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A Stochastic Approach to Designing Plug-In Electric Vehicle Charging Controller for Residential Applications

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The increase of Plug-in Electric Vehicles (PEVs) penetration in distribution systems necessitates processing strategic assets in order to deal with their energy needs. A careful investigation into matters related to PEV charging management under actual circumstances can be regarded as the critical step towards enabling this process. Accordingly, this paper intends to design a practical controller capable of performing charging scheduling under uncertainties related to the lack of access to crucial PEV information accounting for departure time, energy requirement, and power demand nonlinearity. Although such an issue can be encountered when developing charging models for real-world conditions, it has not been adequately taken into consideration. The proposed controller carries out charging scheduling through a procedure with a set of effective straightforward algorithms, essential for actual applications. Particularly, it takes advantage of a Bayesian forecasting model that is able to efficiently predict charging energy demand according to car owner’s behavior. In addition, it employs a stochastic optimization framework to schedule PEV charging based on the dynamic electricity price and user preference. Several case studies are conducted to examine the performance of suggested controller in optimal scheduling by exploiting real data. The evaluation process is executed through a comparative analysis by using a deterministic method, as the ideal case, which exploits a full-information space. The results show that the proposed procedure can offer competitive charging schedules, which can minimize the cost while satisfying user desires. The designed controller can successfully manage PEV charging in the presence of stochastic phenomena with limited information access, and thus, enable physical implementations.
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Received April 15, 2022, accepted May 7, 2022, date of publication May 17, 2022, date of current version May 23, 2022.
Digital Object Identifier 10.1109/ACCESS.2022.3175817
A Stochastic Approach to Designing Plug-In
Electric Vehicle Charging Controller for
Residential Applications
1Department of Electrical and Computer Engineering, Hydrogen Research Institute, Université du Québec à Trois-Rivières, Trois-Rivieres, QC G8Z 4M3, Canada
2Department of Mechanical Engineering, Hydrogen Research Institute, Université du Québec à Trois-Rivières, Trois-Rivieres, QC G8Z 4M3, Canada
3Laboratoire des Technologies de l’Energie, Institut de Recherche Hydro-Québec, Shawinigan, QC G9N 7N5, Canada
Corresponding author: Abdoul Wahab Dante (
This work was supported in part by the Laboratoire des Technologies de l’Énergie (LTE) d’Hydro-Québec, in part by the Natural Science
and Engineering Research Council of Canada, and in part by the Foundation Université du Québec à Trois-Rivières.
ABSTRACT The increase of Plug-in Electric Vehicles (PEVs) penetration in distribution systems necessi-
tates processing strategic assets in order to deal with their energy needs. A careful investigation into matters
related to PEV charging management under actual circumstances can be regarded as the critical step towards
enabling this process. Accordingly, this paper intends to design a practical controller capable of performing
charging scheduling under uncertainties related to the lack of access to crucial PEV information accounting
for departure time, energy requirement, and power demand nonlinearity. Although such an issue can be
encountered when developing charging models for real-world conditions, it has not been adequately taken
into consideration. The proposed controller carries out charging scheduling through a procedure with a set
of effective straightforward algorithms, essential for actual applications. Particularly, it takes advantage of
a Bayesian forecasting model that is able to efficiently predict charging energy demand according to car
owner’s behavior. In addition, it employs a stochastic optimization framework to schedule PEV charging
based on the dynamic electricity price and user preference. Several case studies are conducted to examine
the performance of suggested controller in optimal scheduling by exploiting real data. The evaluation
process is executed through a comparative analysis by using a deterministic method, as the ideal case,
which exploits a full-information space. The results show that the proposed procedure can offer competitive
charging schedules, which can minimize the cost while satisfying user desires. The designed controller can
successfully manage PEV charging in the presence of stochastic phenomena with limited information access,
and thus, enable physical implementations.
INDEX TERMS Plug-in electric vehicle, energy management, charging scheduling, load modeling,
ηUser satisfaction probability considering the
final state of energy.
TDeparture time horizon decision space.
TOptimization horizon corresponding to the
kOptimal control input at the time slot k.
The associate editor coordinating the review of this manuscript and
approving it for publication was Alon Kuperman .
TsAverage temperature in the day of the sth charg-
ing session.
1tTime step.
kPredicted charging power profile at k.
sAverage sunlight in the day of the sth charging
λkElectricity price at the time slot k.
ξDeparture time uncertainty parameter.
bav Average value of the estimated charging power
for the charging session s.
52876 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see VOLUME 10, 2022
A. W. Dante et al.: Stochastic Approach to Designing Plug-In Electric Vehicle Charging Controller for Residential Applications
kActual observation of charging power during the
sth charging session at k.
Dtest Test database.
Dtrain Training database.
kTime index.
sAverage precipitation in the day of the sth charg-
ing session day.
SkPEV parking status at the time slot k.
yslActual charging energy requirement during the
last lhome charging sessions.
γEBattery charging efficiency.
ukBinary decision variable of ON/OFF charging
control of the PEV battery..
ˆysEstimate of energy requirement for PEV charg-
ing in sth charging session.
xsVector of the exogenous input variables of the
energy predictive model, f.
ysVector of the historical endogenous variable of
the predictive model f.
ykState variable of accumulated charging energy in
the PEV battery at k.
Over the last decade, Plug-in Electric Vehicles (PEVs),
spurred by ambitious political announcements and technolog-
ical advances, have expanded significantly [1]. Total sales of
PEVs have reached an annual increase of 40% [2]. In the fist
trimester of 2021, the global fleet of these cars made a record
by surpassing 10 millions, 3 millions more than the previous
year [2]. In the long run, the rapid integration of PEVs into
the distribution network can dramatically increase grid peak
demand and cause uncertainty and instability in the operation
of existing electric power systems [3]. Several investigations
have shown that PEV charging is most often performed at
home [4]–[6]. Therefore, PEV is progressively becoming a
new major residential electrical appliance.
Similar to other domestic appliances with flexible energy
usage such as dishwashers, the charging of PEVs can be
managed by the Home Energy Management System (HEMS)
to avoid demand during peak periods with relatively high
prices [7], [8]. PEV charging is typically scheduled to reduce
the cost considering the price signal and the user com-
fort preference. The scheduling is performed through an
optimization problem, formulated based on PEV charging
parameters. Arrival time, departure time, charging energy
requirements (initial and desired State Of Charge (SOC)),
battery capacity, charging power, and conversion efficiency
are the main parameters of the optimization procedure.
A PEV charging controller that is aimed at practical imple-
mentations must be able to handle uncertainties related to the
lack of access to specific parameters. These factors account
for departure time, energy requirement, and power demand
non-linearity, which are essential for an effective charging
management. Although the lack of such information can be
encountered under real conditions, it has not been adequately
taken into consideration. From a general viewpoint, research
studies have neglected to address the charging scheduling
problem considering the above issue. For instances, most
analyses have considered a perfect knowledge about the
departure time [9], [10] that is not feasible especially in a
long run. In addition, other works have neglected the non-
linear behavior of PEV charging power. Besides, several
studies have assumed automatic access to either the battery
SOC or travelled distance. However, PEV manufactures seem
to be reluctant to provide this information in near future.
Therefore, charging stations are not able to communicate
with PEV on-board charging controller in order to receive
relevant information. It should be also added that some of
these assumptions can lead to further challenges. For exam-
ple, exploiting the travelled distance to estimate the initial
SOC, as a common strategy, can be unreliable for PEVs that
utilize external (home-away) charging sessions. On the other
side, few research works have investigated the aforemen-
tioned concern. They have normally employed Model Pre-
dictive Control (MPC) and stochastic optimization methods
to address the PEV charging uncertainties [11]. The biggest
challenge of the former is the need of an accurate and viable
predictive model in order to perform efficiently. Nevertheless,
the related literature does not provide sufficient details about
utilized predictive models. On the other hand, studies on the
latter have not examined the effect of unreliable decisions due
to the existing uncertainties on user satisfaction, particularly
with the final SOC. In fact, the lack of such an examination
has brought about scenarios under which, their proposed
methods have led to insufficient charging regarding mobility
constrains [12]. More importantly, the relevant research is
limited in scope due to concentrating on specific matters.
Accordingly, it cannot enable actual applications that should
be performed under the entire circumstance, i.e., the lack
of information on essential parameters, which are intercon-
nected. Accordingly, this study focuses on the development of
a PEV charging scheduling system with the aim of addressing
the aforementioned challenges.
The main contribution of this paper is designing a practical
PEV controller that is able to perform charging scheduling
under uncertainties related to the lack of access to critical
charging parameters. The novelty of the proposed approach
can be detailed in terms of:
1) A charging management strategy that unlike other sim-
ilar methods, does not rely on departure time and SOC
information from PEV on-board controller at the plug-
in time;
2) A stochastic optimization framework that can offer the
optimal horizon and control actions for PEV charging
considering a monetary value for customer dissatisfac-
tion related to final energy state and electricity price;
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A. W. Dante et al.: Stochastic Approach to Designing Plug-In Electric Vehicle Charging Controller for Residential Applications
3) An online control algorithm that is able to deal with
the non-linearity of charging power profile as well as
the uncertainties of energy demand and departure time.
It should be added that the charging scheduling procedure
utilizes a forecasting model to estimate charging energy
requirement based on driver habits. The performance of this
process is assessed across multiple charging sessions within
almost one year regarding real-world conditions. In addition,
a comparative study is used to demonstrate the efficiency of
the designed controller, which can be easily integrated into
existing charging infrastructures.
The rest of the paper is organized as follows. Section II
provides the literature review. The PEV charging problem
formulation is presented in Section III. The stochastic pre-
dictive model of PEV charging demand and the PEV charg-
ing control process are also detailed in this section. The
evaluation framework of the proposed system is described
in Section IV. The results of case studies and comparative
analysis are discussed in Section V, followed by conclusion
in Section VI.
The literature provides a variety of studies about charging
scheduling of PEVs in the context of smart grids. This sub-
ject has been examined for various objectives on different
scales of individual to fleets of PEVs. Energy cost mini-
mization [11], [13], ancillary services provision [14]–[18],
integration with renewable energy systems [19]–[21], power
grid planning [22], [23], and investment decision in the
transportation sector [24] are among PEVs popular matters.
Particularly, PEVs charging cost reduction has been intended
through scheduling methods due to the flexibility of their
energy demand. Individual and coordinated Charging are
general approaches to scheduling with regard to the electricity
market design [25].
PEV charging scheduling is normally formulated in terms
of an optimization problem. Accordingly, existing meth-
ods can be classified into deterministic and stochastic tech-
niques [26], [27]. The former assumes a full accurate access
to PEV critical parameters such as on-board SOC mea-
surement data, arrival and departure time, user preference,
charging power, and future driving needs [27]. On the other
hand, the latter takes into account these factors along with
their uncertainties. A large portion of relevant studies in the
literature is based on the deterministic approach [27]. Ref [9]
developed a real-time home energy management algorithm
to control multiple home appliances and a PEV with the
aim of minimizing overall electricity bill. The proposed sys-
tem utilized a fuzzy logic controller that was supplied by
exact information of PEV parameters. An energy manage-
ment algorithm for PEV smart home charging was proposed
in [10] to minimize the cost. The smart charging was carried
out in both ’vehicle-to-home’ and ’vehicle-to-grid’ modes by
means of linear programming. Similarly, it exploited accu-
rate values of PEV parameters. Ref [28] explored a long-
term electricity bill minimization problem based on an online
HEMS that controlled the energy demand of a PEV along
with other appliances. The developed method employed a
stochastic optimization based on the Lyapunov technique to
handle uncertainties related to electricity price, outdoor tem-
perature, renewable energy generation, electricity demand,
comfort level, and occupancy status. However, it did not take
into account uncertain parameters related to PEV charging
demand. Furthermore, the suggested HEMS was assumed
to receive charging request details including arrival time,
departure time, and energy requirements directly from the
PEV owner. A coordinated, centralized framework for PEV
charging and HVAC control in a neighborhood area was
explored in [29]. The PEV charging was modeled by using
users’ travel patterns, which must be communicated with
the aggregator before the performing day. Ref [30] assessed
the potential of PEV and four other domestic loads for peak
shaving. Unlike [29], it developed a decentralized control sys-
tem whose performance was evaluated over 100 households
based on different price signals. The above studies have not
taken into account a practical examination of their propo-
sitions under real-world conditions. In fact, in real cases,
the PEV controller should consider uncertainty sources for
effective scheduling regarding charging flexibility and bat-
tery storage (vehicle-to-grid) potentials. Nonetheless, some
studies have attempted to investigate the stochastic nature of
PEV charging parameters. Ref [26] explored the stochastic
modeling of PEVs arrival time, departure time, and travelled
distance by means of Probability Density Functions (PDFs).
It aimed to improve power system planning by predicting
PEVs aggregated power profile. Likewise, PEV demand was
modeled by using the PDF of its parameters in [31], [32].
The proposed model was evaluated through different cost and
energy management strategies in a power grid with photo-
voltaic and wind turbines generation. It accounted for real-
world scenarios by dealing with the stochastic behavior of
PEV demand. However, these studies did not integrate uncer-
tainties associated with PEV modeling parameters into their
decision-making process. Indeed, the uncertainty parameters
should be incorporated into the PEV charging optimization
problem for practical implementations.
Ref [33] presented an energy management strategy for
controlling PEV and other home appliances according to the
future vehicle state and household energy demand predic-
tions. It utilized an MPC to minimize the impact of PEV
state prediction uncertainty on charging and discharging.
A multi-level, day-ahead, real-time optimization framework
for PEVs charging management in a commercial building was
proposed in [25]. The Building Energy Management System
(BEMS) was equipped with solar production. It was intended
to regulate PEVs charging within two steps in a transactive
market. First, the BEMS practiced a profit maximization
by estimating building energy demand regarding charging
requirements and PV generation. Afterwards, it performed
a real-time optimization problem by use of MPC to minimize
the difference between the actual and pre-scheduled energy
use. However, the BEMS did not aim to schedule PEVs
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charging since it assumed that owners were either unwilling
or unable to interact their detailed information. In fact, the
BEMS was focused to provide PEV owners with incentives
based on their flexibility potentials for charging power in
every market period. The performance of the suggested sys-
tem was evaluated by using simulated PEV charging behav-
ior, provided by the Danish National Travel Survey data.
[12] proposed a Stochastic Dynamic Programming (SDP)
framework for optimal energy management of a smart home
with PEV. The SDP problem was formulated to minimize the
instantaneous energy cost of the home at each time interval
considering the expected charging demand. The charging
request was managed based on a Markov chain model of PEV
parking status, captured from its historical data. Different
charging strategies comprising vehicle-to-grid, vehicle-to-
home, and grid-to-vehicle were carried out to evaluate cost
saving potentials of PEV. Although the proposed SDP con-
sidered the uncertainty of departure time, it did not deal with
its impact on user satisfaction in terms of final energy state
adequacy in the decision process. Besides, it was acknowl-
edged that charging optimization practice could lack to meet
PEV mobility constraints under certain electricity prices.
PEVs charging scheduling is generally formulated as a short-
term optimization problem considering HEMS needs.
The main objective of PEV charging system is to find opti-
mal control actions, u
kthat minimize charging cost while
satisfying system constraints. Let SOCkbe the PEV battery
SOC at the time step kand ukbe the decision variable that
controls the ON/OFF status of its charging. Considering the
departure time, T, the deterministic optimization problem of
PEV charging can be formulated as,
λkbnom1t uk(1a)
subject to 0 uk1 (1b)
Ecap (1c)
SOC0=SOCpi (1d)
where λkstands for the price of electricity at kin /kWh, bnom
is the rated charging power in kW, and 1trepresents the time
step. Additionally, γEis the charging efficiency and Ecap is
the PEV battery capacity in kWh. SOCpi is the battery initial
SOC at the plug-in time, tpi.SOC min
Tand SOCmax
the minimum and maximum battery SOC, required at the
departure time.
The deterministic approach assumes that all modeling param-
eters are perfectly known and accessible by the controller
FIGURE 1. General PEV charging process.
in an automated way within each charging session. As dis-
cussed, this assumption can hinder real implementations
since PEV charging scheduling can be subject to uncertainties
related to the lack of critical charging parameters. Particu-
larly, this method neglects the nonlinear behavior of PEV
charging power, which is governed by two modes of operation
comprising constant current mode and constant voltage mode
(CCCV). However, the aforementioned matters are crucial
to PEV charging services. This has been demonstrated in
Figure 1that presents a PEV charging session based on the
CCCV modes, switched at tCC . In this figure, the variance of
the charging profile (grey boundary) is attributed to uncer-
tainty in charging duration due to external factors such as
ambient temperature, and the accuracy of the battery SOC
In the proposed stochastic optimization, the departure time
is assumed to be unknown or at least unavailable across the
charging session. Once the PEV plugs in, the connection
time is identified. However, the charging controller can be
unaware of PEV leaving time. Notwithstanding, it needs to
operate such a way that minimizes the cost and the user
dissatisfaction considering the final battery SOC. In order
to achieve this aim, the controller requires to manage the
uncertainty of departure time, charging duration, and energy
requirements when operating in real-world conditions i.e.
the absence of complementary information [12], [34], [35].
On the other side, HEMS is presumed to be unable to directly
retrieve battery SOC information from the vehicle. This is due
to insufficient communication protocols between third-party
systems such as HEMS and PEV on-board controller. There-
fore, HEMS only utilizes exchanging information between
PEV and charging station, particularly charging power mea-
surements. In fact, such information, provided by the con-
troller, allows HEMS to effectively manage PEV charging in
the lack of their direct communication. In fact, measurement
data from charging station is accessible to PEV controller
without any specific communication protocol. Moreover, this
charging data is the richest information that can be used to
capture PEV behavior, specifically the non-linear nature of
charging power profile. Such statistics, collected from station
services, are more accurate than travel distance information
that is affected by charging sessions, performed outside the
house [36].
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Due to the lack of SOC information, the Coulomb Count-
ing (CC) method, used to compute this variable in (1c), should
be reformulated. In this regard, the alternative equation of CC
to determine energy state dynamic of the PEV by exploiting
charging power as the only available information is defined
by [37],
yk+1=yk+γEbk1t uk(2)
where at discrete time, k,ydenotes accumulated charging
energy in the battery with an initial value of zero in the plug-in
time and bis the actual charging power. It should be noted that
previous studies have mostly used the rated charging power
to estimate SOC dynamics. However, this is not the case in
real conditions where charging time is more due to the CCCV
charging mode of the PEV battery as shown in Fig. 1.
Considering departure time uncertainty, charging duration,
and energy requirement, PEV charging can be formulated in
terms of a stochastic problem [12], [38] through,
E[Q(yT, ξ )](3a)
subject to Prob(yTypref)η(3b)
that Q(yT, ξ )is the total cost of overall charging energy at
the departure time, yT, according to the departure uncertainty
parameter, ξ. The problem subject is a chance constraint to
meet user preference for charging amount, ypref.ηis the user
satisfaction probability considering the final state of energy
with normally a large value. Accordingly, ηcloser to one
conveys that the user tolerates yT<ypref by less probability
(1 η). The objective function in (3a) is determined by,
Q(yT, ξ )=C(yT, ξ)+D(yT, ξ )(4)
where based on uncertain departure time, C(yT, ξ )and
D(yT, ξ )are charging cost and dissatisfaction level functions
related to the final state of energy. In this manner, the opti-
mal control actions, u
kmust minimize both C(yT, ξ )and
D(yT, ξ )considering ξ. In the developed stochastic problem,
the departure time, Tand the control actions, ukare the
decision variables.
The formulated problem can be solved by the Monte Carlo
simulation and Sample Average Approximation (SAA),
described by Algorithm 1[39]. In this Algorithm, the decision
space to select the departure time, Tis defined according to
its distribution. To be specific, the decision is made based on
a limited number of samples by dividing the departure time
distribution into Nlarger intervals as illustrated in Figure 2.
This is due to the fact that searching the main distribution can
be computationally expensive for shorter time steps, k. The
method to capture departure time distribution is detailed in
Subsection III-C.
Subsequently, the controller solves the optimization prob-
lem for a decided Tthrough,
arg min
λkbav1t uk(5a)
TABLE 1. Monte Carlo simulation.
FIGURE 2. Exemplified conditional probability distribution of the
departure time with respect to the plug-in time.
subject to yk+1=yk+γEbav 1t uk(5b)
ytpi =0 (5c)
yT≥ ˆymin (5d)
0uk1 (5e)
that bav is the average charging power. The chance constraint
in (3b) is realized by (5d) where ˆymin is the minimum esti-
mated energy, required by the charging session to meet η
level of satisfaction. This constraint aims to ensure that the
final energy state at the departure time satisfies user energy
needs. It can be deduced that rated power, bnom, is not a prac-
tical choice for PEV charging according to its time-variant
behavior, presented in Figure 1. Considering this value leads
to shorter charging duration that is not the case of actual situa-
tions. Nevertheless, the relevant literature has mainly utilized
the rated value for charging scheduling. In order to relieve
this issue, the formulated problem in (5a) has considered
average power, bav, which is more sensible. Additionally, this
decision results in a time-invariant estimation of charging
state dynamic, (5b), that consequently, facilitates classic opti-
mization problem solving. The process to determine ymin and
bav is explained in Subsections III-D and III-E.
Afterwards, the solution of the deterministic optimization
problem is assessed under different departure scenarios by
the controller. These cases are provided by sampling the
conditional probability distribution over the departure time,
captured based on the plug-in time. Figure 2exemplifies such
a distribution where Tmin and Tmax are the earliest and latest
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FIGURE 3. Typical example of the user dissatisfaction profile.
departure time, respectively, according to the historical data.
ξsis a sample from this range. Consequently, the examination
of the solution yTis carried out by calculating the charging
and dissatisfaction costs through (6) and (7), respectively,
considering the departure scenario, ξs,
CyT, ξ s=
λkbav1t u
DyT, ξ s=κ111
where κ1and κ2are the amplitude and shape parameters of
the dissatisfaction function, respectively, and yξsis the energy
state, defined by yξs=Pξs
k=0γEbav1t u
k. This function
has been exemplified in Figure 3. In this figure, two regions
can be distinguished that have been separated by a grey
dashed line. The hardly tolerable zone presents user’s highest
dissatisfaction to depart due to lower energy amounts. On the
other hand, the highly tolerable zone corresponds to energy
levels where user’s willingness to depart start increasing pro-
portionally. The parameters of the dissatisfaction function are
defined in such a way that a trade-off between both types of
costs is realized. To be specific, the amplitude of the dissatis-
faction function is decided with regard to the energy price
to avoid the dominance of charging cost. The significance
of user’s desire can be justified by κ1values for which the
final charging energy is selected within the tolerable area.
Furthermore, κ2manipulates the steep decrease of the dis-
satisfaction curve. In order to choose the shape parameter,
additional source of information related to user behavior is
required, which is not in the scope of this study. Therefore,
a value that ensures a smooth decreasing rate of the curve
is considered. Indeed, the properties of the dissatisfaction
function should be investigated through adequate information
to improve the HEMS convenience.
Finally, the expectation value of the total cost can be cal-
culated by SAA based on,
E[Q(yT, ξ )]1
QyT, ξ s(8)
The above process is carried out for all the decided hori-
zons, T, in T. Subsequently, the solution of the proposed
FIGURE 4. Overview of the proposed controller.
stochastic optimization, applied to the current charging ses-
sion, is the horizon whose corresponding control action
results in the minimum overall cost.
The PEV charging controller uses only data from residen-
tial Electric Vehicle Supply Equipment (EVSE) as assumed.
Particularly, it exploits historical power measurement infor-
mation as an alternative for charging demand prediction and
scheduling. For each charging session, the controller, pre-
sented in Fig. 4, performs the following three steps at the
plug-in time.
1) Forecasting: A predictive model estimates the charg-
ing demand, ˆys, according to predictor variables, xs.
Subsequently, the energy demand estimate, ˆys, is used
to model the charging power profile for the prediction
horizon, T.
2) Optimization: The stochastic optimization problem is
solved in order to define the best charging policy based
on the actual electricity price signal and the predicted
charging demand across T. At this stage, the controller
assumes that the estimates of the charging demand and
departure time are precise.
3) Execution: The PEV charging system implements the
control actions, resulted from the previous step.
The departure time (parking duration) information is one
of the critical inputs that the controller needs to optimally
schedule the PEV charging since it defines the time-horizon
of the optimization. Uncertainty in this factor can lead to
insufficient charging at the plug-out time and, in turn, user
dissatisfaction. Therefore, it should be addressed for real
applications since it is an inherent component of the charging
practice. As a random variable, departure time is unknown
to the controller at the plug-in time unless the PEV owner
specifies it. Nevertheless, the latter situation is uncommon
due to either users’ ignorance of the true leaving time or
their unwillingness to share such information on a regular
basis. The Markov chain [12] and Semi-Markov [33] models
are the most popular methods that have been used to rep-
resent PEV parking status in the literature. Since Markov
chain-based models process the probability of parking status
change (through state transition matrix) at each time step,
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their integration in stochastic optimization leads to a com-
plex decision space especially for large number of PEVs.
This, in turn, makes the optimization problem complicated to
solve [11]. The Semi-Markov-based designs, which employ
a similar procedure, are also complex. They capture the
vehicle state by modeling the duration of all possible PEV
travels. Generally, incorporating an uncertain parameter into
a stochastic decision process can result in model complexity,
high computational cost, and convergence issues regarding
the optimization problem. These matters can bring challenges
to both PEV controller software and hardware designs. For
example, they can simply increase the equipment cost and
avoid customer adoption. Since dealing with these circum-
stances is the primary step towards feasibility, utilizing effi-
cient straightforward methods in the analytical process is
stimulated. Accordingly, the PEV parking status modeling
can be simplified while maintaining its significance for charg-
ing scheduling. Our analysis using actual data evidences that
the parking duration can be decided based on the plug-in
time. As a result, a clustering method is utilized to classify
the PEVs according their arrival time. Afterwards, the Kernel
Density Estimation (KDE) technique is used to model the
departure time distribution of each group of PEVs by exploit-
ing their corresponding historical data through [40],
where Nsis the total number of samples, h>0 is the band-
width parameter, T(j) is the jth observation data, and Kis
the Gaussian Kernel function. As a non-parametric method,
KDE is a perfect fit for modeling departure time patterns
through estimating their densities. It is a reliable choice for
uncertain conditions since it can effectively describe time-
series with unknown underlying distributions [41].
Considering the objective of the controller, a forecasting
system is developed that is not only able to estimate charging
demand but also capable of quantifying its relevant uncer-
tainty. This mechanism examines the stochastic behavior of
PEV energy demand in the beginning of every charging ses-
sion. Accordingly, let ˆysbe the estimated energy demand for
charging the PEV in the sth charging session, and xsand ys
be the input vectors of exogenous and historical endogenous
variables, respectively. The goal is to define the forecasting
model, f, that predicts ˆyswith minimum error. The general
mathematical formulation of this model is described by (10),
ˆys=fxs,ys, θx, θy(10)
where θxand θyare model parameters associated with xs
and ys, respectively. The vector of exogenous variables, xs
is composed of calendar and weather components as the
predictors. The calendar factor contains the plug-in time in
decimal hours, the day of the week, wd
s, and the number
of the week, wk
s. The weather factor comprises the average
temperature, ¯
Ts, in C, the average sunlight, ˆ
s, in kJ/m2,
the average wind speed, ¯vw
s, in m/s, and the precipitation,
s, in mm during the day of charging session. The vector
of autoregressive variables, ysencompasses the history of
charging energy requirements during the last lhome charging
The proposed strategy considers all the predictors and
employs the Sequential Forward Selection method to select
the best ones based on their forecasting performance [36].
Different predictive models can be used to create the
function f. Here, a linear modeling approach is used as,
where θxand θyare the vectors of coefficients. Given n
number of observations, the objective is to estimate {θx;θy}
in order to have an efficient prediction of the current PEV
charging demand. The model parameters are estimated by
a Bayesian inference technique. The Bayesian inference
expresses the regression parameters in terms of probability
distributions [42]. It uses the Bayes’ theorem to provide
the posterior distribution of the model parameters instead of
their single best estimations as for Frequentist methods [43].
Accordingly, this approach is able to quantify model uncer-
tainties. The Bayesian learning process begins by defining
the prior probability distribution of the model parameters,
as the initial belief, before observing any data. The prior
distribution is updated by using the observed data based on
the Bayes’ theorem to construct the posterior distribution,
explained by [43],
P(θ , σ |X,Y)P(Y|θ, X, σ )P(θ)P(σ)(12)
where θ=θx, θyTand σstand for the model parameters,
and Xand Yare the historical observations of the predictors
as the input and the charging demand as the output, respec-
tively. P(Y|θ , X, σ )is the observation likelihood, and P(θ)
and P(σ) are the prior distributions over θand σ, respectively.
The likelihood P(Y|θ, X)can be computed through,
P(Y|θ, X, σ )=
P(yi|θ, xi,yi, σ )(13)
From the Bayesian perspective, it can be assumed that
yiis a univariate random variable that follows a Gaussian
distribution based on [44],
P(yi|θ, xi,yi, σ )=Nyi;f(xi,yi, θ ), σ 2(14)
that Npresents the Gaussian function, f(xi,yi, θ ), as the
model prediction, is the mean, and σ2stands for the vari-
ance. Due to its unknown value, it is assumed that σcan be
explained by an inverse-Gamma prior distribution according
P(σ)=Inv-Gamma (α, β)(15)
where αand βare the shape and scale parameters, respec-
tively. The prior probability distribution of θcan be also
52882 VOLUME 10, 2022
A. W. Dante et al.: Stochastic Approach to Designing Plug-In Electric Vehicle Charging Controller for Residential Applications
considered as a Gaussian distribution, explained by [43],
Z(υ)exp υ
where υis a hyperparameter and Z(υ) denotes a normal-
izing constant. The equations (14)-(16) are used to derive
the posterior distributions of the model parameteres in (12).
Subsequently, the charging demand of the current session can
be estimated by calculating the expectation of the posterior
distribution of the predictive model, defined by [45],
ˆys=E(ys|xs, θ )fxs,ys,ˆ
where ˆ
θMAP is the maximum a posteriori estimation of θ
given by ˆ
θMAP =arg max
(P(Y|θ, X)P(θ)). To be specific,
the expectation in (17) is estimated by sampling the pos-
terior distribution of θbased on the Markov Chain Monte
Carlo (MCMC) technique [45]. Afterwards, the expectation
value is used to quantify the minimum charging energy
requirement of the corresponding session considering ηlevel
of user satisfaction through,
s= ˆys+δησ(18)
where δηis a positive constant. This value is chosen so that
the right side of (18) offers the upper bound of ηlevel of
The CCCV charging mode causes the PEV charging power
to have a non-linear behavior. The PEV charging controller
should consider this behavior to minimize its effect specifi-
cally on the final state of charge constraint. Unlike other simi-
lar works, the proposed controller estimates the PEV charging
power profile by using both its estimated energy requirement
at the plug-in time and historical charging pattern. Particu-
larly, it exploits the duration information of the constant volt-
age (CV) and constant current (CC) phases to construct this
profile. This information is obtained from charging demand
behavior across these phases. The length and energy needs of
the CV stage are taken from a complete historical charging
session since the PEV battery behavior within this stage is
similar [46]. Subsequently, the charging requirement of the
CC stage can be computed by,
s= ˆymin
where in the current session s,yCC
sand yCV
lare the energy
demand in the CC and CV phases. Additionally, the duration
of this phase, ˆ
tCC , i.e. the switching time as shown in Fig. 1,
can be estimated by,
tCC =ˆyCC
that b0is the actual charging power measurement at
the plug-in time. Subsequently, the charging profile can be
created through,
0for ktpi,ˆ
jfor kˆ
tCC :ˆ
tCC +tl
CV (21)
where bl
jis the actual charging power of the CV phase during
the last full charge. As a result, the average of the constructed
power profile provides bav in (5b) in order to facilitate the
provision of an optimal solution by the proposed optimization
problem, as mentioned.
The controller continuously monitors the actual output signal,
k, to detect the connection time. Once the PEV is plugged in,
it solves the optimization problem over the decided control
horizon, T, based on the predicted energy demand. At this
point, the controller performs the PEV charging by utilizing
the control actions as the solution of the optimization process.
After each charging session, the performance of the controller
is evaluated by analyzing the saving that is obtained from the
controlled charging through,
Saving(%) =CUC CCC
CUC ×100 (22)
where CUC and CCC denote the cost of the uncontrolled and
controlled charging, respectively.
The proposed controller eases the incorporation of the PEV
owners in the charging scheduling by providing them with
the choice of approving or modifying its decision. Informa-
tion that can be communicated with the owners includes the
amount of required charging energy, the potential savings,
the estimated driving range, and the charging schedule. The
rough range corresponding to the estimated energy require-
ment can be obtained by using [47],
RDR =ˆymin
dEPA (23)
where RDR represents the rough range estimate and dEPA
expresses the EPA-rated combined fuel economy. For exam-
ple, for the Nissan leaf 2016 (30 kWh), the dEPA is
19.1 kWh/100 km [48].
The performance of the proposed online PEV charging con-
troller is extensively discussed in this section. Two scenarios
based on two types of electricity price signals are considered.
Herein, actual charging data and electricity price signals are
used to demonstrate a realistic perception of the controller
The performance of the proposed controller for managing
PEV home charging is evaluated by using actual charging
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A. W. Dante et al.: Stochastic Approach to Designing Plug-In Electric Vehicle Charging Controller for Residential Applications
FIGURE 5. Local institutional charging station as data supplier.
TABLE 2. PEV specifications [49].
data. This data has been collected from a level-2 local charg-
ing station (240V), located in an institutional center in Trois-
Rivières, Quebec as shown in Fig. 5. A National Instruments
acquisition system has been connected to each EVSE to mea-
sure charging voltage and current data. The PEV, considered
in this case study, is a Nissan Leaf 2016 whose specifications
are detailed in Table 2. The charging data has been collected
from March 27, 2017, to January 15, 2018. The total number
of charging sessions, performed by the PEV, during this
period is 112.
Since the controller is intended for home charging appli-
cations, a preprocessing step is applied to the collected data
from local EVSE in order to advertise a pertinent attribute.
This step is mainly executed by shifting the time index
(charging time) of charging demand. Accordingly, the charg-
ing station arrival (departure) time is interpreted as house-
hold departure (arrival) time with a smooth shift in order to
comply with the Canada National Household Survey (NHS)
statistics [50]. It is worth mentioning that this procedure has
been carried out due to difficulties in supplying adequate data
from homes, which can enable feasible investigations. Nev-
ertheless, the values of the resultant charging power profile
remain unchanged. Fig. 6depicts the KDE applied to arrival
and departure time according to home charging scenario i.e.
shifted profiles. It can be observed that the plug-out normally
occurs around 7:40AM while the plug-in happens around
6:40PM, which is consistent with NHS information. Besides,
two types of actual price signals are considered as illustrated
in Fig. 7. Both signals are based on time-variant prices. The
first profile corresponds to Ontario actual TOU pricing. The
second one is a modified version of the first signal that has
the same average value but higher variations to reflect other
possible dynamics.
FIGURE 6. Distribution of arrival and departure time.
FIGURE 7. Electricity price signals.
The clustering procedure, explained in III-C, is applied to
the data, resulted from the preparation phase. In the first
step, this process yields three different arrival time clusters.
These groups account for evening and night (5pm to 5am),
afternoon (1pm to 5pm), as well as morning (5am to 1pm)
regarding the descending order of their density values. Such
classification is manifested by the overall plug-in time distri-
bution, presented in Fig. 6. In the second stage, the clustering
method provides the controller with three different departure
time distributions corresponding to the plug-in time classes
as depicted in Fig. 8. The departure time distributions are
updated based on new observations after each charging ses-
sion. In fact, the charging database is gradually enriched by
new measurements. This, in turn, assists with capturing the
seasonality of data and improves departure-time inferences.
It is noted that efficiency in modeling conditional departure
time is a result of differentiating between charging sessions
according to their plug-in time. Such an approach can be
useful for other charging locations.
In this section, the performance of the designed predictive
model is assessed. Accordingly, a comparative study is car-
ried out by using the Ridge Regression (RR) method. As a
frequentist-based technique, the RR is an appropriate choice
considering the suggested scheme, which is based on the
Bayesian inference. To be specific, RR uses the Ordinary
Least Squares (OLS) to estimate the model parameters while
52884 VOLUME 10, 2022
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FIGURE 8. Different departure time distributions, resulted from the
clustering phase.
FIGURE 9. Sensitivity analysis of predictive model inputs.
the Bayesian method infers the posterior probability dis-
tribution of those parameters by utilizing a set of priors.
In addition, a sensitivity analysis is performed prior to this
comparison in order to evaluate the most important predictive
Although the predictors, xs, defined in Subsection III-D, are
typical components of time series forecasting methods, only
a few of them are significant for PEV energy requirement
prediction. Therefore, it is important to perform a sensitiv-
ity analysis to examine the degree of predictability of each
predictor and consequently select the most relevant ones.
In order to avoid the computational complexity of Bayesian
algorithm for the feature selection, this procedure is carried
out by the Ridge regression model. For this purpose, a portion
of data is divided into the training set comprising 56 data
samples (28 charging sessions), and the test set containing
100 data samples (56 charging sessions). The result of the
sensitivity analysis is presented in Fig. 9. This figure shows
the coefficient of determination score, R2, for the combi-
nation of the most effective predictors, which are selected
sequentially by starting from the best one. It can be observed
that the most important predictor is the connection time,
tpi, which is responsible for about 50% of R2. The result
accuracy increases to around 64 % for the combination of
five best predictors, x15. Afterwards, the value of R2slightly
increases by adding new predictors.
TABLE 3. Results of the comparative study between the forecasting
In order to exercise the comparative analysis, both predictive
models are trained with data from March 27 to May 30, 2017.
The total number of charging sessions is 29 during this period.
Afterwards, the methods are tested by exploiting data from
May 31 to January 8, 2018 in an on-line manner. It should be
mentioned that the training phase is processed over a window
that is expanded with the arrival of new charging session
data. Bayesian model is performed by using the PyMC3
Python package. A Gamma distribution with the shape and
scale parameters equal to 3 is considered as the prior for σ
according to (15). Furthermore, a Normal distribution with
the mean and variance of zero and 20 is used as the prior for
θin accordance with (16). These priors have provided the best
results based on an extensive number of tests.
Table 3and Fig. 10 show the results of both models, applied
to the test data. The outcomes are evaluated by R2, Root Mean
Square Error (RMSE), and Mean Absolute Error (MAE) as
the accuracy metrics. Regarding the forecasting precision, the
Bayesian approach operates efficiently, and its performance
is relatively higher than the RR technique for a different
number of predictors, as presented in the Table 3. More
importantly, the Bayesian inference is superior to the RR
due to its ability to offer a means for quantifying the model
uncertainty, as shown in Fig. 10 (light-orange regions). This
advantage can result in a robust control over PEV charging
by decreasing the risk of missing energy storage, essential
for user satisfaction. In fact, the upper bound of the quantified
uncertainty is exploited to characterize ymin in (18). However,
this is not the case for RR that estimates only the expected
value of charging demand. Only the five best predictors
consisting of tpi,ys7,¯
s, and ys6are used in the rest
of the analysis considering the outcomes similarity, implied
by Table 3. It should be added that yslrefers to the last lth
charging session.
The performance of the proposed controller is evaluated over
the entire database, which contains the information of all
VOLUME 10, 2022 52885
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FIGURE 10. PEV charging estimation results of the predictive models based on Bayesian inference and Ridge regression.
possible daily trips. The evaluation is carried out within the
following steps by exploiting the data of Dtest.
As depicted in Fig. 11, the charging scheduling is performed
within two main phases. The series of events within the
first stage is illustrated in Fig. 11.a. In this step, the con-
troller detects the PEV connection time (blue dashed line) by
observing the actual power measurement, bk, and estimates
the required amount of energy to charge its battery, ˆymin
by using the forecasting model. Subsequently, it constructs
the charging power profile by using the estimated energy
demand and the charging session history. Afterwards, the
optimization problem is solved in order to define the best
control action according to the price signal and the decided
horizon in terms of parking duration (blue line). At this point,
the controller informs the user about the optimal charging
policy, especially the likely driving range (RDR). For exam-
ple, the RDR corresponding to the PEV charging case in
Fig. 11 is 81 km. In the second stage, the on-line charging is
implemented based on the decided control action as indicated
in Fig. 11.b. It can be observed that in the implementation
step, the estimated charging needs are managed by the binary
control signal. The controller allows for charging the bat-
tery only at the ON state according to this signal (control
action = 1). This can lead to situations in which the minimum
demand is not satisfied because of the lack of an accurate
estimation of the initial energy requirement. As illustrated
in Fig. 11.b, this case is likely to occur where the expected
charging power is exploited (orange-dashed line). A control
action that relies on the single best estimate (exact expec-
tation) by employing non-Bayesian methods like RR can
notably deteriorate this issue. However, a design that inte-
grates parameters uncertainties into the controller’s decision
can offer a robust process. Therefore, it can relieve this con-
cern by using parameters’ posterior distributions to satisfy
the user preference through a confidence level. This has been
achieved by the proposed design as depicted by Fig. 11.b
(green-dashed line). Figure 10 clarifies this matter by demon-
strating single point and posterior distribution estimations of
PEV charging demand as the key difference between RR and
Bayesian techniques, respectively. It should be highlighted
FIGURE 11. Online operation of the proposed controller during the
scheduling and control inputs implementation phases.
that the on-line decision making process can be perceived
from the actual charging profile following the current time
across the decided horizon in Figs. 11.a and 11.b.
Regarding the operation time, the controller takes less
than 2 minutes to provide the decision on charging schedul-
ing. This time mainly belongs to the forecasting process
and optimization problem, which generally take 40 seconds
and 30 seconds, respectively. The controller operates every
10 minutes (time step), and thus, its decision needs are not
violated by the computational time. It should be noted that
the simulations are run on an Intel i7-9700 CPU@3 GHz
processor with 16 GB of RAM.
52886 VOLUME 10, 2022
A. W. Dante et al.: Stochastic Approach to Designing Plug-In Electric Vehicle Charging Controller for Residential Applications
FIGURE 12. The cumulative charging cost of different charging strategies
including the proposed controller.
The performance of the proposed controller is evaluated over
the test data, Dtest , which contains the information about
different daily trips within around one year. The evaluation
is carried out through a comparative study by using two other
scenarios. The first case represents the uncontrolled charging
where the PEV charging starts immediately after plug-in. The
second case accounts for the controlled charging based on the
deterministic approach. A controller based on this method
has direct and complete access to PEV critical parameters
comprising exact departure time, SOC (from the on-board
controller), and charging power profile shape to perform
charging scheduling. As a full information-based method,
the deterministic scheme leads to the best result. Therefore,
this scheme is a perfect choice for a benchmark to evaluate
the performance of the stochastic technique, which does not
utilize complete information.
Fig. 12 presents the cumulative cost of charging. Through-
out the charging sessions, the average saving of the pro-
posed controller is about 29.1% and 45.4% more than the
uncontrolled case for the dynamic and TOU pricing, respec-
tively. In addition, the designed controller is very competitive
with the deterministic scheme, which takes advantage of full
information to provide the optimal charging schedule. To be
specific, the slight difference between both methods can be
attributed from one side to the high performance of the pro-
posed stochastic process and from the other side to the influ-
ence rate of the uncertain parameters. Nevertheless, the latter
does not justify the utilization of the deterministic approach
since the full information modeling is not a feasible scenario
due to inherent departure time uncertainty, charging power
non-linearity, and on-board controller information inacces-
sibility, especially in a long run. In other words, real-world
circumstances make a stochastic approach to PEV charging
scheduling inevitable, as the main focus of this paper. In this
regard, the suggested charging scheduling method achieves
a remarkable efficiency despite the uncertainties related to
the predictive model and the departure time. It significantly
reduces the charging cost while ensuring that the PEV battery
is sufficiently charged at the departure time.
The results show that the proposed controller is capa-
ble of handling PEV charging under uncertainties of real
practices. It can be deduced that the developed mechanism
can significantly reduce users intervention in the decision-
making process and facilitate owners’ adoption. In addition,
the proposed data-driven approach is able to learn different
charging patterns if presented with sufficient data. This can
be acknowledged from the forecasting model that is applied
to historical observations with charging period diversity (day
and season types). Moreover, the design takes advantage of
a stochastic decision making mechanism based on robust
optimization, which can assist with handling randomness of
real-world circumstances.
Besides, the whole analysis provides important materi-
als, in terms of data and methods, that can facilitate the
development of efficient PEV charging systems for other
practices. Additionally, it points out important remarks with
regard to future investigations. Considering prerequisites for
a useful modeling practice, this research suggests a com-
prehensive dataset that comprises the information related
to plug-in/plug-out time, actual SOC from PEV on-board
controller, and charging power of multiple charging sessions.
Furthermore, it offers the development of a proper infrastruc-
ture to provide the PEV charging controller with the essen-
tial data in order to build relevant models for the charging
scheduling analysis. Regarding car owners’ role in realizing
useful energy management systems, this investigation recom-
mends exploring users’ willingness to regularly share their
information, especially departure time and charging desires
(final SOC). This suggestion, in turn, promotes the study on
customized charging models based on user preferences as an
interesting subject. Such an analysis can be conducted in the
context of power grid services where users’ satisfaction rate,
in terms of flexibility, is examined to benefit them with cost
saving opportunities while maintaining the system operator
This study proposes a practical PEV controller to perform
charging scheduling under uncertainties related to real-world
circumstances. The suggested controller does not require sig-
nificant resources and can be easily implemented by users.
The utilized methodology comprises two main steps. The first
step deals with predicting the required energy for charging
at the plug-in time based on a predictive model. The second
step involves utilizing a stochastic optimization to minimize
the cost of charging considering the predictive model and
departure time. The performance of the proposed approach
has been evaluated by exploiting actual charging data. The
designed stochastic framework carries out PEV charging
scheduling with a remarkable efficiency, similar to deter-
ministic scenarios with full information access. It ensures an
adequate battery charge at the departure time while reducing
the energy cost.
[1] T. Morstyn, C. Crozier, M. Deakin, and M. D. McCulloch, ‘‘Conic opti-
mization for electric vehicle station smart charging with battery voltage
constraints,’IEEE Trans. Transport. Electrific., vol. 6, no. 2, pp. 478–487,
Jun. 2020.
VOLUME 10, 2022 52887
A. W. Dante et al.: Stochastic Approach to Designing Plug-In Electric Vehicle Charging Controller for Residential Applications
[2] IEA. (2021). Global EV Outlook 2021. Paris. [Online]. Available:
[3] J. D. Kim, ‘‘Insights into residential EV charging behavior using energy
meter data,’Energy Policy, vol. 129, pp. 610–618, Jun. 2019.
[4] J. Rolink and C. Rehtanz, ‘‘Large-scale modeling of grid-connected elec-
tric vehicles,’IEEE Trans. Power Del., vol. 28, no. 2, pp. 894–902,
Apr. 2013.
[5] J. G. Smart and S. D. Salisbury, ‘‘Plugged in: How Americans charge
their electric vehicles,’’ U.S. Dept. Energy Office Sci. Tech. Inf., USA,
Tech. Rep., 2015.
[6] M. Ahmadi, S. H. Hosseini, and M. Farsadi, ‘‘Optimal allocation of electric
vehicles parking lots and optimal charging and discharging scheduling
using hybrid metaheuristic algorithms,’J. Electr. Eng. Technol., vol. 16,
no. 2, pp. 759–770, Mar. 2021.
[7] N. G. Paterakis, A. Tascikaraoglu, O. Erdinc, A. G. Bakirtzis, and
J. P. S. Catalao, ‘‘Assessment of demand-response-driven load pattern
elasticity using a combined approach for smart households,’IEEE Trans.
Ind. Informat., vol. 12, no. 4, pp. 1529–1539, Aug. 2016.
[8] V. Moghaddam, A. Yazdani, H. Wang, D. Parlevliet, and F. Shahnia,
‘‘An online reinforcement learning approach for dynamic pricing of elec-
tric vehicle charging stations,’’ IEEE Access, vol. 8, pp. 130305–130313,
[9] S. Zhou, Z. Wu, J. Li, and X. Zhang, ‘‘Real-time energy control approach
for smart home energy management system,’Electr. Power Compon. Syst.,
vol. 42, nos. 3–4, pp. 315–326, 2014.
[10] H. Turker and S. Bacha, ‘‘Optimal minimization of plug-in electric vehicle
charging cost with vehicle-to-home and vehicle-to-grid concepts,’’ IEEE
Trans. Veh. Technol., vol. 67, no. 11, pp. 10281–10292, Nov. 2018.
[11] Z. N. Pan, T. Yu, L. P. Chen, B. Yang, B. Wang, and W. X. Guo, ‘‘Real-time
stochastic optimal scheduling of large-scale electric vehicles: A multidi-
mensional approximate dynamic programming approach,’Int. J. Electr.
Power Energy Syst., vol. 116, Mar. 2020, Art. no. 105542.
[12] X. Wu, X. Hu, X. Yin, and S. Moura, ‘‘Stochastic optimal energy manage-
ment of smart home with PEV energy storage,’IEEE Trans. Smart Grid,
vol. 9, no. 3, pp. 2065–2075, May 2018.
[13] J. A. Dominguez, A. W. Dante, K. Agbossou, N. Henao, J. Campillo,
A. Cardenas, and S. Kelouwani, ‘‘Optimal charging scheduling of electric
vehicles based on principal component analysis and convex optimiza-
tion,’’ in Proc. IEEE 29th Int. Symp. Ind. Electron. (ISIE), Jun. 2020,
pp. 935–940.
[14] S. S. Hosseini, A. Badri, and M. Parvania, ‘‘The plug-in electric vehi-
cles for power system applications: The vehicle to grid (V2G) concept,’’
in Proc. IEEE Int. Energy Conf. Exhib. (ENERGYCON), Sep. 2012,
pp. 1101–1106.
[15] X. Liu, S. Li, H. Yu, and L. Zhang, ‘‘Coordinated charging optimization
mode of electric vehicles in the residential area,’Trans. China Electrotech.
Soc., vol. 30, no. 20, pp. 238–245, 2015.
[16] M. B. Rasheed, M. Awais, T. Alquthami, and I. Khan, ‘‘An optimal schedul-
ing and distributed pricing mechanism for multi-region electric vehicle
charging in smart grid,’IEEE Access, vol. 8, pp. 40298–40312, 2020.
[17] E. Hadian, H. Akbari, M. Farzinfar, and S. Saeed, ‘‘Optimal allocation of
electric vehicle charging stations with adopted smart charging/discharging
schedule,’IEEE Access, vol. 8, pp. 196908–196919, 2020.
[18] Y. Zheng, J. Luo, X. Yang, and Y. Yang, ‘‘Intelligent regulation on demand
response for electric vehicle charging: A dynamic game method,’’ IEEE
Access, vol. 8, pp. 66105–66115, 2020.
[19] H. Lund and W. Kempton, ‘‘Integration of renewable energy into the
transport and electricity sectors through V2G,’Energy Policy, vol. 36,
no. 9, pp. 3578–3587, 2008.
[20] S. S. Hosseini, A. Badri, and M. Parvania, ‘‘A survey on mobile energy
storage systems (MESS): Applications, challenges and solutions,’Renew.
Sustain. Energy Rev., vol. 40, pp. 161–170, Dec. 2014.
[21] D. Ji, M. Lv, J. Yang, and W. Yi, ‘‘Optimizing the locations and sizes of
solar assisted electric vehicle charging stations in an urban area,’’ IEEE
Access, vol. 8, pp. 112772–112782, 2020.
[22] K. Clement-Nyns, E. Haesen, and J. Driesen, ‘‘The impact of charging
plug-in hybrid electric vehicles on a residential distribution grid,’’ IEEE
Trans. Power Syst., vol. 25, no. 1, pp. 371–380, Feb. 2009.
[23] S. S. Hosseini, A. Badri, and M. Parvania, ‘‘Smart parking lot to minimize
residential grid losses based on customer priorities,’’ in Proc. Int. Conf.
Power, Energy Control (ICPEC), Feb. 2013, pp. 728–732.
[24] M. Schücking and P. Jochem, ‘‘Two-stage stochastic program optimizing
the cost of electric vehicles in commercial fleets,’Appl. Energy, vol. 293,
Jul. 2021, Art. no. 116649.
[25] Z. Liu, Q. Wu, M. Shahidehpour, C. Li, S. Huang, and W. Wei, ‘‘Trans-
active real-time electric vehicle charging management for commercial
buildings with PV on-site generation,’IEEE Trans. Smart Grid, vol. 10,
no. 5, pp. 4939–4950, Sep. 2019.
[26] A. Ashtari, E. Bibeau, S. Shahidinejad, and T. Molinski, ‘‘PEV charging
profile prediction and analysis based on vehicle usage data,’IEEE Trans.
Smart Grid, vol. 3, no. 1, pp. 341–350, Mar. 2012.
[27] Y. Noorollahi, A. Aligholian, and A. Golshanfard, ‘‘Stochastic energy
modeling with consideration of electrical vehicles and renewable energy
resources—A review,’J. Energy Manage. Technol., vol. 4, pp. 13–26,
Mar. 2020.
[28] L. Yu, T. Jiang, and Y. Zhou, ‘‘Online energy management for a sustainable
smart home with an HVAC load and random occupancy,’’ IEEE Trans.
Smart Grid, vol. 10, no. 2, pp. 1646–1659, Mar. 2019.
[29] D. T. Nguyen and L. B. Le, ‘‘Joint optimization of electric vehicle and
home energy scheduling considering user comfort preference,’IEEE
Trans. Smart Grid, vol. 5, no. 1, pp. 188–199, Jan. 2014.
[30] A. Bandyopadhyay, B. D. Leibowicz, E. A. Beagle, and M. E. Webber,
‘‘As one falls, another rises? Residential peak load reduction through
electricity rate structures,’Sustain. Cities Soc., vol. 60, Sep. 2020,
Art. no. 102191.
[31] A. Ali, K. Mahmoud, D. Raisz, and M. Lehtonen, ‘‘Optimal allocation
of inverter-based WTGS complying with their DSTATCOM functional-
ity and PEV requirements,’IEEE Trans. Veh. Technol., vol. 69, no. 5,
pp. 4763–4772, May 2020.
[32] A. Ali, K. Mahmoud, and M. Lehtonen, ‘‘Multiobjective photovoltaic
sizing with diverse inverter control schemes in distribution systems host-
ing EVs,’IEEE Trans. Ind. Informat., vol. 17, no. 9, pp. 5982–5992,
Sep. 2021.
[33] A. Ito, A. Kawashima, T. Suzuki, S. Inagaki, T. Yamaguchi, and Z. Zhou,
‘‘Model predictive charging control of in-vehicle batteries for home energy
management based on vehicle state prediction,’IEEE Trans. Control Syst.
Technol., vol. 26, no. 1, pp. 51–64, Jan. 2018.
[34] H. Mohsenian-Rad and M. Ghamkhari, ‘‘Optimal charging of electric
vehicles with uncertain departure times: A closed-form solution,’IEEE
Trans. Smart Grid, vol. 6, no. 2, pp. 940–942, Mar. 2015.
[35] Y. Motoaki, W. Yi, and S. Salisbury, ‘‘Empirical analysis of electric
vehicle fast charging under cold temperatures,’’ Energy Policy, vol. 122,
pp. 162–168, Nov. 2018.
[36] A. W. Danté, K. Agbossou, S. Kelouwani, A. Cardenas, and J. Bouchard,
‘‘Online modeling and identification of plug-in electric vehicles shar-
ing a residential station,’Int. J. Electr. Power Energy Syst., vol. 108,
pp. 162–176, Jun. 2019.
[37] O. Sundstrom and C. Binding, ‘‘Flexible charging optimization for electric
vehicles considering distribution grid constraints,’’ IEEE Trans. Smart
Grid, vol. 3, no. 1, pp. 26–37, Mar. 2012.
[38] J. R. Birge and F. Louveaux, ‘‘Uncertainty and modeling issues,’’ in
Introduction to Stochastic Programming (Springer Series in Operations
Research and Financial Engineering). New York, NY, USA: Springer,
2011, pp. 55–100.
[39] M. A. Quddus, O. Shahvari, M. Marufuzzaman, J. M. Usher, and R. Jaradat,
‘‘A collaborative energy sharing optimization model among electric vehicle
charging stations, commercial buildings, and power grid,’’ Appl. Energy,
vol. 229, pp. 841–857, Nov. 2018.
[40] Y. Chen, ‘‘A tutorial on kernel density estimation and recent advances,’’
Biostatist. Epidemiol., vol. 1, no. 1, pp. 161–187, 2017.
[41] S. S. Hosseini, S. Kelouwani, K. Agbossou, A. Cardenas, and N. Henao,
‘‘Adaptive on-line unsupervised appliance modeling for autonomous
household database construction,’Int. J. Electr. Power Energy Syst.,
vol. 112, pp. 156–168, Nov. 2019.
[42] A. Chis, J. Lunden, and V. Koivunen, ‘‘Reinforcement learning-based
plug-in electric vehicle charging with forecasted price,’’ IEEE Trans. Veh.
Technol., vol. 66, no. 5, pp. 3674–3684, May 2017.
[43] V. Vahidinasab and S. Jadid, ‘‘Bayesian neural network model to predict
day-ahead electricity prices,’Eur. Trans. Electr. Power, vol. 20, no. 2,
pp. 231–246, 2008.
[44] J. Sun, J. Ellerbroek, and J. Hoekstra, ‘‘Bayesian inference of aircraft initial
mass,’’ in Proc. 12th USA/Eur. Air Traffic Manage. Res. Develop. Seminar,
Jun. 2017, pp. 1–10.
[45] J. Lampinen and A. Vehtari, ‘‘Bayesian approach for neural
networks—Review and case studies,’’ Neural Netw., vol. 14, no. 3,
pp. 257–274, Apr. 2001.
52888 VOLUME 10, 2022
A. W. Dante et al.: Stochastic Approach to Designing Plug-In Electric Vehicle Charging Controller for Residential Applications
[46] K. Qian, C. Zhou, M. Allan, and Y. Yuan, ‘‘Modeling of load demand due
to EV battery charging in distribution systems,’’ IEEE Trans. Power Syst.,
vol. 26, no. 2, pp. 802–810, May 2011.
[47] Z. Moghaddam, I. Ahmad, D. Habibi, and Q. V. Phung, ‘‘Smart charging
strategy for electric vehicle charging stations,’’ IEEE Trans. Transport.
Electrific., vol. 4, no. 1, pp. 76–88, Mar. 2018.
[48] J. R. M. D. Reyes, R. V. Parsons, and R. Hoemsen, ‘‘Winter happens:
The effect of ambient temperature on the travel range of electric vehicles,’’
IEEE Trans. Veh. Technol., vol. 65, no. 6, pp. 4016–4022, Jun. 2016.
[49] Nissan Canada Media, Canada. (2019). 2016 Nissan LEAF Press Kit.
[Online]. Available:
[50] (2011). Commuting to Work. National Household Survey (NHS). [Online].
ABDOUL WAHAB DANTE received the B.S.
degree in electrical engineering from the Univer-
sity of Sciences and Technology Houari Boume-
diene (USTHB), Algiers, Algeria, in 2014, and
the master’s degree in electrical engineering from
the Grenoble Institute of Technology, Grenoble,
France. He is currently pursuing the Ph.D. degree
in electrical engineering with the Smart Energy
Research and Innovation Laboratory, Université
du Québec à Trois-Rivières, Trois-Rivieres, QC,
Canada. His research interests include smarts grids, energy management
systems, electric vehicles smart charging, statistical and machine learning
methods, and renewable energies.
received the Ph.D. degree in robotics systems from
the Ecole Polytechnique de Montreal, in 2011.
He completed a Postdoctoral Internship on fuel
cell hybrid electric vehicles at the Université
du Québec à Trois-Rivières (UQTR), in 2012.
He has been a Full Professor of mechatronics
with the Department of Mechanical Engineer-
ing, since 2017, and a member of the Hydrogen
Research Institute. He holds four patents in USA
and Canada, in addition to having published more than 100 scientific
articles. He developed expertise in the optimization and the intelligent control
of vehicular applications. His research interests include optimizing energy
systems for vehicle applications, advanced driver assistance techniques, and
intelligent vehicle navigation taking into account Canadian climatic condi-
tions. He is a member of the Order of Engineers of Quebec. He is the Winner
of the Canada General Governor Gold Medal in 2003. In 2019, his team
received the 1st Innovation Prize in partnership with DIVEL, awarded by
the Association des Manufacturiers de la Mauricie et Center-du-Québec for
the development of an autonomous and natural navigation system. In 2017,
he received the Environment Prize at the Gala des Grands Prix d’excellence
en transport from the Association québécoise du Transport (AQTr) for the
development of hydrogen range extenders for electric vehicles. He is the
Holder of the Canada Research Chair in energy optimization of intelligent
transport systems and the Holder of the Noovelia Research Chair in intelli-
gent navigation of autonomous industrial vehicles. He was the Co-President
and the President of the Technical Committee of the IEEE International
Conferences on Vehicular Power and Propulsion in Chicago, USA, in 2018,
and in Hanoi, Vietnam, in 2019.
received the B.S., M.S., and Ph.D. degrees in elec-
tronic measurements from the Université de Nancy
I, France, in 1987, 1989, and 1992, respectively.
He was a Postdoctoral Researcher (1993–1994)
with the Electrical Engineering Department, Uni-
versité du Québec à Trois-Rivières (UQTR), and
was a Lecturer (1997–1998) at the Electrical Engi-
neering Department. He was also the Director of
graduate studies in electrical engineering, UQTR,
from 2002 to 2004. He was the Head of the Department of Electrical and
Computer Engineering, UQTR, from 2007 to 2011. He was the Head of
the Engineering School, UQTR, from 2011 to 2017. He is currently the
Hydro-Québec Research Chairholder on transactive management of power
and energy with the Residential Sector, and the Chair of the Smart Energy
Research and Innovation Laboratory, UQTR. He is the author of more
than 325 publications and has four patents and two patent pending. His
research activities are in the areas of renewable energy, the use of hydrogen,
home demand side management (HDSM), integration of energy production,
storage and electrical energy generation systems, connection of electrical
vehicle to the grid, control and measurements. He is a member of the
Hydrogen Research Institute and a Research Group ‘‘GREI,’’ UQTR. Since
2015, he has been the Sub-Committee Chair on home and building energy
management of the Smart Grid Technical Committee and the IEEE Industrial
Electronics Society (IES).
NILSON HENAO received the B.S. degree in
electronics engineering from the Universidad de
los Llanos, Villavicencio, Colombia, in 2010, and
the M.Sc. and Ph.D. degrees in electrical engi-
neering from the University of Quebec at Trois-
Rivières (UQTR), Trois-Rivieres, QC, Canada, in
2013 and 2018, respectively. His research interests
include statistical and machine learning methods
with applications to residential energy manage-
ment, distributed optimization, multi-agent con-
trol, smart grids, intelligent energy planning, energy storage, and load
degree in physics engineering from Laval Uni-
versity, Quebec, QC, Canada, in 2002, the M.Sc.
degree in physics from the University of Que-
bec at Trois-Rivières, Trois-Rivieres, QC, Canada,
in 2004, and the Ph.D. degree in mechanical engi-
neering from Sherbrooke University, Sherbrooke,
QC, Canada, in 2007. His research interests
include multiphysics simulations, minimally inva-
sive monitoring of building operations, hardware
in the loop applications, big data analytics, and data driven modeling in the
perspective of electrical grid evolution.
IEEE) received the B.S. degree in electrical engi-
neering from Zanjan University, Zanjan, Iran,
in 2008, the M.S. degree in electrical engineer-
ing from Shahid Rajaee University, Tehran, Iran,
in 2013, and the Ph.D. degree in electrical engi-
neering from the University of Quebec at Trois-
Rivières (UQTR), Trois-Rivieres, QC, Canada,
in 2020. His research interests include smart grid
applications and technologies, power system anal-
ysis, residential appliances load monitoring and diagnosis, and plug-in elec-
trical vehicles.
VOLUME 10, 2022 52889
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In this study, we analyze the potential for time-varying electricity rate structures to reduce and/or shift peak demand in the residential sector. To do so, we develop a convex optimization model in which a household with four major appliances minimizes electricity costs, with marginally increasing penalties for deviating from temperature set-points or operating appliances at inconvenient times. The four specific appliances we include are: heating, ventilation and air-conditioning (HVAC) systems, electric water heaters (EWHs), electric vehicles (EVs), and pool pumps (PPs). The study incorporates a one-parameter thermal model of the home and the electric water heater, so that the penalties can apply to the room and water temperatures rather than the total appliance loads. Analysis is performed on a community of 100 single-family detached homes in Austin, TX. These homes each host a combination of the four end-use devices while some also have onsite solar panels. We find that dynamic pricing effectively shifts the residential peak away from the time of overall peak load across the electricity system, but can have the adverse impact of making the residential peak higher. The energy consumption does not differ significantly across the different rate structures. Thus, we infer that the time-varying rates encourage customers to concentrate their electricity demand within low-price hours to the extent possible without incurring significant inconvenience. By incorporating the novel approach of including monetary value of customer behavior in price-based demand response models, this study builds a tool to realistically quantify peak load reduction and shifts in the residential sector.