REDUCED-ORDER ENERGY MODELING FOR ADVANCED SETPOINT CONTROLS OF RESIDENTIAL BUILDINGS WITH TIME-OF-USE RATES by Andrew J. Speake c Copyright by Andrew J. Speake, 2018 All Rights Reserved A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of Mines in partial fulfillment of the requirements for the degree of Master of Science (Mechan- ical Engineering). Golden, Colorado Date Signed: Andrew J. Speake Signed: Dr. Paulo Tabares Thesis Advisor Golden, Colorado Date Signed: Dr. John Berger Professor and Head Department of Mechanical Engineering ii ABSTRACT In the United States, approximately 40% of energy is consumed by commercial and residential buildings, primarily attributed to a building’s heating, ventilation, and air condi- tioning (HVAC) system. During periods of extreme temperatures, these cooling systems are pushed to their limits and components of the grid system are stressed. This can result in grid system instability, lead to potential health concerns for building occupants, and result in higher energy costs for utilities and building owners. One solution to address this problem is implementing variable electric rates with the use of energy management strategies such as incentivized demand-response (DR) programs and load shifting to control AC units or large appliances. Variable electric rate programs often address the energy demands of commercial and industrial buildings; however, there is increased interest in curtailing the electricity use in the residential sector via the same methods. Key topics of interest regarding load-shifting in residential homes include accurate models to predict costs and electricity use, and the use of advanced controls of temperature setpoints under variable electric rates. Presented in this thesis are (i) an analysis of grey-box and black-box reduced-order models for cooling load predictions of two residential homes; and (ii) a demonstration of the impacts of time-of-use (TOU) rates applied to residential homes using an MPC. Of the two models presented, the black-box model is better suited for application to the MPC. The studies also demonstrate that the electricity rate greatly impacts the benefits of an MPC, both from a consumer cost-savings perspective and in its ability to shift AC electricity. iii TABLE OF CONTENTS ABSTRACT ......................................... iii LISTOFFIGURES .....................................vii LISTOFTABLES.......................................x LISTOFABBREVIATIONS ................................ xi ACKNOWLEDGMENTS ................................. xiii CHAPTER1 INTRODUCTION ...............................1 1.1 ResearchObjectives. .. ....4 1.2 TechnicalApproachOverview . ....5 1.3 ThesisContributions . ....6 1.4 ThesisOrganization.............................. ....6 CHAPTER 2 ANALYSIS OF GREY-BOX AND BLACK-BOX RESIDENTIAL ENERGY MODELS FOR APPLICATION TO BUILDING TEMPERATURECONTROLS. .7 2.1 Introduction.................................... .7 2.2 Methodology ....................................10 2.2.1 Black-BoxModelMethodology . 11 2.2.1.1 Selection of Black-Box Input Parameters . 12 2.2.2 Grey-BoxModelMethodology . 13 2.2.2.1 Grey-BoxModelCalibration. 17 2.2.3 DataforTrainingandValidation . 19 2.2.4 ValidationMethods. 20 iv 2.3 Results........................................21 2.3.1 Black-BoxModelResults. 22 2.3.2 Grey-BoxModelResults . 23 2.3.3 Black-BoxandGrey-BoxComparison . 25 2.4 Discussion...................................... 26 2.5 Conclusion...................................... 30 CHAPTER 3 MODEL-PREDICTIVE CONTROL OF TEMPERATURE SETPOINTS FOR HOMES SUBJECT TO TIME-OF-USE RATES . 31 3.1 Introduction.................................... 31 3.2 ModelPredictiveControlDevelopment . ....... 36 3.2.1 SystemIdentification . 36 3.2.2 PrototypingPlatformDescription . ..... 40 3.2.3 MPCOptimizationModel . 42 3.2.4 MathematicalFormulationoftheMPC . 43 3.3 ApplicationofPlatformForCaseStudy . ..... 45 3.4 PreoptimizatonAnalysis . 47 3.5 OptimizationResults . 48 3.5.1 SimulationTrends ............................. 49 3.6 Discussion...................................... 56 3.7 Conclusions ..................................... 57 CHAPTER 4 SUMMARY AND CONCLUSIONS . 58 4.1 SummaryofEfforts................................. 58 4.2 KeyFindings ....................................58 v 4.3 FutureWork.....................................59 4.4 Outlook .......................................59 REFERENCESCITED ................................... 61 vi LIST OF FIGURES Figure 1.1 Electricity demand of California for a single day inthesummer. .2 Figure 1.2 Two-tiered time-of-use pricing structure in Sacramento,CA. .2 Figure 2.1 Reduced building geometry with RC networks shown for the wall and window. ....................................14 Figure 2.2 New detached (left) and existing detached (right) BEopthomes. 19 Figure 2.3 Temperature setpoint pre-cooling schedule and zone temperature used inmodelvalidation. .............................. 22 Figure 2.4 12-hr ARX model predictions compared to EnergyPlus outputs for a newdetachedhome............................... 23 Figure 2.5 48-hr ARX model predictions compared to EnergyPlus outputs for a newdetachedhome............................... 24 Figure 2.6 12-hr ARX model predictions compared to EnergyPlus outputs for a new detached home. The model is trained using a penalty term applied ′ to the objective function when Yt =0.....................24 Figure 2.7 48-hr ARX model predictions compared to EnergyPlus outputs for a new detached home. The model is trained using a penalty term applied ′ to the objective function when Yt =0.....................25 Figure 2.8 Grey-box predicted cooling loads and indoor temperature compared to EnergyPlus. .................................. 26 Figure 2.9 12-hr predictions using the ARX model and grey-box model, compared to EnergyPlus outputs for new a detached home. 27 Figure 2.10 48-hr predictions using the ARX model and grey-box model, compared to EnergyPlus outputs for new a detached home. 27 Figure 3.1 The operational basis for the receding (t), control (m), and prediction (k) horizons for an MPC over two time steps (t,t + k). ..........32 Figure 3.2 Demonstration of ARX predictions for prediction horizon of four, and modelorderoffour .............................. 39 vii Figure 3.3 12-hr predictions using the ARX model, compared to EnergyPlus outputsforanewdetachedhome. 40 Figure 3.4 48-hr predictions using the ARX model, compared to EnergyPlus outputsforanewdetachedhome. 41 Figure 3.5 MPC modeling environment control loop, constructed with Simulink; the numbers correspond with the steps listed in the preceding paragraph. 42 Figure 3.6 Occupant-dependent temperature setpoint bounds fortheMPC. 46 Figure 3.7 Single-zone new detached residential building model............. 46 Figure 3.8 Three time-of-use rates used in the case study, and the baseline rate appliedtoatypicalsetpointschedule . 47 Figure 3.9 Sensitivity analysis using the sum of the objective function over five days and an increasing prediction horizon (K). ..............48 Figure 3.10 Optimal MPC setpoint schedule and the allowable setpoint bounds. IAT: indoor air temperature; TSP: temperature setpoint. ....... 49 Figure 3.11 Temperature setpoint results from MPC compared to a baseline schedule for the (8-hr, 5x) case. IAT: indoor air temperature; TSP: temperature setpoint; DBT: dry-bulb temperature . ..... 50 Figure 3.12 Resulting cooling electricity from the optimal MPC schedule and TOU rate compared to a baseline schedule for the (8-hr, 5x)case........ 50 Figure 3.13 Optimal temperature setpoint schedules and corresponding electricity use for the 3-hour TOU cases. IAT: indoor air temperature; TSP: temperature setpoint; DBT: dry-bulb temperature. ...... 51 Figure 3.14 Objective function across the global time set for eachTOUcase . 53 Figure 3.15 Electricity cost reduction as a percentage of the total baseline cost for eachTOUcase................................. 53 Figure 3.16 Sum of average hourly pre-cooling temperature foreachTOUcase . 54 Figure 3.17 Sum of the average hourly positive deviation from the desired setpoint temperatureforeachTOUcase . 54 Figure 3.18 Total cooling electricity use for each TOU case . .............55 viii Figure 3.19 Sum of cooling electricity shifted from the peak demand times comparedtoabaselinesetbackschedule. 55 Figure 3.20 Electricity use for a (5-hr, 5x) MPC simulation and baseline, and shiftedpeakdemand. ............................. 56 ix LIST OF TABLES Table 2.1 New and existing detached home details. .........20 Table 2.2 Optimized weighting factors for associated parameters.. 20 Table 2.3 Cooling electricity prediction error metrics for the grey-box and black-box models, compared to EnergyPlus for a new detached home. ..... 28 Table 2.4 Cooling electricity prediction error metrics for the grey-box and black-box models, compared to EnergyPlus for an existing detached home. ...... 28 x LIST OF ABBREVIATIONS AirConditioning ..................................... AC A Modeling Language for Mathematical Programming . ....... AMPL ArtificialNeuralNetwork ................................ ANN ApplicationProgramInterface. API AutoRegressivewithExogenousInputs . ARX Auto Regressive with Moving Average Exogenous Inputs . ARMAX American Society of Heating, Refrigerating, and Air-Conditioning Engineers . ASHRAE BuildingControlVirtualTestBed . BCVTB BuildingEnergyOptimization. .BEopt BoxJenkins.......................................... BJ CoefficientofPerformance . ..