empirical characterization, modeling, and analysis of ... · tv’s electricity usage each second....

1

Empirical Characterization, Modeling, andAnalysis of Smart Meter Data

Sean Barker, Student Member, IEEE, Sandeep Kalra, Student Member, IEEE,David Irwin, Member, IEEE, and Prashant Shenoy, Fellow, IEEE

University of Massachusetts Amherst

Abstract—Smart meter deployments are spurring renewedinterest in analysis techniques for electricity usage data. However,an important prerequisite for data analysis is characterizing andmodeling how electrical loads use power. While prior work hasmade significant progress in deriving insights from electricitydata, one issue that limits accuracy is the use of general andoften simplistic load models. Prior models often associate afixed power level with an “on” state and either no power, orsome minimal amount, with an “off” state. This paper’s goalis to develop a new methodology for modeling electric loadsthat is both simple and accurate. Our approach is empirical innature: we monitor a wide variety of common loads to distill asmall number of common usage characteristics, which we thenleverage to construct accurate load-specific models. We showthat our models are significantly more accurate than binaryon-off models, decreasing the root mean square error by asmuch as 8X for representative loads. Finally, we demonstratethree novel applications that use our empirical load models toanalyze and derive insights from smart meter data, including i)generating device-accurate synthetic traces of building electricityusage, ii) filtering out loads that generate rapid and randompower variations in smart meter data, and iii) detecting thepresence of specific load models in time-series power data.

I. INTRODUCTION

Computing for sustainability—where real-world physicalinfrastructure leverages sensing, networking, and computationto mitigate the negative environmental and economic effectsof society’s energy use—has emerged as an important newresearch area.1 As a result, in addition to improving the energyefficiency of information technology (IT) infrastructure, suchas smartphones, servers, network devices, and data centers,computing researchers are now expanding their focus toinclude building energy efficiency. Since buildings accountfor nearly 40% of society’s energy use [1], compared toan estimated 1-2% for IT infrastructure [2], this researchhas the potential to make a significant impact. In particular,efficiently managing electricity is critical because buildingsconsume the vast majority (73%) of their energy in the formof electricity [1]. Existing management techniques typicallyemploy sense-analyze-respond control loops: various sensorsmonitor the building’s environment (including electricity) viaa smart meter, and transmit collected data in real-time toservers, which analyze it to reveal detailed building usageand occupancy patterns, and finally respond by automatically

1Research supported by NSF grants CNS-1253063, CNS-1143655, CNS-0916577, CNS-0855128, CNS-0834243, CNS-0845349.

controlling electrical loads2 to optimize energy consumption.Research challenges exist at each stage of this control loop.

For example, despite much prior research [3], [4], [5], [6]accurate, fine-grained, e.g., ≥1Hz, in situ sensing of electricityuse in real time at large scales remains impractical, as itis prohibitively expensive, invasive, and unreliable. Unfortu-nately, timely and detailed knowledge of per-load electricityuse is a prerequisite for implementing many sophisticatedautomated load control policies that increase energy efficiency.Since, even modest-sized, residential homes operate hundredsof individual loads, providing per-load data using existingsensors would require a large-scale sensing system [7]. Onepromising approach to address this problem is to use fewersensors that generate less data, and compensate by employingmore intelligence in the analysis phase to infer rich infor-mation from the data. For example, prior research indicatesthat analyzing changes in a building’s aggregate electricityusage at small time granularities, e.g., every 15 minutes orless, reveals a wealth of information: Non-Intrusive LoadMonitoring (NILM) techniques use the data to infer electricityusage for individual loads [8], while recent systems use it toinfer building occupancy patterns [9], [10]. These inferencesthen inform control policies: NILM might enable buildings toidentify opportunities for reducing peak demand by schedulingelastic background loads [11], such as air conditioners andheaters, while occupancy patterns are critical in determiningwhen to turn loads off without disturbing people’s lives [12].

Since electric utilities are rapidly deploying digital smartmeters capable of measuring and transmitting a building’saggregate electricity usage in real time, a substantial amount offine-grained electricity data for buildings is already available.For example, Pacific Gas and Electric now operates overnine million smart meters in California [13]. While today’sdeployed smart meters typically measure average power usageat intervals ranging from fifteen minutes to an hour, thegranularity of data is trending downwards (e.g., some utilitiesalready provide 5-minute data [14]), and commodity metersare available that measure and transmit, via the Internet, energyusage at intervals as small as every second [15], [16]. Com-bined with the emergence of “big data” cloud storage systems,these smart meter deployments are spurring renewed interest inanalysis techniques for smart meter data. While prior researchhas made significant progress in deriving insights from smart

2We use the term electrical load, or simply load, to refer to any distinct,self-contained appliance or device that consumes electricity.

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available at http://dx.doi.org/10.1109/JSAC.2014.2332107

Copyright (c) 2014 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].

2

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70 80

Pow

er

(W)

Time (min)

LCD TV

Fig. 1. An LCD TV’s power usage varies rapidly, significantly, and unpre-dictably while on, and does not conform to a simple on-off load model.

meter data [17], one issue that often limits accuracy is the useof general, and often simplistic, load models. In particular,many prior techniques for analyzing and modeling buildingelectricity data characterize loads using simple on-off models,which associate a small number of fixed power levels with the“on” state (often just one) and either no power usage, or someminimal amount, with the “off” state.

On-off models do have a number of advantages. For in-stance, they exactly capture many simple loads, including lightbulbs and other low-power resistive devices with mechanicalswitches. In addition, on-off models allow researchers to de-scribe buildings as state machines that associate each buildingstate with a fixed power level (implying the set of loads thatare on), and where state transitions occur whenever a loadturns on or off. Characterizing buildings as state machinesadmits a plethora of analysis techniques. For instance, muchprior work maps building state machines to Hidden MarkovModels (HMMs), and applies HMM-based techniques, such asViterbi’s algorithm [18], [19], to determine which loads are onin each state. In this case, using only a few (often two) powerstates per load is advantageous, since it minimizes the numberof distinct power states for the entire building and reducesthe complexity of analyzing the resulting state machine. Ofcourse, even with only two power states per load, the numberof building power states is still exponential in the number ofloads, i.e., 2n for n loads. Thus, even assuming simplistic on-off load models, precise analysis may still be intractable, i.e.,require enumerating an exponential number of states.

Unfortunately, while on-off load models are simple, theyare often inaccurate, since they fail to capture the complexpower usage patterns common to many loads. As a simplemotivating example, Figure 1 shows a time-series of an LCDTV’s electricity usage each second. In this case, the TV’sswitched mode power supply (SMPS) causes power variationsas large as 120 watts (W) by rapidly switching between a full-on and full-off state to minimize wasted energy. The magnitudeof these variations is effectively random—determined by thecolor and intensity of the TV’s pixels. An on-off model clearlydoes not accurately capture the TV’s power usage. As a result,modeling the TV as an on-off load may complicate higher-level analysis techniques for smart meter data. For example,the TV may obscure the use of low-power loads, such as a60W light bulb, since its power usage varies rapidly by >60W.

Our premise is that simple on-off models discard a sig-nificant amount of information that is potentially useful in

analyzing data. As a result, in this paper, we focus explicitly onaccurately characterizing and modeling a variety of commonhousehold loads. Our methodology is empirical: we i) gatherfine-grained electricity usage data from dozens of loads acrossmultiple homes, ii) characterize their behavior by distilling asmall number of common usage attributes, and then iii) deriveaccurate load-specific models based on these attributes. Oneof our contributions is to show that a small number of modeltypes, stemming from basic knowledge of power systems,accurately describe nearly all household loads. Thus, one ofour goals is to highlight how many identifiable load attributes,which are well-known in power systems, manifest themselvesin electricity data collected by smart meters. Our hypothesis isthat accurate load models, which leverage domain knowledgefrom power systems, provide a foundation for designing newelectricity data analysis techniques. In evaluating our hypoth-esis, this paper makes the following contributions.Empirical Data Collection and Characterization. We in-strument a wide variety of common electrical loads in multiplehomes, and collect electricity usage data for each load, everysecond, for over two years. We show empirically that homesoperate similar types of loads, e.g., lighting, AC motors,heating elements, electronic devices, etc., which results in sig-nificant commonality in power usage profiles across loads. Wethen characterize the data to identify distinguishing attributesin per-load power usage, forming the building blocks of ourmodels. While many of these attributes are well-known inpower systems, we show how they manifest in sensor data.Data Modeling Methodology. We use our empirical charac-terization to construct a small number of load-specific modeltypes. We show that our basic models, or a composition ofthem, capture nearly all household loads. Our models go be-yond on-off models, by capturing power usage characteristicsthat i) decay or grow over time, ii) have frequent variations(as with the TV in Figure 1), iii) exhibit complex repetitivepatterns of simpler internal loads, and iv) are composites oftwo or more simpler loads. We show that our models aresignificantly more accurate than on-off models, decreasing theroot mean square error by as much as 8X for representativeloads. Since our methodology is general, it applicable tomodeling other types of loads beyond those in this paper.Model-based Data Analysis. Finally, while we expect ourmodels to have numerous uses, we illustrate three specificexamples of novel applications using these models. First, weconsider generating device-accurate synthetic traces of build-ing electricity usage for use by NILM researchers. One barrierto evaluating NILM techniques is ground-truth data collection,which requires deploying sensors to every building load. Usingour models, NILM researchers can quickly generate differenttypes of synthetic building traces by composing collectionsof load models, and the resulting synthetic trace is morerepresentative of real-world data (e.g., in terms of number andsizes of power steps) than when using trivial models. Second,we design simple filters capable of identifying and removingloads that exhibit rapid power variations (such as an LCDTV). Since these loads introduce numerous spurious buildingpower states, removing them improves the accuracy of analysistechniques that describe buildings as state machines (e.g., by



3

25% in our experiments). Finally, we use our models as queriesto a variable-length subsequence matching algorithm to detectthe presence of specific loads in smart meter data.

II. EMPIRICAL DATA COLLECTION ANDCHARACTERIZATION

A typical home consists of dozens of electrical loads,including heating and cooling equipment, lights, various ap-pliances and electronic equipment. A partial list includes:• Heating, cooling, and climate control equipment such as

a central air conditioner, window air conditioner, spaceheater, electric water heater, dehumidifier, fan, air purifier;

• Kitchen appliances such as an electric range, microwave,refrigerator, coffee maker, toaster, blender, dishwasher;

• Laundry appliances such as a washer and dryer;• Lighting including incandescent and fluorescent lights;• Miscellaneous electronic devices such as a television,

battery charger, computer, and gaming console; and• Other appliances such as a vacuum and carpet cleaner.Below, we briefly describe the data collection infrastructure

we use to gather data from these common household loads.We then derive several insights from our data, which we useto design different types of load models in the next section.

A. Data Collection Infrastructure

Since our methodology is empirical, we instrument threehomes with a large number of energy monitoring sensors togather ground truth electricity usage data from a wide varietyof loads. Each instrumented home consists of a smart homegateway in the form of an embedded Linux server that querieseach sensor to collect data. We have deployed several differenttypes of energy monitoring sensors, as described below.

We use current transducer (CT) sensors to monitor elec-tricity usage for large loads wired to dedicated circuits, suchas air conditioners, washing machines, dryers, dishwashers,and refrigerators. These sensors connect to power metersinstalled in the homes’ electrical panel, such as The EnergyDetective (TED) [16] or eGauge [15], which sample per-circuit electricity usage each second. The sensors transmit datafrom inside the electrical panel using powerline networkingprotocols, such as X10, Insteon, and HomePlug Ethernet-over-Powerline. We use the eGauge in our testbeds due toits support for HomePlug, which provides multiple orders ofmagnitude higher bandwidth (> 100 Mbit/s) than X10 andsupports reliable transport protocols, including TCP. We useplug-level energy sensors to track energy use for smaller loadsplugged into wall outlets. Our plug-level sensors are commod-ity Insteon iMeters [20] and Z-Wave Smart Energy Switchmeters [21], which use powerline and wireless communication,respectively, to transmit readings to our smart home gateway.

The iMeter plug meters do not support the higher band-width HomePlug powerline protocol, which severely limits thefrequency at which our gateway is able to poll outlet powerusage. To prevent saturating the powerline (at the Insteontransmit frequency), our initial prototype polled each iMeter-connected outlet’s power usage once every 10 seconds. Sinceour testbed homes employ more than 30 iMeters, a naı̈ve

round-robin polling strategy results in a power reading onceevery 300 seconds [22]. As a result, we designed a smartpolling strategy [22] that monitors the per-second eGaugecircuit data and only polls outlets on a selected circuit if theeGauge circuit registers a change in power. Thus, we nowonly poll the iMeters to see which outlet’s power changed.We also use Insteon-enabled wall switches to monitor switchedloads wired directly into the electrical system. These switchesreplace normal wall switches, and transmit on-off-dim eventsto the gateway whenever a user manually toggles the switch.

The Z-Wave meters enable more rapid polling of powerdata every second from each outlet, although we have experi-enced numerous issues in our testbed with wireless range andcoverage. For example, many sensors must be placed behindlarge metal appliances that severely attenuates wireless signals.Further, even though our testbed homes are not large (roughly1700ft2), ensuring that each sensor is within range of the gate-way is challenging, and requires careful gateway placement.Larger homes would likely require multiple wireless receiversor mesh networking protocols, both of which significantlyincrease the complexity and cost of the deployment.

While there have been numerous challenges in deployingour measurement testbeds, as described above, they have nowbeen continually monitoring hundreds of individual loads fornearly two years in each of our three instrumented homes.Since the level of instrumentation in our measurement testbedis time-consuming and expensive to replicate, we have mademuch of our collected data available to benefit other re-searchers [7]. More details about our testbed deploymentand multi-year data collection efforts are available in recentwork [7]. We leverage our data to characterize various loadsbased on a few elemental types, described below. In addition,the challenges in deploying and operating our measurementtestbed serve as important motivation for the modeling andanalysis techniques we describe in Sections III and IV. Thesetechniques enable users to analyze smart meter data to inferinformation about individual loads without requiring a powermeter attached to each load. One attractive scenario is forall manufacturers to release load models once at design time,thereby enabling anyone to employ the type of model-basedanalysis techniques we propose in Section IV.

B. Characterizing Different Types of LoadsDespite their tremendous variety, most residential loads fall

into one of a few elemental load types based on how theyconsume power in an alternating current (AC) system. Inparticular, loads are categorized as either resistive, inductive,capacitive, or non-linear based on how they draw current inrelation to voltage, which in an AC system varies along asmooth sinusoidal pattern. These categories reveal propertiesof the loads that we leverage in our models. Since manyresearchers outside of power systems may be unfamiliar withthese load types, for each type of load we first review itssalient characteristics. We then empirically characterize datafrom multiple representative loads of each type to observe howtheir specific characteristics manifest themselves in the data.Resistive Loads. Loads that consist of any type of heatingelement are resistive. Incandescent lights, toasters, ovens,



4

0

50

100

150

200

250

0 1 2 3 4

Pow

er

(W)

Time (min)

light

230

235

240

245

250

255

260

peak zoom

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4

Pow

er

(W)

Time (min)

toaster

1420

1430

1440

1450

1460

1470

peak zoom

0

200

400

600

800

1000

0 1 2 3 4 5 6 7 8 9 10

Po

we

r (W

)

Time (min)

coffee maker

880

900

920

940

960

980

1000

peak zoom

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5 6 7

Pow

er

(W)

Time (min)

sandwich press

1360

1365

1370

1375

1380

1385

1390

1395

1400

peak zoom

1480

1490

1500

1510

1520

1530

1540

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5

Pow

er

(W)

Time (min)

pod coffee maker

peak zoom

(a) Light bulb (b) Toaster (c) Coffee maker (d) Sandwich press (e) Pod Coffee

Fig. 2. Example resistive loads, demonstrating “step” behavior with a possible initial surge and slow decay to a stable power level.

95

100

105

110

115

120

125

0

100

200

300

400

500

600

700

800

0 20 40 60 80 100 120

Po

we

r (W

)

Time (min)

refrigerator 1

95

100

105

110

115

120

125

cycle zoom

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40 45

Pow

er

(W)

Time (min)

freezer

105

110

115

120

125

130

cycle zoom

1800

1900

2000

2100

2200

2300

0

500

1000

1500

2000

2500

0 10 20 30 40 50 60

Pow

er

(W)

Time (min)

Central A/C

growth zoom

0

200

400

600

800

1000

1200

1400

1600

0 10 20 30 40 50 60

Pow

er

(W)

Time (sec)

vacuum cleaner

1160

1170

1180

1190

1200

1210

1220

1230

decay zoom

89

90

91

92

93

94

95

20

40

60

80

100

0

Pow

er

(W)

Time (min)

window ac

growth zoom

(a) Refrigerator (b) Freezer (c) Central A/C (d) Vacuum cleaner (e) Window A/C

Fig. 3. Example inductive loads, demonstrating significant surge current followed by steady power growth or decay.

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5

Pow

er

(W)

Time (min)

LCD TV

110

120

130

140

150

160

zoom

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20

Pow

er

(W)

Time (min)

Mac Mini

5

10

15

20

25

peak zoom

0

200

400

600

800

1000

0 5 10 15 20

Po

we

r (W

)

Time (min)

HRV

0

200

400

600

800

1000

1200

1 min zoom

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5P

ow

er

(W)

Time (min)

microwave

1380

1400

1420

1440

1460

1480

1500fluctuation zoom

14

14.5

15

15.5

16

16.5

17

14

16

18

20

22

24

0 2 4 6 8 10 12 14 16 18 20

Pow

er

(W)

Time (min)

monitor

fluctuation zoom

(a) LCD TV (b) Desktop PC (c) Duct Heater (d) Microwave (e) Monitor

Fig. 4. Example non-linear loads, demonstrating rapid and significant random variations with possible ceilings and/or floors.

space heaters, coffee makers, etc., are examples of commonresistive loads in a home. Formally, if a load draws currentalong a sinusoidal pattern in the same phase as the voltage,i.e., the maximum, minimum, and zero points of the voltageand current sine waves align, then the load is purely resistive.

Figure 2 depicts a time-series of the power usage for fivedifferent resistive loads with heating elements: an incandescentlight bulb, a toaster oven, a coffee maker, a sandwich press,and a pod coffee maker, e.g., a Keurig or Tassimo. In general,the power usage of these loads resembles a “step” when turnedon, with usage that remains relatively stable and flat. Theincandescent light acts as a nearly perfect resistive load witha power usage equal to the bulb’s wattage. While the toasteroven, coffee maker, sandwich press, and pod coffee makeract similar to the light bulb, they experience an initial higherpower usage that slowly decays to a relatively stable usage,highlighted in Figure 2. The initial high power is due to thelarge inrush (or surge) current that occurs as the device warmsup and the resistance decreases, after which it stabilizes.Observation 1: Resistive loads exhibit stable power usagewhen turned on, with high-power heating elements exhibitingan initial surge followed by a slow decay to stable power.Inductive Loads. AC motors are the most common andwidely-used examples of inductive loads. Motors are theprimary component of many household devices, includingfans, vacuum cleaners, dishwashers, washing machines, andcompressors in refrigerators and air conditioners. Formally,if a load draws current along a sinusoidal pattern that peaks

after the voltage sine wave, i.e., the current waveform lags thevoltage waveform, then the load is purely inductive.

Figure 3 depicts a time-series of the power usage forfive inductive loads: a refrigerator, a freezer, a central airconditioner (A/C), a vacuum cleaner, and a window A/Cunit. All five loads operate AC motors. Unlike the resistiveloads above, each inductive load experiences a significant, butbrief, initial power usage. The surge is also due to inrushcurrent that occurs when starting an AC motor, although it istypically much higher than for heating elements. Intuitively,the underlying reason is that, while heating elements heatup slowly, the rotor inside a motor must transition fromcompletely idle to full speed within seconds. Power usagethen exhibits either a decay or growth, depending on themotor’s operation, that eventually stabilizes. In contrast toresistive loads, motors exhibit small variations even during this“stable” phase. For instance, the refrigerator shown in Figure3(a) exhibits small fluctuations that repeat during each cycleof the compressor. The freezer, central A/C, vacuum cleaner,and window A/C depicted in Figures 3(b), (c), (d), and (e) allshow an initial spike followed by a sharper, smoother growth(central and window A/C) or decay (freezer and vacuum),with small variations as the usage stabilizes. These patternsdemonstrate that, unlike resistive loads, modeling inductiveloads using simple on-off step functions is problematic.Observation 2: Inductive loads with AC motors exhibit aninitial power spike followed by a growth or decay to a stablepower level. The growth/decay rate is load-dependent, with



5

0

50

100

150

200

250

300

350

400

450

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35 40 45

Pow

er

(W)

Time (min)

washing machine

0

100

200

300

400

500

600

3 min zoom2 min zoom

0

1000

2000

3000

4000

5000

6000

0 20 40 60 80 100 120 140

Pow

er

(W)

Time (min)

dryer

1920

1930

1940

1950

1960

1970

5 minzoom

0

200

400

600

800

1000

1200

1400

1600

0 10 20 30 40 50 60

Pow

er

(W)

Time (min)

dishwasher 1

1450

1460

1470

1480

1490

1500

0 20 40 60 80

100 120 140 160 180 200 220

3 min zoom

5 minzoom

0

200

400

600

800

1000

1200

0 20 40 60 80 100 120

Pow

er

(W)

Time (min)

dishwasher 2

1000

1020

1040

1060

1080

1100

1120

1140

peak zoom

0

50

100

150

200

250

0 20 40 60 80 100 120 140 160 180 200 220

Pow

er

(W)

Time (min)

hrv

180

190

200

210

220

230

240

peak zoom

(a) Washing machine (b) Dryer (c) Dishwasher 1 (d) Dishwasher 2 (e) HRV

Fig. 5. Example composite loads, demonstrating combinations of the simpler loads above arranged in phases.

the stable power level also exhibiting fine-grained variations.Capacitive Loads. Capacitive loads are the dual of inductiveloads. Formally, if a load draws current along a sinusoidalpattern that peaks before the voltage sine wave, i.e., the currentwaveform leads the voltage waveform, then the load is purelycapacitive. While many loads have capacitive elements, theygenerally occur in addition to other resistive and inductiveelements which dominate their overall behavior. Thus, thereare no significant capacitive loads in buildings, particularlywhen considering real (as opposed to reactive) power.Non-linear Loads. Finally, any load that does not draw currentalong a sinusoidal pattern is called non-linear. Non-linearloads may also be resistive, inductive, or capacitive based onwhen their current waveform peaks. The most predominantnon-linear (and largely inductive) loads are electronic devices,including computers and TVs. The non-linear nature of theseloads is primarily due to the use of switched-mode powersupplies (SMPSs). Fluorescent lights are another example ofa non-linear (inductive) load. Smaller electronic devices thatconvert AC to low-voltage DC, such as battery chargers forportable devices and digital clocks, are also non-linear.

Figure 4 shows the power usage of five different non-linearloads: an LCD TV, a Mac Mini desktop computer, a microwaveoven, a duct heater for a heat recovery ventilator (HRV), anda computer monitor. These loads exhibit significant powerfluctuations when active, but also have a stable floor or ceilingfrom which these fluctuations derive. The LCD TV shown inFigure 4(a) exhibits a stable maximum usage with randompower reductions from this ceiling. These fluctuations resultfrom displaying a variety of color and pixel intensities on thescreen. Not surprisingly, the computer monitor in Figure 4(e)has a similar pattern of power usage. In contrast, the desktopcomputer shown in Figure 4(b) has a stable minimum powerdraw, with random power spikes above this floor depending onits workload, e.g., causing the CPU to ramp up, etc. Both theTV and desktop computer consist of a switched mode powersupply (SMPS) that regulate the power usage of the device andswitch between a full-on and full-off state to minimize wastedenergy. The duct heater shown in Figure 4(c) demonstratestwo regular modes of operation; an active heating mode—with instantaneous intensity managed by the HRV controller—and a passive mode. In both modes, there are large, randomvariations in power usage. In the active state, there is also aclear stable maximum usage. Finally, the microwave shown inFigure 4(d) has what initially appears to be a straightforwardstep, similar to the resistive loads. However, zooming in showsthe microwave’s non-linear behavior, with rapid, albeit small,variations in the second-to-second usage, along with larger

periodic power shifts. These examples show that on-off modelsare inappropriate for non-linear loads, since two power statescannot capture their wide range of power variations.Observation 3: Non-linear loads exhibit significant randomvariations in power usage. These fluctuations are often range-bound and capped by a floor or ceiling in the power level.

C. Composite Loads and Reactive Power

Composite Loads. Many household loads, particularly largeappliances, are not purely resistive, inductive or non-linear.Instead, these loads consist of multiple components, each ofwhich may be one of the simpler load types. For instance, acentral air conditioner may consist of a compressor, a fan toblow air into ducts, duct dampeners to control air flow, andcentral humidifiers to control humidity. A refrigerator, whichhas a compressor that is an inductive load, may also consistof door lights, an ice maker, and a water dispenser. Simi-larly, electric dryers, washing machines, and dishwashers alsoconsist of a motor—to spin clothes and circulate water via apump—and a heating element—to dry clothes or warm water.In addition, these appliances often operate in repetitive cyclesthat activate each of their constituent loads differently, such aswashing, draining, and then drying for a dishwasher. Figure 5depicts the power usage of a washing machine, a dryer, twodishwashers, and the HRV. As shown, these loads exhibitdistinct behavior in different parts of their cycle dependingon which appliance component is in use. For example, basedon the observations above, distinguishing when a complexload, such as the dryer, activates its heating element versus itsmotor is straightforward. Finally, an appliance may activateits various components in sequence, in parallel, or both. Forinstance, a central air conditioner may operate the compressor,the fan and the dampeners concurrently, while a dishwashermay operate its motor, pump and heater in sequence.Observation 4: Composite loads consist of simpler resistive,inductive and non-linear loads that operate in parallel, insequence, or both. As a result, composite loads exhibit distinctbehaviors in different operating regions of their active cycle.Reactive Power. Finally, another important characteristic ofthe elemental load types above is how they consume reactivepower. While real power is the amount of power delivered toa load, and is often referred to as simply electricity or power(without the qualifier), reactive power is the amount of powergenerated, but not delivered, to the load; it is also measured inunits of watts, but written as voltage-amperes reactive (VAR)to distinguish it from real power. Reactive power arises whena load draws current out of phase with the voltage. Thus,



6

0

50

100

150

200

250

0 5 10 15 20

Pow

er

(W / v

ar)

Time (min)

dimmable light (real)dimmable light (reactive)

0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30

Pow

er

(W / v

ar)

Time (min)

Fridge (real)Fridge (reactive)

0

100

200

300

400

500

600

1 min zoom

0

200

400

600

800

1000

0 5 10 15 20

Po

we

r (v

ar)

Time (min)

HRV (reactive)

0

200

400

600

800

1000

1200

0 10 20 30 40 50 60 70

Pow

er

(W)

Time (min)

Dishwasher (reactive)

50

100

150

200

250

peak zoom

(a) Dimmable light (0% to 100%) (b) Refrigerator (c) Duct Heater (d) Dishwasher 1

Fig. 6. Reactive power demonstrates the same types of patterns as real power and can help in identifying different types of electrical loads.

only non-resistive loads generate reactive power. At a highlevel, reactive power is the result of the instantaneous power(the product of current and voltage) occasionally becomingnegative within each AC cycle, due to out-of-phase currentand voltage. This state causes power to flow towards thegenerator and away from the load. Reactive power is typicallydissipated as heat in power lines. For our purposes, reactivepower provides additional useful information for modeling,and many commodity power meters are capable of measuringit. As a result, our models include both real and reactive power.

Figure 6 depicts companion graphs for selected loads thatshows their reactive, rather than real, power usage. Figure 6(a)shows that, similar to real power, a resistive dimmable incan-descent light produces a stable—zero if not dimmed—amountof reactive power when on, although the magnitude of the drawpeaks at 50% dim level and decreases as the light approacheseither 0% or 100% dim level. Likewise, an inductive load likethe refrigerator in Figure 6(b) exhibits a spike followed by aflat reactive draw; a non-linear load like the duct heater inFigure 6(c) has a rapidly varying power usage; and compositeload like dishwasher 1 in Figure 6(d) operates a sequence ofsimpler internal loads. In each case, the pattern of a load’sreactive power usage follows its pattern of real power usage.Observation 5: While the magnitude of reactive power differsfrom real power, a load’s pattern of reactive power consump-tion is qualitatively similar to its real power consumption.

D. Summary

In classifying loads in terms of the elemental load typesabove, we observe that nearly every common household elec-tric load is a composition of one or more of the small numberof resistive, inductive, and non-linear loads described above,with heating elements and AC motors consuming the majorityof electricity in homes. Further, each type of elemental loadexhibits similar characteristics when active: heating elementshave a stable power usage or one that decays slowly over time,AC motors have a spike in power on startup and then varytheir power usage smoothly over time, while SMPSs exhibitrapid and significant power variations. As we discuss in thenext section, the presence of only a few elemental load typesin homes simplifies model design, enabling us to accuratelycapture their behavior using a few basic types of models.

III. LOAD MODELING METHODOLOGY

Based on our empirical observations from the previoussection, we develop models to capture key characteristics of

each load type. We first present four basic model types—on-off, on-off growth/decay, stable min-max, and random range—to describe simple loads, and then use these models as buildingblocks to form compound cyclic and composite models thatdescribe more complex loads. Ideal models describe i) howmuch real and reactive power a load uses when active, ii) howlong a load is active, and iii) when a load is active. However,in many cases, users manually control loads, such that whena load is active and for how long is non-deterministic. Forexample, a user may run a microwave any time for either tenseconds or ten minutes. For these loads, we assume a randomvariable captures this non-determinism, and focus our efforts,instead, on modeling how each load behaves when active.

Given each model type, we employ an empirical method-ology to construct accurate load-specific models: we leverageour observations of the load’s power usage as a training set,and employ curve-fitting methods to map one of the modeltypes onto the time-series data. If the best model type is notclearly evident a priori, we fit multiple models and then choosethe one that yields the best fit. As described below, dependingon the model type, we may employ simple regression or morecomplex curve-fitting methods, such as LMA [23], to constructa load-specific model for a given model type. As discussed inSection II, reactive power for loads exhibits similar behavior asreal power, and thus constructing a model of a load’s reactivepower consumption uses the same methodology as above.

A. Basic Model Types

On-off Model. As discussed in Section I, prior work oftenuses simple on-off load models. An on-off model includes twostates—an on state that draws some fixed power pactive and anoff state that draws zero, or some minimal amount of, powerpoff . Conventional, non-dimmable incandescent lights are thecanonical example of an on-off load. Dimmable lights alsoconform to on-off models, although pactive depends on thedim level. As shown in Figure 6(a), a N% dim level yields aproportionate reduction in real power usage. In addition, whilereal power is a simple linear function of dim level, reactivepower is a quadratic function that peaks at 50% dim level.Constructing an on-off model is simple—we use regression todetermine appropriate values pactive and poff . In particular, wepartition the time series of load power usage into two mutuallyexclusive time-series, with data for the on and off periods, todetermine the best values of pactive and poff .On-off Growth/Decay Model. An on-off growth/decay modelis a variant of the on-off model that accounts for an initial



7

880

900

920

940

960

980

1000

0

200

400

600

800

1000

0 1 2 3 4 5 6 7 8 9

Po

we

r (W

)

Time (min)

coffee maker modelcoffee maker data

decay zoom

(pactive, ppeak,�) = (905, 990, 0.045)

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4

Po

we

r (W

)

Time (min)

toaster modeltoaster data

1420

1430

1440

1450

1460

1470

1480

decay zoom

(pactive, ppeak,�) = (1433, 1470, 0.02)

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

Pow

er

(W)

Time (min)

dryer mini-cycle modeldryer mini-cycle data

5300

5350

5400

5450

5500

5550

5600

5650

5700

decay zoom

(pactive, ppeak,�) = (5340, 5685, 0.078)

1800

1900

2000

2100

2200

2300

0

500

1000

1500

2000

2500

0 2 4 6 8 10

Po

we

r (W

)

Time (min)

central A/C modelcentral A/C data

growth zoom

(pbase,�) = (1800, 72)

(a) Coffee maker (b) Toaster (c) Single dryer mini-cycle (d) Central A/C

Fig. 7. An on-off growth/decay model closely matches the average power usage measured each second for a variety of resistive and inductive loads.

power surge when a load starts, followed by a smooth in-crease or decrease in power usage over time. As discussedin Section II, AC motors are the most common example ofa load exhibiting this behavior, e.g., refrigerator, central A/C,vacuum. Resistive loads with high-power heating elements,such as the toaster or coffee maker, also conform to an on-off growth/decay model, although the surge and the decayin these devices is far less prominent than in AC motors.We characterize on-off decay models using four parameters:pactive, poff , ppeak, and λ. The first two parameters are thesame as in on-off models, while ppeak represents the level ofinrush current when a device starts up and λ represents therate of growth or decay to the stable pactive power level. Wemodel decay using an exponential function as follows, wheretactive is the length of the active interval.

p(t) =

pactive + (ppeak − pactive)e−λt, 0 ≤ t < tactive

poff , t ≥ tactiveSimilarly, we model on-off growth as a logarithmic function

(i.e., the inverse of the exponential function) using startingpower level pbase and growth parameter λ:

p(t) =

pbase + λ ln t, 0 < t < tactive

poff , t ≥ tactiveWe can optionally augment the growth model with an

additional parameter pceil to prevent unbounded growth thatsimply caps the maximum output of the model. In the growthmodel, the surge current must also be modeled separately (suchas in the central A/C shown in Figure 7d). Here, we can simplyadd a parameter pspike specifying the power at t = 0.

As with the on-off models above, the length of the activeinterval for on-off growth/decay models is often not knowna priori since it may depend on user behavior. However, wehave observed that in many cases users repeatedly operatedevices in the same way, e.g., a toaster that toasts a bagelevery morning. In many cases, the device determines tactiveautomatically, e.g., the compressor for a refrigerator or freezermay turn on for an average of 20 minutes in each cycle. Inthese cases, we incorporate the mean value of tactive into themodel. Constructing an on-off growth/decay model requiresfitting an exponentially decaying (or logarithmically growing)function onto the time-series data, in addition to determiningppeak, pactive, and poff . We employ the LMA algorithm [23]to numerically find the exponential or logarithmic function thatbest fits the data, i.e., based on a least-squares nonlinear fit.

Figure 7(a) shows the specific on-off decay model for acoffee maker in parallel with its real power data. The figuredemonstrates that the exponential decay is a highly accurateapproximation of the coffee maker’s power usage. In this case,pactive = 905, ppeak = 990, poff = 0, and λ = 0.045.Likewise, Figures 7(b) and (c) show on-off decay modelsand real power data for a toaster and a portion of a dryercycle. Finally, Figure 7(d) shows how well an on-off growthmodel fits the real power data for the central A/C fromFigure 3(c). For comparison, we also fitted the lowest-erroron-off model for each of the four representative device cyclespictured in Figure 7. We then calculated the root mean squareerror (RMSE) for both the on-off and on-off decay modelsfor (a) each load’s duration, and (b) its first 30 seconds ofactivity (including the ‘on’ event). As seen in Figure 8, thegrowth/decay model decreases the error in the on-off modelby as much as 8X, particularly in the first 30 seconds wherethe on-off model is unable to capture the rapid decay behavior.Stable Min-Max Model. While on-off and on-off decay mod-els accurately capture the behavior of resistive and inductiveloads, they are inadequate for modeling non-linear loads. Asseen in Section II, many non-linear loads maintain a stablemaximum or minimum power draw when active, but often varyrandomly and frequently from this stable state. These varia-tions are due to the device rapidly regulating their electricityusage to “match” the current needs of the device. Our stablemin-max model captures this behavior by first specifying astable maximum or minimum power when active, denoted bypactive. The power usage then deviates, or “spikes,” up ordown from this stable value at some frequency. The magnitudeof each spike is chosen uniformly at random between pactiveand a specified maximum deviation, denoted pspike. The inter-arrival times of the spikes are exponentially distributed withmean λ. Thus, the stable min-max model is specified by thechoice of pactive, pspike, and λ (as well as whether pactivedenotes a stable minimum or a stable maximum).

Empirically constructing a load-specific stable min-maxmodel requires determining the stable power level pactiveand characterizing the magnitude and frequency of the powerspikes. We employ simple regression to determine the stablepower level pactive from the data, e.g., after filtering outthe data for spikes and finding the fit for pactive. The meanobserved duration between spikes then yields the parameterλ. Figure 9 shows our stable-max model for the LCD TV(from Figure 1) using a maximum pactive of 160W and a λ of10.82, which we derive from the TV’s real power usage data.



8

0

50

100

150

200

Coffee maker Toaster Dryer Central A/CRo

ot

Me

an

Sq

ua

re E

rro

r (W

)

Device Name

Growth/DecayGrowth/Decay (first 30s)

On-offOn-off (first 30s)

Fig. 8. On-off growth/decay models are more accurate than on-off models.

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14 16

Pow

er

(W)

Time (min)

TV model

(pactive, pspike,�) = (160, 120, 10.82)

Fig. 9. A stable-max model of the LCD TV from Figure 1.Importantly, as we discuss in Section IV, both the model andthe raw data have similar statistical properties, which simplefilters can recognize by detecting when power variations aresignificant, frequent, and symmetric, e.g., a decrease and thenimmediate increase in power of similar magnitude.Random Range. Finally, we found that some devices drawa seemingly random amount of power within a fixed rangewhen active. This is likely due to the fact that taking averagepower readings each second is too coarse a frequency tocapture the device’s repetitive behavior. We model such loadsby determining upper and lower power usage bounds, denotedby pmax and pmin. When active, our model randomly variespower within these bounds using a random walk. Note that therandom range model is similar to the stable min-max modelin that both employ upper and lower bounds on power usage.However, while the deviations in the stable min-max modelare spikes from a stable value, those in the random rangemodel are power variations within a range. The microwave isan example of a load that exhibits this behavior. As shown inFigure 4(d), when turned on, the power usage of the microwavefluctuates continuously between 1400W and 1480W.

Random range models require determining the minimumand maximum of the load’s range of power usage. We de-termine these values by simply choosing the minimum andmaximum power values observed in training data, or byderiving a distribution of power values from the data andchoosing a high and low percentile of the distribution to bethe minimum and maximum, pmin and pmax. We then modelthe variations with a random walk within the range.

B. Compound Model Types

While the models above accurately capture the behavior ofsimple loads, many loads, including large appliances, exhibitcomplex behavior from operating a variety of smaller con-stituent loads. We devise two types of compound models for

complex loads that use the basic building blocks above.Cyclic Model. Cyclic loads repeat one of the basic modeltypes in a regular pattern, often driven by timers or sensors.For example, the HRV heater employs a timer that activatesfor 20 minutes each hour. Similarly, a refrigerator duty-cycleis based on sensing its internal temperature, which rises andfalls at regular intervals and fits our model well, as shown inFigures 3(a) and (b). A cyclic model augments a basic modelby specifying the length of the active and inactive period,tactive and tinactive, each cycle. Constructing cyclic models isstraightforward, since it only requires extracting the durationof the active and inactive periods from the empirical data. Wecurrently use the mean of the active and inactive periods fromthe time-series observations to model tactive and tinactive.Composite Model. Composite loads exhibit characteristicsof multiple basic model types either in sequence or parallel.Example composite loads include dryers, washing machines,and dishwashers, as shown in Figure 5. Sequential compositeloads operate a set of basic load types in sequence; wemodel them as simple piecewise functions that encode thesequence of basic load models, including how long eachload operates. For instance, a model for a dishwasher is asequence of stages: modeled as the operation of the motor(wash stage), pump (drain stage), motor (rinse stage), pump(drain stage) and heater (dry stage), where each individualstage uses an inductive or resistive load. Some loads alsoexhibit characteristics of two or more basic models in parallelif two basic loads operate simultaneously. For example, arefrigerator may simultaneously activate both a compressorand an interior light. We model parallel composite loads bysumming the power usage for two or more of the basic modeltypes. Finally, composite loads may also be cyclic, referred toas cyclic composite loads, which repeat a pattern of individualmodel types at regular intervals. Our methodology permitsarbitrary compositions of sequential, parallel or cyclic loads.

Constructing load-specific composite models is more com-plex and requires additional manual inputs. For example,constructing a sequential composite model requires manuallypartitioning and isolating load time-series data into individualsequences that reflect the activation of the various load com-ponents. Each individual component of the composite loadis modeled using a basic model type. The composite modelis then simply a concatenation of these piecewise models insequence (the duration of each component may be specifiedin the model or left as a variable).

As an example, Figure 10 shows an extended operatingcycle of the washing machine with the annotations for differentbasic load model types in the sequence. We represent thesemodels as large piecewise functions of the basic modelsdescribing each constituent load. In addition, many of the largeappliances that have composite models also have numerousoperating states. For example, the washing machine and dryerin one of our homes has over 25 different types of cycles.Ideally, a model includes a different piecewise function foreach cycle type. However, in the homes we monitor we havefound that most residents operate devices using only a fewstates—in most cases one.

Constructing parallel composite models poses additional



9

0

100

200

300

400

500

600

0 5 10 15 20 25 30 35 40 45

Pow

er (

W)

Time (min)

washing machine

random range, cyclic

on-off decay,cyclic

stable minrandomrange

on-off decay, cyclic

on-off decay(growth)

Fig. 10. A single complete cycle of a washing machinenannotated with the model types for the operation of simpler internal loads.

challenges. Since the time-series data for a load capturesthe power usage for all components that are concurrentlyactive, there is no straightforward general-purpose technique toextract individual models from the composite time-series data.In practice, however, extracting basic models is often possiblethrough exogenous means. For instance, many loads permitoperating individual components to isolate them for profiling,e.g., such as a running a dryer on tumble mode without anyheat or using an air conditioner’s fan without any cooling.After separately profiling a constituent load, such as thetumbler or fan, it is possible to operate the compressor and thefan, and then infer the compressor power usage by “filteringout” the tumbler or fan usage from the aggregate. In somedevices, such as a refrigerator, it also might be possible todeploy additional sensors that monitor important events, suchas a door opening that triggers lights, to filter them out. Ideally,the model of a complex composite device would be providedby the device manufacturer, as the problem of identifying thecomponents of a composite device is largely orthogonal tothe problem of modeling each component. However, usingthe techniques described previously, it is generally possible toidentify the key components even without detailed knowledgeof the internals of the device (though for many devices,substantial information on the components and operation ofthe device is readily available, e.g., in an owner’s manual).

IV. MODEL-BASED DATA ANALYSIS

While we expect our models to have numerous uses in avariety of analysis and optimization tasks in building energymanagement, below, we illustrate three examples of novelapplications we have designed: i) generating device-accuratesynthetic data of a building’s aggregate electricity usage, ii)designing filters to identify and remove random and frequentpower variations from stable min-max loads, and iii) detect-ing the presence of specific load models in filtered powerdata using an existing variable-length subsequence matchingalgorithm for time-series data. Each of these applicationsfocuses on improving the analysis of smart meter data thatrecords a residential home’s average electricity usage eachsecond. We assume the smart meter not only transmits datato the utility for billing purposes, but also provides homeusers an interface to access the data. In this architecture,similar to our measurement testbeds, home users may employa programmable gateway (either on-site or cloud-based) undertheir control to record and analyze the data to inform either

manual or automated energy-efficiency improvements, e.g., viaprogrammatic load control and scheduling. As we show, ourapplications should prove useful in both i) developing newtechniques for analyzing smart meter data and ii) supple-menting existing well-studied techniques, e.g., NILM, alreadydeveloped by researchers and in broad use.

A. Device-accurate Synthetic Building DataEvaluating new techniques for analyzing electricity data

requires actual building data for testing. Unfortunately, whilerecording a building’s aggregate electricity usage is simple,requiring only a single smart meter, recording detailed aspectsof the building’s environment is not. For instance, evaluat-ing the accuracy of a NILM algorithm, which disaggregatesbuilding electricity data into power data for individual loads,requires power data from both the entire building and eachof its constituent loads. However, NILM’s entire purpose isto prevent the need for recording such ground truth data ateach load. As our own experience from Section II-A indicates,setting up even a test infrastructure for collecting groundtruth data is expensive, invasive, and time-consuming, sinceit requires a power meter attached to each load in the home.While there are a few data sets for select buildings availablefor NILM researchers to use in evaluation [7], [24], [25], theytypically do not instrument every load nor do they cover awide range of building types or load characteristics.

To address this problem, our first application uses ourmodels to automatically generate device-accurate syntheticelectricity data for buildings. Being device-accurate meansthat the synthetic trace data includes both the synthetic ag-gregate time-series power data for a building, as well astime-series power data for each of the constituent loads inthe building generated using our models. While prior worktargets generating synthetic traces of the power usage forentire buildings [26], we are not aware of any previous workthat focuses on being device-accurate. Unlike real-world tracedata collected from specific buildings, the synthetic tracesgenerated using our models will provide researchers explicitcontrol over the number and types of loads present in thedata, enabling them to control the statistical properties of thedataset and discover which properties have the most influenceon their results. Importantly, synthetic data does not not requireresearchers to deploy a large number of per-load power meters.

Figure 11 shows an example of how our device-accuratesynthetic building data compares with data collected from



10

0

1000

2000

3000

4000

5000

6000

7000

8000

0 2 4 6 8 10 12 14 16

Pow

er

(W)

Time (hours)

Measured Power Data

0

1000

2000

3000

4000

5000

6000

7000

8000

0 2 4 6 8 10 12 14 16

Pow

er

(W)

Time (hours)

Synthetic Model-based Power Data

3000

4000

5000

6000

7000

8000

0 5 10 15

Pow

er

(W)

Time (minutes)

Measured Power DataModel-based Synthetic

(a) Raw Power Data (b) Synthetic Model-based Power Data (c) Zoom-in ComparisonFig. 11. Aggregate home power from measured data (a) and from our corresponding device models (b), along with a zoom-in comparison over 15 minutes.

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200 1400

Pow

er

(W)

Time (min)

disaggregated

0

100

200

300

400

500

600

700

800

900

0 200 400 600 800 1000 1200 1400

Pow

er

(W)

Time (min)

disaggregated

(a) NILM on actual data (b) NILM on synthetic dataFig. 12. Disaggregation of the refrigerator’s power usage when performing NILM on both real power data and synthetic data.

a real building. To generate the synthetic trace shown inFigure 11(b), we replace each occurrence of a given devicein the ground-truth data shown in Figure 11(a) (i.e., eachperiod when a device is using power) with our model ofthat device over the same time period. Figure 11(c) showsa zoomed-in comparison of the two traces over a 15 minuteperiod to graphically illustrate their similarity. The ground-truth and model-based traces look qualitatively similar, butthey also have similar statistical properties: the real data (a) hasan average power of 1200W, a standard deviation of 1072W,and 5591 changes in power >15W, while the synthetic data(b) has an average power of 1165W, a standard deviationof 1073W, and 5833 changes in power >15W. Since thesynthetic data is composed of data from models of individualloads, it is useful for analysis techniques that look for patternsin the aggregate usage data. By comparison, if we generateon-off models that include at most 4 power states per load(as in recent work [24]), there are only 1985 changes inpower >15W, which eliminates many identifiable load-specificcharacteristics useful in analysis.

In addition to comparing our model-based trace data withthe real building data, we also show that a state-of-the-artNILM disaggregation algorithm produces similar results usingboth datasets. Formally, a NILM algorithm analyzes changesin smart meter time-series power data, P (t), to compute aseparate power time-series pi(t) for each i = 1 . . . n loadsin a home. NILM is a well-studied problem first proposedover 20 years ago [27]. We use the same NILM algorithm asKolter and Johnson [24] to evaluate their Reference EnergyDisaggregation Dataset (REDD), which was based on thetechnique by Kim et al. [28] and models building power data asa Factorial Hidden Markov Model (FHMM). We quantify thealgorithm’s accuracy using the dissaggregation error factor.For n loads with predicted power p̃it and actual power pitat time t for all times T , the disaggregation error factor is

computed as follows:

ErrorFactor =

∑Tt=1

∑ni=1 |pit − p̃it|∑T

t=1

∑ni=1 p

it

(1)

The numerator is the sum of the absolute value of thedifference between the predicted and actual power for eachload for all time periods T , while the denominator is twotimes the aggregate energy. An error factor of zero indicatesprecise second-to-second disaggregation, while an error factorof one indicates that the second-to-second errors equal theenergy use of the home. Thus, simply predicting power for allloads to be zero every second results in an error factor of one.Note that, since we monitor average power each second, thenumerator and the denominator are in units of watt-seconds orjoules. Based on the equation above, we can also compute adisaggregation error factor for each individual load, called theload error factor. In this case, the numerator and denominatordo not sum over all n loads, but only over the single load.

The FHMM-based NILM algorithm requires a trainingphase that uses data from each load to learn a power usagemodel for each load. Unlike our empirical models, the per-load models used by the FHMM include only 4 power states,although we do not explore how our models might applyto NILM in this paper. We train the FHMM on the sameper-load data to generate the 4-state models, and then runthe NILM algorithm on both the real building data and oursynthetically generated trace data. Our results show that theNILM algorithm has a disaggregation error factor of 0.796when using the real building data and 0.735 when usingour synthetically generated data – a difference of only 7.5%.This similarity in error factors demonstrates that our syntheticdata produces similar results for NILM algorithms as realdata. In addition, Figure 12 shows both the disaggregatedrefrigerator and actual refrigerator trace using the real building



11

0

2000

4000

6000

8000

10000

Active

HR

V

Wash

ingM

ach

ine

Drye

r

Livin

gR

oom

Refrig

era

tor

Passive

HR

V

Micro

wave

Cella

rOutle

ts

Dish

wash

er

Cella

rLig

hts

Bedro

om

Lig

hts

Kitch

enLig

hts

Counte

rOutle

ts1

Maste

rOutle

ts

Counte

rOutle

ts2

Maste

rLig

hts

GuestH

allL

ights

Livin

gR

oom

Patio

Bedro

om

Outle

ts

Po

we

r E

ven

ts (

>1

0W

)

Circuit

49827

5324

3162

2432

393 175 173 115 76 55 55 53 30 22 21 20 15 7 3

0

2000

4000

6000

8000

10000

Active

HR

V

Wash

ingM

ach

ine

Drye

r

Livin

gR

oom

Refrig

era

tor

Passive

HR

V

Micro

wave

Cella

rOutle

ts

Dish

wash

er

Cella

rLig

hts

Bedro

om

Lig

hts

Kitch

enLig

hts

Counte

rOutle

ts1

Maste

rOutle

ts

Counte

rOutle

ts2

Maste

rLig

hts

GuestH

allL

ights

Livin

gR

oom

Patio

Bedro

om

Outle

ts

Po

we

r E

ven

ts (

>1

0W

)

Circuit

49827

5324

3162

2432

393 175 173 115 76 55 55 53 30 22 21 20 15 7 3

Fig. 13. A few highly variable (non-linear) loads are responsible for the vastmajority of power variations in a home’s per-second smart meter data.

0

200

400

600

800

1000

1200

1400

0 10 20 30 40 50 60 70 80

Po

we

r (W

)

Time (min)

60W bulb

TV onHRV on HRV off

TV on

Fig. 14. The stable maximum power enables a filter that removes powervariations in smart meter data, making it easier to detect on-off transitions.

data (a) and the disaggregated refrigerator and model-derivedrefrigerator trace using our synthetic trace data (b). The figuregraphically illustrates the similarity in results from the NILMalgorithm operating on the real versus the synthetic data, anddemonstrates that our synthetic traces are device-accurate.Result: Our load models are useful in generating device-accurate synthetic datasets that enable researchers to test andvalidate new analysis techniques for smart meter data.

B. Stable Min-max Filters

Since stable min-max loads account for the large majorityof power variations in a home, filtering out their variations cansignificantly improve subsequent data analysis techniques, in-cluding the HMM-based NILM algorithms above that modelsa building as a state machine composed of on-off loads. Toillustrate this point, Figure 13 shows a bar graph of the numberof second-to-second power variations in a single day for eachof 19 active circuits in one of the homes we monitor. Thegraph demonstrates that a small number of circuits accountfor the vast majority of the power variations in the home—notably resulting from two non-linear loads (the HRV’s ductheater and the living room TV) and two composite loads withnon-linear components (the washing machine and dryer), eachof which is highlighted in Figure 4. In total, there were 61958variations in power (>1W) out of a total of 86400 data pointsover the 24-hour period, out of which 49827 (or 80.4%) werecaused by the HRV’s non-linear duct heater from Figure 4(c).The washing machine and dryer, combined, caused another8486 variations (or 13.7%), followed by the living room TV,which caused 2432 variations (or 3.9%). Collectively, 98% ofthe second-to-second power variations over the course of theday derived from the four loads above, while only 2% of thevariations derived from the home’s other 90 loads.

The large number of power variations caused by non-linearloads makes data analysis challenging. For instance, it maybe difficult to discern if a 60W increase in power is due to alight bulb turning on or simply one of many random variationscaused by a large non-linear load. Unfortunately, existingtechniques, such as the NILM algorithm from the previoussection, that model loads using a few discrete power statesare not equipped to detect these rapid and seemingly randomvariations. However, our modeling indicates that these loadsexhibit highly identifiable features, namely by maintainingstable minimum or maximum power levels. Thus, we design asimple filter to identify rapid variations from a stable minimumor maximum power level and remove them from the aggregatetrace. Filtering these loads out of the smart meter data not onlyenables a new way to identify this special class of load, italso simplifies the data by removing a large number of powervariations, which, as we show below, improves the results ofthe existing NILM algorithm from the previous section.

Our stable min-max filter works by simply scanning throughthe power data time-series for a home and maintaining a stablepower parameter, which only updates if power deviates fromthe current parameter setting for more than time T by somethreshold power Pthreshold, both of which are chosen basedon the load’s model. The idea is to update the stable powerwhen other devices operate (e.g., a lamp that is turned on) andleave these steps unchanged. Power steps that do not updatethe stable power are attributed to the stable min-max deviceand filtered – the settings of Pthreshold and T determine howlarge and how long a power change may be to be considereda transient change stemming from the stable min-max device.

To clearly illustrate the filter’s effect, Figure 14 appliesthe filter to aggregate power data that includes only the TVand duct heater (from Figure 4) combined with a 60W lightbulb. Since the TV and the duct heater exhibit rapid powervariations every few seconds (see Figure 4), the value of Tneed only be slightly greater than the typical frequency of thevariations. In both cases we set T = 5 seconds. In addition,we select a value of 10W for Pthreshold since both loadshave a narrow maximum power usage that varies by less than10W. As the figure shows, the filter makes the duct heaterand TV appear to be simpler loads with discrete power states,making it possible to easily identify a 60W light bulb turningon or off by observing changes in power in the filtered data.However, without filtering, any data analysis technique, e.g.,using HMMs, that uses changes in aggregate power usageto identify when the light bulb turns on or off would havedifficulty, since operating either the TV or duct heater obscureschanges in the light bulb’s power by introducing significantand frequent power variations. In fact, the duct heater’s powervariations alone are large enough—greater than 800W in somecases—to obscure all but the largest loads in the home.

Finally, we also ran the NILM algorithm described in theprevious subsection on the unfiltered smart meter data and thedata with the duct heater filtered out. We then computed theload error factor for each load in both cases, and found thatthey were generally less when the duct heater had been filteredout. As an example, Figure 15 shows time-series power datafor the home’s refrigerator (a), as well as the disaggregated



12

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200 1400

Pow

er

(W)

Time (min)

refrigerator

-600

-400

-200

0

200

400

600

800

0 200 400 600 800 1000 1200 1400

Pow

er

(W)

Time (min)

refrigerator

-600

-400

-200

0

200

400

600

800

0 200 400 600 800 1000 1200 1400

Pow

er

(W)

Time (min)

refrigerator

(a) Actual refrigerator trace (b) With duct heater included (c) With duct heater filtered outFig. 15. Disaggregating refrigerator trace with the duct heater included and with the duct heater filtered out

refrigerator power trace using the unfiltered (b) and filtered(c) smart meter data. The figures illustrate that the refrigeratorpower trace disaggregated after filtering the smart meter datamore closely resembles the ground truth power usage ofthe refrigerator. The load error factor for the disaggregatedrefrigerator trace quantifies this resemblance to ground truth:it is 1.328 from the unfiltered data (b), while it is 0.987 (or25% less) from the filtered data (c).Result: Uniquely identifiable properties in our load models en-able new analysis techniques, such as our filter, and improvesexisting techniques, such as the NILM algorithm above.

C. Load Detection

Finally, a third use of our models is detecting the presence ofspecific loads within a building’s aggregate power trace. Loaddetection can reveal many useful pieces of information, such aswhen devices turn on, how long they tend to operate, and howmuch power they consume. Load detection is distinct fromthe well-studied NILM (or load disaggregation) problem [8],[29], in that the latter attempts to attribute a building’s entirepower usage across a known set of loads, while the formeronly attempts to detect the presence of a single load. Here,we study a simple distance-based matching technique as onerepresentative example of using our models for load detection.

The core idea in distance-based matching is to use load-specific models to generate representative time-series of de-vices, which can then be compared against real-world us-age data. By computing the ‘distance’ between the model-generated time-series and the observed data, we can identifyclose ‘matches’ corresponding to the operation of specificdevices. Performing this matching requires the use of a spe-cific distance measure. The most natural distance measure isstandard Euclidean distance, computed as the square root ofthe sum of squared differences between energy values (i.e.,predicted and actual) at the same times – i.e., for time-seriesa and b each with N points, the Euclidean distance is given byDEuclidean =

√(∑ni=1 |ai − bi|2). The primary advantage of

Euclidean distance is simplicity and computational efficiency(i.e., O(N) complexity). However, matching accuracy maysuffer when two time-series are similar in shape, but are notwell-aligned in time. This issue tends to arise with deviceswhere the length of the active period is not known a priori,but rather determined by users at runtime, such as a light bulbthat might be active either for ten minutes or an hour.

Results of matching model-generated time-series againstaggregate data with Euclidean distance are shown in Fig-

ures 16, 17, and 18, for three different devices. Here wesimply construct models of each device and specify the modelparameters (e.g., magnitudes) manually, though we envisiona better scenario in which models are drawn from a globaldatabase containing (known) models for many devices. Notethat we match second-to-second power deltas, i.e., changesin power, rather than absolute power values. The absolutevalues of the aggregate energy trace are typically much greaterthan the power usage of a specific device, which makesthem largely meaningless when comparing with a model fora specific device. Matches are observed when the distancemeasure experiences a drop, indicating a closer similarityto the device model time-series. For example, the distancemeasure in Figure 16(b) experiences significant drops (circled)whenever the refrigerator compressor cycles on. These dropsare due to the close similarity of the refrigerator model tothe actual refrigerator operating within the aggregate trace.Furthermore, the drops make it relatively straightforwardto closely approximate the actual refrigerator operation; forexample, we can simply insert the refrigerator model whenspecified by local minima in the distance measure. Circled inFigure 16 are drops exceeding a fixed threshold, which is asimple but concrete way to detect device ‘on’ events.

We see similar drops in Figures 17(c) and 18(b); however,using our naı̈ve threshold-based method to identify deviceoperation leads to a significant number of false positives,e.g., roughly 200 false positives for the washing machinefor only three actual device cycles. However, most of thesefalse positives are clustered around the true positives, sosimple locality-based heuristics, e.g., such as averaging withina window and accounting for knowledge of the approximatecycle length, can still result in accurate load detection.

Some of the shortcomings above with using Euclidean dis-tance matching can also be mitigated by incorporating a notionof temporal stretching and amplitude transformation whenmatching traces. For example, we may know the consistentshape of a given device’s usage, but not how long it operates(i.e., the temporal dimension) or exactly how much power ituses at a given time (i.e., its amplitude). Despite the ease withwhich we may be able to visually identify such devices withina trace (based on their shape alone), Euclidean distance mayperform quite poorly on these devices due to slight differencesbetween measured data and the device’s model.

We explore an alternate matching technique detailed in[30] that aims to account for these issues, which we referto as ‘augmented Euclidean matching.’ The idea behind this



13

0

500

1000

1500

2000

2500

3000

3500

4000

0 200 400 600 800 1000 1200

Pow

er

(W)

Time (min)

grid

0

500

1000

1500

2000

2500

0 200 400 600 800 1000 1200

Pow

er

(W)

Time (min)

refrigeratordistance

0

200

400

600

800

1000

1200

1400

120 140 160 180 200 220

Pow

er

(W)

Time (min)

refrigeratordistance

(a) Aggregate trace (b) Refrigerator Euclidean distances (c) Zoomed-inFig. 16. Refrigerator matches using Euclidean distances

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 200 400 600 800 1000 1200 1400

Pow

er

(W)

Time (min)

grid

0

200

400

600

800

1000

1200

1400

1600

1800

0 200 400 600 800 1000 1200 1400

Pow

er

(W)

Time (min)

washing machinedistance

0

200

400

600

800

1000

1200

1400

1600

1800

300 350 400 450 500

Pow

er

(W)

Time (min)

washing machinedistance

(a) Aggregate trace (b) Washing Machine Euclidean distances (c) Zoomed-inFig. 17. Washing Machine matches using Euclidean distances where the model used is one entire cycle of the washing machine turning on

0

500

1000

1500

2000

2500

3000

3500

4000

0 200 400 600 800 1000 1200

Pow

er

(W)

Time (min)

grid

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 200 400 600 800 1000 1200

Pow

er

(W)

Time (min)

dishwasherdistance

0

500

1000

1500

2000

2500

3000

3500

320 330 340 350 360 370 380P

ow

er

(W)

Time (min)

dishwasherdistance

(a) Aggregate trace (b) Dishwasher Euclidean distances (c) Zoomed-inFig. 18. Dishwasher matches using Euclidean distances

0

500

1000

1500

2000

2500

3000

3500

4000

0 200 400 600 800 1000 1200

Pow

er

(W)

Time (min)

grid

200

300

400

500

600

700

800

900

1000

1100

120 140 160 180 200 220

Pow

er

(W)

Time (min)

refrigerator

0

200

400

600

800

1000

1200

1400

1600

0 200 400 600 800 1000 1200

Pow

er

(W)

Time (min)

refrigerator matches

(a) Aggregate trace (b) Zoomed-in aggregate (c) Refrigerator matchesFig. 19. Refrigerator matches using augmented Euclidean matching

technique is to account for amplitude scaling by searchingfor matches of a linear function of the input, i.e., searchingfor a and b such that aX + b matches the aggregate, and toaccount for temporal scaling by averaging consecutive points,i.e. changing the effective length of the time-series. After ap-plying these changes, multiple candidate time-series windowsare searched to determine matches, using an optimization tolimit the number of windows that must be searched. Detaileddiscussion of this technique is omitted for brevity’s sake butcan be found in [30]. The technique is one of many withinthe time-series database community that looks for patterns intime-series data that are similar to a query time-series.

Figure 19 shows the aggregate trace (a) and the refrigeratortrace (b) with matches marked as before when given by theaugmented Euclidean technique. We see that the technique

accurately identifies matches towards the start and end of thetrace when fewer devices are operating (and thus the device tomatch is least obscured) but has difficulty in the interim timeperiods when many other devices are operating. This is notsurprising, since this technique, as with most in the time-seriesdatabase community, was not designed for matching againstdata with variable amounts of noise from other sources. Oneinteresting area of future research is applying these techniquesto load detection by adapting them to account for such noise.

Similarly, Figure 20 shows the results of matching the on-off decay and cyclic components of the washing machinetrace shown in Figure 10(a). We see in Figure 20(c) thatmatches are found in the initial as well as latter cyclic phasesof the washing machine, despite the multiple amplitudes anddurations of the device. However, we see that the initial phases



14

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 200 400 600 800 1000 1200 1400

Pow

er

(W)

Time (min)

grid

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

300 350 400 450 500

Pow

er

(W)

Time (min)

washing machine

0

200

400

600

800

1000

300 350 400 450 500

Pow

er

(W)

Time (min)

washing machinematches

(a) Aggregate trace (b) Zoomed-in aggregate (c) Washing Machine matchesFig. 20. Washing Machine matches using augmented Euclidean matching where the model used to match is the on-off decay cyclic part at the end

0

500

1000

1500

2000

2500

3000

3500

4000

0 200 400 600 800 1000 1200

Pow

er

(W)

Time (min)

grid

0

500

1000

1500

2000

2500

3000

3500

320 330 340 350 360 370 380

Pow

er

(W)

Time (min)

dishwasher

0

200

400

600

800

1000

1200

1400

1600

1800

0 200 400 600 800 1000 1200

Pow

er

(W)

Time (min)

dishwashermatches

(a) Aggregate trace (b) Zoomed-in aggregate (c) Dishwasher matchesFig. 21. Dishwasher matches using augmented Euclidean matching

of the third device cycle are not matched, as the match isobscured by another large device operating during this period,which we can see around t = 480 min in Figure 20(a).

Finally, we tried the augmented Euclidean matching on thedishwasher cycle as shown in Figure 21, but here, no realmatches were located at all – the technique simply ‘matches’the entire trace, which provides no useful information. Thisbehavior is likely due to the fact that the dishwasher exhibitsfairly simple stepping behavior between static states as shownin Figure 5(c) – as a result, it can be morphed in the timeand amplitude domains to match the entire aggregate trace.Despite this, augmented Euclidean matching tends to be moreconservative in matching than straight Euclidean distance,which tends to result in more false positives.

Both strategies demonstrate that matching within aggregatetraces is a difficult problem given the noisiness and complexityof typical aggregate traces. Despite this, we believe that ourmodels can be useful across a variety of matching techniques,as demonstrated in the examples above.Result: Our models are useful in detecting the presence ofspecific loads in smart meter data by matching them againsta home’s aggregate time-series power data.

V. RELATED WORK

In this paper, we focus explicitly on modeling the powerusage of common electrical loads. While recent work targetsmodeling for specific appliances, e.g., a particular brand ofrefrigerator [31], it does not generalize to a broad rangeof devices. Much of the prior research on modeling powerusage for individual loads has been done in the context ofNon-Intrusive Load Monitoring (NILM). While we expect ourmodels to be broadly useful for data analysis, including, butnot limited to, NILM, we survey related work in NILM below.

NILM techniques differ significantly based on the granular-ity of the current, voltage, and power readings. For instance,fine-grain readings that sample current or voltage frequently

within each cycle, e.g., �60Hz, differ significantly from themodels we present, since they attempt to capture the behaviorof the AC current and voltage waveform. In addition, gatheringdata at such high frequencies presents challenges: it requiresexpensive and highly calibrated equipment, while storing andtransmitting the data in real time is beyond the capabilities oftoday’s embedded power meters. While other types of devicemodels may be supported by higher-frequency data (such asturn-on transient power signatures in [32]), our models targeta data granularity of one reading per second, since this isthe finest granularity that commodity low-cost power meterssupport. We could also build load models using the coarse-grain data, e.g., 5 minutes to an hour, supported by today’sutility-installed smart meters [33]. Unfortunately, coarse-graindata measured every minute or more eliminates importantdetails of each load’s operation that are useful in analysis.

Recently, a number of researchers have focused on NILMapproaches for the per-second power data we use to buildour models. Most of these approaches employ generic on-off load models that, as we show, are not accurate. Thetechniques generally use these simple models to either i) detectchanges in load power states by observing changes in buildingpower, [8] or ii) use Viterbi-style algorithms [18] to determinethe most likely set of “hidden” states, e.g., combinations ofpower states for multiple loads, from a sequence of changesin building power [28]. These prior techniques generally donot scale to the large numbers of, often low-power, loadsfound in typical buildings. For instance, we are not awareof any prior approach that focuses on large-scale scenarios—>100 loads—with many low-power loads <50W, which is acommon characteristic of many homes. The lack of researchmay be due to the inaccuracy of the underlying load models.

VI. CONCLUSION

This paper presents a new methodology for modeling com-mon electric loads. We derive our methodology empirically



15

by collecting data from a variety of loads and showing thecommonalities between them. Finally, we illustrate examplesof how to use our models for data analysis.

REFERENCES

[1] J. Kelso, Ed., 2011 Buildings Energy Data Book. Department of Energy,March 2012.

[2] J. Koomey, “Data Center Electricity Use 2005 to 2010,” Analytics Press,Tech. Rep., August 2011.

[3] S. Dawson-Haggerty, S. Lanzisera, J. Taneja, R. Brown, and D. Culler,“@scale: Insights from a Large, Long-Lived Appliance Energy WSN,”in IPSN, April 2012.

[4] T. Hnat, V. Srinivasan, J. Lu, T. Sookoor, R. Dawson, J. Stankovic,and K. Whitehouse, “The Hitchhiker’s Guide to Successful ResidentialSensing Deployments,” in SenSys, November 2011.

[5] X. Jiang, M. V. Ly, J. Taneja, P. Dutta, and D. Culler, “Experiences with aHigh-fidelity Building Energy Auditing Network,” in SenSys, November2009.

[6] Y. Kim, T. Schmid, Z. Charbiwala, and M. Srivastava, “ViridiScope:Design and Implementation of a Fine Grained Power Monitoring Systemfor Homes,” in Ubicomp, September 2009.

[7] S. Barker, A. Mishra, D. Irwin, E. Cecchet, P. Shenoy, and J. Albrecht,“Smart*: An Open Data Set and Tools for Enabling Research inSustainable Homes,” in SustKDD, August 2012.

[8] M. Zeifman and K. Roth, “Nonintrusive Appliance Load Monitoring:Review and Outlook,” IEEE Transactions on Consumer Electronics,vol. 57, no. 1, February 2011.

[9] W. Kleiminger, C. Beckel, T. Staake, and S. Santini, “OccupancyDetection from Electricity Consumption Data,” in BuildSys, November2013.

[10] D. Chen, S. Barker, A. Subbaswamy, D. Irwin, and P. Shenoy, “Non-Intrusive Occupancy Monitoring using Smart Meters,” in BuildSys,November 2013.

[11] S. Barker, A. Mishra, D. Irwin, P. Shenoy, and J. Albrecht, “SmartCap:Flattening Peak Electricity Demand in Smart Homes,” in PerCom, March2012.

[12] J. Lu, T. Sookoor, V. Srinivasan, G. Gao, B. Holben, J. Stankovic,E. Field, and K. Whitehouse, “The Smart Thermostat: Using OccupancySensors to Save Energy in Homes,” in SenSys, November 2010.

[13] “Pacific Gas and Electric, leveraging Smart Meter Installation Progress,”http://www.pge.com/myhome/customerservice/smartmeter/deployment/,February 2013.

[14] M. Plaisance, “Holyoke gas and electric customers could net sav-ings from ongoing meter study involving high performance computingcenter,” http://www.masslive.com/news/index.ssf/2014/04/holyoke gasand electric custo.html.

[15] “eGauge Energy Monitoring Solutions,” http://www.egauge.net/, 2013.[16] “Energy, Inc.” http://www.theenergydetective.com/, July 2012.[17] S. Barker, S. Kalra, D. Irwin, and P. Shenoy, “Empirical characterization

and modeling of electrical loads in smart homes,” in IGCC, June 2013.[18] G. Forney, “The Viterbi Algorithm,” Proceedings of the IEEE, vol. 61,

no. 3, pp. 268–278, 1973.[19] A. Viterbi, “Error Bounds for Convolutional Codes and an Asymptoti-

cally Optimum Decoding Algorithm,” IEEE Transactions on InformationTheory, vol. 13, no. 2, pp. 260–269, 1967.

[20] iMeter Solo, http://www.insteon.net/2423A1-iMeter-Solo.html.[21] http://aeotec.com/z-wave-plug-in-switch.[22] D. Irwin, A. Wu, S. Barker, A. Mishra, J. Albrecht, and P. Shenoy,

“Exploiting home automation protocols for load monitoring in smartbuildings,” in BuildSys, November 2011.

[23] K. Levenberg, “A Method for the Solution of Certain Non-LinearProblems in Least Squares,” Quarterly of Applied Mathematics, 1944.

[24] J. Kolter and M. Johnson, “REDD: A Public Data Set for EnergyDisaggregation Research,” in SustKDD, August 2011.

[25] K. Anderson, A. Ocneanu, D. Benitez, D. Carlson, A. Rowe, andM. Berges, “BLUED: A Fully Labeled Public Dataset for Event-BasedNon-Intrusive Load Monitoring Research,” in SustKDD, August 2012.

[26] O. Ardakanian, S. Keshav, and C. Rosenberg, “Markovian Models forHome Electricity Consumption,” in GreenNets, August 2011.

[27] G. Hart, “Residential Energy Monitoring and Computerized Surveillancevia Utility Power Flows,” IEEE Technology and Society Magazine,vol. 8, no. 2, June 1989.

[28] H. Kim, M. Marwah, M. Arlitt, G. Lyon, and J. Han, “UnsupervisedDisaggregation of Low Frequency Power Measurements,” in SDM, April2011.

[29] K. Carrie Armel, A. Gupta, G. Shrimali, and A. Albert, “Is disaggrega-tion the holy grail of energy efficiency? the case of electricity,” EnergyPolicy, 2012.

[30] T. Argyros and C. Ermopoulos, “Efficient subsequence matching in timeseries databases under time and amplitude transformations,” in ICDM,November 2003.

[31] J. Taneja, D. Culler, and P. Dutta, “Towards Cooperative Grids: Sen-sor/Actuator Networks for Renewables Integration,” in SmartGridComm,2010.

[32] H.-H. Chang, K.-L. Chen, Y.-P. Tsai, and W.-J. Lee, “A new measure-ment method for power signatures of non-intrusive demand monitoringand load identification,” in Industry Applications Society Annual Meeting(IAS), 2011 IEEE, Oct 2011.

[33] J. Kolter and A. Ng, “Energy disaggregation via discriminative sparsecoding,” in NIPS, December 2010.

Sean Barker is a Ph.D. candidate in computerscience at the University of Massachusetts Amherst.He received his M.S in Computer Science from theUniversity of Massachusetts in 2012 and his B.A inComputer Science from Williams College in 2009.His research interests are in the areas of distributedsystems, cloud computing, smart buildings, and sus-tainability.

Sandeep Kalra is an M.S./Ph.D. student in com-puter science at the University of MassachusettsAmherst. He received his B.E from Sardar PatelUniversity in Information Technology in 2009. Hisresearch interests lie in the areas of smart grids andconnected homes, sustainability, data science, andanalytics.

David Irwin is an Assistant Professor in the Depart-ment of Electrical and Computer Engineering at theUniversity of Massachusetts Amherst. He receivedhis Ph.D. and M.S. in Computer Science from DukeUniversity in 2007 and 2005, respectively, and hisB.S. in Computer Science and Mathematics fromVanderbilt University in 2001. His research interestsare broadly in experimental computing systems witha particular emphasis on sustainability.

Prashant Shenoy received the B.Tech degree incomputer science and engineering from the IndianInstitute of Technology, Bombay, in 1993, and theM.S and Ph.D. degrees in computer science fromthe University of Texas, Austin, in 1994 and 1998,respectively. He is currently a Professor of ComputerScience at the University of Massachusetts. Hiscurrent research focuses on cloud computing andgreen computing. He is a distinguished member ofthe ACM and a Fellow of the IEEE.



empirical characterization, modeling, and analysis of ... · tv’s electricity usage each second....

Documents