971.4 0.0100.002 A-FC 85172.90.0130217071.40.0000.06663583.60.0100.043 A-MPC specialcase173276.70.0000215271.70.000061584.10.000 0 A-MPC specialcase281574.10.0000258066.00.0000110371.50.00 00 A-MPC 70377.60.0000209172.50.000060784.40.0000 100

PAGE 101

unoccupiedtimesthanwhatthebaselinecontrollerallows. Thesecondreasonis thechangeoftheRAratiobasedontheenthalpiesofOA,RA,CA ,SAinsuchaway thatthetotalenergyisreduced.Duringpleasantweatherwh entheOAenthalpylies betweentheCAenthalpyandRAenthalpy,theRAratioislowas lowerenergyis requiredbyAHUtoconditiontheoutsideairthantoconditio nthereturnair.Whenthe outsideweatherishot,theRAratioishighaslowerenergyis consumedtocondition thereturnairthantoconditionthehotoutsideair.Thethir dreasonistheresettingofthe CAtemperaturebasedonthezonehumidityandenthalpiesofM AandCA.Whenthe MAenthalpyislessthantheCAenthalpyandthezonehumidity iswithintheallowable range,theCAtemperatureisincreased.IncreasingtheCAte mperatureincreases humidityratioastheCArelativehumidityisassumedconsta nt,whichleadstothe energysavingsduetolessconditioningenergyconsumedbyt hecoolingcoils.Someof thesearenotapplicabletothe Z-FC controllerasitcannotcommandtheAHUinputs. ImportanceofControlInputsandMeasurements:The Z-FC controller,whichis aspecialcaseofthe A-FC controllerwhenboththeSAtemperatureandRAratioare keptconstantwhiletheSAtemperatureandSAowratearevar ied,resultsin 56 69% energysavings.Ifthe A-FC controllerisallowedtovarytheRAratioasinthespecial case 1 ,theadditionalenergysavingsoverthe Z-FC controllerare 5 26% .Ifthe AFC controllerisallowedtovaryonlytheCAtemperatureinstea doftheRAratioasin thespecialcase 2 ,theadditionalenergysavingsare 4 15% .Whenthe A-FC controller isallowedtovaryboththeCAtemperatureandRAratio,thead ditionalsavingsover the Z-FC controllerare 4 27% thatareverysimilartothesavingsinthespecialcase 1 whentheCAtemperatureiskeptconstant.Asimilartrendiso bservedforthe AMPC controller.TheseresultssuggestthatvaryingtheCAtempe raturewithRAratio doesnotofferanyadvantageintermsofenergysavingsoverv aryingtheRAratioalone. Also,theeffectoftheSAowrateandtemperatureontheener gysavingsismaximum amongallthecontrolinputs.Therefore,theeffectofcontr olinputsontheenergysavings 101

PAGE 102

decreasesinthefollowingorder:1)SAowrateandtemperat ure2)RAratio3)CA temperature. The Z-FC controller,whichonlyusestheadditionalmeasurementsof occupancy, resultsin 56 69% energysavingsoverthebaselinecontrollerthatdoesnotus e occupancymeasurements.Ifacontrollerusesthemeasureme ntsofthezonehumidity andoutsideweatheralongwiththeoccupancymeasurementsa sinthe A-FC and AMPC controllers,theenergysavingsarealmost 71 85% .Therefore,intermsofthe importanceofmeasurements,occupancymeasurementisakey factorinreducingthe energyusage. 5.5DiscussionandFutureWork WeexaminehowtheperformanceofanAHU-levelcontrolleris affectedby itscomplexity;thegoalofthecontrolleristominimizeene rgyconsumptionwhile maintainingcomfortandIAQforasingle-zonevariable-air -volumeHVACsystem. Tocomparetheperformancevs.complexity,wechoosevariou scontrollersthat requirevaryingamountofinformation,computation,desig n,andimplementation effort.Simulationresultsshowthatthesavingsarehighly dependentonthetype ofmeasurementsprovidedtothecontrollers.Controllerst hatuseonlyoccupancy measurementsresultin 56 69% energysavings,andthecontrollersthatuseoccupancy measurementsalongwiththemeasurementsofzonehumiditya ndoutsideweather, resultinenergysavingsof 71 85% withnegligibleeffectonIAQorthermalcomfort. Itshowsthatoccupancymeasurementisakeyfactortoreduce theenergyusagein buildings.Anotherkeyndingisthatafeedback-basedcont rollerthatissimpleand easytoimplement,performsaswellasacomplexandcomputat ionallyexpensive MPC-basedcontroller,ifthesamemeasurementsareprovide dtoboththecontrollers. Thisissignicantinlightofthemuchhighereffortrequire dtodesignandimplement theMPC-basedcontrollerduetotheneedformodelidentica tion[ 34 ]andon-line optimization. 102

PAGE 103

Thestudyshowsthattheeffectofcontrolinputsontheenerg ysavingsdecreases inthefollowingorder:1)supplyairowrateandtemperatur e2)returnairratio3) conditionedairtemperature,andtheconditionedairtempe raturehasalmostnegligible impactonenergysavingswhenthereturnairratioisvaried. Therefore,afeedback controller,withsupplyairtemperature,returnairratio, andsupplyairowrateasthe controlvariables,isthemostappropriatecontrolalgorit hmtobeusedforsingle-zone VAVHVACsystemsduetoitssimplicity,lowcomputation,and similarperformanceto thatofmorecomplexcontrolalgorithms. Thecontrolalgorithmspresentedhereareapplicabletomul ti-zoneVAVsystems thoughtheyarepresentedonlyforasingle-zonesystem.Ade tailedstudyisrequired toevaluatetheperformanceofthecontrollersformulti-zo nebuildings.Implementing thecontrollersinarealbuildingisrequiredtoverifythes imulationresults.Workonthe implementationofthe Z-FC controllerineachzoneofthePughHallisongoing.Also, theeffectofmeasurementserroranduncertaintyontheperf ormanceofthecontrollers needstobestudiedfurther. 103

PAGE 104

CHAPTER6 QUALITYOFTHEMPCSOLUTION 6.1MotivationandProblemStatement InChapter 3 ,theperformanceoffeedbackandoptimal-basedcontroller sis comparedagainsttheperformanceofbaselinecontroller.I twasconcludedinthe chapterthatthefeedbackcontrollerperformsaswellasMPC -basedcontrollerwhen boththecontrollersareallowedtohaveoccupancymeasurem ents.Thefeedback-based controller, MOBS ,isacombinationof“if-else”logicsandPID(Proportional -Integral-Derivative) controller.Ontheotherhand,MPC-basedcontroller( MOBO )requiressolvingan optimizationproblemtodeterminethecontrolinputs.Theo ptimizationproblemsolved bythe MOBO controllerisnon-convex[ 68 ]innatureduetothenon-quadraticobjective function( 3–9 )andnonlinearequalityconstraintsinthehygro-thermald ynamics model( 2–7 )-( 2–8 ).OnemightarguethatthesolutionobtainedbytheMPC-base d controllercorrespondstoalocalminimainsteadoftheglob alminima.Therefore,the additionalsavingsobtainedbytheMPC-basedcontrollerov erfeedbackcontroller areverysmall.Itispossiblethatthesolutioncorrespondi ngtotheglobalminimum mayresultinhighadditionalsavings.However,obtainingt heglobalminimumofa non-convexproblemisquitechallenging[ 69 ]. Ideally,weareinterestedinobtaininganexactconvexica tionofthenon-convex problem.Sincewedonothaveanexactconvexicationanditi shardtondthe convexication,atransformationintoaconvexproblemiso newaytoaddressthese issues.Inthischapter,therefore,weattempttotransform thenon-convexprobleminto anapproximateconvexproblemthroughlinearizationandap proximationofresulting costfunction.Theseapproximationswillleadtoaconvexop timizationproblem,which willhaveonlyoneoptimalsolutionthatistheglobalminimu m.Therefore,weremove theargumentonthequalityofthesolutionobtainedbytheMP C-basedcontroller—local vs.global—bysolvingtheapproximatedconvexoptimizatio nproblem.Notethatthe 104

PAGE 105

optimizationproblemssolvedinthischapterareapproxima tionsofthenon-convex optimizationproblemsthatwewouldwanttosolve. WecomparetheperformanceofthefeedbackandMPC-basedcon trollersagainst theperformanceofbaselinecontroller.Itisreallyimport anttoknownotonlythesavings obtainedbytheMPC-basedcontrollerwhenitprovidesaglob alsolution,butalsohow MPCperformsascomparedtofeedbackcontrol.Inthisway,we wouldalsobeable toverifyiftheconclusioninChapter 3 —feedbackresultsinsimilarperformanceas MPC—holds. Therestofthechapterisorganizedasfollows.Thelineariz edmodelofpower andhygro-thermaldynamicsisdescribedinSection 6.2 .Theconvexoptimization problemthatthe MOBO controllerneedstosolve,alongwithseveraltypesofconve x approximationsoftheobjectivefunction,isdescribedinS ection 6.3 .Section 6.4 showsthesimulationresultsobtainedbythecontrollers.S ection 6.5 concludesthis chapteranddiscussesfuturework.Theanalysisoftheerror duetoseveraltypesof approximationsofenergyconsumptionisshowninSection 6.6 6.2ApproximatedLinearModelofPowerandHygro-themalDyn amics Asecond-ordernonlinearmodel[ 34 ]ofthethermaldynamicsinasinglezoneofa buildingcanbewrittenas C r T = 1 R w ( T w T )+ Q people n p + H; (6–1) C w T w = 1 R w ( T T w )+ 1 R w ( T OA T w ) ; where T iszonetemperature, Q people istheamountofheatreleasedbyaperson, C r ;C w and R w arethermalcapacitancesandresistance,respectively.Th eterm H isthe enthalpydifferenceofthesupplyairandtheairleavingthe zone.Theequationsto calculate H areshowninSection 2.2 .Theinterestedreadershouldreferto[ 34 ]for thedetails.Asimpliedmodelofthehumiditydynamicsinth ezone,whichisobtained 105

PAGE 106

from( 2–33 ),canbewrittenas W = 293 R g VP da n p H 2 O + m SA ( W SA W ) : (6–2) Supposethat [ T eq ;T w eq ;W eq ;T SA eq ;W SA eq ;n peq ;m SAeq ] isanequilibriumpointofthesystem( 6–1 )-( 6–2 ). Linearizingtheabovesystemaroundtheequilibriumpointl eadstothefollowing setofordinarydifferentialequations,whichwecall“Appr oximatedLinearModelof Hygro-thermalDynamics”: X = A linc X + B lin c U; (6–3) where X =[ TT w W ] T U =[ T SA m SA W SA n p ] T T SA = T SA T SA eq m SA = m SA m SAeq W SA = W SA W SA eq n p = n p n peq T SA = T SA T SA eq m SA = m SA m SAeq W SA = W SA W SA eq n p = n p n peq ,andtheexpressionsfor A linc and B lin c matricesareshownbelow A linc = 266664 1 R w C w m SAeq C pa C r 1 C r R w m SAeq h we C r 1 R w C w 1 2 R w C w 0 00 293 m SAeq R g VP da 377775 ; B lin c = 266664 C pa ( T SA eq T eq )+ h we ( W SA eq W eq ) C r m SAeq h we C r C pa m SAeq C r Q people C r 0000 293 R g ( W SA eq W eq ) VP da 0 293 R g m SAeq VP da 293 R g w H 2 o VP da 377775 : NotethattheCAhumidityratio,OAtemperatureandhumidity ratioarekeptconstant forthesakeofsimplicity.ItisalsoassumedthattheRArati oiszero.Adiscretized hygro-thermaldynamicsmodelwith k beingthetimeindexand t asthetimestep,can bederivedfromthecontinuouslinearmodel( 6–3 )as X k +1 = A lind X k + B lin d U k : (6–4) 106

PAGE 107

Theenergyconsumptioncorrespondingto0RAratiocanbeobt ainedbycombining( 3–7 ) and( 3–8 )as E ( k )= tm SA ( k )[ C pa ( T CA ( k ) T OA ( k ))+ h we ( W OA ( k ) W CA ( k ))+ + C pa ( T SA ( k ) T CA ( k ))] : (6–5) SincetheCAtemperature,CAhumidity,OAtemperature,andO Ahumidityarekept constant,theexpressionfortheenergyconsumptioncanbew rittenas E ( k )= tm SA ( k )[ r + + C pa ( T SA ( k ) T CA ( k ))] ; where r = C pa ( T CA ( k ) T OA ( k ))+ h we ( W OA ( k ) W CA ( k )) : (6–6) Rearrangingthetermsin( 6–6 ),theenergyconsumption,whichisbilinearin m SA and T SA ,canbewrittenintermsofdeviationvariablesas E = t [ C pa T SA m SA + m SAeq C pa T SA +( m SAeq + m SA )( r + + C pa ( T SA eq T CA ))] : (6–7) Linearizingtheenergyconsumptionaroundtheequilibrium pointgivesusthe followingequation: E E lin = t ( P lin F + P lin R + P lin U ) ; (6–8) where P lin F P lin R ,and P lin U arethelinearapproximatedmodelsoffan,reheating,and conditioningpowerconsumption,respectively.Theexpres sionsforthelinearizedmodel offan,reheating,andchillerpowerareshownbelow P lin F = m SAeq + m SAeq ; P lin R = m SAeq C pa ( T SA eq T CA )+ C pa [( T SA eq T CA ) m SAeq ] 264 m SA T SA 375 ; (6–9) P lin U =[ C pa ( T CA T OA )+ h we ( W OA W CA )]( m SAeq + m SA ) : 107

PAGE 108

Theanalysisoftheerrorduetothelinearapproximationofe nergyconsumptionis showninSection 6.6 6.3ConvexOptimizationProblems Sincetherearetwooptimizationproblemssolvedbythe MOBO controllerbasedon occupiedandunoccupiedmodes,weneedtondtwoapproximat econvexoptimization problemsforeachmode,whicharedescribednext. OccupiedMode:Thecontrolleroperatesintheoccupiedmode ifthezoneis occupiedatthe k -thtimeindex.Theoptimalcontrolinputsforthenext K timeindices arecomputedbysolvingthefollowingapproximateconvexop timizationproblem: U ? := arg min U G ( U ) ; (6–10) where U =[ v ( k ) T ; ;v T ( k + K )] T 2 R 2( K +1) v ( k )=[ m SA ( k ) T SA ( k )] T ,and thechoiceofthecost G ( U ) isexplainedlaterinthissection,subjecttothedynamic constraintsin( 6–4 )andthefollowingconstraints: T ( i ) ( T occ high T eq ) 0 ; T ( i )+( T occ low T eq ) 0 ; W ( i ) ( W occ high T eq ) 0 ; W ( i )+( W occ low T eq ) 0 ; m SA ( i ) ( m SAhigh m eq ) 0 ; m SA ( i )+( m SAp n p ( i )+ m SAlow m SAeq ) 0 ; T SA ( i ) ( T SA high T SA eq ) 0 ; T SA ( i )+( T CA T SA eq ) 0 ; 9>>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>>; 8 i = k;:::;k + K: (6–11) Theconstraintsin( 6–11 )arethesameconstraintsasin( 3–10 )butexpressedinterms ofthedeviationvariablesusedinlinearization.Thereaso nfortheseconstraintsis explainedpreviouslyinSection 3.2.3.1 UnoccupiedMode:Thecontrolleroperatesintheunoccupied modeifthemeasured occupancyis 0 atthetimeindex k .Atthe k -thtimeindex,theoptimalcontrolinputs 108

PAGE 109

forthenext K timeindicesareobtainedbysolvingthefollowingapproxim ateconvex optimizationproblem: U ? := arg min U G ( U ) ; (6–12) subjecttothedynamicconstraintsin( 6–4 )andthefollowingconstraints: T ( i ) ( T unocc high T eq ) 0 ; T ( i )+( T unocc low T eq ) 0 ; W ( i ) ( W unocc high T eq ) 0 ; W ( i )+( W unocc low T eq ) 0 ; m SA ( i ) ( m SAhigh m eq ) 0 ; m SA ( i )+( m SAlow m SAeq ) 0 ; T SA ( i ) ( T SA high T SA eq ) 0 ; T SA ( i )+( T CA T SA eq ) 0 ; 9>>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>>; 8 i = k;:::;k + K: (6–13) Theseconstraintsarethesameconstraintsasin( 3–12 )butexpressedintermsofthe deviationvariablesusedinlinearization.Thereasonfort heseconstraintsisexplained previouslyinSection 3.2.3.1 Ideally,wewanttheobjectivefunctionintheproblems( 6–10 )and( 6–12 )asclose aspossibletothetotalenergyconsumption( 6–7 ).However,choosingthisenergy function( 6–7 )asanobjectivefunctionwillleadtoanon-convexproblems incethe energyfunctionisbilinear.Fortheproblems( 6–10 )and( 6–12 )tobeconvex,we considerthefollowingthreecasesinwhichvarioustypesof approximationsaredoneto decidetheobjectivefunction G ( U ) : Case1:Inthiscase,theobjectivefunctionischosenasthel inearapproximation oftheenergyconsumption( 6–8 )overtheoptimizationtimeperiod,i.e., G ( U )= P k + K i = k E lin ( i ) .Sincetheobjectivefunctionislinearandalltheconstrai ntsarealso linear,theoptimizationproblems( 6–10 )and( 6–12 )areconvex[ 70 ].Theanalysisofthe errorduetothelinearapproximationofenergyconsumption isdoneinSection 6.6.1 109

PAGE 110

Case2:Inthiscase,theobjectivefunctionischosenasthes umofthesquaresof thelinearapproximatedenergyconsumption( 6–8 )overtheoptimizationtimeperiod, i.e., G ( U )= P k + K i = k E lin ( i ) 2 .Thefunction ( E lin ) 2 usedherecanbewritteninthefollowing form: ( E lin ) 2 = u T Q linm u +( c linm ) T u + d linm ; (6–14) where u =[ T SA m SA ] T c linm isavector, d linm isaconstant,and Q linm isapositivedenite matrixduetothesquareofalinearfunction.Since Q linm 0 ,thefunction ( E lin ) 2 is convex.Therefore,theoptimizationproblemisconvex[ 70 ]. Case3:Recallthattheenergyfunction( 6–7 )isbilinearin T SA and m SA ,which canalsobewritteninthefollowingform: E = u T Q m u + c Tm u + d m ; (6–15) where u =[ T SA m SA ] T Q m isamatrix, c m isavector,and d m isaconstant.For theenergyconsumptionfunctiontobeconvex,the Q m matrixshouldbepositive semi-denite.However,oneoftheeigenvalueof Q m matrixisnegativeasthediagonal entriesof Q m arezeroandoff-diagonalentriesarepositive,whichmakes theenergy functionnon-convex.Therefore,weaddanadditionalterm( t m SA ( i ) 2 + t T SA ( i ) 2 )to theenergyconsumption,andchoosetheobjectivefunctiona s G ( U )= k + K X i = k E ( i )+ t m SA ( i ) 2 + t T SA ( i ) 2 : (6–16) Eq.( 6–16 )canbewritteninthesimilarformasin( 6–15 ).Forthefunctionin( 6–16 )to beconvex, C pa = 2 ;seeSection 6.6.2 forthedetails.If C pa = 2 ,theoptimization problems( 6–10 )and( 6–12 )areconvex.Wecanevenchoosesmaller ,whichwill provideabetterapproximationoftheenergyconsumptionbu ttheoptimizationproblems willnotbeconvexinthatcase.Theanalysisoftheerrorduet otheadditionaltermfor approximatingtheenergyconsumptionisdoneinSection 6.6.2 110

PAGE 111

6.4SimulationResults Simulationsarecarriedoutforthemodelofanauditoriumfr omtherstoorinPugh Hall,whichisshowninFigure 5-2 .SimulationsareperformedusingMATLAB c r ;while IPOPT[ 64 ]isusedtosolvetheoptimizationproblemsforthe MOBO controlalgorithms. Theparameters R w C r ,and C w arechosenas 1 : 3 K=kW 34000 kJ=K 51000 kJ=K respectively.TheRAratio,CAtemperature,CAhumidityrat io,OAtemperature,andOA humidityratioareassumedtohaveconstantvaluesof 0 12 : 8 C 7 : 4 g=kg 15 : 6 C ,and 4 : 0 g=kg ,respectively. Forthebaselinecontroller,thetemperatures:RTG,HTG,an dCLGaresetto 21 : 8 C, 21 : 9 C,and 23 : 6 C,respectively,from 6:30 a.m.to 10:30 p.m.During thetime 10:30 p.m.– 6:30 a.m.,thetemperatures:RTG,HTG,andCLGforthe baselinecontrollerarechosenas 20 : 9 C, 21 : 1 C,and 24 : 4 C,respectively.Thisnighttime setbackisthesameasusedinthelastchapter.Itisassumedt hattheauditoriumis occupiedby150peoplefrom 8:00 a.m.to 6:00 p.m.,andunoccupiedduringtherest oftheday.Thisoccupancyproleischosenfromtheclasssch eduleoftheauditorium duringthesemesterofSpring2013.Otherdesignparameters andequilibriumpoints usedbythecontrollersareshowninTables 6-1 and 6-2 ,respectively. Table6-1.Designparametersusedinthevariouscontroller s. Temperatureandtimerelatedparameters T set T SA high T unocc RTG T occ RTG T occ low T occ high T unocc low T unocc high K t ( C )( C )( C )( C )( C )( C )( C )( C )(no.)(min) 22.2230.020.921.821.923.621.124.4301 Humidityandotherparameters W unocc low W occ low W unocc high W occ high m OAp m Az m SAhigh n pd A z ( g kg )( g kg )( g kg )( g kg ) ( kg sec )( kg m 2 )( kg sec )( m 2 ) 7.47.411.511.50.0042 3 : 05 10 4 1.982.3210238 AsshowninTable 6-2 ,wechoosetheequilibriumpointofthezonetemperature thesameas T set ,whichisthetemperaturepreferredbytheoccupants.Theeq uilibrium pointoftheSAhumidityratioisthesameasthehumidityrati oofCAsincereheating 111

PAGE 112

attheVAVboxdoesnotchangethehumidityratio.Weselectth eequilibriumpointfor thenumberofpeople( n peq )ashalfofthetypicalnumberofpeopleinthezoneduring daytime.Theequilibriumpointfortheowrateischosenast heminimumowrate requiredby n peq numberofpeople.Therestoftheequilibriumpointsarecalc ulated using( 6–1 )and( 6–2 ). Table6-2.Equilibriumpointsusedforlinearization. T SA eq T eq T w eq m eq W SA eq W eq n peq ( C )( C )( C )( kg s )( g kg )( g kg ) 21.1822.2218.91.137.58.770 Forthesakeofsimplicity,thefollowingassumptionsarebe ingconsideredduringthe simulations:1.Thetemperatureandhumidityratioofoutsideairarekept constant. 2.Theonlycontrolinputsthatareallowedbythecontroller sareSAtemperatureand owrate,whicharethecontrolinputsatthezone-level. 3.Thereisnorecirculationofthereturnair,i.e.,onlyout sideairissuppliedtoAHU. 4.TheCAtemperatureandCAhumidityratioarekeptconstant 5.Measurementsofallthestates(2temperaturesand1humid ity)areavailableto thecontrollers. Thetotaldailyenergyconsumption,averagetemperaturevi olation,average humidityviolation,and % savingsofthefeedbackandMPCcontrollersoverthebaselin e controllerareshowninTable 6-3 .Notethatthebaselineandfeedbackcontrollers arethe BL (inSection 3.2.1 )and MOBS (inSection 3.2.2 )controllers,respectively. TheMPC-basedcontrollersisthesameasthe MOBO controllerasexplainedin Section 3.2.3.1 exceptthattheoptimizationproblemssolvedbytheMPC-bas ed controlleraretheonesdescribedforvariouscasesinSecti on 6.3 .Wehavesimulated theperformanceofthe MOBO controller(case3)fortwoscenarios:1) =0 : 01 ,which meansthattheobjectivefunctionisagoodapproximationof energyconsumptionbut 112

PAGE 113

theoptimizationproblemisnotconvex,and2) =0 : 51 ,whichmakestheoptimization problemconvexbutdoesnotleadtoagoodapproximationofth eenergyfunction. Itisclearfromthetablethatboththefeedback-basedandMP C-basedcontrollers (exceptcase3when =0 : 51 )resultin 38 45% savingsoverthebaselinecontroller. TheMPC-basedcontroller(case3with =0 : 51 )leadstoonly 10% savingsduetothe poorapproximationoftheobjectivefunction,whichisexpe ctedfromtheanalysisdone inSection 6.6.2 .Anotherimportantndingisthatthefeedback-basedcontr ollerresults insimilarenergysavingsastheMPC-basedcontroller,even whenthesolutionobtained bytheMPCcontrollercorrespondstotheglobalminimum.Bot hthefeedback-based andMPC-basedcontrollershaveverysmallaveragetemperat ureviolation.Theaverage humiditydiscomfortisuniformlyzerobyallthecontroller s.RecallthatIAQismaintained atalltimesduetotheconstraintontheminimumairowrate. Theresultsindicatethat theenergysavingsfromtheproposedcontrollersareachiev edwithminimalimpacton eitherthermalcomfortorIAQ.Table6-3.Dailyenergyconsumption,averagecomfortviola tion,and % Savings. ControlScheme E ( MJ )% Savings D T ( C ) D H ( g kg ) Baseline( BL )1611-0.00140 Feedback( MOBS )997380.0110 MPC( MOBO )Case1892450.0160 MPC( MOBO )Case2891450.0160 MPC( MOBO )Case3, =0 : 01 884450.0160 MPC( MOBO )Case3, =0 : 51 150370.0130 6.5ConclusionandOpenProblems WeexaminetheperformanceoftheMPC-basedcontrolleragai nstthebaselineand feedback-basedcontrollers,whenthesolutionobtainedby theMPC-basedcontroller correspondstotheglobalminima.Thetotalenergyconsumpt ionisanon-convex functionofdecisionvariables,sovariousconvexapproxim ationsareusedtoformulate anumberofMPCcontrollers.Inthisway,weensurethattheMP Ccontrollernds 113

PAGE 114

agloballyoptimalsolution.Thefeedbackcontrolleristhe sameasdescribedin Section 3.2.2 ItisobservedfromthesimulationresultsthattheMPC-base dcontroller,which providestheglobalsolution,resultsin 45% energysavingsoverthebaselinecontroller withoutsacricingthermalcomfortandIAQ.Moreover,thef eedback-basedcontroller performsaswellasMPC-basedcontroller,evenwhenthesolu tionobtainedbythe MPCcontrollercorrespondstotheglobalminima.Thiscompa risoneliminatesthe argument—MPCmightbeobtainingalocalminimaduetothenon -convexoptimization problemthatresultsinsmalladditionalsavings—thatcoul dariseduringthecomparison doneinChapters 3 and 4 Itispossiblethattheconvexproblemmaynotbeanaccuratea pproximationof theoriginalnon-convexproblem.Betterapproximationoft henon-convexproblemmay leadtoevenmoresavingsandincreasedcomfort.Theworkpre sentedinthischapteris oneofthepreliminarysteptowardsthisdirection.Morewor kisrequiredtoinvestigate theoptionsthatcouldleadtomoreaccurateapproximationo fthenon-convexproblem, whichisaninterestingdirectiontopursue.Inthischapter ,weonlyfocusedononetype ofzonewithoneoutsidecondition.However,adetailedsimu lationanalysiswithmultiple zonetypes,outsideweather,climates,andoccupancyprol esneedstobestudiedin future. 6.6ErrorAnalysisinEnergyApproximation Inthissection,weshowtheerroranalysisofdoingtwotypes ofapproximationsto maketheenergyfunctionconvex:1)Linearand2)Quadratic.6.6.1LinearConvexApproximation Whiledoingthelinearapproximationoftheenergyequation ,weignoretherstterm ( C pa T SA m SA )from( 6–7 )asthistermcontributeslittletothetotalenergyconsump tion. Theothertermsarebasicallythesumofthelinearizedpower consumption,i.e., P lin F + P lin R + P lin U = m SAeq C pa T SA +( m SAeq + m SA )( r + + C pa ( T SA eq T CA )) : 114

PAGE 115

Removingthersttermmakestheenergyequationlinear.The reasonthattherstterm issmallerisexplainednext.Considerthefollowingexpres sion: E t =[ C pa T SA m SA ]+[ m SAeq C pa T SA +( m SAeq + m SA )( r + + C pa ( T SA eq T CA ))] : Dividingtheaboveexpressionby C pa T SA m SA leadstothefollowingequation: E tC pa T SA m SA =1+ m SAeq m SA +( m SAeq m SA +1)( r + + C pa ( T SA eq T CA ) C pa T SA ) # : Themaximum/minimumvaluesfortheSAowrateandtemperatu reare 0 : 283 = 1 : 98( kg=sec ) and 30 = 12 : 8 C,respectively.TheequilibriumpointsfortheSAowratea ndtemperature are 1 : 133( kg=sec ) and 21 : 1 C,respectively.Itmeansthat j T SA j < 9 C and j m SA j < 0 : 849 .Thesechoicesleadtothefractions m SAeq m SA > 1 : 33 and r + + C pa ( T SA eq T CA ) C pa T SA > 2 Thisimpliesthatthesecondterminthesquarebracketsinth eaboveexpressionis lowerboundedby 7 .Itmeansthatthetermweareignoringduringtheapproximat ionis lessthan 15% ofthetotalenergyconsumption,whichisagoodapproximati onforthis preliminarycomparisonofthecontrollers'performance.6.6.2QuadraticConvexApproximation Theexpressionforenergyequationcanbewrittenas E = u T Q m u + c Tm u + d m ; (6–17) where u =[ T SA m SA ] T d m = t [ m SAeq ( r + + C pa ( T SA eq T CA ))] Q m = t 264 0 C pa 2 C pa 2 0 375 and c m = t [ m SAeq C pa ;r + + C pa ( T SA eq T CA )] T .The Q m matrixisnotpositivedenite asoneofitseigenvalueisnegative.Therefore,theoptimiz ationproblemthatuses E as anobjectivefunctionisnon-convex.Toapproximateitasac onvexfunction,weaddan additionalterm( t m SA ( i ) 2 + t T SA ( i ) 2 )totheenergyconsumptionas E quad = k + K X i = k E ( i )+ t m SA ( i ) 2 + t T SA ( i ) 2 : (6–18) 115

PAGE 116

Eq.( 6–18 )canbeexpressedinthesimilarformof( 6–17 )as E quad = u T Q newm u + c Tm u + d m ; (6–19) where Q newm = t 264 C pa 2 C pa 2 375 : (6–20) For E quad tobeconvex, Q newm hastobepositivesemi-denite,whichispossiblewhen >C pa = 2 .Ifwechoose >C pa = 2 ,thentheerrorduetotheadditionaltermislargeas comparedtotheotherterms.Suppose m SA =0 and T SA =8 ,thenthecontribution fromtheadditionalterm( t m SA ( i ) 2 + t T SA ( i ) 2 )canbeashighas 32 andthe contributionfromtherestofthetermscanbeashighas 24 .Therefore,theerrorin energyconsumptionduetotheadditionaltermcouldbeupto 60% ,whichisnotsmall. Hence,theuseofthistypeofconvexapproximationisnotrec ommendedfortheenergy function. 116

PAGE 117

CHAPTER7 CONCLUSIONANDFUTUREWORK Inthischapter,weconcludetheresultsobtainedintheprev iouschapters.Wealso discussthepossibledirectionsandtheresearchproblemst hatcanbetargetedinthe future. 7.1ConclusionoftheChapters Inchapter 2 ,werstdevelopafull-scalephysicsbasedmodelofhygro-t hermal dynamicsforamulti-zonebuilding,whichisobtainedbycom biningthedynamicsof temperature(“thermal”)andhumidity(“hygro”)inazone.T hen,wedevelopanovel modelreductiontechnique,whichusesaspecicsparsityst ructureofthefull-scale hygro-thermaldynamicsmodelandbalancedtruncationtore ducethemodelorder. Thefull-scalethermalmodelhasalinearpartandanon-line arpart.Thelinear partcomesfromtheRCnetworkthatmodelsheattransferbetw eenzones,andthe non-linearpartcomesfromtheenergyexchangebetweenthea irsuppliedtoazone andtheairextractedfromthatzone.Thedynamicsofhumidit yarederivedusing massbalancelaws,whichareasetofnon-linearODEs.Sincet hefull-scalemodelis basedonbasicmassandheatbalance,weexpectthemodelredu ctionmethodtobe applicabletoawiderangeofbuildingsystems.Itisshownth atthezonetemperature andhumiditypredictionsbythereducedmodelarequiteclos etothepredictionsbythe full-scalemodel;thecomputationtimetakenbythereduced ordermodeldecreased approximatelybyafactorof 6 asthatofthefull-scalemodel. InChapter 3 ,wehaveproposedthreezone-levelcontrolalgorithms— MOBS MOBO ,and POBO —ofvaryingcomplexityandrequiringvaryingdelityofinf ormation. Thegoalofthecontrollersistominimizeenergyconsumptio nwhilemaintaining comfortlevelinazoneinacommercialbuildingwithaVAV-ba sedHVACsystem. Theinputsthatcanbecommandedbythezone-levelcontrolle rsareSAtemperature andowrate.Weexaminehowtheperformanceofacontrolleri saffectedbyits 117

PAGE 118

complexitythroughsimulations.Theoverallcomplexityof thecontrolstrategies increasesintheorder1) BL ,2) MOBS ,3) MOBO ,and4) POBO .The BL controller usestemperaturemeasurementsbutnotreal-timeoccupancy information.Incontrast, theproposed MOBS and MOBO controlalgorithmsrequireoccupancyandtemperature measurements,andthe POBO controllerrequiresoccupancypredictionsinadditionto thetemperaturemeasurements.While MOBS controllerisafeedbackcontrolalgorithm, the MOBO and POBO controllersareMPC-basedalgorithmsthatrequireamodelo f buildinghygro-thermaldynamics. Simulationresultsshowthatalltheproposedcontrollersl eadto 50% energysavings onaverage(dependingonzonetype,weather,climate,desig noccupancy,etc.)with negligibleimpactonIAQorthermalcomfort.Theresultssho wthatevenasimple feedback-basedalgorithmcanperformaswellasanMPC-base dalgorithmaslong asonlyoccupancymeasurementsareavailableandthecomman dedcontrolinputs areSAowrateandtemperature.Anotherconclusionfromthe simulationresultsis thattheadditionalenergysavingswithanMPC-basedcontro lthatusesoccupancy predictions—overonethatonlyusesmeasurements—aresmal l.Thesmalladditional savingsareduetotherestrictionontheminimumairowduri ngtheunoccupiedtimes thatcomesfromcurrentASHRAEventilationstandard62.1-2 010[ 17 ].Itisshown throughsimulationsthatoccupancymeasurementisanimpor tantcomponentof energy-efcientzone-climatecontrol.Theseconclusions areveriedthroughthe experiments,whichareperformedinazoneofPughHallinthe UniversityofFlorida campus.Theexperimentalsetupandtheresultsobtainedfro mexperimentsare describedinChapter 4 InChapter 5 ,weproposeseveralcontrolalgorithmsthatcanbeimplemen ted atAHU-level,andinvestigatethepotentialofenergysavin gsasafunctionofthe complexityofcontrolalgorithm.Theinputsthatcanbecomm andedbythecontrollers attheAHU-levelaresupplyairowrate,supplyairtemperat ure,returnairratio,and 118

PAGE 119

conditionedairtemperature.Tocomparetheperformancevs .complexity,wechoose variouscontrollersthatrequirevaryingamountofinforma tion,computation,designand implementationeffort.Simulationresultsshowthatoccup ancymeasurementisakey factortoreducetheenergyusageinbuildings.Thecontroll ersthatuseonlyoccupancy measurementsresultin 56 69% energysavingsascomparedtothecontrollersthat donotusesuchmeasurements.Thecontrollersthatuseoccup ancymeasurements alongwiththemeasurementsofzonehumidityandoutsidewea ther,resultinenergy savingsof 71 85% withnegligibleeffectonIAQorthermalcomfort.Anotherke ynding isthatafeedback-basedcontrollerthatissimpleandeasyt oimplement,performsas wellasacomplexandcomputationallyexpensiveMPC-basedc ontroller,ifthesame measurementsareprovidedtoboththecontrollers.Thisiss ignicantinlightofthe muchhighereffortrequiredtoimplementtheMPC-basedcont rollerduetotheneedfor modelidentication[ 34 ]andon-lineoptimization. Thestudyshowsthattheeffectofcontrolinputsontheenerg ysavingsdecreases intheorder:1)supplyairowrateandtemperature2)return airratio3)conditionedair temperature.Theconditionedairtemperaturehasalmostne gligibleimpactonenergy savingswhenthereturnairratioisvaried.Therefore,afee dbackcontroller,withsupply airtemperature,returnairratio,andsupplyairowrateas thecontrolvariables,isthe mostappropriatecontrolalgorithmtobeusedforsingle-zo neVAVHVACsystemsdueto itssimplicity,lowcomputation,andsimilarperformancet othatofmorecomplexcontrol algorithms. Ithasbeenshowninthepreviouschaptersthatfeedbackperf ormsaswellasMPC whenbothofthemareallowedtohavethesamemeasurements.T heoptimization problemsolvedbytheMPC-basedcontrollersisnon-convexd uetothenon-quadratic objectivefunction( 3–9 )andnonlinearequalityconstraintsinthehygro-thermald ynamics model( 2–7 )-( 2–8 ).ItispossiblethatthesolutionobtainedbytheMPCcontro ller correspondstoalocalminimainsteadoftheglobalminima.T herefore,theadditional 119

PAGE 120

savingsobtainedbytheMPC-basedcontrolleroverfeedback -basedcontrolleraresmall. Theglobalminimumsolutionoftheoptimizationproblemsol vedbytheMPC-based controllermayresultinhighadditionalsavings.Therefor e,weapproximatethe non-convexoptimizationproblemintoaconvexoptimizatio nproblembylinearizing thepowermodelandhygro-thermaldynamicsmodelaroundane quilibriumpointin Chapter 6 .Oncetheproblemisconvertedintoconvexoptimizationpro blemthathas onlyoneoptimalsolution,wecomparetheperformanceofthe MPC-basedcontroller againstthebaselineandfeedback-basedcontrollers.Inth isway,weremovethe argumentonthequalityofthesolutionobtainedbytheMPCco ntroller—localvs. global—bysolvingtheapproximatedconvexoptimizationpr oblem. ItisobservedfromthesimulationsthatthefeedbackandMPC controllersresultin 38 45% energysavingsoverthebaselinecontrollerwithoutsacri cingthermalcomfort andIAQ.Moreover,thefeedbackcontrollerperformsaswell asMPCcontroller,even whenthesolutionobtainedbytheMPCcontrollercorrespond stotheglobalminimum. Thiscomparisoneliminatestheargument—MPCmightbeobtai ningalocalminimadue tonon-convexoptimizationproblemthatresultsinsmallad ditionalsavings—thatcould ariseduringthecomparisondoneinChapters 3 and 4 7.2OverallConclusion Theoverallconclusionofthisdissertationforthezone-le velandAHU-level controllersismentionedbelow.Atthezone-level:1.Anaverageof 50% energysavingsisobtainedatthezone-levelbyusingthe proposedMPCandfeedbackcontrollers. 2.FeedbackperformsasgoodasMPCatthezone-level,whenoc cupancy measurementsareavailabletoboththecontrollers. 3.Theconclusions1and2forthezone-levelcontrollershav ealsobeenveriedby conductingexperimentsinaroominPughHallattheUniversi tyofFloridacampus. 120

PAGE 121

4.Ourpreliminarysimulationstudy(withtheassumptionsa smentionedinSection 6.4 ) showsthattheconclusions1and2arestillvalidwhenthesol utionobtainedbythe MPCcontrollercorrespondstoglobalminima. 5.AdditionalsavingswithMPCcontrollerthatusesoccupan cypredictionsare 5% onaverage.Thisisduetotherestrictionontheminimumair owduring theunoccupiedtimesthatcomesfromcurrentASHRAEventila tionstandard 62.1-2010[ 17 ]. 6.AdditionalsavingsbytheMPCcontroller,whichusesoccu pancypredictions, increaseto 35% ifearlierstandardsareadopted[ 65 ]. AttheAHU-level:1.Energysavingsof 71 85% areobtainedattheAHU-levelbyusingtheproposed MPCandfeedbackcontrollers. 2.FeedbackperformsasgoodasMPCattheAHU-levelifthesam emeasurements areprovidedtotheboththecontrollers. 3.Occupancymeasurementisakeyinformationtoreduceener gyconsumptionat bothzone-levelandAHU-level. Basedontheconclusions,afeedbackcontroller,whichuses occupancymeasurements, isthemostappropriatecontrolalgorithmtobeusedforsing le-zoneVAVHVAC systemsduetoitssimplicity,lowcomputation,andsimilar performancetothatof optimization-basedcontrolalgorithms. 7.3FutureWork Therearemanypossiblewaystoextendthepreviousworkinth edirectionofboth modelingandcontrol.7.3.1ImprovedModeling Thehygro-thermalmodelthatwehavedevelopeddoesnotcons iderinter-zone thermalconvection.Constructingareducedordermodelofi nter-zoneconvectiveheat transferisanotherimportantdirectiontoproceed.Wehave donesomepreliminary workinidentifyingreducedorderRCnetworkmodelsofinter -zoneconvection, whichisreportedin[ 58 ].Sincetheinter-zoneconventionmodelisalsoalumped resistance-capacitancenetworkmodel,itcanbedirectlyc ombinedwiththefull-scale 121

PAGE 122

model.Insuchacase,theproposedmodelreductioncanbedir ectlyappliedsincethe structuralpropertiesdonotchangewiththeaugmentationo ftheinter-zoneconvection model.However,thereareseveralhurdlesinidentifyingR, Cparametersfromdata,as shownin[ 34 ].Identicationofmulti-zoneinteractionmodelsislikel ytobechallenging. Intheproposedmodelreductionmethod,thestatesloosethe irphysicalmeaning afterthereduction.Todevelopareducedordermodelwhilep reservingthestructureand physicalinterpretationofthestatesisalsoaninterestin gdirectiontoproceed.Wehave donesomepreliminaryworkalongthesamelines[ 71 72 ]. 7.3.2DetailedAnalysisandImprovingControl Alltheproposedcontrolalgorithmsrequirechoiceofsever alparameters,which involveatrade-offbetweenenergysavingsandpotentialdi scomfort.Thistrade-off needstobemorecarefullyexaminedtodetermineasetofguid elinesonhowtochoose theseparameters.Workontheimplementationofthe Z-FC controllerineachzoneof thePughHallisongoing.Infact,wehaveimplementedthe Z-FC controllerin19zones ofthePughHallforoneweek.However,weneedtoimplementth e Z-FC controllerfora longerdurationoftimetoevaluatethepotentialofthistec hnologyandidentifypotential implementationissuesthatarenotseeninnumericalstudie s.Forinstance,uncertain actuatorresponsewasidentiedasafactorthataffectsthe controller'sperformancein experimentsinvolvingthezone-level MOBS and MOBO controllers.Implementationof the A-FC controllerinarealbuildingscanleadtointerestingpract icalissuesandopen newareasofresearch. Effectofvarioustypeofuncertaintiesneedstobestudiedf ortheAHU-level controllers.Wehavedoneadetailedrobustnessanalysisfo rthezone-levelcontrollers, whichispresentedinourrecentwork[ 73 ].ItispossiblethatMPCmayprovidea signicantadvantageoverfeedbackcontrolintermsofrobu stnesstotheseuncertainties, especiallyfortheAHU-levelcontrollerswhenallthecontr olinputsarevaried.Another possibleresearchdirectionistoobtainabetterapproxima tionoftheoptimization 122

PAGE 123

problemusedintheMPC-basedcontrollers,orabetterconve xrelaxationofthe problem. 123

PAGE 124

REFERENCES [1]USEIA,Annualenergyreview(October2011).[2]W.Angel,HVACDesignSourcebook,McGraw-HillEngineer ing,2012. [3]M.Brambley,D.Hansen,P.Haves,D.Holmberg,S.McDonal d,K.Roth, P.Torcellini,Advancedsensorsandcontrolsforbuildinga pplications:Market assessmentandpotential R & D pathways,Tech.rep.,PacicNorthwestNational Laboratory(April2005). [4]M.Rahman,M.Rasul,M.Khan,Energyconservationmeasur esinaninstitutional buildinginsub-tropicalclimateinAustralia,AppliedEne rgy87(2010)2994–3004. [5]S.Goyal,H.Ingley,P.Barooah,Zone-levelcontrolalgo rithmsbasedonoccupancy informationforenergyefcientbuildings,in:AmericanCo ntrolConference(ACC), 2012,pp.3063–3068. [6]V.Erickson,M.Carreira-Perpinan,A.Cerpa,OBSERVE:O ccupancy-based systemforefcientreductionofHVACenergy,in:Informati onProcessinginSensor Networks(IPSN),2011,pp.258–269. [7]A.Aswani,N.Master,J.Taneja,D.Culler,C.Tomlin,Red ucingtransientandsteady stateelectricityconsumptioninHVACusinglearning-base dmodel-predictive control,ProceedingsoftheIEEE100(1)(2012)240–253. [8]J.Siroky,F.Oldewurtel,J.Cigler,S.Privara,Experim entalanalysisofmodel predictivecontrolforanenergyefcientbuildingheating system,AppliedEnergy88 (2011)3079–3087. [9]F.Oldewurtel,A.Parisio,C.Jones,D.Gyalistras,M.Gw erder,V.Stauch, B.Lehmann,M.Morari,UseofModelPredictiveControlandWe atherForecastsfor EnergyEfcientBuildingClimateControl,EnergyandBuild ings45(2012)15–27. [10]S.Afshari,S.Mishra,A.Julius,F.Lizarralde,J.Wen, Modelingandfeedback controlofcolor-tunableLEDlightingsystems,in:America nControlConference (ACC),2012,pp.3663–3668. [11]F.Oldewurtel,A.Parisio,C.Jones,M.Morari,D.Gyali stras,M.Gwerder,V.Stauch, B.Lehmann,K.Wirth,Energyefcientbuildingclimatecont rolusingstochastic modelpredictivecontrolandweatherpredictions,in:Amer icanControlConference, 2010,pp.5100–5105. [12]D.Gyalistras,M.Gwerder,Useofweatherandoccupancy forecastsforoptimal buildingclimatecontrol(opticontrol):Twoyearsprogres sreport,Tech.rep., SiemensSwitzerlandLtd(2010). 124

PAGE 125

[13]P.Morosan,R.Bourdais,D.Dumur,AdistributedMPCstr ategybasedonbenders decompositionappliedtomulti-sourcemulti-zonetempera tureregulation,Journalof ProcessControl21(2011)729–737. [14]M.Mossolly,K.Ghalib,N.Ghaddar,Optimalcontrolstr ategyforamulti-zone airconditioningsystemusingageneticalgorithm,Energy3 4(1)(2009)58–66. doi:10.1016/j.energy.2008.10.001 [15]X.Xu,S.Wang,Z.Sun,F.Xiao,Amodel-basedoptimalven tilationcontrolstrategy ofmulti-zoneVAVair-conditioningsystems,AppliedTherm alEngineering29(1) (2009)91–104. doi:10.1016/j.applthermaleng.2008.02.017 [16]USEIA-DepartmentofEnergy,CBECSdetailedtables(20 03). [17]ASHRAE,ANSI/ASHRAEstandard62.1-2010:Ventilation foracceptableairquality (2010). [18]C.Liao,P.Barooah,Anintegratedapproachtooccupanc ymodelingandestimation incommercialbuildings,in:AmericanControlConference, 2010,pp.3130–3135. [19]T.Teixeira,G.Dublon,A.Savvides,Asurveyofhumanse nsing: Methodsfordetectingpresence,count,location,trackand identity, www.eng.yale.edu/enalab/publications/human_sensing_ enalabWIP.pdf unpublished. [20]S.Goyal,H.Ingley,P.Barooah,Occupancy-basedzonec limatecontrolforenergy efcientbuildings:Complexityvs.performance,AppliedE nergy106(2013) 209–221. [21]F.Oldewurtel,D.Sturzenegger,M.Morari,Importance ofoccupancyinformationfor buildingclimatecontrol,AppliedEnergy101(2013)521–53 2. [22]S.Goyal,P.Barooah,Amethodformodel-reductionofno nlinearbuildingthermal dynamics,in:Inproceedingsofthe2011AmericanControlCo nference,2011,pp. 2077–2082. [23]S.Goyal,P.Barooah,Amethodformodel-reductionofno nlinearbuildingthermal dynamicsofmulti-zonebuildings,EnergyandBuildings47( 2012)332–340. [24]M.Gouda,S.Danaher,C.Underwood,Buildingthermalmo delreduction usingnonlinearconstrainedoptimization,BuildingandEn vironment37(2002) 1255–1265. [25]M.M.Gouda,S.D.C.P.Underwood,Low-ordermodelforth esimulationofa buildinganditsheatingsystem,BuildingServicesEnergyR esearchTechnology21 (2000)199–208. [26]T.Nielsen,Simpletooltoevaluateenergydemandandin doorenvironmentinthe earlystagesofbuildingdesign,SolarEnergy78(2005)73–8 3. 125

PAGE 126

[27]ASHRAE,TheASHRAEhandbookfundamentals(SIEdition) (2005). [28]B.Tashtoush,M.Molhim,DynamicmodelofaHVACsystemf orcontrolanalysis, Energy30(2005)1729–1745. [29]S.Wang,X.Xu,Simpliedbuildingmodelfortransientt hermalperformance estimationusingGA-basedparameteridentication,Inter nationalJournalof ThermalSciences45(2006)419–432. [30]R.Yao,N.Baker,M.McEvoy,Asimpliedthermalresista ncenetworkmodelfor buildingthermalsimulation,in:TheCanadianConferenceo nBuildingEnergy Simulation(eSim'02),2002. [31]M.Zaheer-Uddin,G.Zheng,Adynamicmodelofamultizon eVAVsystemfor controlanalysis,Transactions-AmericanSocietyofHeati ngRefrigeratingandAir ConditioningEngineers100(1994)219. [32]J.Kampf,D.Robinson,Asimpliedthermalmodeltosupp ortanalysisofurban resourceows,Energyandbuildings39(2007)445–453. [33]S.Wang,DynamicsimulationofbuildingVAVair-condit ioningsystemand evaluationofemcson-linecontrolstrategies,Buildingan dEnvironment36(1999) 681–705. [34]Y.Lin,T.Middelkoop,P.Barooah,Issuesinidenticat ionofcontrol-orientedthermal modelsofzonesinmulti-zonebuildings,in:IEEEConferenc eonDecisionand Control,2012,pp.6932–6937. doi:10.1109/CDC.2012.6425958 [35]A.C.Antoulas,D.C.Sorensen,S.Gugercin,Asurveyofm odelreductionmethods forlarge-scalesystems,Vol.280,2001,pp.193–219. [36]S.Al-Baiyat,M.B.U.Al-Saggaf,Newmodelreductionsc hemeforbilinearsystems, InternationalJournalofSystemsScience25(1994)1631–16 42. [37]S.Al-Baiyat,M.Bettayeb,Anewmodelreductionscheme fork-powerbilinear systems,in:32ndIEEEConferenceonDecisionandControl,V ol.1,1993,pp. 22–27. [38]W.Gray,J.Mesko,Energyfunctionsandalgebraicgrami ansforbilinearsystems, in:4thIFACNonlinearControlSystemsDesignSymposium,19 98. [39]L.Zhang,J.Lam,On h 2 modelreductionofbilinearsystems,Automatica38(2002) 205–216. [40]J.Scherpen,Balancingfornonlinearsystems,Systems andControlLetters21 (1993)143–153. 126

PAGE 127

[41]S.Lall,J.Marsden,S.Glavaski,Asubspaceapproachto balancedtruncationfor modelreductionofnonlinearcontrolsystems,JournalofRo bustandNonlinear Control12(2002)519–526. [42]J.Hahn,T.Edgar,Animprovedmethodfornonlinearmode lreductionusing balancingofempiricalgramians,Computers&ChemicalEngi neering26(2002) 1379–1397. [43]Y.Agarwal,B.Balaji,S.Dutta,R.Gupta,T.Weng,Dutycyclingbuildings aggressively:ThenextfrontierinHVACcontrol,in:Inform ationProcessingin SensorNetworks(IPSN),2011,pp.246–257. [44]A.Persily,A.Musser,S.Emmerich,M.Taylor,Simulati onsofIndoorAirQuality andVentilationImpactsofDemandControlledVentilationi nCommercialand InstitutionalBuildings,U.S.Dept.ofCommerce,Technolo gyAdministration, NationalInstituteofStandardsandTechnology,2003. [45]Y.Tachwali,H.Refai,J.Fagan,MinimizingHVACenergy consumptionusinga wirelesssensornetwork,in:IndustrialElectronicsSocie ty,2007.IECON2007.33rd AnnualConferenceoftheIEEE,2007,pp.439–444. [46]V.Dhummi,D.Demetriou,H.Palanthandalam-Madapusi, H.Khalifa,C.Isik,Robust occupancy-baseddistributeddemandcontrolventilation, InternationalJournalof Ventilation9(5)(2011)359–369. [47]S.Wang,X.Jin,Model-basedoptimalcontrolofVAVairconditioningsystemusing geneticalgorithm,BuildingandEnvironment35(2000)471– 487. [48]N.Nassif,S.Kajl,R.Sabourin,OptimizationofHVACco ntrolsystemstrategyusing two-objectivegeneticalgorithm,HVAC&RResearch11(3)(2 005)459–486. [49]S.Cheng,Y.Chen,C.Chan,T.Lee,H.Chan,J.Qin,Q.Zhou ,A.Cheung, K.Yu,ArobustcontrolstrategyforVAVAHUsystemsanditsap plication,in: S.Sambath,E.Zhu(Eds.),FrontiersinComputerEducation, Vol.133ofAdvances inIntelligentandSoftComputing,SpringerBerlinHeidelb erg,2012,pp.635–642. doi:10.1007/978-3-642-27552-4_85 [50]Y.-H.Cho,G.Wang,M.Liu,Applicationofterminalboxo ptimizationofsingle-duct air-handlingunits,InternationalJournalofEnergyResea rch34(1)(2010)54–66. [51]J.Bourdouxhe,M.Grodent,J.Lebrun,Referenceguidef ordynamicmodelsof HVACequipment,ASHRAE,1998. [52]A.Aswani,N.Master,J.Taneja,V.Smith,A.Krioukov,D .Culler,C.Tomlin, Identifyingmodelsofhvacsystemsusingsemi-parametricr egression,in:American ControlConference,2012,pp.3675–3680. [53]M.Turner,D.Bates(Eds.),MathematicalMethodsforRo bustandNonlinear Control,1stEdition,Springer,2007. 127

PAGE 128

[54]M.Dahleh,M.Dahleh,G.Verghese, Lecturesondynamicsystemsandcontrol (1999).URL http://ocw.mit.edu/index.htm [55]K.Zhou,J.Doyle,Essentialsofrobustcontrol,Prenti ceHall,1998. [56]U.Mackenroth,RobustConrolSystems:TheoryandCaseS tudies,Springer,2004. [57] Nationalsolarradiationdatabase(NSRDB) (2005). URL http://rredc.nrel.gov/solar/old_data/nsrdb/1991-200 5/tmy3/ [58]S.Goyal,C.Liao,P.Barooah,Identicationofmulti-z onebuildingthermal interactionmodelfromdata,in:50thIEEEConferenceonDec isionandControl andEuropeanControlConference,2011,pp.181–186. [59]ASHRAE,TheASHRAEhandbook-HVACapplications(SIEdi tion)(2011). [60]J.Kreider,HandbookofHeating,Ventilation,andAirC onditioning,Handbook SeriesforMechanicalEngineering,Taylor&FrancisGroup, 2001. [61]S.Doty,W.Turner,EnergyManagementHandbook,Fairmo ntPress,Incorporated, 2009. [62]S.Sugarman,S.Monger,TestingandBalancingHVACAira ndWaterSystems, FairmontPress,2000. [63]H.Bohanon,GoodIAQpractices,ASHRAEJournal54(2012 )106–107. [64]A.W a chter,L.Biegler,Ontheimplementationofaninterior-poi ntlterline-search algorithmforlarge-scalenonlinearprogramming,Mathema ticalProgramming106 (2006)25–57. [65]ASHRAE,ANSI/ASHRAEstandard62.1-2001:Ventilation foracceptableairquality (2001). [66]K.Atkinson,W.Han,D.Stewart,NumericalSolutionofO rdinaryDifferential Equations,JohnWiley&Sons,2009. [67] [link] URL www.wunderground.com [68]A.Kelman,Y.Ma,F.Borrelli,Analysisoflocaloptimai npredictivecontrolforenergy efcientbuildings,JournalofBuildingPerformanceSimul ation. [69]C.Long,Model-basedProcessControlUsingNonconvexO ptimization,University ofSouthCarolina,2006. 128

PAGE 129

[70]S.Boyd,L.Vandenberghe,Convexoptimization.2004,C ambridgeUniversity Press,2004. [71]K.Deng,P.Barooah,P.Mehta,S.Meyn,Buildingthermal modelreductionvia aggregationofstates,in:AmericanControlConference,20 10,pp.5118–5123. [72]K.Deng,S.Goyal,P.Barooah,P.G.Mehta, Structure-preservingmodelreduction ofnonlinearbuildingthermalmodels, ,Automatica106. URL http://humdoi.mae.ufl.edu/ ~ prabirbarooah/publications.html [73]S.Goyal,H.Ingley,P.Barooah,Effectofvariousuncer taintiesontheperformance ofoccupancy-basedoptimalcontrolofHVACzones,in:IEEEC onferenceon DecisionandControl,2012,pp.7565–7570. 129

PAGE 130

BIOGRAPHICALSKETCH SiddharthGoyalwasborninHisar,Indiain1986.Hereceived hisPh.D.from theUniversityofFloridainthesummerof2013.Hiscurrentr esearchisfocusedon Energy-EfcientIntelligentBuildings,whereheisworkin gonmakingthehumanlife betterbysavingenergyandmaintainingthecomfortableind oorenvironmentthrough theuseofadvancedsensingandcontrolalgorithms.Hisprof essionalexperience consistsofworkingasaresearch/teachingassistantatsev eraluniversitiesandasan intern/engineerinvariouscompanies.Hehasalsodonerese archinotherareassuchas aircraft-control,satelliteattitudedetermination,and robotics. In2005,hestaredhisindustrialexperienceasasummerinte rnintheR & D departmentattheGEMotors,India.Ayearlater,hewasappoi ntedasaresearch internatoneofthepremierresearchinstituteinIndia,the IndianInstituteofScience (IISc).AtIISc,heworkedontheF-16aircraftscontrolproj ectsponsoredbytheDefense ResearchandDevelopmentOrganization. Hisrstinternationalexperienceasaresearchinternduri ngtheyear2006inthe eldofroboticsattheNationalUniversityofSingaporeinc reasedhiseldofresearch. Hewasawardedthebachelor'sinelectricalengineeringwit hhonorsfromthePunjab EngineeringCollege.Duringhisundergraduatestudies,he wasanexecutivebody memberofmultipletechnicalorganizations. In2007,hejoinedtheRelianceEnergyLimited—thelargestp owerutilityenterprise inIndianprivatesector—asaGraduateEngineer,wherehewo rkedforayearinthe projectmanagementdivisionofa1250MWthermalpowerplant .Until2008,hewas alsoavisitingresearcherattheIndianInstituteofScienc e. HewasadmittedtotheUniversityofFloridain2008directly intothePh.D. programwiththeAchievementAward.Initially,heworkedin spacesystemsgroup onpico-satellitesforayear.Then,hestartedworkingonth eEnergyBuildingsProject undertheguidanceofDr.PrabirBarooah. 130

PAGE 131

DuringhisPh.D.program,hehasbeenateachingassistantfo rseveralcourses. Hehasgiventalksatvariousinternationalconferences.He hasalsopublishedseveral papersandpostersintheInternationalConferencesandJou rnals. 131