table figure

# Planning for Electric Vehicles Coupled with Urban Mobility

Yanyan Xu,1† Serdar Çolak,1,2† Emre C. Kara,3 Scott J. Moura,4
Marta C. González1,5∗

1Department of Civil & Environmental Engineering,
MIT, Cambridge, MA, 02139, USA
2Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
3SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
4Department of Civil & Environmental Engineering,
UC Berkeley, CA, 94720, USA
5Center for Advanced Urbanism, MIT, Cambridge, MA, 02139, USA

†Equal contribution
∗To whom correspondence should be addressed; E-mail<EMAIL_ADDRESS>
> The rising adoption of plug-in electric vehicles (PEVs) leads to the
> alignment of their electricity and their mobility demands. Therefore,
> transportation and power infrastructures are becoming increasingly
> interdependent. In this work, we uncover patterns of PEV mobility by
> integrating for the first time two unique data sets: (i) mobile phone
> activity of 1.39 million Bay Area residents and (ii) charging activity of
> PEVs in 580,000 sessions obtained in the same region. We present a method to
> estimate individual mobility of PEV drivers at fine temporal and spatial
> resolution integrating survey data with mobile phone data and income
> information obtained from census. Thereupon, we recommend changes in PEVs
> charging times of commuters at their work stations that take into account
> individual travel needs and shave the pronounced peak in power demand.
> Informed by the tariff of electricity, we calculate the monetary gains to
> incentivize the adoption of the recommendations. These results open avenues
> for planning for the future of coupled transportation and electricity needs
> using personalized data.

## Introduction

The excessive exploitation of petroleum and coal affect not only the security
of energy supply but also air quality and climate change. These shortcomings
have triggered the search for cleaner alternative fuels for transportation (?,
?, ?). Today’s plug-in electric vehicle (PEV) technology is one of the most
promising candidates up to date (?, ?). The main issues that hindered their
adoption were: range anxiety, charger unavailability, and high prices (?).
However, improvements in battery technology, tax breaks and subsidized
charging programs (?, ?) have improved these limitations. As a result, PEVs
are becoming a more viable means to move and are being adopted by drivers at
steadily increasing rates (?). According to the US Energy Information
Administration, the number of PEVs in the USA doubled between 2013 and 2015
and is expected to reach 20 million by 2020 (?).

Planning for the mobility needs of PEVs is particularly important in the
context of the vulnerability of the power grid to outages that can cascade
drastically (?). Large scale failures signified a need to reexamine the
balance between power demand and the electricity infrastructure, opening the
need for interdisciplinary approaches to study this complex system (?). A body
of literature has focused on the nature of network reliability of power grids,
the role of network topology on the spread of cascading failures (?, ?, ?, ?,
?, ?, ?). In the subject of PEVs and their impact on the grid, methods of
optimization and control of PEV electricity consumption have a rich set of
avenues (?, ?, ?). Research topics on this front include measuring impact on
the grid (?, ?, ?, ?, ?, ?, ?), developing accurate PEV energy consumption
models (?), energy management (?, ?), smart charging strategies that probe
centralized and decentralized approaches (?, ?), scheduling (?, ?), peak
shaving, emissions, pricing models (?, ?), and joint optimization of power and
transportation networks (?). A common shortcoming in these works is the narrow
scope in incorporating individual mobility needs into the analyses, often
limited to the estimation of arrival or departure hours. Up to date, data on
individual mobility demand at metropolitan scale has not yet been incorporated
into the planning schemes to manage electricity demand.

In this work, we target these gaps in the literature to extend the current
knowledge of transportation based electricity. For this purpose, we bring
together three independent data sources: (i) mobile phone activity of a large
sample of the residents of the San Francisco Bay Area, (ii) charging sessions
obtained from the commercial PEV supply equipment in the same region, and
(iii) surveys on the use of conventional and electric vehicles, together with
census data for income information at the zipcode level (see Data in Materials
and Methods). In the first part of the work, we estimate individual vehicular
mobility per week day in the Bay Area using the mobile phone activity of a
large sample of residents. We then present a Bayesian methodology to sample
the PEV drivers from all travelers by utilizing information obtained from
surveys regarding the household income and daily travel distances of PEV
drivers. In the second part, with the charging session data, we analyze the
various aspects of charging activity to characterize the nature of electricity
demand at charging stations. We present observations regarding visitation
frequencies, arrival and departure hours, typical per session energy
consumption patterns, and power levels. We observe that PEV charging patterns
are highly regular with morning and evening peaks following the traffic peaks.
These peaks of demand are undesired because they can cause instabilities in
the power grid. Currently, the power consumption happens immediately upon
arrival and makes no use of this flexibility. To tackle this problem, we
explore the relationship between the consumption of simulated PEV commuters
working in the selected zipcodes and the observed energy demand at individual
commercial charging stations in the same region. We calibrate the charging
behaviors of PEV drivers to match the observed demand. As an application, we
lay out a charging scheme that minimizes the peak power changing the start and
end of the charging sessions, while also taking into account the constraints
in changing departures and arrivals. We show how not knowing the mobility
constraints decreases the potential of the peak minimization schemes. In
contrast, introducing the awareness of individual mobility increases the
feasibility of their adoption, affecting less the benefits of peak
minimization. The resulting effects on the commuting travel times and the
monetary benefits from the changes in charging times support the viability of
the charging time shifts. Fig. 1 depicts a summary of the proposed framework.

## Results

### Estimating Individual Mobility of PEV Drivers

We simulate the individual mobility of the entire population of the Bay Area
using a fine-scale urban mobility model, TimeGeo (?). This process begins with
the extraction of stay locations in the trajectories of each individual (?, ?,
?). Each location is then accordingly labeled as _home_ , _work_ , or _other_
, based on temporal properties of the call activities. Sequences of trips are
collected for each individual and categorized by their time and purpose.
According to whether the workplaces are detected or not, we model the trips of
commuters and non-commuters respectively (see Individual Mobility Model in
Materials and Methods). Fig. 2A represents the simulated trajectory and the
labeled activities of a mobile phone user. The simulations of individual
mobility based on mobile phone data, compare very well with the results using
two travel surveys, the 2010-2012 California Household Travel Survey (CHTS)
(?), and the 2009 National Household Travel Survey (NHTS) (?). As shown in
Fig. 2B-D, the daily visited locations and fraction of departures per time of
the day agree well between our model based on phone data and the travel
surveys. Further comparisons between our model and the travel diaries are
presented in the Supplementary Figs. 1 and 2.

Mobility motifs (?) describe the individual daily trips. Specifically, motifs
constitute directed networks where nodes are visited locations and edges are
trips from one location to another. For example, the motif of an individual
whose only trips in a day are to and from work will consist of two nodes with
a two directed edges (one in both directions). While on average, individuals
visit three different places per day, when constructing all possible directed
networks with $6$ or fewer nodes, there exist over $1$ million ways for an
individual to travel between. However, $90\%$ of people use one of just $17$
networks, called motifs (?). While nearly half of the population follow the
simple two-locations motif. These results can be modeled with a probabilistic
Markov model (?) that assigns particular rates to each individual informed by
their trip behavior. The top $10$ motifs of nearly $6$ million simulated
drivers in the Bay Area are summarized in Fig. 2C., the distribution of our
simulated motifs agrees well with the information gathered from mobile phone
users. After simulated individual mobility overall, we can probabilistically
estimate the individual mobility of PEVs. To that end, we make use of the
vehicle usage rate from the US census data and the California Plug-in Electric
Vehicle Driver Survey (?). According to this survey, PEV drivers’ income
distribution is skewed towards higher income segments. In particular, the
percentage of those with average annual income above 150K$ among conventional
vehicle drivers is 15%, compared to the 47% observed among PEV drivers. The
survey also highlights the typical distances PEV drivers travel: 64% of PEV
drivers travel less than 30 miles per day (see Table 1). This information is
used to subsample PEV trips from total vehicular trips by implementing the
Bayesian sampling procedure. Namely, we use the individual income estimated
from the US census data at the census tract level and daily route distance
from TimeGeo to estimate the probability of that the driver travels with a
PEV, both for commuters and non-commuters (see Electric Vehicle Mobility
Estimation in Materials and Methods).

Figure 3A depicts the number of PEVs estimated from the Bayesian method at
each zipcode and the number obtained from the data set on PEVs collected by
the California air resources board clean vehicle rebate project (?), that will
be referred here as the CVRP data set. Fig 3B shows a good agreement between
the number of PEVs obtained via the Bayesian estimates and the mobility model
vs. the ground truth of PEVs usage. Fig. 3C-D compare the distributions of the
morning route distance, $D$, made by all commuters vs. PEVs drivers, as well
as the commuting travel time, $T$, under free flow conditions. There are fewer
PEV trips shorter than $5$ km and longer than $25$ km, in agreement with the
findings of the survey. Figure 3E depicts the four mobility motifs from PEV
commuters, showing that approximately $60\%$ of PEV commuters mostly travel
between home and work during weekdays. The simple motifs (with ID=1) is more
prevalent among PEV drivers than among commuters using conventional vehicles,
this may be a sign of the driver’s concerns on the range of PEVs.

### Electric Vehicle Charging Session Data Profiles

In this section, we analyze PEV charging in non-residential regions by
examining: visitation patterns and adoption rates, temporal features of
arrivals and departures, and typical energy and power consumption levels. PEV
drivers display varying degrees of regularity in terms of how often they visit
charging stations. Fig. 4A reveals that for the majority of PEV drivers the
average number of charging sessions per day, $N_{day}$ is less than 1. The
bottom left inset in Fig. 4A displays the logarithmic distribution of the
number unique PEV charging stations (EVSEs) visited by each PEV driver,
$N_{EVSE}$. Noticeably the great majority of PEV drivers (95.6%) is observed
in less than 20 distinct EVSEs. The top right inset of Fig. 4A depicts the
rate of PEV adoption observed throughout the year. The 3000 drivers observed
in January 2013 increases by an average of 1000 per month, doubling twice over
the course of 2013.

We look at the arrival and departure hours of charging sessions, $h_{a}$ and
$h_{d}$, in Fig. 4B. Approximately 50% of all arrivals take place in the
6am-11am morning period, and as expected, the morning and the evening peaks
are highly pronounced. This points to the parallels between the temporal
component of overall travel demand to electricity demand. We compare the
distribution of departure time in the morning of commuters with the arrival
time of charging sessions and find notable delay between these two
distributions (see Supplementary Fig. 6A). Such delay represents the driving
time of commuters from home to work in the Bay Area, which is around 30 min on
average (?). In the inset of Fig. 4B we look at the distribution of inter-
arrival and inter-departure times, $\Delta h_{a}$ and $\Delta h_{d}$, i.e. the
time between two consecutive charging sessions for the same driver ID. These
distributions are peaked at multiples of 24 hours, pointing to the diurnal
periodicity of PEV drivers’ charging behavior. These findings reinforce the
notion that commuting and charging behavior in the non-residential regions are
highly related.

Next, we shift our focus to measures per session, such as energy, duration,
and power. Fig. 4C exhibits the average energy consumption per session,
$E_{S}$. The battery sizes of Nissan Leaf (24 kWh) and Chevrolet Volt (16
kWh), two of the most commonly used PEVs in the region are marked (see also
Supplementary Fig. 4) (?). Typically $E_{S}$ are well below these capacities,
indicating that PEV drivers typically stay within the range of their PEVs. PEV
drivers can charge at home or they not necessarily start their commute at full
capacity. On the other hand, the distribution of session durations reveals
that 98.4% of all charging sessions last less than a day (Fig. 4C), in line
with the ubiquitous charging at work places. Given the flexibility in terms of
battery capacity and mobility patterns, here we assume that the session energy
$E_{S}$ represents not a single commuting trip, but rather a number of them.

The actual charging activity does not last as long as the session duration
$\delta_{S}$, as seen in Fig. 4D. We divide sessions into four categories
based on their session duration, and plot the average power consumption for
each segment at various percentages of the total duration. We observed three
levels of power rate that are most common, denoted here as Level 1 (L1), Level
2 (L2) and Level 3 (L3). The first two deliver 120V and 240V, typically
corresponding to 3.3kW and 6.6kW, respectively. L3 chargers are mainly for
fast charging at 480V and are relatively uncommon. As faster charging
technology becomes more abundant, the peak load yielded by PEVs will be even
higher as the charging sessions start intensively in the morning. In the
charging dataset, L1 and L2 chargers make up 99.9% of all the sessions in the
dataset (see Supplementary Fig. 6C). This composition of power ratings
explains the 4 kW upper limit to average power consumption observed in Fig.
4D. For sessions lasting less than 4 hours, average power stays above 3 kW up
to 80% of the duration into the session. Conversely, for sessions that last
longer than 12 hours but less than a day, only in the starting 25% of the
session duration there is active charging. This corresponds approximately to
3-6 hours, and the power remains zero thereafter. This is consistent with
constant-current constant-voltage battery charging behavior and it suggests
that currently there is no strategy to charging involved: PEVs are charged
immediately upon arrival.

### Coupling PEVs Energy Demand and Individual Mobility Patterns

This section presents the coupling of the mobility model with the energy
demand at each destination. First, we measure the distribution of electricity
demand at a zipcode from the charging sessions, we connect that to the
distribution of estimated energy demand of simulated PEVs commuting to that
zipcode. The charging sessions data is provided by a private company with a
partial coverage of the market with reasonable agreement of the most popular
destinations for charging (see Data in Materials and Methods, and the
comparison of estimated PEVs vs. the charging data in Supplementary Fig. 5).
To estimate the energy demand of each PEV trip, we first assign each PEV a
mode from the four most popular modes (see Supplementary Fig. 4). Each PEV
mode is associated an energy consumption model. Specifically, we use the
drivetrain model for the two battery electric vehicle (BEV) modes, Nissan Leaf
and Tesla Model S (?), and the charge-depleting model for the two plug-in
hybrid electric vehicle (PHEV) modes, Chevrolet Volt and Toyota Prius (?). For
each PEV trip, we estimate the energy demand using its average speed and route
distance (see details in Energy Consumption Models of Materials and Methods
and in Supplementary Fig. 6B).

Due to the limited information from charging sessions data, we can not infer
the state of charge of each vehicle. Therefore, we assign different shares of
charging states: morning consumption, daily consumption, and two-days
consumption. This corresponds to different charging behaviors respectively:
charging both at home and work every day, charging at work once per day, or
charging at work once every other day, indicating that the energy consumption
at the arrival equals to the consumption of the trips in the last two days. In
Fig. 3F, we show the comparison of probability distributions of the energy
consumption of the three scenarios together with the actual charge, $E_{S}$ in
a selected zipcode. The peaks in the distribution of $E_{S}$ demonstrate the
heterogeneity in the electricity demand, which is mainly caused by the travel
distance, the battery capacities, and the charging behaviors of various PEVs.
The 3-4 kWh peak, which can be observed in both actual and estimated
consumptions, is a combination of low energy demand as a consequence of short
commuting trips and PHEVs that typically have a battery capacity around 4 kWh
(?). Further comparisons between daily consumption estimates and the charging
station data in selected zipcodes are shown in Fig. 3G. The charging data have
more pronounced peaks than our daily curves, this may be because our charging
behaviors are simplified, leaving room for further improvements.

To estimate the charging behavior in the given zipcode, we limit the amount of
charging sessions to 30 kWh. The charging behavior is distributed to match the
demand of the zipcode with most charging sessions. Corresponding to average
charging schemes that result in: $10\%$, $35\%$, $55\%$ of the PEVs drivers
respectively (see also Supplementary Fig. 6C). Note that only $10\%$ of the
drivers charging at home is in agreement with a recent report by the
Department of Energy that states that 80% of partners in their Workplace
Charging Challenge program provide free PEV charging (?). We randomly assign
the charging speed from the charging session data to the simulated PEVs to
make the distribution of charging speed match with the ground truth (see
Supplementary Fig. 6D).

### Strategies to mitigate peak demand coupling energy demand with mobility
needs

Our goal in this section is to transform the load curve into one that is more
uniformly distributed across the day. To that end we propose changes in the
start and end of the charging sessions such that the total load is minimized.

We cast the problem as a mixed-integer linear program with discrete shifts in
arrival times and charging end times as inputs (see Optimization Model in
Materials and Methods). The program modifies the total power $P_{t}$ measured
through the day resulting from the overlapping charging activities of a
population of PEVs in a way that minimizes the peak power while keeping the
total energy consumed constantly. In this context, we test two different
strategies. The first fixes the departure times for PEVs and shifts the
arrival time in advance by $d^{i}$, an amount specific to session $i$ within
the interval $[0,d]$, to minimize the peak power load $P_{peak}$. We refer to
this strategy as end bound. The second strategy, referred to as flexible,
offers modifications to both of the arrival and departure times. In this
approach, charging activity is shifted in the interval $[-d,d]$. In both of
the two strategies, the PEVs are charged once they are plugged in the charging
station and PEV driver could depart at their scheduled time if the charging
session has finished. As a future scenario, we show the peak load saving when
the charging station is able to control the PEV start of the charging session
independent of the arrival time. The current infrastructure does not allow the
start of charging at an optimized time and it is couple to the PEV arrival.
With a smarter charging-shift scenario, the charging could be freely shifted
between the plug-in/arrival and plug-out/departure time. We test the time
shifting scenarios on the $448$ PEVs traveling to our zipcode with the largest
number of incoming users.

Fig. 5A illustrates an instance where an actual section is of $2.25$ hours and
it is modified in $d=4$ (60 minutes) to start earlier. The right panel of the
figure shows all charging sessions for the _flexible_ strategy where some
users are charged earlier and others later than their actual request. Fig. 5B
depicts how the power curves are modified under the _flexible_ strategy with
varying value of $d$ (Supplementary Fig. 7 presents the results for the _end
bound_ strategy). The _flexible_ strategy reduces $P_{peak}$ down $47\%$ from
$1019$ kW to approximately $479$ kW for $d=4$, or 1 hour. In contrast, the
_charging-shift_ strategy reduces the peak load by $66\%$ as we have more room
to operate the PEV charging.

We also evaluate the effects of introducing by the constraints of the
individual mobility motifs of each PEV. Mobility constraints are introduced
via the $4$ motifs depicted in Fig. 3E. More than $30\%$ of PEV drivers have
other activities before or after work, therefore, they are limited to accept
the recommendations of a time-shift strategy if the recommendation falls
before their usual arrival and departure times. Namely, we impose the
following restrictions per motif ID. (1) _home-work-home_ , can change both of
the arrival and departure time; (2) _home-work-other-home_ , indicates
activities after work, and they can not delay their departure time; (3) _home-
other-work-home_ , which indicates activities before work, and they can not
change their arrival time; (4) _home-other-work-other-home_ , which indicates
the PEV drivers can change neither the arrival nor the departure time.

Figure 5C contrasts the estimates of peak saving with and without the
consideration of individual mobility constraints in the optimization strategy,
looking at the percentage of peak loads of three schemes with variant $d$. The
three schemes are (i) The _Optimal_ strategy, where all PEV drivers can follow
the time shifts; (ii) The _Motif blind_ subtracts to the _Optimal_ estimates,
all the PEV drivers that will not accept the recommendations due to the
individual mobility constraints (iii) The _Motif aware_ is a customized
strategy informed by the individual mobility constraints to distribute the
time shifts. These three strategies are evaluated under the _end bound_ and
_flexible_ schemes. The comparisons of the power curves of the three schemes
and the two strategies are shown in Supplementary Fig. 7 and 8.

The _Optimal_ results are the best case scenario because all sessions can be
shifted. The _Motif aware_ scheme represents the more feasible gains by
coupling the charging strategies with the constraints of the drivers. The
_Motif blind_ scheme is added to show how optimization strategies based on
charging data only overestimate the benefits of the savings from $3\%$ to
$15\%$, while this loss can be overcome with the mobility information.

For the _Motif aware_ scheme, we examine the peak load saving versus the PEV
driver’s adoption rate (a.k.a. flexibility) of the time shifts. Fig. 5D shows
a linear relationship with the acceptance rate and the savings for both of the
_Motif blind_ and _Motif aware_ schemes. With the increase of adoption rate,
_Motif aware_ contributes more on peak load saving than _Motif blind_. For
instance, when $80\%$ of PEV drivers accept the time-shift recommendations,
the _Motif aware_ scheme reduces the peak load by 424kW on average, while the
_Motif blind_ scheme reduces 279kW on average.

In Fig. 5E, we present the peak load saving of the three flexible schemes
versus the number of PEVs traveling to the selected zipcode. The inset of Fig.
5E shows the estimated peak load without energy demand management. Both the
peak load and the three saving powers grow linearly with the numbers of PEVs.
The gap between _Optimal_ and _Motif aware_ is negligible in comparison with
_Optimal_ vs. _Motif blind_.

This framework allows us to evaluate how the time shifts in their departures
affect the commuting travel times of the PEV trips into the subject zipcode.
Figure 5F shows that the peak load reductions can be achieved without causing
major discomfort to commuters in terms of travel times. The most negatively
influenced drivers end up losing a maximum of 20 minutes in the case of $d=4$
(1 hour), and are far less than those who are unaffected by the proposed
changes. There is a number of drivers that even achieve travel time savings.

Finally, we examine the monetary outcomes of the proposed strategies, _end
bound_ and _flexible_. We use the E-19 rate structure for the region to
calculate the change in demand charge as a proxy of the cost in terms of
dollars (?, ?). We use the max part-peak demand summer rates. The peaks we
observe fall in the shoulder period of 8:30am-12:00pm, for which the demand
charge rate is 4.07$/kW. When implemented, the possible benefits of the
schemes we proposed are displayed in Fig. 5G: monthly potential savings in the
demand charge can reach up to 2500$ for the motif customized and _flexible_
strategy, correspond to roughly 5$ per month per session. Without managing
charging, these savings remain unrealized, and are paid by PEV drivers or the
companies that subsidize the charging activity. As a sum the savings are
substantial, yet for the number of sessions on a typical weekday considered
here, the amount saved per individual is relatively small, making the uniform
distribution of savings a relatively unexciting reward for cooperation.
However, as the biggest beneficiary of the PEV traveling management, the power
grid operator could pay the PEV drivers to encourage their initiatives on the
travel schedule shift. In addition, recent studies have suggested that
gamified systems are successful in promoting behavior that helps achieve
social good (?). More specifically, these systems encourage engagement by
building raffles in which each participant has a chance to win a bigger reward
with a probability proportional to their cooperation level. This type of
mechanisms may make incentivization more attractive in the context of PEVs and
their electricity demand management.

Moreover, we analyze the potential impact of the PEV travel demand management
strategy on the non-EV charging electricity demand in both of the residential
regions and commercial buildings. Among the PEV drivers involved in the time-
shift strategy, $60\%$ of them are recommended to depart from home earlier and
$40\%$ are recommended to depart from home later. Considering most of the
household electricity usages have two peaks, morning and evening peak (?), we
argue that the time-shift strategy is more likely to relieve the morning peak
of electricity usage in the residential area as a part of PEV drivers are
leaving home earlier than usual. Similarly, as the PEV drivers arrive home at
variant time, the time-shift strategy is also likely to relieve the evening
peak load. For the commercial buildings, the power load curve is more stable
during the working hours (?). The change of arrival time to or departure time
from the commercial building will not have significant influence on the power
load.

## Discussion

This work presents, to the best of our knowledge, the first exploratory
analysis that couples two unique large datasets on urban mobility and energy
consumption of electric vehicles. We address a gap in existing PEV management
literature, namely the simplistic modeling of urban mobility, by generating a
model of individual mobility informed by large scale mobile phone data.
Moreover, we extend the proposed methodology by demonstrating a charging
management scheme and assess its applicability by using the information on
individual mobility constraints of the drivers.

We evaluate recommendation schemes of time shifts in the charging sessions
constrained by the individual mobility motif of PEV drivers. That is, about
$30\%$ of PEV drivers could be limited to change their travel plan due to
their schedule in other activities before or after work. Following these, peak
power values can be shed by up to $47\%$. To assess the feasibility of the
recommendations, we estimate the possible monetary benefits and the travel
time losses resulting from the proposed schemes. The resulting daily savings
while modest at the individual level, are certainly substantial enough to fund
game based prizes that induce cooperation and raise awareness. On the other
hand, the travel time losses are almost imperceptible to the majority of the
drivers, and a substantial number of drivers in fact benefit from the
adjustment of their arrival times as it aids them to escape morning traffic.

The presented framework relies on individual location data from mobile phones
and a survey of PEV drivers. We designed a Bayesian inference framework to
estimate the PEV usage probability of each vehicle driver. The Bayesian
inference framework relies on three properties of the PEV users: the
distribution of their household income, the distribution of their daily
driving distances, and the adoption rate of PEV in the city. While in the
profiles of PEV adopters may change due to the rebate policy, new battery
technique, etc., the surveys can be updated based on sales. Thus, via changing
one or more properties, it’s easy to estimate the use of PEV in each zipcode
under different scenarios. Associated with the mobility information, the
proposed model is adaptable and can be used to evaluate different scenario
analysis of future energy demand of PEVs in time and space. In contrast, the
prevalent data-driven energy demand methods mainly predict the future demand
in a given region with the historical data, which can not estimate long-term
consumption under different scenarios (?).

There are various avenues in which this work can be extended. Better
understanding of the charging behavior of PEV drivers and the energy demand in
residential regions would complete and enrich our planning estimates. As the
PEVs are widely spreading these years, a stronger comprehension of the tie
among mobility, socioeconomic characteristics of PEV owners, and the PEV
incentive policies is necessary to accurately grasp the future energy demand
as well as the pressure of the power grid. Another interesting avenue is to
investigate PEVs management when the future energy structure changes, such as
the rise of the wind and solar power.

## Materials and Methods

### Data

The three main sources of data used in this study are described below.

  1. 1.

Mobile Phone Activity: Also referred to as Call Detail Records (CDRs), this
data has been widely popular in the last decade, especially in the context of
mobility modeling (?, ?, ?, ?, ?, ?). For this work, we make use of the CDRs
for the Bay Area including approximately 1.39 million users and more than 200
million calls they made over 6 weeks. Each record contains the anonymized user
ID, timestamp, duration, and the geographic location of the associated cell
tower. The spatial resolution is discretized to the service areas of 892
distinct cell towers. This information is used to build the TimeGeo mobility
model for the Bay Area for a typical weekday. More details of the CDRs can be
found in (?)

  2. 2.

PEV Charging Sessions: This data provided by Chargepoint Inc. (?), a charging
station construction company, contains 580,000 records of PEV charging
sessions in a part of commercial PEV supply equipment (EVSE) locations across
the Bay Area in 2013, including any vehicle with a battery that can be
charged. For each charging session, the following information is available:
(i) one-time information on the EVSE location type, unique driver ID, total
energy transferred, and plug-in/plug-out times; and (ii) charging power
readings obtained every 15 minutes. The locations of the charging stations are
anonymized to zipcode level. As a preprocessing step, we filter out records
lasting shorter than 1 minute, are not in 2013, or have erroneous power
measurements exceeding typical cable capacity and maximum charging rates.

  3. 3.

Census and Survey Information: The census data used in this study consists of
shapefiles describing census tracts, their population, and income information
(?). The survey information is obtained from the California Plug-in Electric
Vehicle Driver Survey carried out in 2013 (?). This survey contains
information on various sociodemographic characteristics and travel behavior of
PEV drivers in California. We utilize information regarding income and average
daily vehicle miles traveled in the estimation of PEV mobility.

### Individual Mobility Model

From the CDRs data, we are able to extract the visited places and time during
the period of the dataset for each user. With that information, TimeGeo models
and integrates the flexible temporal and spatial mobility choice of the
individual. In the model, each day of a week is divided into 144 discrete
intervals. For each interval, the individual decides to stay or move, and then
where to go if she chooses to move. To represent the movement mechanisms,
TimeGeo introduces time-inhomogeneous Markov chain model with three
individual-specific mobility parameters: a weekly home-based tour number
($n_{W}$), a dwell rate ($\beta_{1}$), and a burst rate ($\beta_{2}$).
Besides, $P(t)$ is defined as the global travel circadian rhythm of the
population in an average week and it is different for commuters and non-
commuters.

For the temporal movement choices, TimeGeo begins with determining if the
individual is at home. If true, she will move with probability $n_{w}P(t)$,
which represents her likelihood of making a trip originated from home in a
time-interval $t$ of a week. If false, she will move with probability
$\beta_{1}n_{w}P(t)$. Then, if she decides to move, she goes to $other$ places
with probability $\beta_{2}n_{w}P(t)$ and goes back to home with probability
$1-\beta_{2}n_{w}P(t)$. The $P(t)$, distribution of $n_{w}$, $\beta_{1}n_{w}$,
and $\beta_{2}n_{w}$ are illustrated in Supplementary Fig. 3.

For the spatial movement choices, TimeGeo uses a rank-based exploration and
preferential return (r-EPR) to determines the next place of the individual. In
detail, when the individual chooses to move to an $other$ place, she could
return to a visited place or explore a new place. The model assumes that the
individual explores a new place with probability $P_{new}=\rho S^{-\gamma}$,
which captures a decreasing propensity to visit new locations as the number of
previously visited locations ($S$) increases with time. If the individual
decides to return, the return location is selected from the visited locations
according to her visiting frequency. If she decides to explore a new location,
the alternative destinations are selected according to the distance to her
origin with probability $P(k)\sim k^{-\alpha}$. More details of the TimeGeo
model can be found in (?). To assess the simulation of individual mobility in
Bay Area, we compare the aggregate performance of TimeGeo with NHTS and CHTS
and show the results in Fig. 2, Supplementary Fig. 1 and Fig. 2.

### Electric Vehicle Mobility Estimation

With the purpose of sampling PEV users from all vehicular drivers in Bay Area,
we first extract the vehicular drivers from the entire population with the
vehicle usage rate at census tract scale. Then, each vehicular driver is
associated with a probability of using PEV, $P(EV|I_{u},D_{u})$ on the basis
of the driver’s household income $I_{u}$ and daily driving distance $D_{u}$.
$I_{u}$ is the random variable that denotes the income of the trip maker and
follows a standard normal distribution centered at the median income of the
residential tract. The median income information at tract scale is from census
data (?). $P(I_{u})$ is the probability density of the household income of all
trip makers in Bay Area. Similarly, $D_{u}$ is the random variable that
denotes the daily travel distance of the trip maker. The visited locations of
the trip maker are obtained from the TimeGeo model and the routing distance is
calculated by using a publicly available online API service for routing.
$P(D_{u})$ is the probability density of the daily travel distance of all
travelers in Bay Area. We assume that for a given trip maker, his or her
income $I_{u}$ and daily travel distance $D_{u}$ are independent, thereby,
$P(I_{u},D_{u}\mid EV)=P(I_{u}\mid EV)P(D_{u}\mid EV)$, that is, $I_{u}$ and
$D_{u}$ are also conditionally independent given a PEV driver.

To estimate the probability of using PEV, $P(EV|I_{u},D_{u})$, we begin by
expressing the Bayesian relation,

$P(EV\mid I_{u},D_{u})=\frac{P(I_{u},D_{u}\mid EV)P(EV)}{P(I_{u},D_{u})}$ (1)

By imposing our aforementioned assumptions on Eq. 1, we have

$P(EV\mid I_{u},D_{u})=\frac{P(I_{u}\mid EV)P(D_{u}\mid
EV)P(EV)}{P(I_{u})P(D_{u})}$ (2)

In estimating this value, the share of PEVs within all cars in the Bay Area in
2013 equals to $0.62\%$ according to the CVRP data (?), that is,
$P(EV)=0.62\%$. We make use of the PEV driver survey information regarding
income and daily travel distance, namely $P(I_{u}\mid EV)$ and $P(D_{u}\mid
EV)$, respectively. Once $P(EV\mid I_{u},D_{u})$ is estimated, the
probabilities are used to select the PEV drivers from all vehicular drivers.
Fig. 3C represents the distribution of travel distance in the morning of all
vehicular and PEV commuters.

### Energy Consumption Models

We design different energy consumption models for the four popular PEV modes
in Bay Area. In detail, we estimate the power demand of Nissan Leaf with a
drivetrain model and the trip information. This drivetrain model builds the
relationship between the energy consumption and two aggregate properties of
the trip, the average travel speed and the route distance, which we estimate
from a publicly available online API service for each PEV trip. That is,

$E_{trip}^{Nissan}=f(V_{trip})D_{trip}$ (3)

where $V_{trip}$ and $D_{trip}$ are the average speed and route distance of
the trip respectively. $f(V_{trip})$ implies the consumed power per mile
(kWh/mi) when the PEV is traveling at speed $V_{trip}$ (mi/hr). However,
$f(V_{trip})$ depends on the battery used by the PEV model, meaning that
different PEV models show different shapes of $f(V_{trip})$. In this work, we
fit $f(V_{trip})$ with a piecewise linear function using the data observed
from Nissan Leaf (?). The curve of $f(V_{trip})$ is given in Supplementary
Fig. 6B and the formulation is given as follows:

$f(V_{trip})=\begin{cases}\begin{aligned} &-23.12\times 10^{-3}\cdot
V_{trip}+0.439&\ \ V_{trip}\leq 6.70\\\ &-8.14\times 10^{-3}\cdot
V_{trip}+0.338&\ \ 6.70\leq V_{trip}\leq 12.71\\\ &-0.38\times 10^{-3}\cdot
V_{trip}+0.240&\ \ 12.71\leq V_{trip}\leq 21.75\\\ &2.11\times 10^{-3}\cdot
V_{trip}+0.185&\ \ 21.75\leq V_{trip}\leq 60.00\end{aligned}\end{cases}$ (4)

The consumption of Tesla Model S is the estimated by scaling the consumption
of Nissan Leaf in the same trip by $1.229$, as the Tesla model S consumes
$22.9\%$ more energy on average than the Nissan Leaf (?). That is,
$E_{trip}^{Tesla}=1.229f(V_{trip})D_{trip}$.

For the PHEVs, we introduce the charge-depleting (CD) models to estimate their
energy consumptions,

$E_{trip}^{PHEV}=min\\{D_{trip}\cdot r,C_{PHEV}\\}$ (5)

where $r$ and $C_{PHEV}$ are the electricity consumption rate and the battery
capacity of the PHEV, respectively. Wu et al. calibrated that $r=0.288$kWh/mi
for PHEVs with 10 miles electric range; $r=0.337$kWh/mi for PHEVs with 20
miles electric range; and $r=0.342$kWh/mile for PHEVs with 40 miles electric
range (?). In the Bay Area, the two most popular modes of PHEVs are Chevrolet
Volt and Toyota Prius, and their electric ranges are 40 miles and 10 miles,
respectively. The energy consumption models used here also match with the EV
efficiency ratings released by the US Department of Energy (see Supplementary
Table 1).

### Optimization Model

We begin by discretizing a day into 15-minute intervals such that each day
starts at $t=0$ and ends at $t=95$ (?). For each charging session $i$ among
$N$ in a day happen in a selected zipcode, we define $t^{i}_{a}$ as the
arrival time index, $t^{i}_{c}$ as the time index where charging is complete,
and $t^{i}_{d}$ as the departure time index. We represent the time indices by
the vector $\tau^{i}$, and the power consumption by vectors $\bm{P}^{i}$ and
$\bm{Q}^{i}$, all defined as follows:

$\displaystyle\bm{\tau}^{i}$
$\displaystyle=[t^{i}_{a},\ldots,t^{i}_{c}]^{\intercal}$ (6)
$\displaystyle\bm{P}^{i}$
$\displaystyle=[P^{i}_{0},\ldots,P^{i}_{95}]^{\intercal}$
$\displaystyle\bm{Q}^{i}$
$\displaystyle=[P^{i}_{t^{i}_{a}},\ldots,P^{i}_{t^{i}_{c}}]^{\intercal}$

By shifting $\bm{Q}^{i}$ within $\bm{P}^{i}$ by an amount $d^{i}$ for all
sessions, we can modify the overall power demand curve. We define
$M^{i}=(t^{i}_{c}-t^{i}_{a})+1$ as the total number of non-zero power
measurements in this charging session (i.e. total number of elements in
$\bm{Q}^{i}$), given that charging sessions start immediately upon arrival. We
enforce continuity of the charging process, the non-violation of departure
times, and amounts of session energy.

To capture the constraints proposed above, we introduce the following formal
constraints:

$\left.\begin{aligned} &\tau^{i}_{j}\geq 0\\\ &\tau^{i}_{j}\leq 95\\\
&\tau^{i}_{j}\geq t^{i}_{a}+d^{i}\\\ &\tau^{i}_{j}\leq t^{i}_{c}+d^{i}\\\
&t^{i}_{d}\geq t^{i}_{c}+d^{i}\\\ &\tau^{i}_{j}<\tau^{i}_{j+1}\\\
\end{aligned}\right\\}\begin{aligned} &\forall i\in[1,N],\\\ &\forall
j\in[1,M^{i}]\end{aligned}$ (7)

where $d^{i}$ is the delay of the charging session of the $i$-th PEV driver.
As the mobility motif of the PEV driver limits the acceptability of the
recommendations, we customize $d^{i}$ for the PEV drivers with different
mobility motifs as shown in Fig. 5B. Assuming that the delay of strategy is
$d$, we introduce the following constraints:

$d^{i}=\begin{cases}\begin{aligned} &d&&\text{H-W-H}\\\
&min\\{0,d\\}&&\text{H-W-O-H}\\\ &0&&\text{H-O-W-H \ \& H-O-W-
O-H}\end{aligned}\end{cases}$ (8)

In this customization of delay, the drivers with mobility motif _home-work-
home_ (H-W-H) could accept any change of arrival and departure time; the
drivers with mobility motif _home-work-other-home_ (H-W-O-H) can not delay
their departure time, that is, the delay $d$ must be non-positive; the drivers
with mobility motif _home-other-work-home_ (H-O-W-H) can not change their
arrive time; the drivers with mobility motif _home-other-work-other-home_
(H-O-W-O-H) can change neither their arrival time nor departure time.

We construct the proposed constraints using a binary decision matrix to
represent charging or non-charging time slots within the optimization
duration. To represent the candidate time slot at which $Q^{i}_{j}$ can be
positioned, we create binary row vectors $\bm{x^{i}_{j}}$ each consisting of
95 binary decision variables: $x^{i}_{j,k}\in\\{0,1\\},\forall
j\in[1,M^{i}],\forall i\in[1,N],\forall k\in[0,95]$.

$\bm{X^{i}}=\begin{bmatrix}\bm{x^{i}_{1}}\\\ \vdots\\\
\bm{x^{i}_{M^{i}}}\end{bmatrix}=\begin{bmatrix}x^{i}_{1,0}&\ldots&x^{i}_{1,95}\\\
\vdots&\ddots&\vdots\\\ x^{i}_{M^{i},0}&\ldots&x^{i}_{M^{i},95}\end{bmatrix}$
(9)

Finally, we write the variables in the constraints given in (7) using the
binary decision variable as follows:

$\displaystyle\bm{\tau^{i}}=\bm{X^{i}}\begin{bmatrix}0\\\ \vdots\\\
95\end{bmatrix}$ (10)

The aggregate power vector $\bm{AP}$ is given as follows:

$\bm{AP}=\sum_{i=0}^{N}\bm{P}^{i}=\begin{bmatrix}\bm{Q}^{1}\\\ \vdots\\\
\bm{Q}^{N}\end{bmatrix}^{\intercal}\begin{bmatrix}\bm{X}^{1}\\\ \vdots\\\
\bm{X}^{N}\end{bmatrix}\\\ $ (11)

The resulting formulation is a mixed-integer linear program, with decision
variables $\bm{X}^{i}$, $P_{peak}$, and $d^{i}$ of which the latter two are
integers. The problem can be proposed to minimize the daily peak load
$P_{peak}$ for a group of PEVs arriving to the same zip code location:

$\displaystyle\underset{\bm{X}^{i},P_{peak},d^{i}}{\text{minimize}}$
$\displaystyle P_{peak}$

subject to (7) and the following additional constraints:

$AP^{i}_{t}\leq P_{peak},\hskip 5.0pt\forall i\in[1,N],\hskip 5.0pt\forall
t\in[0,95]$ (12)

## References

  * 1. J. J. Michalek, et al., Valuation of plug-in vehicle life-cycle air emissions and oil displacement benefits.  Proceedings of the National Academy of Sciences 108, 16554–16558 (2011).
  * 2. R. Atia, N. Yamada, More accurate sizing of renewable energy sources under high levels of electric vehicle integration.  Renewable Energy 81, 918–925 (2015).
  * 3. Z. A. Needell, J. McNerney, M. T. Chang, J. E. Trancik, Potential for widespread electrification of personal vehicle travel in the united states.  Nature Energy 1, 16112 (2016).
  * 4. B. Nykvist, M. Nilsson, Rapidly falling costs of battery packs for electric vehicles.  Nature Climate Change 5, 329–332 (2015).
  * 5. N. Melton, J. Axsen, D. Sperling, Moving beyond alternative fuel hype to decarbonize transportation.  Nature Energy 1, 16013 (2016).
  * 6. X. Hu, S. J. Moura, N. Murgovski, B. Egardt, D. Cao, Integrated optimization of battery sizing, charging, and power management in plug-in hybrid electric vehicles.  IEEE Transactions on Control Systems Technology 24, 1036–1043 (2016).
  * 7. J. DeShazo, Improving incentives for clean vehicle purchases in the united states: Challenges and opportunities.  Review of Environmental Economics and Policy 10, 149–165 (2016).
  * 8. T. Trigg, et al., Global ev outlook: understanding the electric vehicle landscape to 2020.  Int. Energy Agency pp. 1–40 (2013).
  * 9. P. Hines, J. Apt, S. Talukdar, Large blackouts in north america: Historical trends and policy implications.  Energy Policy 37, 5249–5259 (2009).
  * 10. C. D. Brummitt, P. D. Hines, I. Dobson, C. Moore, R. M. D’Souza, Transdisciplinary electric power grid science.  Proceedings of the National Academy of Sciences 110, 12159–12159 (2013).
  * 11. S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, S. Havlin, Catastrophic cascade of failures in interdependent networks.  Nature 464, 1025–1028 (2010).
  * 12. C. D. Brummitt, R. M. D’Souza, E. Leicht, Suppressing cascades of load in interdependent networks.  Proceedings of the National Academy of Sciences 109, E680–E689 (2012).
  * 13. S. Pahwa, C. Scoglio, A. Scala, Abruptness of cascade failures in power grids.  Scientific reports 4 (2014).
  * 14. T. C. McAndrew, C. M. Danforth, J. P. Bagrow, Robustness of spatial micronetworks.  Phys. Rev. E 91, 042813 (2015).
  * 15. F. Mwasilu, J. J. Justo, E.-K. Kim, T. D. Do, J.-W. Jung, Electric vehicles and smart grid interaction: A review on vehicle to grid and renewable energy sources integration.  Renewable and Sustainable Energy Reviews 34, 501–516 (2014).
  * 16. A. Halu, A. Scala, A. Khiyami, M. C. González, Data-driven modeling of solar-powered urban microgrids.  Science Advances 2, e1500700 (2016).
  * 17. M. Mureddu, G. Caldarelli, A. Chessa, A. Scala, A. Damiano, Green power grids: How energy from renewable sources affects networks and markets.  PloS one 10, e0135312 (2015).
  * 18. I. S. Bayram, G. Michailidis, M. Devetsikiotis, F. Granelli, S. Bhattacharya, Control and Optimization Methods for Electric Smart Grids (Springer, 2012), pp. 133–145.
  * 19. D. S. Callaway, I. A. Hiskens, Achieving controllability of electric loads.  Proceedings of the IEEE 99, 184–199 (2011).
  * 20. S. J. Moura, H. K. Fathy, D. S. Callaway, J. L. Stein, A stochastic optimal control approach for power management in plug-in hybrid electric vehicles.  IEEE Transactions on control systems technology 19, 545–555 (2011).
  * 21. K. Clement-Nyns, E. Haesen, J. Driesen, The impact of charging plug-in hybrid electric vehicles on a residential distribution grid.  Power Systems, IEEE Transactions on 25, 371–380 (2010).
  * 22. G. Tal, M. Nicholas, J. Davies, J. Woodjack, Charging behavior impacts on electric vehicle miles traveled: Who is not plugging in?  Transportation Research Record: Journal of the Transportation Research Board pp. 53–60 (2014).
  * 23. C. B. Harris, M. E. Webber, An empirically-validated methodology to simulate electricity demand for electric vehicle charging.  Applied Energy 126, 172–181 (2014).
  * 24. Z. Lin, Optimizing and diversifying electric vehicle driving range for us drivers.  Transportation Science 48, 635–650 (2014).
  * 25. S. Rajakaruna, F. Shahnia, A. Ghosh, Plug In Electric Vehicles in Smart Grids (Springer, 2015).
  * 26. M. A. Tamor, P. E. Moraal, B. Reprogle, M. Milačić, Rapid estimation of electric vehicle acceptance using a general description of driving patterns.  Transportation Research Part C: Emerging Technologies 51, 136–148 (2015).
  * 27. P. Hines, et al., Understanding and managing the impacts of electric vehicles on electric power distribution systems, Tech. rep., University of Vermont (2014).
  * 28. T. Yuksel, J. J. Michalek, Effects of regional temperature on electric vehicle efficiency, range, and emissions in the united states.  Environmental science & technology 49, 3974–3980 (2015).
  * 29. P. Rezaei, J. Frolik, P. D. Hines, Packetized plug-in electric vehicle charge management.  Smart Grid, IEEE Transactions on 5, 642–650 (2014).
  * 30. K. Valogianni, W. Ketter, J. Collins, D. Zhdanov, AAAI (2014), pp. 472–478.
  * 31. Z. Ma, D. S. Callaway, I. A. Hiskens, Decentralized charging control of large populations of plug-in electric vehicles.  Control Systems Technology, IEEE Transactions on 21, 67–78 (2013).
  * 32. E. C. Kara, et al., Estimating the benefits of electric vehicle smart charging at non-residential locations: A data-driven approach.  Applied Energy 155, 515 - 525 (2015).
  * 33. A. Subramanian, M. J. Garcia, D. S. Callaway, K. Poolla, P. Varaiya, Real-time scheduling of distributed resources.  Smart Grid, IEEE Transactions on 4, 2122–2130 (2013).
  * 34. L. Yang, J. Zhang, H. V. Poor, Risk-aware day-ahead scheduling and real-time dispatch for electric vehicle charging.  Smart Grid, IEEE Transactions on 5, 693–702 (2014).
  * 35. A. Zakariazadeh, S. Jadid, P. Siano, Multi-objective scheduling of electric vehicles in smart distribution system.  Energy Conversion and Management 79, 43–53 (2014).
  * 36. J. García-Villalobos, I. Zamora, J. San Martín, F. Asensio, V. Aperribay, Plug-in electric vehicles in electric distribution networks: A review of smart charging approaches.  Renewable and Sustainable Energy Reviews 38, 717–731 (2014).
  * 37. M. Alizadeh, et al., Joint management of electric vehicles in coupled power and transportation networks.  arXiv preprint arXiv:1511.03611 (2015).
  * 38. S. Jiang, et al., The timegeo modeling framework for urban mobility without travel surveys.  Proceedings of the National Academy of Sciences p. 201524261 (2016).
  * 39. S. Jiang, et al., Proceedings of the 2nd ACM SIGKDD International Workshop on Urban Computing (ACM, 2013), p. 2.
  * 40. S. Çolak, L. P. Alexander, B. G. Alvim, S. R. Mehndiratta, M. C. González, Analyzing cell phone location data for urban travel: current methods, limitations, and opportunities.  Transportation Research Record: Journal of the Transportation Research Board pp. 126–135 (2015).
  * 41. J. L. Toole, et al., The path most traveled: Travel demand estimation using big data resources.  Transportation Research Part C: Emerging Technologies 58, 162 - 177 (2015).
  * 42. National Renewable Energy Laboratory, Transportation secure data center, www.nrel.gov/tsdc (2015). [Online; accessed 15-Jan-2015].
  * 43. U.S. Department of Transportation, Federal Highway Administration, National household travel survey, http://nhts.ornl.gov (2009). [Online; accessed 01-Oct-2016].
  * 44. C. M. Schneider, V. Belik, T. Couronné, Z. Smoreda, M. C. González, Unravelling daily human mobility motifs.  Journal of The Royal Society Interface 10, 20130246 (2013).
  * 45. California Center for Sustainable Energy, California plug-in electric vehicle driver survey results - may 2013, Tech. rep., California Center for Sustainable Energy (2013).
  * 46. Center for Sustainable Energy, California air resources board clean vehicle rebate project, rebate statistics, https://cleanvehiclerebate.org/rebate-statistics (2017). [Online; accessed 05-April-2017].
  * 47. Vital Signs, Commute time, http://www.vitalsigns.mtc.ca.gov/commute-time (2017). [Online; accessed 16-May-2017].
  * 48. S. Saxena, C. L. Floch, J. MacDonald, S. Moura, Quantifying EV battery end-of-life through analysis of travel needs with vehicle powertrain models.  Journal of Power Sources 282, 265 - 276 (2015).
  * 49. X. Wu, J. Dong, Z. Lin, Cost analysis of plug-in hybrid electric vehicles using gps-based longitudinal travel data.  Energy Policy 68, 206–217 (2014).
  * 50. M. Yilmaz, P. T. Krein, Review of battery charger topologies, charging power levels, and infrastructure for plug-in electric and hybrid vehicles.  IEEE Transactions on Power Electronics 28, 2151-2169 (2013).
  * 51. U.S. Department of Energy, Workplace charging challenge, mid-program review: Employees plug in, Tech. rep., U.S. Department of Energy (2015).
  * 52. Pacific Gas and Electric Company, Electric schedule e-19: Medium general demand-metered TOU service (2010).
  * 53. D. Merugu, B. S. Prabhakar, N. Rama, Proc. of ACM NetEcon Workshop (Citeseer, 2009).
  * 54. S. Xu, E. Barbour, M. C. González, Proceedings of the 6nd ACM SIGKDD International Workshop on Urban Computing (ACM, 2017), p. 2.
  * 55. X. Luo, T. Hong, Y. Chen, M. A. Piette, Electric load shape benchmarking for small-and medium-sized commercial buildings.  Applied Energy 204, 715–725 (2017).
  * 56. E. Xydas, et al., A data-driven approach for characterising the charging demand of electric vehicles: A uk case study.  Applied Energy 162, 763–771 (2016).
  * 57. V. D. Blondel, A. Decuyper, G. Krings, A survey of results on mobile phone datasets analysis.  EPJ Data Science 4:10 (2015).
  * 58. L. Alexander, S. Jiang, M. Murga, M. C. González, Origin–destination trips by purpose and time of day inferred from mobile phone data.  Transportation Research Part C: Emerging Technologies 58, Part B, 240 - 250 (2015).
  * 59. S. Çolak, A. Lima, M. C. González, Understanding congested travel in urban areas.  Nature communications 7 (2016).
  * 60. Chargepoint Inc., https://www.chargepoint.com/ (2016).
  * 61. United States Census Bureau, Census data, https://www.census.gov/data.html (2016). [Online; accessed 15-Oct-2016].
  * 62. C. Fiori, K. Ahn, H. A. Rakha, Power-based electric vehicle energy consumption model: Model development and validation.  Applied Energy 168, 257–268 (2016).

Acknowledgements: We would like to thank Chargepoint Inc. for providing the
electric vehicle charging data, and Airsage for providing the call detail
records used in this study. We also would like to thank Sila Kiliccote and
Michaelangelo Tabone for their valuable feedback.
Funding: This work was supported by the Siebel Institute and MIT Energy
Initiative.
Author Contributions YX, SC, and ECK conceived the research and designed the
analyses. YX, SC, and MCG performed the analyses and wrote the paper. ECK
helped perform the analyses. SJM and MCG provided general advice and
supervised the research.
Competing Interests The authors declare that they have no competing financial
interests.
Data and materials availability: All data needed to evaluate the conclusions
in the paper are present in the paper. Additional data related to this paper
may be requested from the authors.

Fig. 1. Coupling PEV charging with urban mobility. A Mobile phone data is used
to model individual mobility. B Charging sessions data is used to characterize
individual and total electricity demand curves. C The Bayesian inference
method is proposed to find the probability that the vehicular trip is made by
a PEV. Z is the work zipcode of users $U_{1}$, $U_{2}$, and $U_{3}$. D
Charging activity is shifted to create a recommendation scheme that relieve
peaks in demand and generate monetary savings to the drivers based on
electricity tariffs.

Table 1. Characteristics of PEV drivers. Distribution of A average daily miles
driven and B annual income by PEV drivers in California, USA (?).

| (1000$) | Conventional | PEV
---|---|---
Unknown | 20% | 17%
$<$ 50 | 20% | 2%
50-100 | 30% | 13%
100-150 | 14% | 20%
$>$ 250 | 15% | 47%
(miles) | %
---|---
$<$ 15 | 14%
15-30 | 50%
30-45 | 28%
$>$ 45 | 8%

Fig. 2. Validation of individual mobility simulation in Bay Area. A Simulated
trajectory of a mobile phone user who is labeled as commuter. The blue
triangles represent the actually recorded activities of the selected user from
October 22 to 25, 2012. The red and green circles are the recognized home and
work from the mobile phone data respectively. B Population distribution
comparison of daily visited locations between simulation and two travel survey
datasets, 2010 CHTS, and 2009 NHTS. Supplementary Fig. 1A and 1B respectively
present the comparisons of two more properties of mobility, stay duration and
trip distance. C Validation of individual mobility motifs for the active users
in simulation and CDRs data. The distribution of the 10 primary motifs shows a
high degree of similarity to the CDRs data. The comparison of motifs of
commuters and non-commuters are shown in the Supplementary Fig. 1C. D Fraction
of trip departures by time of the day, comparing the simulation, the 2010
CHTS, and the 2009 NHTS. Supplementary Fig. 2 shows the comparisons for
various trip purposes.

Fig. 3. Validation of PEV mobility estimation and calibration of PEV charging
behavior. A Number of PEVs in the residential zipcodes of the Bay Area from
the simulation and the CVRP datasets in the end of 2013. The total number of
PEVs is $15963$ from our simulation, which is close to the actual number from
CVRP datasets, $16103$. B Correlation between the simulated PEV and the PEV
from CVRP data. C, D Probability distributions of commuting distances, $D$,
and commuting travel times, $T$, of all vehicle trips and EV trips estimated
through income information and trip distances. E Fractions of four types of
mobility motifs of all commuters and PEV users. $58\%$ of commuters only
travel between home and work on weekdays, while the rest $42\%$ have other
activities before or after work. Similarly, $66\%$ of commuters using PEVs
only travel between home and work, and the rest $34\%$ have other activities
before or after work. F Probability distributions of charging energy $E_{S}$
obtained from charging sessions compared to those of the energy demand
estimated by energy consumption model on three charging behavior scenarios,
morning, daily, and two-days. G Probability distributions of charging energy
$E_{S}$ and those of the daily energy demand of simulated PEVs for the
zipcodes which have most charging session records.

Fig. 4. PEV charging session profiles. A Distribution of $N_{day}$ the number
of sessions per day for each driver ID starting from the day of first record
(right inset: number of new driver IDs added every month, left inset:
distribution of $N_{EVSE}$, the number of unique EVSEs visited by every driver
ID.) B Distributions of $h_{a}$ and $h_{d}$, the arrival and departure hours
to and from an EVSE. (inset: the distributions of $\Delta h_{a}$ and $\Delta
h_{d}$, the interarrival and interdeparture times for a driver ID visiting a
specific EVSE.) C Distribution of $E_{S}$, the total energy withdrawn per
session (inset: the distribution of $\delta_{S}$, session durations.) D Power
consumption as a function of the normalized session duration segmented by
total duration groups.

Fig. 5. Assessing the benefits of minimizing peak power. A An illustration of
a sample of sessions in the _flexible_ strategy. The charging event within a
session is shifted such that the overall peak power is minimized. B Decrease
in peak power measurements for the varying $d$ of the _flexible_ and
_charging-shift_ strategy. The flexible time shifts are constrained by
mobility motifs of PEV users, and the peak shaving of $47\%$ can be achieved.
The _charging-shift_ strategy reduces the peak load by $66\%$. C Percentage
peak load of the three schemes _Optimal_ , _Motif blind_ and _Motif aware_ are
presented. The positive value on the bar implies the gap in the estimates
between the _Optimal_ vs. _Motif blind_ , showing the effects of lacking
mobility information. The negative value on the bars implies the improvements
using _Motif aware_ information vs. _Motif blind_ , customizing the
optimization strategy to the mobility constraints. D Peak load saving versus
PEV driver’s adoption rate of the time-shift recommendations, for the _Motif-
blind_ and _Motif-aware_ schemes when $d=4$. For each adoption rate, we
randomly choose PEV drivers who accept the recommendations and average over
$50$ realizations. The error bar shows the $10th$ and $90th$ percentile of the
savings of _Motif aware_ for the given acceptance rate. The red solid (green
dash) line presents the linear fit between the saving of _Morif aware_
(_blind_) and adoption rate. E Projected peak load saving of the _flexible_
strategy when $d=4$ vs. the number of PEV users working in the selected
zipcode. Inset shows the projected peak load versus the number of PEV users. F
Changes on travel times of morning and evening trips. The majority of the
drivers are not influenced, the worst case is a few individuals suffering from
an additional 20 minute delays for $d=4$. G Monthly savings for varying values
of $d$. The _flexible_ strategy restrained by mobility motifs is able to
generate savings worth approximately 2500$ for $d=4$.