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Modeling Building Thermal Response to HVAC Zoning
Virginia SmithDepartment of Computer
ScienceUniversity of Virginia85 Engineer’s WayP.O. Box 400740
Charlottesville, Virginia [email protected]
Tamim SookoorDepartment of Computer
ScienceUniversity of Virginia85 Engineer’s WayP.O. Box 400740
Charlottesville, Virginia [email protected]
Kamin WhitehouseDepartment of Computer
ScienceUniversity of Virginia85 Engineer’s WayP.O. Box 400740
Charlottesville, Virginia [email protected]
ABSTRACTHVAC systems account for 38% of building energy usage.Studies have indicated at least 5-15% waste due to unoccu-pied spaces being conditioned. Our goal is to minimize thiswaste by retrofitting HVAC systems to enable room-levelzoning where each room is conditioned individually basedon its occupancy. This will allow only occupied rooms to beconditioned while saving the energy used to condition un-occupied rooms. In order to achieve this goal, the effect ofopening or closing air vent registers on room temperatureshas to be predicted. Making such a prediction is compli-cated by the fact that weather has a larger effect on roomtemperatures than the settings of air vent registers, mak-ing it hard to isolate the influence of the HVAC system.We present a technique for dynamically estimating the heatload due to weather on room temperatures and subtractingit out in order to predict the effect of the HVAC systemmore directly.
Categories and Subject DescriptorsH.1 [Models and Principles]: Miscellaneous; I.6.5 [Simulationand Modeling]: Model Development—modeling method-ologies
General TermsDesign, Experimentation, Measurement
KeywordsBuilding energy, energy, environment, sensing
1. INTRODUCTIONBuildings account for 75% [4] of the electricity and 43% ofthe greenhouse gas emissions in the United States [9] andthe Heating, Ventilation, and Cooling (HVAC) system isthe single largest energy consumer in residential buildings,accounting for 43% of the residential energy consumption inthe US [5], and over 60% in Canada [6] and the UK [12],
which have colder climates. This accounts for 38% of allthe building energy used in the United States and over 15%of the total energy used in the U.S., making HVAC sys-tems one of the nation’s largest energy consumers. Stud-ies have indicated that at least 5-15% of this waste is dueto the course-grained, manual configuration of thermostatsby users, whereby spaces are heated or cooled even if notneeded by the occupants. Much of this wasted energy isused to heat or cool unoccupied spaces during long periodswhen people use only a small fraction of a house, such aswhen they work in an office or sleep in a bedroom. Our vi-sion is to minimize this energy wastage through room-levelzoning, where each room is conditioned individually basedon its occupancy. This would allow most, if not all, of theenergy used by the HVAC system to be focused on maintain-ing occupied rooms at a comfortable temperature withoutwasting any energy conditioning unoccupied rooms.
Many homes in the United States have centralized HVACsystems that have a single compressor or furnace. Such sys-tems have to be configured for zoning during installation ifhomeowners want to minimize energy wastage. Most, if notall, zoned HVAC systems are implemented in multi-storyhouses where each floor is configured to be a separate zone.Due to the room usage generally being separated by floor,so that the bedrooms are on the upper floor and the livingspaces on the lower floor, a coarse-grained zoning schedulecan be manually configured for such a system allowing en-ergy savings. For example, the system can be configured tocondition the upper floor only during the night, when thebedrooms are in use, and the lower floor only during the day,when the living spaces are most likely to be used. Such ascheme cannot be used in a single-story house because thenight and day living spaces are adjacent to each other. Also,the fact that rooms on a single floor are not as thermally iso-lated as rooms on separate floors reduces the energy savingsthat can be achieved through coarse-grained zoning withina floor.
Our goal is to implement a system that can retrofit the cen-tralized HVAC systems that are in most homes in the UnitedStates so that air vents can be controlled individually androom-level zoning can be achieved. Such a system wouldrequire an automated controller that decides which roomshave to be conditioned and dynamically alters the zonesbased on occupancy and room temperature by opening andclosing air-vent registers in rooms. In order for such a con-
troller to be efficiently implemented, the affect of openingor closing registers on the temperatures in the room have tobe predictable. Thus, in this paper we present and evalu-ate techniques to learn and predict the effect of opening orclosing each vent register, in a set of R air vent registers, onthe temperature at each sensor, in a set of T temperaturesensors placed within a house.
The main challenge to modeling the thermal characteristicsof a house is the effect of weather on the indoor temperature.For instance, wind, solar gain, and outdoor temperaturehave a greater influence on indoor temperature than any in-dividual air vent register. It is difficult to build a model thatcompletely captures the effect of weather on indoor tempera-tures because outdoor weather conditions constantly changeand rarely repeat. The difficulty of attributing the influenceon weather conditions on indoor temperature makes it dif-ficult to isolate the effect of the state of any particular airvent register on the indoor temperature.
Our approach to overcoming this problem is to model theindoor temperature in two stages. In the first stage, we mea-sure the rate of heat gain or loss due exclusively to outdoorweather conditions. This stage is modeled with data col-lected when the HVAC system is off using a linear functionof current temperature. Then, when the HVAC system isturned on, we measure the change in the rate of heat gainedor lost in a room due to the conditioned air provided bythe HVAC system. We expect this change to be constantthroughout the year because the HVAC system always out-puts the same amount of conditioned air. Thus, we isolatethe HVAC effects by learning and subtracting out a dynamicestimate of weather effects over long periods of time.
In this paper, we present three iterations of a thermal modeland analyze its accuracy in terms of predicting the effect ofopening and closing various combinations of registers with acentralized HVAC system. An analysis of the HVAC systemitself is beyond the scope of this paper. Performing ten-foldcross validation over three weeks of data sampled over threemonths, we demonstrate that even with the simplest modelwe can predict temperatures to within two degrees 30 min-utes into the future. We focus on a 30 minute time windowbecause longer time windows are not beneficial when makingHVAC control decision. We also demonstrate that even thesimplest of the three models we present in this paper is ableto provide this level of accuracy allowing temperature pre-diction to be incorporated into an HVAC zoning controllereasily and without much computation overhead.
2. BACKGROUNDHeating, Ventilation, and Air Conditioning (HVAC) controlsystems are devised in order to maintain comfort within anenclosed space. In addition to meeting a desired tempera-ture, this comfort is maintained by achieving a certain levelof humidity, pressure, radiant energy, air motion, and airquality within a building [2]. The testbed in this studyutilizes a centralized heat pump air conditioner. This isthe most common method of residential air conditioning inthe United States. Centralized HVAC systems do not per-mit fine-grained room-level control of the HVAC equipmentbeyond opening and closing air-vent registers that feed airinto rooms. Thus, knowing the affect of opening or closing
dampers is critical to the efficient retrofitting of a centralizedHVAC system to enable room-level zoning.
2.1 Centralized HVAC SystemThe framework for the HVAC system is the air handlingunit. The main responsibility of the air handling systemis to deliver conditioned air throughout the building, whileremoving exhaust air and carbon dioxide (CO2) from therooms. Most of the equipment is hidden from occupants,being located outside and in ducts within the building [2].
The air handling system may include fans, compressors,heating/cooling coils, and ducts, in addition to system con-trollers. The air handling process works in the following way:First, outdoor air is mixed with the return air of the system.The pressure of this air is determined by the supply air fan.The air is then heated/cooled to a preset temperature, andis released into specific spaces through the dampers. Theexhaust air from the room is sent into the ducts accordingto the exhaust fan speed, and it is returned to begin theprocess again.
The damper is a mechanical device that allows for a variableamount of supply air to be released into a room. It consistsof a thin metal sheet, rotated on an axis by an actuator. Ifthe damper is set at 90 degrees, or 0% open, the damperis fully shut and no air is supplied to the room. When thedamper is set to 0 degrees, or 100% open, the maximumamount of air is released [2].
2.2 System LogicA centralized HVAC system can run in four possible stateswhen heating/cooling: Float; Hold; Heat/Cool 1; and, Heat/Cool2. Float causes the HVAC system to turn off, and hold tellsthe system to remain at the same temperature. Heat/Cool1 corresponds to running the system at 67%, which pro-vides a lower level of heating/cooling that can supply a baselevel of conditioned air throughout the day. Heat/Cool 2turns on when temperature needs to be changed by a sig-nificant amount, and the system runs at 100%. The systemin our testbed runs stage 2 conditioning if the current tem-perature is more than two degrees above/below the currentsetpoint [13].
2.3 ZoningMost of the energy wasted by HVAC systems go towardsheating or cooling unoccupied spaces during long periodswhen people use only a small fraction of a house. For in-stance, at night the bedrooms are used while the rest ofthe house is unoccupied and during the day the living roomand kitchen maybe used with the bedrooms being unused forlong periods of time. Zoning systems attempt to exploit thisfact, and save energy for homeowners, by dividing a buildinginto two or more zones that are controlled by separate ther-mostats, so that the occupants can schedule each zone to beheated or cooled separately. However, zoning systems areexpensive, and are, therefore, typically only used for verycourse-grained zoning of the house: a typical configurationcan condition the first floor living spaces separately from thesecond floor sleeping quarters for example. Such systems areboth spatially and temporally course grained allowing largeareas, in this case floors of a building, to be zoned separately
and scheduled with a low frequency, for example switchingbetween the living and sleeping areas only twice a day.
3. PROBLEM DEFINITIONOur problem is defined by a set of air vent dampers D anda set of temperature sensors T that are dispersed across ahouse (Figure 2). The dampers can be opened or closed,determining if conditioned air is delivered directly into aroom. Due to the lack of thermal isolation between rooms,even if the air vent dampers of a room are closed, its tem-perature could still be affected by the HVAC system due toleakage from neighboring rooms. The temperature sensorsmonitor the temperatures at different points throughout thehouse. Figure 1 shows the readings at the twelve tempera-ture sensors in our deployment during a day with all air ventdampers open. As the figure shows, the HVAC system beingoff (blue) causes drops in temperature while the HVAC sys-tem being on (red) usually causes temperature increases. Weare attempting to learn and predict these effects on the tem-perature sensors when different sets of air vent dampers areopened and closed. In other words, we want to answer thequestion “What effect does each register being open have onthe reading of each temperature sensor?” Being able to makesuch a prediction allows us to implement a fine-grained au-tomated zoning controller that can dynamically alter zoneswithin a single floor to maintain occupied rooms at a com-fortable temperature while allowing unoccupied rooms todrift. Yet, answering this question is difficult due to the ef-fect of the weather on the internal temperature of houses.Wind, solar gain, outdoor temperature, and other weatherconditions have a much greater influence on indoor tempera-ture than the conditioned air provided by an HVAC system.These weather conditions constantly change, and rarely re-peat, therefore including it as part of a model is impossiblewithout greatly increasing the complexity of the model. But,ignoring the effect of weather on internal temperature makesit impossible to isolate the effect of a particular register ona temperature sensor. Thus, a secondary question we areattempting to answer is “Can we learn the effect of damperson temperature sensors without knowing the weather duringthe training phase?” In other words, we are attempting tocapture the effect of the weather on the temperature sensorreadings while ignoring the actual weather conditions, suchas the external temperature or the position of the sun.
There have been a number of approaches proposed for learn-ing the thermal response of buildings in order to controlHVAC systems efficiently [7, 3, 11, 8, 10, 1]. Yet, theseapproaches require a large amount of data or sophisticatedsensors that will hinder our goal of developing a cheap andeasy to install retrofit to enable room-level zoning of existingcentralized HVAC systems.
4. EXPERIMENTAL SETUPThe room-level zoning system described has been deployedin a single-story, 8-room, 1,200-square-foot residential build-ing. A model of the home is shown in Figure 2. The hallwayand porch are depicted, but not included within our anal-ysis because of the inability to actuate temperature withinthese regions. The HVAC system setup is overlaid in or-der to show the position of vents, ducts, and the central airhandler.
Figure 2: The residential testbed used for this study.Red and blue overlays show an example of two room-level zones, the green ducts terminate in air ventregisters that can be opened or closed, and the redcircles show the locations of the twelve temperaturesensors with the sensor IDs indicated.
Figure 2 shows the deployment from which data for thispaper was collected. We used twelve temperature sensordeployed across the house and air vent registers that areremotely actuatable and collected data over a three monthperiod. Three weeks of the collected data was used for theanalysis presented in this paper.
4.1 Temperature DetectionSensors deployed throughout the building allow us to moni-tor the temperature and HVAC status within each room/zone.We collect temperature data at a fine granularity using tem-perature sensors placed at various points along the walls. Inorder to ensure the scalability of this system, we use 12 stan-dard, off-the-shelf temperature sensors manufactured by LaCrosse Technology [13].
One challenge with sensing temperature in this way is thattemperatures are not uniform throughout the rooms/zonesand along the walls. This can present problems when tryingto determine the true temperature of each room. As shownin Figure 3, the placement of wall sensors has a large im-pact on the variability of the temperatures detected. Whilethe sensors on the internal wall vary within the temperaturerange dictated by the return duct, the sensors on the ex-ternal wall are subject to large temperature swings. This isbecause the external wall sensors pick up temperatures fromoutside of the building through windows, doors, and the wallitself. This is also compounded by the fact that most ventsare placed on external walls, making these sensors subjectto direct air from the duct [13].
Thus, we use two methods to ensure accuracy within our
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Figure 1: The effect on temperature sensors, within a 24-hour period, of the HVAC system being on (red)and off (blue) when heating with all air vent dampers open. The locations of the twelve sensors are presentedin Figure 2
temperature data collection. The first is to only place sen-sors along the interior walls of the rooms. The second is torecord the temperature as an average of these sensors, help-ing to detect the temperature more uniformly throughoutthe room.
4.2 HVAC Status DetectionThe HVAC system used in this study can run in four possiblestates when heating/cooling: Float; Hold; Heat/Cool 1; and,Heat/Cool 2. Data on these system states are collected byinterfacing with a standard internet-controlled thermostatmanufactured by BAYweb. These stages are described indetail in the following section.
5. MODEL OF TEMPERATURE DYNAM-ICS
The parameters of the model include the position of thedamper, temperature, system status, and time. These val-ues are recorded through a wireless sensor network deployedin the testbed and stored in a database. The temperaturevalues are measured in degrees Fahrenheit, and the damperpositions take one of two values: 0 (closed) or 1 (open 100%).The system status allows us to see whether the system is inoff, heat/cool 1, or heat/cool 2 mode. An example of thedamper, temperature, and system status for one room isshown in Figure 3.
In analyzing this system, we explore a number of differentmodels. Three iterations of our final model are shown in the
following sections. Each is a dynamic, linear model that isdeveloped in two stages. The first stage aims to estimatethe effects of heating/cooling due to external factors suchas solar radiation, wind, and cloud coverage. This effect iscalculated when the system is turned off, and the values arethen used to develop the model when the system turns backon. This two-stage approach allows us to compensate forexternal factors without having to measure them directly.Furthermore, the results allow us to predict temperaturedynamics due to the HVAC configuration with greater ac-curacy.
dTk/dt = αT + βD (1)
The models we discuss follow the same format (Equation 1)in which the temperature of a specific room Tk over timet is a result of external factors (calculated through α), andthe current damper configuration, D. The three iterationsof this model differ in the way that the external factor coef-ficient, α, is calculated. These differences are as follows: 1)The first iteration calculates a universal α value by poolingthe data when the system is off. 2) The second iterationcalculates a constantly changing α value when the system isoff, and uses this constantly calculated α value in the modelwhen the system turns on. 3) The third iteration adds tothe model complexity by using universal α values for allneighbors T1, ..., Tn of the temperature in room k, Tk.
5.1 Static AlphaThe first iteration of the model we describe is one in whichthe α values, which estimate the temperature change due
Figure 3: The system status (on/off), temperature (◦F), and damper position (open/closed) for one room inour testbed over the period 11/30/2011-12/04/2011.
to weather patterns, are constant throughout the day. Inorder to calculate these values, we pool the data from timeswhen the system is off together and fit one α value across alltimesteps for each of the n rooms. This value is calculatedthrough linear regression, and assumes that the heat loaddue to weather remains relatively constant throughout theday.
5.2 Dynamic AlphaIn the second iteration, we explore the idea that the heatload due to weather conditions may be changing continu-ously throughout the day. In order to do this, we calculatea dynamically changing α value for each off segment, andinclude that value in the on segment that directly followsit. This method aims to compensate for weather by assum-ing that the heat load due to weather changes significantlythroughout the day, but by very little between one cycle ofthe system.
5.3 Adjacency ModelThe third iteration increases the complexity of the first byincluding the other n rooms into the model. This assumesthat the current temperature of the room is affected notonly by its own weather conditions, but also by the tem-perature dynamics within the other rooms of the building.This model also calculates the α values universally throughlinear regression. The form of this room adjacency model isas follows:
dTk/dt = α1T1 + α2T2 + · · · + αnTn + βD (2)
6. RESULTSWe compare the three iterations of our model described insection 5 using 21 days worth of data tested with 10-foldcross validation which involves randomly dividing the 21days of data into ten equal sets, training the model usingnine of those sets, and testing with the remaining set. Allcombinations of nine sets for training and one set for testingare used. The 21 days we have selected for model develop-ment and testing have been sampled from 3 months worthof data between October and December 2011. Using thetraining data, we develop the β values for the model. Wethen use these values with the α value scheme dictated bythe model iteration in order to predict temperatures whenthe system turns on.
6.1 PredictionOur predictions assume that temperature grows linearly whenthe system turns on as a result of the current damper config-uration and the previous weather patterns estimated through
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Figure 4: An example of a prediction made for tem-perature up to 30 minutes into the future after thesystem turns on. The solid blue line shows the actualtemperature when the system is off; the dashed blueline shows the actual temperature when the systemis on; and the dashed red line shows temperaturepredicted after the system has just turned on.
α. Though temperature dynamics within a building are of-ten nonlinear, we find a reasonable estimate by predictingtemperature linearly into the future. This is because thetemperature and airflow of the system operate within a nar-row regime, making it reasonable to approximate changewith a linear model. An example of a prediction 30 minutesinto the future is shown in Figure 4. Here, the blue linesrepresent the actual temperatures and the red line plots ourprediction. The solid blue line shows the temperature whenthe system is off, and the red/blue dashed lines show the pre-dicted/actual temperatures when the system has just turnedon.
6.2 Error MetricOne difficulty in determining the effectiveness of these mod-els is that we aim to use them to predict temperatures atmore than one timestep into the future. This involves cal-culating predictions at each point that the system is on, upto t minutes into the future until the system turns off again.
The error metric that we have chosen for this comparisonis to determine the distribution of prediction error as wepredict t minutes into the future. For each minute, t, wecalculate the mean and standard deviation of the predictionerrors t minutes away from the initial time. The results fromthese analyses for the static α, dynamic α, and adjacencymodel are shown in Figure 5, Figure 6, and Figure 7 respec-tively. These results are calculated on a per-sensor basis for
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Figure 5: Error distribtuions for the static α model, up to 30 minutes into the future. The locations of thetwelve sensors are presented in Figure 2
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Figure 6: Error distributions for the dynamic α model, up to 30 minutes into the future. The locations ofthe twelve sensors are presented in Figure 2
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Figure 7: Error distributions for the adjacency model, up to 30 minutes into the future. The locations of thetwelve sensors are presented in Figure 2
each of the 12 sensors in the 7 rooms of the building.
Visually examining the error distributions highlights a fewimportant things about the model. One is that the varianceof the errors tends to increase as we predict further into thefuture. The error can get quite large in some places, partic-ularly in the dynamic α model. However, most of the valuesfor each model remain within 2 degrees for the 30 minuteprediction. This is a reasonable interval with which to en-able the control of the system that we aim to accomplish.
The results from this analysis also indicate that the simple,pooled α model performs better than the dynamic model.This may be counterintuitive since weather tends to changesignificantly throughout the day. However, because of thewindow we are looking at and the narrow range of tempera-ture change, it is reasonable that this model should performwell. It also has the added benefit of being computable andeasy to implement within a control setting.
7. WORK-IN-PROGRESSAn observation we made with the model presented in thispaper is that its linear nature fails to capture the mixingperiod experienced when the HVAC system first turns on.As Figure 4 shows, the temperature measured at a sensorcontinues to drop for about twenty minutes after the HVACsystem is turned on before it begins warming up. This couldbe caused by the time taken for the conditioned air to suffi-ciently mix with the cold air in the room before the increasein temperature is detectable by a sensor and the absorptionof heat by the structure of the room, such as walls and floors,as well as objects in the room such as furniture before theair get heated because these objects have a higher heat ca-pacity than air. In order to capture this mixing period, wemodify the thermal model by introducing a variable γ thatvaries with time and influences the effect the conditioned airfrom the HVAC has on the temperature sensor.
We estimate values of γ by creating a set of equations, suchas the following, at various times from the time the HVACturns on until 30 minutes into the future:
T1 − T0 = α+ γ1βD (3)
T2 − T0 = α+ γ2βD (4)
T3 − T0 = α+ γ3βD (5)
Solving these equations for historical temperature data andHVAC state provides a set of γ values. Using these γ valuesa new iteration of the model can be specified as follows:
dTk/dt = αT + γkβD (6)
We are currently in the process of training and evaluatingthis model.
8. CONCLUSIONSWe have presented our residential testbed, studied the char-acteristics of the dual stage HVAC, identified and analyzedmathematical models of the system, and discussed the im-pact of our results. The two-stage, dynamic model that wehave developed provides an accurate way to predict the tem-perature in a zone based on a few, accessible parameters inthe system. It also allows the calculation of highly variableterms, such as the heat load due to solar radiation, wind,
and cloud coverage, without the need to explicitly measurethese terms.
These results will be used in future work in order to developa new, energy efficienct control scheme for the system. Themodel gives us better insight into the dynamics of the controlscheme and allows for a more efficient design. This controlscheme may then be used to create a more energy efficientdesign for similar HVAC units. This type of work is a crucialstep in the developing the type of energy-agile systems thatcan ultimately be used to quell our dependency on fossilfuels.
9. ACKNOWLEDGMENTSThis work is based on work supported by the National Sci-ence Foundation under Grant No. 1038271.
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