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Quantitive analysis of electric vehicle flexibility:
A data-driven approach
N. Sadeghianpourhamamia, N. Refab, M. Strobbea, C. Develdera
aGhent University – imec, IDLab,Dept. of Information Technology,
Technologiepark Zwijnaarde 15, 9052 Ghent, Belgium5
bElaadNL
Utrechtseweg 310, building B42, 6812 AR Arnhem, The Netherlands
Abstract
The electric vehicle (EV) flexibility, indicates to what extent the charging load
can be coordinated (i.e., to flatten the load curve or to utilize renewable en-
ergy resources). However, such flexibility is neither well analyzed nor effectively
quantified in literature. In this paper we fill this gap and offer an extensive
analysis of the flexibility characteristics of 390k EV charging sessions and pro-
pose measures to quantize their flexibility exploitation. Our contributions in-
clude: (1) characterization of the EV charging behavior by clustering the arrival
and departure time combinations that leads to the identification of type of EV
charging behavior, (2) in-depth analysis of the characteristics of the charging
sessions in each behavioral cluster and investigation of the influence of weekdays
and seasonal changes on those characteristics including arrival, sojourn and idle
times, and (3) proposing measures and an algorithm to quantitatively analyze
how much flexibility (in terms of duration and amount) is used at various times
of a day, for two representative scenarios. Understanding the characteristics of
that flexibility (e.g., amount, time and duration of availability) and when it is
used (in terms of both duration and amount) helps to develop more realistic
price and incentive schemes in DR algorithms to efficiently exploit the offered
flexibility or to estimate when to stimulate additional flexibility.
Keywords: Electric Vehicles, Flexibility Quantization, Smart Grid
Email addresses: nasrin.sadeghianpourhamami@ugent.be (N. Sadeghianpourhamami),
nazir.refa@elaad.nl (N. Refa), matthias.strobbe@ugent.be (M. Strobbe),
chris.develder@ugent.be (C. Develder)
Preprint submitted to Elsevier September 4, 2017
1. Introduction10
Partly because of environmental constraints, electric vehicles (EVs) are in-
creasingly being adopted as an alternative for internal combustion engine (ICE)
cars. However, the load from EVs may increase the peak to average ratio of
demand and hence create a need for additional generation and network capacity.
That extra capacity would only be required to meet the increased peak demand15
and therefore is used very infrequently [1]. Integration of information technology
into the power grid (in the smart grid paradigm) alleviates this challenge by en-
abling the exploitation of demand side flexibility to reshape the consumption to
meet the supply or network constraints (i.e., by flattening demand or by balanc-
ing against renewable generation). Consequently, a substantial body of research20
has focused on proposing demand response (DR) algorithms to coordinate EV
charging and establish their benefits (a review of various DR algorithms for
charging coordination is given in [2],[3],[4], and [5]). However, one of the main
limitations of such proposed DR algorithms is their potentially unrealistic as-
sumptions about the EV owner behavior (e.g., time of availability of EV, sojourn25
times and the fraction of the sojourn time that is not spent for charging and
is named idle time). To design an efficient and practical DR algorithm, it is
necessary to accurately understand the flexibility stemming from EVs and how
to influence it (through price based and incentive based schemes) to maximize
DR benefits. However, despite various efforts in proposing DR algorithms, EV30
flexibility characteristics as DR’s main asset have not been quantitatively an-
alyzed. We believe such analysis can pave the way to more realistic demand
response schemes (price-based or incentive based DR) in order to facilitate EV
integration in the grid and therefore is the focus of this paper.
1.1. Objectives and Contributions35
Understanding the flexibility characteristics, the influencing factors, and the
motivation for its exploitation is an inevitable part of designing a realistic DR
algorithm. Flexibility, despite its apparent simplicity, is neither straightforward
to analyze nor to quantify.
2
We pursue two objectives in this paper. Our first objective is to perform an40
in depth analysis of the flexibility characteristics of EVs based on a reasonably
large real-world dataset (which to the best of our knowledge amounts to the
largest dataset reported in literature, see Section 2.1 for further details). Our
second objective is to quantify the flexibility exploitation and identify how the
observed flexibility is utilized for various objectives (e.g., load flattening and load45
balancing against renewable (energy) sources) and whether there is any typical
pattern in its exploitation. More precisely, we aim to answer the following
research questions:
1. Do EV owners have specific habits to charge their cars (e.g., taking their
cars to a charging station at particular times of the day)? To answer50
this question, we characterize the EV charging behavior by clustering the
arrival and departure time combinations, as such identifying three behav-
ioral clusters in our EV charging data (Section 2.2).
2. Are the characteristics of the charging sessions (e.g., arrival, sojourn and
idle times) sensitive to seasonal changes or weekdays? To address this55
question, we systematically analyze the characteristics of the charging
sessions in each behavioral cluster on weekdays and weekends and across
various seasons. We also characterize the flexibility stemming from the
sojourn times of EVs that are longer than the time required to (fully)
charge their battery (Section 2.3).60
3. How is flexibility (in terms of amount, time and duration of the shifted
energy) exploited? Which aspect of flexibility (time and duration of avail-
ability or amount of deferrable energy) is more useful at various times
of the day? We address these questions by considering two case studies
(i.e., load flattening and load balancing scenarios) to investigate to what65
extent the observed flexibility would be exploited. To do so, we propose
two measures and an algorithm to quantitatively analyze when flexibility
is used in terms of the EV load volume as well as amount of time the load
is deferred(Section 3.3 and Section 3.4).
3
1.2. Related Work70
Estimating the EV charging load to assess its impact on the power grid
has been the primary focus of research in facilitating EVs integration to the
grid. In initial studies, before the wide-spread use of EVs, probabilistic models
of driving behavior (with conventional ICE cars) were used to characterize a
charging session. This was done by estimating arrival and departure patterns,75
energy requirements and the covered distance in between trips. For example
Lampropoulos et al. [6] derive an EV charging data profile from statistical char-
acteristics of the driving behavior of conventional ICE cars. Clement-Nyns et al.
[7] base their analysis on extrapolation of non-EV car usage in Belgium. Paevere
et al. [8] model the spatio-temporal impact of EV load based on a linked suite80
of models of future EV uptake, their travel and charging/discharging models.
Grahn et al. [9] derive EV charging behavior from non-EV driving behavior in
Sweden. Pashajavid et al. [10] derive the demand profile of EVs from traveling
and refueling information of non-EV in Tehran, and a more recent study [11] es-
timates possible states of EVs, regarding their demand, location and connection85
period, based on synthetic data which mimics reality.
Later studies, when EV penetration had increased, relied on the availability
of EV charging datasets to use data-driven approaches to model the charging
behavior of EVs and assess their impact on the grid. For instance, Xydas et
al. [12] characterize the charging demand of EVs by statistically analyzing and90
clustering a dataset of 22k sessions in UK. Khoo et al. [13] derive the impact of
EV charging on peak load based on around 5k sessions from an Australian field
trial and establish the expected impact on the total power demand in 2032-33
for the state of Victoria. Brady et al. [14] use a probabilistic charging module
to translate the travel patterns of EVs into the respective power demand of95
the vehicles. Quir`os-Tort`os et al. [15] and Navarro-Espinosa et al. [16] use the
probability distribution of start charging time and energy demanded during a
connection of charging sessions in a one-year EV trial in Ireland to obtain the
EV load demand and assess their impact in the low voltage distribution grid.
The aforementioned works focus mainly on analyzing the impact of EVs on100
4
the load curve and do not provide any quantitative analysis of the flexibility
characteristic of EV charging sessions. The objective of our analysis presented
here rather is to quantify the flexibility of the EV load, and quantitatively study
user behavior.
User modeling (not focusing on flexibility) has been the subject of earlier105
works to assess the influence of charging behavior of different user categories
on the load curve. For example, Franke et al. [17] examine the psychological
dynamics underlying charging behavior of EV users. Spoelstra [18] aims at un-
derstanding the charging behavior of EV users and the factors constituting such
behavior. Khoo et al. [13] have modeled the charging sessions for households110
and EV fleets during weekends and on weekdays in terms of arrival times and
energy demands. Quir`os-Tort`os et al. [19] produce probability distribution func-
tions (PDF) of different charging features (e.g., start charging time) for both
weekdays and week-ends based on 68k samples from 221 residential EV users.
They further discuss the effects of the EV demand on future UK distribution115
networks. Similarly, Richardson et al. [20] produce PDF of connection times
and daily energy requirements of EV based on the charging behavior of 78 users
for a duration of 1 year. Helmus et al. [21] distinguish a priori defined different
user types (residents, commuters, taxis, etc.) and characterize them in terms
of EV charging session start and end times and the associated energy needs.120
Similarly, Aunedi et al. [22] characterize the charging behavior and the demand
diversity of two predefined user categories: residential users and commercial
users. Instead of defining the user categories a priori, Xydas et al. [12] cluster
the observed charging sessions into distinct types of behavior. They derive ag-
gregate models for three specific geographical areas, characterized by different125
clusters of “typical EV charging demand profiles”. Similar characterization of
charging session timing is presented by Kara et al. [23]. Similar to [12] and [23]
(but using different clustering technique), we cluster the EV charging sessions
into behavioral clusters. However, our work differs from the aforementioned
papers: instead of focusing on the impact of EVs on the load curve, we char-130
acterize the flexibility stemming from the EVs as well as how such flexibility
5
is used (in terms of both amount and duration) to flatten the load or balance
against renewable energy.
Quantification of demand side flexibility and assessing its impact on alle-
viating the EV charging burden on the grid has been tackled before. Aunedi135
et al. [22] characterized the flexibility of EV charging demand in terms of the
amount of load shifted in time from the peak consumption without compro-
mising the ability of EV users to make their intended journeys. Their analysis
suggested that it is possible to shift 70% to 100% of EV demand from peak
hours towards the night. Kara et al. [23] defined the flexibility matrix as the140
fraction of total connection time that is not spent on charging. They presented
the variation of this measure over different months. Teng et al. [1] defined the
potential flexibility of EV demand as the amount of the shifted energy in the
coordinated vs. the uncoordinated charging. They further establish the ben-
efits of this flexibility in reducing carbon emissions and cost of integration of145
renewable energy sources (RES) through appropriate measures. Pavi´c et al.
[24] estimated the EV flexibility benefits for providing spinning reserve services
through matrices expressed as operational costs, environmental benefits and re-
duced wind curtailment. Salah et al. [25] used the parking data from a car
park in southern Germany, which is mainly used for shopping and working.150
They modeled parking duration distribution for two types of parking behavior:
shopping and workplace. They inferred the flexibility thereof by assuming an
average EV charging time of 45 min at 11 kW per car. Kheserzadeh [26] inferred
the probability of availability of EVs in the parking lots for different EV owners
including: residential, industrial and commercial customers (using the statistics155
of their traveling habits and traveling loads). The impact of various EV owners
charging behavior on flattening the micro-grid load was investigated. Schuller
et al. [27] evaluate to what extent the charging of EVs can be accommodated
using RES in two sociodemographic groups: retired vs. employed people.
The listed works give valuable insights on the benefits of EV flexibility in160
various aspects including load reduction, environmental benefits and RES inte-
gration. However, they characterize the flexibility only in terms of the amount
6
of shifted energy and not the duration. We on the other hand provide a com-
plete quantification of flexibility in terms of not only the deferrable amount
but also time of availability and the deferrable duration. Furthermore, detailed165
analysis of how the flexibility is used is also missing in the literature. We thus
present an extensive analysis on how flexibility is exploited (using our proposed
measures) to meet two representative objectives: peak reduction and balancing
against RES.
Note that this paper is a substantial extension of our work in [28] since we170
now offer a more extensive analysis of the charging session characteristics and
investigate the effect of seasonal changes and weekends on the characteristics of
the charging sessions. Additionally, in [28], we quantized flexibility as the max-
imal load that could be deferred for a specific duration at any time of the day,
independent of any DR scheme. In other words, our previous analysis showed175
the flexibility potential that is available for utilization and not the flexibility that
would be utilized to meet various DR objectives. In this paper, we complement
our previous flexibility potential analysis and propose measures to quantify the
actually exploited flexibility under two DR schemes: load flattening and load
balancing.180
2. Analysis of EV Charging Behavior
In this section, we address the first two research questions raised in Sec-
tion 1.1: Do EV owners have specific habits in terms of charging their cars?
Are the characteristics of the charging sessions (e.g., arrival, sojourn and idle
times) sensitive to seasonal changes and weekdays? Our analysis is based on a185
reasonably large real-world dataset which is explained next.
7
2.1. Dataset Description
The data for our analysis was collected by ElaadNL1between 2011 to 2015
from public charging infrastructure deployed throughout the Netherlands. The
dataset has more than 1.5M charging sessions characterized by arrival time,190
departure time, charging duration, and total power consumption. The EVs in
this dataset are privately owned cars and thus comprise a mixture of various and
a priori unknown types, without further information on their driving behavior.
For our analysis, we took the subset of sessions from 22nd Dec 2014 to 21st
Dec 2015 (i.e., 387,524 sessions) to ensure the observed charging behavior is195
not dominated by (potentially distinctive) behavior of novice users, since by
that date the system had been deployed a few years already. Moreover, in this
period there were not substantial extensions of the charging infrastructure: the
number of deployed charging stations remained almost constant through 2015.
The selected horizon effectively covers the four seasons and hence facilitates200
analysis of seasonal influences.
2.2. Clustering of Charging Session Times
The first question we address is: are there any typical behaviors in terms of
arrival and departure times in the dataset? To answer this question, we have
plotted the data in 2D space in terms of arrival time vs. departure time as shown205
in Fig. 1. We then adopted DBSCAN [29] clustering to cluster the data in that
2D space.
DBSCAN clustering is a density based clustering algorithm and we deemed
1ElaadNL is the knowledge and innovation center in the field of charging infrastructure
in The Netherlands, providing coordination for the connections of public charging stations
to the electricity grid on behalf of 6 participating distribution system operators (DSOs). It
also performs technical tests of charging infrastructure, researches and tests smart charging
possibilities of EVs, and develops communication protocols for managing EV charging. The
EV charging session data is available upon request for non-commercial research purposes,
subject to signing an agreement. For more information, please contact Chris Develder (email:
chris.develder@ugent.be)
8
Fig. 1: behavioral clusters of sessions in terms of EV arrival and departure times. Both X-
and Y-axis denote time-of-day (i.e., we report times as tmod 24 h): points below the X=Y
diagonal have departures on the day after the arrival or later. (Note that also some sessions
plotted above the diagonal actually have departures ≥24h after arrival)
it to be more suitable than other clustering algorithms (e.g., k-means and G-
means [30]) for two reasons: (1) unlike k-means, DBSCAN does not require210
to a priori specify the number of clusters to distinguish and (2) DBSCAN is
able to identify arbitrary shaped clusters without prior assumptions about the
underlying distribution of data in each cluster, as opposed to the normal distri-
bution assumed by the G-means clustering algorithm. One of the disadvantages
of DBSCAN is its sensitivity to the parameters of the algorithm (i.e., ε, which215
specifies how close points should be to each other to be considered part of the
same cluster; and minP ts, which specifies the minimum number of points re-
quired to form a dense region). The values of εand minP ts are empirically
obtained from the data. To examine the sensitivity of DBSCAN to these pa-
9
rameter values, we considered clustering the data separately for each month. We220
were able to identify 3 behavioral clusters in each month using similar values of
εand minP ts (i.e., ε= 0.4 and minP ts = 90).
Figure 1 shows the resulting behavioral clusters for the entire dataset. We
named the clusters according to our interpretation of the observed behavior:
charge near home, charge near work and park to charge clusters. The charge225
near home cluster (27.84% of the total data) has arrivals in the afternoon/evening
with departures mostly in the morning of the next/subsequent days. We hy-
pothesize these are mostly people that live nearby the public charging station
and park their car until they leave for work in the morning. Hence, the charging
usually occurs at night for the sessions in this cluster. The charge near work230
cluster (9.3% of the total data), which accounts for the smallest share of the
data, is characterized by arrivals in the morning and departures in the evening.
We assume these are people who either work near a public charging station
or take their car to the station on their way to work (e.g., as a part of their
commute, near a train station) and leave their car there while at work. Hence,235
this cluster has significantly smaller fraction of arrivals in weekends compared
to the other two clusters (see Table 1 for fraction of weekend arrivals in each
cluster). This type of behavior is absent in the datasets collected from residen-
tial charging (e.g., iMove [28]). The park to charge cluster (62.86% of the total
data) is the largest cluster and has arrivals/departures scattered throughout the240
day with sojourns that last not much longer than the time required to charge
the battery. We hypothesize these are people that park specifically for the sake
of charging the EV battery.
The aforementioned behavioral clusters provoke questions pertaining to what
factors exactly distinguish them from each other, which we analyze next.245
2.3. Analysis of Behavioral Clusters: Weekdays and Seasonal Impacts
In this section, we further analyze the sessions within each of the behavioral
clusters in terms of their arrival time, sojourn time (i.e., how long the car is
connected at the charging station) and idle time (i.e., the time between the
10
Weekday
Weekend
Autumn
Spring
Summer
Winter
3 6 9 12 15 18 21 24 3 6 9 12 15 18 21 24
Time (h)
Seasons
Behavioral clusters Charge near home Park to charge Charge near work
Fig. 2: Violin and box plots of time of arrivals for the behavioral clusters over weekends and
weekdays in each season (Note that the reference is changed from midnight to 3 am (2.30 am to
3.30 am is the interval with least number of arrivals) to acount for the fact that the activities
right after the midnight are continuation of the late night activities)
completion of the charging and departure of the car). More formally, we define:250
Sojourn time ,δsojourn =tdepart −tarrive,(1)
Charging time ,δcharging =tend charging −tstart charging,(2)
Idle time ,δidle =δsojourn −δcharging.(3)
We also investigate the impact of weekends and seasonal changes on the
aforementioned properties.
11
2.3.1. Analysis of Arrival Times
Figure 2 shows the violin and box plots of arrival times for the behavioral
clusters over weekends and weekdays in each season. In general, weekends and255
seasons impact the shape of the distributions. Seasonal changes usually shift
the arrivals to earlier times in summer and spring for all the clusters. This is
possibly due to the earlier sunrise and people’s preference to start their days
earlier in summer and spring. Arrivals are also earlier on weekdays than in
weekends. More details about the weekend and seasonal impacts on the arrival260
times of the cars in each behavioral cluster are listed below.
For sessions in the charge near work cluster, the distribution of arrival times
are unimodal and right-skewed during the weekends and multi-modal in the
weekdays. Arrivals on weekdays are approximately 1 hour earlier than during
weekends in all seasons. Additionally, the interquartile range is slightly longer265
in weekends compared to weekdays. The longest interquartile range is observed
for spring weekends. Across seasons, in summer and spring arrivals are earlier
by around 1 hour.
For sessions in the park to charge cluster, the distribution of arrival times
has a single mode and peaks around noon during the weekends, whereas on270
weekdays it is multi-modal with 3 peaks (in morning, noon and evening). The
arrivals in this cluster are scattered throughout the day,resulting in the largest
interquartile range amongst the behavioral clusters. The interquartile range is
approximately an hour longer on weekdays for all seasons. Across seasons, the
arrivals are typically 30 to 45 min earlier in summer and spring compared to275
autumn and winter.
For sessions in the charge near home cluster, the distribution of arrival times
are uni-modal and right-skewed with a heavy tail on weekdays in all seasons.
During weekends, the distributions are also uni-modal but right-skewed in sum-
mer and spring while left-skewed for winter and autumn. This can be explained280
by people’s preferences to stay out longer during weekends to enjoy longer day-
light and warmer weather in summer and spring. The interquartile ranges are
12
Fig. 3: Violin and box plots of sojourn times for the behavioral clusters over weekends and
weekdays in each season
longer in weekends in all seasons. Seasonal changes do not significantly affect the
interquartile ranges. Finally, arrivals are typically earlier during the weekdays
of summer and spring but similar in all seasons during the weekends.285
2.3.2. Analysis of Sojourn Times
Looking at each individual behavioral cluster, we observe that a minority of
sessions have sojourn times of more than 24 h (see Table 1). We also find that
for these clusters, the sojourn time distribution is multi-modal, where the modes
correspond to subsequent days and are well separated. We thus partition the290
data into sub-clusters based on the departure time (i.e., depending on whether
it is within the first, second, etc. period of 24 h following the arrival). Figure 3
shows the violin and box plots of sojourn times for the behavioral sub-clusters
13
Table 1: Summary of cluster and sub-cluster fractions and average sojourn and idle times
Cluster Weekend
arrival
fraction
Sub-cluster
departures
Sub-
cluster
fraction
Mean
sojourn
time
Mean idle
time
Park to
charge
(62.86%)
28.24%
in 1st 24 h 98.9% 2 h 28 min 48 min
in 2nd 24 h 0.85% 26 h 18 min 22 h 48 min
in 3rd 24 h 0.21% 66 h 18 min 62 h 42 min
in 4th 24 h and later 0.11% 105 h 24 min 101 h 42 min
Charge
near home
(27.84%)
23.24%
in 1st 24 h 95.09% 13 h 24 min 10 h
in 2nd 24 h 3.44% 39 h 36 min 36 h 12 min
in 3rd 24 h 0.9% 63 h 48 min 60 h 6 min
in 4th 24 h and later 0.57% 113 h 30 min 109 h 54 min
Charge
near work
(9.3%)
6.33%
in 1st 24 h 99.51% 8 h 42 min 5 h 30 min
in 2nd 24 h 0.33% 33 h 24 min 29 h 12 min
in 3rd 24 h 0.4% 38 h 12 min 34 h 24 min
in 4th 24 h and later 0.09% 119 h 42 min 115 h 18 min
14
over weekends and weekdays in each season. We only show the first 2 sub-
clusters (i.e., sessions with departures within first and second 24 h from their295
arrivals) since the later sub-clusters constitute less than 1% of the data (see
Table 1). In general, seasonal changes have minor effects on sojourn times in the
behavioral clusters, but weekends impact the sojourn times more significantly.
Further details about the weekend and seasonal impacts on the sojourn times
in each behavioral cluster are listed below. Note that our explanations here300
are based on the 1st sub-clusters (i.e., departures within 1st 24 h) since in the
second sub-clusters (i.e., departures within second 24 h), distributions of the
sojourn times have similar characteristics as ones in the first sub-clusters. One
interesting characteristic is the approximate shift of 24 h in the average sojourn
times in the second sub-clusters from the average values of the first sub-clusters305
(as seen from Table 1)
For the sessions in the charge near work cluster, the distribution of sojourn
times are right-skewed in weekends and symmetrical or left-skewed during week-
days. This implies that typically the sessions have shorter sojourn times in
weekends (average sojourn times are 8 h 18 min and 8 h 48 min for arrivals in310
weekend and weekdays respectively). Additionally, the interquartile ranges are
smaller in the weekdays, implying a more predictable sojourn time. The largest
interquartile range is in summer weekends.
Sessions in the park to charge cluster typically have smaller sojourn times
than sessions in other clusters. As shown in Fig. 3, the distributions are left315
skewed for both weekend and weekdays, with slightly larger interquartile ranges
during weekdays. This implies that sojourn times are typically shorter in week-
ends (average sojourn times are 2 h 36 min and 2 h 48 min for arrivals in weekend
and weekdays respectively). The seasonal changes do not impact the distribu-
tions significantly in this cluster.320
Sessions in the charge near home clusters have considerably larger sojourn
times than the sessions in other clusters. The distribution of the sojourn times
are symmetrical for both weekends and weekdays, with larger interquartile
ranges in weekends. Unlike the other clusters, the charge near home sessions
15
Fig. 4: Violin and box plots of Idle times for the behavioral clusters over weekends and
weekdays in each season
have longer sojourns during weekends (the average sojourn times are 13 h 6 min325
and 14 h 18 min for arrivals in weekends and weekdays respectively). This is
mainly because they are night time charging sessions, and people leave home
later in the morning in the weekend.
2.3.3. Analysis of Idle Times
We have used the same sub-clustering approach to present the distribution330
of the Idle times in each behavioral cluster. Additionally, to improve the read-
ability of the plots in Fig. 4, we have removed sessions with short idle times
(i.e., less than 15 min). This amounts to 43.08% and 33.58% of the data in
16
weekends and weekdays respectively.2Note that the majority of the removed
short idle times belong to the park to charge cluster. An overall view of Fig. 4335
suggests that seasonal changes do not influence the distribution of idle times
significantly, unlike weekend impacts, which are more apparent. Further details
about the impact of the weekends on the distribution of the idle times are listed
below.
The sessions in the charge near work cluster typically have 4 to 7 h of idle340
time in the first 24 h sub-cluster and 27 to 28 h of idle time in the second 24 h
sub-cluster during the weekends. On weekdays, idle times are typically around
30 min longer than in weekends. On average (taking into account the sessions
with short idle times), this cluster has 5 h 30 min of idle time in the first 24 h
sub-cluster and 29 h 48 min of idle time in the second 24 h sub-cluster.345
The sessions in the park to charge cluster typically have the shortest idle
times, which suggests that the cars are usually parked with the motive of leaving
as soon as the charging completes. The distribution of idle times are right
skewed even after the removal of short idle times for the first sub-cluster over
both weekends and weekdays. In the second sub-cluster, it looks symmetrical.350
On average, the park to charge sessions have 42 min of idle time in the first
sub-cluster and 22 h 48 min of idle time in the second sub-cluster.
The charge near home sessions offer longer idle times (i.e., 10 h in the first
and 36 h in the second sub-cluster) than the other clusters. The distributions of
the idle times are symmetrical in all the sub-clusters and during both weekends355
and weekdays. The interquartile ranges span from 8 h to 14 h in the weekends
and from 7 h 30 min to 12 h during the weekdays in first sub-cluster.
3. Flexibility Quantization
Our quantitative analysis of flexibility exploitation relies on the aforemen-
tioned EV charging data collected by ElaadNL, and renewable generation data360
2However, the average values in Table 1 do include the short idle times in their calculation.
17
Table 2: Nomenclature
Input parameters
NTotal number of cars in the optimization window
HThe length of the optimization window (the number of 15 min time slots)
γnh Maximum allowable energy consumption for car nin slot h
EnTotal energy to be scheduled for car n
Pavg
nAverage power consumption of car n
αnArrival slot of car n
βnDeparture slot of car n
Decision variables
xnh Energy scheduled to charge car nin slot h
LhTotal energy consumed in slot h
obtained from ELIA (Belgium’s electricity transmission system operator).3The
data obtained from ELIA comprises wind and solar energy generation measure-
ments in 15 min intervals for the region of Flanders in Belgium. We rescaled
the renewable energy production data to keep similar monthly wind to solar
ratios as of the ones in Netherlands.4Additionally, we further scaled the data365
to ensure the total yearly generation is similar to the total yearly demand of
all the EV sessions considered in our study. We provide an assessment of flexi-
bility exploitation in coordinated charging for two scenarios: (i) load flattening
and (ii) load balancing against renewable production. As a reference, we take
uncoordinated charging and refer to it as a business as usual scenario without370
flexibility exploitation.
Each time slot is characterized by a 15 min interval h∈H={1,2, ..., H}
and the EVs are denoted as n∈N={1,2, ..., N }. Table 2 summarizes all the
3http://www.elia.be/en/about-elia
4See http://en-tran- ce.org/ for yearly reports of renewable generations in Netherlands.
18
model parameters and the decision variables.
3.1. Uncoordinated Charging: Bussiness as Usual375
In the business as usual (BAU) scenario, charging starts immediately upon
arrival. In the ElaadNL dataset, vehicles are charged according to this BAU
scenario and the charging time as well as the total energy consumption is re-
ported for each session. The load in each time slot (i.e., of 15 min duration) is
hence calculated as Pslot = ∆t·En/(tBAU −tarrive), where tBAU is the time of380
the completion of charging in the BAU regime and ∆tis the duration (in hours)
of each slot (i.e., ∆t= 0.25 h) in our settings.
3.2. Coordinated Charging: Load Flattening and Load Balancing
In the coordinated charging scenario, charging decisions are optimized by
an aggregator to meet a predefined objective function. We formulate such a385
problem as a quadratic optimization (i.e., a quadratic objective function subject
to linear constraints). To make the problem scalable and solvable in close to real-
time, we define an optimization window of length H= 96 time slots (i.e., 24 h)
which starts at the present time slot (denoted as “Now”) and moves one slot in
each iteration. We thus consider a receding horizon control approach, where we390
repeatedly solve the optimization problem to find the decision variables covering
the window (“Now”,“Now+H”).
For load flattening, the objective function is defined as:
minimize
L,XM
H
X
h=1
L2
h+
N
X
n=1
H
X
h=1
βnxnh (4)
The first term in (4) is a convex quadratic cost function and reflects the
total load that needs to be minimized in the optimization window. We define395
a second term in (4) as a secondary objective which penalizes charging at later
slots. This ensures that charging at earlier slots is preferred when permutations
of charging decisions across different slots have the same cost. Note that we
19
multiply the first term in (4) by M, a large constant, to have the first term
dominate the second term in the objective function.400
For load balancing, the objective function is defined as:
minimize
L,XM
H
X
h=1
(Lh−LRG)2+
N
X
n=1
H
X
h=1
βnxnh (5)
The first term in (5) models the imbalance using a convex quadratic function.
Note that (similar to [31]) we account for negative imbalance to be as bad
as positive imbalance. Similar to (4), the secondary objective function in (5)
ensures earlier charging when charging at various slots has the same cost.405
Both of the objective functions are subject to the following linear constraints:
Lh=
N
X
n=1
xnh ∀h∈H(6)
En−Ea≤
H
X
h=1
xnh ≤En∀n∈N(7)
0≤xnh ≤γnh ∀n∈N, h ∈Hn(8)
xnh = 0 ∀n∈N, h ∈H\Hn(9)
where,
Hn=
{αn, ..., βn}βn≤H
{αn, ..., H}βn> H
and
Ea=
Pavg
n·(βn−H)βn> H
0 otherwise
Constraint (6) ensures that the total load consumed in slot his equal to the
summation of the loads from all the cars scheduled to charge in slot hof the opti-
mization window. Constraint (7) ensures that the charging demand (i.e., En) is
fulfilled within the car’s sojourn time. When a car departs within the optimiza-410
tion window, (7) becomes an equality constraint (i.e., equals En). Constraint (8)
20
limits the energy consumption in each slot to the car’s allowable consumption
level and constraint (9) prohibits any charging outside the sojourn time.
3.3. Measures for Quantification of Flexibility Utilization
As outlined in Subsection 1.2, the demand response potential of EVs has415
already been studied to some extent, but how exactly the offered flexibility is
exploited in real-world scenarios has not been well clarified in literature. In this
section, we address this gap and offer a quantitative analysis of the flexibility
exploitation of EVs using various measures. We first define the flexibility using
3 factors [32]: (1) the amount of deferrable energy (i.e., the amount of energy420
that can be delayed without jeopardizing customer convenience or quality of
the task to be fulfilled), (2) the time of availability (i.e., the time at which a
customer offers the flexibility for exploitation), and (3) the deadline/permissible
duration to exploit the offered flexibility (i.e., the maximum allowable delay for
the energy consumption).425
We define the following measures to adequately quantize the EV flexibility
exploitation:
1. Eflex (flexibility utilization in terms of Energy): fraction of the maximum
energy that could be consumed beyond tBAU . More formally,
Eflex =Energy consumed beyond tBAU
Maximum possible energy consumption beyond tBAU
(10)
2. Tflex (flexibility utilization in terms of duration): fraction of the maxi-
mum delay beyond tBAU . More formally,
Tflex =tcoordinated −tBAU
tdepart −tBAU
(11)
where tcoordinated refers to the time of completion of charging in the coordinated
charging regime.
The combination of Eflex and Tflex values quantizes the fraction of flexibility430
(in terms of time and amount) that was utilized for each charging session. For
example, when Tflex =Eflex = 1, the energy consumption is deferred as much
as possible (i.e., tcoordinated =tdepart) and the consumption beyond tBAU is at
21
Algorithm 1: Calculate shift profile for a charging session
Input :LBAU (with |LBAU |=S), a vector denoting energy
consumption by the EV in each slot in the BAU scenario;
Lcoordinated (with |Lcoordinated |=M), a vector denoting energy
consumption in each slot in the coordinated charging scenario;
Output: The shift profile (Lshift)
1Define Lscheduled with |Lscheduled|=Mand initialize it with zeros;
/* Lscheduled(s)is the energy scheduled from previous slots to s*/
2s0= 1;
/* s
0is used for indexing to save the caclulations in Lshift */
3foreach s= 1, . . . , S do
4shift =LBAU (s)−Lcoordinated(s) + Lscheduled(s) ;
/* the amount of energy that needs to be shifted away from s*/
5m= 1;
6while shift 6= 0 do
7capacity =Lcoordinated (s+m)−Lscheduled(s+m);
/* Lcoordinated(s)≥Lscheduled (s)since this calculation is done
after the optimization and Lcoordinated(s)is the finalized
load to be consumed in slot s. */
8actual shift =min(shift,capacity);
9Lshift(s0) = (s, actual shift, s +m);
10 s0=s0+ 1;
11 Lscheduled(s+m) += actual shift ;
12 shift =shift −actual shift;
13 m=m+ 1;
14 return Lshift
its maximal level. Another interpretation is that 1 −Eflex is the fraction of
state-of-charge (SoC) at tBAU that has been realized in the flex scenario; for435
example, if Eflex = 0.25, it means that at tBAU , we have 1 −0.25 = 75% of the
22
desired SoC.
Although the aforementioned measures indicate how much of the offered
flexibility is effectively utilized in each charging session, they do not provide
information about the volume and the precise time shift of the deferred energy.440
Indeed, we believe it is interesting to know what portion of energy use is shifted
to what time exactly. To quantitatively evaluate this, we define the shift profile
of a charging session: the shift profile indicates how the energy is shifted from
the BAU scenario to obtain the load pattern in the coordinated charging regime.
In other words, it shows how much energy is shifted away from a particular slot445
and which slot it is scheduled to. We now explain how we calculate this shift
profile, as outlined in Algorithm 1.
Given the LBAU and Lcoordinated vectors, respectively denoting the BAU and
the coordinated energy consumption values in each slot, Algorithm 1 returns a
Lshift list as its output. Each element of Lshift is a triple, depicting how much450
energy was shifted away from a particular slot and which slot it was shifted
to (e.g., if 5 kWh of energy is shifted from slot 1 to slot 3, then the triple will
have the following form: (sfrom, Eshifted, sto ) = (1,5,3)).5The algorithm starts
by initializing Lscheduled, a vector that keeps track of the amount of energy
scheduled in a particular slot from the other slots (Line 1). For each slot s,455
starting with the first one, the amount of energy we need to shift away from it
(i.e., shift) is calculated in Line 4. Note that to calculate the shift in each slot,
we take the difference in energy consumption in the BAU and the coordinated
charging scenario. Additionally, since any energy scheduled to be consumed
in a slot also contributes to the delay of the energy consumption from that460
slot, we add the Lscheduled to the subtraction term. In the while loop, the
shift is allocated to the subsequent slots following s, based on their available
capacity. The amount of the allocated energy and the slot number is saved in
Lshift (Line 9) and Lscheduled is updated accordingly (Line 11).
5Note that there could be several feasible shift profiles (e.g., (1, 1, 3) vs. {(1, 1, 2), (2, 1,
3)}) but here we calculate the one with minimal sto −sfrom.
23
0
100
200
300 (a)
BAU load Flattened load Balanced load RES
Energy demand (KWh)
0
100
200
300 (b)
up to 1 hour 1 to 2 hours 2 to 4 hours 4 to 8 hours more than 8 hours
Time (hh:mm)
00:00
06:00
12:00
18:00
24:00
06:00
12:00
18:00
24:00
06:00
12:00
18:00
24:00
06:00
12:00
18:00
24:00
06:00
12:00
18:00
24:00
06:00
12:00
18:00
24:00
06:00
12:00
18:00
24:00
0
100
200
300 (c)
Mon Tue Wed Thu Fri Sat Sun
Shifts:
Fig. 5: (a) Load and renewable generation patterns from 5th to 11th Jan, (b) Amount of
energy that is shifted away from each slot(for arrivals from 5th to 11th Jan 2015) in load
flattening scenario and (c) Amount of energy that is shifted away from each slot (for arrivals
from 5th to 11th Jan 2015) in load balancing scenario.
3.4. Evaluation of Flexibility Exploitation465
In this section, we evaluate the flexibility exploitation using the measures
and the algorithm proposed in the previous subsection. We implemented the
optimization problem using MOSEK6, in a MATLAB runtime environment.
Figure 5 shows how much energy (kWh) has been pushed away, and for
how long, from BAU consumption, assuming 15 min long time slots in the op-470
timization of the coordinated charging scenarios (i.e., load flattening and load
balancing). A week long duration is selected for demonstration in Fig. 5. Fig-
ure 5a shows the energy consumption patterns (in the BAU, load flattening and
load balancing scenarios) and the scaled renewable generation in each slot of the
6MOSEK is a software package for solving mathematical optimization problems, see https:
//www.mosek.com/.
24
selected one week long time period. As seen from the figure, the BAU energy475
consumption patterns are multi-modal with distinct morning (around 9 am) and
evening (around 8 pm) peaks on weekdays. During the weekends, the peak-to-
average ratio is lower than on weekdays and energy consumption patterns have
a small peak around noon and a larger peak around 6 pm.
In the load flattening scenario (i.e., Fig. 5b), we observe the following:480
1. The flexibility utilization is influenced by the BAU energy consumption
patterns as well as the car arrival times (note that the arrival times and
the BAU energy consumption patterns are also highly correlated.)
2. During weekdays: The load is typically shifted away from the morning
peak (around 8-10 am) towards the afternoon valley (around 12-2pm).485
Since the afternoon valley is not long away from the morning peak, the
duration of the shift is typically lower compared to the shift from the
evening peak to the midnight valley. Hence, we see more shifts of “up to
1 hour” long and less shifting of beyond “4 hours” from the morning peak.
On the other hand, the shifts from the evening peaks are longer to fill up490
the night valley, which is deeper and further away.
3. During weekends: The shifts from the evening peak to the night valleys
are longer in weekends (typically more than 8 hours from the Saturday
evening peak and more than 4 hours from the Sunday evening peak). The
longer shifts from Saturday peaks are due to the wider and deeper valley495
between Saturday and Sunday peaks.
In the load balancing scenario, clearly the flexibility utilization is not only
influenced by BAU energy consumption pattern and the car arrival times, but
also by the renewable generation patterns. The flexibility exploitation for load
balancing is depicted in Fig. 5c with the following key observations:500
1. Although the flexibility utilization is not as consistent as for the load
flattening scenario, still, longer shifts are observed in the evening peaks
on weekdays. Additionally, there are still longer shifts from the Saturday
peaks compared to the shifts from the Sunday peaks.
2. In general, longer shifts from the evening peaks are observed when there505
25
Charge near home
0
0.5
1Weekend
0
0.5
1Weekday
Charge near work
0
0.5
1
0
0.5
1
00:00
06:00
12:00
18:00
24:00
Park to charge
0
0.5
1
Arrival time (hh:mm)
00:00
06:00
12:00
18:00
24:00
0
0.5
1
Tflex LF Eflex LF Tflex LB Eflex LB
Fig. 6: Average Tflex and Eflex values for each 15 min long timeslot in a day (LB: load
balancing, LF:load flattening)
is substantial renewable generation in the night valleys.
The observations based on Fig. 5 give insight in the motivation for utilization
of the flexibility and, hence, how much energy is required to be shifted and for
how long. This is particularly useful for price-based or incentive-based demand
response programs aiming to influence the offered flexibility at various hours510
of the day accordingly (using a relevant price or incentives). For example, the
longer shifts from morning peak are not as frequent as the ones from the evening
peak and hence, a lower incentive could be given for longer sojourn time of the
cars arriving before the morning peak.
In addition, it is also useful to know how much of the offered flexibility is515
utilized throughout the day. To quantize the degree of flexibility utilization, we
use the Eflex and Tflex measures. Figure 6 shows, for a given time slot, the
26
average Tflex and Eflex values for the sessions with arrivals in that slot (note
that these sessions may extend until much later slots). The values are depicted
for each behavioral cluster during weekdays vs. weekends. The empty sections520
in the plots indicate there were either no arrivals occurred, or the arrivals had
zero idle times at these times of day. We list our observations for the Eflex and
Tflex in the load flattening scenario, which essentially also apply qualitatively
for the load balancing case.
For Tflex: In general, Tflex close to 1 means that charging lasts almost until525
the end of the sojourn. Yet, this does not mean that all charging is delayed (see
the Eflex which is reasonably low, meaning that the SoC at tBAU is pretty
high). We observe lower Tflex for arrivals at night and in the early morning
(i.e., 0-6 am). The reason is that the sessions with arrival times in those slots
are responsible for the bulk of the load at those times, which is low compared to530
other slots, so there is a lower motivation to push their charging away and make
use of flexibility. Any arrivals in the subsequent slots have their load shifted
away from the peaks, hence, the Tflex value increases and approaches 1. Tflex
starts to decrease again for the arrivals near midnight.
For Eflex: similar to Tflex, lower Eflex is observed for arrivals at night and535
early morning (i.e., 0-6 am) since the bulk of the load at those times is low and
hence, there is little need for deferring the consumption. The Eflex in the late
morning (9-11 am) is lower than in the afternoon/evening. Note that the arrivals
in the late morning are usually used to fill the afternoon valley, but the amount
of energy pushed into afternoon valley from morning peaks is lower compared540
to the amount of energy pushed into night valley (the night valley is deeper and
requires more load to be filled). Additionally, the arrivals in the late morning
are typically from the park to charge or the charge near work clusters: since
their sojourn does not overlap with the night valley, their load cannot be used
to fill the night valley. Another interesting observation is the bell shape of Eflex545
after 12 pm in the park to charge cluster for both weekends and weekdays, which
peaks around 4 pm and 6 pm respectively. Note that since the sessions in this
cluster have very small idle times, a larger portion of their energy consumption
27
is deferred, but for shorter duration, to flatten the load. In the charge near home
cluster, we see a rather linear increase in Eflex. The sessions in this cluster offer550
much longer idle times compared to the park to charge cluster. By observing
the SoC status of the sessions in this cluster, we find that for the sessions whose
sojourns overlap with the evening peak, their charging usually stops during the
peak hours and resumes in the night valley. That is the main reason for Tflex
close to one but rather small Eflex for sessions with arrivals in the afternoon555
and evening.
4. Summary and Conclusion
Motivated by the lack of research in characterizing the flexibility stemming
from EV charging sessions, in this paper we took the first step to (1) offer an
in-depth analysis of the flexibility characteristics of a nearly 390k EV charging560
sessions and (2) propose flexibility measures to quantify its exploitation in two
scenarios, load flattening and load balancing. Our contributions in this paper
pave the way to more realistic evaluation and development of DR algorithms,
which aim to not only exploit the flexibility but also to influence it more effi-
ciently (through price-based or incentive-based schemes).565
To fulfill our first objective (i.e., analysis of flexibility characteristics), we
clustered the EV data in 2D space in terms of arrival and departure times
using the DBSCAN algorithm. As such, we identified three behavioral clusters:
charge near home, charge near work, and park to charge clusters. We then
used box and violin plots to further analyze the characteristics of the charging570
sessions within each cluster and highlighted the differences among the clusters
over weekends and weekdays in each season. A summery of our observations is
listed here:
1. The three behavioral clusters differ substantially in their arrival times,
sojourn times and the idle times. The park to charge cluster (which is575
the largest in terms of number of sessions, 62.86% of all sessions) has
arrivals scattered throughout the day and the sessions in this cluster are
28
characterized by very short idle times (averaging 48min). The charge
near work cluster (27.84% of all sessions) has predictable arrival times
(around 6-9 am) and their sojourn times are typically less than 9 hours580
(with average idle time of 5h 30 min), hence, their charging usually takes
place throughout the day. Finally, the sessions in charge near home cluster
(9.3% of all sessions), with arrivals typically in the evening until midnight,
offer the longest idle times among the clusters (10 h on average). The
charging for these sessions usually occurs at night.585
2. Weekends and weekdays as well as seasonal changes impact the arrival
times in all three clusters. In general, the arrival times are earlier in sum-
mer and spring in all the clusters. The arrivals are also earlier on weekdays
compared to weekends. However, seasons have no substantial impact on
the sojourn and idle times. Sessions in park to charge and charge near590
work clusters have shorter sojourn and idle times in the weekends whereas
the sessions in the charge near home clusters have longer sojourn and idle
times in the weekends compared to weekdays.
To fulfill our second objective (i.e., quantification of flexibility exploitation),
we proposed two flexibility measures to quantify the percentage of the flexibility595
utilization and an algorithm to determine the amount and duration of the shifted
energy. A summary of our analysis using the algorithm and the measures is as
follows.
1. The flexibility exploitation is greatly influenced by the uncontrolled busi-
ness as usual (BAU) load patterns, the distribution of arrival times, and600
the renewable energy generation patterns. The main motivation for ex-
ploitation of the flexibility in both load flattening and load balancing is to
fill the valleys of the BAU load pattern. Hence, longer shifts are observed
from the evening peaks compared to the morning peaks in the weekdays
(since the nighttime valley is larger and deeper). Similarly, longer shifts605
are seen from Saturday peaks compared to Sunday peaks because the night
valley between Saturdays and Sundays is bigger.
2. For arrivals in the afternoon until midnight, flexibility in terms of de-
29
ferrable time is almost fully exploited to ensure the charging takes place
in the nighttime (which corresponds to the lower demand). Yet, this does610
not imply that all the charging is delayed since the Eflex values are rea-
sonably low, meaning that the SoC at the BAU charging completion time
(i.e., tBAU ) is pretty high. Across the behavioral clusters, the offered
flexibility in charge near work cluster is often used to fill the afternoon
valley since these sessions are characterized by morning arrivals and their615
sojourn typically does not cover the night valley. Hence, their exploita-
tion in terms of deferrable time and energy is typically lower compared to
the arrivals in the other clusters which are usually in the afternoon. The
sessions in the charge near home cluster are the better candidate to fill
the night valley.620
We conclude that the sessions in the charge near work cluster should be
targeted to provide long enough flexibility to fill the afternoon valley. Any longer
idle time would not be exploited (unless it is long enough to cover the night
valley). The sessions in the charge near home cluster should be targeted to fill
the night valley and for arrivals after midnight in this cluster, there is less need625
for longer idle times. Finally, in the park to charge cluster, it is recommended
to target the arrivals in the afternoon to stimulate longer flexibility durations
to fill the afternoon valley.
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