# A Data-Driven Framework for Improving Public EV Charging Infrastructure:
Modeling and Forecasting

Nassr Al-Dahabreh, Mohammad Ali Sayed, Khaled Sarieddine,
Mohamed Elhattab, Maurice Khabbaz, Ribal Atallah, Chadi Assi

###### Abstract

This work presents an investigation and assessment framework, which, supported
by realistic data, aims at provisioning operators with in-depth insights into
the consumer-perceived Quality-of-Experience (QoE) at public Electric Vehicle
(EV) charging infrastructures. Motivated by the unprecedented EV market
growth, it is suspected that the existing charging infrastructure will soon be
no longer capable of sustaining the rapidly growing charging demands; let
alone that the currently adopted ad hoc infrastructure expansion strategies
seem to be far from contributing any quality service sustainability solutions
that tangibly reduce (ultimately mitigate) the severity of this problem.
Without suitable QoE metrics, operators, today, face remarkable difficulty in
assessing the performance of EV Charging Stations (EVCSs) in this regard. This
paper aims at filling this gap through the formulation of novel and original
critical QoE performance metrics that provide operators with visibility into
the per-EVCS operational dynamics and allow for the optimization of these
stations’ respective utilization. Such metrics shall then be used as inputs to
a Machine Learning model finely tailored and trained using recent real-world
data sets for the purpose of forecasting future long-term EVCS loads. This
will, in turn, allow for making informed optimal EV charging infrastructure
expansions that will be capable of reliably coping with the rising EV charging
demands and maintaining acceptable QoE levels. The model’s accuracy has been
tested and extensive simulations are conducted to evaluate the achieved
performance in terms of the above-listed metrics and show the suitability of
the recommended infrastructure expansions.

###### Index Terms:

Charging, EV, Infrastructure, Metrics, Performance, QoE.

##  I Introduction

###  I-A Preliminaries:

As the Electric Vehicle (EV) market continues to experience significant
growth, there is a pressing need to expand the EV charging infrastructure
accordingly. This infrastructure should ensure that the increasing demand for
charging stations (CSs) is fulfilled while maintaining a satisfactory quality
of experience (QoE) for users. In 2021 alone, global EV sales have doubled,
bringing the total number of EVs on the road to approximately 24 million,
which is three times higher than the number in 2019. The number of available
public charging stations has also tripled to approximately 2 million. It is
clear that the future growth of the EV market will depend on the affordability
and accessibility of public or private EV charging infrastructure to the
general public.

Indeed, the exponential rise in the number of EVs on the road is accelerated
by efforts and investments by countries worldwide and incentives offered by
governments to phase out Internal Combustion Engine (ICE) vehicles by 2050.
However, there is a global disparity in EV charging network growth rates, even
between different cities and regions of the same country. The International
Energy Agency (IEA) [1] uses the EV-per-Charger Ratio (EVCR) and per-EV
charger power (EVCP) to assess the adequacy of charging networks. From 2015 to
2021, the EVCR for China, Korea, and the Netherlands showed a quasi-constant
trend of just under 10 EVs/charger, indicating that their charging
infrastructure deployment kept pace with the growing number of EVs. This was
not the case for the United States, where the EVCR was recorded at a high of
18 EVs/charger in 2021. Norway’s EVCR was low until 2013 but rapidly grew to
34 EVs/charger in 2021. The Alternative Fuel Infrastructure Directive (AFID)
[2] recommended EU member states achieve an EVCR of 10 EVs/charger and an EVCP
of 1 kW/EV by 2020. However, the EU’s 2020 average EVCR was 11, increasing to
14 in 2021, with some countries such as Italy and the Netherlands
outperforming others through a wide, on-demand, slow charger deployment plan.
In Canada, Quebec currently has an EVCR of 13 [3], of which only 10% is
covered by public chargers using both slow and fast chargers. The EVCR is
expected to increase rapidly to 17 in 2025 and 29 in 2030, given Quebec’s
target of one million EVs on the road by 2030 and a complete ban on ICE
vehicle sales in 2035. Numerous third-party initiatives, such as the Zero
Emission Transportation Association (ZETA) and its members, including Uber and
Tesla, support the proliferation of EVs.

While the growth of the EV market has increased the need for a reliable public
EV charging infrastructure, the current ad hoc approach to deploying
additional charging stations cannot ensure proper long-term control of
critical QoE metrics or instill confidence in the infrastructure. Proper
tracking of events and occurrence times is necessary to provide operators with
visibility into the EV charging system dynamics, allowing for accurate
forecasting and optimal infrastructure expansion strategies [11] to meet the
rising demand and maintain acceptable QoE levels. Indeed, the challenges above
are only a part of the many obstacles hindering the development and expansion
of a reliable public EV charging infrastructure and this paper focuses on
designing and developing such a framework. However, before delving into the
framework, it is important to discuss first the limitations of the currently
used QoE evaluation methods.

###  I-B Current QoE Metrics, Problem Statement and Motivation:

Ever since 2010, the worldwide achieved average EVCR has been fluctuating at
slightly under $10$ EVs/charger [1], though, despite its globally recognized
eloquence, several countries, as indicated in Section I-A have alarmingly
scored two-to-three-fold this value. Keep in mind here that the main
objective, now, is to show the inadequacy of the employed EV charging
infrastructure expansion strategies in the majority of countries around the
globe as well as the inappropriateness of the metrics that have been globally
adopted to measure and indicate whether or not such expansions are being
capable of coping with the rapid growth in EV market penetration rates. For
this purpose, real-world data is required to ensure the correctness and
credibility of the provisioned insights. Hence, following a legal agreement
and officially approved research collaboration with Hydro-Quebec (HQ) 111HQ
owns/operates, through a subsidiary, around $80\%$ of the public EV charging
infrastructure in Quebec, Canada., this work taps into HQ’s complete database
encompassing realistic daily records (overall $6$ million) of a wide range of
EV charging-related measurements pertaining to comprehensive aspects of EV
charging stations’ dynamics (e.g., start time and duration of each charging
session, per-session average drawn power and total drawn energy, initial
installation date pertaining to each EVCS, per-EVCS nominal charging rate and
geographical location)222It is worthwhile noting here that HQ’s database
contains no information about the per-EV arrival time and waiting time until
it starts receiving service. Such are vital QoE metrics that shall be
intelligently derived herein using the available records. Such metrics will
allow for individual per-EVCS performance evaluation as explained hereafter.
for the various sites within Quebec (i.e., around $7,454$ stations distributed
over $3,878$ different locations) and spanning the past five years from 2018
to 2022. With access to such a panoptic database of EV charging records, it
becomes easy to evaluate and graphically visualize (as shown hereafter in
Figures 1 through ) the evolution of Quebec’s EV charging infrastructure using
the same metrics adopted by the IEA. Curves illustrated in these figures shall
serve as tangible proofs of the inappropriate QoE evaluations and, hence, the
ill-suited EV charging infrastructure expansions they inspire.

Figure 1: EV market penetration in Quebec. Figure 2: Number of deployed
chargers in Quebec

Figure 1 shows a steadily increasing total number of EVs over the entire road
network of Quebec starting from year 2017 until this present time. This
induces expectations of further expansion of the EV charging infrastructure at
least at a rate that can ensure such an infrastructure copes with the
increasing EV market penetration rate; hence, maintaining proper consumer-
perceived QoE levels. In addition, Figure 1 also shows that starting from year
2019, the number of fully Battery-powered EVs (BEVs) started to overshadow
that of Plug-in Hybrid EVs (PHEVs). This is a major change that promotes an
increased need for more frequent per-EV charging activities as well as the
need for additional energy supply to cope with this increased energy demand.
This is not to mention that BEV owners would surely highly appreciate faster
charging processes with less waiting; this being an expectation originating
from an innate desire of QoE equity with ICE vehicles’ drivers. As such,
intuitively, one’s thoughts get immediately directed to an increase in the
deployment of advanced Level 3 (L3) fast chargers concurrently to the
expansion of existing EVCSs through the addition of more of the typical Level
2 (L2) chargers. To this end, Figure 2 presents the EV charging infrastructure
expansions observed over the past five years in Quebec; those being mainly
characterized by the total numbers of L2 and L3 chargers that have been
deployed and became operational and accessible by EV drivers. Here, observe
that the number of L2 chargers increased by almost $300\%$ from 2018 to 2022
whereas the number of L3 fast chargers shows a relatively shy ten-fold
increase. Regardless though, one cannot deny that major efforts and
investments have been and continue being made to improve the availability and
accessibility to a QoE-acceptable EV charging infrastructure. Unfortunately
however, such efforts, are mislead to go in the wrong direction. This is
especially true since they are unable to throttle down and control Quebec’s
continuously increasing EVCR with rising slopes as shown in Figure 3. AS a
matter of fact, Quebec’s EVCR today scored $21$ EVs/charger. Factoring in the
chargers deployed by other operators would slightly bring down the province’s
EVCR to $17$; this being way above the world’s global average. In parallel,
look at the achieved EVCP in Quebec; this being computed, following IEA’s
guidelines, as the ratio of the total average per-EV charging power for all
available public chargers to the total number of EVs on the road. Here, note
that the globally achieved EVCP amounts to $2.4$ kW/EV. Figure 3 shows how
Quebec’s EVCP has been drastically decreasing over time for it to stabilize at
around $0.73$ kW/EV towards the end of 2022. At this point, also, when
factoring in the contributions of the chargers pertaining to other operators
in Quebec, the province’s EVCP would only rise to $0.91$ kW/EV.

The above constitutes a tangible proof that the above-adopted metrics and EV
charging network expansion strategies are ill-developed and that there is
urgent need to establish and implement new plans for expanding this
infrastructure in such a way for it to, first, fill in the gap and cope with
the remarkable rise in EV adoption and, second, steadily parallel this
(expected) long-term rise and meet the increasing EV charging demands both in
terms of frequency and QoE-driven performance. Obviously, in light of the
ealier-presented discussion, EVCR and EVCP cannot serve the general purpose of
assessing the suitability of the existing infrastructure and its state-of-the-
art expansion schemes as they hide from operators the factors underlying: i)
the non-homogeneous variations of EV adoption trends corresponding to
different areas within the same country or province (as revealed by thorough
analysis of realistic data), ii) the contrasted location-restrictive EVCS
deployment feasibility, as well as, iii) the disparity in charging demand
levels experienced in different locations. For instance, the number of EVCSs
deployed in a certain touristic area might appear to be satisfactory. Keep in
mind though that in such an area, often, a large proportion of the EVs
requesting to charge at that area’s local EVCSs may happen to be incoming from
other areas. IEA’s adopted metrics, namely EVCR and EVCP, do not account for
these EVs when evaluated for their areas of origin. It is, therefore, of
notable importance to develop adequate real-world-data-driven and location-
aware EVCS QoE performance metrics that can provision insights into the
suitability of existing location-dependent EV charging networks and
appropriate such networks’ expansion schemes.

Figure 3: Quebec’s achieved EVCP v.s. EVCR.

This paper proposes a new set of critical EVCS QoE performance metrics,
namely: i) the per-EVCS achieved maximum and average waiting times, ii) the
per-charger occupancy and iii) the per-EVCS blocking probability. The design
and quantification of all of these metrics is based on HQ’s comprehensive
database of realistic EV charging-related records. Truly, the proposed metrics
herein prevail where their existing counterparts fail at provisioning
operators with visibility and insights into event dynamics of EVCSs; thus,
guiding them in formulating and implementing adequate well-informed EV network
sizing and charger deployment plans coupled with optimal scheduling algorithms
that aiming at improving the end-consumer-perceived EV charging QoE in any
particular location. To gauge their merit, a charging load forecast model
adopting these new metrics is presented hereafter to predict the future
charging demand per EV charging site. The next subsection highlights this
paper’s fundamental novel contributions and summarizes its organization.

###  I-C Novel Contributions and Paper Organization:

This paper aims at filling the identified literature gap consisting of the
non-existence of proper QoE evaluation metrics, and the lack of accurate long-
term EV charging demand forecast tools. Its contributions are briefed as
follows:

$1$) To the extent of the authors’ awareness, this current work is the first
to present a comprehensive data-driven framework targeting the per-EVCS QoE
assessment. A number of metrics are formulated for the purpose of aiding the
EVCS infrastructure operator gain a deeper understanding of their charging
infrastructure utilization. These metrics shall provision EVCS infrastructure
operators with in-depth visibility into the event-driven system dynamics
pertaining to any particular EVCS deployed at any arbitrary location; hence,
promoting operators’ understanding of their charging infrastructure
utilization allowing them to optimize additional chargers’ deployment, and
charging network sizing.

$2$) Comprehensive EV-charging-related historical data is exploited and fed
into a newly developed Machine Learning (ML) based algorithm for long-term EV
charging demand forecast. Measurement values pertaining to the number of
requests in addition to external factors impacting the charging demand are fed
as inputs to this algorithm allowing it to accurately predict up to one year
of future per-EVCS EV charging demand.

The remaining of the paper is organized as follows. The related work is
surveyed in Section II and data pre-processing is done in Section III. Section
IV is dedicated to the formulation of the new QoE performance metrics as well
as the presentation of the ML-based forecast model. The methodology is
presented in Section V and Section VI lays out results and discussions on the
state of utilization of $14$ sites based on the developed QoE metrics herein
together with the charging demand forecasts. Finally, Section VII concludes
the paper.

##  II Related Work

EV charging demand forecasting has been a subject that has recently received
significant attention; this being attested by the increasing number of
published studies presenting different approaches and shedding the light on
the goodness of the resulting forecasts. Unfortunately, however, inputs to
these existing forecasting models consist of simulated data generated by
restrictive simulation frameworks that cannot really account for comprehensive
real-world dynamics (e.g., housing stock, area/location characteristics, EV
characteristics, actual travel distances, population growth rates, among so
many others) affecting EV charging processes. In addition, a few publications
do rely on some realistic data sets that, alas, happen to be quite limited in
terms of the number of recorded samples corresponding to a very limited number
of attributes characterizing such processes. A prime selection of these
studies is surveyed hereafter. Howbeit, it is important to keep in mind that
the distinguishing features that differentiate this present work from these
existing publications are: i) the exploitation of a large database of
realistic records provisioning in-depth insights into actual EV charging
processes taking place all over the entire Quebec province, ii) beyond EV
charging demand, this work presents a whole new set of QoE performance metrics
and an accurate model to forecast future values of these metrics with such
predicted results serving as guidelines for optimal EV charging infrastructure
expansion and EV-to-charger assignment and scheduling.

In [4], the authors surveyed existing EV charging infrastructure planning
methodologies that targeted the resolution of specific challenges addressed
from either a transportation system perspective or that of a distribution
network or, also, a combination of both. Most of these studies were
theoretical in nature or based on custom-built simulation frameworks focusing
on a limited subset of EV charging aspects while overlooking a large number of
important factors due to the lack of visibility into them. For instance, the
vast majority of these studies commonly limited their scope to the charging
infrastructure itself with a focus on installation cost optimization while
neglecting end-user QoE.

The work of [5] presented a multi-stage EVCS deployment planning framework in
an attempt to achieve an acceptable trade-off between investment costs and
peak distribution grid demands. Precisely, the authors attempted to balance
between EV drivers’ convenience and investors’ revenues without compromising
capacity constraints imposed by operators over a certain pre-determined time
horizon. It appears that the key driver to this framework’s business succcess
is the actual phase-like expected growth of the EV traffic volume, which
dictates the per-stage needed additional investments targeting EV
infrastructure resizing and revenues thereof originating from EV consumers’
satisfaction; all this being subject to power system constraints. However,
unfortunately, the proposed mathematical model in [5] was, contrary to the
authors’ claims, quite restrictive as, first, it was based on a relatively old
and non-realistic EV traffic model proposed in [6] and its restrictive
assumptions leading to fictitious and non-accurate simulated distributions of
the number of EVs on the road. Second, that model adopted traffic parameter
values that do not conform to EV traffic in particular but rather to the
vehicular mobility of all kinds of vehicles on the roads as described by the
authors’ traffic data source in [7]; let alone, the fact that the collected
data dates since 2016 (quite outdated) and that it does not incorporate any
observations pertaining to the utilization and performance of deployed
charging infrastructure back then. Last but not least, the model was too
simplistic, stochastic in nature and aimed at separately optimizing individual
non-related metrics; hence, failing to reach an even acceptable sub-optimal
trade-off among these metrics that should have been jointly optimized.

The work of [8] presented one among the very few data-driven methodologies
targeting the optimization of EVCS deployment within a given geographical
area. Therein, the authors leveraged the PageRank algorithm (refer to [9]),
Graph Theory, geographical aspects and trip data to estimate the spacial
distribution of EV charging demands. More precisely, a considered study area
was subdivided into cells and each cell received a PageRank score that
described that cell’s appeal to EV drivers. Next, a Regression Model (RM) was
adopted for the purpose of mapping the PageRank scores to actual charging
demands using data from existing EVCS. This RM’s results were fed as input to
a Capacitated Maximal Coverage Location Model (CMCLM) for the purpose of
optimizing EVCS deployments with the objective of maximizing coverage.
Unarguably, this presented methodology in [8] is ingenuous reflecting the
authors’ remarkable technical skills in combining trajectory data (provided by
Inrix333https://inrix.com/ partially extracted using probing sensors (e.g.,
cell phones and automated vehicle location sensors) blending that using Google
Place API with Point of Interest (PoI) data that reflected urban context and
infers executed trip purposes and finally integrating socioeconomic data and
land-use information (provided by Wasatch Front Regional
Council444https://wfrc.org/) used as features of people’s parking behaviors
that could impact the EV charging demand. However, one concern, at this point,
is the fact that the majority of the used data (e.g., transportation-related
data) is outdated (since it dates from 2016 and 2018); let alone that such
data was not solely restricted to EVs but rather an entire fleet of vehicles
of different types, among which are EVs. Consequently, such data may not
accurately reflect current and future trends in EV adoption and EV charging
demands. This is especially true given the rapid evolution of EV adoption and
charging behavior patterns. Second, it is not clear how trip purposes have
been linked to EV charging demand impact. It is understandable that
trajectories do indicate traffic flows in and out of specific regions, of
which those experiencing high traffic flows are more likely to also exhibit
high EV charging demands and, hence, may constitute good locations for new
charging stations. Accordingly, regardless of its purpose, an executed trip
will contribute to traffic flow variations of its outbound origin and its
inbound destination. In this sense, regional clusters with high connectivity
and traffic flows may, to a certain extent be considered as appropriate
locations for further EVCS deployments. Third, the authors presented a complex
chain of interconnected machine learning models to capture the argued
multifaceted nature of EV charging demand and optimal placements of new
charging stations based on a variety of factors. While, to this end, the
complexity of this model appears to be a point of strength, it can also set to
be a limitation of this study when it comes to interpretability, transparency,
credibility and utility of generated results; let alone their accuracy. The
lack of knowledge and visibility into of the existing charging stations’
dynamics and, hence, the per station achieved QoE performance, in a way or
another, truncates future demand expectations and, hence, alters the
optimality of the charging infrastructure resizing. This drawback could not,
however, be worked around by the authors of [8] given not just the difficulty
but, often, the rather impossibility of accessing public EV charging stations
utilization information without due authorization from such stations’
operators/owners. This is an issue that this present work does not suffer from
given our pre-authorized access to such information.

The work of [10] presents a data-driven management framework for EV charging
stations with the objective of allowing operators/consumers to plan for peak
charging times and, hence, avoid congestion. Although the authors criticize
some existing short-term EV demands forecasts, their work does not serve the
purpose of filling such a gap. This is especially true since their deep and
supervised machine learning framework only allows for only up to one-week
forecasts, which, is truly far from being long-term. Also, the utilized models
therein only predict the overall energy consumptions per station. Although,
the authors do consider some nice features (e.g., weather conditions,
distinction between regular weekdays, weekends, and holidays, etc), such are
not enough to give operators/consumers an indication of a station’s load, the
waiting-in-line delay to receive service, the chargers’ utilization and the
possibility of blocking (i.e., inability to provide service to an arriving EV
to the station). All such gaps are accounted for in this present work whereby
the presented model herein is capable of providing one full year of forecasts
(extendable to two years ahead) not just in terms of energy consumption but
also in terms of all of the above-listed crucial metrics as a function of the
expected EV penetration rate.

In [11], a Charging Station Dimensioning and Placement (CSDP) framework was
presented with the objective of provisioning minimum-cost fast charging
infrastructure targeting the accommodation of growing EV charging demands in a
metropolitan area powered by a single power grid. Through CSDP, the authors
jointly accounted for EVCS placement and capacity as well as the EV charging
workload distribution among available EVCS to minimize EV waiting times and
reduce range anxiety. They also factored in the power distribution network’s
voltage sensitivity, the possible need for voltage regulators (for maintaining
voltage stability) and transformers with proper rating (for supporting peak
demand). The above CSDP problem was formulated into an Integer Linear Program
(ILP) characterized by its remarkable complexity that the authors worked
around through the development of two heuristics. The efforts invested in
developing CSDP were, indeed, seminal; especially that very little information
was present at that time about EV integration, charging demands, available
EVCS and their underlying functional and operational dynamics. It was, truly,
an epoch of assumptions and visions that researchers attempted to concretize
through the development of theoretical models and approximations that they
strived to bring as close as possible to reality. Today, available real-world
data continues to rule out these assumptions (e.g., truncated Normal
distribution associated to energy demands in [12], the Normally distributed EV
batter State-of-Charge (SoC) in [13], the exponential EV charging time in [11,
14], among others). Now, although the authors of [11] presented enough
evidence of the feasibility of modelling an EVCS as a multi-server queueing
system, their CSDP Workload Assignment (CSDP-WA) and sizing ILP formulations
were founded on top of a highly restrictive approximation of that EVCS model
using multiple single-server queues that was later shown to reflect overly
pessimistic EV waiting time performance. Consequently, forecasting future
demands and EVCS performances based on such allocated workload and sizing
policies can surely not serve for proper charging infrastructure expansion
planning.

The work of [15] presented a big-data driven EV charging demand forecasting
model accounting for vehicular traffic volume data for both vehicles and
busses as well as weather conditions in addition to other variables typically
considered in other existing models (e.g., initial battery SoC, battery type,
charging power classifications, etc). Compared to older studies (e.g., [16,
17, 18, 19]) the authors of [15] also fed their model with the per-vehicle
starting time of the charging process and initial battery SoC, which they
assumed to be accurately drawn from Gaussian distributions with distinct
parameters. Despite the interesting technically insightful features of the
work of [15], it suffered from major drawbacks, first, pertaining to the non-
realistic and inaccurate distributions the authors used to model the majority
of their above-listed model’s variables. Second, the work restricted the
charging processes to take place in residential and workplaces for regular
consumer EVs and in parking stations for busses. Third and most importantly,
the historical traffic volume data used to train their model pertained to all
types of vehicles on highways, national routes and local roads rather than
just EV data. Regardless of the fact that such data dated since 2014 (i.e.,
non-representative of today’s current traffic states), the authors clearly
mentioned the fact that EV traffic volume at that time was much less than that
pertaining to other conventional vehicles. Yet, because of their ill-paused
assumption that such vehicular traffic patterns may conform to future EV-
exhibited patterns due to the expected significant EV penetration growth,
their reported forecasting results seriously lack accurracy. This is
especially true since the EV penetration growth patterns are way different
than those of conventional vehicles (as attested by currently available data);
let alone, the fact that today’s EV traffic patterns continue to be affected
by those pertaining to typical ICE vehicles. As a matter of fact,
realistically today, roads are being populated by both EV and non-EV vehicles
concurrently and the presence of various publically accessible charging
stations incurs significant changes in the charging demand trends. Of course
such newly impactful factors did not exist back at the time when the work of
[15] was published; hence, could not be considered back then.

In [20], the authors proposed a hybrid LSTM neural network with the objective
of merging heterogeneous features pertaining to EV charging processes and,
hence, accurately predict the discrete EV charging occupancy over a well
defined time horizon. The reported results therein gauged the merit of the
proposed algorithm and evidence its superiority over select existing
benchmarks (e.g., hyper-parameter search [21], logistic regression [22], SVM
[23], random forest [24] and Adaboost [25]). The work of [20], indeed, aims at
quantifying one fundamental metric, namely, the per-charger occupancy,
proposed hereafter in this present paper. As much as it is quite insightful on
a technical aspect, it suffers from several drawbacks, among which, the most
important is the adopted restrictive public data that describes EV charging
sessions in terms of a limited number of variables allowing the designed
complex forecast model to only generate relatively accurate results for only
very short-term predictions ranging from $10$ minutes to only almost $4$
hours. Beyond that, the model’s complexity exponentially overshoots in terms
of the number of features to be considered as well as run-time only to exhibit
incremental improvement over existing benchmarks. Of course, such a model
would not be suitable nor insightful aiming at planning infrastructure
expansion for months (let alone a minimum of a year) ahead. The forecast
models presented in [28] and those surveyed by [29] suffer from exactly the
same issue despite their elevated accuracy of the predicted station
utilization and EV charging demands for a period of time that does not bypass
three days. Those models and deep-learning-based algorithms, obviously, cannot
be of any utility when it comes to long-term EV infrastructure expansion
planning and provide only marginal insights into the per-EVCS QoS performance.

##  III Data Pre-processing and Preparation

As already mentioned in Section I-B, the work presented in this paper is
driven by a comprehensive database of $6$ million realistic charging session
records pertaining to $7,454$ EVCSs deployed in $3,878$ locations. This data
has been collected from the various EVCSs over the past 5 years starting from
January 2018 until December 2022. Each charging session record encompasses the
session’s starting time, ending time, outlet ID, station ID, station postal
code, and the amount of energy drawn from each outlet, among numerous other
parameters that are of less interest to the work presented in this paper.
Nonetheless, a major drawback of this data set is that it lacks any
information about EV arrival times to the different EVCSs as well as the
amount of time spent at the station waiting to start charging. Consequently,
in the absence of such crucial information, the per-EVCS QoE performance
evaluation becomes quite challenging. This is carefully addressed in the
remaining sections hereafter. At this point though, it is quite important to
mention that after closely observing the available records, some of them can
be identified as invalid. For instance, all records pertaining to sessions
that: i) lasted less than $3$ minutes or more than $2$ hours, ii) have no
recorded payments associated with them, and, iii) show that no energy has been
drawn from the corresponding outlet, are assumed to be invalid records, and,
hence, have been removed. Following this cleaning phase, the remaining records
have been, first, arranged in ascending order of their corresponding postal
codes, and then, for each station, records are ordered according to the
starting times of each session. To this end, a careful examination of the
postal codes and site IDs pertaining to each station reveals the operator’s
attempt to cluster regions based on the postal code. Consequently, all
stations having the same postal code are considered as belonging to the same
site and, hence, associated with the same site ID.

##  IV EVCS QoE Performance Metrics

This section presents two sets of novel metrics for assessing the quality of
service (QoS) provided by public electric vehicle charging stations (EVCS) in
Quebec, Canada. The first set of metrics includes the number of charging
requests, per-site utilization, per-site occupancy, idleness, and blocking
probabilities, which are based on a comprehensive database of realistic
measurements taken at different times and pertaining to various EV charging
process variables. These metrics are subsequently used as inputs to a forecast
model developed for predicting future EV charging loads. They are as follows:

$\bullet$ Number of Charging Requests, $N_{R}$, represents the number of
unique charging requests experienced by an EVCS during a given time period.
The provided data reveals that some EVs stop but then resume charging within a
few seconds. In what follows, such short charging interruptions are neglected
(i.e., the continuation of charging is not considered as a new request placed
by the same EV but rather the same request identified using the account
credentials of the user who initiated the charging session). Also, all
charging sessions with only a few seconds durations are discarded.

$\bullet$ Charging Site Utilization, $U$, determines if a site is being
underutilized or over-utilized. Through the observation of the variations of a
site’s daily instantaneous utilization, an operator can determine the exact EV
charging demand at that site at any particular point in time. Also, $U$’s
long-term variations reveal the direct impact of EV consumers’ socio-
economical habits on EV charging requirements. Consequently, $U$ provides
operators with insights into the load experienced per site, which cannot be
provided by $N_{R}$ alone as this latter contains no information about the
different charging sessions’ durations. By discretizing time into mini slots
of duration $1$ minute each:

$U=\frac{1}{T}\displaystyle\sum_{i}\frac{k_{i}}{n}$ (1)

where $T$ is the total number of time slots within an observation period,
$i\in\mathbb{N}$ used for indexing each time slot within $T$, $k_{i}$ is the
number of occupied EVCSs during time slot $i$ and $n$ is the number of per-
site EVCSs.

$\bullet$ Site Occupancy, $\Omega$, represents the probability that at least
one of a given site’s EVCSs is occupied (i.e., the probability of that
charging site being utilized):

$\Omega=\frac{1}{T}\sum_{i}\mathcal{Z}_{i}\\\ \textrm{ where $\mathcal{Z}_{i}$
=}\begin{cases}0\text{ if }k_{i}=0\\\ 1\text{ if }k_{i}\geq 1\end{cases}$ (2)

$\bullet$ Site Idleness Probability, $P_{I}$, represents the fraction of the
total observation duration $T$ during which all EVCSs pertaining to a given
site are idle. This metric quantifies the possibility of an EV arriving at a
given site and finding all EVCSs available. As the complement of $\Omega$:

$P_{I}=\Pr\left[k_{i}=0\right]=1-\Omega$ (3)

$\bullet$ Site Blocking Probability, $P_{B}$, represents the proportion of $T$
during which all of a given site’s EVCSs are found to be completely busy
(i.e., the probability of an EV arriving at a given site and finding all EVCSs
occupied and, hence, suffering from immediate denial of service):

$P_{B}=\frac{1}{T}\sum_{i}\mathcal{X}_{i}\\\ \textrm{ where $\mathcal{X}_{i}$
=}\begin{cases}1\text{ if }k_{i}=n\\\ 0\text{ if }k_{i}\leq n\end{cases}$ (4)

Beyond a certain QoE threshold, $P_{B}$ indicates the failure of the existing
charging infrastructure to sustain the growing EV charging demands experienced
by the given site.

Next, the second set of metrics includes the longest per-site busy period and
average EV waiting time, which are evaluated and reported by a custom-built
simulator. These metrics aim to quantify the quality of perceived service by
EV consumers at different public EVCSs and can be used by EV charging
infrastructure operators worldwide to assess the performance of any charging
site and plan EV charging network expansions as needed. They are:

$\bullet$ Number of Delayed EVs, $N_{D}$, represents the number of EVs that
have experienced a certain delay at a given site waiting to receive service
(i.e., start charging). Any EV that starts charging within at most $t$ minutes
(e.g., $t\leq 5$minutes) from the end of a preceding charging session at a
blocked site is considered to be a delayed EV. The value of $t$ is not fixed
and is empirically estimated and recorded by the operator on a per-site basis
given the fact that it is affected by numerous uncontrollable factors that are
external to the charging process (e.g., parking lots’ availability close to
rest areas and shopping malls and their proximity to EVCSs, in-proximity
services, etc). In the future, several solutions may be adopted to increase
the accuracy of $t$’s values (e.g., the installation of cameras to provide
video footage showing the advancement of a waiting EV into service position
and, hence, the start of a new session).

$\bullet$ Average Waiting Time, $\overline{W}$, is the average queueing delay
experienced by EVs waiting at a given site to start charging. $\overline{W}$
is generated using a custom-built PHYTON-based discrete-event simulator that
models each site as an M/G/$k$ queue.

Figure 4: Sample service time data distribution.

##  V QoE Evaluation Methodology

The adopted per-site QoE-oriented performance analysis methodology is
presented. First, although the above-presented metrics may provide per-EVCS
performance insights for the chosen site, it is observed that performance
trends notably vary for different observation period categories (e.g., regular
weekdays, weekends, holidays, etc). As such, to capture such variations, QoE
performance evaluations shall be conducted on daily basis spanning any
required duration (i.e., week, month, year). Precisely, the examined days
throughout the analysis period shall be grouped based on their different
categories. Then, for each one of these days, each of the above-listed metrics
shall be evaluated. This will indicate the frequency whereby each of these
metrics’ respective values signaled a red flag for each one of these days’
categories; this being of utmost importance to operators when developing EV
charging infrastructure expansion plans. For instance, in touristic areas, the
achieved QoE might be misleadingly perceived as good whenever values of the
$U$, $\Omega$, $P_{B}$, $N_{D}$, and $\overline{W}$, do not bypass a given
threshold when evaluated for one whole month or year in one shot. The
operator, here, may be deluded to trust a site’s operational normality
whereas, truly, these metrics’ daily values may reveal an overall site under-
utilization during normal work days and an over-utilization (i.e. low QoE)
during weekends and holidays.

###  V-A Simulation Framework:

A custom-built discrete-event PYTHON-based simulator is developed herein for
the purpose of modelling any EVCS pertaining to any charging site as an
M/G/$k$ queueing system. This simulator’s input parameters’ values are set
according to simulated EVCS’s information extracted from the given dataset.
Precisely, EV arrivals are assumed to follow a Poisson process with a
parameter $\lambda_{E}=N_{E}\cdot T^{-1}$ EVs/s with $N_{E}$ being the number
of observed EVs arriving to the simulated EVCS within the observation period
$T$. $N_{E}$ is dictated by HQ’s recorded data. The per-EV service time is
drawn from an empirically evaluated Erlang-$k$ distribution that fits HQ’s
service time records for the simulated sites. Due to space limitation, only
one such distribution example is illustrated herein in Figure 4 where the Root
Mean Square Error (RMSE) between the realistic distribution and its
theoretically fitted counterpart is of the order of $10^{-8}$ indicating a
highly accurate fit. Finally, the simulated EVCS’s number of outlets is $k$
and is also provided by the operator. The fundamental objective of this
developed simulator is to generate $N_{D}$ and $\overline{W}$. Furthermore,
future EV arrival forecasts are going to be generated hereafter. Such arrival
forecasts may then serve as inputs to the above-mentioned simulator, which,
then, shall return forecasts for future $N_{D}$ and $\overline{W}$ values
pertaining to a simulated EVCS.

Figure 5: Five year charging requests (a) including the COVID-19 data and (b)
requests after filling the gap caused by COVID-19

###  V-B Filling the Gap in the Dataset Created by COVID-19:

In an attempt to combat the proliferation of COVID-19, governments around the
Globe and, particularly in Quebec, imposed numerous and lengthy curfews,
lockdowns and border closures. In addition, remote work and schooling policies
were implemented all over the province. All these have remarkably affected the
province-wide transportation sector. Precisely, during $18$ months (from
January $2020$ to June $2021$) the number of vehicles on the road decreased by
almost $60\%$ including the number of EVs. The decrease in this latter
reflected itself in an abnormal decrease in EV charging demands as illustrated
in Figure 5(a); hence, the reason behind referring to this time period
hereafter as the ”gap period”. For all purposes of proper QoE performance
forecasting, proper charging demand trend corrections (data augmentation) need
to be applied to this gap period in order for it to appear as a smooth quasi-
normal continuation to its predecessor and successor periods; that is, as if
the pandemic never occurred. This is achieved as follows:

$1$) Among the $5$ years data records pertaining to a given site, disregard
all those corresponding to the gap period.

$2$) Compute an $M$ days weighted moving average whereby, the number of
requests for each target day of the gap period becomes equal to the average
number of requests observed during the $\frac{M-1}{2}$ past and future days.
As such, the target day is that $M^{\text{th}}$ day that appears at the center
of the $M$ days period. This mathematically translates to:

$\overline{N_{R,d}}=\frac{1}{M-1}\displaystyle\sum_{j=d-\frac{M-1}{2}}^{d+\frac{M-1}{2}}N_{R,j}$
(5)

where $d$ is the index of the targeted gap day and $N_{R,j}$ is the actual
number of requests.

$3$) Compute the relative daily charging request difference $\Delta
N_{R}=\left(N_{R,d}-\overline{N_{R,d}}\right)\overline{N_{R,d}}^{-1}$. Use all
relative differences over the entire $42$ months before and after the gap to
generate $\Delta N_{R}$’s empirical probability distribution, $\mathcal{D}$.

$4$) Finally, to each computed $\overline{N_{R,d}}$ over the $18$-month gap
period, add a random $\Delta N_{R}$ value drawn from $\mathcal{D}$.

Figure 5(a) ($M=30$) concurrently plots $N_{R,d}$ and $\overline{N_{R,d}}$
pertaining to one selected site over the entire $5$-year period. The trend
anomaly is clear during the gap period compared to its normal counterparts
appearing before and after the gap. Most importantly, Figure 5(a) tangibly
proves $\overline{N_{R,d}}$’s potency in capturing the seasonal/annual trends
of $N_{R,d}$ while smoothing out its randomness. Figure 5(b) shows the
reconstructed number of charging requests values corresponding to the gap
period following the above-elaborated procedure. These results assert the
suitability of the utilized approach since the reconstructed trend appears
clearly as a smooth quasi-normal bridge connecting its predecessor to its
successor curves.

###  V-C Long-Term Forecast Model:

As anticipated, the EV charging demand is expected to grow at an increasing
pace in the coming years. This stresses the importance of creating a long-term
forecast model that can accurately predict the EV charging load in terms of
served request counts over an entire year while taking the load’s seasonality
into consideration.

$\bullet$ Data Pre-Processing and Feature Engineering: The first pre-
processing step consists of chronologically arranging the charging records to
create a continuously evolving time series and then extract from them the
required features, the fundamental one of which are the timestamps listed in
Table I. Here, timestamp differentiation and proper interpretation are
important especially because of the differential characteristics of regular
weekdays’ charging requests and their weekends/holidays counterparts. Table II
lists additionally extracted categorical features constituting external
factors that impact the charging demand. All of these features are then
encoded using the mean encoding method described in [30] and [31] to reveal a
logical correlation between them and their corresponding label ( i.e.,
$N_{R,d}$). Consequently, during the training phase, the model determines the
relationship between the predicted value and the mean features’ encoding
instead of the actual $N_{R,d}$.

TABLE I: Time stamp features Feature Name | Range of Values
---|---
Weekday (Monday$\rightarrow$Sunday) | $[0;6]$
Day of the month | $[1;31]$
Day of the year | $[1;365]$
Month of the year | $[1;12]$
Week of the year | $[1;53]$
Week of the month | $[1;4]$
Quarter of the year | $[1;4]$
Recorded year | $[2018;2022]$
Working Day | [$0$: Weekend/Holiday; $1$: Business day]
TABLE II: Charging service features Feature Name | Range of Values
---|---
Charging requests weighted rolling average | Float
Province-wide number of available public EVCSs | Integer
Province-wide number of registered EVs | Integer
Region-specific number of available public EVCSs | Integer
Region-specific number of registered EVs | Integer

$\bullet$ Forecast Model: A Seasonal Auto-Regressive Integrated Moving Average
with eXogenous factors (SARIMAX) statistical learning model (e.g., [32]) is
presented hereafter. This model takes as input a time series rendering it
capable of accurately predicting future $N_{R,d}$ values while concurrently
capturing its real-world historical data inputs’ seasonality and patterns. In
the sequel, it is proven that SARIMAX is capable of: i) accurately capturing
and representing this seasonality for $1$-year forecasts, and, ii) integrating
multiple external variables and deduce their impact on the charging demand’s
behavior.

TABLE III: Charging Site Description and Number of EVCSs per Site Site # | Location | Number of EVCSs/Site
---|---|---
1 | City 1 Downtown | 2
2 | City 1 Residential Area | 2
3 | City 2 Residential Area | 2
4 | City 2 Mall Parking Lot | 2
5 | City 3 Downtown | 1
6 | Suburb 1 | 1
7 | Suburb 2 | 2
8 | Rural Area 1 | 1
9 | Rural Area 2 | 2
10 | Touristic Area 1 | 2
11 | Touristic Area 2 | 1
12 | Highway 1 | 2
13 | Highway 2 | 2
14 | Highway 3 | 4

As a matter of fact, the accessible data sets related to the addressed problem
in this paper enclose data sample points that constitute a time series. This
is especially true since these samples represent the magnitude of changes in
the EV charging load as a function of time. The objective here is to forecast
future metric values (and their variations as a function of time as well)
according to what can be learned from the past history embedded in the above-
said time series. As such, given that such data exhibits seasonality patterns
and given the availability of a strong exogenous factor in the time series,
SARIMAX would be the best forecasting model fit in this case.

SARIMAX is defined by three main parameters, p, d, and q, respectively
denoting the number of auto-regressive terms, the order of differentiation,
and the order of moving averages. The determination of seasonal variations is
required to establish a Seasonal Auto-Regressive Function (SARF) in addition
to a Non-seasonal Auto-Regressive Function (NARF) [34]. Additionally, the set
of exogenous variables is fed into the model in an array-like parameter exog.
Proper tuning SARIMAX’s parameters allows for the generation of accurate
forecasts based on the detected patterns and the exogenous features. The
recorded daily per-site number of charging sessions and their corresponding
exogenous variables are aggregated weekly to overcome $N_{R,d}$’s randomness.
This kind of aggregation is acceptable and rather preferred for objectives
similar to those adopted in this paper (i.e., forecasting a charging site’s
QoE future evolution).

Initially, the Box-Jenkins approach is used to estimate the most appropriate
range for the d parameter. Then the Partial Auto-correlation function was used
to determine an appropriate range for p and the Auto-correlation function was
used to determine q. Augmented-Dickey-Fuller tests are executed to verify the
existence of non-stationary conditions. A close examination of these tests’
results reveals that the best model is one to which correspond fractional
parameters’ values. In fact, Fractional ARIMA is used when the data patterns
exhibit long-range dependencies that cannot be captured using integer
parameters. The interpretation of the fractional parameters becomes different
than the interpretation of the integer parameters. Fractional differencing
with d $<1$, is used to smoothen out very long-term data dependencies while
simultaneously preserving the short-term dependencies. A value of $0.5<$ d
$<1$ would indicate the presence of a strong historical dependence in the
data. Additionally, using a fractional d eliminates the issue of over-
differencing which might add white noise when large values greater than $1$
are used. Additionally, it is favorable to choose low values of the p and q
when using fractional values of d to learn the long-term dependencies of the
data while simultaneously preserving the short-term fluctuations and
dependencies. As a result, low values of the fractional auto-regressive term p
are used to capture the short-term dependencies of the data. Finally, low
values for the moving average order q are used to capture the short-term
fluctuations and noise in the data. As a result, grid search is performed here
to tune the parameters of the SARIMAX model adopted herein with low range of p
and q and a fractional d. Additionally, the choice of exogenous variable is
extremely important to improve the model’s accuracy significantly. This is the
number of EVs in the region (scaled by the average charging demand of a
typical EV) was selected as an exogenous variable.

The model is trained and optimized against the data extending from $2018$ to
$2021$ based on the above-described approach. Then, it is tested against non-
training data (i.e., pertaining to year $2022$), to validate its ability to
forecast an entire year accurately. Several accuracy metrics are used to
evaluate the model’s accuracy such as RSME, MSE, MAE, and MAPE.

The SARIMAX model proposed herein forecasts the weekly average number of
requests with $99\%$ confidence. This allows, at this point, to utilize this
model to forecast the charging requests for the selected sites throughout the
entire next year $2023$. Note that the model requires re-training using the
data of each individual site for accurate forecasts to be generated.
Additionally, a second year forecast is generated to guide the operator with
some longer-term forecasts. However, it is important to highlight that the
farther future forecasts are generated with a reduced results’ confidence.
Yet, every new year of data that is added to the data set enables longer and
more accurate the forecasts.

Now, indeed, there are so many different prediction and forecasting models. It
is quite interesting to compare the performance of the adopted SAIMAX model
with fractional parameters to other models such as LSTM, ETS, ARIMA, and
SARIMA. This is done in Section VI below.

##  VI Analysis and Forecast Results

This section presents an evaluation of the performance of $14$ selected
charging sites in terms of the presented metrics in Section IV. Moreover, $4$
of these sites are selected to showcase the prediction accuracy of the
developed SARIMAX. The reported results also illustrate the average waiting
time evolution between $2021$ and $2022$ as well as the predicted waiting time
for $2023$ highlighting the impact of the increasing EV charging demand on the
user-perceived QoE.

TABLE IV: Charging Site Occupancy in $2021$ and $2022$ | # Days 10%$\leq\Omega\leq$30% | # Days $\Omega\geq$ 30%
---|---|---
Site Location | 2021 | 2022 | 2021 | 2022
City 1 Downtown | 239 | 131 | 107 | 232
City 1 Residential Area | 182 | 192 | 8 | 13
City 2 Residential Area | 247 | 233 | 14 | 20
City 2 Mall Parking Lot | 178 | 245 | 20 | 67
City 3 Downtown | 139 | 206 | 6 | 12
Suburb 1 | 127 | 190 | 3 | 10
Suburb 2 | 160 | 229 | 84 | 34
Rural Area 1 | 170 | 198 | 52 | 113
Rural Area 2 | 145 | 159 | 70 | 161
Touristic Area 1 | 154 | 85 | 110 | 263
Touristic Area 2 | 187 | 230 | 21 | 41
Highway 1 | 91 | 147 | 5 | 6
Highway 2 | 31 | 107 | 0 | 1
Highway 3 | 220 | 111 | 88 | 252
TABLE V: Charging Site Utilization in $2021$ and $2022$ | # Days 10%$\leq U\leq$30% | # Days $U$ $\geq$ 30%
---|---|---
Site Location | 2021 | 2022 | 2021 | 2022
City 1 Downtown | 267 | 303 | 12 | 38
City 1 Residential Area | 69 | 70 | 0 | 0
City 2 Residential Area | 108 | 116 | 0 | 0
City 2 Mall Parking Lot | 91 | 186 | 0 | 0
City 3 Downtown | 139 | 206 | 6 | 12
Suburb 1 | 127 | 190 | 3 | 10
Suburb 2 | 149 | 127 | 17 | 0
Rural Area 1 | 170 | 198 | 52 | 113
Rural Area 2 | 135 | 187 | 17 | 63
Touristic Area 1 | 165 | 210 | 27 | 123
Touristic Area 2 | 187 | 230 | 21 | 41
Highway 1 | 29 | 47 | 0 | 1
Highway 2 | 1 | 21 | 0 | 1
Highway 3 | 63 | 220 | 0 | 0
TABLE VI: Number of Days the Charging Sites experienced $P_{I}>90\%$. Figure
6: Number of Days with $P_{I}=100\%$. Figure 7: Evolution of $N_{D}$ on the
$14$ sites between $2021$ and $2022$. TABLE VII: Blocking probability
evolution from $2021$ to $2022$.

###  VI-A Occupancy, Utilization and Idle Probability:

The number of EVCSs varies from one to another of the $14$ sites selected from
diverse province-wide locations to capture EV charging load variability. For
privacy reasons, these sites’ actual locations are replaced with generic names
as listed in Table III. Note that a site with $1$ EVCS, yields $\Omega=U$.

Table IV presents a summary of the number of days where the per-site occupancy
belonged to the normal range of $10\%$ to $30\%$ as well as the number of days
where that occupancy exceeded $30\%$. Table V on the other hand presents the
number of days where the per-site utilization belonged to similar intervals.
$\Omega$ and $U$ are presented for both $2021$ and $2022$ to demonstrate the
evolution of PCI utilization. Observe that $13$ out of the $14$ sites,
witnessed an increase in $\Omega$ and $U$. Particularly, Touristic Area (TA)
$2$ and Suburban Area (SA) $1$ exhibited an $\Omega>30\%$ for more than double
the days. Another insight that can be extracted from Table IV and V is that
the charging sites next to the Highways $1$ and $2$ are being lightly
underutilized with a $U>30\%$ on zero and one day respectively in $2021$ and
$2022$. This could indicate the user’s tendency to charge at their origin or
destination points rather than spending time charging en route. Also, the
charging site on Highway $3$ suffers an $\Omega>30\%$. However, its $U<30\%$
throughout all of $2021$ and $2022$. A third observation can be made regarding
the charging site in City $2$’s Mall Parking Lot. Even though the number of
days where $10\%\leq U\leq 30\%$ doubled, it has never been over-utilized as
the number of days where its $U>30\%$ remains zero. However, this serves as an
indicator that another EVCS should be added to that site.

On the other hand, $P_{I}$ indicates whether or not a charging site is being
underutilized. Table VI presents the number of days where the $14$ charging
sites experienced a $P_{I}>90\%$. This means that on those days the charging
site was vacant and remained idle for $90\%$ of the time; thus, indicating a
very low utilization on that day. Table VI that charging sites at Highways $1$
and $2$ are severely underutilized. As such, no new EVCSs need to be added at
these locations in the near future. However, one important observation is that
all sites experienced a drop in $P_{I}$ including Suburb $2$. This means that,
even though the overall utilization of these sites decreased from $2021$ to
$2022$, it became less likely to find them idle. The shaded bars in Table VI
represent the percentage of the year during which $P_{I}>90\%$.

Finally, Figure 6 presents the number of days during which the charging sites
were not used at all (i.e. $P_{I}=100\%$). This figure can give us three very
important observations. The first is that even though certain sites have a
high possibility of being idle, the number of days during which no charging
occurred on these sites is relatively low. The second observation is on the
site at Highway $2$ that had a $P_{I}>90\%$ for $258$ days of the year but
only had $32$ days during which it was not used. This means that although such
charging sites will experience low utilization, they are indeed needed almost
every day by EV drivers. The third observation was seen at the charging site
in City $3$. Although this city experienced higher utilization and occupancy
in $2022$, the number of days during which it experienced an $N_{R}$ of zero
slightly increased. This type of anomaly represents a trend of more
centralized EV charging. It can possibly mean that although user demand on
this site increased, this demand was concentrated on certain days. This
clearly demonstrates the importance of examining these metrics per day instead
of aggregating entire months or entire years together.

Figure 8: SARIMAX testing accuracy for charging site at Touristic Area 1.
Figure 9: SARIMAX testing accuracy for charging site at City 1 Downtown.
Figure 10: SARIMAX Touristic Area 1’s weekly forecasts during $2023$. Figure
11: SARIMAX City 1 Downtown’s weekly forecasts during $2023$.

###  VI-B Blocking Probability:

Another important metric studied at these $14$ sites is the blocking
probability, $P_{B}$. Due to the sensitivity of this metric, it is presented
in Table VII in steps of $10\%$. $P_{B}=0$ means that a site was not blocked
on a given day. A close inspection of Table VII evides that the charging site
next to Highway $1$ was never blocked for $295$ and $256$ days in $2021$ and
$2022$ respectively; hence, confirming that EV drivers were less likely to use
this specific site. Also, the number of days during which $P_{B}=0$ for most
of the $14$ sites decreased between $2021$ and $2022$. This goes in line with
the results reported in Table IV and Table V indicating an increase in these
sites’ $U$ and $\Omega$ respectively in $2022$. Unexpected, however, is
$P_{B}$ pertaining to Rural Area $1$’s site. While in $2021$ this site had a
$P_{B}\geq 20\%$ for $116$ days, this number almost doubled to reach $206$
days in $2022$. That is, an arriving EV at this site had a $20\%$ chance of
not finding an available EVCS on $206$ out of $365$ days that year. This is a
clear indication that an additional EVCS needs to be added within that site’s
region. While the charging site in City $1$ Downtown also had a low chance of
having $P_{B}=0$, its performance was still acceptable in $2022$ as most of
the days experienced $0\%\leq P_{B}\leq 10\%$. These results are also
reflected by $N_{D}$ as discussed below.

###  VI-C Delayed EVs:

Recall that $N_{D}$ represents the number of EVs that had to wait at a blocked
charging site; hence, the direct relationship between the $P_{B}$ and $N_{D}$.
This is revealed in Figure 7, which illustrates the evolution of $N_{D}$
between $2021$ and $2022$ at the $14$ sites. The figure indicates that the
site in Touristic Area 1 experienced an increase in $N_{D}$ by $67\%$ meaning
that the service will quickly deteriorate at this site in the coming year if
the PCI in that area is not properly expanded. The results pertaining to
Highway $1$’s charging site are consistent with their counterparts for $U$,
$\Omega$ and $P_{B}$ reported in their above-indicated respective tables. In
confirmation of this site’s low $U$ and $P_{B}$, only $9$ and $12$ EVs had to
wait to receive service there for during the entire years $2021$ and $2022$
respectively. Another important observation is the decrease in $N_{D}$ in the
Suburban Area $2$ from $134$ EVs in $2021$ to $41$ EVs in $2022$. This result
is consistent with the drop in this site’s $P_{B}$.

Figure 12: Evolution of $\overline{W}$’s distribution during $2021$ (left), $2022$ (center), and $2023$ (right) for the site at Touristic Area 1. TABLE VIII: Tabulated Quarterly Forecast Results. Quarter | Touristic Area 1 | City 1 DownTown | Rural Area 1 | City 2 Mall
---|---|---|---|---
2023 Q1 | $1539$ | $1452$ | $526$ | $1098$
2023 Q2 | $2263$ | $1709$ | $811$ | $895$
2023 Q3 | $2841$ | $1772$ | $1278$ | $1008$
2023 Q4 | $2339$ | $1898$ | $801$ | $1178$
2024 Q1 | $2382$ | $2260$ | $795$ | $1655$
2024 Q2 | $3267$ | $2444$ | $1206$ | $1202$
2024 Q3 | $3927$ | $2462$ | $1740$ | $1422$
2024 Q4 | $2979$ | $2500$ | $1010$ | $1526$
TABLE IX: Tabulated Model Parameters. Site Location | p | d | q | P | D | Q | Model MAPE
---|---|---|---|---|---|---|---
Touristic Area 1 | 0 | 0.6 | 1 | 0 | 1 | 1 | $12.12\%$
City 1 Downtown 1 | 1 | 0.8 | 1 | 0 | 1 | 1 | $8.15\%$
City 2 Mall 1 | 1 | 0.8 | 0 | 1 | 1 | 0 | $14.28\%$
Rural Area 1 | 0 | 0.4 | 1 | 0 | 1 | 1 | $10.83\%$

###  VI-D SARIMAX Model Testing and Forecast:

The SARIMAX model presented earlier in Section V-C is now used to predict
future values of $N_{R}$ for $4$ of the $14$ sites examined in this
manuscript, namely, Touristic Area 1, City 1 Downtown, Rural Area 1, and City
2 Mall. The model is trained using the $2018$ through $2021$ data pertaining
to each of these charging sites individually and then tested against the
$2022$ data. The grid search algorithm is then utilized to evaluate the best
parameters that would achieve the most accurate results when validated against
the $2022$ data. The p, q, and d parameters of these models are presented in
Table IX for the reader’s convenience. Figures 8 and 9 constitute tangible
proofs of the model’s forecast accuracy for the sites at Touristic Area 1 and
City 1 Downtown. The SARIMAX model was able to accurately forecast the
charging demand while very closely following the behavior of the actual time
series. The shaded region in the figure also indicates that future demands are
predicted with $99\%$ confidence. The fine-tuned models are now used to
forecast the demand for the entire year of $2023$ for these $4$ sites.
textcolorblueAdditionally, these models were also used to generate a forecast
for the weekly number of requests for a second year, $2024$. Due to space
limitation, only the forecast results of textcolorbluethe year 2023 of $2$
sites are presented in Figure 10 and Figure 11. However, the total quarterly
number of requests for the $4$ sites for the entire $2$-year period is
presented in Table VIII. Additionally, the accuracy evaluation metrics
pertaining to the adopted model herein are presented in Table X. For the sake
of completeness, the accuracy of this model is compared to those of 5 other
counterparts proven in the literature to outperform the presently suggested
SARIMAX model with fractional parameters. Precisely, the results of the
SARIMAX model presented above are compared with two ETS models, with and
without seasonality, an LSTM model, an ARIMA model without seasonality, and
finally with an SARIMA model without an exogenous variable. Table X clearly
demonstrates the superiority of the presented SARIMAX model with fractional
parameters in terms of forecast accuracy. Here, it is very interesting to
observe the relatively poor performance of the LSTM model despite notable
efforts to optimize its performance as well as the inclusion of the exogenous
parameter as a feature for the LSTM’s NN. This is a consequence of the
relatively young age of the charging infrastructure, which would severely
limit the success of training a Deep Learning algorithm due to the limited
number of training samples in a $4$-year period ($201$ weekly values per
site). Also, traditionally, such forecasts rely on extensive historical
information spanning tens of years (such as stock market forecasts).

TABLE X: Performance metrics for different models. Site | Model | MSE | RMSE | MAPE | MAE
---|---|---|---|---|---
| ETS Without Seasonality | $754.32$ | $27.46$ | $21.04\%$ | $21.53$
| ETS With Seasonality | $530.74$ | $23.04$ | $17.65\%$ | $18.67$
| LSTM | $690.50$ | $26.28$ | $19.11\%$ | $19.10$
Touristic Area 1 | ARIMA | $486.29$ | $22.05$ | $17.28\%$ | $17.71$
| SARIMA | $621.69$ | $24.93$ | $18.78\%$ | $19.40$
| SARIMAX | $423.76$ | $20.59$ | $12.12\%$ | $15.06$
| ETS Without Seasonality | $688.89$ | $26.24$ | $22.82\%$ | $21.77$
| ETS With Seasonality | $276.84$ | $16.79$ | $12.55\%$ | $11.78$
| LSTM | $375.68$ | $19.38$ | $17.56\%$ | $15.39$
City 1 Downtown | ARIMA | $187.39$ | $13.69$ | $11.55\%$ | $10.84$
| SARIMA | $189.44$ | $13.76$ | $11.33\%$ | $10.60$
| SARIMAX | $90.04$ | $9.49$ | $8.15\%$ | $7.57$

###  VI-E Waiting Time Evolution:

After forecasting the number of charging requests for $2023$ the M/G/$k$
simulator presented in Section V-A is used to study the evolution of the
waiting time on the $4$ selected sites throughout the years $2021$ (including
the filled Gap), $2022$, and $2023$ (forecasts). The daily number of requests
is first extracted from the weekly forecast values. Then, these values are
used to determine the EV arrival rates to the charging site. Subsequently,
extensive simulations are performed with $25,000$ EV arrivals per simulation
round generated using the determined arrival rates for all of the $365$ days
corresponding to each year. This guarantees the achievement of at least $95\%$
confidence interval and reduces the impact of any outliers.

The results of the three years’ simulations for Touristic Area 1 are presented
in Figure 12. This figure demonstrates how the probability of low waiting
times is decreasing while the probability of experiencing high waiting times
is increasing year after year. This is demonstrated by the bulkier tale of the
distribution and the more frequent $\overline{W}$ values above $60$ minutes.
To put things into perspective, the probability of experiencing a waiting time
of zero is $20.4\%$ and $9.3\%$ in $2021$ and $2022$ respectively. This value
drops to $3.8\%$ in $2023$. Additionally, the average waiting time in $2021$
was $3.49$ minutes and rises to $6.73$ minutes and $14.68$ minutes in $2022$
and $2023$ respectively. Additionally, $99\%$ of the anticipated waiting times
are within $30$ minutes, $40$ minutes, and $110$ minutes in $2021$, $2022$,
and $2023$ respectively. The statistics related to the $\overline{W}$ results
of the $4$ analyzed sites are presented in Table XI.

TABLE XI: Waiting Time Statistics for 2021, 2022, and 2023 2021 | Average | Probability $\overline{W}=0$ | 99% Interval
---|---|---|---
City 1 Downtown | 2.22 min | 26% | 6 min
City 2 Mall | 1 min | 50% | 2 min
Rural Area 1 | 19.95 min | 0% | 36 min
Touristic Area 1 | 3.49 min | 20.4% | 30 min
2022 | Average | Probability $\overline{W}=0$ | 99% Interval
City 1 Downtown | 3.68 min | 10.5% | 10 min
City 2 Mall | 1.3 min | 44% | 3 min
Rural Area 1 | 24.98 min | 0% | 43 min
Touristic Area 1 | 6.73 min | 9.3% | 40 min
2023 | Average | Probability $\overline{W}=0$ | 99% Interval
City 1 Downtown | 11.32 min | 4.9% | 24 min
City 2 Mall | 2.9 min | 22.6% | 7 min
Rural Area 1 | 35.36 min | 0% | 85 min
Touristic Area 1 | 14.68 min | 3.8% | 110 min

###  VI-F Case Study: Charging Site at Touristic Area $2$:

Finally, a case study related to Touristic Area $2$ is considered. By the end
of $2021$, this site contained a total of $9$ Level $2$ EVCSs and $2$ Level 3
EVCs. The site under study contains $1$ of these Level $3$ EVCSs. This region
experienced a rapid deployment of Level $2$ EVCS rising to reach a total of
$33$ Level $2$ EVCSs by the end of $2022$. However, no new Level $3$ EVCSs
were added in $2023$ to this region. Based on the earlier conducted analysis,
the utilization of the specific site of interest kept increasing in $2023$
despite the addition of $24$ new Level $2$ EVCSs within a very short distance.
This site’s $P_{B}$ and $\overline{W}$ also increased. This confirms the fact
that, even though the Level $2$ PCI was greatly expanded in this region, it
failed to catch up with the increasing EV charging demands; hence, the extreme
importance of utilizing the herein presented methodology to determine the
sites worthy of new Level $3$ EVCS deployments for the purpose of maintaining
adequate QoE performance and supporting the growing number of EVs and their
charging demands.

##  VII Conclusion

This is the first data-driven study that develops a comprehensive set of
metrics to evaluate the EV PCI performance of future smart cities. Also, the
herein-developed forecast model accurately predicts the evolution of charging
requests at a given site. The performance pertaining to $14$ representative
sites was analyzed through a close examination of the evolution of the
occupancy, utilization, blocking probability, and the number of waiting EVs. A
custom-built simulator is then used to estimate the average waiting time
experienced by EVs during $2021$ and $2022$ as well as the predicted waiting
time given the $2023$ predicted charging demand. This study demonstrates the
necessity of expanding the EV PCI in order to satisfy the ever-increasing
charging demand and maintain acceptable consumer-perceived QoE levels.

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