# High resolution synthetic residential energy use profiles for the United
States

Swapna Thorve  Network Systems Science and Advanced Computing, Biocomplexity
Institute and Initiative, University of Virginia  Department of Computer
Science, University of Virginia  Young Yun Baek  Network Systems Science and
Advanced Computing, Biocomplexity Institute and Initiative, University of
Virginia  Samarth Swarup  Network Systems Science and Advanced Computing,
Biocomplexity Institute and Initiative, University of Virginia  Henning
Mortveit  Network Systems Science and Advanced Computing, Biocomplexity
Institute and Initiative, University of Virginia  Engineering Systems and
Environment, University of Virginia  Achla Marathe  Network Systems Science
and Advanced Computing, Biocomplexity Institute and Initiative, University of
Virginia  Anil Vullikanti  Network Systems Science and Advanced Computing,
Biocomplexity Institute and Initiative, University of Virginia  Department of
Computer Science, University of Virginia  Madhav Marathe  Network Systems
Science and Advanced Computing, Biocomplexity Institute and Initiative,
University of Virginia  Department of Computer Science, University of Virginia

###### Abstract

Efficient energy consumption is crucial for achieving sustainable energy goals
in the era of climate change and grid modernization. Thus, it is vital to
understand how energy is consumed at finer resolutions such as household in
order to plan demand-response events or analyze impacts of weather,
electricity prices, electric vehicles, solar, and occupancy schedules on
energy consumption. However, availability and access to detailed energy-use
data, which would enable detailed studies, has been rare. In this paper, we
release a unique, large-scale, digital-twin of residential energy-use dataset
for the residential sector across the contiguous United States covering
millions of households. The data comprise of hourly energy use profiles for
synthetic households, disaggregated into Thermostatically Controlled Loads
(TCL) and appliance use. The underlying framework is constructed using a
bottom-up approach. Diverse open-source surveys and first principles models
are used for end-use modeling. Extensive validation of the synthetic dataset
has been conducted through comparisons with reported energy-use data. We
present a detailed, open, high resolution, residential energy-use dataset for
the United States.

## Background & Summary

Modernization of the U.S. electric grid is occurring at a noteworthy rate due
to the installation of new technologies within the grid such as smart meters.
They enable two-way communication between the customer and utilities,
providing information and granular control of power usage for individual
households [1, 2]. The grid is also witnessing rapid transformations due to
increasing penetration of electric vehicles (EV) and distributed energy
resources (DER) such as rooftop photovoltaics (PV), community solar, and wind
energy. While this wave of modernization is beneficial, the electric grid is
simultaneously facing a sharp increase in crisis situations as a result of
climate change phenomena [3, 4] such as extreme weather events and global
warming. One example of extreme weather is the February 2021 North American
cold wave that caused a tremendous strain on the power grid especially in
Texas where millions lost power for days [5]. Another example is where global
warming impacts household HVAC energy use. Although the rise of 1∘ to 2∘C in
winter temperatures is expected to decrease heating requirements, a similar
rise in summer temperatures is expected to increase cooling needs
significantly [6].

In the face of these challenges, achieving sustainable energy goals has become
paramount for maintaining a healthy grid. To this end, the research community
is faced with important questions regarding reduction of carbon footprints [7,
8, 9, 10, 11], incentivizing DER adoption [12], studying benefits of building
energy retrofit [13, 14, 9], integration of electric vehicles [15] and
consumer behavior [16] in the grid, and mechanisms for designing electricity
pricing [17, 18] to create efficient residential consumption patterns.
Answering many of these questions requires comprehensive knowledge of energy-
use patterns, building stock, the structure of distribution networks, consumer
behaviors, and so on. However, such exhaustive datasets are rarely freely
available (or available at all) for research use, making it hard for the
research community to pursue these endeavours [19]. Reasons for unavailability
of such data range from privacy concerns to the lack of a system for making
data available to researchers.

Figure 1: Data overview. This figure shows examples of the spatio-temporal resolutions of multiple facets of the dis-aggregated synthetic energy demand data. The figure shows sample data at state, county, and household level at different temporal granularities. The data is generated for all households in the U.S. Table 1: Energy-use datasets published in the residential sector. Authors/Dataset |  Description
---|---
Klemanjak et al. [20, 21] |  A synthetic energy demand dataset was released for 21 appliances in Austria in 2020. Data collected from two households was used to train models and then appropriate noise was added for appliance start times and durations to mimic variations in actual consumption patterns.
Kolter et al. [22, 23] |  The Reference Energy Disaggregation Data Set (REDD) is published by MIT. The dataset contains high-frequency current/voltage waveform data of the power mains in households along with labeled circuits in the house.
Makonin et al. [24] |  The Rainforest Automation Energy (RAE) dataset was published by Harvard in 2017. The dataset contains 1Hz data (mains and sub-meters) from two residential houses.
Murray et al. [25, 26] |  Load measurements from 20 households of UK from a two year longitudinal study.
Pecan Street[27, 28] |  Labeled circuit data for households across major cities in the U.S. This is said to be the most comprehensive dis-aggregate energy data available for the U.S.
Rashid et al. [29, 30] |  The I-blend dataset has recorded minute-level consumption of all the buildings at an academic institute in India over a period of 52 months
Paige et al. [31, 32] |  The flEECe dataset provides energy data at a 1Hz sampling rate for four circuits for six net-zero energy senior housing units in Virginia, USA for nine months
Shin et al. [33, 34] |  The first Korean dataset measuring appliance-level energy data was released in 2019 for 22 houses in Korea.
Kelly et al. [35, 36] |  Power demand is recorded from five houses UK houses at two levels – whole house and individual appliances. This dataset is referred to as the UK-Dale dataset. Two versions of this dataset have been released.
Anderson et al. [37, 38] |  Building-Level fUlly-labeled dataset for Electricity Disaggregation (BLUED) for one household in Pittsburg U.S. for one week. State transition of appliances are labeled and time-stamped, providing the necessary ground truth for the evaluation of NILM algorithms.
Barker et al. [39, 40] |  Electricity usage data is monitored every minute from nearly every plug load from 400 anonymous homes.
Beckel et al. [41] |  Electricity consumption is monitored via smart plugs for six households in Switzerland over a period of 8 months.
Pereira et al. [42, 43, 44] |  Power usage for 44 apartments and 6 homes in Portugal is collected for 264 days at 30 minute intervals. The advanced version of this dataset ‘SustDataED2’ dataset contains 96 days of aggregated and individual appliance consumption from one household in Portugal.
Monacchi et al. [45, 46] |  Common household devices are monitored for power consumption in Austria and Italy (GREEND dataset).
Pullinger et al. [47, 48] |  1-second electricity data is gathered over a period of 23 months from 255 UK homes (IDEAL household energy dataset).
Ruhnau et al. [49, 50] |  Synthetic national time series of heat demand that covers over 16 countries in the EU from 2008 to 2018.

Most of the published energy use data are metered data, a result of
longitudinal studies conducted by researchers (Table 1) with relatively small
samples of households that may not be representative of the wider geographical
region and demographics. Some of these studies monitor households over a
longer period of time (e.g. two years), however, the downside of such
experiments is that it takes a considerable amount of time (e.g. participant
consent, equipment setup, monitoring) and manual effort (e.g., data cleaning,
imputing missing values) before such data is usable. Although these studies
release energy data for free use, many of them limit publishing participant
details (e.g. building characteristics and location, household level
demographics). Participant details are usually withheld due to privacy
reasons/participant consent, lack of information, or unavailability of these
attributes in the free version of the data. Literature has attempted to
address some of these issues by creating appropriate data structures for
releasing appliance metadata information for households alongwith their energy
use data [51, 35]. However, we observe that many of the issues still persist
in the U.S. context. One such example is the Pecan Street Dataport [28]. Pecan
Street Inc. [27] is the largest publisher of energy-use data in the U.S.
through their portal – _Dataport_. They collect energy-use data in California
(CA), Texas (TX), New York (NY), and Colorado (CO). This is a potentially very
useful data set. However, only a small sample ($\sim$25 households in CA and
TX) of energy-use data is freely available for public use and do not contain
sufficient (or any) demographic or building information.

A dataset synthesized over a larger spatial scope offers the opportunity to
study regional and temporal differences in energy use while a smaller region
dataset offers studying energy use patterns that may be particular to the
region. Irrespective of spatial scope, small sample size makes it difficult to
get a good representation of the population variation in the region (e.g.
explaining/exploiting role of household demographics, behavior, and building
characteristics in energy use). In addition to the spatial scope and number of
samples, many of the datasets do not release sufficient (or any) participant
details. Such limited data restricts the usage of these energy-use data for
detailed practical analyses or studying scenario interventions and equity
questions in the grid (e.g., which type of demographic and building stock is
best suited for EV adoption, or how much carbon footprint can be reduced by
retrofitting buildings). Thus, we observe that there is a general sparsity of
large scale high resolution energy use datasets along with detailed metadata
information at household level such as appliance ownership, building data,
important demographic features.

We summarize key drawbacks of energy datasets for the U.S. as follows –
limited spatial scope, small sample size, lack of sufficient household,
appliance, & building metadata. Given these wide array of problems with the
state-of-art energy-use data availability, we introduce synthetic energy use
datasets that are able to address many of these issues. Synthetic data is
defined as data generated by models that provide accurate statistical
representations of the real world. Examples of such data for the smart grid
are synthetic power distribution networks [52], energy consumption profiles
for offices and commercial buildings [53] and for residential buildings [54,
20, 55, 56]. Our work specifically addresses the data scarcity gap in energy
use research for the U.S. residential sector. We propose a synthetic framework
for modeling large-scale high resolution energy use data by integrating
diverse datasets and end-use models for bottom-up dis-aggregate energy
modeling. This results in a novel synthetic energy use dataset (i.e., a
digital twin of household level energy demand) comprising hourly electrical
energy demand profiles for U.S. households. The total electrical energy use is
published as a composition of eight primary end-uses in a household –
heating/air-conditioning (HVAC), lighting, dishwashing, cooking, laundry
(clothes washer and clothes dryer), refrigeration, hot water, and
miscellaneous plug load (vacuuming, computer use, TV). A detailed data-
intensive bottom-up framework is developed to generate synthetic energy-use
profiles by integrating multiple open-source surveys and a synthetic
population for the U.S [57]. A mixture of methods (stochastic, machine
learning, physics-based engineering methods) is used to model different end-
uses in all households that consume electricity as a primary fuel across the
48 contiguous states and Washington, D.C. in North America. To the best of our
knowledge, this synthetic energy-use dataset is the first detailed, large-
scale, freely available household-level electricity consumption behaviors
dataset for the U.S. Our synthetic energy-use infrastructure is well-suited to
solve the newer smart grid problems mentioned earlier. We publish the dis-
aggregated energy use timeseries for all the synthetic households. The
published data is representative of the U.S. households, provide household
level metadata, and are a good representation of the real world energy use.

Table 2: List of primary datasets used for constructing the residential demand models. Dataset |  Description
---|---
| American Time Use
---
Survey (ATUS 2015)
ATUS provides nationally representative estimates of how, where, and with whom
people in the U.S. spend their time, and is the only federal survey providing
data on the full range of activities, from childcare to volunteering. This
survey provides demographic information as well as information on energy-
related activities [58]. 24-hour data is recorded for 5115 participants.
| Synthetic Populations
---
and Ecosystems of
the World (SPEW)
SPEW [59, 57] is a framework that produces synthetic populations for various
countries. We used the open-sourced version of the synthetic population
available for the U.S. constructed for the year 2013. The sampled base
population is the byproduct of American Community Survey (ACS) Public Use
Microdata Sample (PUMS) data. Statistical methods such as Simple Random
Sampling (SRS) and Iterative Proportional Fitting (IPF) [60, 61] are used to
estimate joint distributions of population characteristics given their
marginal distributions at a small geographic level (e.g. PUMA-level for the
U.S.). Data records are available at household level for all of U.S.
Descriptors are available for mapping records from PUMS data onto the base
synthetic population.
| Public Use Microdata
---
Sample (PUMS 2013)
PUMS is a 5% representative sample for a larger region than block group
referred to as a Public Use Microdata Area (PUMA) [62]. PUMAs are described by
the Census as “a collection of counties or tracts within counties with more
than 100,000 people”. These statistical areas are defined for the circulation
of PUMS data. PUMS contains individual records of the characteristics for a 5%
sample of people and their households. One PUMS record is a complete Census
record.
| North American Land
---
Data Assimilation
System (NLDAS)
Hourly temperature data for North America. Data resolution is at 1/8th-degree
grid over North America [63].
| Residential Energy
---
Consumption Survey
(RECS 2015)
U.S. Energy Information Administration (EIA) Residential Energy Consumption
Survey (RECS) [64] data is a national sample survey that collects energy-
related data for housing units. For 2015, data was collected from 5,686
households to represent 118.2 million U.S. households. We use this dataset to
obtain housing unit-specific information such as floor area, main heating
fuel, fuel equipment, indoor temperature setting, presence of air conditioner,
dishwasher, washer, dryer, refrigerator, water heater fuel, water heater size,
water heater age, number of lighting units, etc,.
| National Solar Radiation
---
Database (NSRDB)
NREL provides solar radiation data for the U.S. We use hourly data that comes
from the physics-based approach called the Physical Solar Model (PSM). Data is
available for the U.S. for 1998–2014 [65]. The GHI variable is used as an
indicator of irradiance level in the lighting model. GHI is modeled solar
radiation on a horizontal surface received from the sky. This is measured in
$\frac{\textrm{watt}}{\textrm{meter}^{2}}$.
Miscellaneous |  Appliance power and efficiencies, gallons of hot water required for activities, and any other input data required for models is drawn from surveys and data collected from ground and/or testing [66, 67, 68, 69].
Table 3: Notations Notation |  Description
---|---
$H_{i}$ | Household $i$ drawn from the synthetic population
$P_{i,j}$ | Synthetic household member $j$ of household $H_{i}$
$A_{k}$ | Respondent $k$ from ATUS survey
$S_{l}$ | Household $l$ from RECS survey
${\mathsf{Irr}}^{\mathsf{i}}$ | Irradiance threshold for $H_{i}$. Drawn from a Normal distribution $\mathsf{Normal}(60,10)$
$\langle O_{i,0},\ldots,O_{i,t},\ldots,O_{i,23}\rangle$ | Occupancy time series of synthetic household $i$ over 24 hours, $t\in\\{0,1,\ldots,23\\}$
$\langle\mathrm{Irr}_{0},\ldots,\mathrm{Irr}_{t},\ldots,\mathrm{Irr}_{23}\rangle$ | Hourly irradiance time series of a census tract for a given day in the year 2014
$\langle T^{\mathsf{out}}_{0},\ldots,T^{\mathsf{out}}_{t},\ldots,T^{\mathsf{out}}_{23}\rangle$ | Hourly temperature series of the outside environment for a given day (${}^{\circ}F$)
$\langle T^{\mathsf{in}}_{0},\ldots,T^{\mathsf{in}}_{t},\ldots,T^{\mathsf{in}}_{23}\rangle$ | Thermostat setpoint (${}^{\circ}F$)
$\eta$ | Efficiency of the HVAC equipment and water heaters
$R^{\mathsf{roof}}$ , $R^{\mathsf{wall}}$ | Thermal resistance coefficient for roof and wall for different climate zones
$T^{\mathsf{hot}}_{v}$ |  Temperature (${}^{\circ}F$) of hot water end-point category $v$, where $v\;\in\;\\{\mathsf{shower,bath,cwasher,dishwasher}\\}$
$T^{\mathsf{cold}}_{m,z}$ | Mains water temperature (${}^{\circ}F$) for month $m$ and climate zone $z$
$d\in\mathsf{D}$ |  End-use $d\in\mathsf{D}$ where $\mathsf{D}=\\{\mathsf{hvac},\mathsf{h2o},\mathsf{light},\mathsf{refr},\mathsf{dwasher},\mathsf{cook},\mathsf{cwasher},\mathsf{cdryer},\mathsf{TV},\\\ \mathsf{computer},\mathsf{cleaning}\\}$
$\langle E^{d}_{i,0},E^{d}_{i,t},\ldots,E^{d}_{i,23}\rangle$ |  Hourly energy use profile of $H_{i}$ for a end-use ${d}$ and $t\in\\{0,\ldots,23\\}$
$E^{d}_{i}$ |  Daily energy consumed over 24 hours by end-use $d$ in household $H_{i}$. $E^{d}_{i}=\sum^{23}_{t=0}E^{d}_{i,t}$ and $d\in\mathsf{D}$ and $t\in\\{0,1,\ldots,23\\}$
$\langle G^{\mathsf{h2o}}_{i,0},G^{\mathsf{h2o}}_{i,t},\ldots,G^{\mathsf{h2o}}_{i,23}\rangle$ |  Hourly profile of hot-water use (gallons per hour) of $H_{i}$ for a end-use $\mathsf{h2o}$ and $t\in\\{0,\ldots,23\\}$. $G^{\mathsf{h2o}}_{i,t}=\sum_{v\in\mathsf{V}}G^{\mathsf{h2o}}_{i,t,v}$ where $\mathsf{V}=\\{\text{shower},\text{bath},\text{dishwasher},\text{clothes washer}\\}$
${G}^{\mathsf{h2o}}_{i}$ |  Daily amount of hot water consumed (in gallons) by a household $H_{i}$ in a day. ${G}^{\mathsf{h2o}}_{i}=\sum^{23}_{t=0}G^{\mathsf{h2o}}_{i,t}$
${G}^{\mathsf{h2o}}_{i,v}$ |  Daily amount of water consumed (in gallons) by a household $H_{i}$ in a day by an event $v$. ${G}^{\mathsf{h2o}}_{i,v}=\sum^{23}_{t=0}G^{\mathsf{h2o}}_{i,t,v}$

## Methods

Figure 2: Overview of the energy modeling infrastructure. Many different types
of input data are used in the proposed modeling framework. These are shown at
the top. For complete description of input datasets refer to Table 2. These
datasets are input to different modeling components of the framework. Some
datasets support augmentation of the synthetic population while others are
input to the energy-use models. All the models are described in the
_Methodology_ section. The bottom rectangle describes the recorded data/smart
meter data from different climate zones of the U.S. These datasets are used
for validation of the synthetic energy-use timeseries. The validation block
(yellow backdrop) describes three components of V&V – regional, magnitude, and
structural/shape comparisons. This line of validation covers (a) different
temporal aspects (hourly and daily), (b) spatial aspects in terms of regions
and seasons, (c) diversity aspect of the large-scale synthetic data. The blue
text refers to the V’s of big data. Each colored block possesses the given V
characteristic.

This section describes the datasets and models employed to generate synthetic
energy use time series at the household level, see Table 2. All notations used
in the paper are described in Table 3.

The presented framework is composed of a synthetic representation of the U.S.
population, regression models for surveys, and bottom-up energy use models. A
synthetic population is composed of households and people in households. The
synthetic households are generated using census surveys and statistical
methods such that the synthetic population is _statistically similar_ to the
original population. An open-source version of the U.S. synthetic population –
Synthetic Populations and Ecosystems of the World (SPEW) [59, 57] is used in
our framework. The SPEW synthetic population is comprised of demographic
characteristics of synthetic households and synthetic individuals. The
synthetic population is created using U.S. census data such as PUMS (Table 2)
and statistical methods such as sampling and the Iterative Proportional
Fitting (IPF) method [70].

The SPEW households are made of basic demographic (e.g., income, age) and
locality information. Although the SPEW population is representative of the
U.S. population on a finer spatial resolution, it is not equipped with energy
and activity related information (e.g., building characteristics, time spent
at home, number of cooking activities) necessary for estimating energy use at
household level or person level. Building stock, energy and activity related
information is collected by national surveys in the U.S. – Residential Energy
Consumption Survey RECS [64] and American Time Use Survey ATUS [58]
respectively. The basic synthetic population is augmented with energy and
activity related attributes by building machine learning models. This
augmentation is called as the _enrichment step_. The enriched synthetic
population along with other freely available data sources can be used together
as inputs to the energy use modeling framework. The energy use modeling
framework has six models for representing nine energy uses – HVAC, lighting,
domestic hot-water, refrigerator, dishwasher, cooking, clothes washer, clothes
dryer, and miscellaneous plug load such as TV, computer use, cleaning
activities (e.g., vacuuming). The first subsection describes the modeling
details of the _enrichment step_ and the following subsection describes energy
demand models.

### Enrichment models

The enrichment models support creating comprehensive synthetic structures for
calculating residential energy usage. This step is called as the _enrichment
step_. Refer to Figure 2 for a pictorial representation of the overview of the
framework. Datasets used in this workflow are described in Table 2. Since the
demographic features available in the synthetic population are not sufficient
for computing energy usage, it is made richer by adding layers of information
related to building stock and energy consumption from the RECS survey such as
building characteristics, appliance ownership, and thermostat set-point
behaviors. This mapping of features is made by building inference tree models.
Activity schedules for a normative day of an ATUS survey respondent are
attached to synthetic individual by building a multivariate random forest
regression model. These models are described below.

The ATUS model. The ATUS data provides nationally representative surveys of
people’s activities in different location types such as childcare in or
outside the house, time spent at work, laundry time at home, waiting times in
hospital, and so on, see Table 2 for a description. The time-use diaries of
the survey individuals can be attached to synthetic individuals by matching an
appropriate survey individual to a synthetic individual. In our work, we
consider _appropriate matching_ based on amount of time a person spends in
different location types such as home, work, school, shopping, and other
miscellaneous locations. This seems a reasonable approach because we are
interested in learning how an individual spends 24 hours of the day by
categorizing the amount of time spent at important location types – for e.g.,
the time spent in different location types for a person works full-time is
quite different than a house bound senior citizen or a college student. This
rationale of assigning survey respondents to synthetic individuals is also
presented in prior work by Lum et al [71].

Random forest regression method is used to build a model that predicts the
amount of time a person spends in locations types such as home, work,
shopping, other, school, and trip counts during the day. Thus, six dependent
variables are modeled – trip count during the day and time spent at each
location type - home, work, shopping, other, school. Independent variables
used to build the model are as follows – number of members in the household
($\mathsf{hsize}$), number of children ($\mathsf{nchild}$), age
($\mathsf{age}$), working hours ($\mathsf{wrkhrs}$), gender
($\mathsf{gender}$), income modeled as a categorical variable
($\mathsf{hinc2,hinc3}$), and binary variables such as an American citizen or
not ($\mathsf{nativity}$), worker or not ($\mathsf{worker}$), owns home or not
($\mathsf{ownhome}$), has a phone or not ($\mathsf{tel}$), and race related
variables such as if person is white, Hispanic, black, or Asian
($\mathsf{white}$, $\mathsf{hispanic}$, $\mathsf{black}$, $\mathsf{asian}$).
Figure 3 shows example of feature importance for two dependent variables.

Figure 3: Impurity-based feature importance and correlation. Each plot shows
Gini importance of features for two dependent variables – home and work. The
x-axis shows independent variables in order of importance based on
_IncNodePurity_. The selection of the parameters for ‘ntree’ (number of
decision trees) and ‘node size’ (minimum size of terminal nodes). Eight
conditions are tested for the combination of the two parameters: ntree=500,
1000, 1500, and 2000; node size=5, and 10. The plots show robust results
across the different conditions. According to the plots, the following five
independent variables – $\mathsf{wrkhrs,worker,age,hinc3,hsize}$ mostly affect
all the dependent variables. The right-hand y-axis shows the absolute Pearson
Correlation Coefficient. The positive and negative coefficients are
distinguished by blue dots and squares, respectively. Except
$\mathsf{wrkhrs,worker}$, all other independent variables weakly correlated
with the dependent variables.

Once the model is trained on ATUS respondents, a synthetic person $P_{i,j}$ is
randomly assigned a survey individual from the leaf nodes in the trained
ensemble model. Thus, the result gives every synthetic individual a time-use
diary. The energy-use models will extract home activities from a time-diary
and also build a household-level occupancy schedule over the 24-hour duration,
denoted as $\langle O_{i,0},O_{i,1},\ldots,O_{i,23}\rangle$. These are used as
an input to the energy use models. Synthetic household member activity
scheduling conflicts are handled in the activity model.

The RECS mapping model. The baseline synthetic population does not have any
building structural characteristics and appliance ownership information. These
salient features are important for modeling different categories of energy use
and are available in the RECS survey. We overlay RECS household attributes
onto a synthetic household by building multivariate conditional inference
trees [72, 73]. Conditional inference tree is a non-parametric class of
regression trees that uses recursive partitioning of dependent variables based
on the value of correlations. Four dependent variables are modeled – square
footage of the dwelling, presence of laundry appliances, presence of air
conditioner, presence of dishwasher. The independent variables are year in
which the house was built, occupancy time of the current tenants, own or rent
the residence, total number of rooms, income, number of refrigerators, number
of members in the household, dwelling type, dwelling is located in urban or
rural area, primary heating fuel type. The independent variables are common
attributes between RECS survey records and synthetic household records.
Conditional inference trees are trained on different census regions in the
U.S. to tease out regional differences. A RECS household $S_{l}$ is randomly
selected from the appropriate leaf nodes of the conditional inference tree and
assigned to the synthetic household $H_{i}$ every time a new simulation is
run. This dynamic assignment introduces stochasticity when the simulation is
executed for same and/or different days.

### Energy use modeling

The enriched synthetic population (i.e., the output of the _enrichment step_)
enables encoding of behaviors (time spent in different energy related
activities at home), normative attributes (e.g., square footage, age, income,
gender), declarative attributes (e.g., individual activities as a sequence)
and procedural attributes (e.g., behaviors capturing dependencies,
interactions, frequency of performing activities) into the knowledge required
for building energy use profiles [74]. The synthetic infrastructure is
leveraged to build six energy use models (Figure 2). Nine end-uses are
synthesized for each household. These end-uses are divided into two parts –
Thermostatically Controlled Loads (TCL) and appliance use. For a household
$i$, nine end-uses published in the data are –

  1. 1.

HVAC ($E^{\mathsf{hvac}}$). This category includes heating and cooling
electric load from central air conditioning during hot days and electric
furnace/heater used during cold days. This is a TCL load.

  2. 2.

Domestic hot water use ($E^{\mathsf{h2o}}$). Energy consumed for heating water
that is needed for personal grooming activities such as shower/bath, laundry
activities such as using clothes washer, and dishwasher. This is a TCL load.

  3. 3.

Dishwasher ($E^{\mathsf{dwasher}}$). Energy used by dishwashers.

  4. 4.

Clothes Washer ($E^{\mathsf{cwasher}}$). Energy used by electric clothes
washers.

  5. 5.

Clothes Dryer ($E^{\mathsf{cdyer}}$). Energy consumed by dryer.

  6. 6.

Cooking ($E^{\mathsf{cook}}$). Energy consumed by electric cooking range,
oven, and other kitchen appliances such as coffee maker, microwave, toaster,
etc.

  7. 7.

Miscellaneous plug load ($E^{\mathsf{misc}}$). This type of energy indicates
plug load attributed to cleaning activities and electronic devices such as TV,
computers, other smaller electronic gadgets.

  8. 8.

Refrigeration ($E^{\mathsf{refr}}$). Energy consumed by refrigerators.

  9. 9.

Lighting ($E^{\mathsf{light}}$). Energy consumed by lighting units.

Table 3 describe the notations used in the methodology sections. The total
energy summed over 24 hours (${E}^{\mathsf{total}}_{i}$) of a household $i$ is
given by the equations below –

$\displaystyle{E}^{\mathsf{total}}_{i}$
$\displaystyle={E}^{\mathsf{TCL}}_{i}+{E}^{\mathsf{appliances}}_{i}$ (1a)
$\displaystyle{E}^{\mathsf{TCL}}_{i}$
$\displaystyle={E}^{\mathsf{hvac}}_{i}+{E}^{\mathsf{h2o}}_{i}$ (1b)
$\displaystyle{E}^{\mathsf{appliances}}_{i}$
$\displaystyle={E}^{\mathsf{dwahser}}_{i}+{E}^{\mathsf{cook}}_{i}+{E}^{\mathsf{cwasher}}_{i}+{E}^{\mathsf{cdryer}}_{i}+{E}^{\mathsf{light}}_{i}+{E}^{\mathsf{refr}}_{i}+{E}^{\mathsf{misc}}_{i}$
(1c) $\displaystyle{E}^{\mathsf{misc}}_{i}$
$\displaystyle={E}^{\mathsf{tv}}_{i}+{E}^{\mathsf{computer}}_{i}+{E}^{\mathsf{cleaning}}_{i}$
(1d)

### HVAC model $E^{\mathsf{hvac}}$

According to the U.S. Energy Information Administration (EIA) [75], HVAC is
responsible for the highest proportion of energy consumption in households.
The HVAC model calculates how much energy is required to maintain
ambient/comfort temperature indoors. This is dependent on factors ranging from
the area of the house, outdoor temperature, efficiency of HVAC equipment, and
so on. Occupant behaviour of thermostat settings in different seasons and
household occupancy during the day play an important role in understanding
thermal comfort levels and how its effect on electricity consumption.
Engineering and statistical approaches [76] are presented in the literature to
simulate energy consumption of heaters/furnace and air conditioners [77, 78,
79, 80]. We adopt the engineering based approach from Subbiah et al. [80]
where the function of heating/cooling a household $H_{i}$ at hourly intervals
is defined as:

$E^{\mathsf{hvac}}_{i,t}=\frac{\Delta
T}{\eta}\times\left(\frac{\textrm{FloorArea}_{i}}{R^{\mathsf{roof}}}\;+\;\frac{\textrm{WallArea}_{i}}{R^{\mathsf{wall}}}\right)$
(2)

Here $E^{\mathsf{hvac}}_{i,t}$ is the energy consumed by household $H_{i}$ at
the end of hour $t$ in kWh by heating/cooling equipment to maintain thermal
comfort. $\textrm{FloorArea}_{i}$ is the floor area and
$\textrm{WallArea}_{i}$ is the wall area (extrapolated from floor area [80])
of $H_{i}$. The quantities $R^{\mathsf{roof}}$ and $R^{\mathsf{wall}}$ are
R-values (insulation level) for households in different climate zones, while
$\eta$ is defined in Table 3. Next, $\Delta T$ is the absolute difference
between $T^{in}_{t}$ and $T^{\mathsf{out}}_{t}$, and $T^{\mathsf{in}}_{t}$ is
indoor thermostat temperature at hour $t$. The hourly outside temperature
($T^{\mathsf{out}}_{t}$) is obtained from NOAA NLDAS data mentioned in Table
2. Efficiency and insulation data is obtained from guidelines published by
EIA. All other household attributes are obtained from the enriched synthetic
population. Depending upon occupancy patterns throughout the day, changes in
thermostat behaviors are assigned to each household. Heating and cooling
threshold temperatures for appliance on/off times are taken from the
thermostat study published by NREL in 2017 [81].

### Domestic Water Heating Model $E^{\mathsf{h2o}}$

The EIA [75] EIA shows that 17%-32% of the household energy use is attributed
to domestic hot water use (DHW). Literature shows models used for estimating
hot water demand at multiple temporal resolutions – annual, daily, hourly, and
minute intervals. One of the initial models for estimating load profiles of
hot water demand was developed in 2001 by Jordan et al. [82] for a period of
one year for temporal resolutions of 1 min, 6 min, and 1 hour. However, this
work does not consider historical nor factual flow rates to determine how much
hot water ($\mathrm{gallons/day}$) is used by a household. A follow-up paper
was developed for synthesizing water demand profiles for Switzerland [83] by
calibrating this model using field data. A model to simulate yearly DHW event
schedule for a single-family household was developed by Hendron et al. [84]
from the National Renewable Energy Laboratory (NREL) in 2010. The simulator
used two surveys that collected information about water demand in U.S.
households for five categories: sink, bath, shower, clothes washer, and
dishwasher. This model has been widely accepted in the literature. One recent
example of the adaptation of Hendron’s model is for simulating hot water
demand in Canadian households [85]. The model is calibrated for survey data
collected for Canada and appropriate adjustments are made with respect to
Canadian lifestyles.

For our model, we use the distributions of duration and flow rates of
activities involving hot water usage such as bath/shower, clothes washer, and
dishwasher from Hendron et al. Note that duration and flow rates can take
negative values (Table 4). The flow rate is capped to 0.05gpm and the duration
is capped to 1 minute for any negative value [84]. Table 4 characterizes the
average count of daily events, duration, and flow rates. The values of hot
water temperature for different uses and the cold water inlet temperature are
obtained from studies conducted by NREL in different regions of U.S. [68, 69,
86] An engineering based approach is used to estimate hot water usage [68, 80]
in household $i$ for event $v$ at time $t$

$\begin{array}[]{l}E^{\mathsf{hot}}_{v}=\frac{G^{\mathsf{hot}}_{v,i,t}\;\times\;\Delta
T}{\eta}\times 0.00189\;,\quad\text{where}\\\
G^{\mathsf{hot}}_{v,i,t}\;=\;\mathsf{duration}_{v}\;\times\;\mathsf{flow\\_rate}_{v}\;,\quad\text{and}\quad\Delta
T\;=\;T^{\mathsf{cold}}_{m,z}\;-\;T^{\mathsf{hot}}_{v}\;.\end{array}$ (3)

The gallons of hot water $G^{\mathsf{hot}}_{v,i,t}$ consumed by event $v$ is
computed as a product of $\mathsf{flow\\_rate}$ (gpm) and $\mathsf{duration}$
(minutes). Both these characteristics are drawn from distributions in Table 4.
$E^{\mathsf{hot}}_{v}$ is the energy consumed by the event $v$ to heat
$G^{\mathsf{hot}}_{v}$ gallons of water. Last four entries in the Table 3
shows summation of multiple events occurring across the time horizon. Here
$\eta$ is the efficiency of the electric water heaters. Surveys conducted by
NREL have shown that $\eta$ is a complex function of storage capacity of water
heater, type of water heater, age of water heater. No distributions are
available for $\eta$ in the current studies. Field data collected from NREL
surveys [69, 68, 86] show that the efficiency varies anywhere between 80%-99%.
Here 0.00189 ($\frac{\text{kWh}}{\text{gal}\;^{\circ}\text{F}}$) is a
conversion constant obtained from Subbiah et al. [80], and $\Delta T$ is the
temperature difference (${}^{\circ}\text{F}$) between mains (inlet) water
temperature $T^{\mathsf{cold}}_{m,z}$ for a given month $m$ in a climate zone
$z$ and the water temperature required for a particular end-point. The values
for $T^{\mathsf{cold}}_{m,z}$ and $T^{\mathsf{hot}}_{v}$ are obtained from
NREL surveys [68, 69]. Whenever the activity model detects the presence of an
event $v$, we calculate the energy used by hot-water for the event using
Equation 3. Note that we compute hot water energy usage only for synthetic
households having electric water heaters.

Table 4: Hot water model characteristics Event $v$ | Range of $T^{\mathsf{hot}}_{v}$ (F) |  | Flow rate (gpm)
---
$\mu$, $\sigma$, distribution
| Duration (minutes)
---
$\mu$, $\sigma$, distribution
Shower | [105,116] | 2.25, 0.68, $\mathsf{Normal}$ | 7.81, 3.52, $\mathsf{Normal}$
Bath | [105,116] | 4.40, 1.17, $\mathsf{Normal}$ | 5.65, 2.09, $\mathsf{Normal}$
Dishwasher | [120,140] | 1.39, 0.20, $\mathsf{Normal}$ | 1.53, 0.41, $\mathsf{LogNormal}$
Clothes washer | [60,130] | 2.20, 0.62, $\mathsf{Normal}$ | 3.05, 1.62, $\mathsf{Normal}$

### Lighting $E^{\mathsf{light}}$

Lighting accounts for 5–10% [75] of the consumption with lighting usage in
residential setting mainly characterized by outdoor lighting conditions and
occupancy schedules in households [87]. A Markov-chain approach is adopted by
Widen et al. [88] for modeling lighting demand in Swedish households using
time use data in Sweden. A stochastic model is developed for residential
lighting estimation for the city of Cordova in Spain by Palacios-Garcia [89]
based on a model developed by Stokes et al. [90] using measured lighting data
for 100 UK homes. Another stochastic model is developed by Richardson et al.
[91] for UK households using time-use data and lighting data from the Energy
Information Administration(EIA).

We build a stochastic model for lighting demand in U.S. dwellings by building
on design concepts from work done by Richardson et al. [91], Stokes et al
[90], and Paatero & Lund et al. [92]. Richardson’s model is particularly
interesting since it supports important characteristics of light usage such as
‘co-use’ and ‘relative weights’. The model uses the concept of ‘co-use’ of
lighting, i.e., lighting in a dwelling is often shared by household members in
the same space of the dwelling at the same time. The model also considers that
all lighting units are not used at the same frequency (e.g. frequently
occupied rooms such as kitchen space and living area will use more lighting
than other rooms) and employs a weighting scheme to indicate relative usage.

Outdoor lighting conditions are modeled using irradiance time series. It is
obtained from NSRDB described in Table 2. Hourly irradiance data is collected
using the NSRDB API for the 365 days of the year 2014 at census tract
resolution for the U.S. Thus, all synthetic households in a census tract use
the same irradiance time series for a given day. The household level hourly
occupancy profile $\langle O_{i,0},O_{i,1},\ldots,O_{i,23}\rangle$ is
developed by examining activities of awake synthetic household members of
$H_{i}$ at home. Presence of awake occupants in the dwelling support the
decision making of light switch-on event. The distribution of lighting units
in households are derived from the RECS survey. In general, distribution of
lighting units of a $H_{i}$ is taken from the matching $S_{l}$. Three types of
lighting units are considered: incandescent, CFL, and LED. Power ratings of
lighting unit categories are taken from a study conducted by the Bonneville
Power Administration (U.S.) where lighting fixtures were analyzed for a sample
of 161 Northwest residences [93]. For a given simulation day, we define an
irradiance threshold ($\mathsf{Irr}^{\mathsf{i}}$) for a household $H_{i}$. It
indicates that occupants may consider switching on lights when outdoor
lighting is less than $\mathsf{Irr}^{\mathsf{i}}$. $\mathsf{Irr}^{\mathsf{i}}$
is sampled from a normal distribution [91] $\mathbf{\mathsf{Normal}}(60,10)$.
All notations used in the model are described in Table 3. Annual lighting data
for the U.S. is summarized for different household sizes from the RECS survey.

Literature shows that lighting usage increases by number of occupants in the
household, however, the lighting usage does not double for every occupant
added in the house. In order to simulate shared lighting usage, the concept of
effective occupancy [91] of a household
$\langle\hat{O}_{i,0},\hat{O}_{i,t},\ldots,\hat{O}_{i,23}\rangle$ is
introduced. Effective occupancy ($\hat{O}_{i,t}$) is defined as a function of
active occupancy ($O_{i,t}$). The values for effective occupancy are derived
by scaling the annual lighting demand by household size such that the
effective occupancy of a dwelling with one active occupant is one. The next
step is to obtain the details of lighting units in a household. The proportion
of lighting unit types are obtained from a RECS household $S_{l}$ that matches
$H_{i}$ (RECS Model). Power ratings are attached to each lighting unit. In
general, not all lighting units are used at the same frequency. This is
observed in literature surveys such as DECADE report [94]. The frequency of
usage of lighting units in households can be roughly modeled as a natural log
curve [91], however, no formal methods have been presented in the literature
due to lack of quantitative data. We use the natural log curve presented in
Richardson et al. [91] to model the relative usage of a lighting unit. Once
weights are assigned to lighting units, the probability of a switch-on event
for every lighting unit is calculated at a regular time interval (in our case
1 hour). The probability of a switch-on event $P^{\mathsf{on}}_{b}$ of
lighting unit $b$ at hour $t$ is calculated as

${}\begin{array}[]{l}P^{\mathsf{on}}_{b}\;=\;\mathbb{I}_{b}\;\times\;b^{\mathsf{weight}}\;\times\;\hat{O}_{i,t}\;\times\;\gamma\;,\quad\text{where}\\\
\mathbb{I}_{b}\;=\;\begin{cases}1&\text{irradiance threshold condition is
$\mathsf{True}$ for bulb $b$ at time $t$
$\mathsf{if}$}\;\;\mathsf{Irr}_{t}\leq\mathsf{Irr}^{\mathsf{i}}\;,\\\
0&\text{otherwise.}\end{cases}\end{array}$ (4)

Here $b^{\mathsf{weight}}$ is sampled from a natural logarithmic curve,
$\gamma$ is a calibration constant used to achieve the appropriate annual
lighting consumption for the U.S., and $\hat{O}_{i,t}$ is the effective
occupancy of $H_{i}$ at time $t$. If a switch-on event occurs, then energy
consumption is calculated for the respective lighting unit $b$. The lighting
duration is picked randomly from the distribution described in Stokes et al.
[90].

### Refrigeration $E^{\mathsf{refr}}$

The energy consumed by a refrigerator depends upon its size, age, ambient
temperature, and several other factors as described in literature. They
consume 3%–5% of the total residential energy usage. Shimoda et al. [78] show
that the daily refrigerator consumption is affected by outside temperature,
while Tsuji et al [79] show a linear relationship between outside temperature
and annual refrigerator demand. Both these work are done in context of
refrigerators in Japan. The Lawrence Berkeley National Laboratory in
California uses field metered energy use data from $\sim$1500 refrigerators
and freezers to develop a model that predicts annual usage of different
freezer and refrigerator categories [95]. All of the above models collected
relevant data from the field or utilized detailed surveys on refrigeration.

Our approach is to develop a regression model for predicting daily
refrigerator usage (kWh/day) of a household (${E}^{\mathsf{refr}}_{i}$) as a
function of outside environment temperature. The model is trained with the
metered refrigerator usage data from Pecan Street Inc, where 30% of the total
metered data is used for training and testing the model. The 30% data is
obtained by conducting stratified sampling based on climate zones and daily
average temperature bins. The dependent variable is the daily refrigerator
usage ${E}^{\mathsf{refr}}_{i}$ in kWh/day for $H_{i}$. The independent
variables are daily average temperature $\hat{T}^{\mathsf{out}}$
(${}^{\circ}F$) and categorical attributes indicating three major climate
zones. The 24 hour load profile of a refrigerator $\langle
E^{\mathsf{refr}}_{i,0},E^{\mathsf{refr}}_{i,1},\ldots,E^{\mathsf{\mathsf{refr}}}_{i,23}\rangle$
is constructed from the daily usage, and the variation in the hourly usage of
the refrigerator is modeled using a Guassian distribution. The refrigerator
operates in an automated/standby mode, that is, occupant presence does not
influence the energy consumption of this activity [79, 80]. Thus, computing
the 24 hour profile of the refrigerator by adding a small Gaussian noise to
the hourly load can be considered acceptable. The validation section shows
that addition of this noise creates good match to real data.

Table 5: Summary of referenced end-use modeling methods, including how these models are extended in this paper. End-use | Relevant models |  Our approach
---|---|---
$\mathsf{HVAC}$ |  Muratori et.al [77], Subbiah et.al [80], Thorve et.al [54], Tsuji et.al [79] |  Our model is based on the approach adopted in Subbiah et.al [80] and Thorve et.al [54]. These models were specific to Virginia state. The method employed in these works as well as ours is a physics model. This model is also documented in NREL Technical Reports. Additional details about thermostat settings, building characteristics such as insulation are obtained from RECS survey, EIA website, and NREL Technical Reports.
$\mathsf{DHW}$ |  Maguire et.al [68], Hendron et.al [84], Thorve et.al [54] |  Hendron et.al [84] and Maguire et.al [68] present a general stochastic method to reproduce sample hot water draws based on two water usage surveys conducted in the U.S. The analyses concludes by reporting distributions related to hot water usage events such as showering, using dishwasher, and using clothes washer. Some of these results are summarized in Table 4 and used in our model. Hot and cold water temperatures for specific end-uses are obtained from NREL surveys. The above model does not consider the setting of specific household schedules. This context of household occupancy and occurrence of events is added to an existing model in literature presented in Thorve et.al [54] in order to schedule these hot water usage events.
$\mathsf{light}$ |  Richardson et.al [91], Stokes et.al [90], Paatero & Lund et.al [92] |  We mainly improve upon the stochastic lighting model developed for U.K. household by Richardson et.al by adding context of U.S. households such as household size, household occupancy, annual lighting consumption in the U.S. for different household sizes, calibration of $\gamma$ for U.S. households, and proportion of light bulbs in the U.S. households and their power ratings. The probability of switch-on event is modeled from Paatero & Lund et.al [92] and Richardson et.al [91]. Duration of switch-on event is taken from Stokes et.al [90]. Power ratings for different categories of lighting units in U.S. is obtained from a study conducted by Bonneville Power Administration [93]. Proportion of lighting units in U.S. households and annual lighting consumption by household size is derived from RECS survey. Irradiance data for the U.S. is obtained from NREL.
$\mathsf{refr}$ |  — |  A linear regression model is developed to predict daily refrigerator usage for a household based on outside temperature and climate zones.
$\mathsf{misc}$, $\mathsf{act}$ |  Subbiah et.al [80], Thorve et.al [54], Tsuji et.al [79] |  All the three referenced models have inspired the design of activity models involving use of appliances. The actual activity occurrence is obtained from the individual/household occupancy schedule. Duration and power usage distributions of appliances is modeled from NIST datasets [66, 96, 67] and other datasets [97, 98, 99, 100]. The start time is chosen randomly within the duration reported by ATUS individuals and the power ratings and duration of the activity/appliance is selected from the above mentioned distributions.

### Activity model $E^{\mathsf{appliances}}$

The energy consumption in a households that is attributed to appliance usage
and plug load is 20%–26%. This energy is a result of the occupants’ desires to
perform activities such as taking baths, making hot meals, using the
dishwasher, doing laundry, charging electronics such as TVs and computers, or
using any other appliances that consume electricity. Equations 1b and 1c are
used in this model. Based on the aforementioned end-uses, appliance usage
behavior is characterized by [79] through operational mode of appliances,
duration of operation, power consumption, limit on daily event occurrence, and
saturation rate. Operational mode of appliances describes the functioning
appliances and related behavior that can be categorized into three types:
automatic (appliance use is independent of person), semi-automatic (appliance
turned on by household member but turned off automatically), and manual
(appliance turned off and on manually). The saturation rate can be used to
determine the presence and/or penetration of certain appliances in households.
Generally, the operational mode of appliances and saturation rate are
deterministic in nature. However, parameters such as probability of activity
occurrence, start time, duration, power consumption, and maximum occurrences
vary from household to household and day to day. In general, some appliance
usages can overlap and/or occur in parallel. These details are handled in this
model.

Table 6 outlines all the modeled activities and related appliances, their
modes of operation, maximum allowed daily occurrences, activity duration, and
power consumption. The distributions marked with an asterisk (*) denote that
they are modeled by engineering judgement and/or other sources such as Energy
Calculator (energyusecalculator.com). Power rating distributions for
dishwashers are obtained from a survey conducted by NIST [67, 96]. Power
ratings and duration distributions for laundry appliances are derived from
literature [80, 54] and surveys [96]; power ratings for appliances in
$\mathsf{cook}$ activity include electric ovens, microwaves, and electric
cooktops (small- and large burners.) Power rating distributions for these
appliances are derived from the NIST efficiency study [66], and durations of
appliance usage are obtained from ATUS data, where the maximum limit for
cooking activities is capped to three. Sample power ratings for TVs are
observed from EnergyStar reports [98] and modeled using a normal distribution.
The $\mathsf{tv}$ activity duration is modeled as a log-normal distribution
after examining the ATUS survey data. Power ratings for $\mathsf{computer}$
use activity are derived from a small study conducted by EnergyStar [97].
Standard values for charging duration are used from reputed laptop
manufacturers. Vacuum related data are obtained from EnergyStar vacuum report
and a survey conducted by Electrolux covering 28,000 consumers from 23
countries including U.S. [99, 100]. We assume that all households have vacuum
cleaners. The usage frequency of vacuuming is 1-5 times per week [100] and the
maximum number of daily occurrences is 1. Assuming $\mathsf{Normal}$
distribution for power ratings and duration of appliance usage is reasonable
after examining rudimentary results from surveys/reports. The results of the
hot water usage study conducted by NREL [86, 84] as summarized in Table 4 show
that most of the processes can be modeled as a $\mathsf{Normal}$ distribution.

Table 6: Modeled activity and appliance usage behaviors Activity | Appliance | Mode |  | Max
---
occ.
| Duration
---
(minutes)
Power (W) | Hot Water
$\mathsf{dwasher}$ | dishwasher | Semi-automatic | 2 | $\mathsf{Normal}(90,30)^{*}$ | $\mathsf{Normal}(900,100)$ | Yes
$\mathsf{cwasher}$ | clothes washer | Semi-automatic | 2 | $\mathsf{Normal}(45,20)^{*}$ | $\mathsf{Normal}(400,50)^{*}$ | Yes
$\mathsf{cdryer}$ | clothes dryer | Semi-automatic | 2 | $\mathsf{Normal}(45,20)^{*}$ | $\mathsf{Normal}(2500,200)^{*}$ | No
$\mathsf{cook}$ |  | oven
---
microwave
cooktop (large)
cooktop (small)
| Manual/
---
Semi-automatic
3 | $\mathsf{LogNormal}(3,0.96)$ |  | $\mathsf{Normal}(1426,13.3)$
---
$\mathsf{Normal}(880,14)$
$\mathsf{Normal}(213,1.2)$
$\mathsf{Normal}(393,3.1)$
No
$\mathsf{tv}$ | television | Manual | – | $\mathsf{LogNormal}(4.24,0.79)$ | $\mathsf{Normal}(120,20)^{*}$ | No
$\mathsf{computer}$ |  | desktop
---
notebooks
Manual | – | $\mathsf{Normal}(90,30)^{*}$ |  | $\mathsf{Normal}(191.5,32.7)$
---
$\mathsf{Normal}(60.5,20.5)$
No
$\mathsf{cleaning}$ | vacuum | Manual | 1 | $\mathsf{Normal}(30,15)$ | $\mathsf{Normal}(1200,300)$ | No

The activity model simulates appliance usage based on activity indicators
provided by ATUS when the occupant is present in the house. Considering the
presence of appliance in each household (from matching RECS household) The
time use diaries of adults in the synthetic population and frequency of
occurrence of appliance usage such as dishwasher and laundry, and activities
such as cooking are taken from RECS household. The activity model focuses on
activities performed by an individual when at home. Similar to lighting,
activities such as cooking, vacuuming, and leisure activities such as watching
TV are shared by household members. A procedure is outlined below for
generating household level activity sequence $\mathsf{ActSeq}_{i}$. Let $M$ be
the number of adult members in the synthetic household. Then each household
member $P_{i,j}$ has an activity sequence $\mathsf{ActSeq}_{i,j}$. The goal is
to find one household level activity sequence $\mathsf{ActSeq}_{i}$ composed
of $n$ activities (individual + shared appliance usage related activities)
such that the sequence satisfies following constraints:

  1. 1.

Each activity is performed when at least one occupant is home.

  2. 2.

The limit on repeated usage is respected for each activity type.

  3. 3.

Presence of appliance is considered for activities such as dishwasher, and
laundry appliances.

Once the above constraints are satisfied, a start time is randomly selected
for each activity from the activity duration reported by ATUS. The actual
duration and power ratings for appliances used in different activities is
chosen from Table 6.

Figure 4: Data organization. Dataset is available in the form of csv files.
The files are organized by dates (temporal) and states (spatial). The blue
text indicates the type (e.g. folder, file, record). The text within angular
brackets denotes nomenclature templates of folders and files. A record csv
file contains energy use data and metadata for a synthetic household in the
SPEW population. There will be one file per county and date. One day generates
several GBs of data.

## Data Records

The dataset for the entire year of 2014 for U.S. households is publicly
available for download from the net.science repository through University of
Virginia Dataverse [101]. The dataset is available in the form of csv files.
It is organized in folders according to date and state. Figure 4 shows the
hierarchy of data organization and file name templates. Each file corresponds
to a U.S. county identifier and date. A county identifier is a FIPS code. FIPS
codes are numbers which uniquely identify geographic areas by the U.S. census.
A record in the file corresponds to a synthetic household. The record includes
synthetic household metadata and energy data for that particular date. All
energy related data is in kWh. All the energy data is timestamped by local
timezones in the country. A data header codebook is also included in the
downloads. Note that, this work was reviewed by the University of Virginia’s
Institutional Review Board (IRB) and was determined to be exempt from board
IRB approval, as this research project did not involve human subject research.

Figure 5: Data Attributes. 24-hour dis-aggregated hourly household energy demand profiles are made available. 1-24 indicates the hour starting midnight. Eight end-use profiles are described (lines 3-10). Table 7: Datasets used for validation Climate | Location | Source | Year |  | Sample
---
size
| Area
---
type
Resolution |  | Is open-
---
source
| Is data
---
complete?
| Is data
---
dis-
aggregated?
| Hot-
---
Humid
Austin,TX |  | Pecan
---
Street
2018 | 25 | Urban |  | 15-min
---
Yes | Yes | Yes
| Hot-
---
Humid
Horry,SC |  | NRECA
---
2017 |  56000 |  | Rural
---
Semi-
urban
| Hourly
---
No | Yes | No
| Mixed-
---
Humid
| Rappaha-
---
nnock
in VA
| NRECA
---
2016 | 100 | Rural |  | Hourly
---
No | Yes | No
Cold |  | Tompkins
---
Cayuga
in NY
| Pecan
---
Street
2019 | 25 | Urban |  | 15-min
---
Yes | No | Yes
Cold |  | Los Alamos
---
in NM
| Open data
---
Dryad
repository
| 2014
---
1600 |  | Semi-
---
urban
| Hourly
---
No | Yes | No
Cold |  | MT
---
| NEEA
---
2019 | 9 | - |  | Hourly
---
Yes | No | Yes
Cold |  | ID
---
| NEEA
---
2019 | 19 | - |  | Hourly
---
Yes | No | Yes
| Cold
---
Marine
| OR
---
| NEEA
---
2019 | 102 | - |  | Hourly
---
Yes | No | Yes
| Cold
---
Marine
| WA
---
| NEEA
---
2019 | 78 | - |  | 15-min
---
Yes | No | Yes
| Hot-Dry/
---
Mixed-
Dry
| San Diego
---
in CA
| Pecan
---
Street
| 2014
---
2015
2016
25 | Urban |  | 15-min
---
Yes | No | Yes

## Technical Validation

Three studies are presented for validating the synthetic energy profiles. The
first study quantifies the similarity between the real and synthetic energy
use probability distributions using Jensen-Shannon and Hellinger distance.
Comparisons are performed by end-use for real and synthetic data in all
representative locations of the U.S. Strong similarities are observed for
appliance use distributions between real and synthetic data as well as across
spatial locations. TCL loads show differences in distributions across
locations. The second study examines variations in the 24-hour energy use
timeseries in real and synthetic data in all representative locations in the
U.S. We uncover unique energy use patterns in the real and synthetic datasets
and study similarities in patterns using unsupervised learning. We introduce
two metrics in the process – coverage and closeness. The synthetic data has
patterns similar to that of real data. The last study is focused on observing
trends in the synthetic energy use in different representative locations in
the U.S. We notice that the synthetic data is able to incorporate the effects
of mixture of variables such as weather, irradiance, building attributes and
demographic characteristics on household level energy usage. The study is a
quick demonstration of energy use variability at multiple spatio-temporal
levels in different end-uses.

The remaining V&V section is outlined as follows. First, we describe
challenges in validating a large synthetic dataset for energy use. Then, we
highlight the temporal and spatial resolutions of the data that are considered
in the validation experiments. Next, ground truth datasets
(real/recorded/actual data) used for evaluation are briefly described. This is
followed by description of the experimental setup and results.

Validating the quality of the large-scale synthetic timeseries data for a
sizeable region such as the U.S. is challenging, owing to the vast extent,
diversity, and contrasting climates in the country. One of the challenges of
validating an energy consumption timeseries at household level is the large
variety and variability of the load patterns within and between households. In
addition to external elements such as weather and building characteristics,
consumer lifestyles and affordances play a vital role in shaping the demand
such as a curve with morning peak, or a curve with a small afternoon peak and
sharp evening peak. This leads to a big spectrum of variations and patterns in
energy use. Thus, in-depth comparative analyses of synthetic data to actual
data is required. However, it is conditioned on the availability of a
reasonable amount of representative real data. Here, we employ real/recorded
data such as load research data, end-use metering data, and smart meter data
from ten locations in the country that are representative of the U.S. climate
zones (Table 7). The availability of public smart meter data in the U.S. is
limited, which may cause a potential skew towards the selected sample of
households and may not be spatially representative. Thus, framing our
understanding of validation in this context is important.

We address the quality of the synthetic energy consumption data on two
intrinsic qualities of energy use data : magnitude (usage over 24 hours) and
load shape (pattern of consumption). Magnitude and load shape can be examined
across the temporal (hour/day/month/year) and spatial (household/census
tract/city/county/state/climate zones) axes. Thus, the verification and
validation (V&V) process covers:

  * •

_Spatial representativeness and resolutions._ Due to limited availability of
real data, we define spatial representativeness by choosing atleast one
location in each climate zone in the U.S. to carry out validation experiments.
The major climate zones [102] in the contiguous United States are as follows:
($i$) marine, ($ii$) hot-dry/mixed-dry, ($iii$) hot-humid, ($iv$) mixed-humid,
and ($v$) cold/very-cold. Comparisons are then performed at household and
city/county resolutions.

  * •

_Temporal representativeness and resolutions._ Temporal representativeness is
studied by observing similarities between real and synthetic hourly demand
profiles. Furthermore, daily and seasonal energy usage is studied for
different locations.

  * •

_Dis-aggregate energy use._ Note that we publish dis-aggregated energy use
data at household level. Thus, a finer level of evaluation such as an energy
use sub-type (e.g. HVAC, cooking, etc,.) is possible at various temporal and
spatial levels.

All the real datasets used in the V&V process are listed in Table 7. Recorded
datasets are obtained from Pecan Street Dataport [27], Northwest Energy
Efficiency Alliance (NEEA) [103], National Rural Electric Cooperative
Association (NRECA). The Los Alamos dataset is obtained from a public data
sharing repository Dryad [104]. Unfortunately, we do not have any metadata
about households (e.g. household size, dwelling type, etc) in these datasets.
The datasets only have energy use timeseries.

Three studies are presented to cover temporal, spatial, and dis-aggregate
nature of the synthetic time-series:

I. Comparing real and synthetic end-use energy usage (magnitude)

II. Comparing real and synthetic energy use patterns (shape/structure)

III. Observing differences and similarities in synthetic energy use data in
spatially representative locations

### I. Comparing real and synthetic end-use energy usage (magnitude)

(a) HVAC (Jensen-Shannon)

(b) HVAC (Hellinger)

(c) Refrigerator (Jensen-Shannon)

(d) Refrigerator (Hellinger)

(e) Cooking appliances (Jensen-Shannon)

(f) Cooking appliances (Hellinger)

Figure 6: Left column: Jensen-Shannon distance matrices, Right column:
Hellinger distance matrices. Each of the column shows Jensen-Shannon distance
and Hellinger distance matrices between end-use probability distributions.
Each matrix represents distances between two energy usage distributions for a
particular enduse (e.g. HVAC, refrigerator, cooking). The row and column
headers of the matrix represent different data-sources and different regions
and each cell represents the probability distribution similarity/distance
value in the form of heatmap, where the bar shows the range of the values on a
continuous scale.

In this experiment, distributions of synthetic and real daily end-use data are
compared using statistical metrics. One way of comparing these distributions
is by measuring distance between the real and synthetic end-use distributions.
Many metrics can be used to perform this task (e.g., Kullback–Leibler
divergence (KL), the Hellinger distance, total variation distance (TVD), the
Wasserstein metric, the Jensen-Shannon divergence (JS), and the
Kolmogorov–Smirnov statistic (KS)). Klemenjak et al. [20] use JS distance and
Hellinger distance as examples to compare distributions of appliance energy
use between different datasets. A similar method is implemented in this
section using the JS distance and the Hellinger distance metric. In our case,
computing the distances between daily end use distributions allows us to
perform regional comparisons as well as comparisons between real and synthetic
datasets.

The Jensen-Shannon distance is the square root of the Jensen-Shannon
divergence [105]. The range of this metric ranges between $[0,1]$ where 0
implies the distributions are similar. We prefer JS divergence over KL
divergence since it is a symmetric measure. If $P$ and $Q$ are two probability
vectors, then the JS distance $\mathsf{JS}(P,Q)$ is given by

$\mathsf{JS}(P,Q)\;=\;\sqrt{\frac{\mathsf{KL}(P||M)+\mathsf{KL}(Q||M)}{2}}\;,$
(5)

where $M$ is the pointwise mean of $P$ and $Q$ and $\mathsf{KL}$ is the
Kullback-Leibler divergence. To supplement our study, we use Hellinger
distance as a second metric to quantify the similarity between two probability
distributions. Hellinger distance is also a symmetric measure. Its range of
values is $[0,1]$ with 0 encoding that the distributions are similar. The
Hellinger distance of two probability vectors $P$ and $Q$ is denoted by
$\mathsf{H}(P,Q)$ and defined as

$\mathsf{H}(P,Q)\;=\;\frac{1}{\sqrt{2}}\sqrt{\sum^{k}_{i=1}(\sqrt{p_{i}}-\sqrt{q_{i}})^{2}}\;,$
(6)

where $k$ is the length of the vectors, and $p_{i}$, $q_{i}$ are the
$i^{\text{th}}$ elements of the vectors $P$ and $Q$, respectively.

Daily end-use energy usage (e.g. ${E}^{\mathsf{hvac}}_{i}$) at household level
are compared in the real and synthetic data for every location specified in
Table 7. Vectors $P$ and $Q$ denote values in a single end-use for two
datasets. Tables 6(a)(b)(c) list JS distances and Tables 6(d)(e)(f) list
Hellinger distances for selected end-uses (HVAC, refrigerator, cooking
appliances). Each matrix represents distances between two energy usage
distributions for an end-use. The row and column headers represent different
data-sources and different regions and each cell represents the probability
distribution similarity/distance value in the form of heatmap where the bar
shows the range of the values on a continuous scale.

The JS and Hellinger distance tables for end-uses show strong similarities
(the distance is close to zero). Furthermore, within each matrix three types
of comparisons are performed. We compute similarity between end-use
distributions for different regions within synthetic data, different regions
within real data, and different regions in different data sources (namely real
and synthetic data). For appliance usage (e.g. cooking), the distributions are
quite similar across regions and data-sources. This supports findings from
Figure 11 that there exists significant similarities between different regions
for synthetic daily energy consumption of different appliances. For HVAC end-
use, it is observed that the distributions grow apart between regions for both
– synthetic and real data sources. This is particularly true due to the strong
association of HVAC with outdoor/environment temperature conditions and the
time span for which these temperature conditions prevail (e.g., warmer
temperatures are observed for a longer time in Texas (TX))

### II. Comparing energy use patterns (load shape/structural similarity)

(a) Case 1: $closeness(\mathscr{R},\mathscr{S})$

(b) Case 2: $closeness(\mathscr{S},\mathscr{R})$

Figure 7: Example of _closeness_ in different cases with varying $k$. Figures
show the distances of data points from sets $\mathscr{R}$ and $\mathscr{S}$ to
their respective cluster center. (a) demonstrates histograms of distances for
different $k$. The plot on left is for real data points and on right is for
synthetic data points. Then, we calculate $closeness(\mathscr{R},\mathscr{S})$
using Hellinger distance (corresponds blue line in Figure 8(c)). For $k=5$ a
bimodal pattern is observed in distances for synthetic data points which tends
to diminish as the number of clusters $k$ increases. Figure (b) shows
histograms of distances for different $k$ for case 2. The plot on left is for
synthetic data points and on right is for real data points.
$closeness(\mathscr{S},\mathscr{R})$ is calculated using Hellinger distance
(corresponds to orange line in Figure 8(c)).

(a) Coverage

(b) Closeness

Figure 8: Summary of the two case scenarios. Orange color is denoted for
findings of case 1 where we cluster real data set $\mathscr{R}$ and assign a
cluster label to synthetic data set $\mathscr{S}$. Blue color is denoted for
findings of case 1 where we cluster synthetic data set $\mathscr{S}$ and
assign a cluster label to real data set $\mathscr{R}$. (a) illustrates 100%
coverage in both cases even as $k$ varies. This means that, in each case at
least one data point belongs to every cluster for a given $k$. (b) shows the
closeness between the two distance vectors : distance of real data points in a
cluster to its respective centroid and distance of synthetic data points in a
cluster to its respective centroid. Closeness is given by the Hellinger
distance which suggests that a value of 0 signifies that the two distributions
are similar. The value of distances is close to 0 for all values of $k$ in
both the cases. However, an upward trend is observed as $k$ increases. Overall
we see the robustness of results w.r.t. $k$.

In this section, the synthetic energy use timeseries are evaluated using the
concepts of diversity, coverage, and closeness. The diversity in energy use
patterns is captured by segmenting the normalized timeseries
$\langle\overline{e}_{0},\ldots,\overline{e}_{23}\rangle$ using unsupervised
learning techniques such as clustering. This is followed by studying
_coverage_ in terms of what percentage of synthetic timeseries population is
represented in the real timeseries population and vice versa. Thus, coverage
is used to measure diversity. However, learning only coverage is not
sufficient. It is necessary to measure the accuracy of the matches found.
Hence, we introduce the _closeness_ metric. It studies how close (e.g.
$dist(i,j)$) are the synthetic and real data points.

Let $\mathscr{R}$ and $\mathscr{S}$ be the set of load shapes of real and
synthetic energy use timeseries. Let $K_{\mathscr{R}}$ be the number of unique
load shapes (segments/patterns/clusters) found in set $\mathscr{R}$. Then, we
define the ${coverage(\mathscr{S})}$ as a ratio

$\begin{array}[]{l}coverage(\mathscr{S})\;=\;\frac{\textrm{Number of unique
shapes in $\mathscr{R}$ that contain atleast one data point from
$\mathscr{S}$}}{\textrm{Number of unique shapes in $\mathscr{R}$}}\\\ \\\
\quad\quad\quad\quad\quad\;\;=\;\frac{1}{K_{\mathscr{R}}}\times\sum_{b=1}^{K_{\mathscr{R}}}\mathbb{I}_{b}\quad\text{where}\\\
\\\ \mathbb{I}_{b}\;=\;\begin{cases}1&\text{if cluster $b$ contains atleast
one timeseries $j\in\mathscr{S}$ }\;,\\\
0&\text{otherwise.}\end{cases}\end{array}$ (7)

Thus, $coverage(\mathscr{S})$ reflects the degree to which samples from set
$\mathscr{S}$ cover the patterns in set $\mathscr{R}$. Similarly, if
$K_{\mathscr{S}}$ is the number of unique segments in set $\mathscr{S}$, then,
$coverage(\mathscr{R})$ reflects the the percentage of unique patterns in set
$\mathscr{S}$ covered by data points in set $\mathscr{R}$. Coverage is bounded
between 0 and 1. Figure 13(b) shows $coverage(\mathscr{S})$ and
$coverage(\mathscr{R})$ as $K$ varies.

To measure closeness we calculate distance of individual timeseries to it’s
respective cluster center/representative. If $K_{\mathscr{R}}$ is the number
of clusters in set $\mathscr{R}$, then, the _closeness(
$\mathscr{S}$,$\mathscr{R}$)_ of set $\mathscr{S}$ to set $\mathscr{R}$ is
measured by comparing the distributions of distances of individual timeseries
$i\in\mathscr{R}$ and $j\in\mathscr{S}$ in each cluster $c\in K_{\mathscr{R}}$
to the respective center/representative timeseries of the cluster. Figure
13(b) illustrates the schematic of building the distance distributions. Let
$P_{\mathscr{R}}$ and $P_{\mathscr{S}}$ denote the probability vectors of
distances of sets $\mathscr{R}$ and $\mathscr{S}$ respectively. To measure the
degree of closeness, we compare the two probability distributions using
Hellinger distance $\mathsf{H}(P_{\mathscr{R}},P_{\mathscr{S}})$ (Equation 6).
If distributions $P_{\mathscr{R}}$ and $P_{\mathscr{R}}$ are similar, then we
say that set $\mathscr{S}$ is close to set $\mathscr{R}$.

$closeness(\mathscr{S},\mathscr{R})\;=\;\mathsf{H}(P_{\mathscr{R}},P_{\mathscr{S}})$
(8)

Closeness is bounded between 0 and 1. 0 implies that the two sets are close.
Note that closeness is not a symmetric metric i.e.
$closeness(\mathscr{S},\mathscr{R})\neq closeness(\mathscr{R},\mathscr{S})$.
Figure 13(b) describes the variation in similarity score of the probability
with different number of segments $K$.

Now, we briefly describe the experimental setup. Two cases are considered to
examine coverage, closeness and robustness of cluster groupings ($k$). For
each case the energy use timeseries is normalized resulting in a _load shape_
$\langle\overline{e}_{0},\ldots,\overline{e}_{23}\rangle$. We choose
normalization by total consumption (Equation 9) in order to consider
pronounced effects of peak-load in the profile. Household preferences or
lifestyles can be typically captured by one or more load shapes [106], hence
we choose this representation for uncovering patterns in the data. Thus, every
$i\in\mathscr{R}$ and $j\in\mathscr{S}$ are normalized energy use vectors of
length 24.

$\overline{e}_{t}\;=\;\frac{e_{t}}{E^{\mathsf{total}}}\;,\quad\textrm{where}\;\;E^{\mathsf{total}}=\sum^{23}_{t=0}e_{t}$
(9)

In the first case (Case 1), we generate $K_{\mathscr{R}}$ patterns from set
$\mathscr{R}$ by clustering the real normalized energy use vectors using
k-means clustering algorithm with Euclidean distance. This is followed by
assigning a cluster label $k\in K_{\mathscr{R}}$ to each synthetic energy use
timeseries $j\in\mathscr{S}$. Let $c_{k}$ be the center/representation vector
of group $k$. Then, $j\in\mathscr{S}$ is assigned to the cluster whose cluster
center distance is minimum from $j$ and is given by
$min(dist(j,c_{0}),\ldots,dist(j,c_{K_{\mathscr{R}}}))$. Then, we calculate
the coverage of synthetic data $coverage(\mathscr{S})$ and closeness of
synthetic data to real data among all clusters as
$closeness(\mathscr{S},\mathscr{R})$. In Case 2, we generate $K_{\mathscr{S}}$
clusters from set $\mathscr{S}$ (synthetic data) by segmenting the normalized
energy use vectors using k-means clustering algorithm with Euclidean distance.
This is followed by assigning a cluster label $k\in K_{\mathscr{S}}$ to each
real energy use timeseries $i\in\mathscr{R}$. $i$ is assigned to the cluster
whose cluster center distance is minimum from $i$ and is given by
$min_{\forall k\in K_{\mathscr{S}}}dist(i,c_{k})$. Then, we calculate the
coverage of real data in synthetic groups $coverage(\mathscr{R})$ and
closeness of real data and synthetic data among all synthetic clusters as
$closeness(\mathscr{R},\mathscr{S})$.

Results of both the cases are summarized in Figures 8. A 100% _coverage_ is
observed in both the cases for different values of $k$. Observations for
_closeness_ metric are interesting. The Hellinger distance is close to zero in
all the scenarios, however there is a slight uptake in the value as $k$
increases. We inspect this further in Figure 7. Figure 7 shows histograms of
distances of real data points and synthetic data points from their assigned
cluster center. In case 1, the distribution of distances of synthetic data
points is slightly broader than the distribution of distances of real data
points for all $k$. Thus, we see a distance for _closeness(
$\mathscr{R},\mathscr{S}$)_ in Figure 8(c). As $k$ increases it is observed
that some individual clusters have a broad and/or bimodal distance
distribution indicating that there are data points that are very close to the
cluster center while a few are far away. This difference is apparent as the
number of clusters increases.

The goal of this V&V exercise was to verify if the diversity and trends of the
real energy use profiles are replicated in the synthetic energy use profiles.
Due to a biased and skewed sample of the real energy use data, it is
challenging to perform validation of synthetic data. Some of the
characteristics of the real datasets that hinder the implementation of using
existing evaluation metrics _as is_ are mentioned below. No supporting
information of the real households is available (e.g. household size, dwelling
type, square footage, indoor thermostat setting). We have shown that all of
these factors are extremely important in the generation of household demand at
a given time. Some of households in the real data may also be participants in
demand-response programs resulting in unique load shapes due to shifting
demand/reducing peak demand that may not be found in households not
participating in DR programs (e.g. synthetic data). The real datasets are
collected for different years for each region. The data are incomplete for
some regions (e.g. San Diego samples do not have lighting data). The sample
size (number of households) is highly skewed. It varies from 9 households in
Montana to 56000 households for Horry,SC. Thus, it is important to note that
$|\mathscr{R}|<<|\mathscr{S}|$ (e.g. the number of households simulated in our
framework for Washington state is far greater than that of 78 households in
real data for Washington state.) All of these observations are summarized in
Table 7.

### III. Observing differences and similarities in synthetic energy use data
in spatially representative locations

(a) Arlington, VA

(b) Cook, IL

(c) Houston, TX

(d) Maricopa, AZ

(e) King, WA

(f) Legend

Figure 9: Composition of synthetic electric consumption in the representative
target locations. Heating and cooling constitute the majority part of the
residential electric consumption. Refrigerators consume slightly higher energy
in hotter regions such as Maricopa and Houston. Activities such as
dishwashing, laundry, and cooking represents between 8-17% for different
regions. Lighting and water heating have a consistent proportion of
consumption across all locations. The proportions bear similarities with data
published by EIA.

This empirical study uses only the synthetic data to conduct a comparative
regional analyses to examine similarities and dissimilarities between energy
use for different end-uses. We observe the spatio-temporal patterns and
variations in different end-uses with respect to environmental elements such
as irradiance and temperature as well as demographic and structural
characteristics of the households. The selected target locations are spatially
representative of different climate zones of the U.S.:

_Arlington, VA_ ; _Cook County, IL_ ; _Houston County, TX_ ; _Maricopa County,
AZ_ ; _King County, WA_

The composition of electric consumption by end-uses is shown in the form of
pie diagrams in Figure 9. EIA reports the shares of the major end-uses as
follows: DHW 17-32%, lighting 5-10%, refrigerator 3-5%, activities/appliances
20-26%, space heating 25-47%, and air conditioning 5-10%. In general, the
percentages of major end-use categories lie in the ranges similar to those
reported by EIA. HVAC has a dominant share in the energy consumption in
households as compared to usage of appliances and/or other activities.

(a) HVAC energy use

(b) Refrigerator energy use

(c) Hot water energy use

(d) Outside temperature

Figure 10: Monthly synthetic energy use changes in end-uses such as HVAC,
refrigerator, domestic hot water w.r.t. temperature. The above line charts
monthly energy use changes in end-uses such as HVAC, refrigerator, domestic
hot water w.r.t. outside temperature. The line chart shows average daily
consumption over all households in the target regions. The scatter plot in the
background describes average daily consumption for an end-use for sampled days
color coded by location. The size of the markers denotes the standard
deviation of the end-use consumption. Legend: Arlington, VA (green); Cook
County, IL (blue); Houston County, TX (yellow); Maricopa County, AZ (brown);
King County, WA (cyan)

(a) Dishwasher

(b) Laundry

(c) Cook

(d) Cleaning

(e) TV use

(f) Computer use

Figure 11: Synthetic appliance energy use variation in target locations
throughout the year. The line charts show variation in daily energy
consumption for different appliance energy use throughout the year averaged by
month. The lines depict average daily consumption over all households in the
target region. The scatter plot in the background describes average daily
consumption for an end-use for sampled days color coded by location. The size
of the markers denotes the standard deviation of the end-use consumption.
There are noticeable similarities in appliance-usage throughout all locations
indicating that people in different parts of the country use appliances in a
similar style. This is a reasonable observation since day-to-day activities
such as cooking and cleaning will occur in all households. Their usage pattern
may change during the day, but the total energy consumed by the appliance at
the end of the day is similar. Arlington, VA (green); Cook County, IL (blue);
Houston County, TX (yellow); Maricopa County, AZ (brown); King County, WA
(cyan)

Seasonal energy use variations for HVAC, refrigerator, and hot water is
captured in Figure 10. The plot shows variation in daily average energy use of
the four end-uses on a monthly basis alongwith temperature across the year
2014. Refrigerator energy use increases slightly with temperature while energy
used to heat water decreases with increase in temperature.

Electricity usage for heating water is the lowest during summer months for all
locations (Figure 10c). In particular, regions from hot-humid and hot-dry
climate zones consume the least amount of energy. This observation stems from
the relation between $E^{\mathsf{h2o,v}}$ and $T^{\mathsf{cold}}_{m,z}$
described in Equation 3. The water inlet temperature (
$T^{\mathsf{cold}}_{m,z}$) differs across temporal as well as spatial scale
and is dependent on outside environment temperatures [68] (Details in
Appendix). Figure 13 shows plots describing relation between household size
and the number of gallons of hot water consumed and energy required to heat
water. Note that, we consider only electric water heaters in this work.

Figure 10(a) shows that the HVAC consumption varies significantly throughout
the year. HVAC use is higher in hot-dry areas in summer as compared to other
regions possibly due to higher temperatures. Structural characteristics such
as dwelling size (square footage), insulation quality, age and efficiency of
HVAC equipment also affect household HVAC consumption. Another important
variable that drives HVAC consumption is indoor thermostat behavior which is
related to household occupants’ behavior/actions. In this work, indoor
thermostat temperatures are set constant throughout the day. Insulation
quality is not monitored in households (due to lack of data). We assume that
the dwelling is well-insulated and the insulation values are implemented
according to the DOE standards for the respective climate zones. In Figure 12a
we show effect of square footage (conditioned space) of a dwelling on hvac
energy use. In general, we observe that as the conditioned space in the
dwelling increases, the HVAC consumption increases.

Lighting energy-use varies by seasons in all regions as irradiance levels
change with weather events and seasons. Figure 14b shows average irradiance
time series for the target locations. The corresponding lighting usage is
shown in Figure 14a. As an example, we look at monthly irrandiance profiles
across 24 hours in Virginia for the year 2014 (Figure 14d). The corresponding
monthly lighting energy use time series is shown in Figure 14c. Example of
lighting consumption w.r.t. household size is explored in Figure 12b.

Figure 11 shows the breakdown of appliance usage for different appliances and
electronic devices. Both figures show a line chart indicating average daily
consumption for the month. The scatter plot in the background describes
average daily consumption for an end-use for sampled days color coded by
location, where the size of the markers denotes the standard deviation of the
end-use consumption. It is observed that appliance usage in activities such as
cooking, dishwashing, performing laundry, watching TV, using computer, and
cleaning are fairly similar in different regions. The above comment is
intuitively true since appliance use duration and their ratings may not vary
across regions. However, the occurrence timing throughout the day may vary
from house to house depending upon occupant schedules irrespective of which
geographic regions they belong to.

(a) HVAC vs. house area (i.e. floor area)

(b) Lighting vs. household size

Figure 12: (a) Synthetic HVAC use and house area (i.e. floor area). Boxplot
comparing daily HVAC consumption in a winter day for the selected target
locations by house area (i.e. floor area). The x-axis groups floor area of
houses in five bins denoted in two units sq. ft ($\text{ft}^{2}$) and sq m
($\text{m}^{2}$). The bins are as follows : $\leq$ 1000 $\text{ft}^{2}$, 1000
- 1500 $\text{ft}^{2}$, 1500 - 2000 $\text{ft}^{2}$, 2000 - 3000
$\text{ft}^{2}$, $\geq$ 3000 $\text{ft}^{2}$. It is observed that as floor
area of the house increases HVAC consumption increases in all regions. Winter
temperatures are relatively moderate in AZ and TX, thus, the HVAC consumption
is less as compared to other regions. (b) Synthetic lighting use and household
size. Lighting consumption increases as household size increases. Household
size indicates number of members in a household.

(a) Hot water (gallons) vs. household size

(b) Hot water (energy) vs. household size

Figure 13: Synthetic hot water usage and energy vs. synthetic household size.
Household size indicates number of household members. The clustered bar charts
show the amount of hot water consumed (in gallons in (a)) and corresponding
energy usage in (b) according to household size in a winter day. The vertical
black line on each bar shows the variation. Water usage and its variation
increases with household size. The amount of energy for hot water end-use
increases with household size and differs by region.

(a) Lighting profile

(b) Irradiance profile

(c) VA lighting profile

(d) VA irradiance profile

Figure 14: Heatmap depicting relation between hourly synthetic lighting usage
and hourly irradiance. (a) shows average annual 24-hour lighting profiles of
representative target locations. (b) shows average annual 24-hour irradiance
profile of representative target locations. (c) and (d) present the variation
in lighting usage and corresponding irradiance profiles at monthly level for
Arlington, VA. (c) presents lighting consumption variation throughout the day
in different months across the year. (d) shows variation in monthly irradiance
profile. The units of measurements for energy usage is kWh and irradiance is
Watts/m2. The lighting energy use is inversely proportional to the irradiance.
The energy usage is higher in evening and night hours when the occupant is
active in the dwelling. The average lighting and irradiance profiles show
regional differences in irradiance availability and subsequent lighting energy
usage. The VA profiles show that the day light is available for longer
durations leading to lower lighting energy consumption as compared to winter.

## Usage Notes

In order to analyze the dataset, researchers can use any programming languages
such as Python, Java, Matlab, or R. As described in the ‘Data Records’
section, the files are stored in csv format, so most of the file reading
functions in the above languages can support reading/accessing the dataset.
Next, we discuss the potential applications of the released synthetic data. We
also highlight important challenges and limitations of this work.

### Applicability and benefits of the dataset.

We are releasing a comprehensive household level dataset for energy use. In
addition to the household level disaggregated energy use data, household
composition is also included from census data. This work was reviewed by the
University of Virginia’s Institutional Review Board (IRB) and was determined
to be exempt from board IRB approval, as this research project did not involve
human subject research. The dataset can be effectively employed in various
applications such as NILM (non-intrusive load monitoring), load profile
analyses for observing similarities/differences between end use consumption of
different regions and seasons, evaluating effects of retrofits in buildings,
studying effects of temperature rise in different regions, and so on. In
addition, this data can also be used for energy model calibration, occupant
behavior evaluation, implementing demand response strategies and policy
interventions. The dataset can be especially leveraged in training deep
learning models where massive amount data is appreciated. Such models can be
used for real-time residential demand forecasting. The dataset released are
essentially time-series along with categorical and numerical attributes. Thus,
any statistical tool or programming language can be used to analyze them.
Study III in the ‘Technical Validation’ study illustrates examples of the
possible uses of the dataset.

### Challenges and limitations.

The use of synthetic residential energy demand data has its pros and cons.
National scale hourly synthetic data can be used to carry out national and
even potentially international policy analysis. The spatio-temporal
variability allows one to access important emerging questions related to
energy equity, fairness and accessibility at a fine scale. A systems level
approach can be taken to vexing questions outlined in the 2030
Intergovernmental Panel on Climate Change (IPCC) goals. On the other hand,
synthetic data sets have their limitations as well. For instance, the fine-
scale variability (minutes level as well as weekly variation) of usage amongst
households cannot be captured easily in such synthetic data sets.
Additionally, the behavior exhibited by any single synthetic family might be
biased by the data used for synthesis. Thus, any insight generated from high
resolution analyses should be considered carefully.

An important challenge in developing the realistic synthetic residential load
profiles at a national scale and at a high spatio-temporal resolution is to
find appropriate datasets for representing different types of climates,
demographics, appliances, and activity patterns. Accessibility and
availability of all the above information from legitimate sources is crucial
to maintain trustworthiness in the resulting models. A robust and extensible
infrastructure is developed to synthesize diverse data sources into detailed
information structure at various spatial resolutions (e.g. combining household
level data with climate zone related data such as insulation values). The
infrastructure consists of methods to compose multiple models and data sets.
The overall time to generate the synthetic data was reduced by using high
performance computing capabilities.

Some of the limitations of our work are discussed. The current synthetic data
does not include power consumption by electric vehicles and energy generation
via renewable generation (e.g. solar panel, wind). The ATUS data is available
for a normative day for individuals. Thus, activity and appliance related
demands are generated for a normative day with minor variations coming from
the activity model. Hence, our synthetic data might not be able to capture
daily activity variation appropriately (e.g. as observed in real-time smart
metering). This can be challenging to work with especially when studying
demand response scenarios. The building envelop considered for a synthetic
household is simplified due to lack of information needed to represent a large
population group, thus limiting our ability to employ state-of-the-art and
sophisticated building modeling techniques. (e.g. we use a simple HVAC physics
based model to generate heating and cooling related energy demand).

### Concluding remarks.

The paper describes a bottom up approach to generate large-scale digital twin
data of dis-aggregated residential energy use hourly timeseries for the
residential sector at household resolution across the contiguous United States
for millions of households. The approach integrates diverse open-source
surveys and datasets, where the end-use models are developed by either
extending well-established methods or by building new models. Extensive
validation of the synthetic datasets is conducted using real/recorded energy-
use data across spatial and temporal resolutions.

## Code availability

Programming languages such as Python 3 and Java 8 are used for modeling,
analyzing, and developing the framework. The code is deposited in the
repository [101] alongwith the dataset.

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## Acknowledgements

We thank the anonymous reviewers for their very helpful comments that helped
us improve the manuscript. We thank members of National Rural Electric
Cooperative Association (NRECA) for providing validation data for Rappahannock
county, Virginia and Horry county, South Carolina. This work is partially
supported by University of Virginia Strategic Investment Fund award number
SIF160, NSF EAGER CMMI-1745207, NSF Grant OAC-1916805, and NSF BIGDATA
IIS-1633028.

## Author contributions statement

S.T. collected data for the models, developed and implemented the modeling
framework and all the individual energy use models, prepared the manuscript;
Y.Y.B. implemented the ATUS model, read and edited the paper; H.M and S.S.
helped with model development, data collection, read and edited the
manuscript, provided guidance in writing Background and Summary; M.M. worked
on model development, validation, manuscript preparation, provided feedback
for the Methodology and Validation section; A.M. read and edited the
manuscript and helped with validation; A.V. edited the manuscript and helped
with validation. All authors participated in writing and reviewing the
manuscript.

## Competing interests

The authors declare no competing interests.