#  Achieving Reliable Coordination of Residential Plug-in Electric Vehicle
Charging: A Pilot Study

Polina Alexeenko Polina Alexeenko and Eilyan Bitar are with the School of
Electrical and Computer Engineering, Cornell University, Ithaca, NY, 14853,
USA. Emails: {pa357<EMAIL_ADDRESS>Eilyan Bitar11footnotemark: 1

###### Abstract

We report findings from a real-world pilot study exploring a novel pricing and
control mechanism to coordinate residential EV charging loads. The proposed
pricing mechanism presents EV owners with a “menu of deadlines” that offers
lower electricity prices the longer they’re willing to delay their charging
completion times. Given customers’ reported charging preferences, a smart
charging system dynamically optimizes the power drawn by EVs in real-time to
minimize their collective strain on the grid while ensuring all EVs are
charged by their user-requested deadlines. We find that customers allow their
charging to be delayed by over eight hours on average. Using this flexibility,
the smart charging system reliably eliminates demand spikes by reshaping EV
loads to flatten the aggregate load curve. Importantly, customer participation
rates remained stable throughout the study, providing evidence that the
proposed mechanism is a viable “non-wires alternative” to meet the growing
demand for electricity from EVs.

##  1 Introduction

The US transportation sector is on the brink of a major transformation. The
internal combustion engine’s hold on American transportation is beginning to
slip, and for the first time a vision of an all-electric vehicle (EV) future
is coming into focus. Driven by declining battery costs (Nykvist and Nilsson,
2015; Lutsey and Nicholas, 2019; Bloomberg NEF, 2021), progressive policy
(Fung, 2016; Grandoni et al., 2020; International Energy Agency, 2020),
consumer demand (International Energy Agency, 2020; Daramy-Williams et al.,
2019; Parker et al., 2021), and the world’s largest automakers (Colias, 2021),
it’s a vision that may become a reality in a matter of decades. A recent study
by the International Energy Agency anticipates that there will be between 140
and 245 million EVs on the road worldwide by 2030 (International Energy
Agency, 2020).

But even with this great momentum, the transition to an all-electric vehicle
future won’t be possible without careful coordination with the power grid. If
left unmanaged, the power demanded by many EVs charging at the same time in
the evening will amplify existing peak loads (Quiros-Tortos et al., 2018),
resulting in significant power losses (Clement-Nyns et al., 2010), reduced
power quality (Gruosso, 2016; Leou et al., 2013), and potentially exceeding
the grid’s capacity to reliably meet demand (Muratori, 2018; Jardini et al.,
2000; Gong et al., 2011; Hilshey et al., 2012; Powell et al., 2020).

To accommodate the increase in load driven by the unmanaged charging of EVs,
electric power utilities and grid operators would need to build new generators
to produce enough power, and expand transmission and distribution
infrastructure to deliver that power to the electric vehicles. In states like
Texas and California, where EV adoption is growing rapidly, these enhancements
to the grid infrastructure would potentially cost tens of billions of dollars,
and could take decades to complete (Davidson et al., 2018).

Timing matters. While most EV owners typically begin charging their cars when
they come home in the evening—when demand for electricity is peaking—their
charging requirements are usually flexible in the sense that their EVs
remained connected to their chargers long after they’ve completed charging.
Providing concrete evidence for this claim, The EV Project—a nation-wide study
spanning three years and involving more than 8000 EV owners—found that most
EVs, when charging overnight, usually finished charging within three hours of
plugging in, but remained connected to their chargers for an average of twelve
hours (Smart and Salisbury, 2015). In other words, most EV owners don’t need
their cars charged immediately, but within a reasonable window of time before
they expect to unplug and depart next for their next trip. This finding
suggests the possibility that some EV owners, being flexible in this way,
might be willing to delay the time required to charge their cars given the
right incentive.

###  1.1 Limitations of time-of-use pricing

In an effort to unlock this flexibility in EV charging, a number of electric
power utilities have begun to offer their EV-owning residential customers
time-of-use (TOU) rates, where the price of electricity varies over the course
of the day according to a predetermined and fixed schedule, typically being
cheapest during off-peak hours. As of September 2019, there were over fifty
different TOU rates being offered by utilities to residential EV owners across
the US (Myers et al., 2019).

While this might seem like a reasonable approach, nondiscriminatory111An
electricity rate is defined to be _nondiscriminatory_ if all customers within
a particular service class and territory are charged identical rates for their
electricity consumption. Price discrimination is prohibited by the Federal
Energy Regulatory Commission to limit the possibility of inequity among
customers (Eisen, 2015). TOU rates are constrained in terms of their ability
to attenuate the impact that EVs will have on peak load. By offering customers
lower prices to charge during hours of the day that are ordinarily off-peak,
TOU rates can have an unintentional synchronizing effect on EV charging
patterns. For example, a number of utility-run trials have observed a “timer
peak” phenomenon in which many EV owners program their vehicles to begin
charging simultaneously at the start of the off-peak pricing period (Smart and
Salisbury, 2015). Related to this effect, several recent studies have shown
that TOU rates can sharpen aggregate EV load profiles to such an extent that
they accelerate distribution transformer aging more rapidly than unmanaged
charging (Wu et al., 2011; Hilshey et al., 2012; Powell et al., 2020).
Importantly, these issues can arise even at relatively low levels of aggregate
EV penetration, because EV registrations tend to be geographically clustered
(Idaho National Laboratory, 2013). TOU rates will ultimately fail to eliminate
demand peaks driven by EV charging at scale. A greater degree of coordination
is needed.

To address these drawbacks of TOU rate designs, a number of alternative
dynamic pricing mechanisms have been proposed in the literature, where the
retail price of electricity is allowed to vary in proportion to the realized
aggregate demand over the course of the day (Ma et al., 2011; Karfopoulos and
Hatziargyriou, 2012; Tushar et al., 2012). While such dynamic pricing schemes
are shown to effectively ‘flatten’ the aggregate demand profile in theory,
their effectiveness hinges on the assumption that individual EV owners will
possess the capacity to solve nontrivial decision making problems where they
correctly anticipate the impact of their charging control strategies on the
determination of prices. Another practical shortcoming of such dynamic pricing
mechanisms is the risk they impose upon customers in the form of uncertainty
about future prices and the subsequent payments that they must make. Because
income levels are known to be negatively correlated with risk aversion
(Grable, 2016), price uncertainty is likely to disproportionately impact lower
income customers.

###  1.2 Direct control of EV charging

Direct load control is an alternative approach to managed EV charging which
addresses many of the shortcomings of dynamic pricing mechanisms while
offering additional benefits such as the potential for vehicle-to-grid (V2G)
services. Under direct load control, a central coordinating authority (e.g.,
the utility) provides each participating customer with an incentive in
exchange for the ability to directly control their EV charging subject to a
set of constraints specified by the customer. As a result, the central
coordinating authority can dynamically reshape EV charging profiles to
optimize a variety of objectives including minimizing the cost of energy
(e.g., (Jin et al., 2013; Jiang and Zhen, 2019)), maximizing the integration
of intermittent renewables (e.g. (Honarmand et al., 2014; Szinai et al.,
2020)), or minimizing peak aggregate load (e.g., (Gan et al., 2012; Zhang et
al., 2017)). There is a vast theoretical literature on direct control of
electric vehicle charging; for example, Yang et al. (Yang et al., 2015) and
Wang et al. (Wang et al., 2016) survey a wide variety of approaches to
scheduling EV charging load considering various objectives, computational
methods, and models of vehicle and customer behavior.

While direct load control mechanisms have been studied extensively using
theoretical models, there are relatively few real-world experimental studies
to date evaluating their effectiveness. To more effectively manage EV charging
loads on their distribution networks, some utilities and charging facility
operators have begun to explore the possibility of directly controlling EV
chargers in both residential (Quiros-Tortos et al., 2018; Bauman et al., 2016)
and workplace charging environments (Lee et al., 2016; Chynoweth et al., 2014;
Bohn and Glenn, 2016; Andersen et al., 2019). For example, in the ChargeTO
Program (Bauman et al., 2016), the Adaptive Charging Network Project (Lee et
al., 2016), and the ChargeForward program (Spencer et al., 2021),
participating EV owners use a web or mobile interface to initiate a charging
request—specifying when they need their EVs charged by—and a centralized
smart-charging system actively manages the power being drawn by their EVs
while ensuring that all EVs are fully charged by their user-specified
departure times. An important drawback of these frameworks for managed EV
charging is that they do not provide their users with explicit incentives to
accurately report their expected departure times. As a result, users may
underreport their departure times, preferring to have their EVs fully charged
well in advance of their anticipated departure times. Indeed, data from the
Adaptive Charging Network Project reveals that users of their platform
frequently underreport their departure times by more than several hours on
average (Lee et al., 2019). Such a reduction in the charging flexibility
provided by users constrains the extent to which their EV charging loads can
be reshaped and shifted in time, which ultimately limits the effectiveness of
managed EV charging programs and their capacity to minimize peak aggregate
loads.

###  1.3 The OptimizEV Project

In this article, we report findings from the OptimizEV Project—a pilot study
that tests a novel rate structure and technology for managed EV charging. As
one of its primary objectives, OptimizEV seeks to maximize the charging
flexibility procured from customers by offering them monetary incentives to
delay the time required to charge their EVs. Each time a customer initiates a
charging session, they are presented with a “menu of deadlines” that offers
lower electricity prices the longer they’re willing to delay the time required
to charge their EV. Using their smartphones, customers specify a desired
state-of-charge and select a corresponding deadline by which their requested
energy must be delivered. Given a collection of active charging requests, a
smart-charging system dynamically adjusts the power being drawn by each
participating EV in real time to minimize their collective impact on peak
system load, while simultaneously ensuring that every customer’s car is
charged up to the desired level by the requested deadline. Customers get their
energy when they need it and the smart-charging system optimally coordinates
the delivery of that energy to limit demand spikes.

In 2019, 34 plug-in EV owners residing in Tompkins County, New York were
recruited to participate in the OptimizEV Project on a voluntary first-come,
first-served basis.222We refer the reader to Appendix A.4 for the demographic
information of project participants. A level 2 charging station with cellular
communication and control capabilities was installed in the home of each
project participant. The project was divided into two phases: an initial two-
month _unmanaged charging phase_ (Phase I) where baseline EV charging data was
collected while project participants were exposed to the preexisting flat
electricity rate between January 1, 2020 – February 29, 2020. This was
followed by a fifteen-month _managed charging phase_ (Phase II), between March
8, 2020 – May 31, 2021, during which time all project participants were
required to initiate charging sessions using the OptimizEV platform. Project
participants were taught to use the OptimizEV platform during the transition
week between Phase I and Phase II.

During Phase I of the OptimizEV Project, the unmanaged charging patterns of
project participants frequently resulted in a substantial increase in peak
aggregate load. The user charging data collected over the course of this
project also sheds light on several undesirable effects that TOU pricing may
have on EV load patterns. We find that when many of the participating EV
owners respond to the TOU price signal by delaying their charging until the
start of the off-peak pricing period, the synchronization of EV power demand
that results when many EVs start charging simultaneously induces new aggregate
demand peaks in the middle of the night that are sometimes sharper and larger
in magnitude than the unmanaged aggregate demand peaks that would have
otherwise resulted in the absence of TOU rate-based incentives. This suggests
that at increased EV penetration levels, passive load coordination mechanisms
like TOU pricing will likely fail to attenuate the peak load associated with
unmanaged charging, and may make matters worse.

During the managed charging phase of the project, the proposed incentive and
control mechanism was highly effective in shifting the majority of EV charging
loads off-peak into the night-time valley of aggregate load curve. In
particular, the increase in peak load driven by EV charging was significantly
reduced, if not entirely eliminated, on a majority of days during the fifteen-
month span of the project. The observed efficacy of the mechanism is due in
part to high customer participation rates that remained stable over the course
of the pilot—customers frequently engaged in optimized charging sessions,
allowing the smart charging system to delay the completion of their charging
by nine hours on average. Interestingly, we also find that the majority of
sessions in which users decide to opt out of controlled charging are typically
characterized by inflexible charging requirements—revealing that users are
less likely to opt out if they do in fact have flexibility to offer. The
sustained user engagement over the course of the pilot not only confirms the
presence of substantial flexibility in real-world residential EV charging
loads, but also demonstrates that EV owners are frequently willing to cede
control of this flexibility to a smart charging system given a modest monetary
incentive. Collectively, these observations provide concrete evidence in
support of the proposed incentive and control mechanism as a potentially
viable “non-wires alternative” to support the increased demand for electricity
driven by the growing adoption of EVs.

##  2 Flexibility-differentiated pricing of EV charging services

The underlying premise of the OptimizEV Project is that different customers
have different needs when charging their electric vehicles. Some customers are
flexible and may be willing to delay the time required to charge their EVs in
exchange for a discounted electricity price, while other less flexible
customers will pay the full electricity price (or perhaps a premium on that
price) to have their EVs charged as quickly as possible. Consequently, if
customers are presented with a menu of charging options that are
differentiated according to the length of time required to charge their EVs
(with more flexible charging options being offered at lower prices), then
different customers will prefer to have their EVs charged with different
degrees of flexibility. The flexibility procured from customers can, in turn,
be utilized to optimally coordinate the charging patterns of EVs in a manner
that minimizes the utility’s supply and delivery costs, while respecting
customers’ stated charging preferences. Ultimately, the ability to better
align the utility’s cost structure with the diverse preferences of customers,
through this special form of product differentiation, has the potential to
improve both supplier and customer welfare.333Of course, in order for such
programs to be cost effective at scale, the benefit to the utility, in the
form of reduced energy costs or avoided infrastructure costs, must exceed the
program implementation and operational costs. These include administrative
costs, the cost of the rate discounts paid out to participating customers, and
the cost of the additional metering, communication, and control equipment
required to perform direct EV load control.

$0$$2$$4$$6$$8$$10$$12$$0$$2$$4$$6$$R$$d$Time (hours)Power (kW) (a) Charging
at maximum power with no delay

$0$$2$$4$$6$$8$$10$$12$$0$$2$$4$$6$$R$$d$Time (hours)Power (kW) (b) Charging
at maximum power with partial delay

$0$$2$$4$$6$$8$$10$$12$$0$$2$$4$$6$$R$$d$Time (hours)Power (kW) (c) Charging
at minimum constant power

$0$$2$$4$$6$$8$$10$$12$$0$$2$$4$$6$$R$$d$Time (hours)Power (kW) (d) Charging
with time-varying power levels

Figure 1: Four examples of feasible EV charging profiles associated with (a)
an inflexible charging request and (b)-(d) a flexible charging request. (a) EV
Charging profile induced by an inflexible charging request given by ($R=5$ kW,
$E=20$ kWh, $d=4$ hours). Because this charging request results in a slack
time of $s=0$ hours, the EV is charged without delay at its maximum rate until
its deadline. (b)-(d) Three different EV charging profiles that satisfy a
flexible charging request given by ($R=5$ kW, $E=20$ kWh, $d=10$ hours). This
charging request has a slack time of $s=6$ hours.

As part of the OptimizEV Project, we price differentiate customers’ charging
requests according to a standard measure of scheduling flexibility in queueing
systems known as _slack time_. The slack time associated with a charging
request is defined as the length of time between the minimum time required to
supply the desired state-of-charge (when charging at the maximum rated power)
and the maximum time that the customer is willing to wait to receive that
energy. More formally, the _slack time_ $s$ (units: hours) of an EV charging
request is a function of three user-specified parameters: (1) the amount of
_energy_ $E$ (units: kilowatt-hours) that the customer would like to receive;
(2) the maximum amount of time that the customer is willing to wait to receive
their requested energy, which we referred to as their deadline $d$ (units:
hours); and (3) the _maximum rate_ $R$ (units: kilowatts) at which the
customer’s EV can be charged. It follows that the slack time associated with a
charging request can be expressed as

$\displaystyle s=d-\frac{E}{R},$ (1)

where $E/R$ equals the minimum amount of time required to supply $E$ kilowatt-
hours to an EV at a maximum charging power of $R$ kilowatts. Equation (1)
offers an intuitive interpretation of slack time as the extra amount of time
available to complete a charging request. It follows that a charging request
with zero slack ($s=0$) is completely inflexible, since the corresponding EV
must be charged at maximum power from start to finish in order to deliver the
customer’s desired energy by their deadline. Figure 1 depicts an inflexible
charging profile induced by a charging request with zero slack time. By
contrast, a charging request with positive slack ($s>0$) can be satisfied
using one of a wide variety of charging profiles, some of which are
illustrated in Figures 1-1. The greater the slack time in a charging request,
the greater its flexibility.

In exchange for their willingness to delay the time required to charge their
EVs, customers receive a discount on the total cost of electricity required to
charge their EVs given by

$\displaystyle\text{EV Charging Discount}=p(s)\times E.$ (2)

Here, $s$ denotes the slack time associated with a particular customer’s
charging request ($E$, $d$, $R$), and $p(s)$ (units: $/kilowatt-hour) denotes
the corresponding discount (per unit of requested energy) given to that
customer. To incentivize flexibility in the charging requests made by
customers, the proposed _slack-differentiated discount mechanism_ is
structured so that (i) completely inflexible charging requests with zero slack
receive no discount, i.e., $p(0)=0$; and (ii) charging requests with larger
slack times are rewarded with larger discounts, i.e., $p(s)\geq p(s^{\prime})$
for all $s\geq s^{\prime}$. We also note that customers are not permitted to
make charging requests with negative slack ($s<0$), since such requests are
impossible to satisfy by their deadlines.

$0$$2$$4$$6$$8$$10$$12$$14$$0$$2$$4$$6$$\cdot 10^{-2}$$p^{\rm
max}$$s^{\max}$Slack (hours)$p(s)$ ($/kWh) Figure 2: A graphical illustration
of the slack-differentiated discount mechanism used in the OptimizEV Project.
The discount $p(s)$ (per unit of request energy) given to customers increases
linearly from $p(0)=0$ $\cent$/kWh to the maximum available discount of
$p^{\rm max}=4.3$ $\cent$/kWh at a maximum slack time of $s^{\rm max}=10$
hours. While customers are permitted to make charging requests with slack
times exceeding $s^{\rm max}$, they are not rewarded for providing additional
flexibility beyond this ten hour threshold.

Apart from these requirements, the structure of the proposed discount
mechanism is highly versatile and can be adapted to reflect the value of
charging flexibility (slack time) as determined by the particular cost
structure being optimized by the utility. For example, the discounts can be
chosen to reflect expected distribution-level infrastructure costs that can be
avoided through optimized charging using the flexibility provided by
customers. In the OptimizEV Project, specifically, the slack-differentiated
discount mechanism $p(s)$ is structured as a piecewise-linear function of the
slack time $s$ (depicted in Figure 2). The maximum discount (per unit of
requested energy) available to customers under this mechanism was chosen to
equal the delivery rate paid by residential electricity customers in NYSEG’s
territory at the time of the pilot.444An electric utility’s delivery rate
reflects costs associated with the infrastructure required to transport and
distribute energy (e.g., transformers, feeders, and substation hardware).

##  3 Optimized delivery of flexible EV charging services

Given a collection of active charging requests, an effective smart-charging
system must coordinate the charging patterns of the corresponding EVs to
minimize their aggregate contribution to peak system load, while ensuring that
every EV is charged by its requested deadline. This coordination problem is
complicated by the presence of many sources of uncertainty, including
uncertainty in the timing and nature of future charging requests, unexpected
variations in total system load, fluctuating wholesale electricity prices,
unanticipated EV charging characteristics, and failures in the communication
network being used for control.

(a) Landing page

(b) Charging preferences page

(c) Charging session status page

Figure 3: User interface of the OptimizEV system. Subfigure (a) shows the
landing page, where customers select whether to engage in a controlled or
uncontrolled charging session. Subfigure (b) shows the preferences page, where
customers select their controlled charging session preferences. Subfigure (c)
shows the status page, where customers can see information about an ongoing
charging session (e.g., which preferences were selected, the session’s
duration, and how much energy has been delivered).

In order to effectively adapt to changing system conditions in real time, the
smart-charging system developed for the OptimizEV Project utilizes a model
predictive control approach Camacho and Alba (2013) to continuously re-
optimize the active EVs’ charging profiles every minute of the day. At a high
level, the OptimizEV smart-charging system functions as follows:

  1. 1.

_Customer Inputs:_ To initiate a charging session, a customer begins by
connecting their EV to their charging station and logging into the OptimizEV
user interface (UI) using their smart phone. The UI (depicted in Figure 3)
allows customers to make charging requests and monitor the progress of their
ongoing charging sessions. When making a charging request, a customer must
provide their EV’s present state-of-charge (SOC), in addition to providing
their desired state-of-charge and completion deadline. The difference between
their desired SOC and present SOC is used to calculate their energy
requirement. Customers can also choose to opt out of optimized charging at any
time prior to or during an ongoing charging session. To limit their
“interaction costs” with the UI, customers can also preset default charging
preferences, bypassing the need to manually input these preferences in
subsequent charging sessions.

  2. 2.

_Data Acquisition:_ Every minute, the smart-charging system collects
information from all newly and previously connected EVs that are actively
being charged. These measurements include connection status, current state-of-
charge, energy consumption, and the actual power drawn by active EVs during
the previous one-minute time interval.

  3. 3.

_Computation:_ This information is passed to an optimization algorithm, which
determines optimal charging profiles for all active EVs. These optimal
charging profiles are designed to collectively minimize peak aggregate load,
while respecting the individual constraints associated with each EV, e.g.,
charging completion deadlines, charging rate constraints, and battery charging
dynamics.

  4. 4.

_Control:_ The optimized charging profiles are then transmitted to each EV’s
charging station as a sequence of time-varying power commands that each EV is
instructed to track. The EVs adjust their charging rates to track the updated
power commands as closely as possible, while respecting the safe operating
limits specified by their battery management systems. We use the SAE J1772
standard for level-2 charging stations to dynamically control each vehicle’s
charging rate.

  5. 5.

_Repeat:_ This data acquisition, computation, and control process repeats
periodically every minute to enable real-time adaptation to changing system
conditions and unexpected EV charging characteristics, while ensuring the
complete satisfaction of all customers’ charging requests and constraints.

We refer the reader to Appendix A.2 for a detailed description of the
underlying optimization model and the model predictive control algorithm used
to repeatedly optimize the EV charging profiles in the manner described above.
In Appendix A.3, we discuss a number of practical challenges encountered when
deploying the proposed real-time scheduling algorithm in a real-world setting.

(a) Weekday unmanaged charging patterns

(b) Weekend unmanaged charging patterns

Figure 4: Unmanaged charging patterns during Phase I (January 1, 2020 to
February 29, 2020) of the OpimizEV Project for weekdays (left column) and
weekends (right column). The top figures depict kernel density estimates of
session start times (solid yellow), session end times (dotted purple), and the
times at which charging is finished (dashed green). The bottom figures provide
plots of aggregate unmanaged EV charging patterns during Phase I. The baseline
(non-EV) load is depicted as a solid black curve. The median EV charging load
is shown as a solid red curve, the interdecile range of the EV charging load
is shaded in dark red, and the range between the maximum and minimum EV
charging load is shaded in light red.

##  4 Unmanaged charging patterns and latent flexibility

During Phase I of the OptimizEV Project (January 1, 2020 to February 29,
2020), all customers participated in unmanaged charging: their EVs were
charged at maximum power whenever connected to their in-home charging
stations, and charging was not delayed or controlled. During this time, we
continuously monitored and recorded the connection status and power drawn by
each user’s EV at regular one-minute intervals. In our analysis, we make use
of EV connection and disconnection times as surrogates for user arrival and
departure times to and from their homes. In Figure 4, we summarize several key
attributes of unmanaged charging patterns revealed by these data.

Using the data collected during the unmanaged charging phase of the project,
we are able to empirically estimate distributions over user plug-in times,
unplug times, and charging completion times, which are depicted in the upper
plots of Figures 4-4. Unsurprisingly, these distributions reveal that users
typically plug in and start charging in the late afternoon and early evening,
and typically unplug the following morning, presumably departing for their
next trip. The resulting concentration of unmanaged EV charging loads in the
evening is shown to manifest in a substantial amplification of peak load. The
maximum and median increases in weekday peak loads are observed to be 47 kW
(39% of the baseline peak) and 18 kW (15% of the baseline peak), respectively.
The impact of unmanaged EV charging patterns on peak load is less pronounced
on weekends, as user plug-in times are more dispersed, which results in a more
even spreading of EV charging loads across time.555The baseline (non-EV) load
profile used in our analysis is based on load data taken from a primarily
residential distribution circuit in Tompkins County, NY, which we re-scaled to
reflect an aggregate demand profile associated with approximately 60
households. We refer the reader to Appendix A.1 for a more detailed
description of how the baseline load profile is constructed.

We also note that, while there is significant heterogeneity in the day-to-day
connection patterns across different users, the aggregate behavior of users is
more predictable. As can be seen in Figure 5, the total number of EVs
connected to the grid as a function of time exhibits a clear diurnal pattern,
with the total number of EVs connected overnight averaging between 14-15
vehicles on weekdays and 11-13 vehicles on weekends.

The unmanaged charging data also reveals that users typically keep their EVs
connected to their charging stations far longer than the amount of time
required to fully charge their batteries. In particular, we find that EVs
remained plugged in for 11 hours on average, while actively drawing power for
only 2 hours on average. This implies that charging requests have an average
slack time of 9 hours—revealing the presence of a significant amount of latent
flexibility in users’ charging requirements, and the potential to harness this
flexibility to minimize the contribution of residential EV charging loads to
evening peak demand.

Figure 5: User-level connection patterns during Phase I (January 1, 2020 to
February 29, 2020) of the OptimizEV Project. Each row of the heatmap depicts
the empirical probability that a particular user’s vehicle is connected during
each minute of the week. The plot above the heatmap depicts the average, lower
quartile, and upper quartile of the number of EVs connected to the grid
throughout the week.

(a) Unmanaged

(b) OptimizEV

(c) TOU pricing

Figure 6: Aggregate load profiles (a) simulated under unmanaged charging, (b)
realized under managed (OptimizEV) charging, and (c) simulated under TOU
pricing between March 9, 2020 and March 14, 2020. In each subfigure, the
baseline load is depicted by a black curve, unmanaged EV loads are shown in
red, managed (OptimizEV) loads are shown in green, and loads under TOU pricing
are shown in blue.

(a) Unmanaged

(b) OptimizEV

(c) TOU pricing

(d) Unmanaged

(e) OptimizEV

(f) TOU pricing

Figure 7:  Daily charging patterns under unmanaged charging (left column),
OptimizEV (middle column), and TOU pricing (right column). Subfigures (a)-(c)
depict aggregate loads realized under each scenario on March 11, 2020. In each
subfigure, the baseline load is depicted by a black curve, unmanaged EV loads
are depicted in shades of red, optimized loads in shades of green, and loads
responding to TOU pricing in shades of blue. Subfigures (d)-(f) depict the
empirical range (lightly shaded region), interdecile range (darkly shaded
region), and median (solid line) associated with the aggregate EV load data
under each scenario during Phase II of the Optimize Project.

##  5 Flattening peak demand with optimized charging

During Phase II of the OptimizEV Project (March 8, 2020 to May 31, 2021), we
offered all customers flexibility-differentiated pricing to incentivize
delayed charging of their EVs. Utilizing the flexibility provided by
customers, a smart charging system continuously optimizes customers’ EV
charging profiles to flatten the resulting aggregate load profile, while
simultaneously ensuring that all customers’ EVs are charged by their requested
deadlines. Here, we describe the transformation of aggregate load patterns
enabled by this flexibility-differentiated pricing and control mechanism.

As a basis for comparison, we simulate unmanaged EV charging during Phase II
of the project. We do so by generating an unmanaged charging profile for every
charging session initiated during that time frame, where every EV is assumed
to draw power at its maximum rate upon connecting to its charging station,
until the energy requirement associated with its charging session is
fulfilled. Figures 6 and 6 depict the aggregate load profiles induced by
unmanaged charging and OptimizEV, respectively, between March 9 and March 14,
2020. Notice that unmanaged charging results in a substantial amplification of
peak load on these days, while OptimizEV effectively redistributes the
aggregate EV load to fill the nighttime valley in the baseline load profile.

To better illustrate the contribution of individual EVs to the aggregate load
profile, we disaggregate the EV load profile across different vehicles under
unmanaged and optimized charging in Figures 7 and 7, respectively, on March 9,
2020. From Figure 7, it can be seen that EVs participating in optimized
charging sessions are typically delayed in time and are charged at lower power
levels over longer stretches of time, as compared to their unmanaged
counterparts depicted in Figure 7. It’s also worth noting that on this
particular day, OptimizEV does not entirely eliminate the contribution of EVs
to peak load, as a small subset of users do opt out of optimized charging,
deciding instead to have their EVs charged at maximum power without delay.
Interestingly, we find that participation rates in optimized charging sessions
are strongly correlated with the underlying flexibility (slack) in users’
charging requirements, where users are more likely to opt out if they have
little flexibility to offer. We discuss user participation rates and trends at
more length in Section 7.

Beyond these specific days, the OptimizEV mechanism is also shown to reliably
flatten the aggregate load profile on a majority of days over the fifteen
month course of Phase II. To show this, we plot the empirical range,
interdecile range, and median associated with the aggregate EV load data under
unmanaged charging and OptimizEV during Phase II in Figures 7 and 7,
respectively. As can be seen from these plots, unmanaged charging results in a
median increase in peak demand of 6% (over the baseline peak of 120 kW), while
OptimizEV results in a 0% median increase in peak demand. This contrast
between unmanaged and optimized charging is even more pronounced when
considering days in the bottom 90% of the aggregate load distribution, where
unmanaged charging is shown to induce aggregate load profiles that increase
peak demand by as much as 18%, while OptimizEV only results in a 6% increase
in peak demand on these days.

We also find that unmanaged charging results in aggregate loads which exceed
the baseline peak for significantly longer periods of time than under
OptimizEV. In particular, the load duration curves depicted in Figure 8 show
that unmanaged charging induces aggregate loads that exceed the baseline peak
by at least 20 kW for a total duration of approximately 40 hours over the
course of Phase II. In comparison, under OptimizEV, aggregate loads exceed the
baseline peak by at least 20 kW for only 20 minutes over that same fifteen-
month time span. These findings confirm that unmanaged charging will likely
result in considerable and sustained increases in peak demand, while direct
control mechanisms that effectively harness the underlying flexibility in
customers’ charging requirements can significantly minimize these impacts.

Figure 8: Load duration curves for three scenarios: unmanaged charging (red),
OptimizEV (green), and TOU pricing (blue). Each colored curve depicts the
number of minutes during which load was greater than or equal to a particular
power level throughout Phase II of the OptimizEV Project under the
corresponding scenario.

##  6 Unintended consequences of time-of-use pricing

Many electric power utilities and regulators have advocated for the use of
nondiscriminatory time-of-use (TOU) electricity rates to minimize the impact
of EV charging on peak demand. Under TOU rates, customers are exposed to a
high electricity price during “on-peak” time periods, and a lower electricity
price during the complementary “off-peak” time periods. TOU rates are designed
with the intent of shifting a fraction of the on-peak electricity demand to
off-peak periods to flatten the aggregate demand profile. While this might
seem like a reasonable approach, the user charging data collected over the
course of this project reveals that TOU rates can have perverse consequences.

To understand the potential impact of TOU rates on aggregate demand, we
simulate EV charging patterns under TOU rates using actual customer
participation and charging data collected during Phase II of the OptimizEV
Project. For every managed (opt-in) charging session initiated during that
time frame, we generate a corresponding delayed charging profile, where a
user’s EV does not begin charging until the start of the ensuing off-peak
pricing period at midnight, at which time the EV begins drawing power at its
maximum rate until its energy requirement is satisfied. A charging profile is
only delayed to the off-peak period if it is feasible to do so given its
underlying energy and completion time requirements. Finally, all of the
charging profiles associated with unmanaged (opt-out) charging sessions are
left unchanged.

Figure 7 depicts the empirical median, interdecile range, and range of the
aggregate load data simulated under TOU pricing during Phase II of the
OptimizEV Project. Notice that TOU pricing is successful in keeping the median
aggregate load profile beneath the baseline peak of 120 kW, suggesting that
TOU rates may be effective in combating the adverse effects of unmanaged
charging at modest EV penetration levels. However, the synchronization of EV
power demand that results when multiple EVs begin charging simultaneously at
the start of the off-peak pricing period (midnight) induces new aggregate
demand spikes that are sharper and sometimes larger in magnitude than the
unmanaged aggregate demand peaks that would have otherwise resulted in the
absence of TOU rate-based incentives. This unintended consequence of TOU
pricing is clearly illustrated in Figure 6, which depicts a realization of the
aggregate load profile simulated under TOU pricing between March 9 and March
14, 2020. Notice that on several days during that week, the peak demand under
TOU pricing significantly exceeds the peak demand realized under unmanaged
charging on the same days. These observations suggest that at increased EV
penetration levels, passive load coordination mechanisms like TOU pricing will
likely fail to attenuate the peak demand driven by EV charging, and may make
matters worse.

##  7 Why do customers opt out of managed charging?

We find that a large majority of “opt-out” sessions are characterized by
inflexible charging requirements. Unsurprisingly, customers were more likely
to opt out of managed charging if they needed their EVs charged very quickly,
in time for their upcoming trips. On the other hand, customers were more
inclined to opt in to managed charging if they did in fact possess a
reasonable degree of flexibility (slack) in their charging requirements.

To illustrate this behavior, we plot the empirical opt-in rate as a function
of realized session slack time in Figure 9. The _realized slack time_
associated with a session is defined as the difference between the actual
session duration and the minimum amount of time required to deliver the energy
consumed during that session given the user’s maximum charging rate. Among all
Phase II charging sessions, the empirical opt-in rate is lowest (at roughly
10%) for sessions with realized slack times that are less than one hour. This
is unsurprising, since customers with limited flexibility in their charging
requirements have very little to offer (or gain) by relinquishing control of
their EVs for managed charging. Remarkably, however, the empirical opt-in rate
increases steadily as realized session slack times increase from zero to seven
hours, and remains relatively constant (hovering around 80%) for realized
session slack times between seven and eighteen hours—revealing that customers
are unlikely to opt out of managed charging if they have several hours or more
of slack time in their charging requirements. Surprisingly, the empirical opt-
in rate decreases slightly for realized session slack times between 18 and 24
hours. A possible explanation for this behavior is that sessions with very
long sojourn times may be associated with lower opt-in rates because they tend
to occur on weekends, when customers’ commuting patterns are more variable and
departure times may be more difficult to anticipate, resulting in a lower
willingness to participate in managed charging sessions.

Figure 9: Empirical opt-in frequency as a function of realized session slack
time based on all Phase II sessions with realized slack times that are less
than or equal to 24 hours. The opt-in frequency associated with Phase II
sessions excluded from this plot (i.e., those having realized slack times in
excess of 24 hours) is 71%. Figure 10: Scatter plot of Phase II session start
times versus session end times, where opt-in (opt-out) sessions as blue
circles (red squares). The distributions along the vertical and horizontal
axes depict kernel density estimates of the marginal distributions for session
start and end times, respectively.

Opt-in and opt-out charging sessions also differ significantly in terms of
their timing. In Figure 10, we visualize the relationship between Phase II
session start times and session end times in the form of a scatter plot that
depicts opt-in (opt-out) sessions as blue circles (red squares). Notice that
opt-in sessions typically correspond to overnight charging patterns, starting
in the evening and ending the following morning. In comparison, opt-out
sessions are more commonly associated with daytime commuting patterns, which
result in charging sessions that are much shorter in duration and have start
times that are more evenly distributed throughout the day. This contrast
between the timing of opt-in and opt-out sessions suggests that customers are
more likely to opt in to managed charging when their commuting needs are
flexible and follow regular and predictable patterns, e.g., when they arrive
home in the evening and expect to depart the following morning. It is also
worth noting that, although opt-out sessions do occur regularly, the uniform
dispersion of opt-out session start times throughout the daytime softens their
expected contribution to peak demand, as they are unlikely to cluster during
on-peak hours.

Figure 11: The plot depicts the average number of EVs connected to the grid
throughout the week for three different phases of the COVID-19 pandemic in New
York State during this pilot study: _Pre-lockdown_ from January 1, 2020 to
March 14, 2020 (black curve), _lockdown_ from March 15, 2020 to June 7, 2020
(red curve), and _phased re-opening_ from June 8, 2020 to May 31, 2021 (blue
curve).

##  8 COVID-19 impacts on user charging behaviors

The first recorded U.S. case of COVID-19 was reported on January 20, 2020. In
the months following, federal, state, and local governments enacted a sequence
of interventions designed to mitigate the spread of infections through
“shelter-in-place” orders and closure of non-essential businesses.
Unsurprisingly, the impacts of these interventions can be clearly seen in the
shifting charging patterns throughout the OptimizEV Project. In Figure 11, we
plot the average number of EVs connected to the grid throughout the week for
three different phases of the COVID-19 pandemic. Prior to the lockdown,
customers typically connected their vehicles to charge in the evening and
disconnected their vehicles the following morning. During the lockdown, as
customers started working from home, their charging patterns—previously
dictated primarily by their commute to and from work—became less rigid. The
average number of vehicles connected throughout the week flattened
considerably as customer session start and end times became less concentrated,
their session duration became longer, and their charging more infrequent. As
New York State gradually reopened, user connection patterns partially reverted
to pre-lockdown patterns, as charging sessions shortened and concentrated more
heavily during overnight hours.

The frequency with which customers charge their EVs also appears to have been
impacted by the COVID-19 pandemic. Figure 12 shows the evolution of charging
session frequency between January 2020 and May 2021. Prior to the lockdown,
customers were found to charge their EVs three or more times per week on
average. Immediately after the start of the lockdown, the average number of
weekly charging sessions per customer drops to approximately 1 session per
week, as customers traveled less frequently and spent more time at home.
Between May and November, the average number of weekly charging sessions per
customer gradually rises as pandemic related restrictions are loosened. In
December, weekly charging session frequency falls again, likely driven in part
by the resurgence in COVID-19 cases during that time frame. Despite these
shifts in user connection patterns and charging session frequency, the rate at
which customers participated in managed charging sessions remained relatively
constant over time, hovering around a 60% opt-in rate throughout Phase II of
the pilot study. Interestingly, this suggests that customers’ willingness to
participate in managed charging sessions was not impacted by the various
lockdown and reopening measures implemented over the course of the COVID-19
pandemic.

Figure 12: Plot of average number of charging sessions per customer for each
week during Phase I (Jan. 1, 2020 to Feb. 29, 2020) and Phase II (Mar. 8, 2020
to May 31, 2021) of the OptimizEV Project (excluding the transition week
between Phase I and Phase II). During Phase II, opt-in (opt-out) sessions are
depicted in blue (red). The weekly empirical opt-in rate during Phase II is
depicted as a green curve. Sessions with zero energy consumption are excluded
from these calculations.

##  9 Conclusion

The flexibility-differentiated pricing and control mechanism studied as part
of the OptimizEV Project was shown to be highly effective in reshaping
residential EV charging loads to minimize their impact on peak electricity
demand. The observed effectiveness of the mechanism is due in large part to
high customer participation rates—when customers exhibited flexibility in
their charging requirements, they frequently engaged in managed charging
sessions, allowing the smart charging system to delay the completion of their
charging by nine hours on average.

While these initial observations provide concrete evidence in support of the
proposed incentive and control mechanism as a potentially viable “non-wires
alternative” to support the increased demand for electricity driven by the
growing adoption of EVs, larger experimental studies and surveys are needed to
better understand customer attitudes towards managed charging and the
feasibility of such programs at scale. In particular, because of the
differences between early EV adopters and the general population of
electricity customers (Powells and Fell, 2019; Fjells et al., 2021), studies
involving a more diverse population of customers are necessary. Although
personal vehicle usage patterns in the general population suggest the presence
of significant charging flexibility across the general population (Anwar et
al., 2022), it is difficult to ascertain how a typical person’s willingness to
engage in managed charging compares to that of the project participants.
Moreover, because the typical electricity customer tends to be less
technologically savvy and less motivated by sustainability considerations than
the early adopters participating in the OptimizEV Project, the monetary
incentive required to elicit flexibility from the general population may be
larger.

Finally, in order for managed EV charging programs like OptimizEV to be cost
effective at scale, the benefit to the utility company, in the form of reduced
energy procurement or avoided infrastructure costs, must exceed the program
implementation and operational costs. These include administrative costs, the
total cost of incentives paid out to participating customers, and the cost of
the additional metering, communication, and control equipment required to
perform direct EV load control. If the estimated benefits are expected to
exceed the costs, then it may be prudent for the utility company to pursue
programs of this kind to manage the increasing penetration of EV loads on
their networks.

##  10 Acknowledgments

There are a number of partners without whom the OptimizEV Project would not
have been possible. These partners include New York State Electric and Gas
(NYSEG), New York State Energy Research and Development Authority (NYSERDA),
New York State Department of Public Service, Cornell Cooperative Extension,
Taitem Engineering, and Kitu Systems. This research was supported in part by
the the Holland Sustainability Project Trust and the National Science
Foundation under a Graduate Research Fellowship, Grant No. ECCS-135162, and
Grant No. IIP-1632124.

##  Appendix A Methods

###  A.1 Baseline non-EV load profile

Throughout Phase II of the OptimizEV Project, we utilized a fixed baseline
non-EV load profile as an input to our real-time scheduling algorithm. The
load profile is based on a 24-hour long time series of aggregate load
measurements taken from a distribution circuit in Tompkins County, New York,
which serves 623 residential customers and 69 commercial and industrial
customers. In order to obtain a load profile that reflects a small residential
neighborhood consisting of 60 households, we re-scaled the given time series
so that the resulting peak load equals 120 kW.

###  A.2 Real-time scheduling algorithm

In what follows, we provide a detailed mathematical formulation of the real-
time scheduling algorithm that was used as part of the OptimizEV Project. We
index time periods by $t=1,2,\dots$, and let $\Delta=(1/60)$ (units: hours)
denote the length of each time period. We let
$\mathcal{N}(t)\subseteq\\{1,\dots,34\\}$ denote the set of EVs that are
actively engaged in _managed_ (opt-in) charging sessions at time $t$. The
charging profiles associated with EVs engaged in managed sessions can be
adjusted within the constraints implied by their users’ stated charging
requirements. We denote the charging requirements associated with each user
$i\in\mathcal{N}(t)$ at time $t$ by

  * •

$R_{i}$: user $i$’s maximum charging rate (units: kilowatts),

  * •

$E_{i}(t)$: user $i$’s residual energy requirement at time $t$ (units:
kilowatt-hours),

  * •

$d_{i}(t)$: number of remaining time periods by which the energy requirement
$E_{i}(t)$ must be satisfied.

The SAE J1772 charging protocol also imposes a charging constraint in the form
of a minimum non-zero charging rate, which we denote by $R^{\mathrm{min}}$. At
each time $t$, the scheduling algorithm generates a charging profile for every
actively managed EV spanning the next $T=1440$ time periods (24 hours). We
denote the sequence of charging power commands sent to each active EV
$i\in\mathcal{N}(t)$ at time $t$ by $r_{i}(1),\,r_{i}(2),\,\dots,\,r_{i}(T)\
\text{(units: kilowatts).}$ The managed charging profiles are chosen to
collectively flatten the aggregate load profile by solving the following
optimization problem at each time $t$:

minimize
$\displaystyle\sum_{k=1}^{T}\left(\ell(t+k-1)+\sum_{i\in\mathcal{N}(t)}r_{i}(k)\right)^{2}$
(3a) subject to
$\displaystyle\sum_{k=1}^{d_{i}\left(t\right)}r_{i}(k)\Delta=E_{i}(t),\hskip
29.63095pt\forall\,i\in\mathcal{N}(t),$ (3b) $\displaystyle
r_{i}(k)\in\left\\{0\right\\}\cup\left[R^{\mathrm{min}},\,R_{i}\right],\hskip
7.94974pt\forall\,k\in\left\\{1,\dots,d_{i}(t)\right\\}\ \,\text{and}\
\,i\in\mathcal{N}(t),$ (3c) $\displaystyle r_{i}(k)=0,\hskip
75.16031pt\,\forall\,k\notin\left\\{1,\dots,d_{i}(t)\right\\}\ \,\text{and}\
\,i\in\mathcal{N}(t).$ (3d)

In the above optimization problem, the sequence
$\ell(t),\,\dots,\;\ell(t+T-1)$ (units: kilowatts) denotes the baseline non-EV
load profile plus the aggregate _unmanaged_ EV load profile stemming from all
EVs engaged in unmanaged (opt-out) charging sessions at time $t$. Note that
EVs engaged in unmanaged charging sessions are charged at their maximum rates,
without delay, until their energy requirements are satisfied. Constraint (3b)
ensures that each user’s requested energy is delivered prior to their
deadline. Constraint (3c) ensures that the charging power commands computed
for each actively managed EV are either zero valued, or between the charging
station’s minimum non-zero charging rate and the EV’s maximum charging rate.
Constraint (3d) ensures that no actively managed EV is charged after its
deadline has passed. The optimization criterion, defined on line (3a),
promotes EV charging profiles with a “valley-filling” characteristic.

In order to effectively adapt to changing system conditions in real time, the
smart-charging system developed for the OptimizEV Project utilizes a model
predictive control approach to continuously re-optimize the active EVs’
charging profiles every minute of the day. We provide pseudocode that clearly
specifies the recursive nature of this real-time optimization routine in
Algorithm 1.

1 for  _$t\in\left\\{1,2,\dots\right\\}$ _ do

2 Solve optimization problem (3) to compute optimal charging profile
$(r^{*}_{i}(1),\dots r^{*}_{i}(T))$ for each actively managed EV
$i\in\mathcal{N}(t)$ ;

3 for  _$i\in\mathcal{N}(t)$ _ do

4 Transmit optimal charge rate ${r}^{*}_{i}(1)$ to EV $i$ ;

5 Measure charge rate $\widehat{r}_{i}\left(t\right)$ implemented by EV $i$ ;

6 Set $E_{i}\left(t+1\right):=E_{i}(t)-\widehat{r}_{i}\left(t\right)\Delta$ ;

7 Set $d_{i}\left(t+1\right):=d_{i}\left(t\right)-1$ ;

8

9 end for

10

11 end for

Algorithm 1 Real-time Scheduling Algorithm

We briefly summarize each step of the pseudocode provided in Algorithm 1.
Immediately prior to time period $t$, the smart-charging system solves problem
(3) to determine optimal charging profiles for all actively managed EVs, which
we denote by $r^{*}=\left\\{r^{*}_{i}\left(k\right)\mid
i\in\mathcal{N}(t),k\in\\{1,\dots,T\\}\right\\}$. These optimal charging
profiles are then transmitted to each EV’s charging station as a sequence of
time-varying power commands. Each EV $i\in\mathcal{N}(t)$ is instructed to
execute the first component of the sequence of power commands that it
receives, $r^{*}_{i}(1)$. Because there may be deviations between the actual
power drawn by an EV and the commanded power, each active EV $i$ transmits a
measurement of the actual power drawn during time period $t$ to the smart-
charging system, which we denote by $\widehat{r}_{i}(t)$. The smart-charging
system uses this information to update each user’s residual energy requirement
according to $E_{i}(t+1)=E_{i}(t)-\widehat{r}_{i}(t)\Delta$. This information,
together with an updated forecast of the baseline non-EV load and aggregate
unmanaged EV load, is used to resolve problem (3), generating a new sequence
of power commands for the subsequent time period $t+1$.

###  A.3 Practical algorithmic considerations

In this section, we discuss a number of practical challenges encountered when
deploying the proposed real-time scheduling algorithm in a real-world setting.
This first challenge pertains to the need to ensure that all necessary
computations that are carried out at each time period are completed within the
allowable time budget (less than one minute). Problem (3) is a nonconvex
optimization problem due to the disjunctive constraint (3c). Specifically, it
belongs to the class of mixed integer quadratic programs (MIQP). Although it
is possible to solve MIQPs exactly using branch and bound methods, these
approaches can be extremely slow when the number of decision variables is
high. To circumvent these computational challenges, we employ a convex
relaxation of the disjunctive constraint (3c) by allowing the charging rate to
take any value between zero and the maximum charging rate. The resulting
relaxation is a convex quadratic program that can be solved to optimality
within seconds on a standard desktop computer using interior point methods. We
convert solutions generated by the relaxed problem into feasible solutions for
the original problem by appropriately rounding those solutions to ensure that
the original disjunctive constraint (3c) is satisfied.

The second challenge is related to the occasional constraint infeasibility
that results from nonidealities in EV charging characteristics and uncertainty
in user inputs. Specifically, in order to maintain feasibility of the
optimization problem (3), it must be possible to satisfy every user’s residual
energy requirement prior to their stated deadline subject to their maximum
rated charging capacity. In other words, the slack associated with every
active charging requirement must always be non-negative. Formally, this
corresponds to the requirement that

$\displaystyle d_{i}(t)-\frac{E_{i}(t)}{R_{i}\Delta}\,\geq\,0,$ (4)

for all users $i\in\mathcal{N}(t)$ and time periods $t$. In order to enforce
the satisfaction of this requirement, users are not permitted to make
infeasible charging requests. However, because the power drawn by an EV may
deviate from the power commands that it’s instructed to follow, charging
requests may become infeasible over time. When a user’s charging request
becomes infeasible, it is modified by reducing the user’s residual energy
requirement $E_{i}(t)$ to the maximum amount of energy that can be delivered
prior to the user’s stated deadline, to ensure the feasibility of the
optimization problem (3).

###  A.4 Demographics

Prior to the start of the OptimizEV Project, households with EVs registered in
Tompkins County were surveyed to assess their demographic characteristics and
attitudes toward energy. Survey respondents were mostly middle or upper class,
with 65% reporting an annual household income greater than $75,000.
Respondents also tended to be highly educated, with 55% having a graduate or
professional degree. Unsurprisingly, respondents also demonstrated positive
attitudes toward energy innovation and conscientiousness in energy
consumption: over half of the respondents reported being receptive to changing
their energy consumption habits and adopting novel technologies, and
approximately a third of the respondents reported strongly valuing
sustainability.

## References

  * (1)
  * Andersen et al. (2019) Andersen, P. B., Toghroljerdi, S. H., Sørensen, T. M., Christensen, B. E., Høj, J. and Zecchino, A. (2019), ‘The Parker Project’, Final Report 1.
  * Anwar et al. (2022) Anwar, M. B., Muratori, M., Jadun, P., Hale, E., Bush, B., Denholm, P., Ma, O. and Podkaminer, K. (2022), ‘Assessing the value of electric vehicle managed charging: a review of methodologies and results’, Energy & Environmental Science .
  * Bauman et al. (2016) Bauman, J., Stevens, M., Hacikyan, S., Tremblay, L., Mallia, E. and Mendes, C. (2016), ‘Residential smart-charging pilot program in toronto: results of a utility controlled charging pilot’, World Electric Vehicle Journal 8(2), 531–542.
  * Bloomberg NEF (2021) Bloomberg NEF (2021), ‘Hitting the EV inflection point: Electric vehicle price parity and phasing out combustion vehicle sales in europe’.
  * Bohn and Glenn (2016) Bohn, T. and Glenn, H. (2016), A real world technology testbed for electric vehicle smart charging systems and PEV-EVSE interoperability evaluation, in ‘2016 IEEE Energy Conversion Congress and Exposition (ECCE)’, IEEE, pp. 1–8.
  * Camacho and Alba (2013) Camacho, E. F. and Alba, C. B. (2013), Model predictive control, Springer science & business media.
  * Chynoweth et al. (2014) Chynoweth, J., Chung, C.-Y., Qiu, C., Chu, P. and Gadh, R. (2014), Smart electric vehicle charging infrastructure overview, in ‘ISGT 2014’, IEEE, pp. 1–5.
  * Clement-Nyns et al. (2010) Clement-Nyns, K., Haesen, E. and Driesen, J. (2010), ‘The impact of charging plug-in hybrid electric vehicles on a residential distribution grid’, IEEE Transactions on Power Systems 25(1), 371–380.
  * Colias (2021) Colias, M. (2021), ‘GM aims to go all electric by 2035’, Wall Street Journal .
  * Daramy-Williams et al. (2019) Daramy-Williams, E., Anable, J. and Grant-Muller, S. (2019), ‘A systematic review of the evidence on plug-in electric vehicle user experience’, Transportation Research Part D: Transport and Environment 71, 22–36.
  * Davidson et al. (2018) Davidson, F. T., Tuttle, D., Rhodes, J. and Nagasawa, K. (2018), ‘Switching to electric vehicles could save the us billions, but timing is everything’, The Conversation .
  * Eisen (2015) Eisen, J. B. (2015), ‘Ferc’s expansive authority to transform the electric grid’, UCDL Rev. 49, 1783.
  * Fjells et al. (2021) Fjells, I. F., Silvast, A. and Skjølsvold, T. M. (2021), ‘Justice aspects of flexible household electricity consumption in future smart energy systems’, Environmental Innovation and Societal Transitions 38, 98–109.
  * Fung (2016) Fung, B. (2016), ‘The states where it pays to buy a new electric car’, The Washington Post .
  * Gan et al. (2012) Gan, L., Topcu, U. and Low, S. H. (2012), ‘Optimal decentralized protocol for electric vehicle charging’, IEEE Transactions on Power Systems 28(2), 940–951.
  * Gong et al. (2011) Gong, Q., Midlam-Mohler, S., Marano, V. and Rizzoni, G. (2011), ‘Study of PEV charging on residential distribution transformer life’, IEEE Transactions on Smart Grid 3(1), 404–412.
  * Grable (2016) Grable, J. E. (2016), Financial risk tolerance, in ‘Handbook of consumer finance research’, Springer, pp. 19–31.
  * Grandoni et al. (2020) Grandoni, D., Siddiqui, F. and Dennis, B. (2020), ‘California to phase out sales of new gas-powered cars by 2035’, The Washington Post .
  * Gruosso (2016) Gruosso, G. (2016), Analysis of impact of electrical vehicle charging on low voltage power grid, in ‘2016 International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles & International Transportation Electrification Conference (ESARS-ITEC)’, IEEE, pp. 1–6.
  * Hilshey et al. (2012) Hilshey, A. D., Hines, P. D., Rezaei, P. and Dowds, J. R. (2012), ‘Estimating the impact of electric vehicle smart charging on distribution transformer aging’, IEEE Transactions on Smart Grid 4(2), 905–913.
  * Honarmand et al. (2014) Honarmand, M., Zakariazadeh, A. and Jadid, S. (2014), ‘Integrated scheduling of renewable generation and electric vehicles parking lot in a smart microgrid’, Energy Conversion and Management 86, 745–755.
  * Idaho National Laboratory (2013) Idaho National Laboratory (2013), What Clustering Effects have been Seen by the EV Project, Technical report.
  * International Energy Agency (2020) International Energy Agency (2020), Global EV Outlook 2020, Technical report.
  * Jardini et al. (2000) Jardini, J. A., Schmidt, H. P., Tahan, C. M., De Oliveira, C. C. and Ahn, S. U. (2000), ‘Distribution transformer loss of life evaluation: a novel approach based on daily load profiles’, IEEE Transactions on Power Delivery 15(1), 361–366.
  * Jiang and Zhen (2019) Jiang, W. and Zhen, Y. (2019), ‘A real-time ev charging scheduling for parking lots with pv system and energy store system’, IEEE Access 7, 86184–86193.
  * Jin et al. (2013) Jin, C., Tang, J. and Ghosh, P. (2013), ‘Optimizing electric vehicle charging with energy storage in the electricity market’, IEEE Transactions on Smart Grid 4(1), 311–320.
  * Karfopoulos and Hatziargyriou (2012) Karfopoulos, E. L. and Hatziargyriou, N. D. (2012), ‘A multi-agent system for controlled charging of a large population of electric vehicles’, IEEE Transactions on Power Systems 28(2), 1196–1204.
  * Lee et al. (2016) Lee, G., Lee, T., Low, Z., Low, S. H. and Ortega, C. (2016), Adaptive charging network for electric vehicles, in ‘2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP)’, IEEE, pp. 891–895.
  * Lee et al. (2019) Lee, Z. J., Li, T. and Low, S. H. (2019), ACN-data: Analysis and applications of an open EV charging dataset, in ‘Proceedings of the Tenth ACM International Conference on Future Energy Systems’, pp. 139–149.
  * Leou et al. (2013) Leou, R.-C., Su, C.-L. and Lu, C.-N. (2013), ‘Stochastic analyses of electric vehicle charging impacts on distribution network’, IEEE Transactions on Power Systems 29(3), 1055–1063.
  * Lutsey and Nicholas (2019) Lutsey, N. and Nicholas, M. (2019), ‘Update on electric vehicle costs in the united states through 2030’, The International Council on Clean Transportation 2.
  * Ma et al. (2011) Ma, Z., Callaway, D. S. and Hiskens, I. A. (2011), ‘Decentralized charging control of large populations of plug-in electric vehicles’, IEEE Transactions on control systems technology 21(1), 67–78.
  * Muratori (2018) Muratori, M. (2018), ‘Impact of uncoordinated plug-in electric vehicle charging on residential power demand’, Nature Energy 3(3), 193–201.
  * Myers et al. (2019) Myers, E. H., Hargrave, J., Farinas, R., Hledik, R. and Burke, L. (2019), Residential electric vehicle rates that work, Technical report, Smart Electric Power Alliance.
  * Nykvist and Nilsson (2015) Nykvist, B. and Nilsson, M. (2015), ‘Rapidly falling costs of battery packs for electric vehicles’, Nature climate change 5(4), 329–332.
  * Parker et al. (2021) Parker, N., Breetz, H. L., Salon, D., Conway, M. W., Williams, J. and Patterson, M. (2021), ‘Who saves money buying electric vehicles? heterogeneity in total cost of ownership’, Transportation Research Part D: Transport and Environment 96, 102893.
  * Powell et al. (2020) Powell, S., Kara, E. C., Sevlian, R., Cezar, G. V., Kiliccote, S. and Rajagopal, R. (2020), ‘Controlled workplace charging of electric vehicles: The impact of rate schedules on transformer aging’, Applied Energy 276, 115352.
  * Powells and Fell (2019) Powells, G. and Fell, M. J. (2019), ‘Flexibility capital and flexibility justice in smart energy systems’, Energy Research & Social Science 54, 56–59.
  * Quiros-Tortos et al. (2018) Quiros-Tortos, J., Ochoa, L. and Butler, T. (2018), ‘How electric vehicles and the grid work together: Lessons learned from one of the largest electric vehicle trials in the world’, IEEE Power and Energy Magazine 16(6), 64–76.
  * Smart and Salisbury (2015) Smart, J. G. and Salisbury, S. D. (2015), Lessons learned about plug-in electric vehicle charging infrastructure from the EV project and chargepoint america, Technical report, Idaho National Lab (INL), Idaho Falls, ID, USA.
  * Spencer et al. (2021) Spencer, S. I., Fu, Z., Apostolaki-Iosifidou, E. and Lipman, T. E. (2021), ‘Evaluating smart charging strategies using real-world data from optimized plugin electric vehicles’, Transportation Research Part D: Transport and Environment 100, 103023.
  * Szinai et al. (2020) Szinai, J. K., Sheppard, C. J., Abhyankar, N. and Gopal, A. R. (2020), ‘Reduced grid operating costs and renewable energy curtailment with electric vehicle charge management’, Energy Policy 136, 111051.
  * Tushar et al. (2012) Tushar, W., Saad, W., Poor, H. V. and Smith, D. B. (2012), ‘Economics of electric vehicle charging: A game theoretic approach’, IEEE Transactions on Smart Grid 3(4), 1767–1778.
  * Wang et al. (2016) Wang, Q., Liu, X., Du, J. and Kong, F. (2016), ‘Smart charging for electric vehicles: A survey from the algorithmic perspective’, IEEE Communications Surveys & Tutorials 18(2), 1500–1517.
  * Wu et al. (2011) Wu, D., Aliprantis, D. C. and Ying, L. (2011), ‘Load scheduling and dispatch for aggregators of plug-in electric vehicles’, IEEE transactions on smart grid 3(1), 368–376.
  * Yang et al. (2015) Yang, Z., Li, K. and Foley, A. (2015), ‘Computational scheduling methods for integrating plug-in electric vehicles with power systems: A review’, Renewable and Sustainable Energy Reviews 51, 396–416.
  * Zhang et al. (2017) Zhang, G., Tan, S. T. and Wang, G. G. (2017), ‘Real-time smart charging of electric vehicles for demand charge reduction at non-residential sites’, IEEE Transactions on Smart Grid 9(5), 4027–4037.