A method for the Assessment of Multi-Objective Optimal Charging of
Plug-in Electric Vehicles at Power System Level
AIKATERINI AGAPI KARANDINOU, FOTIOS D. KANELLOS
School of Electrical and Computer Engineering
Technical University of Crete
University Campus, Electrical and Computer Engineering School Building, Chania, Crete
GREECE
Abstract: Nowadays, plug-in electric vehicles (PEVs) have gained popularity because of their operational and
environmental advantages. As a result, power systems must deal with new operation challenges from their
integration. In this article, a method for the assessment of the effects of multi-objective optimal charging of
PEVs at power system level is proposed. The proposed multi-objective optimization method takes into
consideration the forecasts of power system load, Renewable Energy Sources (RES) and electricity price.
Moreover, it is enhanced by the detailed modeling of the daily EV activity taking into consideration the
characteristics of the area they are having activity, the type of the activity, the charging preferences of the
driver as well as the technical characteristics of the EV. Moreover, Vehicle to Grid (V2G) operation can be
modeled by the proposed method. Real-world data were used and the method was applied to the power system
of Crete. The results obtained from the study of indicative application scenarios are presented and finally prove
the efficiency of the proposed method.
Key-Words: Electric Vehicles; Energy Management; Optimization; Vehicle to Grid; Virtual Electricity Price;
Renewable Energy Sources.
Received: June 27, 2021. Revised: April 29, 2022. Accepted: May 28, 2022. Published: July 6, 2022.
1 Introduction
Nowadays, automotive industry and researchers
have focused their attention on Plug-in Electric
Vehicles (PEVs) and Electric Vehicles (EVs)
because of the lack of fossil fuels, the rise in oil
prices and environmental concerns. In addition, EVs
offer a lot of advantages such as low gas emissions
and low operational costs. EVs may also help to
improve grid reliability, operation security and the
increase of the penetration of Renewable Energy
Sources (RES). EVs can help RES as under suitable
control EVs total power can be used to alleviate
large power generation deviations from RES and fill
the “valleys” of system load while “shave” the peak
loads [1].
Although PEVs feature many advantages in
several aspects of power system operation, they can
also be the source of power system operation
problems. These problems become more evident if
they are not suitably controlled and their penetration
to the power system increases significantly.
Distribution network is the part of the power system
that will provide charging power to the PEVs or
absorb the power injected by them (V2G operation)
and therefore the first that will face overloading
problems, voltage instability, protection
coordination etc [1]. Hence, it is deemed important
to adopt smart charging and power and energy
management techniques to alleviate these problems
or even change them to opportunity for power
system operation improvement and in this way,
enable their further integration to the electric power
system. For instance, their use as a large smart
distributed energy storage devices will help the
integration of more RES [2],[3].
Regarding the PEV and distribution network
cooperation, a lot of research has been done in PEV
optimal charging control that will reduce the
distribution load demand peaks, reduce voltage
instability, reduce distribution network active and
reactive power losses and alleviate network
congestion [4], [5]. Moreover, PEVs will be able to
offer ancillary services to the network. Depending
on charging conditions and equipment PEVs may be
able to inject power to the grid (V2G), provide
frequency support and reactive power regulation
providing that they employ suitable charging
converters [6], [7]. In [8], power and energy
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management techniques like peak load shaving and
valley filling are applied to PEVs via suitable smart
charging. In [9], the financial impact for of EV
charging is assessed at distribution network level. A
charging cost minimization strategy is compared
with one aiming to peak load shaving at distribution
network level. In [10], it is shown that EV charging
system using solar PVs can reduce the charging cost
in the range of 50–100%. In [11], a method that
minimizes PEVs’ charging cost and at the same time
ensures the normal operation of the distribution grid
is proposed. In [12], a method that optimally
maintains the frequency fluctuations between the
acceptable limits under a large penetration of PEVs
is proposed. In this work, frequency support is
optimally provided taking into consideration the
flexibility of the PEVs. In [13], another charging
method that minimizes the total charging cost of the
PEVs at parking lot level is proposed. In [14], the
goal is to minimize the charging cost in real time
considering all constraints at EV and distribution
network levels and with the minimum dependence
on the forecasting of some critical inputs of the
charging optimization algorithm. In [15], a particle
swarm based optimization method is exploited to
optimally charge or discharge PEVs. Parameters like
electric network power losses, daily load
smoothness and EV owners’ charging preferences
were taken under consideration.
In [16] research on charging price estimation
during valley filling taking into account the RES
power generation has been done. In [17], a power
management algorithm is applied to a system
comprising RES, Energy Storage Systems, and EVs.
It aims to provide virtual inertia supporting the
frequency of the system. In [18], a stochastic linear
programming model for EV charging is proposed for
various operation scenarios. In [19], a method that
solves a multiple vehicle routing problem with time
constraints is proposed and compared with various
algorithms. In [20], a simulation method of an
electricity market that depends on prosumers and
electric vehicles and reduces the electricity cost is
proposed.
In this article, a method for the efficient multi-
objective optimal charging of PEVs is proposed.
The main targets of the method are to minimize the
charging cost of the PEV and at the same time
reduce the variations of the net load (the load
remaining after subtracting RES power generation)
of the power system. The proposed method was
applied to the power system of Crete and evaluated
for different operation scenarios. The efficiency of
the method is proved by simulation results and their
statistical analysis.
The method proposed in this article comprises a
number of features listed in the following that can be
jointly included in other research works very rarely.
1. A realistic model of EV activity, based on
real world data, is developed to simulate the
daily schedule of the EV. The developed model
considers several parameters associated with the
EV type, driver behavior and the characteristics
of the area the EV is travelling. In this way, the
charging time periods and the energy needs of
the EV are estimated.
2. A simple and easy to apply charging
optimization method at EV level is proposed. It
is based on the estimation of a virtual electricity
price which is defined in a way to incorporate the
real electricity price and the net load of the
power system. In this way a multi-target optimal
charging problem is solved taking into account
all associated technical and operational
constraints of the EV charging system and
battery.
3. The proposed method can be easily applied
as it does not employ time consuming
computations and does not require sophisticated
hardware. The inputs required by the proposed
method are only the forecasts of electricity price,
RES production and power system load. The
above inputs are available by power system
operator.
4. The proposed multi-target optimal charging
method is integrated with the detailed modeling
of EV activity to provide an accurate assessment
of the impacts of their charging to the power
system load.
The article is structured as it follows. The
formulation of EV activity model, the inputs and all
data used by the model are described in Section 2.
Moreover, the formulation of PEV optimal charging
problem is provided in paragraph 2.3. In Section 3
the method is applied to the power system of Crete
and detailed simulation results obtained for several
operation scenarios are presented. The results are
discussed, and the efficiency of the proposed
method is highlighted. Finally, the major
conclusions drawn by this study are provided in the
concluding section of the paper.
2 Formulation of the Method
The purpose of this work is to jointly minimize the
charging cost of EVs plugged into the grid and the
variation of the net load of the power system to
alleviate any possible repercussion from RES
integration. The input data and the implementation
of the proposed method were based on the
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exploitation of real-world data as well as realistic
probability density function where it was necessary
to simulate the stochastic behavior of system
components.
It is noted that it is essential to create realistic
daily driving schedules of the EVs as they affect
both charging load throughout the day and
consequently the total electrical power system load.
2.1 General Inputs of the Model
2.1.1 Input Daily Time Series
The daily forecasts of photovoltaic power
production, wind power production and electricity
price are inputs of the developed model. For
application purposes, real time series of the above
quantities recorded in Crete power system were
used.
2.1.2 EV Types
The selection of the EV types was based mainly on
their purchase cost. Four different EV models with
generally affordable cost were chosen as low and
medium cost EVs are expected to dominate the
market. Their characteristics e.g. battery capacity,
maximum/minimum rate of charging in the Results
Section.
2.2 EV Activity Model
The basic data which are necessary to produce the
daily schedule of an EV are stored in a data structure
with several fields of the general form: EV.field. The
EV structure consists of vectors and variables stored
in its fields and are presented next.
2.2.1 Variables
Single value parameters of the simulated system are
stored in the respective fields of the EV structure
which are called next as variables. The most
significant of them are described next in this
paragraph.
denotes the initial state of charge (SoC)
of the EV at the begging of the simulation. It takes
values from a normal distribution, with μ=90 and
σ=3.5.
and refer to the
maximum and minimum SoC of the EV battery,
respectively, and depend on the type of battery.
and are the maximum and
the minimum charge power of the EV battery.
The specific energy consumption variable,
EV.Spec_Cons, comprises the typical energy
consumption per 100km of travel of an EV type.
2.2.2 Vectors
Multiple value quantities are stored in the respective
fields of the EV structure, which are called next as
vectors. The most significant of them are described
next in this paragraph.
() defines the type of the
type of EV travel destination travel. Three
destination types are considered: “home”, “shop-
social” and “work”. The EV starts its daily schedule
from home and the algorithm randomly selects the
next destination according to a predefined
probability distribution in day time. Travel
destination highly depends on the starting time of
the travel.
vector comprises the starting time of
the next trip of the EV (EV departures). The first
element of the vector is defined randomly using the
normal distribution, with μ=7.5 and σ=1.5. This
ensures that most people start their daily schedule
from home around 7:30 am. The most common
starting time for social activities and shops is at
11:00 am to 18:00 pm and for home is at 3:00 pm.
Let us assume that j denotes the number of the jth
EV departure then the jth element of vector
is estimated by the following equation:
(1)
vector comprises the durations of the
EV trips in a day. It is obtained by using a normal
distribution with characteristics depending on the
size of the city the travels take place.
vector comprises the arrival times of
the EV in a day. According to the calculation of
the jth element of is calculated
according to the following equation.
(2)
vector comprises the travelling speeds
of the EV during its trips. It is randomly obtained
using the normal distribution, with μ=35 and σ=7.
The selection of the distribution was based on the
assumption that the travelling speed inside a city
usually ranges between 15 and 55 km/h with an
average value of 35 km/h.
vector comprises the distances covered
by the EV during its trips in a day. Knowing the EV
travelling speed and the duration of the jth travel of
the EV then the jth element of is estimated
as in the following:
(3)
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The time vector comprises the
durations of the idle periods the EV (charging or
parking). Its elements are selected randomly by
using suitable probability density distributions
depending on the activity of the driver while the EV
is parked e.g. “home”, “shop - social” or “work”.
vector comprises the energy
consumption during the trips of the EV in a day.
Knowing the travelled distance and the
specific consumption of the EV
then the jth element of the vector is calculated as in
the following.
(4)
The specific energy consumption of the EVs used in
this work is provided in the Results section.
vector comprises the energy stored in
the battery of the EV when it arrives at its
destination. Knowing the stored energy at the
beginning of the jth travel and the energy consumed
during it then the jth element of
is calculated as in the following.
vector comprises the energy stored in the
battery at the beginning of a trip.
In this work, is also used by the EV
driver to decide if the EV batteries will be charged
or not. Specifically, it was assumed that the
possibility of charging increases linearly with the
decrease of battery SoC. An indicative SoC –
probability of charging characteristic used in this
work, is shown in the Results section.
2.3 PEV optimal charging
First, a virtual electricity price is estimated in order
to be used for the optimal charging scheduling of the
PEVs. The idea behind the formulation of virtual
electricity price is to combine the information from
the forecast of the real electricity price and the
forecast of the net electric power system load in a
single variable.
Let us assume that the optimization horizon is
defined by the arrival and the departure of the EV
from the parking lot [T0,i Tf,i] and the electricity
price forecast in of the ith PEV is normalized as in
the following,
With,
Where,
(in p.u.) is the normalized forecasted
electricity price,
(in €/MWh) is the forecasted
electricity price,
(in €/MWh) is the minimum
electricity price and
(in €/MWh) is the
maximum electricity price in the optimization period
.
Let us assume that RES power generation
forecast in the optimization horizon [T0,i Tf,i] of the
ith PEV is
and the respective forecast of
power system load is
. Then the forecast of the net
load of the electric power system is,
Then the forecasted net load of the power system
is normalized as in the following,
with,
(10)
Where,
is the forecasted RES power
generation,
(in p.u.) is the normalized
forecasted net load of the power system,
is the minimum(maximum) value of
the forecasted net power system load in the
optimization period.
Forecasted electricity price and RES power
generation were normalized as described above in
order to be integrated in a single variable called next
as virtual electricity price.
Then the virtual electricity price (in p.u.) can be
defined as,
(11)
Where, is a parameter varying between [0-1]
defining the weight of the electricity price in the
calculation of virtual electricity price. The remaining
part of the virtual electricity price corresponds to the
net load of the electric power system. α can be set by
the operator of the system.
The optimal PEV charging problem solved in
this work is defined in (12)-(17) where the “virtual
charging cost” of the EVs is minimized. In this way,
the charging power is appropriately estimated to
jointly minimize the real charging cost and the
variations of the net load of the electric power
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system taking into account the technical constraints
of the EV battery and its charging system.
Subject to,
Where, i denotes the ith EV, is the optimal
active power the EV exchanges with the electricity
grid (load convention), is the used time interval
(12 min in this study), and is the energy stored
in the battery of the ith EV.
It should be noted that there are no particular
numerical stability problems to be addressed in this
method. Instability could occur if the proposed
optimal PEV charging method in not able to find a
solution. However, this will not happen due to the
scale of the problem as it is of small scale, but only
when the required charging energy cannot be met by
the available charging power and charging duration.
This is solved by a preliminary check of the above
and if the charging targets cannot be met then they
are suitably re-calculated and dumb charging is
applied as it is shown in Fig. 1.
2.4 Tour Generation Algorithm
The daily schedule and the optimal charging process
of each EV are synopsized next and shown in Fig. 1.
All EVs depart from ‘home’ at time obtained from
the respective probability density distribution.
The next destination as well the duration of the trip
are generated using respective probability density
distributions.
The arrival time of the EV is obtained using the
duration of the trip.
When the EV arrives to the parking the charging
decision is made according to the SoC of its
battery.
The duration of PEV charging is obtained by using
suitable probability density distributions according
to the type of the activity of the EV driver is
having during the charging period.
The proposed optimal charging method to the PEV
or dumb charging is applied if this is decided by
the driver or the parking duration and the available
maximum charging power are not enough to
achieve the desired SoC target.
Fig. 1 Algorithm of the EV daily schedule
estimation and charging optimization.
3 Results
The proposed method was used to estimate the
impact of PEV charging to the load of the electric
power system of Crete.
According to the National Energy and Climate
Plan target the EV penetration rate should reach
30% of vehicle’s number in 2030. In the following,
we chose to apply an aggressive scenario where the
number of EVs is considered to correspond to the
40% of the number of total vehicles in Crete by
2030. In addition, the total fleet of vehicles in Crete
START
Selection of Travel Type Destination
Set Travel Duration
Estimate Arrival Time
Estimate Energy Consumption
Estimate Stored Energy at the destination
T<24
YES
NO
Departure location= Home
Set departure time using the
respective distribution
END
Charging?
Set Parking Duration
Set SoC target
Estimate Virtual Electricity Price
Constrained Optimization of PEV Charging
YES
SoCdep=SoCarr
NO
t=t+ΔΤparking
Is parking duration and available
charging power enough?
YES
Set new maximum SoC
target that could be
achieved with the
available maximum
charging power
Apply Dumbcharging
NO
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is estimated to amount approximately to 500,000 in
2030 [21]. The above lead to of the assumption that
the number of EVs in Crete in 2030 will
approximate 200,000. This total number of EVs was
dispatched to the four bigger Cretan cities, namely,
Heraklion, Chania, Rethimno and Agios Nikolaos
according to their populations. Hence, the EV
activity and charging load were calculated for each
city separately according to their local
characteristics and sizes.
In Fig. 2, the probability distributions used for
the reproduction of the initial SoC, the first
departure time and the travelling speed of the EVs
are shown. In Fig. 3, the distribution of the
probability of specific EV travel destination types
with regard to the daytime are shown.
Normal distribution has been used to simulate the
travel duration in the major cities of Crete. More
specifically, normal distributions with μ=15, 20, 13,
9 and σ=3.5, 5, 2.7, 2.2 were used to reproduce
travel duration in Chania, Heraklion, Rethimnon and
Agios Nikolaos, respectively. The respective
distributions are shown in Fig. 4.
Fig. 2 Probability distributions of the initial
departure time, travelling speed and initial SoC.
Fig. 3 Probability of the EV travel destination types
over the day.
Fig. 4 EV travel duration probability distributions.
Fig. 5 Parking duration probability distributions for
different EV’s driver activities while parking.
Fig. 6 Probability of charging according to the state
of charge of PEV’s battery.
The probability distributions used to estimate
parking duration while staying home, being at work,
shopping or having social activities are shown in
Fig. 5. Finally, the probability of the EV to charge
its battery with regard to its SoC before plugging
into the charger is shown in Fig. 6.
Next, three application scenarios of the proposed
method are presented.
In Scenario 1 (SC1), the optimal charging of the
PEVs is done using a virtual electricity price formed
only by the normalized net electric load of Crete.
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In Scenario 2 (SC2), the optimal charging of the
PEVs is done using a virtual electricity price formed
only by the normalized electricity price.
In Scenario 3 (SC3), the optimal charging of the
PEVs is done using a virtual electricity price formed
by the normalized net electric load of Crete and the
normalized electricity price with a weight of 50%.
It was also considered that the 75% of the PEVs
will apply the proposed smart charging method. The
remaining 25% will apply dumb charging, absorbing
a constant amount of power during the charging
period.
Moreover, the scenario SC3 was divided in three
sub-scenarios to examine different acceptance rates
of V2G and V1G (optimal charging without
injecting power to the network). More specifically, it
was considered in sub-scenarios SC3.a, SC3.b and
SC3.c that 70%, 60% and 40% of the PEVs
applying smart charging will use V2G, respectively.
The remaining will use V1G. All the examined
scenarios are tabulated in Table 1.
In Fig. 7, the time series used for the electric load
of the power system of Crete, the wind power
production, the PV power production and their sum,
are shown. In Fig. 8, the used electricity price time
series is shown.
Table 1 Examined operation scenarios.
Method Application Scenarios
SC1
SC2
SC3
SC3(a)
Low
V2G
SC3(b)
Medium
V2G
SC3©
High
V2G
a
0
1
0.5
0.5
0.5
Smart
Charging
(% of PEV
population)
75
75
75
75
75
Dumb
Charging
(% of PEV
population)
25
25
25
25
25
V2G
(% of PEV
population)
45
45
30
45
52.5
V1G
(% of PEV
population)
30
30
45
30
22.5
Table 2 PEVs’ Parameters
EV Model
1
2
3
4
Pmax (kW)
4.6
3.7
11
7.2
Emax (kWh)
17.6
16
35
36.8
Specific Cons.
(kWh/100km)
25. 5
25.8
25
26
Fig. 7 Crete load, Wind and PV power production
time series.
Fig. 8 Electricity price.
Fig. 9 Total power that PEVs exchange with the
network.
Fig. 10 Crete net load and net load with PEVs’ total
power for SC1, SC2 and SC3.
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In Fig. 9, the total power of the PEVs is depicted
for scenarios SC1-SC3. In SC1, PEVs inject power
to the grid when the net load of the system features
peaks i.e. 14:30 am and 22:00 am) while they absorb
power when the net load of the system features low
value i.e. 05:00 am - 07:00 am and 17:00 pm. In
SC2, PEVs absorb more power, when the electricity
price is low (05:00 am and 15:00 pm) and inject
power to the grid when the electricity price is high.
In SC3, PEVs absorb more power when the
electricity price and at the same time the net load
demand are low (05:00 am and 15:00 pm) and inject
power to the grid when the electricity price and the
net load demand are high (10:00 am - 13:00 pm and
18:00 pm – 21:00 pm).
In Fig. 10 the net load of Crete with the load of
the EVs added is depicted for SC1-SC3. In
particular, SC1 helps the network to feature smaller
net load variations with peak load shaving and
valley filling applied at the appropriate time periods.
Hence, the major objective to balance the load curve
is achieved. In SC2, only the electricity price is
taken into consideration and not the net load of the
power system while both factors are jointly taken
into consideration in SC3.
Fig. 11 PEVs’ total power for different V2G
acceptance rates.
Fig. 12 Net load with PEVs’ total power for
different V2G acceptance rates.
Fig. 13 Charging power of two indicative PEVs.
Fig. 14 Stored energy of two indicative PEVs.
In Fig. 11 and Fig. 12 the total electric power of
the PEVs is depicted for different V2G acceptance
rate scenarios (SC3.a-SC3.c). It is observed that the
bigger the V2G penetration is, the better balance of
the load is achieved and the lower the charging cost.
In Fig. 13, the optimal charging power
trajectories of two indicative PEVs are shown.
PEV1 uses V1G while PEV2 uses V2G. Obviously,
the two PEVs adjust optimally their charging power
according to the formed virtual electricity price. The
two trajectories were taken under the SC3 operation
scenario. The respective trajectories of the stored
electric energy of the two PEVs are shown in Fig.
14.
The daily operation cost of the electric power
system of Crete and the charging cost of the PEVs
for SC1-SC3 are tabulated in Table 3. The obtained
costs confirm the above remarks.
Furthermore, the standard deviation of the sum of
net load of Crete power system with the total PEV
load is given in Table 4. It is noted that the standard
deviation of the net load of Crete power system is
44.24MW. The obtained results confirm that the
proposed method decreases the deviation of the net
load of the power system with the biggest reduction
obtained in SC1 where only the net load is used for
the definition of the virtual electricity price (α=1).
Moreover, the bigger the V2G the lower the
obtained standard deviation of the sum of the net
load of the power system and the PEV load.
0 4 8 12 16 20 24
-5
0
5
10
Time (h)
Power (kW)
PEV 1
PEV 2
0 4 8 12 16 20 24
5
10
15
20
25
30
Time (h)
Energy (kWh)
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Finally, t-test was applied to the results obtained
for total PEV load and virtual electricity price. The
total load of the PEVs will behave in an opposite
way to the virtual electricity price i.e. when virtual
electricity price is increasing then PEV load is
decreasing and vice versa. Hence, the transformation
and normalization of the equations (18) (19) was
applied to the two variables to ensure the above
remark and zero mean value. The t-test was
successful for all examined operation scenarios.
Where,
and denote the transformed
virtual electricity price and total PEV load used to
apply the t-test, respectively.
Table 3 Operation Cost
PEV Charging Cost
(x106 €)
Power System Operation
Cost (x106 €)
SC1
SC2
SC3
SC1
SC2
SC3
0.01455
0.00918
0.01159
0.9737
0.9684
0.9708
Table 4 Standard deviation of the net load and
PEV load of Crete electric power system
SC1
SC2
SC3(a)
SC3(b)
SC3(c)
σ(MW)
36.42
41.55
40.21
38.43
37.13
4 Conclusion
A method that simulates accurately the daily activity
schedule of EVs and optimizes their charging
according to it and taking into consideration
multiple objectives is proposed in this article. The
method can be easily applied while it provides to the
user a powerful tool to analyze in detail the effects
of PEVs’ charging on the power system taking into
account a multitude of parameters. The proposed
method was applied to the power system off Crete
under several different application scenarios. The
obtained simulation results prove that a significant
reduction in PEVs’ charging cost in conjunction
with the reduction of power system load variability
is possible. Specifically, the method can help the
power system to feature smaller load variations
applying peak shaving and valley filling while the
charging cost of the PEVs is reduced at the same
time.
A future expansion of this work could be the
application of the proposed method at PEV
aggregator level and the modelling of the electric
power generation and transmission systems.
Moreover, some peripheral applications of artificial
intelligence could be exploited. More specifically,
the forecast of the next day PEV activity level,
electricity price, RES production and charging
decision based on the state of charge of PEV battery,
driver’s anxiety, electricity price level, V2G
application etc. could be exploited, provided that the
required training data are available.
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WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2022.17.36
Aikaterini Agapi Karandinou, Fotios D. Kanellos
E-ISSN: 2224-2856
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Volume 17, 2022
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Contribution of individual authors to
the creation of a scientific article
(ghostwriting policy)
Aikaterini-Agapi Karandinou wrote the original
draft of the manuscript, developed the software, and
contributed to visualization, modelling and
simulation.
Fotios D. Kanellos carried out the conceptualization
and supervision, revised and edited the manuscript,
contributed to the software, modelling and
simulation.
Creative Commons Attribution
License 4.0 (Attribution 4.0
International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2022.17.36
Aikaterini Agapi Karandinou, Fotios D. Kanellos
E-ISSN: 2224-2856
323
Volume 17, 2022
